Auditory Mechanisms: Proceedings of the Ninth International Symposium Held at Portland, Oregon, USA 23 - 28 July 2005

Auditory Mechanisms Processes and Models (with CD-Rom) Alfred L. Nuttall Tianying Ren Peter Gillespie Karl Grosh Egbert...

Author: Alfred L. Nuttall | Tianying Ren | Peter Gillespie | Karl Grosh | Egbert de Boer

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Auditory Mechanisms Processes and Models (with CD-Rom)

Alfred L. Nuttall Tianying Ren Peter Gillespie Karl Grosh Egbert de Boer editors

Auditory Mechanisms Processes and Models

Auditory Mechanisms Processes a n d Models Proceedings of the Ninth International Symposium held at Portland, Oregon, USA

23 - 28 July 2005

Editor

Alfred L. Nuttall Oregon Health & Science University, USA Associate Editors

Tianying Ren Peter Gillespie Oregon Health & Science University, USA

Karl Grosh University of Michigan, USA

Egbert de Boer Academic Medical Center, The Netherlands

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World Scientific

NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

AUDITORY MECHANISMS: PROCESSES AND MODELS (with CD-ROM) Proceedings of the Ninth International Symposium Copyright © 2006 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN 981-256-824-7

Printed by Mainland Press Pte Ltd

PREFACE Dysfunction of the cochlea is the most common of all human forms of sensory loss. The World Health Organization estimates that 250 million people have a significant level hearing loss. In the United States, 1 of every 1000 newborns has a severe to profound hearing loss. With age, about 60% of those over 70 years old will have a serious loss of auditory capability. More than 40 genes have been associated with cochlear sensory impairment. Critical to the prevention of hearing loss as a serious global health problem is the detailed knowledge of cochlear function. The Workshop on Auditory Mechanisms: Processes and Models was the ninth in a series that has also come to be known as the "Mechanics of Hearing Workshops." Inner ear mechanics is a special area of study that explores the details of function relevant to understanding normal hearing and hearing loss. It is easy to recognize the relevance of cochlear mechanics study to both basic and applied auditory science. The otoacoustic emission is one such topic. Otoacoustic emissions potentially provide a view into the cochlea to observe the micro-mechanics. However, interpretation of changes in the emissions requires a greater understanding of their origin and wave propagation. During the past 20 years since the start of the Workshops, research into the mechanics of hearing has undergone numerous major developments. Particularly important are the experimental procedures have been developed for manipulating and viewing the micromechanical responses of the inner ear, even down to the sub-cellular level. The Workshop brought together an interdisciplinary group of scientists including the leading researchers working on the cochlea from the level of the whole system through the structural protein level. One character of the meeting that differs from the typical auditory neuroscience gatherings is the strong representation of mathematical modeling. This combination of experimentalists and modelers enables a deeper presentation and discussion of theoretical issues. Indeed, much time was available for formal discussion of two major scientific controversies: 1) On the role of outer hair cell stereocilia in "powering" cochlear amplification and 2) On the amount of reverse propagation of energy from the cochlea by fluid acoustic compression waves. The book organization begins with papers on the function of the organ of Corti as a system in the chapter titled "Whole-Organ Mechanics." "Hair Cells" follows concerning the soma of outer hair cells. Hair cell transduction is addressed in the chapter "Stereocilia" and otoacoustic emissions make up the chapter titled "Emissions." Finally, modeling of cochlear function is treated in the chapter "Cochlear Models." Each chapter has a paper from one or more plenary speakers. Of particular note is that this Workshop honored Prof. Egbert de Boer as a founder of the Mechanics Workshop series of meetings. His paper derives from a plenary lecture. Questions and answer responses are included at the end of the papers and there is a separate "Discussion" chapter that presents the content of a lively evening session of the Workshop.

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The Workshop was supported and made possible by generous funding support from public and private sources. An NIH conference grant was provided by the National Institute on Deafness and Other Communication Disorders. Instrument manufacturers Polytec Inc., Tucker-Davis Technologies and Etymotic Research Inc. provided support. Of particular relevance, the Workshop received generous support from hearing aid manufacturers, The Oticon Foundation, Starkey Hearing Research Center, and a cochlear implant manufacturer, Advanced Bionics. The Workshop also established a new model for scientific conferences, as there was a linked but financially separate, public science outreach/training event. Held at the Oregon Museum of Science and Industry in Portland, Drs. James A. Hudspeth and Billy Martin delivered an interactive lecture to a group of high school students. The Workshop attendees were also present. A reception followed, allowing the personal interaction of the students and the scientists. This event was generously funded by the Burroughs Wellcome Foundation. The editors would like to thank the International Organizing Committee for their role in the planning of the Workshop and for efforts on finding financial support. We are grateful to the Plenary Lecturers for their stimulating presentations, to the session chairs and discussion moderators in helping run the meeting, and to all the participants for maintaining the tradition of a high quality meeting. We are indebted to many others for the success of the Workshop and for this book. The Department of Otolaryngology at the Oregon Health & Science University is the home of the Oregon Hearing Research Center (OHRC) and responsible for creating the rich basic and clinical research environment that enables meetings such as this Workshop. The faculty and students of OHRC deserve praise for their assistance. We have deep gratitude for the core group of OHRC staff that contributed so much of their time and energy, Linda Howarth, Jill Lilly, Scott Matthews, Theresa Nims and Edward Porsov, without whose help the Workshop would have been ordinary at best, instead of extraordinary as it was. Finally I wish to thank my scientist colleagues, many of whom are close friends, for creating such an exciting and fruitful scientific environment as the Mechanics of Hearing Workshop, and for the honor and pleasure of hosting this ninth Workshop.

A.L. Nuttall Oregon Health & Science University Portland, Oregon April 2006

The International Organizing Committee J. Allen - Illinois, USA W. E. Brownell - Texas, USA N. P. Cooper - Keele, United Kingdom P. Dallos - Michigan, USA A. Gummer - Tubingen, Germany S. Puria - California, USA C. Shera - Massachusetts, USA R. Withnell- Indiana, USA The Local Organizing Committee: A. L. Nuttall - Oregon, USA E. de Boer - Amsterdam, The Netherlands P.G. Gillespie - Oregon, USA K. Grosh - Michigan, USA T. Ren - Oregon, USA R. Walker - Oregon, USA Plenary Lecturers W. E. Brownell, Texas, USA E. de Boer - Amsterdam, The Netherlands R. Fettiplace, Wisconsin, USA J. Guinan, Massachusetts, USA J. A. Hudspeth, New York, USA P. Nairns, California, USA

DATA DIPS AND PEAKS (WITH APOLOGIES TO ELLA FITZGERALD) Heaven, I'm in heaven And my heart beats so that I can hardly speak. 'Cause I finally found the funding that I seek. Now I'm measuring those data dips and peaks. Heaven, I'm in heaven And the cares that hung around me 50 weeks Finally vanished like a gambler's lucky streak With acquiring all those data dips and peaks. Now I love to go to meetings. And to hear or give a speech But I don't enjoy them half as much As data dips and peaks. I love to read and write a paper. And a physics course to teach But they don't thrill me half as much Basilar membrane velocity al the 17 kH? As data dips and peaks best frequency location evoked by 100 microA current applied to tho cochlea

Oh points on my screen I want to analyze you Just one effect new Will carry me through to

•

Heaven, I'm in heaven And my heart beats so that I can hardly speak. 'Cause I finally found the funding that I seek. Now I'm measuring those data dips and peaks.

Laura Greene, professor of physics at the University of Illinois at UrbanaChampaign, wrote this song in 2001. The melody is that of "Cheek to Cheek. " Says Greene, "Maybe the apologies should have been to Irving Berlin, who wrote the original song, but I copied the words and style from the Ella Fitzgerald/Louis Armstrong rendition, trying to follow Ella's phrasing as much as possible. I am also a great fan of Ella in general." Attendees of the Mechanics of Hearing Banquet at Mount Hood's Timberline lodge will, perhaps painfully, remember the role this song played in the evening's entertainment. Inset graphic: Cochlear mechanics dips and peaks with thanks to Drs. Alfred Nuttall, Karl Grosh, and Jiefu Zheng. Reprinted with permission from Physics Today, July 2005, page 58. Copyright 2005, American Institute of Physics.

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PREVIOUS PUBLICATIONS FROM THIS SERIES OF WORKSHOPS: Mechanics of Hearing. Edited by E. de Boer and M.A. Viergever. Nijhoff, the Hague/Delft University Press, 1983. Peripheral Auditory Mechanisms. Edited by J.A. Allen, J.L. Hall, A. Hubbard, S.T. Neely, and A. Tubis. Springer, Berlin, 1986. Cochlear Mechanisms: Structure Function and Models. Edited by J.P. Wilson and D.T. Kemp. Plenum, New York. 1989. The Mechanics and Biophysics of Hearing. Edited by P. Dallos, CD. Geisler, J.W. Matthews, M.A. Ruggero, and C.R. Steele. Springer, Berlin, 1990. Biophysics of Hair Cell Sensory Systems. Edited by H. Duifhuis, J.W. Horset, P. van Dijk, and S.M. van Netten. World Scientific, Singapore, 1993. Diversity in Auditory Mechanics. Edited by E.R. Lewis, G.R. Long, R.F. Lyon, P.M. Narins, C.R. Steele, and E. Hecht-Poinar. World Scientific, Singapore, 1996. Recent Developments in Auditory Mechanics. Edited by H.Wada, T. Takasaka, K. Ideda, K. Ohyama, and T. Koike. World Scientific, Singapore, 2000. Biophysics of the Cochlea: From Molecules to Models. Edited by A.W. Gummer, E. Dalhoff, M. Nowotny, and M.P. Scherer. World Scientific, Singapore, 2002.

IX

This conference was supported by a generous grant from the National Institutes of Health National Institute on Deafness and Other Communication Disorders. It is also supported by the following organizations: Advanced Bionics Etymotic Research, Inc. The Oticon Foundation Phonak Hearing Systems Polytec, Inc. Starkey Hearing Research Center, Berkeley Tucker Davis Technologies

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PHOTOLEGEND 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Siegel, J.H. Withnell, R.H. Howarth, L.C. Large, E. Mammano, F. Cooper, N. Narins, P.M. Ren, T. Jedrzejczak, W. Aranyosi, A.J. Van Dijk, P Eberl, D.F. Meulenberg, C.J.W. Zheng, J. Song, L. RimskayaKorsakova, L. Hallworth, R. Deo, N. Cheatham, M.A. van Netten, S Grosh, K. Rosowski, J. Bell, A. Brownell, W. Songer, J. He, D.Z.Z. Lane, C. Lilly, D. He,W. Boutet de Monvel, J.H.R. Unknown Chadwick, R.S. Ruggero, M. Fettiplace, R. Furst, M Fahey, P.F. Hackney, C. Iwasa, K.H.

39 40 41 42 43 44 45 46 48 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Guinan, J.J. Freeman, D. Dong, W. Long, G.R. Jianwen, G. Duifhuis, H. Manley, G.A. Koppl, C. Zou, Y. Corey, D.P. Khanna, S.M. Kalluri, R. Karavitaki, K.D. Fulton, J. Richter, C.P. Rhode, W. Wada, H. Unknown Hubbard, A.E. Tubis, A. Decreamer, W.F. Neely, S.T. Talmadge, C.L. Sen, D. Koch, D. Steele, C.R. Gummer, A.W. Nuttall, A.L. Wittbrodt, M.J. Ulfendahl, M. Liao,Z. Allen, J.B. Lilly, J. Fridberger, A. Oghalai, J.S. Shera, C.A. Farrell, B. Spector, A.A. Qian, F. Sarpeshkar, R.

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79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94

Olson, E. LePage, E.L. Bortolozzi, M.M. Dallos, P. Murakoshi, M. Puria, S. Yoon, Y. Harasztosi, C. Raviczm, M. de Boer, E. Mountain, D.C. Dhar, S. Kemp, D.T. Han, W. Masaki, K. deLa Rochefoucauld, O. 95 Scarborough, J. 96 Chen, F. 97 Dimitriadis, E.K. 98 Chan, D. 99 Santos-Sacchi, J. 100 Lu, S. 101 Tempel, B. L 102 Lu, T. 103i Choudhury, N. 104 Newburg, S. 105 Funnel, F. 10<:> Knisely, A. 107 108 109 110

Unknown Chien, W. Nakajima, C. Vetesnik. A.

I l l . Nowotny, M. 112Nobili,R. 113 Bustard, G. 114 Julicher, F. 115 Martin, P. IK > Gopfert, M.

CONFERENCE PARTICIPANTS (numbers after names identify persons in the photo) Allen, J.B. (70) Beckman Institute, Room 2061 - 405 N. Mathews, Urbana, IL 61801, USA jontalle@uiuc. edu Aranyosi, A.J. (10) Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 36-893, Cambridge, MA 02139, USA [email protected] Bell, A. (23) Research School of Biological Sciences, The Australian National University, PO Box 475, Canberra, ACT, 2601, AUSTRALIA andrew. bell@anu. edu. au Bergevin, C. SHBT-MIT, 77 Massachusetts Ave, 36-873, Cambridge, MA, 2139, USA dolemite@mit. edu Bian, L. University of Kansas Medical Center, 3901 Rainbow Boulevard, Kansas City, KS 66160, USA lbian@kumc. edu Bortolozzi, M.M. (81) University of Padova; VIMM (Venetian Institute of Molecular Medicine), Via Orus 2, Padova, PD 35129, ITALY mario. bortolozzi@unipd. it Boutet de Monvel, J.H.R. (30) Karolinska Institutet, M1:00-ONH, Karolinska Sjukhuset, Stockholm 17176, SWEDEN / boutet. de. monvel@cfh. ki.se Breneman, K.D. University of Utah, 50 S. Central Campus Drive, Room 2480, Salt Lake City, UT 84102, USA katiebre@comcast. net Brownell, W.E. (24) Dept of Otolaryngology, NA505, Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030 USA brownell@bcm. tmc. edu

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xvi Bustard, G.D. (113) Hearing Research Center, Boston University, 44 Cummington Street, Boston, MA 2215, USA gbustard@bu. edu Cai, H. Northwestern University, 2240 Campus Drive, Evanston, IL 60208, USA cai@northwestern. edu Castellano-Munoz, M. Dept. of Medical Physiology and Biophysics, University of Seville, Avda. Sanchez Pizjuan 4, Sevilla 41009, SPAIN mcastellano@us. es Chadwick, R.S. (32) National Institute on Deafness and Communication Disorders, Bldg. 10 Room 5D/49, 10 Center Drive MSC 1417, Bethesda, MD 20892 USA [email protected] Chan, D. (98) The Rockefeller University, 1230 York Avenue, Campus Box 6, New York, NY, 10021, USA chand@rockefeller. edu Cheatham, M.A. (19) Northwestern University, 2-240 Frances Searle Bldg., 2240 Campus Drive, Evanston, IL 60208-3550 USA m-cheatham@northwestern. edu Chen, F. (96) Oregon Health & Science University, Oregon Hearing Research Center, NRC-04, 3181 S.W. Sam Jackson Park Road, Portland, OR 97239 USA chenfa@ohsu. edu Chien, W. (108) Massachusetts Eye and Ear Infirmary, Harvard Medical School, Eaton Peabody Lab, 243 Charles Street, Boston, MA, 02114-3002, USA [email protected] Cooper, N.P. (6) Keele University, MacKay Institute of Communication and Neuroscience, Keele University, Keele, Staffordshire, ST5 5BG, UK n.p. cooper@cns. keele. ac. uk Corey, D.P. (48) Harvard Medical School, Department of Neurobiology, 220 Longwood Avenue Boston, MA 02459 USA dcorey@hms. harvard, edu

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Dallos, P. (82) Northwestern University, 2240 Campus Drive, Evanston, IL, 60208 USA [email protected] de Boer, E. (88) Academic Medical Center, Meibergdreef 9, Amsterdam, 1105 AZ, THE NETHERLANDS e. d. boer@hccnet. nl de La Rochefoucauld, L.O. (94) Columbia University, P&S 11-452, 630 West 168th Street, New York, NY 10032 USA or210 7@columbia. edu Decraemer, W.F.S. (59) University of Antwerp, Groenenborgerlaan 171, Antwerpen, B-2020, BELGIUM wim. decraemer@ua. ac. be Deo, N. (18) University of Michigan, 1815 Willowtree Lane #A7, Ann Arbor, MI, 48105 USA ndeo@umich. edu Dhar, S. (90) Northwestern University, 2240 Campus Drive, Evanston, IL, 60208 USA s-dhar@northwestern. edu Dimitriadis, E. K. (97) OD, National Institutes of Health, 13 South Drive, MSC 5766, Bldg.13, Room 3N17, Bethesda, MD 20892 USA [email protected] Dittberner, A. GN ReSound, 4201 West Victoria Street, Chicago, IL 60646 USA wwhitme@luc. edu Dong, W. (41) Columbia University, 630 West 168th Street, P&S, 11 - 452, New York, NY 10032 USA wd2015@columbia. edu Duifhuis, H. (44) University of Groningen, BME - NIC, Antonius Deusinglaan 2, Groningen, 9713AW THE NETHERLANDS H.Duifliuis@rug. nl

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Eberl, D.F. (12) University of Iowa, Department of Biological Sciences, Room 259 BB, Iowa City, IA 52242 USA daniel-eberl@uiowa. edu Fahey, P. (36) University of Scranton, Department of Physics/Electrical Engineering, Scranton, PA 18510 USA [email protected] Fan, Y-H. Northwestern University, 2240 Campus Drive, Evanston, Illinois 60208 USA yhfan@northwestern. edu Farrell, B. (75) Baylor College of Medicine, One Baylor Plaza NA517, Houston, TX 77030 USA bfarrell@tmc. bcm. edu Fettiplace, R. (34) University of Wisconsin-Madison, 185 Medical Sciences Building, 1300 University Avenue, Madison, WI 53706 USA [email protected] Freeman, D.M. (40) Massachusetts Institute of Technology, 50 Vassar Street, Room 36-889, Cambridge, MA 02139 USA freeman@mit. edu Fridberger, A. (72) Karolinska Institutet, Center for Hearing and Communication Research, Ml Karolinska University Hospital, Stockholm, SE171 76, SWEDEN [email protected] Fulton, J.T. (52) Vision Concepts, 1106 Sandpiper Dr., Corona Del Mar, CA 92625-1407 USA jtfulton@cox. net Funnell, R. (105) Depts. BioMedical Engineering & Otolaryngology, McGill University, 3775, rue University, Montreal, QC, H3A 2B4 CANADA robert.funnell@mcgill. ca Furst-Yust, M. (35) Tel Aviv University, School of Electrical Engineering, Tel Aviv University, Tel Aviv 69978 ISRAEL mira@eng. tau. ac. il

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Ghaffari, R. Massachusetts Institute of Technology, 934 Massachusetts Avenue, Cambridge, MA 02139 USA [email protected] Gillespie, P.G. Oregon Health & Science University, Oregon Hearing Research Center, L335A, 3181 S.W. Sam Jackson Park Road, Portland, OR 97239 USA gillespp@ohsu. edit Glassinger, E. Rice University, Department of Bioengineering, MS-142, PO Box 1892, Houston, TX 77005 USA eglass@rice. edu Gopfert, M.C. (116) University of Cologne, Institute of Zoology, VW-Lab, Weyertal 119, Cologne D90523 GERMANY [email protected] Grosh, K. (21) Department of Mechanical Engineering , University of Michigan, 2350 Hayward St, Ann Arbor, MI, 48109-2125 USA grosh@umich. edu Gu, J.W. (43) Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 36-873, Cambridge, MA, 02139, USA fwendie@mit. edu Guinan, J.J. (39) Massachusetts Eye and Ear Infirmary, Harvard Medical School, Eaton Peabody Lab, 243 Charles Street, Boston, MA, 02114-3002, USA jjg@epl. meei. harvard, edu Gummer, A.W. (65) University Tubingen, Tubingen Hearing Research Centre, Elfriede-Aulhorn-Strasse 5, Tubingen, 72076, GERMANY [email protected] Hackney, CM. (37) MacKay Institute of Communication and Neuroscience, School of Life Sciences, Keele University, Keele, Staffordshire, ST5 5BG, UK coa38@keele. ac. uk Hallworth, R.J. (17) Creighton University, 2500 California Plaza, Omaha, NE, 68178, USA hallw@creighton. edu

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Harasztosi, C. Department of Otolaryngology, Elfriede-Alhorn Str. 5., Tubingen, 72076 GERMANY [email protected] Hardelin, J.P. Institut Pasteur (INSERM U587), 25 rue du Dr Roux, Paris, 75015, FRANCE [email protected] He, D.Z.Z. (29) Creighton University, 2500 California Plaza, Omaha, 68135, USA hed@creighton. edu Hubbard, A.E. (57) Boston University, 8 St. Mary's Street, Boston, MA, 02052 USA [email protected] Hudspeth, A.J. Howard Hughes Medical Institute and The Rockefeller University, 1230 York Avenue, Campus Box 314, New York, NY, 10021-6399, USA hudspaj@rockefeller. edu Iwasa, K.H. (38) National Institutes of Health, 50 South Drive, Bethesda, Maryland, 20892-8027 USA [email protected] Jedrzejczak, W.W. (9) Department of Biomedical Physics, Institute of Experimental Physics, Warsaw University, Hoza 69, Warszawa, 00-681, POLAND wjedrz@fuw. edu.pl Jensen-Smith, H.C. Creighton University, Department of Biomedical Sciences, 1912 California Plaza, Omaha, NE 68178 USA heather! 7 77@earthlink. net Julicher, F. (114) Max Planck Institute for the Physics of Complex Systems, Nothnitzerstrasse 38, Dresden, 1187, GERMANY julicher@mpipks-dresden. mpg. de Kalluri, R. (50) Massachusetts Institute of Technology; Harvard-MIT Division of Health Sciences and Technology, 243 Charles Street, Eaton Peabody Laboratory, Massachusetts Eye and Ear Infirmary, Boston, MA, 2114, U.S.A [email protected]

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Karavitaki, D. (51) Harvard Medical School, Department of Neurobiology, 220 Longwood Avenue, Goldenson 443, Boston, MA 02115 USA [email protected]. edu Kemp, D.T. (91) UCL Centre for Auditory Research, Institute of Laryngology and Otology, 332 Gray's Inn Road, London, WC1X 8EE UK emission@dircon. co. uk Khanna, S.M. (49) Department of Oto laryngology/HNS, Columbia University College of Physicians and Surgeons, 630 West 168th Street, New York, NY 10032 USA smk3@columbia. edu Kimm, J. Center for Scientific Review, National Institutes of Health, Bethesda, MD 20814 USA [email protected] Koch, D.B. (63) Advanced Bionics Corporation, 2542 Princeton Avenue, Evanston, IL, 60201 USA dawnkoch@northwestern. edu Koppl, C. (46) Zoology, Technical University Munich, Lichtenbergstrasse 4, Garching, 85747, GERMANY Christine. Koeppl@wzw. turn, de Lane, C.C. (27) Rice University, Electrical and Computer Engineering Department, MS-380, PO Box 1892, Houston, TX, 77251-1892 USA [email protected] Large, E.W. (4) Center for Complex Systems and Brain Sciences, 777 Glades Road, Box 3091, Boca Raton, FL 33431 USA [email protected]. edu LePage, E.L. (80) OAEricle Laboratory, Sydney Australia, P.O. Box 6025, Narraweena, NSW, 2099, AUSTRALIA ericlepage@oaericle. com. au Liao, B. (69) Johns Hopkins University, Department of Biomedical Engineering , 720 Rutland Ave., 613 Traylor Bldg., Baltimore, MD 21205 USA [email protected]. edu

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Long, G.R. (42) Graduate Center of the City University of New York, Speech and Hearing Sciences, 365 Fifth Ave, New York, NY, 11109, USA glong@gc. cuny. edu Lonsbury-Martin, B. School of Medicine, Loma Linda University, Loma Linda, CA 92350 blonsburymartin@asha. org Lu, S. (100) Boston University, 8 Saint Mary's Street, Room 324, Boston 02215 USA [email protected] Lu, T. (102) Harvard-MIT Health Sciences and Technology, 632 Massachusetts Avenue, Apr#612, Cambridge, MA 02139 USA [email protected] Mammano, F. (5) University of Padova, Venetian Inst. Mol. Med., via G.Orus 2, Padova, 35129, ITALY fabio.mammano@unipd. it Manley, G.A. (45) Technische Universitaet Muenchen, Lehrstuhl fur Zoologie, Lichtenbergstrasse 4, Garching, 85747, GERMANY geoffrey. manley@wzw. turn, de Martin, G. Jerry Pettis Memorial Veterans Medical Center, Research Service (151), 11201 Benton Street, Loma Linda CA 92357 [email protected] Martin, P. (115) CNRS (UMR 168), Laboratoire Physico-Chimie Curie, Institut Curie recherche, 26, rue d'Ulm, Paris, 75005, FRANCE pascal, [email protected] Masaki, K. (93) Harvard/MIT Health Science and Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 USA [email protected] Meulenberg, C.J.W. (13) Department of Neurobiophysics, University of Groningen, Nijenborgh 4, Groningen, 9747 AG, THE NETHERLANDS c.j. w. meulenberg@rug. nl

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Mountain, D. (89) Boston University, Department of Biomedical Engineering, 44 Cummington Street, Boston, MA, 02215 USA [email protected] Murakoshi, M. (83) Wada laboratory, Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai, 980-8579, JAPAN michio@wadalab. mech. tohoku. ac.jp Murdock, D.R. Baylor College of Medicine, 3715 Turnberry, Houston, TX 77025 USA david. murdock@bcm. tmc. edu Nakajima, C. (109) Wada Laboratory, Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai 980-8579 JAPAN [email protected] Narins, P.M. (7) UCLA, Department of Physiological Science, 621 Charles E. Young Drive, South, Los Angeles, CA 90095-1606 USA pnarins@ucla. edu Neely, S.T. (60) Boys Town National Research Hospital, 555 North 30th Street, Omaha, NE 68131 USA neely@boystown. org Newburg, S.O. (104) Boston University, 44 Cummington Street, Room 420, Boston, MA 02215 USA [email protected] Nobili, R. (112) Physics Department of Padova University, via Marzolo 8, Padova, 35131 ITALY rnobili@pd. infn. it Nowotny, M. ( I l l ) Department Otolaryngology, Elfriede-Aulhorn-Strasse 5, Tuebingen, 72076 GERMANY [email protected] Nuttall, A.L. (66) Oregon Health & Science University, Oregon Hearing Research Center, NRC-04, 3181 SW Sam Jackson Park Road, Portland, OR 97239 USA nuttall@ohsu. edu

xxiv

Oghalai, J.S. (73) Baylor College of Medicine, One Baylor Plaza, NA 102, Houston, TX 77030 USA jso@bcm. tmc. edu Olson, E.S. (79) Columbia University, P & S 11 - 452, 630 West 168th Street, New York, NY 10032 USA eao2004@columbia. edu Pineda, M. Polytec Inc, 1342 Bell Avenue, Ste. 3A, Tustin, CA 92780 USA m.pineda@polytec. com Puria, S. (84) 496 Lomita Mall, Durand Building, Room 283, Stanford, CA 94305 USA puria@stanford. edu Qian, F. (77) Rice University, Department of Bioengineering, PO Box 1892, MS 142, Houston, TX 77251-1892 USA fengqian@rice. edu Rabbitt, R.D. University of Utah, Bioengineering, 20 East, 2030 South, Bioengineering, 506 BPRB, Salt Lake City, UT 84112 USA [email protected] Rapheal, R. Rice University, Department of Bioengineering, MS-142, PO Box 1892, Houston, TX 77005 USA rraphael@rice. edu Ravicz, M.E. (87) Eaton-Peabody Laboratory, Massachusetts Eye & Ear Infirmary, 243 Charles Street, Boston, MA 02114 USA mike_ravicz@meei. harvard, edu Ren, T. (8) Oregon Health & Science University, Oregon Hearing Research Center, NRC-04, 3181 SW Sam Jackson Park Road, Portland, OR 97239 USA [email protected] Rhode, W.S. (54) University of Wisconsin, 1300 University Avenue, Madison, WI 53706 USA rhode@physiology. wise, edu

XXV

Richter, C.P. (53) Northwestern University, 303 East Chicago Ave, Chicago, IL 60611-3008 USA cri529@northwestern. edu Rimskaya-Korsakova, L.K. (16) N. N. Andreyev Acoustics Institute, Shvernika 4, Moscow 117036, RUSSIA [email protected] Rosowski, J.J. (22) Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles Street, Boston, MA 02476 USA john_rosowski@meei. harvard, edu Ruggero, M.A. (33) Northwestern University, Department of Communication Sciences and Disorders, 2240 Campus Drive, Evanston, IL 60208-3550 USA mruggero@northwestern. edu Santos-Sacchi, J. (99) Yale University School of Medicine, BML 244, 333 Cedar Street, New Haven, CT 06510 MSA. [email protected] Sarpeshkar, R. (78) Massachusetts Institute of Technology, 77 Massachusetts Ave., Rm. 38-294, Cambridge, MA, 02139-4307, USA rahuls@mit. edu Sen, D. (62) School of Electrical Engineering, University of New South Wales, Sydney NSW 2052, AUSTRALIA dsen@ieee. org Shera, C. (74) Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles St, Boston, MA, 02114 USA shera@epl. meet harvard, edu Shoelson, B.D. National Institute on Deafness and Other Communication Disorders, 10 Center Drive, 5D49, MSC 1417, Bethesda, MD 20892 USA [email protected] Siegel, J.H. (1) Northwestern University, 2240 Campus Drive, Evanston, IL 60208 USA j-siegel@northwestern. edu

xxvi

Songer, J.E. (25) Speech and Hearing Bioscience and Technology, Harvard-MIT, Eaton Peabody Lab, MEEI, 243 Charles St., Boston, MA 02114 USA jocelyns@mit. edu Spector, A.A. (76) Johns Hopkins University, Department of Biomedical Engineering, Traylor 411, 720 Rutland Ave., Baltimore, MD, 21205 USA [email protected]. edu Steele, C.R. (64) Stanford University, Department of Mechanical Engineering, Durand Building, Room 262, Stanford, CA 94305 USA chasst@stanford. edu Talmadge, C.L. (61) University of Mississippi, National Center for Physical Acoustics, 1 Coliseum Drive, Oxford, MS, 38677, USA clt@olemiss. edu Temchin, A.N. Northwestern University, 2240 Campus Drive, Evanston, IL 60208-3550 USA a-temchin@northwestern. edu Tempel, B.L (101) University of Washington, Virginia Merrill Bloedel Hearing Research Center, Box 357923, Seattle, WA 98195 USA bltempel@u. Washington, edu Tubis, A. (58) University of California, San Diego in La Jolla, 8099 Paseo Arrayan, Carlsbad, CA 92009 USA tubisa@aol. com Ulfendahl, M. (68) Karolinska Institutet, Building Ml - ENT, Karolinska University Hospital - Solna, SE-171 76 Stockholm, SWEDEN [email protected] van der Heijden, M. Laboratory of Auditory Neurophysiology, K.U.Leuven, Herestraat 49 - bus 801, Leuven 3000, BELGIUM Marcel. Vanderheyden@med. kuleuven. ac. be Van Dijk, P. (11) University Hospital Groningen, Dept. of Otorhinolaryngology, P.O. Box 30001, Groningen, 9700 RB, THE NETHERLANDS p. van. dijk@med. rug. nl

xxvii van Netten, S.M. (20) Department of Neurobiophysics, University of Groningen, Nijenborgh 4, Groningen 9747 AG, THE NETHERLANDS s. van. netten@phys. rug. nl Vetesnik, A. Department of Otolaryngology, University of Tuebingen, Elfriede-Aulhorn-Str. 5, Tuebingen, 72076 GERMANY ales. vetesnik@uni-tuebingen. de Wada, H. (55) Wada laboratory, Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai, 980-8579 JAPAN wada@cc. mech. tohoku. ac.jp Whitmer, B. GN ReSound, 4201 West Victoria Street, Chicago, IL 60646 USA whitmerb@beltone. com Withnell, R.H. (2) Indiana University, Department of Speech and Hearing Sciences, 200 South Jordan Avenue, Bloomington, IN 47405 USA rwithnel@indiana. edu Wittbrodt, M.J. (67) Mechanical Engineering Stanford University, 251 Stanford Avenue, Menlo Park 94025 USA wittbrod@stanford. edu Yoon, Y.J. (85) Stanford University, OtoBiomechanics Lab, Stanford University, Mechanical Engineering, 496 Lomita Mall, Stanford, CA 94305 USA yongjiny@stanford. edu Zheng, J. (14) Oregon Health & Science University, Oregon Hearing Research Center, NRC-04, 3181 SW Sam Jackson Park Road, Portland, OR 97239 USA zhengj@ohsu. edu

CONTENTS I. Whole Organ Mechanics

1

Medial-olivocochlear-efferent effects on basilar-membrane and auditorynerve responses to clicks: Evidence for a new motion within the cochlea J. J. Guinan Jr., T. Lin, H. Cheng and N. P. Cooper

3

Pulsating fluid motion and deflection of the stereocilia of the inner hair cells due to the electromechanics of the outer hair cells A. W. Gummer, M. Nowotny, M. P. Scherer and A. Vetesnik

17

Atomic force microscopic imaging of the intracellular membrane surface of prestin-expressing Chinese hamster ovary cells H. Wada, M. Murakoshi, K. Iida, S. Kumano, T. Gomi, K. Kimura, H. Usukura, M. Sugawara, S. Kakehata, K. Ikeda, Y. Katori and T. Kobayashi

26

Action of furosemide on the cochlea modeled with negative feedback S. M. Khanna

34

Modulation of cochlear mechanics: Model predictions and experimental findings of the effect of changing perilymph osmolarity J. S. Oghalai, C. -H. Choi and A. A. Spector

41

Measuring the material properties of normal and mutant tectorial membranes K. Masaki, D. M. Freeman, G. Richardson and R. J. H. Smith

49

Tuning and travel of two tone distortion in intracochlear pressure W. Dong and E. S. Olson

56

Response characteristics of the 6 kHz cochlear region of chinchilla W. S. Rhode

63

Stiffness properties of the reticular lamina and the tectorial membrane as measured in the gerbil cochlea C.-P. Richter and A. Quesnel

70

XXIX

XXX

Backward propagation of otoacoustic emission in the cochlea T. Ren, W. X. He and A. L. Nuttall

79

Medial olivocochlear efferent effects on basilar membrane responses to sound N. P. Cooper and J. J. Guinan Jr.

86

Modulation patterns and hysteresis: Probing cochlear dynamics with a bias tone L. Bian and M. E. Chertoff

93

What do the OHCs move with their electromotility? M. Nowotny and A. W. Gummer

101

Noise improves peripheral coding of short stimuli L. K. Rimskaya-Korsakova

103

Phase and amplitude transfer in the apex of the cochlea M. van der Heijden and P. X. Joris

105

Manipulations of chloride ion concentration in the organ of Corti alter outer hair cell electromotility and cochlear amplification J. Zheng, Y. Zou, A. L. Nuttall and J. Santos-Sacchi

107

Cochlear transducer operating point adaptation Y. Zou, J. Zheng, T. Ren and A. L. Nuttall

109

Low coherence interferometry of the cochlear partition N. Choudhury, S. L. Jacques, S. Mathew, F. Chen, J. Zheng and A. L. Nuttall

111

Superior semicircular canal dehiscence: Mechanisms of air-conducted hearing J, E. Songer and J. J. Rosowski

113

On the coupling between the incus and the stapes W. R. J. Funnell, S. J. Daniel, B. Alsabah and H. Liu

115

Novel otoacoustic baseline measurement of two-tone suppression behaviour from human ear-canal pressure E. L. Le Page, N. M. Murray and J. D. Seymour

117

xxxi

Is the scala vestibuli pressure influenced by non-piston like stapes motion components? An experimental approach W. F. Decraemer, S. M. Khanna, O. de La Rochefoucauld, W. Dong and E. S. Olson

119

Biomechanics of dolphin hearing: A comparison of middle and inner ear stiffness with other mammalian species B. S. Miller, S. O. Newburg, A. Zosuls, D. C. Mountain and D. R. Ketten

121

II. Hair Cells

125

An experimental preparation of the mammalian cochlea that displays compressive nonlinearity in vitro A. J. Hudspeth and D. K. Chan

127

Ca2+ dynamics in auditory and vestibular hair cells: Monte Carlo simulations and experimental results M. M. Bortolozzi, A. Lelli and F. Mammano

138

Electro-mechanical waves in isolated outer hair cell S. Clifford, W. E. Brownell and R. D. Rabbitt

146

"Area change paradox" in outer hair cells' membrane motor K. H. Iwasa

155

Chloride and the OHC lateral membrane motor J. Santos-Sacchi, L. Song, J. P. Bai and D. Navaratnam

162

Fast adaptation in vestibular hair cells depends on myosin-lc P. G. Gillespie, J. D. Scarborough, J. A. Mercer, E. Stauffer and J. R. Holt

169

The piezoelectric outer hair cell: Bidirectional energy conversion in membranes W. E. Brownell

176

Outer hair cell mechanics are altered by developmental changes in lateral wall protein content H. C. Jensen-Smith and R. Hallworth

187

xxxii

Outer hair cell mechanics reformulated with acoustic variables J. B. Allen and P. F. Fahey

194

A model of high-frequency force generation in the constrained cochlear outer hair cell Z. Liao, A. S. Popel, W. E. Brownell and A. A. Spector

202

Theoretical analysis of membrane tether formation from outer hair cells E. Glassinger and R. M. Raphael

210

Nonlinear responses in prestin knockout mice: Implications for cochlear function M. A. Cheatham, K. H. Huynh and P. Dallos

218

Mechanical impedance spectroscopy on isolated cells M. P. Scherer, Z. Farkas and A. W. Gummer

226

Heat stress-induced changes in the mechanical properties of mouse outer hair cells M. Murakoshi, K. Iida, S. Kumano, H. Wada, N. Yoshida and T. Kobayashi

228

Frequency dependence of admittance and conductance of the outer hair cell B. Farrell, R. Ugrinov and W. E. Brownell

231

Modeling outer hair cell high-frequency electromotility in microchamber experiment Z. Liao, A. S. Popel, W. E. Brownell and A. A. Spector

233

Chlorpromazine and force relaxation in the cochlear outer hair cell plasma membrane — An optical tweezers study D. R. Murdock, S. Ermilov, B. Anvari, A. A. Spector, A. S. Popel and W. E. Brownell

235

Estimation of the force generated by the outer hair cell motility and the phase of the neural excitation relative to the basilar membrane motion: Theoretical considerations M. Andoh, C. Nakajima and H. Wada

237

Quantification of calcium buffers in various subcellular locations in rat inner and outer hair cells S. Mahendrasingam, R. Fettiplace and C. M. Hackney

240

xxxm III. Stereocilia

243

Signal transformation by mechanotransducer channels of mammalian outer hair cells R, Fettiplace, A. C. Crawford and H. J. Kennedy

245

Stereociliary vibration in the guinea pig cochlea A. Fridberger, I. Tomo, M. Ulfendahl and J. Boutet de Monvel

254

The cochlear amplifier: Is it hair bundle motion of outer hair cells? S. Jia, J. Zuo, P. Dallos and D. Z. Z. He

261

Prestin-lacking membranes are capable of high frequency electromechanical transduction B. Anvari, F. Qian, F. A. Pereira and W. E. Brownell

270

Ca2+ changes the force sensitivity of the hair-cell transduction channel E. L. M. Cheung and D. P. Corey

277

Hair bundle mechanics at high frequencies: A test of series or parallel transduction K. D. Karavitaki and D. C. Corey

286

Hair cell transducer channel properties and accuracy of cochlear signal-processing C. J. W. Meulenberg and S. M. van Netten

293

Ca2+ permeability of the hair bundle of the mammalian cochlea C. Harasztosi, B. Miiller and A. W. Gummer

295

IV. Emissions

297

Comparative mechanisms of auditory function: Ground sound detection by golden moles P. M. Narins

299

DPOAE micro- and macrostructure: Their origin and significance D. T. Kemp and P. F. Tooman

308

xxxiv Physical mechanisms of OAE generation and propagation: The hydrodynamic approach A. Vetesnik, R. Nobili and A. W. Gummer

315

Measuring cochlear delays using otoacoustic emissions R. H. Withnell

322

Distortion product otoacoustic emissions in the amphibian ear P. van Dijk and S. W. F. Meenderink

332

Calcium waves, connexin permeability defects and hereditary deafness V. Piazza, M. Beltramello, F. Bukauskas, T. Pozzan and F. Mammano

339

Resonant modes of OAE in the investigation of hearing W. W. Jedrzejczak, K. J. Blinowska, P. J. Durka and W. Konopka

346

DPOAE fine structure changes at higher stimulus levels — evidence for a nonlinear reflection component G. R. Long and C. L. Talmadge

354

The biophysical origin of otoacoustic emissions J. H. Siegel

361

Spontaneous otoacoustic emissions in lizards, air pressure effects on them and the question of point sources and global standing waves G. A. Manley

369

Development of micro mechanically-relevant hair-cell properties: Late maturation of hair-cell orientation in the basilar papilla of birds C. Kdppl, A. Achenbach, T. Sagmeister and L. Schebelle

377

Prediction for audiograms and otoacoustic emissions M. Furst and Y. Halmut

384

Are click-evoked and stimulus-frequency OAEs generated by the same mechanism? R. Kalluri and C. A. Shera

386

A comparative study of evoked otoacoustic emissions in geckos and humans C. Bergevin, D. M. Freeman and C. A. Shera

388

XXXV

V. Cochlear Models

391

Cochlear activity in perspective E. de Boer

393

A mechanical - electrical - acoustic model of the cochlea K. Grosh, N. Deo, L. Cheng and S. Ramamoorthy

410

Cochlear coiling and low-frequency hearing R. S. Chadwick, D. Manoussaki, E. K. Dimitriadis, B. Shoelson, D. R. Ketten, J. Arruda and J. T. O'Malley

417

Multi-scale model of the organ of Corti: IHC tip link tension C. R. Steele and S. Puria

425

A micromechanical model for fast cochlear amplification with slow outer hair cells T. K. Lu, S. Zhak, P. Dallos and R. Sarpeshkar

433

The cochlea box model once again: Improvements and new results R. Nobili and A. Vetesnik

442

Four counter-arguments for slow-wave OAEs C. A. Shera, A. Tubis and C. L. Talmadge

449

The evolution of multi-compartment cochlear models A. E. Hubbard, S. Lu, J. Spisak and D. C. Mountain

458

What stimulates the inner hair cells? D. C. Mountain and A. E. Hubbard

466

Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity P. Martin, B. Nadrowski and F. Julicher

474

Wave propagation by critical oscillators D. Andor, T. Duke, A. Simha and F. Julicher

482

Mechanical energy contributed by motile neurons in the Drosophila ear M. C. Gbpfert and J. T. Albert

489

xxxvi Short-wavelength interactions between OHCs: A "squirting" wave model of the cochlear amplifier A. Bell

496

Wave propagation in a complex cochlear micromechanics model with curvature H. Cai, R. S. Chadwick and D. Manoussaki

498

A 'Twin-engine' model of level-dependent cochlear motion A. J. Aranyosi

500

A hydro-mechanical, biomimetic cochlea: Experiments and models F. Chen, H. I. Cohen, D. C. Mountain, A. Zosuls and A. E. Hubbard

502

Six experiments on a 1-D nonlinear wave-digital filter modeling of human click-evoked emission data E. L. LePage and A. Olofsson

504

Measurements and models of human inner-ear function with superior semicircular canal dehiscence M. E. Ravicz, W. Chien, J. E. Songer, S. N. Merchant and J. J. Rosowski

506

A new multicompartments model of the cochlea S. Lu, J. Spisak, D. C. Mountain and A. E. Hubbard

508

A 3D finite element model of the gerbil cochlea with full fluid-structure interaction G. D. Bustard, D. C. Mountain and A. E. Hubbard

510

Developing a life-sized physical model of the human cochlea M. J. Wittbrodt, C. R. Steele and S. Puria

512

Fully micromachined lifesize cochlear model R. D. White and K. Grosh

514

A generic nonlinear model for auditory perception E. W. Large

516

VI. Discussion Session

519

Quick questions

521

Stereocilia and tip links

524

Somatic motility of outer hair cells

526

Waves in the cochlea

529

Fluid flow in the cochlea

532

Traveling waves in the cochlea

534

Are traveling waves in the cochlea going in both directions?

537

Author Index

545

I. Whole-Organ Mechanics

MEDIAL-OLIVOCOCHLEAR-EFFERENT EFFECTS ON BASILARMEMBRANE AND AUDITORY-NERVE RESPONSES TO CLICKS: EVIDENCE FOR A NEW MOTION WITHIN THE COCHLEA J. J. GUINAN JR., TAILIN*,

HOLDEN CHENG

Eaton-Peabody

Lab, Massachusetts Eye & Ear Infirmary, and Harvard Medical School, 243 Charles St. Boston MA 02114, USA ^Present address: Hearing Emulations LLC, 8825 Page Ave., St Louis MO 63114-6105 E-mail:jjg@epl. meet harvard, edu N. P. COOPER MacKay Institute of Communication & Neuroscience, Keele University, Staffordshire, ST5 5BG, UK We recorded guinea-pig, basilar-membrane (BM) motion, and cat, single auditory-nerve-fiber (AN) responses to clicks, with and without electrical stimulation of medial-olivocochlear (MOC) efferents. In both BM and AN responses, MOC stimulation inhibited almost completely at low click levels. However at moderate-to-high click levels, MOC inhibition was small on the first half cycle and built up over many cycles in BM click responses, but was large on the first half cycle and negligable in the second cycle in AN click responses. The data support the hypothesis that OHCs produce or influence a motion which bends inner-hair-cell stereocilia and can be inhibited by MOC efferents, a motion that is present through most, or all, of the cochlea, but that is not apparent in basal-turn BM motion. These data, from normally-working cochleas, highlight the need to shift the conceptual paradigm for cochlear mechanics to one in which the classic BM traveling wave is not the only motion that excites AN fibers.

1 Introduction Medial olivocochlear (MOC) efferents synapse directly on outer hair cells (OHCs) and provide a way to reversibly change OHC properties without opening or damaging the cochlea. MOC effects have not been previously studied on basilar membrane (BM) or single auditory-nerve (AN) fiber click responses. Results at these levels shows a surprising difference in the inhibition of the first response peak, a difference that has important implications for cochlear mechanics. 2 Methods Experiments were performed on deeply anesthetized animals in accordance with local, NIH, UK and US guidelines. BM motion was measured in the first turn of guinea-pig and chinchilla cochleae as in [1]. Single AN-fiber responses were monitored in cats, and recovered probability post-stimulus-time (rpPST) histograms

3

4

were calculated as in [2]. Compound action potentials (CAPs) were recorded from a silver round-widnow electrode, and CAP audiograms were used to monitor cochlear condition. MOC efferents were stimulated via a bipolar electrode at the floor of the fourth ventricle using a paradigm that selected the efferent fast effect [1,3]. Controls were done to insure that the results were not due to middle-ear-muscle contractions. 3 Results The most salient MOC effects on BM click responses were: 1. The biggest inhibition of BM click responses was at low sound levels. 2. The inhibiton was near zero on the first half-cycle of the response and grew over many cycles to nearly full inhibition. 3. The final growth to full inhibition began later at higher click levels. 4. MOC stimulation produced a small phase advance early in the response. Points one and two can be seen in Fig. 1, left. Results similar to these were found in three guinea pigs with good thresholds and six other animals with poorer thresholds including one chinchilla. — Clicks Alone — Clicks plus MOC Shocks 80 dB pSPL

—\/WMMflfww*M^

If

P1

WvA> »£-•>CP*» vs^Ny^*'

88 dB pSPL

76dBpSPL 64 dB pSPL 52 dB pSPL

CF = 2.2 kHz

0.5 1 Time after click (ms)

1

2 3 4 5 Time after click (ms)

Figure 1. MOC effecls on click responses in BM motion (Left) and AN firing (Right). Right: compound histograms with the ipPST from rarefaction plotted upwards and from condensation plotted downward.

In AN click responses, MOC stimulation inhibited [3]: 1. The whole response at low sound levels, 2. The decaying part of the response at all sound levels (in most fibers), and 3. The first peak of the response at moderate to high sound levels. The "first peak" is the peak with the shortest latency across all sound levels; the earliest peak at low sound levels is not the "first peak". Above 100 dB pSPL, some responses showed a reversal of the click polarity which produced the first peak [2]. In these cases, there

was inhibition of the first peak at levels below the reversal, but little MOC effect at levels above the reversal. Points 1 and 3 can be seen in Fig. 1, right. We quantified AN inhibition by counting spikes in the peaks with and without MOC stimulation for sound levels 75-100 dB pSPL and fibers with CFs <4-6 kHz (where individual peaks could be seen). For CFs > 4-6 kHz, we compared responses with and without MOC stimulation in two abutting, 0.2 ms windows starting at the onset of the click response. The resulting data are shown in Fig. 2A-D with loess-fit [4] trend lines superimposed in Fig. 2E. The data in Fig. 2 show that for CFs < ~8 kHz, MOC stimulation inhibited rarefaction peak 1 significantly more (t-test, P<0.01) than rarefaction or condensation peak 2. Peak 1 Rarefaction Clicks

Condensation Clicks

Peak 2 Rarefaction Clicks

Comparison of Trend Lines

Condensation Clicks E

30 0.3 1

3

10

30 c

CF (kHz) Figure 2. MOC-induced changes in the first and second click-response peaks. A-D: changes from individual fibers. E: Loess-fit [4] curves from A-D. "MOC-induced change" is the rpPST peak amplitude with MOC shocks, S, minus the rpPST peak amplitude without shocks, W, normalized by their sum, S+W. For each fiber, rarefaction and condensation responses were considered separately, the response was segmented into peaks, responses from levels 75-100 dB pSPL were averaged, the average number of spikes in each peak was computed, and the MOC-induced change was calculated from these averages. Points from 104 fibers from 10 cats. Vertical lines mark 4 kHz. (adapted from [3]).

4 Discussion The lack of MOC inhibition of the first peak of BM responses to clicks fits with current conceptions of mammalian cochlear mechanics, but the inhibition of the AN first peak does not. The usual view [5] is that all motion of the organ of Corti is produced by the BM traveling wave which mimics BM motion in the basal turn and extends throughout the cochlea (although it is recognized that the classic traveling wave does not explain some phenomena in the apical turn, e.g. downward glides [6]).However, MOC inhibition of the AN click-response first peak cannot be explained by inhibition of the first peak of the classic traveling wave because, as shown by basal BM responses, the classic traveling wave first peak receives little or no cochlear amplification, and is little changed by MOC stimulation or by death [79]. Thus, the strong MOC inhibition of the AN first peak must be due to inhibition of something other than a classic traveling wave that extends throughout the cochlea.

6

Possible hypotheses are that MOC inhibition of the AN first peak is due to: (HI) Electrical coupling from OHCs to IHCs via local extracellular fields (i.e. by cochlear microphonic). (H2) Efferent synapses on IHCs or AN fibers (i.e. Lateral Efferents). (H3) MOC-induced hyperpolarization of OHCs causing OHC lengthening which changes the coupling of BM motion to IHC stereocilia. (H4) Inhibition of the BM first peak, and that BM motion in the middle and apical turns is substantially different from the classic traveling wave. (H5) Motion of structures or fluid that bends IHC stereocilia and is in addition to motion of the classic traveling wave. (This second motion may, or may not, be seen at the basilar membrane). H1-H3 each has specific reasons for rejection, and a potent argument against all three is that they do not explain how the efferent stimulation can inhibit the first click-response peak without also inhibiting the later peaks. H4 and H5 differ in that H5 considers that there are two superimposed modes of motions in the organ-of-Corti, the classic traveling wave and a new motion, and H4 considers that there is only one motion, the motion of the BM which drives all other motions. For H4 to explain the data, BM motion in the middle and apex of the cochlea would have to look quite different from the classic traveling wave; it would have to have a substantial first peak that is not passive but is dependent in a strong way on OHCs. Against this is the slow base-to-apex variation of cochlear dimensions & physical properties, plus a wealth of models, that indicate that the a traveling wave that is not drastically different from the classic wave should be present throughout the cochlea. While we cannot rule out H2, we think it more likely that the classic BM traveling wave does exist throughout the cochlea, and that MOC inhibition of the first peak of some other motion explains the inhibition of the AN first peak. Considering the above, our working hypothesis is that MOC inhibition of the AN first peak is due to an OHC-dependent motion of structures or fluid that bends IHC stereocilia and is separate from motion of the classic traveling wave. To account for strong AN first-peak inhibition, there must normally be an OHCdependent motion of structures and/or fluid that bends IHC stereocilia and produces the AN initial peak (ANIP), and this ANIP motion must be reduced by MOC activation. The ANIP motion could come from OHC stereocilia motility or OHC somatic motility as long as MOC efferents can inhibit the motion. Presumably, the ANIP motion is the first part of a vibrational response mode that continues past the first peak. However, the lack of MOC inhibition of the second AN click-response cycle (Fig. 2) suggests that the ANIP motion decays quickly so that by the second cycle it is less than the little-inhibited motion that evokes the second AN peak, presumably motion due to the classic traveling wave. A variety of previous data provide evidence for cochlear motion that is separate from, or in addition to, the motion of the classic traveling wave: (1) In the apex, two group delays in AN responses and cochlear motion have been reported many times [10-15]. Although an artifactual "fast wave" from opening the cochlea can contaminate apical mechanical measurements [13], Zinn and coworkers [14] found that computationally removing the fast wave still left response dips and multiple

7

group delays. Furthermore, in intact cochleae, AN responses show tuning curves (TCs) with multi-lobed shapes [16] and different group delays in each lobe [11]. These data provide evidence from intact cochleae that two interacting drives with different group delays excite apical AN fibers (These data provide perhaps the best reason for choosing H5 over H4). (2) The previously-anomalous phenomenon of downward glides in the apex may be explained by the interaction of two motions, a first-arriving, above-CF wave and a later-arriving CF wave [17]. (3) Interference of two motions may explain many observations of cancellations and phase reversals in AN and BM responses (reviewed in [18]). Although all of the phenomena just cited indicate the presence of two cochlear motions, these two motions do not necessarily correspond to the ANIP motion and the classic traveling wave. The ANIP motion appears to extend through most the cochlea. MOC inhibition of the ANIP motion is evident, for CFs up to 8-10 kHz, as inhibition of the AN click-response first peak (Fig. 2). For fibers with CFs > 5 kHz, additional evidence comes from inhibition of short-latency, tail-frequency tone responses [3, 19]. The dividing line between supposed basal and apical patterns of BM motion is often thought to be ~1 kHz, the region where click-response glides change from upward to downward [17,21] and tuning-curve "tails" change from below CF to above CF [11]. There are, however, almost no motion measurements in living cochleae with good thresholds between the basal turn and the apex on which to base a judgment of the dividing line. It seems plausible that the classic traveling wave and the ANIP motion are both present throughout the cochlea, perhaps with their relative strengths changing from base to apex. In this view, the classic traveling wave is dominant in the base and the ANIP motion gains in prominence going toward the apex. 4.1 What is the origin of the ANIP motion? Since the ANIP motion is not apparent in the classic traveling wave and is inhibited by MOC efferents that synapse on OHCs, it appears to be due to OHCs, or at least is strongly influenced by OHCs. It seems possible that the ANIP motion is due to an active, energy consuming process and may be, in some sense, an amplified motion. Even though we have quantified the AN first-peak inhibition only at moderate to high sound levels, it may be present at low sound levels, especially in the apex. Which mechanisms in OHCs produce and/or modify the ANIP motion are unknown. Nonetheless, it is useful to elaborate some hypothetical mechanisms by which the ANIP motion might be produced and to consider their consequences. To fit the data, the mechanism should excite AN fibers early enough to produce the first click-response peak in the middle and apex of the cochlea and to produce the short-group-delay tone response in the base, and should be inhibited by MOC efferents without changing the first peak of the basal-turn BM response. 4.1.1 Possible ANIP source: OHCfluid pumping One hypothesis for the origin of the ANIP motion is OHC "fluid pumping". Soundfrequency electrical stimulation in an excised gerbil cochlea causes OHC

8

contractions which squeeze the cochlear partition producing sound-frequency fluid motion along the tunnel of Corti, i.e. OHCs act as fluid pumps [21]. OHC squeezing of the organ of Corti has also been reported in guinea pigs [22] and may be the origin of phase differences between BM arcuate- and pectinate-zone motions [2326]. With this hypothesis, pressure differences across the cochlear partition produce the classic traveling wave, and pressure differences inside to outside the organ of Corti produce the ANIP motion which is a squeezing wave in which the walls of the organ of Corti expand and contract. Presumably, the pressure difference inside to outside the organ of Corti produces a large ANIP motion at the reticular lamina but not at the BM because the first peak is primarily from below-CF energy (where stiffness dominates) and the effective stiffness of the reticular lamina is much less than that of the BM [27]. Thus, the ANIP motion should be much greater at the reticular lamina (and presumably, at IHC stereocilia and in AN firing) than at the BM. Finally, the ANIP motion might have a shorter delay than the classic traveling wave because tunnel fluid motion extends ahead of OHC contractions [21]. 4.1.2 Possible ANIP source: Stereocilia motility Another possible source of the ANIP motion is stereocilia motility. One appeal of this mechanism is that an OHC stereocilia twitch could be readily coupled from OHC stereocilia to IHC stereocilia by the tectorial membrane without requiring intervening BM motion. In this hypothesis, the ANIP motion is the motion of the tectorial membrane and/or nearby fluid that bends IHC stereocilia. For calciummediated stereocilia motility [28, 29], a drawback of this hypothesis is the lack of a clear mechanism by which MOC synapses affect this motion. Although this stereocilia motility is influenced by membrane voltage, MOC synapses hyperpolarize OHCs which would be expected to increase calcium-mediated OHC stereocilia motility, not inhibit it. On the other hand, if the stereocilia motility was mediated by Prestin [30], then the OHC hyperpolarization could inhibit it. 4.1.3 Possible ANIP source: Direct acoustic coupling to OHCs Yet another mechanism that might produce the ANIP motion is direct acoustic coupling from the forward cochlear pressure wave. Ren [31] and Ruggero [32] have suggested that mammalian OAEs may be generated by organ-of-Corti motion that is coupled back to stapes motion by fast fluid-pressure waves. Any cochlear process that couples organ-of-Corti motion to fluid pressure waves is likely to be reciprocal, which would imply that normal (forward) cochlear pressure waves may directly produce motion of the organ of Corti. To account for the ANIP motion, such motion, or the amplification of this motion, must be affected by OHCs. This mechanism has the advantage that it readily explains how the ANIP motion can produce a response peak that starts before the lowest-frequency part of the traveling wave. However, it is difficult to account for the long delays of the ANIP motion in the apex of the cochlea if the classic traveling wave is bypassed completely.

9 As can be noted from the above, a question related to the origin of the ANIP motion is how the ANIP motion travels along the cochlea. Is the ANIP motion a second wave along the cochlea, a separate vibrational mode excited by the classic traveling wave, or a vibrational mode excited directly by the fast cochlear pressure wave (e.g. due to OHC pressure sensitivity)? An important constraint is that the latency of the click-response first peak changes over -2.5 ms from the base to the apex [2], but this does not separate the hypotheses. Since the ANIP response is clearly first in the apex (Figs. 1-2), it seems unlikely that the ANIP response is a separate vibrational mode excited by the classic traveling wave. As the above hypotheses point out, there are many possible ways by which the ANIP motion may be produced and determining which one is correct, or if more than one, requires additional data. Whatever mechanisms are involved, the presence of the OHCgenerated ANIP motion early in the response puts it at a time that could influence, shape, or be a first step in cochlear amplification. 4.2 Effects of the ANIP motion on signal coding Excitation of AN fibers by the ANIP motion seems likely to have a different frequency filter than the classic traveling wave, but does not appear to sharpen the response and produce an old-style "second filter". Our click results suggest that the ANIP motion has an important influence on neural responses at moderate-to-high sound levels (Figs. 1-2). For tones, a component of the AN response due to ANIP motion was not evident at threshold at the base of the cochlea [33], but an ANIP response may be evident at higher sound levels in the base, and perhaps at low sound levels in the apex. MOC inhibition of the AN first peak can be expected to have behavioral consequences. Medial efferents improve the detection of transient sounds in background noise and provide protection from sound trauma. MOC inhibition of the ANIP response may be involved in both of these, as well as in any MOC effect at moderate to high sound levels. Acknowledgments Supported by NIDCD RO1DC00235, RO1DC005977 and the Royal Society.

1. Cooper, N.P., Guinan, J.J., Jr., 2003. Separate mechanical processes underlie fast and slow effects of medial olivocochlear efferent activity. J Physiol 548, 307-312. 2. Lin, T., Guinan, J.J., Jr., 2000. Auditory-nerve-fiber responses to high-level clicks: interference patterns indicate that excitation is due to the combination of multiple drives. J Acoust Soc Am 107, 2615-30.. 3. Guinan, J.J., Jr., Lin, T., Cheng, H., 2005. Medial-olivocochlear-efferent inhibition of the first peak of auditory-nerve responses: Evidence for a new motion within the cochlea. J Acoust Soc Am 118, (in Press). 4. Cleveland, W.S., 1993. Visualizing Data AT&T Bell Labs, Murray Hill, N.J. 5. Patuzzi, R. 1996. Cochlear Micomechanics and Macromechanics. In: Dallos, P.J., et al., (Eds.), The Cochlea. Springer-Verlag, New York. pp. 186-257. 6. Shera, C.A., 2001. Frequency Glides in Click Responses of the Basilar Membrane and Auditory Nerve: Their scaling behavior and origin in travelingwave dispersion. J Acoust Soc Am 109, 2023-2034. 7. Recio, A., Rich, N.C., Narayan, S.S., Ruggero, M.A., 1998. Basilar-membrane responses to clicks at the base of the chinchilla cochlea. JASA 103, 1972-1989. 8. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea. Physiological Reviews 81, 1305-1352. 9. Guinan, J.J., Jr., Cooper, N.P., 2005. Medial Olivocochlear Efferent Inhibition of Basilar-Membrane Click Responses. Assoc. Res. Otolaryngol. Abstr 28:340. 10. Pfeiffer, R.R., Molnar, C.E., 1970. Cochlear nerve fiber discharge patterns: Relationship to the cochlear microphonic. Science 167, 1614-1616. 11. Kiang, N.Y.S., 1984. Peripheral neural processing of auditory information, Handbook of Physiology, Section 1: The Nervous System, Vol. 3 (Sensory Processes). Am. Physiological Soc, Bethesda, MD. pp. 639-674. 12. Gummer, A.W., Hemmert, W., Zenner, H.P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning. Proc Natl Acad Sci U S A 93, 8727-32. 13. Cooper, N.P., Rhode, W.S., 1997. Apical Cochlear Mechanics: A review of recent observations. In: Palmer, A.R., et al, (Eds.), Phychophysical and Physiological Advances in Hearing. Whurr, London, pp. 11-17. 14. Zinn, C , Maier, H., Zenner, H., Gummer, A.W., 2000. Evidence for active, nonlinear, negative feedback in the vibration response of the apical region of the in-vivo guinea-pig cochlea. Hear Res 142, 159-83. 15. van der Heijden, M., Joris, P.X., 2003. Cochlear phase and amplitude retrieved from the auditory nerve at arbitrary frequencies. J Neurosci 23, 9194-8. 16. Liberman, M.C., Kiang, N.Y.S., 1978. Acoustic trauma in cats. Cochlear pathology and auditory-nerve activity. Acta Otolaryngologica Suppl. 358, 1-63.

11 17. Lin, T., Guinan, J. J., Jr., 2004. Time-frequency analysis of auditory-nerve-fiber and basilar-membrane click responses reveal glide irregularities and noncharacteristic-frequency skirts. J Acoust Soc Am 116,405-416. 18. Ruggero, M.A., Narayan, S.S., Temchin, A.N., Recio, A., 2000. Mechanical bases of frequency tuning and neural excitation at the base of the cochlea: comparison of basilar-membrane vibrations and auditory- nerve-fiber responses in chinchilla. Proc Natl Acad Sci U S A 97, 11744-50. 19. Stankovic, K.M., Guinan, J.J., Jr. 1999. Medial efferent effects on auditorynerve responses to tail-frequency tones I: Rate reduction. JASA 106, 857-869. 20. Carney, L.H., McDuffy, M.J., Shekhter, I., 1999. Frequency glides in the impulse responses of auditory-nerve fibers. J Acoust Soc Am 105, 2384-2391. 21. Karavitaki, K.D., Mountain, D.C., 2003. Is the Cochlear Amplifier a Fluid Pump? In: Gummer, et al., (Eds.), The Biophysics of the Cochlea: Molecules to Models. World Scientific, Singapore, pp. 310-311. 22. Mammano, F., Ashmore, J.F., 1993. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature 365, 838-841. 23. Xue, S., Mountain, D.C., Hubbard, A.E., 1993. Direct measurement of electrically-evoked basilar membrane motion. In: Duifhuis, H., et al. (Eds.), Biophysics of hair cell sensory systems. World Scientific, Singapore, pp.3618. 24. Nilsen, K.E., Russell, I.J., 1999. Timing of cochlear feedback: spatial and temporal representation of a tone across the basilar membrane membrane. Nature Neurosci. 2, 642-648. [erratum in Nat Neurosci 1999;2:848]. 25. Nuttall, A.L., Guo, M., Ren, T., 1999. The radial pattern of basilar membrane motion evoked by electric stimulation of the cochlea. Hear Res 131, 39-46. 26. Cooper, N.P., 1999. Radial variation in the vibrations of the cochlear partition. In: Wada, H., Takasaka, T., Ikeda, K., Ohyama, K., (Eds.), Recent Developments in Auditory Mechanics. World Scientific, Singapore, NJ. 27. Scherer, M.P., Gummer, A.W., 2004. Impedance analysis of the organ of corti with magnetically actuated probes. Biophys J 87, 1378-91. 28. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat Neurosci 6, 832-6. 29. Chan, D.K., Hudspeth, A.J., 2005. Ca(2+) current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci.8, 149-55. 30. Jia, S., Zuo, J., Dallos, P., He, D.Z., 2005. The Cochlear Amplifier: Is it hair bundle motion of outer hair cells? In: Nuttall, A., et al. (Eds.), Auditory Mechanics: Processes and Models. World Scientific, Singapore, NJ 31. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat Neurosci 7, 333-4. 32. Ruggero, M., 2004. Comparison of group delays of 2f1-12 distortion product otoacoustic emissions and cochlear travel times. Acoustic Research Letters Online 5, 143-147.

12 33. Narayan, S.S., Temchin, A.N., Recio, A., Ruggero, M.A., 1998. Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae. Science 282, 1882-4. Comments and Discussion Santos-Sacchi: Why is there expected to be a causal link between the first peak of the BM response and that first peak of the neural response? Can't it be that not all initial cycles of the click BM response sufficiently excite the IHC? Answer: The expected causal link between the first peak of the BM response and the first peak of the AN response comes about from the hypothesis that BM motion drives the motion of the rest of the organ of Corti. The first AN peak, as we defined it, is not present at low sound levels, presumably because the amplitude of the BM first peak is too small, as you suggest. However, the first peak of the BM response to clicks grows linearly and becomes very large at high sound levels where it might be expected to be producing the first peak of the AN response. It seems worth noting that there is evidence for more than one drive that excites AN fibers at the time of the first peak. Lin and Guinan (2000) found that the polarity that excited the first AN peak reversed at click levels above 100 dB pSPL. We found that MOC stimulation inhibited the AN first peak at levels below this reversal but not above the reversal. Presumably, the ANIP motion saturates and some other motion (perhaps one due directly to the first peak of the classic traveling wave) becomes bigger at high levels and this other motion is not inhibited by MOC efferents. Ruggero: I think that your interpretation of the effects of electrical stimulation of the medial olivocochlear system on the responses to clicks of the basilar membrane and auditory nerve fibers is flawed in two respects. 1) The first flaw arises from comparing responses to clicks of the basilar membrane at the base of the cochlea and of auditory-nerve fibers recorded largely at apical locations. Contrary to your implicit assumption, the first peak of basilar-membrane responses to clicks differs fundamentally between basal and apical regions of the cochlea. At the base, the first peak of the basilar-membrane response grows linearly as a function of click intensity and grows at increasingly compressive rates over a time course of a few hundreds of microseconds (for a characteristic-frequency period of 100 microseconds at the 10-kHz place) [Recio et al., JASA, 1998]. In contrast, at the apex of the cochlea the first basilar-membrane response peak exhibits pronounced compressive nonlinearity [Cooper and Rhode, Auditory Neuroscience, 1996]. To the extent that (compressive) nonlinearity is a marker for an influence of outer hair cells on the vibrations of the basilar membrane/organ of Corti complex, it is not at all surprising that at the apex, stimulation of the medial olivocochlear system (whose terminals synapse on outer hair cells) reduces the magnitude of the first peaks of responses to clicks both for basilar-membrane vibrations and poststimulus-time histograms for auditory-nerve fibers. [The latter has not been

13 demonstrated yet; I suggest it will be eventually demonstrated.] Similarly, at the base, the first peaks of neither basilar-membrane responses nor of auditory-nerve post-stimulus-time histograms should be affected by stimulation of the medial olivocochlear system, post-stimulus-time histogram largely free of neural recovery effects, such as refractory periods and adaptation. I disagree. Such analysis is successful only when the driven discharge is fully adapted and does not exceed, say, 1 spike per several periods of oscillation in responses to individual clicks (so that, on average, the probability of spike occurrence is unaffected by the occurence of previous spikes). When such conditions do not hold, a spike triggered by the first peak of the basilar-membrane response will cause later peaks of the post-stimulus time histogram to be relatively attenuated vis-a-vis the corresponding peaks in the underlying basilar-membrane ringing. In other words, the "recovered probability" analysis exaggerates the magnitude of the first peak, especially for responses to more intense clicks. Now I summarize my own interpretation of your data. Both at the base and at the apex, auditory-nerve fiber responses follow more or less faithfully the corresponding vibrations of the basilar membrane/organ of Corti complex [see review by Robles and Ruggero, Physiological Reviews, 2001]. The reason why the correspondence between mechanical and neural responses appears to differ between base and apex is because the appropriate comparisons (neural base vs. mechanical base, neural apex vs. mechanical apex) have not yet been carried out. In other words, at any one place of the cochlea, basilar-membrane and auditory-nerve responses to clicks correspond strictly to each other. Finally, I do not deny that inner hair cells are stimulated by basilar-membrane vibrations via two distinct pathways. This has been most clearly demonstrated in the chinchilla cochlea: auditory-nerve fiber responses to tones exhibit peak splitting, Nelson's notches and 180-degree phase shifts which have no basilar-membrane counterpart [Ruggero et al., PNAS, 2000]. Answer: First I respond to Point 2 regarding "recovered probability". Your question incorrectly assumes that we were using low-rate clicks. If we had used such clicks, then at high click levels for every click there would be a spike in the first peak and the result would be no recovered probability for 3 ms after that peak (i.e., 0/0), not a distorted histogram such as you suggest. Also note that recovered probability histograms always reduce the relative size of the first peak, not increase it as you state. Our methods avoided such problems by using high-rate clicks which (in addition to giving data at a faster rate) produce adaptation in the auditory-nerve response so that there was not always a spike in the first peak and spikes occurred at peaks throughout the response. Under these conditions, recovered probability removes the bulk of the effects of refractoriness and short-term adaptation (Gray, 1967. Biophysical J. 7, 759-777).

14 Now I reply to point 1 and the related last two paragraphs of Ruggero's comment. We did not, as your comment asserts, assume that the first peak of the basilar membrane (BM) response to clicks is the same in basal and apical regions of the cochlea. What we asserted is that if the classic BM traveling wave (which is a theoretical construct from basal-turn measurements) is assumed to extend throughout the cochlea, then MOC inhibition of the classic traveling wave response to clicks cannot account for the inhibition of the first click-response peak at the auditory nerve (AN). After ruling out some possible explanations we focused on two possible hypotheses, H4 and H5, both of which allowed there to be a difference in BM motion from the base to apex. There are a few relevant measurements of BM click responses from frequency regions lower than the 15-20 kHz region of most of our BM click data. The one chinchilla in which we measured MOC effects on BM click responses and found negligible first peak inhibition had a best frequency of ~8.5 kHz. In addition, measurements of click responses from the apical turn of the chinchilla (see Cooper, 2003), showed a mild compressive growth of click responses that is about the same on the first four peaks of the response, which suggests that efferent suppression of cochlear amplifier gain would produce a small suppression that would be similar in the first four peaks. So these data, from a similar CF region but a different species (and without efferent effects), suggest that strong efferent suppression of the first peak but not the second peak of the AN response will not be accounted for by an inhibition of BM motion. The problem is that your comments miss the point we are trying to make. Our point is not about the correspondence, or lack thereof, between BM motion and auditory nerve (AN) firing, it is about the underlying motions of the organ of Corti that produce the motions of the BM and the motion of inner-hair-cell stereocilia which drive AN firing. We hypothesize that there are two motions throughout most (perhaps all) of the cochlea, the motion of the classic traveling wave (or a modest modification of it) and a second motion, the AN1P motion. This ANIP motion may, or may not, move the basilar membrane in the middle and apex of the cochlea. We argued that hypothesis 5 (that there are two underlying vibration patterns that produce the motions) is preferred over hypothesis 4 (that there is only one underlying vibrational pattern and it changes dramatically from base to apex) because it allows us to keep the classical traveling wave throughout the cochlea, as a large body of theory suggests. Another reason (not emphasized in my talk) for preferring hypothesis 5 over 4 is that the two motions hypothesis is much better at explaining the AN tuning curves with two lobes and different group delays in each lobe. Cooper, N.P., 2003. Compression in the Peripheral Auditory System. In: Bacon, S.P., Fay, R., Popper, A.N., (Eds.), Compression: From Cochlea to Cochlear Implants. Springer Verlag, New York.

15 Siegel: It would be helpful if you would clarify what you mean by the "classical" traveling wave. The feature most commonly associated with the traveling wave is the increasing phase lag with distance from the base for tonal stimuli and this is clearly evident in auditory nerve recordings. Isn't it likely that the differences in tuning curve shape and click response between the base and apex are a function of macromechanics rather than micromechanics? This is suggested by the observation of nonlinear basilar membrane mechanics throughout the response area in the apex (Cooper and Rhode, 1997). Wouldn't it be likely that MOC effects would be observed in the first peak of the transient response of the basilar membrane as well? Answer: I have used the term "classical traveling wave" to mean the translation and scaling to positions throughout the cochlea of the traveling wave measured from basilar-membrane (BM) motion in the cochlear base. This is what is commonly done when people think about BM motion anywhere in the cochlea, except perhaps in the apex. In the cochlear base, we found no MOC inhibition of the first peak of the BM response to clicks, which is consistent with previous data showing almost linear growth of this peak. In the apex, all peaks of the BM click response have slightly nonlinear growth (Cooper and Rhode, 1997). Thus, presuming that nonlinear growth indicates an amplified response, we expect these peaks, including the BM first and second peaks, to be slightly inhibited by MOC stimulation. In contrast, we have found that AN click responses from the apex and middle of the cochlea show strong inhibition of the first peak and little or no inhibition of the second peak. Thus, the MOC inhibition of early peaks in the AN click response from the apex and middle of the cochlea has a different pattern than the nonlinearity seen in BM motion at either the apex or the base. Your question regarding cochlear micromechanics versus macromechanics reveals a weakness in the application of this terminology to the current situation. If our hypothesis 5 is correct and cochlear motion is a combination of a classical traveling wave and a second wave, with each producing some BM motion (BMm) and some IHC stereocilia bending (IHCsb), but with the two waves having very different ratios of IHCsb to BMm (i.e., each wave has its own macromechanical pattern and its own micromechanical pattern), then different MOC effects might be seen in BM motion and AN firing simply by changing the relative strengths of the two waves from base to apex without any difference in the MOC effect on each wave. In this case, asking whether the change is in macromechanics or micromechanics does not have the same interpretation that it would if there were just one cochlear motion. Thus, if cochlear motion is the sum of two vibrational modes, past ways of attributing effects to macromechanics versus to micromechanics need revision. Chadwick: Comment: Any candidate for the ANIP response must take into account the increase of the response from base to apex. I would like to suggest that curvature increase from base to apex be considered as a possibility for the mechanism.

16 van der Heijden: Phase curves and group delay are very different in the apex and in the base. Auditory-nerve data [1,2] show a gradual change from what you call a "classical traveling wave" in the base to a patterning in the apex that is very different: high-frequency tails in tuning curves, anomalous dispersion, and downward FM glides in impulse responses. So we know it is incorrect to extrapolate high-CF behavior to low-CF regions. The transition of the behavior from base to apex is gradual and, moreover, does not show a "competition" or interference between separate response components. So there seems to be little need to postulate any novel modes of vibration from your neural data. References: 1. Pfeiffer RR and Molnar CE (1970). Science 176, 16-14-1616. 2. van der Heijden M and Joris, PX (2003). J. Neurosci 93, 201-209. Answer: I agree that AN data show a gradual change in response properties from the base to the apex. There are no comparable BM measurements that extend throughout the cochlea, but nonetheless, BM measurements from the base are routinely extrapolated to hold for the rest of the cochlea. Sometimes it is acknowledged that mechanical measurements in the apex are different from the base, but then the apex/base dividing line is typically put near 700 Hz (below which glides are anomalously downward) or 1 kHz (where TC tails change from below to above the tips). However, the smoothly changing AN data (e.g. our Fig. 2) suggest that it may be incorrect to extrapolate high-CF mechanical data from the base even to the middle of the cochlea. A point on which I disagree with Marcel's comment is in the presence of interference patterns in AN data. We have already published several examples of interference patterns in AN click responses (see Lin and Guinan, 2000); also see Ruggero et al. (PNAS 97:11744) and my reply to Joe Santos-Sacchi's comment. Furthermore, your own data shows examples of AN TCs with two lobes and different group delays in each lobe. Thus, I think there is ample evidence for interference between separate response components.

PULSATING FLUID MOTION AND DEFLECTION OF THE STEREOCILIA OF THE INNER HAIR CELLS DUE TO THE ELECTROMECHANICS OF THE OUTER HAIR CELLS A.W. GUMMER, M. NOWOTNY, M.P. SCHERER AND A. VETESNIK Department

Otolaryngology, University Tuebingen, Elfriede-Aulhorn-Strasse 72076 Tuebingen, Germany E-mail: [email protected]

5,

The mechanisms for deflecting inner hair cell (IHC) stereocilia have not been identified experimentally. Here, we describe a deflection mechanism which is capable of mechanically coupling somatic electromotility of the outer hair cells (OHCs) directly to the IHC stereocilia. The description is based on our recent discovery [1] that in response to intracochlear electrical stimulation, the apical surface of the IHC and the lower surface of the overlying tectorial membrane (TM) exhibit antiphasic motion of similar amplitudes for stimulus frequencies up to at least 3 kHz. This results in a pulsatile motion of the fluid surrounding the IHC stereocilia. Based on well-known physical principles of fluid flow between narrowly spaced elastic plates, we show that the fluid motion is amplified relative to that of the two boundary membranes and that this motion is capable of bending IHC stereocilia.

1 Introduction The current model of deflection of the IHC stereocilia postulates that deflection derives from shear motion between the TM and the reticular lamina (RL) [2], which produces a viscous drag force which is coupled to the stereocilia [3]. In a recent report [1] we demonstrate experimentally that electromechanical force derived from the OHC causes the RL of the IHC and the overlying TM to vibrate transversally in opposite phase for frequencies up to at least 3 kHz. This presents, therefore, another mechanism for deflection of IHC stereocilia. Here, we provide estimates of fluidparticle displacement in the subtectorial space and also IHC stereocilia deflection for this anti-phasic motion. The first part of the analysis is based on work by Hassan and Nagy [4] for longitudinal motion in a non-viscous fluid between two identical elastic plates, which flex in opposite phase in the transverse direction. If the separation, d, of the plates is sufficiently small and the frequency sufficiently low, then anti-symmetric transverse vibrations of the plates force the fluid to experience a much larger displacement in the longitudinal direction; that is, the fluid is "squirted" between the plates. However, here we refrain from using the term "squirting" because it can imply steady or dc fluid motion; we prefer to use the term "pulsating" because it captures the notion that the fluid particles oscillate backward and forward about their mean positions. In addition to their analysis, we also consider the effects of viscosity. As a first approximation, we calculate fluid motion in the absence of

17

18 stereocilia. That is, we assume that at sufficiently low frequencies fluid velocity is determined by the motion of the sensory epithelium and TM, and not by the presence of stereocilia [5]. Then, in the second part of the analysis, we calculate the motion of the IHC stereocilia resulting from this pulsating fluid motion. Although our model is by necessity simplified, its justification lies in its ability to demonstrate salient physical principles. 2 Model and Results 2.1 Assumptions for the subtectorial space and its boundaries We choose the coordinate axes, x and z, respectively, parallel and orthogonal to the plate surface, with the z-origin midway between the plates (Fig. 1, upper). We assume linearity because the measured displacements were of the order of a nanometer, and these are much smaller than the effective thickness of the plates and their separation, which in turn are of the order of micrometers. We neglect plate inertia because point impedance measurements on the organ of Corti suggest that the imaginary part of its impedance is negative at all functionally relevant frequencies [6]. We assume that the plates are isotropic and homogeneous, with equal flexural rigidity, D, and are without tension. The value of D for the RL in the IHC region can be readily derived from the impedance measurements of Scherer and Gummer [6]; it is 0.04 nN m and 0.1 nN m for the second and third cochlear turns, respectively. Also, it will be shown that the wavenumber for fluid motion is inversely proportional to D16, so that small differences in the true D-values will have negligible effect on the assessment of fluid motion. For the fluid we assume: (i) incompressible and viscous flow, (ii) zero shear force at both plates, (iii) the transverse velocities at the plates are equal and opposite, and (iv) wave propagation only in the positive x-direction; that is, in the direction of the inner sulcus. This latter assumption appears justified because the mechanical impedance in the opposite direction, laterally along the narrow subtectorial space, is expected to be larger than in the medial direction, which opens up into the relatively large inner sulcus. 2.2 Fluid displacement Extending the analysis of Hassan and Nagy [4] to the case of viscous fluids, one can readily show that for sinusoidal stimulation with radial frequency, m, the solution is a wave traveling in the x-direction with wavenumber, k, dependent on co. Since, for the frequencies of interest (< 3 kHz), the lower surface of the TM was found experimentally to vibrate approximately in-phase along its radial length, the wavelength must be long compared with the radial extent of the subtectorial space. Consequently, the plates can be assumed to vibrate such that the long-wave

19 condition, kd/2 « 1, is satisfied. Then, k and a> are related according to the following dispersion relation: f

2p

\ 1/6

KDd;

CD

where p is fluid density. Notice that k is independent of viscosity; that is, for the long-wave condition, viscosity has no effect on the wave-number. This equation was also obtained by Hassan and Nagy [4] for the non-viscous case. Moreover, one can readily show that the real part of the fluid displacements in the z- and x- directions, denoted by n and f, respectively, are given by the parametric equations of an ellipse: rj(x,z,t) = rjm — sin(A:x - cot) d

(2)

£,{x,z,t) = rjm — cos(A:x -cot) kd

(3)

where r/m is the amplitude of the transverse vibration at the plates (Fig. 1, upper), which was about 1 nm in our experiments [1], and phase is defined relative to TM displacement towards scala vestibuli, or equivalently to OHC elongation. Importantly, according to these equations, the trajectories are not affected by viscosity. These elliptical fluid-particle trajectories have major and minor axes in the x-and z-directions, respectively, of relative magnitudes: alr\m = 2/kd and b/rjm = 2zld. Notice that the magnitude of the major axis is independent of depth, whereas the minor axis increases linearly from a value of zero midway between the plates (Fig. 1, upper). Since kdll « 1, the relative value alnm represents amplification of fluid motion radially within the subtectorial space. The dependence of k on com (Equ. 1) means that for a given cochlear turn, this relative amplitude decreases by only 2 dB for each octave increase of stimulus frequency. Using the dispersion relation (Equ. 1) to evaluate k, we obtain for d = 4 urn, a relative radial displacement of 22 for 800 Hz, the characteristic frequency (CF) of the third-turn recording location, and 12 for 3 kHz, the CF of the second cochlear turn. Doubling the depth of the subtectorial space to d= 8 urn, decreases these values to 13 and 7, respectively. That is, for all frequencies up to CF, the fluid-particle displacement radially is at least an order of magnitude greater than the RL displacement transversally. 2.3 Stereocilia deflection To assess the functional relevance of the pulsating mode for mechanoelectrical transduction of IHC stereocilia, we must estimate the deflection of the stereocilium.

20

For the sake of insight, we base our analysis on the work of Billone and Raynor [3], who derived the viscous drag on a stereocilium for Couette fluid motion in the subtectorial space. The viscous drag produced by the velocity field is considered to be the adequate stimulus for deflection of the stereociha. In their analysis, the velocity field is derived from the relative radial motion between the TM and RL. This represents the classical stimulus mode for stereociha deflection [2]. In their model, the fluid velocity is purely radial, and has amplitude increasing linearly with distance, from zero at the RL to the relative value at the TM. In our analysis, the profile is generated by the anti-phasic motion of the TM and RL in the transversal direction. Since, as discussed above, this results in a radial fluid component that is much larger than the transversal component, we neglect the latter component. Thus, the present analysis differs from that of Billone and Raynor [3] only in the form of the velocity field: here, the velocity is independent of vertical position in the subtectorial space. For an infinite number of stereociha, extending in a row along the cochlea, the viscous drag per unit length on a stereocilium due to radial fluid velocity vx is given by [3]: Fx(z,t) = incfi (v x (z,0 - S(z,t))

(4)

where S(z,t) is the time derivative of the radial displacement of the stereocilium, p. is the dynamic viscosity coefficient and c is a constant depending on the ratio of stereociha radius to distance between the centers of adjacent stereociha; for IHC stereociha c ~ 4. This Stokes-like equation, for which the force acting on a body is proportional to the relative fluid velocity impinging on the body, was originally derived by Miyagi [7] for the case of rigid circular cylinders. An infinite longitudinal row of stereociha is considered to be an adequate approximation for estimating viscous drag because there are a large number of stereociha per row on a hair cell and the cells are closely packed [3]. Stereociha displacement can be calculated by assuming that the stereocilium acts as an ideal, frictionless and massless, clamped cylindrical beam of uniform cross-section and modulus of elasticity [3], which experiences a viscous drag force given by Equ. (4). The beam assumption is justified because it has been shown theoretically that the deflection of a stereociha bundle in response to a point force applied to the longest stereocilium is independent of frequency up to about CF [8]. Then, assuming that deflections are small compared with the stereocilium length, (5(z,t) is given by solution of the standard beam equation, where the driving force is the viscous drag given by Equ. (4) and, in turn, the fluid velocity is derived from the radial pulsating fluid motion, with displacement amplitude,
21

*M0 = "?mKlsin o

ft

- (
N

<pr)

(5)

V 2 where \Sr\ and ^denote, respectively, the amplitude and the phase of the stereocilia tip displacement relative to radial fluid displacement: , (cosdL + cosh#L) e br = 1 -

\p)

1 + cos #L cosh 9L where the argument of the trigonometric and hyperbolic functions is 9L = j 1 / 4 mL

(7)

with N

l/4

(8) where L and Z>j are, respectively, the length and flexural rigidity of a stereocilium. We are now in a position to specify the phase of IHC stereocilia displacement relative to OHC electromotility and, therefore, to predict the phase of the IHC receptor potential relative to that of the OHC. Remembering that phase is defined relative to TM displacement toward scala vestibuli, that is relative to r\ at the TM, the phase of the IHC stereocilia tip displacement towards the shorter stereocilia is (Equ. 5): "tip =-n/2

~
(9)

At low frequencies, Sr ~ -j(wL)4/8, meaning that <pr tends to -nil. Conversely, at high frequencies, Sr ~ 1, meaning that (pr tends to zero. Therefore, at low frequencies, tip displacement of the IHC stereocilia towards the shorter stereocilia (Fig. 1, upper) is in phase with TM displacement towards scala vestibuli, whereas it lags it by 90° at high frequencies (Equ. 9). Since the experimental data showed that the TM and RL displacements at the OHC are approximately in phase [1], and hyperpolarization of the OHC causes somatic elongation, the asymptotic phase conditions imply that this "pulsating" fluid mechanism induces an IHC receptor potential which is in phase with the OHC receptor potential at low frequencies, whereas the IHC receptor potential lags the OHC receptor potential by 90° at high frequencies. Clearly, the frequency region of the transition from low to high frequencies depends on the parameters of the fluid space and the stereocilia.

22

The parameter values required by Equs. (7) and (8) are available in the literature. First, we take Sitc/u = 0.1 Ns/m2 [3]. The parameter Ds can be obtained from the stiffness measurements of guinea-pig stereocilia by Strelioff and Flock [9]. Since m depends on Ds' (Equ. 8), the values of Ds for the first, second and third turns can be treated as being approximately equal; therefore, we set Ds equal to their mean value of 9 x 10"21 Nm2.

Amplitude^-'"''""""

CD

S

0

"5. -6 £

/ /

^.-

/' /

Phase

-

-50 a

<

1 Frequency (kHz)

10

Figure 1. Electromechanical action of the OHCs causing counter-phasic motion of the RL and TM at the IHC. Upper: Elliptical fluid-particle trajectories. The numerals 1^4 track the phases of the trajectories. The radial amplitude is at least an order of magnitude greater than the transverse amplitude, indicative of a "pulsating" fluid mode. The cartoon is not scaled: measured r\m~\ nm, whereas the width of the subtectorial space is 4-8 (im. The three grey vertical rectangles depict the IHC stereocilia. Lower: Amplitude and phase of the tip displacement of an IHC stereocilium in response to viscous drag produced by radial fluid motion, where the fluid velocity is independent of depth within the subtectorial space. Responses are relative to radial fluid displacement. Parameters are: Sncfi = 0.1 Ns/m2 [3], Ds = 9 x 10"21 Nm2 (derived from [9])), L = 4 um. Notice that tip displacement amplitude is greater than fluid displacement amplitude for stimulus frequencies above 587 Hz; this situation extends up to 43.9 kHz (not illustrated).

Figure 1 (lower) shows the amplitude and phase of the displacement of the stererocilia tip relative to radial fluid displacement for a stereocilium of length, L = 4 um. This length spans almost the entire depth of the subtectorial space in the basal turn, and about half of the depth in the third turn. The most salient feature is that for the entire depicted frequency range (100 Hz - 10 kHz), the stereocilia tip displacement is within an order of magnitude of the radial fluid displacement, and in fact above 578 Hz it is slightly greater than it (up to 3.6 dB). The second important feature is that the phase of the tip displacement of the IHC stereocilia relative to radial fluid displacement monotonically increases over the entire frequency range relevant for the pulsatile fluid motion; the phase difference amounts to almost 90° (80°) at 3 kHz (Fig. 1, lower). Expressed relative to TM displacement towards scala vestibuli (Equ. 9), this means that tip displacement towards the shorter IHC stereocilia is in phase at low frequencies and lags by 90° at high frequencies. The transition frequency, where the phase difference is 45°, is at 675 Hz for these parameters. Expressed in detector terminology, the IHC stereocilia act as fluid velocity detectors below about 1 kHz and fluid displacement detectors above this frequency. This transition and the

23

frequency at which it occurs is similar to that usually concluded from intracellular IHC recordings when considering the shearing mode of RL and TM motion. Conclusion In summary, by exposing and untangling electrically induced vibration responses at the two surfaces bounding the subtectorial space, we have discovered a new functionally relevant deflection mode for IHC stereocilia. This mode allows direct mechanical coupling of OHC electromechanical transduction to IHC mechanoelectrical transduction. Acknowledgments Supported by the Deutsche Forschungsgemeinschaft, Gu 194/5-1. References 1. Nowotny, ML, Gummer, A.W., 2006. What do the OHCs move with their electromotility? In: Nuttall, A.L., (Ed.) Auditory Mechanisms: Process and Models, Portland (U.S.A.) World Scientific, Singapore, p. 101-102. 2. Davis, H., 1965. A model for transducer action in the cochlea. Spring Harb. Symp. Quant. Biol. 30, 180-190. 3. Billone, M., Raynor, S., 1973. Transmission of radial shear forces to cochlear hair cells. J. Acoust. Soc. Am. 54, 1143-1156. 4. Hassan, W., Nagy, P.B., 1997. On the low-frequency oscillation of a fluid layer between two elastic plates. J. Acoust. Soc. Am. 102, 3343-3348. 5. Freeman, D.M., Weiss, T.F., 1990. Hydrodynamic analysis of a twodimensional model for micromechanical resonance of free-standing hair bundles. Hear. Res. 48, 37-67. 6. Scherer, M.P., Gummer, A.W., 2004. Impedance analysis of the organ of Corti with magnetically actuated probes. Biophys. J. 87, 1378-1391. 7. Miyagi, T., 1958. Viscous flow at low Reynolds numbers past an infinite row of equal circular cylinders. J. Phys. Soc. Jpn. 13, 493-496. 8. Zetes, D.E., Steele, C.R., 1997. Fluid-structure interaction of the stereocilia bundle in relation to mechanotransduction. J. Acoust. Soc. Am. 101, 35933601. 9. Strelioff, D., Flock, A., 1984. Stiffness of sensory-cell hair bundles in the isolated guinea pig cochlea. Hear. Res. 15, 19-28. Comments and Discussion Santos-Sacchi: On the relationship between the expected fluid gain and the height of the stereocilia within the subtectorial space: if the cilia do not reside within the central space they may not experience the full gain. Could cilia of different heights

24

within the rows experience different forces, since the fluid motion falls precipitously towards the tectorial and reticular lamina boundaries. How might the gain change with frequency location - anatomical differences lead to gain differences? Answer: The gain will, of course, depend on the ratio of the stereocilia length, L, to the depth, d, of the subtectorial space. In the formulation of this model, for a given frequency and wave number (which in itself depends on d), the total force transmitted to a stereocilium is directly proportional to the ratio L/d. That is, "full gain" would be achieved by having the stereocilium span the depth of the subtectorial space. Clearly, according to this model, a shorter stereocilium in a bundle would experience less total force than the longest stereocilium. However, this is an additional degree of complexity, which is not considered in the present form of the model. Yes, as explained at the end of paragraph 2.2, the gain changes with frequency location due to anatomical differences along the cochlea. For example, the gain increases as depth decreases from apex to base of the cochlea. Grosh: Do you have an explanation for the resonance-antiresonance behaviour at high frequencies in the basal turn? Answer: The most parsimonious explanation derives from the experimental observation that this behaviour is not present in the absence of the TM, the response being predominantly low-pass. Thus, we propose that the anti-resonance in the transversal direction is due to a resonance in the radial motion of the TM. Referring to Zwislocki's book, anti-resonance between two resonant peaks is a hallmark of two elastically coupled series resonators. Zwislocki has proposed a cochlear model in which one resonator consists of the inertially loaded viscoelastic basilar membrane (BM), the other is the radially moved mass of the TM viscoelastically coupled to the spiral limbus, and the elastic coupling between the two resonators derives from the bending compliance of the OHC stereocilia. According to this model, the first resonance is due primarily to the BM impedance, whereas the antiresonance is due to the parallel resonance formed by the TM mass and OHC stereocilia compliance. That anti-resonance was not observed in the other cochlear turns, is possibly related to the observation that damping appears to increase with distance from the base of the cochlea. A resonant peak following the anti-resonance was not always readily discernable in our data, but theoretically its amplitude is critically dependent on damping, which is likely to be larger in the post-mortem cochlea. Chan: You described electrically evoked motion of OHC soma that generated antiphase motion of the RL and TM near the IHCs at low frequencies and in-phase motion at high frequencies. If OHC soma movement as part of the feedback loop associated with the cochlear amplifier exhibited a similar phase transition in vivo, what, then, would be the consequences on inner-hair-cell hair-bundle response phase due to this transition?

25 Answer: The situation is perhaps easier to predict for the basal turn, where there is obviously a clear transition. More apical locations are more complicated to discuss because the upper frequency limit of the anti-phasic motion (3 kHz) extends into or even surpasses the in-vivo CF region. For the basal turn, the experimental data suggest that the anti-phasic motion will only be significant on the low-frequency tail of the cochlear responses, that is, outside the region of cochlear amplification. As mentioned in the text, the modeling has suggested that the IHC receptor potential induced by the anti-phasic motion is asymptotically in phase with the OHC receptor potential below some transition frequency (below about 1 kHz), which is dependent on stereocilia length and depth of the subtectorial space, and lags it by about 90° at higher frequencies. This accords with in-vivo intracellular recordings (e.g. Cheatham and Dallos, J. Acoust. Soc. Am. 105, 799-810, 1999; Patuzzi and Yates, Hear. Res. 30, 83-98, 1987), which suggest that IHCs appear to be driven by partition velocity at low frequencies, but by displacement above some transition frequency (somewhere below 1 kHz). The measured vibration amplitudes are of the same order of magnitude as those for low-intensity acoustically induced BM motion in-vivo, as calibrated by the OHC ac receptor potential. That is, displacement of the IHC stereocilia induced by the anti-phasic motion is predicted to be significant if not larger than that from the shear component. Clearly, for frequencies well above about 3 kHz, where experimentally there was no phase difference between the transversal motions of the TM and RL at the IHC, the IHC stereocilia are expected to be stimulated by the shearing mode alone. Chan: What is your explanation for the in-phase motion of tectorial membrane (TM) and reticular lamina (RL) at the inner hair cell (IHC) for high-frequency stimulation in the basal cochlear turn? Answer: I can imagine two possibilities. First, as frequency increases the impedances of the RL and TM tend to that of the fluid, so that the system of RL, TM and fluid acts as a highly coupled composite structure moving in unison. To this end, the real and imaginary parts of the RL impedance have been shown experimentally to decrease with increasing frequency (Scherer and Gummer, Biophys. J. 87, 1378-1391, 2004). Second, it is expected that the pulsating mode will vanish for excessive slip at the TM and RL, as found experimentally by Lloyd and Redwood (Acustica 16, 224-232, 1965) for the case of a narrow fluid layer between elastic plates. This interpretation concurs, of course, with the customary notion that TM and RL move in-phase in the transverse direction because of viscous coupling between their surfaces.

ATOMIC FORCE MICROSCOPIC IMAGING OF THE INTRACELLULAR MEMBRANE SURFACE OF PRESTIN-EXPRESSING CHINESE HAMSTER OVARY CELLS H. WADA, M. MURAKOSHI, K. IIDA, S. KUMANO, T. GOMI, K. KIMURA AND H. USTJKURA Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai 980-8579, Japan E-mail: wada(a),cc.mech.tohoku.ac.ip M. SUGAWARA Department

of Mechanical and Environmental Informatics, Tokyo Institute of 2-12-1 Ookayama, Tokyo 152-8552, Japan

Technology,

S. KAKEHATA Department

ofOtorhinolaryngology, Hirosaki University School of Medicine, 5 Zaifu-cho, Hirosaki 036-8562, Japan

Department

of Otorhinolaryngology, Juntendo University School of Medicine, 3-1-3 Hongo, Tokyo 113-8431, Japan

K. IKEDA

Y. KATORI AND T. KOBAYASHI Department of Otorhinolaryngology - Head and Neck Surgery, Tohoku Graduate School of Medicine, 1-1 Seiryo-machi, Sendai 980-8675,

University Japan

The high sensitivity of human hearing is believed to be achieved by cochlear amplification. The basis of this amplification is thought to be the motility of mammalian outer hair cells (OHCs), i.e., OHCs elongate and contract in response to acoustical stimulation. This motility is made possible by both the cytoskeleton beneath the OHC plasma membrane and the motor protein prestin distributed throughout the plasma membrane. However, these factors have not yet been fully clarified. In the present study, therefore, attempts were made to observe the ultrastructure of the cytoskeleton of guinea pig OHCs and to identify the motor protein prestin expressed in the plasma membrane of Chinese hamster ovary (CHO) cells by atomic force microscopy (AFM). Results indicate that the OHC cytoskeleton is comprised of circumferential actin filaments and spectrin cross-links and that particle-like structures with a diameter of 8-12 nm which exist in the plasma membrane of the prestin-expressing CHO cells are most likely be prestin.

1 Introduction The mammalian ear is characterized by its high sensitivity and sharp frequency selectivity, which is believed to be based on the amplification of basilar membrane vibration in the cochlea. This cochlear amplification is actuated by the motility of outer hair cells (OHCs), i.e., the OHCs are thought to respond to acoustical stimulation with elongation and contraction of their cylindrical soma in vivo [1]. Such responses presumably subject the basilar membrane to force, resulting in

26

27

amplification of its vibration. This motility is thought to be realized due to the characteristic structure of the lateral wall of the OHC. The lateral wall of the OHC consists of three layers: the outermost plasma membrane, the cortical lattice and the innermost subsurface cisternae. In the plasma membrane, there is a protein motor called prestin which possibly changes its conformation according to the membrane potential. As a result of this conformational change, area change in the plasma membrane occurs [2]. The cortical lattice beneath the plasma membrane, which consists of actin and spectrin filaments [3], is thought to convert such change of the plasma membrane to change in the axial direction of the OHC. However, although the mechanism of this motility is related to the motor protein prestin and the cytoskeleton of the OHC lateral wall, these factors are not yet fully understood. In this study, therefore, first, the ultrastructure of the cytoskeleton of the OHC was investigated in the nanoscale range using an atomic force microscope (AFM), which is a powerful tool for studying biological materials [4-7]. Then, in an attempt to visualize the membrane protein prestin, the plasma membranes of prestinexpressing Chinese hamster ovary (CHO) cells and those of untransfected CHO cells were observed by AFM. 2 Materials and methods 2.1 Imaging of the cytoskeleton ofOHCs Temporal bones were removed from guinea pigs weighing between 200 and 300 g. After opening the bulla, the cochlea was detached and transferred to an experimental bath (140 mM NaCl, 5 mM KC1, 1.5 mM CaCl2, 1.5 mM MgCl2-6H20, 5 mM HEPES, 5 mM glucose; pH 7.2; 300 mOsm). The bony shell covering the cochlea was removed and the organ of Corti was gently dissociated from the basilar membrane. The OHCs were isolated by gently pipetting the organ of Corti after enzymatic incubation with dispase (500 PU/ml). The isolated OHCs were transferred to a sample chamber and glued to MAS-coated glass slides. The isolated OHCs were fixed with 2.5% glutaraldehyde and simultaneously extracted with 2.5% Triton X-100 in phosphate buffer (pH 7.4) for 30 min at room temperature. After fixation, the OHCs were rinsed three times with 0.1 M phosphate buffer solution. The care and use of animals in this study were approved by the Institutional Animal Care and Use Committee of Tohoku University, Sendai, Japan. 2.2 Imaging of the intracellular membrane surface of CHO cells Prestin-expressing CHO cells and untransfected CHO cells were used. The prestinexpressing CHO cells were constructed by Iida et al. by transfection of gerbil prestin cDNA into CHO cells using a mammalian expression vector containing the humanized Renilla reniformis green fluorescent protein [8]. They were cultured in

28

RPMI-1640 medium with 10% fetal bovine serum, 100 U penicillin/ml and 100 ug streptomycin/ml at 37°C with 5% C0 2 . After the cells were transferred from a flask into a tube and centrifuged at 250 x g for 5 min, the supernatant was removed and an external solution (140 mM KC1, 3.5 mM MgCl2, 5 mM EGTA, 5 mM HEPES and 0.1 mM CaCl2; pH 7.3) was put into the tube. The external solution containing the cells was diposited on glass-bottomed dishes or plastic dishes. After about ten minutes, these cells were sheared open by exposure to ultrasonic waves for a few 100 ms in a hypotonic buffer (10 mM PIPES, 10 mM MgCl2, 0.5 mM EGTA; pH 7.2) using a sonicator (XL-2000, MISONIX). The membranes attached to the substrate were then incubated with a high salt buffer (2 M NaCl, 2.7 mM KC1, 1.5 mM KH 2 P0 4 , 1 mM Na 2 HP0 4 ; pH 7.2) and 0.05% trypsin to remove the cytoskeletal materials and the peripheral membrane proteins. 2.3 Atomic force microscopy AFM system (NVB100, OLYMPUS) used for the experiments consists of a cantilever, laser, mirror, photodiode array, feedback system and piezoscanner. A Vshaped silicon nitride cantilever (OMCL-TR400PSA-2, Olympus) with a spring constant of 0.08 N/m was used for imaging the cytoskeleton of the OHCs and that with a spring constant of 0.02 N/m was used for imaging the intracelluler membrane surface of the CHO cells. The typical radius of curvature of the cantilever tip was 16 nm. Reducing sample damage during scanning, images were obtained using the oscillation mode (Tapping mode™, Digital Instruments). 3 Results 3.1 Cytoskeleton of OHCs The cytoskeleton of the lateral wall of the fixed OHC, which was extracted with Triton X-100, was imaged with the tapping mode of AFM. Figure 1A depicts a measured rectangular region. Figure IB shows an AFM image of the cortical cytoskeleton obtained in that region. In AFM images, the brighter areas correspond to the higher regions of the sample surface, and the transverse direction in the AFM images corresponds to the axial direction of the OHC. A schematic of the domains and filaments shown in Fig. IB is displayed in Fig. 1C. In this image, differently oriented domains are recognized. Within each domain, relatively thick circumferential filaments run parallel to each other and are cross-linked regularly or irregularly by thinner filaments. Such lattices were observed along the full length of the OHC lateral wall. A schema of the OHC cortical lattice is shown in Fig. ID. The mean spacings ± S.D. of circumferential filaments were 51.5 ± 9.78 nm (« = 550) and 47.0 ± 10.2 nm (n = 352) in the middle and basal regions and in the apical region of the OHC, respectively. The difference between the mean spacing in the middle and basal regions and that in the apical region was statistically significant at P < 0.0001 using Student's /-test. By contrast, the difference between the mean

29 A

0.0

27.5

55.0 nm

Figure 1. An AFM image of the cytoskeleton in the OHC lateral wall. The OHC was fixed by 2.5% glutaraldehydc and demembraned with 2.5% Triton X-100. A: Position of the scanning area. B: AFM image. C: Schema of the domains and filaments in B. In this figure, the schematic only shows clearly recognized areas. Boundary domains, circumferential filaments and cross-links are shown by dotted lines, thick solid lines and thin solid lines, respectively. D: Schema of the OHC cortical lattice. The cortical lattice is formed by some differently oriented domains. Within each domain, thicker circumferential filaments are cross-linked by thinner filaments.

spacing of cross-links in the middle and basal regions and that in the apical region was not statistically different. The mean spacing ± S.D. of cross-links was 25.2 ± 7.23 nm (« = 300) along the full length of the OHC lateral wall. 3.2 Intracellular membrane surface of prestin-expressing CHO cells and untransfected CHO cells The cytoplasmic surfaces of the isolated plasma membranes of the the prestinexpressing CHO cells and those of the untransfected CHO cells were observed by the tapping mode of AFM. Figure 2 represents their original flattened AFM images and the calculated differential AFM images. As indicated by arrows, particle-like structures were recognized in the plasma membranes of both cells; however, no distinctive difference in such particle-like structures was found between the prestinexpressing CHO cells and the untransfected CHO cells. The shape and size of the observed structures in five AFM images of the prestin-expressing CHO cells and five such images of the untransfected CHO cells were then analyzed. Frequency distribution of the observed particle-like structures, i.e., the density of the particlelike structures plotted against the interval of 2-nm classes in the diameter, is shown in Fig. 3. The diameters of the particle-like structures of the prestin-expressing CHO

30 cells ranged from 6 to 40 nm, and those of the untransfected CHO cells ranged from 6 to 30 nm. When the sizes of the particle-like structures in the plasma membranes were 8-10 nm and 10-12 nm, the differences of their densities between the prcstinexpressing CHO cells and the untransfected CHO cells were statistically significant for P < 0.05 using Student's /-test, as indicated by asterisks.

20.0 nm

10.0

Figure 2. AFM images of membranes of Ihe CHO cells. A1: Original flattened AFM image of the prestin-expressing CHO cell. A2: Differential AFM image of Al. Bl: Original flattened AFM image of the untransfected CHO cell. B2: Differential AFM image of Bl. Particle-like structures were recognized in the plasma membranes of the prestin-expressing CHO cells and the untransfected CHO cells, as indicated by arrows. However, no distinctive difference in such particlelike structures was found between these cells.

25 • Prestin-expressing CHO cell Q Untransfected CHO cell • P < 0.05

7 10 £

5-

III

jlillikl.hi

--

6 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 26283032 3436 3840 Diameter of particle-like structure (nm)

Figure 3. Frequency distribution of the observed particle-like structures in the plasma membrane. The density of the particle-like structure is plotted against the interval in 2-nm classes. Data were obtained from five AFM images of the prestinexpressing CHO cells and five such images of the untransfected CHO cells. When the sizes of the particle-like structures were 810 nm and 10-12 nm, differences of their densities between the prestin-expressing CHO cells and the untransfected CHO cells were statistically significant for P < 0.05 using Student's /-test, as shown by the asterisks. Error bars represent standard deviations.

31 4 Discussion 4.1 Structure ofOHC cortical lattice As shown by immunological evidence, the cortical lattice is composed of actin and spectrin [9]. This suggests that the circumferential filaments are actin filaments and that the cross-links are spectrin. This idea is supported by the fact that diamide treatment reduces the axial stiffness of the OHC in a dose-dependent manner [10], which makes the cell highly extendable in the axial direction [11]. As shown in Fig. ID, the cortical lattice is formed by differently oriented domains; such domains consist of parallel circumferential actin filaments and spectrin cross-links connected to adjacent actin filaments. In this study, pillars were not preserved, presumably due to the permeabilization of Triton X-100. 4.2 Particle-like structures in high-magnification AFM images of prestinexpressing CHO cells Since there are many kinds of membrane proteins in the plasma membrane of the CHO cells [12, 13], it is impossible to clarify whether the observed structures are prestin or not. Analysis of the shape and size of the observed structures was therefore performed for AFM images of both the prestin-expressing CHO cells and the untransfected CHO cells. As a result, a difference was found to exist between the densities of the particle-like structures in the plasma membranes of the prestinexpressing CHO cells and those of the untransfected CHO cells; that is, statistical analysis indicated a significant difference of the density of the particle-like structures with a diameter of 8-10 nm and 10-12 nm between the prestinexpressing CHO cells and the untransfected CHO cells for P < 0.05 using Student's /-test, as shown by asterisks in Fig. 3. These diameters were identical to those of the particles which were observed in the P-fracture face of the lateral membrane of the OHC by electron microscopy [14] and those of the particles which were observed in the cytoplasmic face of the lateral membrane of the OHC by atomic force microscopy [15]. Since the difference between the prestin-expressing and untransfected CHO cells is due to the existence of prestin, the difference of the densities of the particle-like structures between the prestin-expressing CHO cells and the untransfected CHO cells is considered to be caused by the presence or absence of prestin. These results suggest that the majority of these particle-like structures with a diameter of 8-12 nm in the prestin-expressing CHO plasma membrane are possibly prestin. Acknowledgments This work was supported by Grant-in-Aid for Scientific Research on Priority Areas 15086202 from the Ministry of Education, Culture, Sports, Science and Technology of Japan, by a Health and Labour Science Research Grant from the Ministry of

32

Health, Labour and Welfare of Japan and by a grant from the Human Frontier Science Program. References 1. Brownell, W. E., Bader, C. R., Bertrand, D., De Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 194196. 2. Adachi, M., Iwasa, K.H., 1999. Electrically driven motor in the outer hair cell: Effect of a mechanical constraint. Proc. Natl. Acad. Sci. USA 96, 7244-7249. 3. Holley, M.C., Ashmore, J.F., 1990. Spectrin, actin and the structure of the cortical lattice in mammalian cochlear outer hair cells. J. Cell Sci. 96, 283-291. 4. Sugawara, M., Ishida, Y., Wada, H., 2002. Local mechanical properties of guinea pig outer hair cells measured by atomic force microscopy. Hear. Res. 174,222-229. 5. Sugawara, M., Ishida, Y., Wada, H., 2004. Mechanical properties of sensory and supporting cells in the organ of Corti of the guinea pig cochlea - study by atomic force microscopy. Hear. Res. 192, 57-64. 6. Wada, H., Kimura, K., Gomi, T., Sugawara, M., Katori, Y., Kakehata, S., Ikeda, K., Kobayashi, T., 2004. Imaging of the cortical cytoskeleton of guinea pig outer hair cells using atomic force microscopy. Hear. Res. 187, 51-62. 7. Wada, H., Usukura, H., Sugawara, H., Katori, Y., Kakehata, S., Ikeda, K., Kobayashi, T., 2003. Relationship between the local stiffness of the outer hair cell along the cell axis and its ultrastructure observed by atomic force microscopy. Hear. Res. 177, 61-70. 8. Iida, K., Tsumoto, K., Ikeda, K., Kumagai, I., Kobayashi, T. and Wada, H., 2005. Construction of an expression system for the motor protein prestin in Chinese hamster ovary cells. Hear. Res. 205, 262-270.. 9. Flock, A., Flock, B., Ulfendahl, M., 1986. Mechanisms of movement in outer hair cells and a possible structural basis. Arch. Otorhinolaryngol. 243, 83-90. 10. Adachi, M., Iwasa, K.H., 1997. Effect of diamide on force generation and axial stiffness of the cochlear outer hair cell. Biophys. J. 73, 2809-2818. 11. Frolenkov, G.I., Atzori, M., Kalinec, F., Mammano, F., Kachar, B., 1998. The membrane-based mechanism of cell motility in cochlear outer hair cells. Mol. Biol. Cell 9, 1961-1968. 12. Yang, B., Brown, D., Verkman, A. S., 1996. The mercurial insensitive water channel (AQP-4) forms orthogonal arrays in stably transfected Chinese hamster ovary cells. J. Biol. Chem. 271, 4577-4580. 13. Van Hoek, A. N., Yang, B., Kirmiz, S., Brown, D., 1998. Freeze-fracture analysis of plasma membranes of CHO cells stably expressing aquaporins 1-5. J. Membrane Biol. 165, 243-254. 14. Forge, A., 1991. Structural features of the lateral walls in mammalian cochlear outer hair cells. Cell Tissue Res. 265, 473-483.

33

15. Le Grimellec, C , Giocondi, M. C , Lenoir, M., Vater, M., Sposito, G., Pujol, R., 2002. High-resolution three-dimensional imaging of the lateral plasma membrane of cochlear outer hair cells by atomic force microscopy. J. Comp. Neurol. 451,62-69.

ACTION OF FUROSEMIDE ON THE COCHLEA MODELED WITH NEGATIVE FEEDBACK SHYAM M. KHANNA Department of Otolaryngology, Head and Neck Surgery, College of Physicians and Surgeons of Columbia University, 630 W. 168,h street, New York NY 10032, USA E-mail: smk3(a),columbia. edu A number of unusual and reversible changes take place in the cochlear mechanics with the administration of the drug furosemide. The purpose of the present paper is to understand and model the effect of furosemide on the cochlear mechanical response.

1 Introduction Furosemide reduces endocochlear potential of experimental animals in a reversible and dose-related manner [9, 11]. Suppression of endocochlear potential in guinea pigs reaches a maximum within minutes of the intravenous administration of furosemide (40-80 mg/kg) and recovers over a period of 120 minutes [8]. A reduction of cochlear microphonic potential and compound action potential is also observed following diuretic administration [1]. The drug may also have a direct effect on hair cells. Cochlear microphonics in the basal turn of guinea pigs following furosemide injection (80 mg/kg) declined after 10-30 minutes reaching a minimum after 40-50 min. The time course of changes produced in the mechanical response in our experiments were similar. The stereociha of third row outer hair cells were disorganized [4]. Furosemide affected the morphology of the hair bundles most extensively in the basal turn. The cross links between the individual cilia swelled, stretched and broken [3]. In interpreting the action of furosemide on the micro mechanical response: 1. Lowered EP may reduce the OHC amplification. 2. Disorganization of the stereociha bundles lowers their stiffness. In the cochlea, the mechanics is stiffness dominated below CF. The reduction in stereociha stiffness should therefore produce an effect below CF. Reduction in stereociha stiffness would reduce the coupling between the stereociha and the reticular lamina. This would reduce the magnitude of nonlinear components originating at the stereociha and seen at reticular lamina below CF. 2 Methods Mechanical vibrations at selected cellular locations have been measured in the apical turn of the guinea pig cochlea before and after administration of furosemide

34

35

(150 mg/kg IV). In some experiments additional doses were given. Eleven guinea pigs were used [10]. The interferometric measurement technique used for measuring vibration has been described earlier [5,6]. The measurement sites were Hensen's cell (HC) at the level of the reticular lamina; Claudius' cell (CC) about 30 um lateral and 110 urn below the surface of the HC and basilar membrane (BM) about 20 um below the CC. Applied sound pressure level was about 94 dB. Velocity waveforms were measured with frequency incremented from 20 Hz to 3000 Hz in 32 steps. Tuning curves were determined repeatedly at HC, CC and BM before and after administration of the drug. The condition of the cochlea was accessed by QiodB of the tuning curve and by the magnitude of the harmonics present in the response [6]. 3 Results 3.1 Changes at HC after administration offurosemide

100

1000 Frequency (Hz)

Figure 1. Hensen's cell vibration amplitude, before (solid line) and after (dotted line) administration of furosemide. In most experiments reduction in velocity below CF (250 Hz) was observed. Ratio of the velocities after/before furosemide is shown with a dashed line. Velocity ratio is nearly unity between 200 and 1200 Hz, it decreases below 200 Hz and above 1200 Hz. The slope of the ratio curve at low frequencies is about 6dB/octave.

At the HC (Fig. 1) the vibration amplitude in the characteristic frequency (CF) region did not change appreciably before and after administration of the drug. This is in contrast to our earlier observations in which the amplitude decreased after sacrifice of the animal. The amplitude below CF decreased after administration of furosemide. The ratio of the HC response before and after furosemide decreases below 250 Hz. The slope of the decrease was about 6 dB/octave. This decrease was seen in most of the preparations. The magnitude of the change was dose related, loss increased when a second dose was given. This change was reversible, after about 30 min the curve started to recover.

36

c. d.

If the initial QiodB was high (2) it was seen to decrease to 1.4 in about 25 minutes after the administration of the drug. If the condition of the cochlea was good, a large number of harmonics were seen. After administration of furosemide their number and magnitude decreased below CF. The process was reversible after about 50 min the harmonic amplitude below CF increased to its initial value. The changes c & d are not illustrated in this paper.

3.2 Changes at the BM and CC after administration of furosemide 1000-

10" 10"M

t.

ia •10

a. E

10 • 1 1

<

=

10 •12 100

1000 Frequency (Hz)

Figure 2. CC vibration amplitude, before (solid line), and after (dotted line) administration of furosemide. Initially the frequency response was jagged. After furosemide the amplitude increased in the CF region (250 Hz) and the curve became much smoother. The increase was reversible with time. The ratio of the velocities after/before furosemide is plotted with a dashed line. The ratio is highest near 300 Hz. It decreases below CF reaching a minimum at 60 Hz. The ratio also decreases above CF.

Changes in response to furosemide were seen at the BM and CC only in cochleae with sharp tuning and strong nonlinear response. These changes were seen usually after the second or third dose, suggesting that a higher concentration of furosemide was needed to elicit this response. a.

b.

At the BM the initial tuning was flat, and the vibration amplitude was low. After the drug the BM amplitude increased and the tuning became sharper. This observation was similar to an earlier one in which the animal was sacrificed [7]. The main difference was that the increase in amplitude with furosemide was smaller. At the CC (Fig. 2), the frequency response was jagged before the administration of furosemide. After, the response increased in magnitude and became smooth. The increase in amplitude after furosemide was smaller compared to earlier experiments [7]. The response at frequencies below 100 Hz decreased sharply.

37 Summed velocity 1 l + JQ,U

o Fluid velocity

1 \+JQAU BM

-+o

T

Hensen F(/t)

U-

J_

p(i+je P c/)

Figure 3. Negative feedback amplifier model used to explain the observed changes. The model was described in detail earlier [7], The effect of stereocilia stiffness change is represented with an added transfer function F(k) in the feedback path. When the stiffness is high the function is given by F(k) and when it is low it is given by G(k). They are plotted in Fig. 4.

4 Modeling the Response The response is modeled with a negative feedback amplifier, which was used to explain the changes observed in the guinea pig cochlear mechanical response after sacrifice [7]. The changes in tuning seen at the BM and CC after furosemide are similar but smaller than those observed earlier after sacrifice. It is assumed that change in hair cell amplification is the basis for these changes. A smaller change in amplification produced by furosemide would explain the difference in the change. HC response amplitude however does not change with furosemide. A smaller change in amplification would also reduce the change in HC response. Lack of this change however requires an additional effect. The decrease in low frequency response is unique to furosemide experiment and requires an addition to the model described earlier. It is suggested that decrease in stereocilia stiffness would result in an increase in negative feedback thereby lowering the response below CF. Therefore B in the original feedback model is replaced with a function F(k). When the stereocilia stiffness is normal the magnitude of F(k) is nearly 0.05 (in the previous model B = 0.05). However when the stiffness is low the function changes to G(k). Functions F(k) and G(k) are shown in Fig. 4. This decreases feedback above CF while increasing it at low frequencies. The response is increased slightly above CF and decreased progressively below CF. This raises the HC response so that it would appear unchanged.

38

-SK

0.3

Figure 4. Feedback functions F(k), and G(k) are shown as a function of normalized frequency (k = f/fmax)- Dotted line shows the function F(k). The solid line shows the function G(k). 0.1

0.1

1 k

10

The changes in response calculated with the model (Fig. 3) are compared with the experimental observations in Fig. 5. The ratio after / before furosemide is compared for the HC with similar ratio calculated for the model. The agreement is good. The ratio for the CC contains many peaks and valleys because the tuning curve before furosemide was jagged. It is compared with the calculated ratio. The model curve fits the experimental curve well in the CF region and up to 0.3k. 5 Discussion A negative feedback amplifier model of the apical turn of the cochlea was originally developed to explain changes in cochlear mechanics after the sacrifice of the animal. This model was applied to changes seen after infusion of furosemide. The fit of the model to the changes at the BM or CC was best when the minimum value of the amplification was between 60 - 100. This suggests that furosemide reduces the hair cell amplification only by a factor of 10. To take into account the unique change associated with furosemide - loss in low frequency response. The original model had to be modified by adding a function in the feedback path. This function increased the feedback at low frequencies. It is remarkable that one model can be used to fit results from two very different experiments.

39

Figure 5. The changes seen experimentally, before and after furosemide, at the HC and CC, are compared with the model calculations. Solid line with triangles shows ratio of HC vibration amplitude after/before furosemide. Dashed line shows the ratio obtained by model calculations. Best fit is obtained under the assumption that furosemide reduced the amplification from 600 to 100 and the tuning sharpness QiodB from 2.0 to 1.4. Ratio of the CC vibration amplitude after / before furosemide is shown by circles. Ratio obtained by model calculations is shown by dashed - dotted line. The curve shown was calculated under the assumption that furosemide reduced the amplification from 600 to 65 and the tuning sharpness QiodB from 2.0 to 0.9. Administration of furosemide produces changes in amplification and QiodB, which increase with time, and then slowly and reversibly decrease with time. The measurements at the HC and CC were made at different times. Therefore the need for slightly different values of amplification and QiodB is quite reasonable.

Acknowledgments Thanks to Elizabeth Olson, Ombeline de La Rochefoucauld, Wei Dong for suggestions and help with preparation of manuscript. References Brown, R. D., 1981. Comparisons of the acute effects of Furosemide and bumetanide on the cochlear action potential (Nl) and on the a.c. cochlear potential (CM) at 6 kHz in cats dogs and guinea pigs. In: Klinke, R. et. al. (Eds), Ototoxic Side Effects of Diuretics. Scandinavian Audiology Supplement 14,71-83. Chodynicki, S., Kostrzewska, A., 1974. Effects of furosemide and ethacrynic acid on endolymph potential in guinea pigs. Otolaryngol. Pol. 28, 5-8. Comis, S.D., Osborne, M.P., Jeffries, D. Jr., 1990. The effect of furosemide upon the morphology of hair bundles in the guinea pig cochlear hair cells. Acta Otolarngol (Stockh) 109,49-56. 4. Forge, A., Brown, A.M., 1982. Ultra-structural and electrophysiological studies of acute ototoxic effect of furosemide. Br. J. Audiol. 16, 109-116.

40

5. Khanna, S.M., Hao L.F., 1999 a. Reticular lamina vibrations in the apical turn of a living guinea pig cochlea. Hear. Res. 132, 15-33. 6. Khanna, S.M., Hao L.F., 1999 b. Nonlinearity in the apical turn of living guinea pig cochlea. Hear. Res. 135, 89-104. 7. Khanna, S.M., 2004. The response of the apical turn of cochlea modeled with a tuned amplifier with negative feedback. Hear. Res. 194, 97-108. 8. Pike, D., Bosher, S.K., 1980. The time course of the strial changes produced by intravenous furosemide. Hear. Res. 3, 79-89. 9. Rybak, L.P., Whitworth, C , Scott, V., Weberg, A., 1991. Ototoxicity of furosemide during development. Laryngoscope. 101(11):1167-74. 10. Scanlon, M.W., Ha-Won, J., Khanna, S.M., 1999. Changes in the vibratory response of the cochlea in the living guinea pig following furosemide application. A.R.O. Midwinter meeting. 11. Whitworth, C , Morris, C , Scott, V., Rybak, L.P., 1993. Dose-response relationships for furosemide ototoxicity in rat. Hear. Res. 71, 202-207.

MODULATION OF COCHLEAR MECHANICS: MODEL PREDICTIONS AND EXPERIMENTAL FINDINGS OF THE EFFECT OF CHANGING PERILYMPH OSMOLARITY

J. S. OGHALAI, C.-H. CHOI Bobby R. Alford Department of Otorhinolaryngology and Communicative Baylor College of Medicine, Houston, Texas 77030, USA E-mail:[email protected]

Sciences,

A. A. SPECTOR Department

of Biomedical Engineering, Johns Hopkins Baltimore, Maryland 21205, USA

University,

Outer hair cells (OHCs) have an intracellular turgor pressure, but maintain a cylindrical shape because of their elastic lateral wall cytoskeleton. In vitro, changing the osmolarity of the extracellular fluid produces changes in OHC morphology, compliance, and force production. We sought to determine the effects of changing perilymph osmolarity on cochlear function in vivo. After perfusing hypoosmotic perilymph (260 mOsm) through the guinea pig cochlea, compound action potential thresholds and distortion product otoacoustic emissions thresholds decreased. These effects reversed after washout with artificial perilymph of normal osmolarity (300mOsm). The opposite effects were seen when hyperosmotic perilymph (340 mOsm) was perfused. We then created a mathematical model of cochlear mechanics that included several of the unique nanoscale biophysical properties of the OHC, allowing us to simulate the effect of OHC turgor pressure on electromotility. The magnitude of the measured effects was consistent with the predictions of our mathematical model. These findings suggest that changing perilymph osmolarity modulates cochlear function by affecting OHC electromotility via changes in cell turgor pressure.

1 Introduction Electromotility originates within the lateral wall of the cylindrically shaped OHC, which contains a highly organized actin-spectin subplasmalemmal cytoskeletal network tethered to the plasma membrane. Unlike all other animal cells, the OHC maintains a turgor pressure. In order to express electromotility, turgor is required to couple the forces produced by each motor complex. Hypoosmotic perfusion causes cells to increase their intracellular volume, and thus their turgor. The orthotropic cytoskeleton of the OHC directs the resultant morphologic changes so that the cell shortens and fattens as its turgor pressure increases. Changing the turgor pressure has major consequences on OHC biomechanical properties and modulates electromotility [1-4]. Hypoosmotic perfusion reduces OHC compliance and membrane lateral diffusion, but increases electromotile force production. Conversely, hyperosmotic perfusion reduces OHC turgor pressure and decreases electromotility. Herein, we describe our findings during in vivo perfusion

41

42

of the guinea pig cochlea with hypoosmotic and hyperosmotic perilymph and correlate the data with a mathematical cochlear model using data from osmotic experiments with isolated OHCs. 2 Methods 2.1 Experimental procedures The Institutional Animal Care and Use Committee at the Baylor College of Medicine approved the study protocol. Our technique of cochlear perfusion has been previously described [5,6]. We measured compound action potential (CAP) and distortion product otoacoustic emission (DPOAE) thresholds by identifying the stimulus intensity required for the response to rise 3 SD above the noise floor. We also measured the cochlear microphonic (CM) quadratic distortion product. The hypoosmotic perilymph (260 mOsm) was composed of, in mM: 130 NaCl, 4 KC1, 1 MgC12, 2 CaC12, and 6 HEPES, at a pH of 7.3. Normoosmotic (300 mM) and hyperosmotic (340 mM) perilymph solutions were created by adding 40 mM or 80 mM of glucose to hypoosmotic perilymph, respectively. The osmolarity of each solution was checked using a freezing pressure osmometer. 2.2 Mathematical model of cochlear mechanics We used a one-dimensional long-wave transmission line approach to model cochlear macromechanics. We modeled mechanical terms as electrical circuits, with voltage being pressure and current being velocity (Fig. 1). Thus, ZSv (x)= ZST (x) = R(x) + icoM(x)

(1)

with the fluid mass at a single segment being M(x) = 2pSI Ac(x), where p is the fluid density, 8 is the number of the cochlear segments divided by the length of the cochlea, and AC is the average cross-sectional area of scala vestibuli (SV) and scala tympani (ST). The damping parameter R was fit to experimental data. The cochlear impedance at the helicotrema (x=n) was Z{n) = Zsv (n) + Zsr(n). Cochlear micromechanics, or the net impedance of one section of the cochlear partition, was modeled using three degrees of freedom. The impedances of the basilar membrane (BM), tectorial membrane (TM), and stereocilia were Zbm(x)

= Kbm(x)

IICO + Rbm(x)

+ iO)Mbm{x)

Ztm{x) = Klm{x)liCD + Rm{x) + iG)Mtm{x) Z,{X) = K,(X)H
(2)

(3) (4)

where K, R, and M are the effective stiffness, damping, and mass, respectively. At a single node, hm = Im + Is , and the velocity of the stereocilia is the difference between the velocity of the BM and the velocity of the TM. Thus,

43

*>ia»*.* -

> *'

*6>4

Figure 1. Electrical circuit model of cochlear mechanics. (A) Macromechanics of the cochlear fluid spaces, (B) micromechanics of the cochlear partition, and (C) nanomechanics of OHC electromotility. -=

Zbm+Zm+(

(5)

v,+i r) 2J(Va+\) where Va is a voltage source representing the active force generated the OHC. We modeled cochlear nanomechanics, or OHC electromotility, as the sole force producing element in the cochlea. We included terms that reliably describe the biomechanics of a single OHC during the generation of electromotility, permitting us to include OHC turgor pressure as a parameter. We combined the data of three experiments: axial loading [1,2,7-9], osmotic challenge [10], and micropipette aspiration [11] to create a highly detailed and reliable orthotropic model of the lateral wall [12]. Thus,

h

—

dw

= - 2 f l K ( C u — — + C I2 ——) d

W

d

¥

(6)

C n = 0 . 2 5 C a + 0 . 2 8 r o , Ca =0.5022+1.08^, C22 =0.2 + 0.8x10^ lya

where y is the transmembrane potential and R is the cell radius. C l l and C12 are the longitudinal and mixed elastic moduli of the OHC orthotropic lateral wall, respectively. The longitudinal and circumferential components of the active strain are ex and e0, respectively, and ya is the stiffness of the whole cell. Additionally, we incorporated the effect of extracellular fluid osmolarity on OHC force production [1,2] to compute the coefficient of osmolarity (Cosm) in our model C„„=a,Oz+a20 + a, (7) where O is the osmolarity relative to 300 mOsm, and al, a2, and a3 are constants. We modeled transfer functions relating OHC receptor potential to stereocilia displacement (Tme) and OHC electromotile length change to receptor potential (Tem) as simple low-pass filters. r « = Mme /(l + ia>zme) , Tem = Mtm /(l + imj)

(8)

44

where M is the magnitude of the transfer function and ime and Tern are experimentally measured time constants [13,14]. We then included the density of OHCs to calculate the total active force per cochlear segment. #OHCs v -^-c )(T d\ff

# segment

""

^ '

Table - Modeling Parameters

Parameter Kbm Ktm Ks Mbm Mtm Rbm Rtm Rs Mme Mem Tme Tem Cll C12 al a2 a3

Base 7.50x108 6.25x105 1.00x105 6.05x10-4 3.70x10-7 3.00x101 1.50x101 9.00x10-1 1.42x105 1.00x10-1 1.40x10-4 1.70x10-5 9.58x10-2 1.61x10-1 1.66x10-4 8.83x10-2 -10.5

Middle 6.50x106 4.25x105 3.00x104 7.05x10-4 6.70x10-7 3.00x100 3.50x101 4.90x101 1.05x104 1.00x10-1 6.92x10-4 5.50x10-5 9.58x10-2 1.61x10-1 1.66x10-4 8.83x10-2 -10.5

Apex 7.25x104 6.30x104 1.00x104 8.05x10-4 8.70x10-7 5.00x10-1 3.00x101 1.70x101 3.68x102 1.00x10-1 5.29x10-3 3.75x10-4 9.58x10-2 1.61x10-1 1.66x10-4 8.83x10-2 -10.5

Units dyn/cm3 dyn/cm3 dyn/cm3 g/cm2 g/cm2 dyn*s/cm3 dyn*s/cm3 dyn*s/cm3 mV/nm nm/mV s s N/m N/m

3 Results We measured CAP and DPOAE responses prior to opening the cochleae, after perfusing with hypoosmotic perilymph, and then after washing out with normoosmotic perilymph. We found that hypoosmotic perilymph lowered CAP and DPOAE thresholds to better than normal values (Fig. 2A,C). Washout with normoosmotic perilymph normalized the thresholds. The converse effect was noted with hyperosmotic perilymphatic perfusion (Fig. 2B,D). In order to distinguish osmotic effects from ionic effects, we performed a series of experiments in which we opened the cochlea and performed an initial perfusion with normoosmotic perilymph prior to the osmotic challenge. Thus, ionic concentrations were identical during subsequent perfusions and only the glucose concentration varied. Statistically significant effects were found across the frequency range of guinea pig hearing. Hypoosmotic perilymph lowered and hyperosmotic perilymph raised CAP and DPOAE thresholds (Fig. 3).

45

Next, we measured the amplitude of the CM quadratic distortion product continuously to study the time course of the effects of perilymph osmolarity on cochlear function. A single perfusion of hypoosmotic or hyperosmotic perilymph was performed for 100 sec during which there was a drop in the CM. This artifact occurs due to the effect of the perfusion pressure and fluid in the middle ear space [14]. After perfusion the pipette was withdrawn, the pressure released, and fluid within the middle ear aspirated. Hyposmotic perilymph caused the CM difference tone to increase while hyperosmotic perilymph caused it to decrease (Fig. 4). These findings are in the same direction as we measured with the DPOAE cubic distortion product and consistent with an osmotic effect on the cochlear amplifier.

B

A • O —-^— — V -

r*

Before cocNooslomies After cochleostomies 260mOsm 300 mOsm washoul

r

— • — O — ^ —»?-

> 10

11

12

13

14

10

c

• O — ••-— V10

12

13

14

» Xx o

i-

11

D

r te^:-*-,. !"

Before cochleostomies After cochleostomies 340mOsm 300 mOsm washoul ___ V

Before cochleosfomies After coctileostomles 260mOsm 300 mOsm washoul

11

12

13

Frequency {kHz)

14

« 30

\ ^ - ^ • O —^ —V— 10

V

V

Before cacftrea$lomi«S O After cochleostomles,^ 340mOsm ^ * 300 mOsm washoul 11

12

13

14

Frequency (kHz)

Figure 2. Perilymph osmolarity modulates CAP and DPOAE thresholds. In one animal, CAP (A) and DPOAE (C) thresholds decreased with hypoosmotic perilymphatic perfusion and recovered with washout. In a different animal, the thresholds reversibly increased with hyperosmotic perilymphatic perfusion (B&D).

Frequency (kHz)

Figure 3. Mean changes in CAP (A) and DPOAE (B) thresholds measured after perfusion with hypoosmotic and hyperosmotic perilymph relative to 300 mOsm. Each data point is the average of measurements from five animals. The error bars represent the SEM.

Our mathematical model predicted a 4 dB increase in basilar membrane velocity with hypoosmotic perilymph and a 18 dB decrease in basilar membrane velocity with hyperosmotic perilymph (Fig. 5). The changes in basilar membrane velocity were concentrated at the characteristic frequency, as would be expected if the cochlear amplifier were predominantly affected. There was little change in the phase of basilar membrane velocity. These results are consistent with the shifts in CAP thresholds at the same resonant frequency (10-12 kHz).

46

4 Discussion Hyperosmotic perilymph inhibits and hypoosmotic perilymph potentiates cochlear function. These data support our hypothesis that perilymph osmolarity modulates the gain of the cochlear amplifier through changes in OHC electromotility. Importantly, these effects are qualitatively consistent with what would be expected based on experiments in isolated OHCs. By incorporating these data from isolated OHCs into our cochlear model, we found that our modeling and experimental results were quantitatively quite similar.

Figure 4. Example of the effect of perilymph osmolarity on the F2-F1 quadratic distortion product cochlear microphonic (CM). The CM within the shaded areas declines because of perfusion artifact and is meaningless. However, the CM immediately following the perfusion (arrows) demonstrates the change due to osmotic challenge. (A) Hypoosmotic perilymph increases the CM. (B) Hyperosmotic perilymph decreases the CM. Both normalize within 100-200 sec as the osmolarity normalizes.

•1'<^Vfl*flfVg

It is possible that other targets within the cochlea besides OHCs were affected by the osmotic manipulations. While nerve terminals can be affected by osmotic changes, modulation of the afferent nerve fibers should not change the cochlear non-linearities responsible for the generation of DPOAEs and the CM distortion product. Additionally, it would be extremely unlikely for changes in the efferent nerve fibers to cause such large changes in cochlear non-linearities and CAP thresholds.

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47

These experiments do not distinguish whether OHC turgor pressure modulates force production due to somatic electromotility associated with prestin or stereociliary force production by the mechanoelectrical transduction channels. Certainly, the biophysical properties of either these transmembrane proteins can be altered by the environment of the surrounding plasma membrane [15,16]. Indeed, the predominant effects of OHC turgor pressure may not be on either protein. Both somatic or stereociliary force production needs to impact either the reticular lamina or the tectorial membrane in order to amplify the deflection of the IHC stereocilia. Changing the turgor pressure of the OHC, and thus its stiffness, could modulate force transmission even if force production is unchanged. Acknowledgments This study was supported by the National Organization for Hearing Research Foundation and NIDCD grant DC05131 (J.S. Oghalai), American Academy of Audiology Foundation (C-H. Choi), and DC02775, DC00354 (A.A. Spector). References 1. Hallworth, R., 1995. Passive compliance and active force generation in the guinea pig outer hair cell. J. Neurophysiol. 74, 2319-28. 2. Hallworth, R., 1997. Modulation of outer hair cell compliance and force by agents that affect hearing. Hear. Res. 114, 204-12. 3. Crist, J.R., Fallon, M., Bobbin, R.P., 1993. Volume regulation in cochlear outer hair cells. Hear. Res. 69, 194-8. 4. Oghalai, J.S., Zhao, H.B., Kutz, J.W., Brownell, W.E., 2000. Voltage- and tension-dependent lipid mobility in the outer hair cell plasma membrane. Science 287, 658-61. 5. Oghalai, J.S., 2004. Chlorpromazine inhibits cochlear function in guinea pigs. Hear. Res. 198, 59-68. 6. Choi, C.-H., Spector, A.A., Oghalai, J.S., 2005. Perilymph Osmolarity Modulates Cochlear Function, Abstracts of the Midwinter Research Meeting of the Association for Research in Otolaryngology, New Orleans, LA. 7. Holley, M.C., Ashmore, J.F., 1988. A cytoskeletal spring in cochlear outer hair cells. Nature 335, 635-637. 8. Iwasa, K.H., Adachi, M., 1997. Force generation in the outer hair cell of the cochlea, Biophys. J., Vol. 73. pp. 546-555. 9. Kossl, M., Russell, I.J., 1995. Basilar membrane resonance in the cochlea of the mustached bat. Proc. Natl. Acad. Sci. U. S. A. 92, 276-9.

48

10. Ratnanather, J.T., Zhi, M., Brownell, W.E., Popel, A.S., 1996. The ratio of elastic moduli of cochlear outer hair cells derived from osmotic experiments. J. Acoust. Soc. Am. 99, 1025-8. 11. Sit, P.S., Spector, A.A., Lue, A.J., Popel, A.S., Brownell, W.E., 1997. Micropipette aspiration on the outer hair cell lateral wall. Biophys. J. 72, 28129. 12. Spector, A.A., 1999. Nonlinear electroelastic model for the composite outer hair cell wall. ORL. J. Otorhinolaryngol. Relat. Spec. 61, 287-93. 13. Denk, W., Webb, W.W., Hudspeth, A.J., 1989. Mechanical properties of sensory hair bundles are reflected in their Brownian motion measured with a laser differential interferometer. Proc. Natl. Acad. Sci. U. S. A. 86, 5371-5. 14. Gale, J.E., Ashmore, J.F., 1997. An intrinsic frequency limit to the cochlear amplifier. Nature 389, 63-6. 15. Hirono, M., Denis, C.S., Richardson, G.P., Gillespie, P.G., 2004. Hair cells require phosphatidylinositol 4,5-bisphosphate for mechanical transduction and adaptation. Neuron 44, 309-20. 16. Sukharev, S., Corey, D.P., 2004. Mechanosensitive channels: multiplicity of families and gating paradigms. Sci STKE 2004, re4.

Comments and Discussion Santos-Sacchi: Could chloride have a role in your model? Answer: Stretch-activated entry of chloride into the OHC may underlie the osmotic modulation of electromotility. Gummer: Which parameters in your simulation account for the difference in the effects of the hyper- and hypo-osmolar manipulations? Answer: We fit Rick Hallworth's data from his 1997 paper with a quadratic function, to create an osmolarity coefficient. This was multiplied times the electromotile force produced by an OHC in normosmotic extracellular medium.

MEASURING THE MATERIAL PROPERTIES OF NORMAL AND MUTANT TECTORIAL MEMBRANES K. MASAKI AND D.M. FREEMAN Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, USA E-mail: kinu @ mit. edu, freeman @ mit. edu

MA,

G. RICHARDSON School of Life Science, Univesity of Sussex, Falmer, Brighton, UK E-mail: g.p. richardson @ Sussex, ac. uk R.J.H. SMITH University of Iowa Hospitals and Clinics, Iowa City, IA E-mail: richard-smith @ uiowa. edu Mutations in Collla2 and Tecta cause a decrease in hearing sensitivity in both humans and mouse models. To determine if these mutations also cause changes in the material properties of the tectorial membrane (TM), equilibrium stress-strain relations of TMs from normals and mutants were measured by applying osmotic pressure using polyethylene glycol (PEG). Results were consistent with a TM model having two components: a compliant component in which compression is resisted by electrostatic repulsion of TM macromolecules, and a component that is not compressed by PEG. While the mutations caused some change in the fixed charge concentration of the compliant components (in mmol/L: —9.9 for normals, —8.7 for Collla2 — /—, and —5.4 for TeciaY 1870C/+) the fractional volume of compliant component showed even larger changes (58% for normals, 42% for ColUa2 - / - , and 11% for TectaY 1870C/+). The simplest interpretation of these results is that the TM normally acts as a composite material with two functionally-different regions. Mutations of the TM alter the relative proportions of these two regions and thereby alter TM mechanics.

1

Introduction

From mouse models of genetic disorders of hearing, we have learned that genetic manipulations of TM proteins can decrease hearing sensitivity [4,7]. However, the effect of these mutations at the mechanical level has not been thoroughly investigated. Presently, we are investigating Collla2 and Tecta mouse mutants. Collla2 is one of the genes which encodes type XI collagen, a quantitatively minor fibrillar component of the TM. Tecta encodes alpha-tectorin, one of the major glycoproteins of the non-collagenous, striated sheet matrix. Mutations in either of these genes have been shown to cause hearing loss. Collla2 —/— mouse mutants have a 4050 dB increase in auditory brainstem response threshold compared to wild-types [7]. TectaY1870C/+ mice have a 50-80 dB hearing loss [5]. To determine whether these mutations led to changes in the material properties of the TM, we measured TM volume changes in response to osmotic pressure applied with polyethylene glycol (PEG).

49

50 Interpreting these measurements in terms of a simple model provides insight into the molecular mechanisms that underlie these changes. 2 Methods Many of the methods used to measure the stress-strain relation of the TM are similar to those used in previous studies of the TM [1,10]. Briefly, the TM was placed on a glass slide, decorated with beads, and immersed in a bathing solution. Images of sections of the TM were recorded after the specimen was immersed in a given solution for at least one hour. Since bright-field images show that beads end up resting on the surface of the TM, bead position was used as a marker for the TM surface. Bead positions were tracked to estimate changes in the TM volume in solutions of different composition. 2.1

Solutions

All the solutions were variations of an artificial endolymph (AE) solution which contained in mmol/L: 2 NaCl, 3 dextrose, 0.02 CaCl2, 5 HEPES, and 174 KC1. This composition closely matches the measured ionic composition of endolymph in the mammalian cochlea [11]. The pH of the solution was adjusted to 7.3. PEG solutions were made by adding PEG to the same stock solution of AE to ensure that the only differences in solutions were due to PEG. PEGs of molecular weights (MW) of 20, 108, 205, 438, and 511 kDa were used to apply osmotic pressures over the range 0-10 kPa. 2.2

Osmotic pressure of PEG solutions

Experimental measurements have shown that the relation between PEG concentration and osmotic pressure is a non-linear function of both concentration and MW [3,8,9]. This relation has been modeled by the virial equation of state [3]. Calibration tests show that this model fits measurements well for PEG with 20 < MW < 511 kDa [6]. 3

Measurements and Model

3.1 Normal Mice Equilibrium changes in TM volume were measured in response to osmotic stresses exerted using 511 kDa PEG. The left panel of Figure 1 shows results for an osmotic stress of 2.5 kPa. The TM shrank at all measured positions. Moreover, the fraction by which the TM shrank was approximately independent of the original thickness, which was 0.62 when the osmotic stress was 2.5 kPa. Similar measurements were made for PEG concentrations exerting osmotic stresses of 0.025, 0.050, 0.250, 1.0, 2.5, 5, and 10 kPa (right panel of Figure 1). The bulk modulus of the TM is equal to the negative reciprocal of the slope of the relation between normalized thickness and

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stress. Thus the large negative slope at low osmotic stress corresponds to a low bulk modulus (0.5 kPa), and the smaller negative slope at high osmotic stress corresponds to a higher value of bulk modulus (60 kPa). At the lowest osmotic stresses, the change in thickness can be predicted by Hooke's law. For higher osmotic stresses, the change in thickness is significantly smaller than that predicted by Hooke's law. We modeled the stress-strain relation using a homogeneous isotropic gel model [12] in which the free parameters were the stiffness of the matrix and the fixed charge concentration. The dashed line in Figure 2 shows the least squares fit of the model parameters to the measured thicknesses. The best-fitting value of fixed charge was —28 mmol/L and the best-fitting stiffness was negligibly small. The fit overestimates the bulk modulus at low osmotic stresses and underestimates it at high osmotic stresses. Changing the fixed charge concentration to —10 mmol/L (lower dotted line) improved the fit at low osmotic stresses but made the fit worse at high osmotic stresses. Changing the fixed charge concentration to —34 mmol/L (upper dotted line) had the reverse effect. In all cases, increasing the stiffness of the matrix made the fit worse. Thus, we conclude that the homogeneous isotropic gel model fits the data best when the applied osmotic stress is resisted by electrostatic charge repulsion alone. However, no single value of fixed charge fit the measured thicknesses across the range of applied osmotic stresses. To better match the experimental measurements, we developed a two component model of the TM, in which one component was modeled as a homogeneous isotropic gel and the other was incompressible. This model has

52

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Figure 2. Fits of a gel model to the measured thickness change. The dashed line represents the best fit of a model in which TM charge (—28 mmol/L) resists compression. The lower dotted line, fit to the measurements at the two lowest stresses, has —10 mmol/L charge. The upper dotted line, fit to measurements at the highest two stresses, has —34 mmol/L charge. The solid line represents a variation of this model in which the TM also contains an incompressible region. In this model 42% of me ™* ' s m c o m P r e s s ible, and the rest has —10 mmol/L charge.

two free parameters: the fixed charge concentration of the first component, and the fraction of the TM volume that is compressible. The best-fitting parameters of this model provide a close match to the measured thicknesses at all osmotic stresses (solid line in Figure 2).

3.2 Collla2 - /- andTectaY1870C/+ mice Mice with mutations in either Collla2 or Tecta, genes which encode proteins found in the TM, show significant hearing loss. Measuring the stress-strain relation of TMs from these mice serves two purposes: to provide a test of the two component model of TM compressibility, and to determine changes in TM material properties that may underlie the hearing loss in mese mutants. The thickness change in response to osmotic pressure was measured as for normal mice. Figure 3 shows the normalized thickness as a function of osmotic pressure for the normal and mutant mice. The slope of this relation decreases with increasing stress for both normal and mutant mice. At low stresses, the bulk modulus was about 0.5 kPa for both normal and Collla2 — J - mice, and was about 1.1 kPa for TectaY1870C/+ mice. At higher stresses, TMs from Collla2 — /— mice shrank slightly less than those from normals. TMs from TectaYl 870C/+ mice shrank significantly less than those of either normal or Collla2 — /— mice at all osmotic stresses. Figure 3 also shows the least squares fit of the two component model to each set of measurements. The model fits were near the median value of measurements at all stresses for both mutants. Beneath each plot, the figure shows the model parameters that best fit the measurements. The predominant effect of either mutation was to increase the fraction of TM in the incompressible component; for the TectaY1870C/+ mutants, the model also predicted a slight decrease in fixed charge concentration in the other component.

53

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Figure 3. TM strain versus applied stress for normal TMs (left) Collla2 — /— mutants (center), and TectaY1870C/+ mutants (right). In the plots, the symbols represent the median and interquartile ranges of measurements, and the solid lines represent least squares fits of the two component model to the measurements. The resulting parameters are shown beneath each plot, where c j represents fixed charge concentration and the percentages represent the fractional thicknesses of the compliant and incompressible components.

4 Discussion TMs from both types of mouse mutants, Collla2 — /— and TectaYI870C/+, shrank less at a given osmotic pressure than did TMs of normals. The two component model suggests that the origin of this difference is not so much a change in fixed charge concentration but rather a decrease in volume of the compressible region. However, the physical basis for this incompressible region is not clear. The most straightforward interpretation of incompressibility is for the elastic matrix of the TM to be extremely stiff. Other collagen-containing tissues, such as cartilage, have bulk moduli in the MegaPascal range, of which roughly half is due to fixed charge [2]. In this interpretation, the effect of the Col\\a2 — /— and TectaYI870C/+ mutations might be to increase the fraction of TM that contains either a stiff elastic matrix or high fixed charge concentration. An alternative interpretation of incompressibility is for the TM to be extremely porous. If PEG can penetrate the pores of one component of the TM, it will not be able to exert an osmotic pressure on that component, so its volume will be unchanged. As a result, that component will appear incompressible. In this interpretation, the effect of the Collla2 - / - and TectaYI870C/+ mutations might be to increase the porosity of the TM. The measurements presented here do not distinguish between

these two interpretations. However, the two proposed mechanisms have dramatically different mechanical implications. The first mechanism predicts that the TMs of mutant mice will be extremely stiff mechanically, while the second predicts that these TMs will be more viscous and maybe extremely compliant. Either change could alter the interaction of the TM with hair bundles, and thereby contribute to the hearing loss seen in these mutants. Acknowledgments We thank the people in the Micromechanics Group at MIT for their insightful feedback and criticism with special thanks to A.J. Aranyosi. This work was supported by NIH grant R01-DC00238(DMF) and R01-DC003544(RS). Kinuko Masaki was supported in part by an NIH grant to the Harvard-MIT Speech and Hearing Biosciences and Technology program. References 1. Freeman, D.M., Masaki, K., McAllister, A.R., Wei, J.L. and Weiss, T.F., 2003. Static Material Properties of the Tectorial Membrane: A Summary. Hearing Research 180, 11-27. 2. Grodzinksy, A.J., 1983. Electromechanical and Physiochemical Properties of Connective Tissues. CRC Crit. Rev. Biomed. Eng. 9, 133-199. 3. Hasse, H., Kany, H.P., Tintinger, R. and Maurer, G., 1995. Osmotic Virial Coefficients of Aqueous Poly(ethylene glycol) from Laser-Light Scattering and Isopiestic Measurements. Macromolecules 28, 3540-3552. 4. Legan, P.K., Lukashkina, V.A., Goodyear, R.J., Kossl, M., Russell, I.J. and Richardson, G.P., 2000. A Targeted Deletion of a-Tectorin Reveals that the Tectorial Membrane is Required for the Gain and Timing of Cochlear Feedback. Neuron 28, 273-285. 5. Legan, P.K., Lukashkina, V.A., Goodyear, R.J., Lukashkin, A.N., Verhoeven, K., Van Camp, G., Russell, I.J. and Richardson, G.P. A Deafness Mutation Isolates a Second Role for the Tectorial Membrane in Hearing. Nature Neuroscience, in press. 6. Masaki, K., Weiss, T.F. and Freeman, D.M., 2005. Measuring the Equilibrium Bulk Modulus for the Tectorial Membrane with Osmotic Stress: Caveats of Using Polyethylene Glycol. Abstracts of the Twenty-Eighth Annual Midwinter Research Meeting , 121-121. 7. McGuirt, W.T., Prasad, S.D., Griffith, A.J., Kunst, H., Green, G.E., Shpargel, K.B., Runge, C , Huybrechts, C , Mueller, R.F., Lynch, E., King, M.-C, Brunner, H.G., Cremers, C , Takanosu, M., Li, S.-W., Arita, M., Mayne, R., Prockop, D.J., Van Camp, G. and Smith, R., 1999. Mutations in Collla2 Cause Nonsyndromic Hearing Loss (DFNA13). Nature Genetics 23,413-419.

55 8. Parsegian, V.A., Rand, R.P., Fuller, N.L. and Rau, D.C., 1988. Osmotic Stress for the Direct Measurement of Intermolecular Forces. Meth. Enzymol. 127, 40CMH6. 9. Schiller, L.R., Emmett, M., Santa Ana, C.A. and Fordtran, J.S., 1988. Osmotic Effects of Polyethylene Glycol. Gastroenterol 94, 933-941. 10. Shah, D.M., Freeman, D.M. and Weiss, T.F., 1995. Osmotic Response of the Isolated, Unfixed Mouse Tectorial Membrane to Isosmotic Solutions: Effect of Na + , K + , and Ca + 2 Concentration. Hearing Research 87, 187-207. 11. Sterkers, O., Ferrary, E. and Amiel, C , 1988. Production of Inner Ear Fluids. Physiol. Rev. 68, 1083-1128. 12. Weiss, T. F. and Freeman, D. M., 1997. Equilibrium Behavior of a Isotropic Polyelectrolyte Gel Model of the Tectorial Membrane: The Role of Fixed Charges. Auditory Neurosci. 3, 351-361.

Comments and Discussion Hackney: It was surprising to hear that the tectorial membrane of the mouse mutants, especially the Tecta Y870C/+ ones, had a similar size and shape to the wild-type ones given that 30% of the protein had been affected by the mutation. Is it possible that another protein has been up regulated thus changing the bulk modiolus in an unexpected way? Answer: Actually, differences in the initial volumes of the TMs (when they were bathed in artificial endolymph with no PEG) are roughly consistent with the volume that might be expected if the modified protein were absent. The initial thicknesses of TMs from normals and Coll la2 mutants were similar, in keeping with the rather small fraction of Coll 1 found in the TM. The initial thicknesses of Tecta mutant TMs were about 2/3 as large as normals, in keeping with the fact that alpha-tectorin comprises nearly 30% of the protein in the mammalian TM. We have not experimentally tested the notion of up-regulation. Shoelson: Did you look at the relative sizes of the undisturbed TMs of the mutant versus the normal animals? A second question: given that your model postulates inhomogeneity, can you comment on the accuracy of judging volumetric change by looking only at the motion of particles in 2-D? That is, how do you know that the deformations in response to osmotic loading are not isovolumetric? Answer: After isolating the TMs and perfusing them with artificial endolymph (no PEG), we found that the initial thicknesses of TMs from normals and Collla2 mutants were similar, but those from Tecta mutants were only approximately 2/3 as thick as those from normals. If the difference in initial volume resulted primarily from a change in the incompressible fraction, then the change in overall thickness could contribute to the change in fractional volume of the compliant layer that we measured in the Tecta mutant. However, the difference in initial volume is not sufficient to fully account for the large fractional change that we observed. In this paper and talk, strain was computed from changes in the (thickness) component of bead position. Previously, we have shown that osmotic responses in the x (radial) and (longitudinal) directions were small compared to those in z. This may well be an artifact of our preparation, in which the TM is attached to the glass slide using a tissue adhesive (Cell-Tak). We are currently developing methods to measure osmotic responses of free-floating TMs, to better understand if the measured anisotropy results from inhomogeneity of the tissue or of its attachment.

TUNING AND TRAVEL OF T W O T O N E D I S T O R T I O N IN I N T R A C O C H L E A R P R E S S U R E

WEI DONG AND ELIZABETH S. OLSON Columbia University Dept. of Otolaryngology, P&S E-mail:

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Two-tone distortion was measured in the intracochlear pressure in the basal turn of the gerbil cochlea, close to the sensory tissue, where the local motions and forces of the organ of Corti can be detected. The characteristics of the distortion reflect several stages of cochlear mechanics, including the nonlinear process that generates distortion, and single-tone cochlear tuning of both the primaries and the distortion products (DPs). In this contribution we present results that illustrate these processing stages. We show (i) the relatively large size of the 2f r f2 component at its own best place, indicating that it traveled there, (ii) that the combined effects of nonlinear processing and cochlear tuning determine the shape of the family of DPs produced by one primary pair, (iii) that the tuning of an individual DP (e.g., 2f r f 2 ) reflects the single-tone tuning of both the primaries and the DP and (iv) that the DP measured at one longitudinal location is often composed of a sum of a local component and a component that emanated from a remote location.

1 Introduction Two-tone distortion has been observed and studied at many levels of the auditory system: perceptual, neural, in auditory emissions, in basilar membrane (BM) motion and in intracochlear pressure. We measured two-tone distortion in intracochlear pressure close to the sensory tissue, where the local motions and forces of the organ of Corti can be detected. The characteristics of the distortion reflect several processes. The nonlinear process that generates two-tone distortion is apparent in the stair-step shape of DP families (the set of DPs generated by a single primary pair). The tuning and travel of the primary components prior to distortion generation, and the tuning and travel of the DPs following their generation influence the behavior of individual DPs, e.g., their frequency response and variation with primary ratio. In a recent paper [1] we described observations of two-tone distortion in intracochlear pressure in relative detail. Here, we choose several results to illustrate specific points regarding the tuning and intracochlear travel of DPs. Measurements of pressure close to the BM are closely akin to those of BM motion, with some differences. One difference is that the pressure can be measured at various distances from the BM, to address the question of how DPs spread and travel in the cochlea [1]. Another difference is that the compressive pressure, timed with stapes motion, forms a background pressure that essentially fills the cochlea at primary frequencies. At a given longitudinal location, at frequencies somewhat

56

57

higher than the BF this pressure dominates the pressure of the cochlear slow-wave (e.g., [4]). 2 Methods Details are in [3]. Measurements were made in vivo in turn one of the gerbil cochlea. The animal was deeply anesthetized throughout the experiment and overdosed with anesthetic at the end of it. The compound action potential (CAP) measured at the round window was used to monitor the cochlear health at several time points during an experiment. Intracochlear pressure measurements were made in the scala tympani (ST) close to BM in the first turn of the cochlea where the best frequency (BF) was approximately 20 kHz. Pressure was measured using specially designed pressure sensors that were narrow enough (100 or 170 ^m outer diameter) to be inserted into the cochlea without causing damage. A sensor tip was inserted through small holes that were handdrilled through the cochlea's bony wall. The base •*— —- apex pressure in the scala vestibuli (SV) just next to Figure 1. Cartoon of excitation patterns upon stimulatin with tones of freqency the stapes was measured, either simultaneously fi, f2, 2fi-f2 and 2f2-fi. The gray area is with the ST pressure measurement or after the fi, f2 overlap region. most of the ST data had been collected. For this study the SV pressure served primarily as a phase reference. The sensors operate linearly and do not introduce distortion [1]. The presence of the sensor close to the BM might perturb cochlear mechanics but based on our estimation that perturbation is small [4]. Stimuli were delivered and responses measured with a TDT system II or III operating at a 5 or 6 ^s sampling rate and a Radio Shack tweeter. Measurements in a cavity confirmed that system distortion was very small. The time averaged signals were analyzed as Fourier transforms, using Matlab. 3 Results We introduce the two-tone results with a sketch that illustrates the excitation patterns of the primaries and 2f r f2, 2f2- fi DPs in the cochlea (Fig. 1). The figure is useful for thinking about the presented results. It is based on single tone data at a level of 50 dB SPL [1], and the frequency-place map of Muller [2].

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3.1 Spectra show travel of 2frf2, tuning of DP families In Fig. 2A the 2f r f2 response was a few dB greater than both of the primary responses when it was measured at its own best place. This was a conclusive observation that the DP was produced at a distant location and traveled to the measurement position. Even more conclusively, in measurements of BM motion, Robles et al. [6] showed that the 2f r f2 component could be measured even when the f\ and f2 primaries were beneath the noise floor; the compressive pressure prevents such an observation in the pressure. Fig. 2B and 2C show the amplitudes of DP families with closely-spaced equalintensity primaries (equal intensity in the ear canal). The single tone tuning (not L, = L2 = 60dBSPL,l 2 /f, = 1.15

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Figure 2. DP families of pressure measured close to the BM. Arrows indicate the BF of the measurement location. (A) shows that when the 2fi-f2 was set atBF, this DP can be bigger than either of the primaries. (B) and (C) were both produced with closely spaced primaries (f2/ fi = 1.05), leading to a family of DPs. (W45, 25 nm from BM)

shown) is important to the interpretation of these plots: at 80 dB SPL the response peaked at 14 kHz; at stimulus levels less than 70 dB the response peaked at 18 kHz - thus 18 kHz was considered the BF [1]. As is predicted by a simple compressive nonlinearity with equal-intensity inputs, the DP side-bands show a nearly symmetric stair-step-shaped distribution (discussed and referenced in [1]). In Fig. 2B the response at fi is slightly bigger than that at f2; based solely on the action of a compressive nonlinearity that inequality is expected to lead to larger low-sidebands, relative to high-side-bands. The fact that the opposite is observed, that the high-side-bands are larger, reflects the cochlear tuning of the side-bands following their generation. (Also note that the intensity dependence of the "best frequency" is reflected in the pattern: the cochlear tuning of the DPs is low-intensity tuning: the 18 kHz low-intensity BF shifts the symmetric stair-step pattern to the highfrequency side. In contrast, the primaries exhibit high-intensity cochlear tuning (15.3 kHz fj favored over 16 kHz f2).) In Fig. 2C the primaries are above the 18 kHz BF, and the cochlear tuning of the DPs favors the low-side-bands.

59 3.2 Increasing the separation of primaries has different effects on 2f-f2, 2f2-f Assuming DPs are generated at sites where fi and f2 overlap, when the f2/fi (A) ratio increases the overlapping region 100 decreases, which will eventually lead 80 to a decrease in the generation of distortion. As long as the overlap region is not too small, distortion will be generated, and individual DPs can travel to their own best places (Fig. 1). S 80 When fi is set at the BF of the recording position, the recording site is apical of the generation location but 1.05 1.1 1.15 1.2 1,25 1.05 1.1 1.15 1.2 1.25 basal of the 2f r f2 best place. Ratio f, / f, Ratio f / f, Therefore, the 2f r f2 DP is expected -6- L.=L,=60 dB SPL to be large at the recording position, -x- L =L,=70 dB SPL - I - L =L,=80 dB SPL and that is seen in Fig. 3A. In contrast, the recording site is apical of Figure 3. In A and B the fi was at BF of 18 the 2f2- fi best place, more so as the kHz, in C and D the f2 was at BF. The ratio increases. Therefore, the 2f2- f[ variation with ratio of the 2frf2 (A and C) and 2f2-fi (B and D) DPs are compared for these DP is expected to be relatively small two conditions. The noise floor is plotted as and to decrease as the primary ratio dot-dash line. (W45, 25 um from BM) increases, and that is seen in Fig. 3B. When f2 is set at the recording position, the recording site is likely close to the generation location, apical of the 2f2 - fi best place, and basal of the 2fi - f2 best place. Therefore, the 2f2 - fj DP might be expected to be primarily due to local generation, which is expected to be relatively large as long as the ratio is not too large. This is observed in Fig. 3D. By the same reasoning, we also expect a relatively large local component of the 2f r f2 DP. We saw in Fig. 2A that the 2f r f2 component travels to and is large at its own best place. If it is large enough there, it might produce a second component of 2f r f2, that gets to the recording position either via a reflected BM wave [7], or via the fluid directly [5]. The zig-zag shape of the 2f r f2 DP in Fig. 3C is supportive of the idea that a locally generated component and a component emanating from an apical location contributed to the DP. 2

60

3.3 DP frequency response reflects both pre- and post-generation tuning 2U-1. 100

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Figure 4. DP tuning (Li = L2 = 80 dB SPL, f2/fi = 1.05, W48, 10 um from BM). The 2f,-f2 and 2f2-fi DPs are plotted both with respect to their own frequency (which emphasizes their tuning following generation) and with respect to the f2 frequency (which emphasizes how their tuning reflects the tuning of the basal primary). The single tone tuning of 50 dB SPL was plotted for comparasion.

Figure 4 shows the amplitude and phase of 2f r f2 and 2f2- fj DPs produced when the primaries were swept at a fixed, low ratio (1.05). As described in more detail in [1], a compressive nonlinearity will produce 2f] - f2 and 2f2 - fi components that are typically 180° out of phase with the primaries. This explains the vertical half-cycle shift in the phase plots (see also Fig. 5). When plotted with respect to the DP frequency (thin solid line in Fig. 4B) the 2f2- f, DP extends to higher frequencies than the single tone extends. When plotted with respect to f2 (bold line, Fig. 4B), the 2f2- f, DP tuning coincides more closely with the single tone tuning. Thus, the tuning of the high-side component depends to a large degree on the tuning of the more basal primary (f2). This agrees with the idea that the distortion arises from the region where the responses to both primaries are large and overlapping. In contrast, the tuning of the low-side 2f r f2 component coincides more closely with single-tone tuning when plotted with respect to its own frequency. This reinforces the observation, introduced in Fig. 2A, that the 2f,- f2 component, once generated, travels within the cochlea, and peaks as a single tone would have.

3.4 DPs generated by low frequency primaries arrived at measurement position from a more apical location Figure 5 is similar to Fig. 4 in showing DP tuning with a fixed, low primary ratio of 1.05. Here, the DPs are plotted relative to their own frequency, and both Li = L2 and

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Figure 5. DPs tuning (W45, 25 |Xm from BM, f2/fi = 1.05). The stimulus tone levels were equal-intensity (A - D) or unequal - intensity (A' - D') of L.2 level 60 (circles), 70 (crosses) or 80 dB SPL (pluses). The upper panels show the amplitude of 2f2 -fi and 2fi -f2. Single tone tuning at 30, 50 & 70 dB SPL are shown (dot-dash lines) for comparison. The bottom panels show the DP phases relative to the SV primaries.

Li = L2 + 10 dB stimulus conditions are presented. Although the similarity between the DP and single-tone tuning is what is most obvious about the plots, the departure from similarity at frequencies well below the BF, particularly for the 2f2 - fi DP, is also notable. Considering the frequency region around 10 kHz in Fig. 5D, the group delay (slope of the phase curve, arrow) is much greater than what would be found if the DP were locally generated. The group delay in evidence is similar to what would occur at the BF (Fig. 1). This suggests that the DP measured was either generated further apical, close to its own best place, or was generated and then traveled apically to its own best place and that disturbance was dominant in the measured response. In either case, that more apical DP was large enough to form the dominant component of the DP at the measurement location. We also expect a 2f2 - fi component that was generated close to the measurement position. This component will add to the apical component. This expected summation is supported in Fig. 5B', where changing the relative levels introduced a notch in the amplitude that is suggestive of interference between two DP components.

62

Summary The characteristics of two - tone distortion in intracochlear pressure are governed by the processing of the compressive nonlinearity that generated them, and further influenced by cochlear tuning and wave mechanics. Acknowledgments This work was funded by a grant from the NIDCD. References 1. Dong, W., Olson, E.S. 2005. Two-tone distortion in intracochlear pressure. J Acoust Soc Am 117, in print. 2. Muller, M. 1996. The cochlear place-frequency map of the adult and developing Mongolian gerbil. Hear Res 94, 148-56. 3. Olson, E.S. 1998. Observing middle and inner ear mechanics with novel intracochlear pressure sensors. J Acoust Soc Am 103, 3445-63. 4. Olson, E.S. 2001. Intracochlear pressure measurements related to cochlear tuning. J Acoust Soc Am 110, 349-67. 5. Ren, T. 2004. Reverse propagation of sound in the gerbil cochlea. Nat Neurosci 7, 333-4. 6. Robles, L., Ruggero, M.A., Rich, N.C. 1997. Two-tone distortion on the basilar membrane of the chinchilla cochlea. J Neurophysiol 77, 2385-99. 7. Talmadge, C.L., Long, G.R., Tubis, A., Dhar, S. 1999. Experimental confirmation of the two-source interference model for the fine structure of distortion product otoacoustic emissions. J Acoust Soc Am 105, 275-92.

RESPONSE CHARACTERISTICS OF THE 6 kHz C O C H L E A R REGION OF CHINCHILLA

WILLIAM S. RHODE Department

of Physiology, University of Wisconsin.Madison, rhode@physio!ogy. wise, edu

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The absence of knowledge of the mechanical response in the mid-frequency region of any species cochlea is due to the difficulty of accessing anything other than very basal or apical regions. The 6kHz region of the chinchilla cochlea was studied to determine whether the assumption that the transfer functions measured in the base are log scale invariant across the length of the cochlea. Measurements show that the 6 kHz region is at least as sensitive as the 9-20 kHz region. Input/output growth rates as low as 0.1 dB/dB. Two-tone suppression maps are consistent with those obtained at higher frequencies. Simultaneous measurements of DPOAEs and basilar membrane mechanics provides a basis for speculation as to OAE origin as either nonlinear (wave-fixed) or reflection (place-fixed). Growth of the 2fl-f2 distortion product as a function of the level of the primary tones generally supports the formula used for optimizing DPOAE production.

1 Introduction There have been numerous studies of the motion of the basilar membrane in chinchilla, perhaps the best studied model for cochlear mechanics, to date. Most of the studies have been limited to either the basal region or to the very apical region due to anatomical realities reviewed by Robles and Ruggero [1]. The 1-6 kHz frequency region remains essentially unstudied. Studies of cochlear mechanics at the 6 kHz region, show that 'scaling' of the response properties holds. Sensitivity, tuning, compression, suppression, and distortion in this region are similar to those previously reported in more basal cochlear regions (8-20 kHz). 2 Methods Basilar membrane (BM) vibration was measured using the laser interferometer described by Cooper and Rhode [2]. Gold-coated polystyrene beads (25 urn) are used as retroreflectors. Small openings (0.5mm) in the cochlea are covered with a glass cover slip to reduce artifacts due to fluid motion. Stimuli were presented using an Etymotics ER IOC phone that was calibrated for each experiment in the ear of the subject. Data were collected at 100 Hz increments around CF and 200 Hz increments below CF and analyzed using MATLAB. Experimental protocol followed guidelines approved by the University of Wisconsin IACUC.

63

64

3 Results A typical set of input/output (I/O) functions for the 6300 Hz region of the chinchilla cochlea are shown in Figure 1. At characteristic frequency (CF) the displacement reaches 3.5 nm at 20 dB SPL and better than 0.5nm at 0 dB SPL, likely corresponding to psychophysical threshold [3]. I/O functions are linear for frequencies below CF and are increasing nonlinear near and above CF. For several frequencies above CF there are notches in the I/O functions that occur at progressively lower intensities as the stimulus frequency increases. The notches are also apparent in isointensity functions constructed from the I/O functions (Fig. 2). Figure 1. Frequency sampled at 200 Hz up to CF and at 100 Hz above CF. Intensity was varied from 0 to 100 dB SPL in 5 dB steps or until the displacement approached 100 nm. Only a portion of the I/O curves are shown for clarity. The heavy dashed-line is a linear reference. 40 60 Intensity (dB SPL)

80

100

Figure 2. BM isointensity functions. The frequency separation of the notches indicated by the dotted lines is -700 Hz. 10X the symbol number = dB SPL. Intensity was varied from 0 to 100 dB SPL in 5 dB increments. I/O functions were collected for 68 frequencies. 6

7 8 Frequency (kHz)

Isointensity functions exhibit compressive growth in the vicinity of CF and linear growth both below CF and in the high-frequency plateau region (f > CF and high levels). Several 'notches' can be seen in high-level functions for frequencies near and beyond CF indicated by the dotted lines. A linear frequency scale is employed to emphasize the frequency spacing of the notches as -700 Hz. It appears that small notches are also present near CF. Whether they occur below CF is not

65

testable because the displacements necessary would exceed those that could result in cochlear damage.When small frequency and intensity steps are taken a very deep notch can be seen with an accompanying rapid phase shift of-180°. A strong case for compression at CF is made by noting that if the growth were linear, the nearly lnm displacement at 0 dB SPL would be lOO^m at 100 dB SPL. Not a good thing. The isointensity functions are nearly flat below 0.6CF with a few ripples that result from the middle-ear transfer function. If the isointensity functions were normalized by the middle-ear transfer function then the low frequency slope would be 6dB/oct. BM-displacement rate-of growth is computed as the slope of the I/O functions. It is a function of level and frequency demonstrating the system is linear (1 dB/dB) below 0.6CF, and has a frequency- and intensity- dependent compression ( 1 dB/dB). The bandwidth of the notch is often small (<100Hz) with the result that with sampling the function every 100 Hz, the deepest portion of the notch is usually missed. Rate-of-growth vs frequency is a complex function that illustrates the continuously varying nature of compression. The I/O function at CF deviates from linearity even at 10 dB SPL with a decreasing rate-of-growth with increasing level that approaches -0.2 dB/dB by 50 dB SPL. Figure 3. Rate-ofgrowth of as determined by the gradient of the I/O functions. Curves with levels < 60 dB SPL were 3-point smoothed. The sharp notches for f > 8kHz correspond to notches in I/O functions. Phase inversions are associated with them. 4 6 Frequency (kHz)

0

Phase changes that accompany the nonlinear I/O curves are similar to those reported previously [3] with the caveat that for high intensity levels there is nearly always a phase lag at intensities > 65 dB SPL for any I/O function that is not linear (Fig. 4). Phase is constant for low frequencies (e.g., 1kHz). As CF is approached (e.g., 4.7kHz), there is a phase lead at low levels followed by a phase lag at high levels. At CF (6.3kHz) there is nearly constant phase up to 55 dB SPL followed by a rapid increase in phase lag with further increases in level. Beyond CF there is an initial phase lead that can attain 90° by 60 dB SPL. Above 60 dB SPL there is a

66

phase lag with a change in phase that is -180°. Phase vs level is constant for stimulus frequencies in the plateau region for high intensities. Figure 4. Phase I/O functions. Frequencies are the same as in Figure 1. Phase at 20 dB SPL was used to nomalize the individual phase I/O functions.

20

40 60 Intensity (dB SPL)

80

100

3.1 Two-tone suppression Two-tone suppression was studied over an octave range centered on CF, the range used in distortion product otoacoustic emission (DPOAE) studies. Figure 5 illustrates the suppression of the probe tone (£2 at CF) by the suppressor tone (fl). The probe can be suppressed by as much as 50 dB for suppressors below CF. For suppressors near CF, suppression begins when the level of f2 is around 5 dB less than that of the probe. Suppression rate grows as level is increased to as much as 1.5 dB/dB. It is a complex function of the frequency ratio and level of the two primary frequencies. The gradient (slope) of the suppression I/O functions is shown in Figure 6 where a separate curve is shown for each intensity (LI) varied between 20 and 80 dB SPL. There is a maximum rate of suppression for LI at 70 dB SPL with a subsequent reduction at 80 dB SPL. When the amplitudes of BM motion for the primaries are equal, the probe amplitude is reduced 1-3 dB for the frequency ratios covered. Figure 5. Suppression for a CF tone of 6.55kHz (dotted vertical line near the characteristic frequency of 6.3 kHz) at a level of 33 dB SPL. L2 (level of the suppressor) was varied from 20 to 80 dB SPL in 5 dB steps as was the probe tone level. Symbols indicate 0.1 level of LI in dB SPL. •IOOO

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67

Figure 6. Rate of suppression of the probe (£2) by fl. lOX's symbol numbers indicate intensity of probe in dB SPL.

40

50 60 L1 (dB SPL)

3.2 Two-tone distortion Two-tone distortion co-incides with two-tone suppression. The most common distortion product studied is 2fl-f2. It is also the largest DPOAE where it has been shown that the combination of LI and L2 that results in the largest 2fl-f2 DP requires LI to be considerably larger than L2 for low levels of L2. Figure 7 illustrates the BM correlate of that relation for three ratios of f2/f 1. For low f2/f1 ratios both components are undergoing the same amount of compression and therefore L1=L2 produces a maximum DP. At f2/fl=1.21, the ratio that results in the largest DP, LI =L2+15 dB at low levels and the difference in levels decreases as .»

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68 4 Discussion An effort was made to extend chinchilla basilar membrane measurements to lower frequencies than typically studied in the base of the cochlea. The sensitivity of the region is at least as good as that reported in the best measurements to date (3.5 nm at 20 dB, CF~ 6 kHz). The response properties are compatible with those in the base, > 50 dB gain, strong nonlinearity that shows rate-of growth of < 0.3 at CF and that approaches 0 dB/dB for frequencies beyond CF, a plateau region for sufficiently high frequencies relative to CF, and notches in the I/O functions for several frequencies at and greater than CF. The high frequency slopes of iso-displacement curves (not shown) can be as large as 400 dB/octave, as steep as any neural threshold curves. Tip-to-tail ratio is > 40 dB. The tail region is nearly constant vs frequency. One of the distinctive features is the notches for frequencies > CF. The notch spacing is -700 Hz in this and several other sets of iso-intensity functions. Rhode and Recio [4] described narrow notches with phase transition of ~180° for intensity changes of a few dB. Notches are rarely or ever seen in a compromised preparation and therefore appear to be a feature of very sensitive preparations. The level at which a notch occurs decreases with increasing frequency. A possibility is that notches represent an interaction of two (or more) modes of vibration [4,5]. Phase at high levels of stimulation always shows a lag that can be as large as 180° similar to what has been reported in auditory nerve recordings at frequencies where phase-locking occurs [6,7]. Two-tone suppression indicates that 50 dB or more reduction of the probe tone amplitude can be obtained along with a corresponding reduction of the suppressor by the probe. That is, there is mutual suppression of each primary tone by the other primary tone. Rate of suppression, is often near 1 dB/dB for frequencies lower than CF, though it can reach nearly 2dB/dB and is lower at higher intensity levels. The reduction at high levels may be a result of the tendency for the single-tone growth rate to approach linearity at high levels of stimulation (>80 dB SPL). Two-tone distortion is also present and can be as large as one of the primaries. The largest amplitudes occur when fl is larger than f2.This is explained by the fact that the two tones have to interact where there is a nonlinear response. This region is where the f2 nonlinearity is present and where fl is typically smaller than £2. However, the relation for optimum production of the 2fl-f2 distortion product is complicated in that is a function of the £2/fl ratio and the level of the tones. In recording otoacoustic emissions, f2/fl is often set to 1.22 as this is about the ratio for DP maximum distortion. At this ratio, BM distortion follows the LI: L2 relation that is employed for OAE recording [8].

69

Acknowledgements This research was supported by NIDCD grant 1910. References 1. 2.

3. 4. 5.

6.

7.

8.

Robles, L. and Ruggero, M.A., 1999. Mechanics of the mammalian cochlea. Physiological Reviews, 81:1305-1352. Cooper, N.P. and Rhode, W.S., 1992. Basilar membrane mechanics in the hook region of cat and guinea-pig cochleae: Sharp tuning and nonlinearity in the absence of baseline shifts. Hear. Res. 63: 163-190. Fay, R.R., 1988. Hearing in Vertebrates: a Psychophysical Databook. HillFay Associates. Rhode, W.S. and Recio, A. 2000. Study of mechanical motions in the basal region of the chinchilla cochlea. J. Acoust. Soc. AM., 107:3317-3332. Lin, T. and Guinan, J.J., 2000. Auditory-nerve-fiber responses mto highlevel clicks: Interference patterns indicate that excitation is due to the combination of multiple drives. J. Acoust. Soc. Am. 107:2615-2630. Ruggero, M.A., Rich, N.C., Shivapuja, B.G. and Temchim, A.N., 1996. Auditory-nerve responses to low-frequency tones: Intensity dependence. Auditory Neurosci. 2:159-185. Liberman, M.C. and Kiang, N.Y.S. 1984. Single-neuron lableing and chronic cochlear pathology. IV. Stereocilia damage and alterations in rate and phase-level functions. Hear. Res. 16:75-90. Kummer, P., Janssen, T., and Arnold, W., 1998. The level and growth behavior of the 2fl-f2 distortion product otoacoustic emission and its relationship to auditory sensitivity in normal hearing and cochler loss, J. Acoust. Soc. Am. 103:3431-3444.

STIFFNESS PROPERTIES OF THE RETICULAR LAMINA AND THE TECTORIAL MEMBRANE AS MEASURED IN THE GERBIL COCHLEA C.-P. RICHTER AND A. QUESNEL Northwestern University Feinberg School of Medicine, Department of Otolaryngologyand Neck Surgery, 303 E. Chicago Ave, Chicago, IL 60611-3008, USA E-mail: cri529@northwestern. edu

Head

Driving point stiffnesses of the reticular lamina with its supporting structures and the tectorial membrane (TM) were determined with a piezoelectric sensor. Measurements were made at several radial positions and at four locations along the cochlea from base to apex. Furthermore, using a stiff probe, static images of the stepwise indentation of the reticular lamina (RL) were captured to monitor relative displacements of structures within the organ of Corti. Stiffness values at the RL approximately matched the stiffness values of the TM for each of the locations along the length of the cochlea. Reticular lamina moved like a rigid lever with its pivot point at the pillar cells' heads. Moreover, reticular lamina displacement was slightly greater than outer hair cell (OHC) or Deiters' cell cups displacement. While basilar membrane displecements were below the detection threshold of the system, the lower two thirds of the Deiters cells were compressed the most.

1 Introduction In addition to outer hair cells, it has been shown recently that the tectorial membrane (TM) is extremely important for the sensitivity and frequency selectivity of the mammalian inner ear. Mutation of the gene for a-tectorin resulted in detachment of the TM and disruption of its non-collagenous matrix [15; 16]. The structural changes were limited to the TM, and hearing function was severely compromised. However, the mechanisms by which the TM contributes to frequency selectivity and sensitivity remain equivocal. Dynamic properties of isolated mouse TMs showed that the TM behaves like a viscoelastic body [1;10;11]. In addition to limited dynamic patterns, physical properties of the TM were measured. Von Bekesy made stiffness measurements along the entire cochlea [21]. A small difference in transversal stiffness was measured between the most basal and the most apical cochlear locations [21]. Stiffness measurements in in vivo experiments produced similar values in gerbils [22;23]. Radial stiffness seemed to be slightly larger compared to longitudinal stiffness. Moreover, results of stiffness measurements on isolated mouse TMs did not differ largely from such measurements provided in earlier studies. Again, longitudinally the TM is less stiff compared to the radial direction [1;12]. To evaluate the effects of the TM's stiffness on cochlear micromechanics and hair cell stimulation, it is necessary to compare it with the stiffness of other structures, in particular with the stiffness of the reticular lamina (RL). With the hemicochlea, we can access the cochlea at many locations from base to apex and

70

71 can measure the physical and dynamic properties of the TM. Furthermore, in the hemicochlea, the TM remains in its natural position, attached to the spiral limbus and the tips of the outer hair cell stereocilia bundles. 2 Methods Driving point TM and RL stiffness measurements were made in the hemicochlea preparation using a piezoelectric stiffness sensor. Measurements were made at four cut edges from base to apex along the cochlea. About 100 um from each cut edge, the transversal stiffness of the TM was measured, which is the stiffness when the sensor is moved perpendicular to the RL. Furthermore, the stiffness of the RL was measured above outer hair cell 1 and outer hair cell 3, while the measuring probe was moved perpendicular to the RL. Siffness measurements: A hemicochlea was produced and secured with high vacuum grease in the lid of a petri dish, filled with bathing medium, either artificial endolymph or artificial perilymph in which lOOmM of the chloride is replaced by lactobionate. For stiffness measurements, the tip of a calibrated probe was advanced under visual control close to the structure of interest. Then, the stiffness sensor was advanced in steps of 1 |im, and stiffness measurements were made at each position of the probe. The point at which the probe came in contact with the tissue was determined via the microscope and from the responses of the measuring probe. After the probe first contacted the tissue, the probe's base was advanced a total of 20 to 25 um, in steps of 1 um. Hemicochlea: The method of producing a hemicochlea has been published and will be described only briefly [5;14;18]. After an intraperitoneal injection of a lethal dose of sodium pentobarbital (180mg/kg), gerbils were sacrificed. Following decapitation, the head was divided in the medial plane and the bullae were removed. Next, one of the bullae was opened. The cochlea was exposed in oxygenated artificial endolymph or perilymph. The pH was adjusted to 7.4 by adding the appropriate amount of HC1 or NaOH (artificial perilymph) and KOH (artificial endolymph). Next, the cochlea was cut along its mid-modiolar plane into two parts. One of the resulting hemicochleae was used for the experiments. Stiffness probe: The stiffness sensor consisted of a needle (12 um diameter tip) attached to a piezoelectric "sensor" bimorph that is attached, in turn, to a piezoelectric "driver" bimorph [6]. The driver bimorph is used to deliver 10 Hz sinusoidal motion to the sensor bimorph and needle. The voltage acquired from the sensor bimorph represents (by way of its flexion) the stiffness load at the needle tip. The inertia of the sensor system is corrected for by using a differential amplifier to subtract a scaled and phase-shifted version of the driver signal from the sensor output. A final correction is applied offline by subtracting the sensor signal obtained in a no-external-load condition. The sensor system is calibrated by pushing the tip against glass test fibers, which in turn are calibrated for their absolute stiffnesses on

72

a "string instrument" [7;8;9;22]. In short, the voltages obtained from the sensor bimorph can be converted directly into stiffness values. Reticular lamina deflection: In addition to the stiffness measurements, we observed the motion of the RL to determine whether the RL bends when deflected. While a stiff probe was pushed against the reticular lamina above outer hair cell 3, the displacement of different locations in the organ of Corti was determined. The locations were the nuclei of the outer hair cells, the nuclei of the Deiters' cells and the upper fiber band of the BM. Furthermore, the displacements of the reticular lamina were used to calculate angle oti = tan (displacement of RL over 1st OHC / distance from pillar head to 1st OHC), and angle a 2 = tan (displacement of RL over 3rd OHC / distance from pillar head to 3 rd OHC). When ax = <x2, RL must be moving like a rigid lever between OHC1 and OHC3 with its pivot point at the pillar heads. All animal experiments were approved by the Northwestern University Animal Care and Use Committee and followed guidelines from the National Science Foundation. 3 Results 3.1 Stiffhess as a function of location along the length of the cochlea Stiffness of the tectorial membrane changed along the cochlea, with the TM being more compliant in the apex compared to the base (Fig. 1). The tectorial membrane stiffness gradient (-3.0dB/mm) was slightly smaller when compared to the basilar membrane stiffness gradient (-4.5dB/mm) obtained from the same animals. When the stiffness was measured above outer hair cell 1 close to the pillar cells, the stiffness was similar to the stiffness obtained at the basilar mid pectinate zone (Fig. 1). Again, stiffness decreased from base to apex (-3.8dB/mm). In general, stiffness at the reticular lamina depended on the radial location and was larger above the first outer hair cell compared to the third outer hair cell. Interestingly, tectorial membrane stiffness was similar to the stiffness of the reticular lamina above the second outer hair cell, was stiffer than the stiffness measured above the third row of outer hair cells and was more compliant than the stiffness above the first row of outer hair cells. (Fig. 1). 3.2 Reticular lamina (RL) displacement is like a rigid beam The reticular lamina was deflected with a rigid probe. Independent of the probes placement above outer hair cell 1 through 3, the reticular lamina moved like a rigid beam. Calculating the angle between the reticular lamina and a reference axis, which was parallel to the lower border of the image, tested this hypothesis. When the RL was not deflected, alpha was zero. After deflection, independent of the radial position along the reticular lamina, the angle was the same.

73

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10

Figure 1. Shown are the stiffness values obtained for a 5am indentation of the stiffness probe.

3.3 Reticular lamina movement couples to the movement of the inner hair cells While the reticular lamina is pushed down, the inner hair cell cuticular plate moves upwards towards the tectorial membrane. Reticular lamina moves downwards, while the inner hair cell is moving upwards. A sea-saw like motion with the pivot point at the tip of the pillar cells can be observed. 3.4 A stiffness gradient exists from the reticular lamina to the basilar membrane A stiff probe is used to deflect the reticular lamina. The displacement of the reticular lamina, the outer hair cell nuclei, the Deiters' cell nuclei and the basilar membrane upper fiber band was measured. The displacement of the reticular lamina was given by the displacement of the probe (steps of 5 urn). The displacement of the outer hair cell nuclei was slightly smaller than the displacement of the displacement of the reticular lamina. The displacement of the Deiters' cell nuclei was in the order of the displacement of the outer hair cell nuclei, and the displacement of the basilar membrane was not measurable. The ratio of RL to outer hair cell nuclei displacement was on average 1.4, and the ratio of outer hair cell nuclei displacement and Deiters' cell nuclei displacement was on average 1.5. The results indicate that a stiffness gradient of cochlear structures exist between the

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reticular lamina and the basilar membrane. While a stiff region exists across the outer hair cells and Deiters' cells cups, the stiffness decreases across the lower two thirds of the Deiters' cells. 4 Discussion Mechanical properties of the RL, the organ of Corti, and the tectorial membrane determine in part the interaction between the TM and the outer hair cell stereocilia bundles. Tectorial membrane driving point stiffness measurements obtained at different locations along the cochlea showed a stiffness gradient along the cochlea as reported previously [7]. The stiffness gradient was -3.0 dB/mm and is similar to the stiffness gradient obtained from basilar membrane stiffness measurements made in the same animal -4.5 dB/mm [9]. The present data are different from the data reported by Shoelson and coworkers [20], who did not find a stiffness gradient along the cochlea. When corresponding locations and animal species are compared, the values for the TM point stiffness is similar to the values published [22]. RL driving point stiffness decreased from the pillar heads towards locations above outer hair cell 3. While the stiffness values at the pillar heads are similar to the stiffness measured at the basilar membrane, they are approximately 10 times the stiffness of the tectorial membrane. Conversely, when the stiffness is measured above the outer hair cell, stiffness values drop below the stiffness values measured at the tectorial membrane. Recently, Scherer and Gummer [19] reported mechanical impedance measurements of the organ of Corti. They measured the impedance of the reticular lamina at several radial locations. While the stiffness at the pillar heads (above the tunnel of Corti) was largest, stiffness above outer hair cell 1 and the inner hair cell was similar and decreased towards the third row of outer hair cells. Their low frequency stiffness values are similar to the stiffness values measured for the reticular lamina in the present experiments. In this paper, we also tested the hypothesis that the stiffness changes from the pillar heads towards the outer hair cell 3 due to the fact that the RL behaves like a rigid lever with its pivot point at the pillar heads. It could be shown that indeed, the reticular lamina behaves like a beam and that this "beam" extends towards the inner hair cells. In other words, when the reticular lamina is "pulled" towards the basilar membrane by the action of outer hair cells, the inner hair cell will move upwards at the same time. Thus, outer hair cells would be able to control the inner hair cell stereocilia position relative to the TM and a connect-disconnect to the stereocilia would be possible. A model that describes attaching and detaching of the inner hair cell stereocilia bundle from Hensen's stripe throughout a stimulus cycle has been proposed by Crane [2;3]. While stiffness of the organ of Corti changes in the radial direction, it also changes from the reticular lamina towards the basilar membrane being most compliant across the lower two thirds of the Deiters' cells. It is important to note that the hemicochlea is cut open, and therefore the resting potential of the outer hair

75 cells is close to zero. He and Dallos [13] showed that outer hair cells decrease stiffness by up to 40% with increasing depolarization. At this point it only can be speculated that outer hair cell stiffness changes might be involved in matching the stiffness between the tectorial membrane and rotating wedge as the rotating section below the tectorial membrane [17]. Acknowledgments This research is supported by a grant from the NSF (IBN-0077476 and IBN0415901). References 1. Abnet, C.C., Freeman, D.M., 2000. Deformations of the isolated mouse tectorial membrane produced by oscillatory forces. Hear Res 144, 29-46. 2. Crane, H.D., 1982 Jul. IHC-TM connect-disconnect and efferent control V. J Acoust Soc Am 72, 93-101. 3. Crane, H.D., 1982 May. IHC-TM connect-disconnect in relation to sensitization and masking of a HF-tone burst by a LF tone. IV. J Acoust Soc Am 71, 1183-93. 4. Dong, W., Cooper, N.P., 2002. Three dimensional, in vivo measurements of the tectorial membrane's vibratory responses to sound. , Assoc Res Otolaryngol, Vol. 25. pp. 905. 5. Edge, R.M., Evans, B.N., Pearce, M., Richter, C.P., Hu, X., Dallos, P., 1998. Morphology of the unfixed cochlea. Hear Res 124, 1-16. 6. Emadi, G., Dallos, P., 2000. Point stiffness in the gerbil hemicochlea. Abtsr. Assoc. Res. Otolaryngol. 23, 706. 7. Emadi, G., Richter, C.-P., Dallos, P., 2002. Tectorial membrane stiffness at multiple longitudinal locations, Abstr Assoc Res Otolaryngol, pp. 906. 8. Emadi, G., Richter, C.-P, Dallos, P , 2003. Stiffness of the gerbil basilar membrane: radial and longitudinal variations. J Neurophysiol, in press. 9. Emadi, G, Richter, C.P, Dallos, P , 2004. Stiffness of the gerbil basilar membrane: radial and longitudinal variations. J Neurophysiol 91, 474-88. 10. Freeman, D.M., Masaki, K , McAllister, A.R., Wei, J.L., Weiss, T.F, 2003. Static material properties of the tectorial membrane: a summary. Hear Res 180, 11-27. 11. Freeman, D.M, Abnet, C.C, Hemmert, W , Tsai, B.S., Weiss, T.F, 2003. Dynamic material properties of the tectorial membrane: a summary. Hear Res 180, 1-10.

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12. Freeman, D.M., Abnet, C.C., Hemmert, W., Tsai, B.S, Weiss, T.F., 2003. Dynamic material properies of the tectorial membrane: a summary. Hear Res 180,1-10. 13. He, D.Z., Dallos, P., 1999. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc Natl Acad Sci U S A 96, 8223-8. 14. Hu, X., Evans, B.N., Dallos, P., 1995. Transmission of basilar membrane motion to reticular lamina motion, Abtsr. Assoc. Res. Otolaryngol, pp. 223. 15. Legan, P.K., Lukashkina, V.A., Goodyear, R.J., Kossi, M., Russell, I.J., Richardson, G.P., 2000 Oct. A targeted deletion in alpha-tectorin reveals that the tectorial membrane is required for the gain and timing of cochlear feedback. Neuron 28, 273-85. 16. Lukashkin, A.N., Lukashkina, V.A., Legan, P.K., Richardson, G.P., Russell, I.J., 2003. Role of the tectorial membrane revealed by otoacoustic emissions from wild-type and transgenic Tecta{Delta}ENT/{Delta}ENT mice. J Neurophysiol, (in press). 17. Richter, C.-P., Dallos, P., 2003. Micromechanics in the gerbil hemicochlea. In: Gummer, T., (Ed.), Meeting on cochlear mechanics, Titisee (Germany), 1 ed. 18. Richter, C.P., Evans, B.N., Edge, R., Dallos, P., 1998. Basilar membrane vibration in the gerbil hemicochlea. J Neurophysiol 79, 2255-64. 19. Scherer, M.P., Gummer, A.W., 2004. Impedance analysis of the organ of corti with magnetically actuated probes. Biophys J 87, 1378-91. 20. Schoelson, B., Dimitriadis, E.K., Cai, H., Kachar, B., Chadwick, R.S., 2004. Evidence and implaications of inhomogeneity in tectorial membrane elasticity. Biophysical Journal 87, 2768-2777. 21. von Bekesy, G., 1953. Description of some mechanical properties of the organ of Corti. J Acoust Soc Am 25, 770-781.. 22. Zwislocki, J.J., Cefaratti, L.K., 1989. Tectorial membrane. II: Stiffness measurements in vivo. Hear Res 42, 211-27. 23. Zwislocki, J.J., Chamberlain, S.C., Slepecky, N.B., 1988 Jun. Tectorial membrane. I: Static mechanical properties in vivo. Hear Res 33, 207-22. Comments and Discussion Chadwick: Could you comment on the relationship of your measurements of Young's modulus of the tectorial membrane the determination of the bulk modulus of the tectorial membrane described by Kinu Masaki earlier this morning? Answer: The direct comparison is difficult because the explanation of Kinu Masaki's data is based on a two-layered model, which has a mechanical and an

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electrostatic component. However, tectorial membrane bulk stiffness values are similar when earlier measurements of tectorial membrane bulk stiffness presented by Kinu Masaki and our group are compared. Keep in mind that these earlier measurements have not been corrected for the nonlinear effects of poly ethylene glycol. Gummer: Could you please compare your measured values of stiffness at the upper surface of the tectorial membrane (TM) with those reported by Schoelson et al. (Biophys. J. 87, 2768-2777, 2004) at the lower surface of the TM. Likewise, compare your stiffness values at the RL with those published by Scherer and Gummer (Biophys. J. 87, 1378-1391, 2004). Answer: Our stiffness data are obtained from the upper surface of the tectorial membrane. The objective of the measurements was to determine the tectorial membrane stiffness acting against the rotating wedge described for the vibration of the organ of Corti (Richter and Dallos (2000) in Physiological and Psychological Bases of Auditory Function, 44-50). In other words, the transversal stiffness of the tectorial membrane interacts with the rotating wedge while the radial component is the important stiffness component for outer hair cell stereocilia bundles. It is well possible that the lower surface of the tectorial membrane is stiffer compared to the remaining sections. When compared to Schoelson's et al. data our stiffness values are about 3 times smaller, which indicates that the tectorial membrane is more compliant. Keep also in mind that our data were obtained from gerbil tectorial membranes and Schoelson's et al. data stem from isolated guinea pig tectorial membranes. Differences between animal species may exist. The reticular lamina stiffness values obtained in the hemicochlea of gerbils compare to the values obtained and published by Scherer and Gummer for the guinea pig. Only low frequency data can be compared since our measurement system did not allow for measurements at audio frequencies. Chadwick: Could you comment on the relationship of your measurements of Young's modulus of the tectorial membrane the determination of the bulk modulus of the tectorial membrane described by Kinu Masaki earlier this morning? Answer: The direct comparison is difficult because the explanation of Kinu Masaki's data is based on a two-layered model, which has a mechanical and an electrostatic component. However, tectorial membrane bulk stiffness values are similar when earlier measurements of tectorial membrane bulk stiffness presented by Kinu Masaki and our group are compared. Keep in mind that these earlier measurements have not been corrected for the nonlinear effects of poly ethylene glycol. Gummer: Could you please compare your measured values of stiffness at the upper surface of the tectorial membrane (TM) with those reported by Schoelson et al. (Biophys. J. 87, 2768-2777, 2004) at the lower surface of the TM. Likewise, compare your stiffness values at the RL with those published by Scherer and Gummer (Biophys. J. 87, 1378-1391, 2004).

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Answer: Our stiffness data are obtained from the upper surface of the tectorial membrane. The objective of the measurements was to determine the tectorial membrane stiffness acting against the rotating wedge described for the vibration of the organ of Corti (Richter and Dallos (2000) in Physiological and Psychological Bases of Auditory Function, 44-50). In other words, the transversal stiffness of the tectorial membrane interacts with the rotating wedge while the radial component is the important stiffness component for outer hair cell stereocilia bundles. It is well possible that the lower surface of the tectorial membrane is stiffer compared to the remaining sections. When compared to Schoelson's et al. data our stiffness values are about 3 times smaller, which indicates that the tectorial membrane is more compliant. Keep also in mind that our data were obtained from gerbil tectorial membranes and Schoelson's et al. data stem from isolated guinea pig tectorial membranes. Differences between animal species may exist. The reticular lamina stiffness values obtained in the hemicochlea of gerbils compare to the values obtained and published by Scherer and Gummer for the guinea pig. Only low frequency data can be compared since our measurement system did not allow for measurements at audio frequencies

BACKWARD PROPAGATION OF OTOACOUSTIC EMISSION IN THE COCHLEA T. REN"'*, W.X. H E a c , A.L. NUTTALL"' r f "Oregon Hearing Research Center, Oregon Health & Science University, 3181 SW Sam Jackson Park Road, NRC04, Portland, Oregon 97239-3098, USA; bThe School of Medicine, Xian Jiaotong University, 76 West Yanta Road, Xian, Shaanxi 710061, P.R. China; "Department of Otolaryngology, The First Teaching Hospital, Xian Jiaotong University, West Yanta Road, Xian, Shaanxi 710061, P.R. China; dKrege Hearing Research Institute, The University of Michigan, 1301 East Ann St., Ann Arbor, MI 48109-0506, USA E-mail: [email protected]; [email protected]; [email protected] Otoacoustic emissions have been commonly believed to be generated in the cochlea and emitted through backward-traveling waves. A recent study (Ren, 2004), however showed that there is no detectable backward traveling wave and that the stapes vibrates earlier than the basilar membrane (BM) at the emission frequency. These findings indicate that a cochlearfluid compression wave is responsible for backward propagation of the emissions. This study contradicts with a widely accepted view that the delay of the otoacoustic emissions is approximately two times the forward traveling wave delay. In this study, the emission was measured in the ear canal, at the stapes, and at different locations on the BM. It was found that the slope of the phase-frequency curve measured from an apical location is always steeper than that measured from basal locations. Derived from the distance between two measured locations and their phase difference, the propagation velocity demonstrates that the BM vibration at the emission frequency propagates from base to apex through the observed region. Moreover, the emission group delay measured at the stapes is less than twice the traveling wave delay.

1 Introduction Otoacoustic emissions (OAEs) are sound generated by the ear, which can be measured in the external ear canal using a sensitive microphone. Since Kemp [1] demonstrated this phenomena in 1978, it has been intensively studied and widely applied in studying cochlear mechanisms and in diagnosing auditory disorders. It is a common belief that OAEs are generated in the cochlea and propagate backward to the cochlear base, appearing in the ear canal. Regarding to how OAEs the reach the cochlear base, there are two completely different theories: the backward-travelingwave and compression-wave mechanisms. It has been reported that roundtrip delays of cubic distortion product otoacoustic emissions (DPOAEs) are approximately twice as large as the forward delay [2, 3]. This phenomenon has been considered to be solid evidence for the backward-travelling-wave theory and against a cochlear-fluid-compression wave mechanism. This preliminary study aims to study the mechanism of backward propagation of the emission by comparing the roundtrip delay of the emission to the forward delay of the BM vibration and by observing the phase relationship of the BM vibration of cubic DPOAE at different longitudinal locations.

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2 Methods 2.1 Animal preparation and general methods Young and healthy Mongolian gerbils (40-80 g) were used in this study. Animal preparation and surgical approach were the same as in previous studies [4], The left auditory bulla was exposed through a ventral-lateral approach. After the middle ear muscles were cut, a microphone and two earphones were coupled to the ear canal. For measuring BM vibration the round window membrane was removed and a thin glass cover slip placed on the enlarged round window. The laser beam of a heterodyne interferometer was focused on the BM through a 20X microscope objective lens. The voltage output of the laser interferometer is proportional to the velocity of the transverse vibration of the BM. The characteristic frequency (CF) in the middle of the observed field was defined as the frequency with the maximum amplitude in the amplitude transfer function measured at 30 dB SPL. Sensitivity of the ear was monitored by measuring the acoustically-induced compound action potential (CAP) with round-window and neck electrodes. Data presented in Fig. 1 and 2 are collected from one animal and the results in Fig. 3 are from a different animal. 2.2 Signal generation and data acquisition A custom-written Lab View-based program was used to control TDT hardware for signal generation and data acquisition. Tone bursts at fl and f2 with 23 ms duration and 1 ms rise/fall time were generated with a D/A converter. The stimulus levels were controlled using two programmable attenuators. The signals were used to drive two earphones through a dual-channel headphone buffer. A microphone-earphone probe, consisting of two ER-2 earphones and one 10B+ microphone (Etymotic Research, Inc., Elk Grove Village, IL) was coupled into the external ear canal. The microphone signal was digitized and averaged for 10 to 40 times depending on the signal level, and the frequency spectrum of the average signal were obtained. 2.3 Delay measurements Sound pressure in the ear canal, the stapes vibration approximately at the center of the stapes footplate, and the BM vibration at the f2 place were measured as a function of frequency 2fl - f2. The emission frequency was varied by changing fl from 16.8 kHz to 9 kHz in 200 Hz steps with £2 fixed at 17 kHz, so that 2fl-f2 changed from 16.6 kHz to 1.0 kHz in 400 Hz steps. Magnitudes and phases of sound pressure and vibration at frequencies fl, f2, and 2fl-f2 were measured at different 2fl-f2 frequencies. The delay from the speakers to the stapes, the total emission delay, and the forward delay of the BM vibration were derived from the fl phase transfer function of the stapes vibration, the phase transfer function of sound pressure in the ear canal, and BM vibration at the f2 site. The delays were calculated based on the phase slopes according to the equation: D=A^/Aa>, where D is the

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group delay in seconds and A is the phase difference in radians over the angular frequency change Aco. 2.4 Basilar membrane vibration of emissions at different longitudinal locations For determining the propagation direction of emissions along the BM, the magnitude and phase transfer functions of the basilar membrane vibration at 2fl-f2 were measured at two longitudinal locations basal to the f2 site. The distance between the two measured locations was calculated based on the readout of the xyzpositioning controller. The propagation direction was determined by the phase relationship of two locations, i.e., from phase-lead location to phase-lag location. 3 Results 3.1 Group delay of the emission in the ear canal Magnitude and phase as functions of 2fl-f2 primary tone levels frequency. The phase

of the cubic DPOAE measured in the ear canal are presented or f2/fl ratio in Fig. 1. Data was collected at equal fl and f2 of 70 dB SPL. The emission magnitude varies with the decreases with the frequency and its slope presents a delay of

462 us. f2/f1 ratio 1.6 1.4

4 8 12 16x10' 2f1-f2 frequency (Hz)

f2/f1 ratio 1.6 1.4

Figure 1. Magnitude (A) and phase (B) of sound pressure at 2fl-f2 frequency recorded in the ear canal. The slope of the phasefrequency curve presents a delay time of 462 us.

4 8 12 16x10 2f1-f2 frequency (Hz)

3.2 Group delays of the emission andfl tone at the stapes Magnitude and phase of stapes vibration at fl, and 2fl-f2 were measured as functions of the frequencies and are presented in Fig. 2. The magnitude of fl (square in Fig. 2 A) changes slightly with the frequency while the magnitude of 2flf2 (triangles) shows a significant change with a peak near 12 kHz. Phases measured at both fl and 2fl-f2 decrease with the frequency but with different rates. The slopes of the phase curves show a delay time of 366 (is for 2fl-f2 and 210 us for fl. The corrected phase-frequency curve for 2fl-f2 was obtained by removing 210 us fl delay from the 2fl-f2 delay. The slope of the corrected phase curve in Fig. 2 C shows the emission roundtrip delay in the cochlea is very short (156 us). In order to study the relationship between the forward delay and the roundtrip delay, the forward delay was obtained from a phase transfer function of the BM vibration at

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the f2 (17 kHz) location. As shown in Fig. 2 D, the forward delay (solid line) increases with the frequency. At f2 (17 kHz), the group delay is 251 us, which is significantly greater than round trip delay of the emission (156 um) (Fig. 2 C). 3.3 Propagation direction of the emission along the basilar membrane In order to determine the propagation direction of the emission along the BM, the phase relationship of the BM vibration at the emission frequency at different longitudinal locations was observed. The magnitude and phase of BM vibration were measured as a function of 2fl-f2 frequency at two longitudinal locations, which are basal to the f2 sites and 283 um apart. As shown in Fig. 3 A, the magnitudes at both locations increase with the frequency. The frequency of this increase is higher for the basal location than that for the apical location. The phase decreases with the frequency for both locations but the decrease rate for the apical site is greater than that for the basal site (B). Phase difference between basal and apical sites is also presented in B (cross). The slope of the phase difference indicates a delay of 31 us. Data in Fig. 3 B indicate that the emission arrives the basal site earlier than the apical site, demonstrating a forward traveling wave. 12

f1 frequency (Hz) 13 14 15 16x103

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Figure 2. Magnitude (A) and phase (B) of stapes vibration at frequency of fl (squares) and 2fl-f2 (triangles), the roundtrip delay of the emission (C), and the relationship between the roundtrip and forward delays (D). Slopes of the phase curves (B) show a delay time of 366 u,s for 2fl-f2 and 210 us for fl. The slope of the phase curve in Panel C shows 156 us roundtrip delay of the emission in the cochlea. The forward delay at 17 kHz (251 us) is significantly greater than the round trip delay (156 um).

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4 Discussion The backward-traveling-wave theory was developed by Kemp in 1986 [5] mainly based on the fact that the cochlea-generated sound can be measured in the ear canal [1] and a mathematical demonstration that the cochlear travelling wave can travel in

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both directions [6]. This theory has been overwhelmingly accepted and extensively studied Since 1986 [3, 8-10]. Cochlear fluid compression-wave theory was developed from a sensory outerhair-cell swelling model described by Wilson [11], in which hair cell volume changes displace the stapes footplate and result in the emission. The cochlear fluid compression theory was further developed by Narayan, et al. and Avan et al. [12, 13] by measuring BM vibration and the pressure in the cochlea. In a recent study, Ren [14] measured spatial patterns of the BM vibration at emission frequency and found a normal forward travelling wave and no sign of a backward travelling wave. This finding indicates that the cochlea emits sounds through its fluid as compression wave. The cochlear fluid compression theory was systematically reviewed by Ruggero recently [15]. f2/f1 ratio 1.4

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Figure 3. Magnitude (A) and phase (B) of BM vibration at frequency 2flf2 at two longitudinal locations basal to the f2 site. The phase-decrease rate for the apical site is greater than that for the basal site. The slope of the phase difference indicates a delay of 31 us.

4 8 12 16x10 2f1-f2 frequency (Hz)

However, the cochlear-fluid compression-wave mechanism cannot account for reports that the roundtrip delay of the emission is approximately two times as great as the forward delay. Since this finding is based on the acoustical measurement in the ear canal, the external- and middle-ear delays have unavoidably contaminated the roundtrip delay measurement. Thus, the group delays of the cubic DPOAE was measured in the ear canal, at the stapes, and on the BM at £2 location in this study. It was found that the emission delay measured in the external ear canal (Fig. IB) is significantly greater than the forward propagation delay (Fig. 2 D), which somewhat agrees with the previous findings that the roundtrip delay of the emission is approximately twice as great as the forward delay. Significantly, the cochlear roundtrip delay of the emission measured at the stapes (Fig. 2 C) is smaller than the forward delay (Fig. 2 D). This result indicates that the emission is likely generated at a cochlear location basal to f2 site, and the backward propagation delay is extremely small. This result supports the cochlear-fluid-compression-wave model and not the backward-travelling-wave theory. Phase data of BM vibration at two different longitudinal locations (Fig. 3 B) demonstrate that the vibration at emission frequency arrives at the basal location earlier than the apical location, indicating a forward travelling wave.

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Acknowledgments We thank E.V. Porsov for writing software, and S. Matthews for technical and editorial help. Supported by the NIH-NIDCD, and the National Center for Rehabilitative Auditory Research (NCRAR), Portland Veteran's Administration Medical Center. References 1. Kemp, D.T., 1978. Stimulated acoustic emissions from within the human auditory system. J Acoust Soc Am. 64(5): 1386-91. 2. Kimberley, B.P., Brown, D.K., Eggermont, J.J., 1993. Measuring human cochlear traveling wave delay using distortion product emission phase responses. J Acoust Soc Am. 94(3 Pt 1): 1343-50. 3. Schoonhoven, R., Prijs, V.F., Schneider, S., 2001. DPOAE group delays versus electrophysiological measures of cochlear delay in normal human ears. J Acoust Soc Am. 109(4): 1503-12. 4. Ren, T., 2002. Longitudinal pattern of basilar membrane vibration in the sensitive cochlea. Proc Natl Acad Sci U S A . 99(26): 17101-6. 5. Kemp, D.T., 1986. Otoacoustic emissions, travelling waves and cochlear mechanisms. Hear Res. 22: 95-104. 6. de Boer, E., 1983. Wave reflection in passive and active cochlear models. Mechanics of Hearing, ed. E. de Boer and M.A. Viergever. The Hague: Martinus Nijhoff. 135-142. 7. von Bekesy, G., 1960. Experiments in Hearing. New York: McGraw-Hill. 8. Shera, C.A., Guinan, J.J. Jr., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: a taxonomy for mammalian OAEs. J Acoust Soc Am. 105(2 Pt 1): 782-98. 9. Bowman, D.M., et al., 1998. Estimating cochlear filter response properties from distortion product otoacoustic emission (DPOAE) phase delay measurements in normal hearing human adults. Hear Res. 119(1-2): 14-26. 10. Knight, R.D. Kemp, D.T., 2001. Wave and place fixed DPOAE maps of the human ear. J Acoust Soc Am. 109(4): 1513-25. 11. Wilson, J.P., 1980. Model for cochlear echoes and tinnitus based on an observed electrical correlate. Hear Res. 2(3-4): 527-32. 12. Narayan, S.S., Recio, A., Ruggero, M.A., 1998. Cubic distortion products at the basilar membrane and in the ear canal of chinchillas, in Twenty-first Midwinter Research Meeting of ARO. Abstract 723. St. Petersburg Beach, Florida.

85 13. Avan, P., et al, 1998. Direct evidence of cubic difference tone propagation by intracochlear acoustic pressure measurements in the guinea-pig. Eur J Neurosci. 10(5): 1764-70. 14. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat Neurosci. 7(4): 333-4. 15. Ruggero, M.A., 2004. Comparison of group delays of 2fl-f2 distortion product otoacoustic emissions and cochlear travel times. 5(4): 143-147. Comments and Discussion Withnell: In measuring the 2fl-f2 OAE delay, it appears that you calculated the phase gradient of the response. The phase gradient is confounded by a mixing of mechanisms. Can you clarify how your measure of group delay is a valid measure of cochlear travel time? I was also unclear about your correction for stimulus delay for the OAE (so that you could reference it to the stapes) - did you reference the stimulus delay to the place of measurement i.e., the microphone in the ear canal? If not, why not (and could you explain what you did)? Answer: Although the 2fl-f2 OAE delay was calculated based on the phase gradient in this study, it was not used to measure cochlear travel time because it is a mixture of the external-, middle-, and inner ear delays. The cochlear round-trip delay of the 2fl-f2 was obtained by subtracting the fl delay measured at the stapes from the 2flf2 delay at the same location. Because the cochlear delay of the OAE was measured based on stapes vibration, there was no need to reference the stimulus delay to the microphone in the ear canal.

MEDIAL OLIVOCOCHLEAR EFFERENT EFFECTS ON BASILAR MEMBRANE RESPONSES TO SOUND

N.P. COOPER 1 AND J.J. GUINAN JR.2. ' MacKay Institute of Communication and Neuroscience., Keele University, Keele, Staffordshire, ST5 5BG, England E-mail: [email protected] Eaton Peabody Laboratory, Mass. Eye & Ear Infirmary, Boston, USA. E-mail: jjg@epl. meei. harvard, edu Sound-evoked responses of the basilar membrane are shown to be influenced by electrical stimulation of the medial olivocochlear efferent system. Both fast (T~50ms) and slow (x~10s) effects can be observed in the basal turn of the cochlea. Differences between the fast and slow effects imply that outer hair cells can influence basilar membrane motion in at least two ways. Differences between the effects observed on the basilar membrane and in the auditory nerve (as assayed using compound action potential recordings in the same cochleae) imply that outer hair cells influence more than just basilar membrane motion.

1 Introduction Medial olivocochlear (MOC) efferent neurones modulate the acoustic sensitivity of the cochlea via synaptic contacts with outer hair cells (OHCs) (for review see [1]). MOC-evoked inhibition of auditory nerve (AN) responses is accompanied by mechanical inhibition at the level of the basilar membrane (BM) [2-6]. It is not known exactly how much of the neural inhibition is mediated mechanically, however. The present study seeks to investigate this issue further. Specifically, we seek to verify (i) whether both the fast and slow effects of MOC stimulation on AN responses [7] have mechanical bases (as shown in [6]), and (ii) whether the fast effects on BM motion are sufficient to explain the AN inhibition [8] which is seen at both low and high sound pressure levels (as shown in [5]). 2 Methods Sound-evoked vibrations of the BM were recorded using a laser interferometer in deeply anaesthetised guinea-pigs and chinchillas (see [9] for details). Electrical stimulation of the MOC efferents was paired with acoustic stimulation of the ear in such a way that the fast and slow effects of the efferent stimulation could be distinguished readily (cf. Fig. 2). Efferent stimuli (100-300 ms long trains of 300 us-wide current pulses at intervals of 3.3-5 ms, presented once every 330-1500 ms) were delivered to the floor of the fourth ventricle using a bipolar electrode (see [8] for details). Ossicular vibration measurements confirmed that the

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87 efferent shocks

300

Time (ms)

Figure 1. Efferent inhibition of BM responses to low-level CF tones. Experiment K3096 (GP, CF=18kHz, 30dBSPL CF tones presented for 600 ms every second. Responses averaged 450x and bandpass filtered from 14-22 kHz. Response phases analyzed over 2 ms windows).

effects of the electrical stimuli originated in the cochlea, as opposed to the middleear. Compound action potential (CAP) recordings were used to assess the the cochlea's acoustic sensitivity both with and without MOC efferent stimulation. 3 Results 3.1 Efferent stimulation has both fast and slow effects on basilar membrane responses to sound BM responses to characteristic frequency (CF) tones were inhibited over two distinct time-scales by efferent stimulation. Each burst of efferent shocks produced a fast effect that began within 5-10 ms of the first shock-pulse, as shown in Figure 1. The fast inhibition developed towards a steady-state with an intensity-dependent time constant of -30-100 ms. The BM recovered from the fast inhibition with a slightly shorter time constant (typically -30 ms), beginning within -10 ms of the last shock-pulse in each train (cf. Fig. 1). A second, slower form of inhibition became evident when intermittent efferent stimulation (shock-burst duty cycles of <30%) was continued for many seconds, as shown in Figure 2. The slow inhibition developed over a time course of ~1 minute, but then faded away (over a similar time period) whether or not the efferent stimulation was continued. Due to the time constraints of each experiment, systematic investigations of the slow effect were difficult to perform. Nonetheless, by combining data from separate experiments, and by presenting multiple tones in an interleaved fashion within each experiment (cf. Fig. 2A), slow effects were found to be: (i) strongest (providing up to 13 dB of inhibition) for low-level near-CF tones; (ii) negligible at frequencies well (e.g. 1-2 octaves) below CF; and (iii) small in amplitude, but with significant phase-changes, for high-level near-CF tones (cf. *** in Fig. 2B). The time constant of the fast effect increased slightly as the slow effects developed in a few experiments, suggesting that the fast and slow effects are not completely 'separate' events.

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Figure 2. Fast and slow effects of efferent stimulation on BM responses to CF tones. Repeated presentations of a series of four 50-ms long CF tone bursts were made over a 6 minute period. Efferent stimuli were paired with every second set of four tones occuring between 70 s and 210 s into this period (shaded region in B). "Fast effects" (B, left) were evidenced by response changes across matching tones within each pair of trials (e.g. compare left and right trials in A). "Slow effects" (B, right) were evidenced by changes in the responses to the 'before shocks' or 'no shocks' trials across trials. Experiment K3096 (GP, CF = 18kHz, responses averaged 4x for each trial and bandpass filtered from 14-22 kHz. Stimulus/Shock repetition period = 1500 ms).

As far as cochlear mechanics is concerned, perhaps the most important observations relating to the fast and slow effects of efferent stimulation are (i) that they seem to operate additively (although they are not completely independent), and (ii) that they can cause oppositely-directed phase-changes in the responses to identical stimuli: for example, fast effects can cause phase-leads for low-level nearCF tones, while slow effects cause phase-lags (cf. * and ** in Fig. 2B). These findings imply that outer hair cells affect cochlear amplification in at least two functionally distinct ways.

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Figure 3. Fast effects of efferent stimulation on BM input-output functions. Top row: IO functions for tones just below, at, and just above the BM's CF, as evaluated immediately before (solid symbols) and during (open symbols) each burst of efferent stimulation (i.e. without and with efferent stimulation, respectively). Middle row: Corresponding phase-data. Bottom row: Efferent evoked fast effects expressed as level shifts (left), gain changes (center) and phase changes (right). Experiment K3096 (GP, CF = 18 kHz, responses averaged 16x at each level. Stimulus/Shock repetition period = 330 ms).

3.2 Fast effects depend on soundfrequency and intensity The fast effects of MOC stimulation were readily separated from any (simultaneously present) slow effects by comparing the "during shocks" and "before shocks" portions of the BM's response to individual tones (e.g., as illustrated by the ** and * symbols in Fig. 1). The fast effects were strongest for low-level, near-CF tones, as illustrated in Figures 3 and 4. The magnitude of the MOC-evoked inhibition was quantified as either a level-shift, to compare with the effects seen in the AN and CAP, or a gain change, to compare with other forms of mechanical suppression (e.g. two-tone suppression - not illustrated, but much faster-acting and much stronger than the MOC-evoked inhibition). As BM vibrations are compressively nonlinear for near-CF tones (cf. top row of Fig. 3), these two metrics can diverge strongly, especially for responses to high-level, just-above-CF tones (e.g. the 20 kHz data in Fig. 3). For CF and below-CF tones, however, the levelshifts and gain-changes show similar trends. Most importanly, both metrics show that the mechanical inhibition decreases systematically with increasing sound level (unlike the situation in some auditory nerve fibers, cf. [8]).

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Figure 5. Fast effects of efferent stimulation on neural responses. A: CAP input-output functions for 18 kHz tones with and without MOC stimulation. Inset: CAPs observed before, during and after the "with shocks" trials at 40 dB SPL. B: MOC-evoked CAP levelshifts (solid symbols, derived from A) compared with BM level-shifts observed in the same experiment (open symbols, from Fig. 3).

The phase changes associated with the fast effects varied systematically with the parameters of the acoustic stimulus, as shown in Figure 3 (for guinea-pigs). The phase behaviour also varied with species: fast inhibition of CF tones in guinea-pigs was accompanied by phase-leads, while that in chinchillas was accompanied by phase-lags at low levels and phase-leads at high levels (this is similar to the situation for below-CF tones in guinea-pigs). 3.3 Comparisons with MOC-evoked inhibition of auditory nerve activity MOC-evoked inhibition of AN responses was assayed using CAP recordings, as illustrated in Figure 5. CAP input-output functions with and without MOC stimulation (Fig. 5A) were measured both before and after the BM recordings from the same cochleae. The MOC-evoked level-shifts evaluated from the CAP recordings were consistently larger than those observed on the BM, but varied in much the same way with sound level.

91 4 Discussion Previous studies of MOC-evoked fast and slow effects on cochlear mechanics [6], and of the effects of acetylcholine on OHC somatic stiffness and motility [10], have implied that fast and slow effects might be caused by OHC-controlled changes in the cochlear partition's damping and stiffness, respectively. Our latest observations, showing that even the slow effects can produce phase changes in different directions for high- and low-level CF tones (at the same time, cf. Fig. 2B), suggest that the situation may be more complex than this. Nonetheless, we can still conclude that OHCs both can and do influence the BM's motion in at least two ways [6]. Our finding that the MOC-evoked inhibition observed on the BM is smaller than that observed in the AN (cf. Fig. 5B) must be considered as preliminary, and is subject to several technical constraints. However, this finding suggests that the OHCs can influence more than just the macro-mechanics of the cochlea. Activation of the MOC efferent system is known to increase the electrical conductance of OHCs and to reduce the endocochlear potential, which in turn reduces the receptor potentials of the inner hair cells and the drive on the AN (cf. [1] for review). The efferents may also reduce the drive to the inner hair cells in a micro-mechanical manner (in addition to having macro-mechanical and electrical effects), as discussed elsewhere (e.g., Guinan et al., this volume). Acknowledgments Supported by grants from the NIH and the Royal Society. References 1. Guinan, J.J., Jr., 1996. Physiology of olivocochlear efferents, in The Cochlea, P. Dallos, A. Popper, and R. Fay, Editors. Springer: New York. p. 435-502. 2. Murugasu, E. Russell, I.J., 1996. The effect of efferent stimulation on basilar membrane displacement in the basal turn of the guinea pig cochlea. J Neuroscil. 6(1): p. 325-332. 3. Russell, I.J., Murugasu, E. 1996. The effect of efferent stimulation and acetylcholine perfusion on basilar membrane displacement in the basal turn of the guinea pig cochlea, in Diversity in Auditory Mechanics, E.R. Lewis, et al., Editors. World Scientific: Singapore, p. 361-367. 4. Dolan, D.F., Guo, M.H., Nuttall, A.L., 1997. Frequency-dependent enhancement of basilar membrane velocity during olivocochlear bundle stimulation. J Acoust Soc Am. 102(6): p. 3587-3596. 5. Russell, I.J., Murugasu, E., 1997. Medial efferent inhibition suppresses basilar membrane responses to near characteristic frequency tones of moderate to high intensities. J Acoust Soc Am. 102(3): p. 1734-1738.

92

6. Cooper, N.P., Guinan, J.J. Jr., 2003. Separate mechanical processes underlie fast and slow effects of medial olivocochlear efferent activity. J Physiol (Lond). 548(1): p. 307-312. 7. Sridhar, T.S., et al., 1995. A novel cholinergic "slow effect" of efferent stimulation on cochlear potentials in the guinea pig. J Neurosci. 15(5 Pt 1): p. 3667-3678. 8. Guinan, J.J. Jr., Stankovic, K.M., 1996. Medial efferent inhibition produces the largest equivalent attenuations at moderate to high sound levels in cat auditory-nerve fibers. J Acoust Soc Am. 100(3): p. 1680-1690. 9. Cooper, N.P., 1999. An improved heterodyne laser interferometer for use in studies of cochlear mechanics. J Neurosci Meth. 88(1): p. 93-102. 10. Dallos, P., et al., 1997. Acetylcholine, outer hair cell electromotility, and the cochlear amplifier. J Neurosci. 17(6): p. 2212-2226.

MODULATION PATTERNS AND HYSTERESIS: PROBING COCHLEAR DYNAMICS WITH A BIAS TONE L. BIAN AND M. E. CHERTOFF Dept. of Hearing & Speech, Univ. of Kansas Medical Center, 3901 Rainbow Blvd., Kansas City, KS 66160, USA E-mail: [email protected] Nonlinearity in cochlear transduction is responsible for the amplification and compression in normal hearing. Distortion products generated from cochlear nonlinearity can be modulated with a bias tone, and the modulation patterns resemble the derivatives of the sigmoid-shaped transducer function. The resting position and inflection point of the cochlear transducer with optimal gain were indicated by quasi-static modulation patterns of even-order distortions. With a high-level bias tone, temporal modulation patterns revealed the dynamic behavior of cochlear transducer. Within one period of the bias tone, two typical modulation patterns formed a hysteresis loop. In force-displacement relation, the counterclockwise traversal of hysteresis represents energy gain. These results suggest that the nonlinearity of cochlear dynamics presents in four aspects: compression, suppression, distortion, and hysteresis.

1 Introduction Normal inner ear maintains high sensitivity and frequency selectivity over a large dynamic range. This is achieved through amplification for low level sounds and compression at high levels. Experimentally, the cochlea demonstrates two phenomena: two-tone suppression and distortion products [1]. Two-tone suppression refers to the reduction of neural or mechanical responses at the characteristic frequency (CF) by presenting a second tone away from the CF. Distortion products (DPs) are frequency components in cochlear responses related to the intermodulations of two pure tones (fl, f2, fl
93

94 Figure 1. Illustration of lowfrequency biasing. A: a sigmoidshaped cochlear FTr- B: input: bias tone + two tone signal. Dotted arrow indicates the initial operating point (OP) shift. C: DPs in the output. The modulated DP magnitudes, £2-fl, 2fl-f2, and 3fl-2f2 resemble the absolute values of the second, third, and fifth derivatives of the Frn respectively.

transducer function (FTr) can be quantitatively estimated with a low-frequency biasing technique [6-8]. Here, we demonstrate that low-frequency modulation of various DPOAEs can provide fruitful information about the nonlinear and dynamical processes of the inner ear. 2 Methods Theoretical basis of using low-frequency biasing to estimate cochlear FTr is that the inner ear responses at low levels are proportional to their appropriate derivatives of the cochlear FTr [6,8]. As illustrated in Fig. 1 (A-B), the operating point (OP) of the probe signal on the FTr can be systemically varied by a bias tone. The transfer characteristics at different OPs modulate the responses such that the DP component f2-fl magnitude resembles the absolute value of the second, 2fl-f2 the third, and 3fl-2f2 the fifth derivative of the FTr (Fig. 1C). Mongolian gerbils were anesthetized with ketamine/xylazine (100/2 mg/kg) and the ear-canal acoustics (Fig. 2) were recorded while presenting a two-tone signal and a low-frequency bias tone. The primary tones were presented by two earphones (Etymotic Research, ER-2A) that were coupled to the ports on a probe microphone (ER-10B) inserted in the ear canal. The bias tone from a subwoofer (Boston Acoustics) was guided to the ear canal by a silicon tube. Two tones: 3968/5120 Hz, £2/fl = 1.28; L1=L2= 50 - 70 dB SPL, in 5-dB steps. Bias tones: 25 Hz; 0 - 2 0 peak Pa; duration: 250 ms, with a flat tail of 40 ms. Data were analyzed in MATLAB to extract DPOAEs using two methods: Fixed-window: Segments at the peaks and troughs of the bias tones with multiple levels were fast Fourier transformed (FFT) and DPs obtained (Fig. 2A). Moving-window: A 512-point FFT window was shifted along the signal to obtain temporal DP magnitudes (Fig. 2B). The original signal was resampled by the center of the window to yield the instantaneous bias tone pressure.

95 Representatives of two DP types were examined: odd-order: 2fl-f2 (2816 Hz) and 3fl-2f2 (1664 Hz); even-DPs: f2-fl (1152 Hz) and fl+f2 (9088 Hz).

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Time (ms) Figure 2. Acoustic signals (two-tone + bias tone). A: Fixed-windows: sections at the peaks and troughs of multiple bias tones were analyzed. B: Moving-window: an FFT window was shifted along the waveform. Data between the vertical lines with stable bias tone amplitudes was used.

3 Results 3.1 Quasi-static modulation patterns Since the DPs obtained with the fixed-window reflect the cochlear nonlinearity at a certain moment in time, the modulation pattern represents a static change in cochlear nonlinearity. The quasi-static modulation patterns of the odd- and evenorder DPOAEs demonstrated opposite behaviors (Fig. 3). Odd-DPs showed peaks near 0 Pa bias level where the even-DPs were minimal. Biasing towards either direction suppressed the odd-DPs and enhanced even-DPs. Compared to Fig. 1C, resemblance of typical modulation patterns to the corresponding absolute derivatives of cochlear FTr is evident. The deep notch of even-DPs represents the inflection point (IP) of the FTr, where the transducer gain is optimal. This suggests that the resting position of the cochlear transducer, indicated by the DPs without biasing (0 Pa), is off-center. The asymmetrically located cochlear transducer OP may represent an efferent regulation so that the gain is less optimal at rest. With sound stimulation, the FTr could move its IP to adjust the sensitivity. For example, moving of IP closer to the OP at 0 Pa would result in sensitization since the transducer operates with maximal gain; in contrast, desensitization occurs when the IP shifts away from the resting position. However, odd-DPs are not sensitive to the adjustments of transducer IP (Fig. 3).

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3.2 Temporal modulation patterns Time waveforms of DPOAEs were also obtained by a narrowband filters (zerophase Butterworth, bandwidth: 300 Hz) centered at the DP frequencies (Fig. 4). The envelopes of the waveforms matched with the DP magnitudes extracted from the moving-window FFT (thicker lines). Thus, no phase- or time-delay, nor modification in magnitudes was introduced by the moving-window method. In time domain, DP magnitudes were modulated by the presence of the bias tone (Fig. 4). At the tail portions of the waveforms with no biasing, the DP magnitudes were constant with odd-order DPs being greater and even-DPs smaller. Compared to the tails, the odd- and even-DPs showed either periodic suppression or enhancement depending on the phase of the bias tone. For odd-DPs, the suppressions occurred at the peaks and troughs, with greater effects at the peaks, i.e., biasing towards scala tympani (ST). For even-DPs, biasing towards either direction produced en-hancements. At zero-crossings of the bias tone, deep notches presented in the even-DP waveforms, whereas odd-DPs showed peaks. For each half biasing cycle, the modulated DP envelopes are similar to their corresponding absolute derivatives of the FTr (Fig. 1C). 3.3 Dynamic modulation patterns and hysteresis Since basilar membrane (BM) displacement at the cochlear base is in-phase with low-frequency stimuli [1,9], plotting DP magnitude as a function of the bias pressure can reveal a dynamical relation between the DPs and BM displacement. Within one biasing period, two typical modulation patterns similar to their related FTr derivatives were observed (Fig. 5). In relation to bias pressure, the two modulation patterns separated from each other forming a loop. For increasing bias

97 pressure or loading of cochlear transducer, the pattern shifted to positive sound pressure or towards ST; whereas unloading led to negative direction or towards scala vestibuli (SV). This dynamic modulation with loop presented for all the oddand even-DPs in a similar manner regardless of shapes.

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Time (ms) Figure 4. Temporal modulation patterns. Envelopes of the filtered DPs are from the moving-window FFT. Compared to the tails, odd-DPs are suppressed and even-DPs are enhanced by the bias tone (bottom) on a per-cycle basis. Arrows indicate displacement towards ST and SV. BP: bias pressure.

Since DPOAEs are pressures generated from the cochlear transducer, the FTr that underlies the dynamic modulation patterns with regard to BM displacement is a "stress-strain" relation. Presence of two modulation patterns in one biasing cycle indicates that there are two FTr curves constituting a hysteresis loop and the traversal of the hysteresis is counterclockwise (Fig. 6A). 4 Discussion Low-frequency biasing of DPOAEs demonstrates many aspects of the essential nonlinearity. The modulation patterns of various DPs are quantitatively related to the nonlinear characteristics of the transduction processes in the OHCs. The dynamic modulation of DPOAEs reveals that the cochlear transducer is hysteretic and produces phase-related responses depending on the direction of motion. Contrary to most mechanical systems, the counterclockwise traversal of the hysteresis loop suggests that the cochlear transducer is mechanically active. In a "stress-strain" relation (Fig. 6B), adding a "negative damping" can exert en-

98 Odd DPs

Figure 5. Dynamic modulation patterns of odd- and even-DPs. Above each labeled panel is the temporal modulation pattern over one biasing cycle (dashed line). Grid lines indicate bias tone phase with 90° increaments. The key difference between the odd- and even-DPs is the peak or notch near zerocrossings of the bias tone. Dynamic modulation patterns are maked by the separation of center peaks or notches. The locations of the center peaks or notches depend on the direction of bias pressure change (arrows). Note: these double modulation patterns are continuous, thus forming hysteresis loops. Dynamic modulation patterns of different DPs resemble their related absolute values of the cochlear Fjy derivatives.

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ergy (Egain) thus boosting force production. A model [7,8] using "negative damping" as a feedback component replicated the DPOAE data. Part of the hysteresis can be attributed to the phase- or time-delay in the response. The similar delay for different DPOAEs (Figs. 4-5) is in agreement with the observations of BM two-tone suppression at the CF place [1,3,9]. This suggests that the nonlinearity responsible for the force production within the cochlear transducer is time-dependant. Perhaps, adjustment of transducer gain from feedback of the OHC soma or adaptation of the stereocilia all require a finite activation time [10]. However, sound propagation time to the f2 cochlear place that contributes to DPOAE delay [11] needs to be excluded for accurate estimates of the hysteresis. In summary, active mechanical hysteresis, an additional nonlinear Negative D a m p i n g

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99 property of the auditory periphery is observed noninvasively from low-frequency biasing of DPOAEs. Acknowledgments Supported by a grant (R03DC006165) from NIDCD/NIH. References 1. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea. Physiol. Rev. 81, 1305-1352. 2. Eguiluz, V.W., Ospeck M. Choe, Y., Hudspeth, A.J., Magnasco, M.O., 2000. Essential nonlinearities in hearing. Phys. Rev. Lett. 84, 5132-5235. 3. Geisler, CD., Nuttall, A.L., 1997. Two-tone suppression of basilar membrane vibrations in the base of the guinea pig cochlea using 'low-side' suppressors. J. Acoust. Soc. Am. 102, 430-440. 4. Patuzzi, R., Sellick, P.M., Johnstone, B.M., 1984. The modulation of the sensitivity of the mammalian cochlea by low frequency tones. III. Basilar membrane motion. Hear. Res. 13, 19-27. 5. Lukashkin, A.N., and Russell, I.J., 1999. Analysis of the f2-fl and 2fl-f2 distortion components generated by the hair cell mechanoelectrical transducer: Dependence on the amplitudes of the primaries and feedback gain. J. Acoust. Soc. Am. 106, 2661-2668. 6. Bian, L., Chertoff, M.E., Miller E., 2002. Deriving a cochlear transducer function from low-frequency modulation of distortion product otoacoustic emissions. J. Acoust. Soc. Am. 112, 198-210. 7. Bian, L., Linhardt, E.E., Chertoff, M.E., 2004. Cochlear hysteresis: Observation with low-frequency modulated distortion product otoacoustic emissions. J. Acoust. Soc. Am. 115, 2159-2172. 8. Bian, L., 2004. Cochlear compression: Effects of low-frequency biasing on quadratic distortion product otoacoustic emission. JASA 116, 3559-3571. 9. Cooper, N.P., 1996. Two-tone suppression in cochlear mechanics. J. Acoust. Soc. Am. 99, 3087-3098. 10. van der Heijden, M., Joris P.X., 2005. The speed of auditory low-side suppression. J. Neurophysiol. 93, 201-209. 11. Ren, T., 2004. Reverse propgation of sound in the gerbil cochlea. Nat. Neurosci. 7, 333-334.

100 Comments and Discussion Siegel: Basilar membrane measurements (i.e., see Rhode's paper in this volume) demonstrate growth at CF that is still compressive at 80 dB SPL. This indicates that the cochlear amplifier still has a significant effect at these levels. Fahey and van der Heijden: In regard to figure 6, the interpretation suggests a negative damping term. How is this possible with the high levels (75 dB SPL) of the primaries? Any cochlear amplification should be gone above ~50 dB SPL. In order to construct Fig. 6a, one must know the timing of the modulation pattern relative to the phase of the bias tone at the site of their interaction at the BM. Sources of delay are: middle ear delays, travel delays both to and from the cochlear interaction site, and possible intrinsic delays of the nonlinear interaction. How do you take these delays into account and how can you disentangle their effect from any hysteresis effect. Answer: 1.) As pointed out by Jon Siegel (referring to Rhode's work in this volume), cochlear BM response is still nonlinear at 80 dB SPL. Cochlear nonlinearity demonstrates at least two aspects: amplification and compression. The former is predominant at lower levels; the latter is significant at higher signal levels. Our DPOAE data showed that the modulation of odd-order DPs are better observed at lower primary levels (50-60 dB SPL), while the even-DPs are more pronounced at higher levels (60-75 dB SPL). Cochlear nonlinearity is also level dependent. To show a more complete view of the behavior of the cochlear transducer, one has to observe cochlear response at low as well as higher input levels. 2.) The measurement is the acoustics in the ear canal, that contains the bias tone, the primary tones, and the DPOAEs. Middle-ear delay is presumably small, both bias tone and DPOAEs could have same amount delay. Backwards travel time can be minimal because the DPOAEs are carried out by compression wave. The only possible delay is the time it takes for cochlear partition at the f2 place to respond to the primary tones. This time delay contains a pure travel time for sound pressure to reach the £2 place and a true response time of the cochlear structure, which is related to the cochlear hysteresis. These two kinds of delay are indistinguishable at this time, but it is definitely a very important future research question that needs to be addressed.

WHAT DO THE OHCS MOVE WITH THEIR ELECTROMOTILITY? M. NOWOTNY and A. W. GUMMER Department Otolaryngology, University Tuebingen, Elfriede-Aulhorn-Strasse 5, 72076 Tuebingen, Germany, E-mail: [email protected] The question of how the somatic electromotility of outer hair cells (OHCs) influences the amplification process in the cochlea is still unanswered. To investigate this, we measured the vibration patterns of the organ of Corti in response to intracochlear electrical stimulation on the reticular lamina (RL), basilar membrane (BM) and the overlying tectorial membrane (TM). Using a laser-Doppler-vibrometer, amplitude and phase responses at altogether 32 different positions from the inner sulcus cells to the Hensen's cells on the RL, BM and upper and lower surfaces of the TM were measured. Low-pass filtered amplitudes were found at all positions. Additionally, a resonance and antiresonance were found in the basal turn on the RL and TM. The BM vibration pattern exhibited a CF-independent resonance in all measured turns. Phase was independent of radial position on the TM but not on the RL and BM. This results in a stimulus-dependent modulation of the width of the subtectorial space. A chloride-channel blocker (9-AC) was used as a control for the influence of the measured electromotility on the organ of Corti vibration. The results suggest that the somatic electromotility of the OHCs is capable of being coupled directly to the stereovilli of the inner hair cells (IHCs).

1 Methods and Results The results derived from an in-situ preparation of 81 pigmented guinea-pig (250500 g) cochleae. The in-vivo characteristic frequency (CF) associated with a given longitudinal position was calculated from the tonotopic map of Tsuji and Liberman [1]. Investigated were the basal turn (CF = 24 kHz), medial turn (CF = 3.0 kHz) and apical turn (CF = 0.8 kHz). The stimulus was a multi-tone signal consisting of 81 frequencies from 480 Hz to 70 kHz, with constant amplitude (0.4 mV per frequency) and random phase. Velocity was measured with a laser Doppler vibrometer (LDV, Polytec OFV 302). The depth resolution was ±1.8 um from the focus plane (at -10 dB), so that optical interference from neighbouring structures was minimal. Velocity data were converted to displacement. A complex vibration pattern of the RL was found. A pivot point was found at the pillar cells between the IHCs and OHCs. In contrast, for frequencies up to at least 6 kHz, TM motion was in phase along its entire lower and upper surfaces (Fig. IB). This leads to counterphasic motion of the RL and TM above the IHCs up to about 6 kHz. The phase difference of 180° between the RL and TM above the IHCs implies squeezing and extension of the subtectorial space caused, respectively, by electromofile contraction and elongation of the OHC. This deformation of the subtectorial space causes radial fluid motion inside this space, which is presumably capable of deflecting the IHC stereocilia.

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Frequency (kHz)

Figure 1. Electrically induced amplitude (A, C) and phase (B, D) of the RL (closed symbols), lower surface of the TM (open symbols) and BM (lines) in the third turn. The arrow indicates the in-vivo CF of the investigated turn. Closed circles = RL at second row of OHC, closed triangles = RL at IHC, open circles = TM lower side above the second row of OHC, open triangles = TM lower surface above the IHC, solid line = BM at the Deiters' cell, dashed line = BM at the outer pillar cell, dash dotted line = BM at the inner pillar cell. GP = guinea pig.

The vibration pattern of the BM, induced by OHC motion, exhibited a resonance at all radial and longitudinal positions, except below the HeC on the pars pectinata in the third turn (Fig. IC). The peak amplitudes were at 11.7 ± 1.4 kHz (n = 18) in the third turn and in the second turn at 18.6 ±1.9 kHz (n = 19). In the first turn, the resonance at the inner pillar cell footplate was at 13.6 ± 2.2 kHz (n = 12) and at the outer pillar cell footplate at 16.6 ± 0.9 kHz (n = 5). At frequencies below this resonance, there was frequently a local minimum in the amplitudes. At in-vivo CF, displacement was up to five times smaller on the BM in the region of the OHCs and IHCs compared with the RL; at the resonance the amplitudes of RL and BM were in a comparable range. The experiments showed that the transversal BM vibration pattern under the influence of OHC somatic electromotility is much smaller than the transversal vibration pattern of the RL and it seems as if OHC-induced fluid motion in the subtectorial space, which will add (vectorially) to the shearing motion between RL and TM to stimulate the IHC stereocilia, is an important consequence of somatic electromechanical transduction. References 1. Tsuji, J., Liberman, M.C., 1997. Intracellular labeling of auditory nerve fibers in guinea pig: central and peripheral projections. J. Comp. Neurol. 381, 188-202.

NOISE IMPROVES PERIPHERAL CODING OF SHORT STIMULI L.K. RIMSKAYA-KORSAKOVA N. N. Andreyev Acoustics Institute, 117036, Shvernika Ul, 4, Moscow, E-mail: [email protected]

Russia

Changes in postspikes excitability of the auditory nerve fibers (ANF) (refractoriness and adaptations) are estimated by responses recovery functions (RF), receiving by the double pulse's method. The method was modified to share RF into stochastic and deterministic components. The simulation shows that the refractoriness has no influence on the fine temporal structure of ANF responses, when the stochastic component exceeds the deterministic one. The conditions appear when stimuli act either in isolation or in noise and when intensity approaches the threshold of the ANF.

1 Introduction and Model Sound's peripheral coding is completed by the auditory nerve fibers (ANF). The coding depends on both synaptic potentials and postspikes excitability (CPE) of ANF. If stimuli are shorter than the ANF recovery process, they should be decoded without losses, because of excitation divergence of the receptor cell of ANFs (the principle of volleys). This study demonstrates the coding has its specific character. CPE are estimated by the responses recovery functions (RF), as dependence of relative amplitudes of the second-pulse response (SPR), P2/P1, on inter-pulse intervals T, using the double pulse's method, where PI, P2 are probabilities of reaction occurrence to the pulses [1,3]. The method was modified [2]. The SPR in the set of ANF can be formed only by two ways. The stochastic way is based upon spontaneous activity. It provides the SPR occurrence in those fibers, which haven't yet reacted to the first pulse. The deterministic way is based upon recovery process. It provides the SPR occurrence in fibers, which have already reacted to the first pulse. The contributions of two ways to SPR estimate the probabilities Ps2 and Pd2, given that SPR occurs under condition of absence or occurrence of the firstpulse response. As P2=Ps2+Pd2, Ps2 and Pd2 are the stochastic and deterministic part of SPR. The stochastic component of the RF, Ps2/Pl, reproduces the synaptic potential properties and the deterministic one, Pd2/Pl, reproduces CPE. Researches have done on a ANF model, the output of which is the sequences of spikes, arisen after compare the model synaptic potential with a threshold function, represented CPE [2]. Stimuli were double pulses with 10 kHz spectrum maximum.

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104 2 Results and Discussion Fig. 1 shows the pulse responses probabilities and the SPR amplitudes depend on T and stimuli intensities. If intensities are near a ANF thresholds (15 dB), P1,P2 are small, but identical at any T. The deterministic component is absent. SPR is formed by the stochastic way. So fibers reproduce the stimuli temporal structure at any T. Probability PI grows up to a maximum and Ps2/Pl grows down to a minimum with intensity increase. At high intensity, P2/P1 are defined by Pd2/Pl, and the temporal structure isn't reproduced. To reproduce the structure, it is necessary to raise the stochastic component, for example, by addition signal with noise. Noise desynchronizes the first pulse responses, it increases the stochastic component, and it also creates conditions for detection of the second pulse. RF achieves 1 at any T. Noise decreases the ANF absolute sensitivity, but increases its differential sensitivity to the temporal structure. For each stimuli level there is a definite noise level when the ANF differential sensitivity grows up. P1 — P 2

P0--

P2/P1—Ps2/P1

Pd2/P1--

P1 — P2

PD--

P2/P1—Ps2/P1

Pd2/P1--

, ?• "L°i | T 5 a °' fo r i n1 i '• i ± Fig 1. Dependences of the probabilities of pulses and noise reactions PI, P2, P0, evaluating in equal time period, and the amplitudes of the second-pulse response P2/P1, Ps2/Pl, Pd2/Pl on the inter-pulse interval T, receiving in the model of the auditory nerve fiber. Parameters are specified stimulus intensitiy and noise level in dB. On abscise: Tin ms, on ordinate: value of probabilities and amplitudes.

The ANF model and real reactions are similar, because of model parameters choice [2]. At high intensities the model and real [1] ANF restore SPR in 30 ms. At threshold intensities the model and real [3] RFs may be equal to 1 at any T. The study shows the fine temporal structure is preserved, when stimuli are acted in isolation or in noise and when intensities are near thresholds of ANF. Supported by the RFBR (grant N° 03-04-48746). References 1. Parham K., Zhao H.B., Kim D.O., 1996. Responses of auditory nerve fibers of the unanesthetized decerebrare cat to click pairs as simulated echoes. J. Neurophysiol. 76, 17-29. 2. Rimskaya-Korsakova L.K., 2005. Sensitivity increasing of stimuli sensor coding by addition of noise. Jour. Optic. Technol. 72, 5 (in press). 3. Siegel J.H., Relkin E.M., 1987. Evidence for presynaptic facilitation in primary cochlear afferent neurons. Hear. Res. 29, 169-177.

PHASE AND AMPLITUDE TRANSFER IN THE APEX OF THE COCHLEA MARCEL VAN DER HEIJDEN AND PHILIP X. JORIS Laboratory of Auditory Neurophysiology, K. U.Leuven, Herestraat 49-bus 801, B-3000 Leuven, Belgium. E-mail: Marcel.Vanderheyden[at]med.kuleuven.ac.be We recorded the responses of auditory nerve (AN) fibers of cats to irregularly spaced tone complexes. Recordings from fibers with low characteristic frequencies (CF<4 kHz) enabled us to reconstruct the cochlear transfer characteristics over the entire range of frequencies that excite these low-CF fibers. In three cats, coverage of CFs was sufficiently dense to allow unambiguous unwrapping of phase across fibers. We determined amplitude and phase in the apex as a function of both CF and stimulus frequency. These panoramic maps of cochlear vibration are a physiological couterpart to Bekesy's measurements in cadaver cochleas.

1 Introduction and Methods The aim of this study is to obtain a map of cochlear amplitude and phase transfer in the apex of the cochlea. To this end, we recorded reponses of AN fibers with CFs below 4 kHz to 45-s-long irregularly spaced tone complexes (see [1] for general methods). Fourier analysis of the spike trains [1] revealed their simultaneous synchronization to multiple components. This immediately yields the phase transfer at those frequencies. Determining the amplitude transfer is complicated by the strongly nonlinear character of the transduction process (rectification, compression), but if multiple components contribute to the response, their relative amplitudes are remarkably unaffected by the nonlinearities [2]. The use of irregularly spaced tone complexes has two advantages over harmonic complexes: 1) it eliminates spurious effects of relative component phases; 2) it prevents low-order distortion products (e.g. 2/2-/i) from coinciding with other primaries, thus allowing a better separation between linear and nonlinear contributions to the response. 2 Results and Discussion The amplitude (Fig. 1A) and phase (Fig. IB) characteristics of 3 low-CF AN fibers illustrate different aspects of our technique. All phase curves have been advanced by 3 ms to emphasize dispersive aspects rather than average delay. The middle curves (circles, CF=1.5 kHz) were obtained from a single 45-sec measurement, yielding a dynamic range of-20 dB. The left curves (CF=600 Hz) were obtained by aligning measurements at different frequencies [1]. The right curves (CF=2.1 kHz) show the effect of SPL (15-65 dB) on cochlear transfer. With increasing sound level, the peaks of the amplitude curves shift downward and tuning becomes less

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sharp. At the highest SPL (65 dB, squares in Fig. IB), an almost uniform phase shift occurs. Our method has several advantages over reverse correlation (RevCor) methods: 1) a much larger dynamic range than the -15 dB customary with RevCor; 2) coverage of the whole range of frequencies that drive the fiber, not just a narrow band around CF; 3) an objective (Rayleigh) criterion for significance, unlike RevCor curves whose flanks dwindle in noise; 4) absence of systematic errors in amplitude curves due to windowing of the RevCor functions prior to Fourier analysis.

H °-5' •2- 0.25

:-0.25 I -0,5 0.5 1 1.5 2 2.5 Frequency (kHz)

0.5 1 1.5 2 2.5 Frequency (kHz)

Fig. 1 amplitude and phase transfer for three low-CF AN fibers. Phase data are advanced by 3 ms

0.5 1 2 Fretpjeney {kHzJ

Fig. 2 Unwrapped phases from a single ear.

Multiple transfer functions can thus be measured, covering many CFs and stimulus frequencies. In Fig. 2 data of a single ear are shown for which coverage of low CFs was sufficiently dense to unwrap phases across CFs. The different curves correspond to different CFs as indicated by the circles; phase curves were advanced by 1.85 ms. Together with the amplitude pattern (not shown), the phase pattern constitutes a detailed map of the vibration pattern along an extended portion of the cochlea. Such panoramic maps are a physiological couterpart to Bekesv's measurements in cadaver cochleas. References 1. van der Heijden, M. and Joris, P.X., 2003. Cochlear phase and amplitude retrieved from the AN at arbitrary frequencies. J. NeuroSci. 23, 9491-9498. 2. de Boer, E., 1976. Spectral transformations by an infinite clipper. J. Acoust. Soc. Am. 60, 960-963.

MANIPULATIONS OF CHLORIDE ION CONCENTRATION IN THE ORGAN OF CORTI ALTER OUTER HAIR CELL ELECTROMOTILITY AND COCHLEAR AMPLIFICATION J. ZHENG 1 , Y. ZOU 1 , A.L. NUTTALL 1 ' 2 Oregon Hearing Research Center, Oregon Health & Science University, 3181 SW Sam Jackson Park Road, NRC04, Portland, Oregon 97239-3098, USA Kresge Hearing Research Institute, The University of Michigan, 1301 East Ann Street, Ann Arbor, Michigan 48109-0506, USA E-mail: [email protected] [email protected] [email protected] J. SANTOS-SACCHI Section of Otolaryngology, Dept. of Surgery, Yale University School of Medicine, 246, 333 Cedar St., New Haven, CT 06510, USA E-mail: joseph.santos-sacchi@yale. edu

BML

There is evidence that intracellular chloride ions modulate prestin function. This study investigated how chloride ions (CI") influence cochlear sensitivity and OHC electromotility. Lowering perilymph CI' concentration greatly reduced the magnitude of basal turn BM motion and the electrically evoked otoacoustic emissions. These effects could be modulated by tributyltin (TBT, a CI" ionophore). The results indicate that the electrochemical drive for CI" is important for normal activity of prestin.

1 Introduction Outer hair cell (OHC) electromotility and cochlear sensitivity depend on the proper function of prestin, the motor protein. Intracellular chloride ions (CI") modulate prestin function [1]. Further, there is evidence that CI" acts in ways other than simply carrying capacitive charge. The intracellular CI" concentration can induce a shift of prestin's operating voltage range and can affect the "gain" of the OHC voltage-to-length relationship as the cell's operating point shifts [2,3]. The purpose of this study is to investigate how CI" influences organ of Corti sensitivity and prestin-mediated OHC electromotility. 2 Methods Guinea pigs were surgically prepared for measurements of basilar membrane (BM) motion in the basal turn. Pure tone (6-24 kHz) evoked BM velocity at the site corresponding to approximately 17 kHz was measured using a laser interferometer (Polytec OFV 1102 Laser Vibrometer) and a lock-in amplifier. Sinusoidal current (35 uArms) was applied into the cochlea through round window. Electrically evoked otoacoustic emissions (EEOAEs) were recorded using an Etymotic ER-10 B + microphone. A perilymphatic perfusion system allowed applications of artificial

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108 perilymph (AP) with different CI" concentrations (by substitution with gluconate) and other agents to be delivered into the scala tympani of the cochlea (2 ul/min). 3

Results

Lowering extracellular CI" by infusing 5mM chloride or chloride free AP greatly reduced acoustically evoked BM velocity responses and the EEOAEs (Figure 1 and 2). Washout with AP completely restored the magnitude of both BM motion and EEOAEs to the control levels. TBT improved the magnitude of the BM velocity response by 3-6 dB near the best frequency (approximately 17 kHz) for low sound level stimuli in certain conditions. The presence of TBT influenced the effect of low CI".

Figure 1. BM velocity transfer functions for 40 dB SPL sound stimuli 4

Figure 2. EEOAE magnitude transfer functions

Discussion

These results indicate that the electrochemical drive for CI" is important for normal activity of prestin. TBT can alter intracellular CI" concentration and is able to modulate the gain of OHC electromotility and cochlear amplification. Acknowledgments Supported by NIH NIDCD DC 00141 (ALN) and DC 00273 (JSS). References 1. Oliver, D. et al., 2001. Science 292, 2340-2343. 2. Rybalchenko, V. & Santos-Sacchi, J., 2003. J. Physiol 547, 873-891. 3. Song, L., Seeger, A., Santos-Sacchi, J., 2005. Biophysical J. 88, 2350-2362.

COCHLEAR TRANSDUCER OPERATING POINT ADAPTATION Y. ZOU a , J. ZHENG a , T. REN a , A.L. NUTTALL a , b "Oregon Hearing Research Center, Oregon Health & Science University, 3181 Jackson Park Road, NRC04, Portland, OR, 97239, USA

SWSam

b

Kresge Hearing Research Institute, The University of Michigan, 1301 East Ann Str., Ann Arbor, MI, 48109, USA E-mail: [email protected], [email protected], [email protected], [email protected] The change of operating point (OP) of outer hair cell mechano-transduction could be determined from the change of the 2nd harmonic of the cochlear microphonic (CM) following a calibration to determine its initial value. To perturb the OP, a constant force was applied to the bony shell of the cochlea using a blunt probe, orce applied over the scala tympani increased the OP. During constant force of the CM underwent a slow partial recovery toward the initial level. Removing the force again initiated a change of 2nd harmonic, which returned to the control level. These data indicate an active mechanism for OHC transduction OP to dynamically be controlled at its normal position.

1 Introduction Cochlear microphonic (CM) can be used to characterize mechano-electrical transduction (MET) in outer hair cells (OHCs) [1]. Operating point (OP) can be defined as the percentage of the maximum transduction current that occurs without sound stimulation. Waveform for the instantaneous CM potential is symmetrical when 50% of the MET channels are open. The OP change for low sound level probe tones can be analyzed based on the 2nd and 3 rd harmonics of CM [2]. The 2nd and 3 rd harmonics of CM are proportional to 2nd and 3 rd derivatives of Boltzmann function respectively. Second harmonic distortion is extremely sensitive to small operating point changes. The 2nd harmonic rapidly increases as OP moves away from 50%. The 3 rd harmonic distortion is less sensitive to small operating point changes but decreases as OP moves away from 50%. By measuring CM distortion, we were able to determine OHC OP change. 2 Methods A constant force (0.17N) was applied to the bony shell over the scala tempani (ST) at the 18kHz best frequency location using a blunt probe that distorts the shape of the otic capsule and displaces the organ of Corti. As a control experiment, the perfusion of artificial perilymph (AP) was used to hydraulically bias the basilar membrane (BM) toward the scala vestibuli (SV) direction.

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110 3 Results Initial OP was dependent on sound level and cochlear sensitivity. The OHC OP was 57% and constant during 74 dB SPL 400Hz tone stimulation (dashed line in Fig. 1A). At 94 dB SPL, the OP underwent a transient increase and then slowly decreased to a value less than 50% (solid line in Fig. 1A). The 2nd and 3rd harmonic changes caused by force application were in the same direction as these caused by AP perfusion in the ST. Thus the stereocilia move towards SV with the force applied to the cochlear shell at the ST. For a 74dB SPL probe tone, this force caused a sudden increase of 2nd harmonic, then underwent a slow partial recovery, which could be described by a fast time constant (TC) of 1.8 ±0.6 s and a slow TC of 9.2 ±3.5. Removing the force caused 2nd harmonic recovery to its normal level with a slow TC of 6.2±0.8 s. For a 94dB SPL probe tone, the 2nd harmonic recovery was much faster than that for the lower sound stimulation level. These data indicate an active mechanism, which controls OHC transduction OP dynamically.

Fig.lA OPs derived from the Boltzmann function of the CM waveform in the first 15 min after first applying a sound of 400 Hz 94 dB SPL (solid) or 74 dB SPL (dashed). Fig. IB Change of 2nd harmonics for a 94 dB SPL (solid) or a 74 dB SPL (dashed) tone with the constant force applied on the cochlea at the 18kHz BF place.

Acknowledgments The study was supported by Grants R01 NIDCD DC00141 & DC04554 from the National Institute of Deafness and Other Communication Disorders, NIH. References 1. Holton, T. and Hudspeth, A.J., 1986. J. Physiol. 375, pp. 195-227. 2. Sirjani DB, Salt AN, Gill RM, Hale SA, J Acoust Soc Am. 115(3): 1219-29.

LOW COHERENCE INTERFEROMETRY OF THE COCHLEAR PARTITION N. CHOUDHURY", S.L. JACQUES", S. MATHEW b , F. CHEN, J. ZHENG b A.L. NUTTALL a , b c "Department of Biomedical Enginering, Oregon Health & Science University, Portland, OR Oregon Hearing Research Center, Oregon Health & Science University, Portland OR c Kresge Hearing Institute, The University Of Michigan, Ann Arbor, MI An optical coherence tomography (OCT) imaging system operating at 1310nm wavelength was used to image the organ of Corti. The spatial resolution of the system was ~13pm. The reflectivity of light intensity for the organ of Corti was ~10'5 ( a mirror defines a reflectivity of 1.00). Operating the system as a low-coherence interferometer allowed us to measure localized vibration of the basilar membrane in the organ of Corti, driven mechanically with a piezo stack coupled to the sample chamber. We were able to detect vibrational signal at 16kHz from three different locations in the organ of Corti. The chamber was vibrated by ±~lnm. The normalized detected signal (vibrational signal amplitude divided by the intensity of reflected light) from all three locations were approximately constant for equal amount of vibration.

1 Introduction An important technique for studying cochlear mechanics is to measure the vibration of the basilar membrane (BM). Low-coherence interferometry allows localized measurements of the vibrations of a membrane surface without interference from other surfaces in front of or behind that of the surface of interest. Such localized measurement is especially useful when measuring through a small access hole in the Cochlear bony wall, when the small numerical-aperture of the objective lens cannot provide such localization. The broad spectrum (~95nm) of a super-luminescentdiode (SLD) light source creates, in our case, a coherence gate that achieves an axial resolution of 13|am. Hence, a measurement can be localized on the upper or lower membrane surfaces of the organ of Corti (i.e. the basilar membrane and reticular lamina). 2 Methods Tissue Preparation: The cochlea of a guinea pig was surgically removed and fixed with paraformaldehyde and mounted in a chamber containing the bathing solution. The basal turn of the cochlear scala tympani was opened to expose the BM. The front of the cylinder had a glass cover slip that allowed the interferometer to illuminate the organ of Corti for vibration measurements. The piezo was attached to the rear of the tissue chamber as a calibrated vibration source.

Ill

112 Optical Coherence Tomography (OCT>: The OCT system used a 1310nm (~95nm bandwidth) SLD from BWTEK (model BWC-SLD), coupled to a network of single-mode optical fibers. The chamber was vibrated at 16kHz and by ±1 nm 3 Models and Results 3.1 OCT Image of organ of Corti

Figure 1. The OCT image of organ of Corti. The white arrows show the locations where the vibration measurements, plotted in Figure 2, were made. The picture on the right shows the intensity profile along the z-direction slice where the vibration measurements were made. 3.2

The normalized vibration signal at 16 kHz. ,

| 1,. J ,,.

o

<*

Figure 2. The sample was vibrated by ±~lnm. The detected vibration signal was normalized by reflected light, plotted on the right in Figure 1. We see from the plot that the detected signal is proportional to the refelected light for the same amount of vibration.

4 Discussion The system is able to measure vibration from the front and back surfaces of the organ of Corti at physiological vibration amplitudes. Images produced by the scanning system have sufficient resolution to allow careful monitoring of measurement location. The use of a cochlea with an opening and approach similar to regular experimental procedure, as well as a simple optics design in the sample arm that can easily be adaptaed to our current velocimetry setup, demonstate the viability of the system for in vivo measurements of cochlear motion. Acknowledgments This work is supported by NIH R01-DC06273 and R01 DC-00141.

SUPERIOR SEMICIRCULAR CANAL DEHISCENCE: M E C H A N I S M S OF A I R - C O N D U C T E D H E A R I N G J. E. S O N G E R AND J.J. R O S O W S K I Eaton-Peabody Laboratory, Massachusetts Eye and Ear Infirmary, 243 Charles St. Boston, MA, 02114- Speech and Hearing Bioscience and Technology, Health Sciences and Technology, Harvard-MIT, Cambridge, MA, 02138 E-mail: [email protected] Both an animal and mechano-acoustic model of superior semicircular canal dehiscence (SCD) were developed. The animal model demonstrates that middle-ear input admittance and stapes velocity increase and that cochlear potential decreases in response to sound after introducing an SCD. These changes are consistent with the 'third-window' hypothesis as illustrated by a mechano-acoustic model of the effects of SCD on audition.

1

Introduction

Superior semicircular canal dehiscence (SCD) syndrome affords a unique opportunity to study the hearing mechanisms of a novel pathology in otolaryngology. An SCD is a break in the petrous bone between the superior semicircular canal and the cranial cavity [1]. Patients with SCD syndrome present with a wide variety of symptoms: ranging from purely vestibular [1] to purely auditory symptoms (including low frequency conductive hearing loss) [2] [3] and some present with both. For this study, we are focusing on the auditory mechanisms of SCD. According to the 'third-window' hypothesis, the SCD acts to shunt airconducted, sound-induced stapes volume velocity away from the cochlea reducing the auditory stimulus. The shunting of volume velocity is hypothesized to lead to decreases in both auditory sensitivity and cochlear impedance and increases in stapes velocity. The relative changes in these parameters are hypothesized to be important in determining whether an SCD causes a conductive hearing loss. 2

Methods

A dehiscence was surgically introduced into the superior semicircular canal of chinchillas. Cochlear potential, middle-ear input admittance and stapes velocity were measured both before and after the introduction of the dehiscence. A mechano-acoustic model of dehiscence was developed using anatomically and physiologically relevant d a t a to predict changes in cochlear potential, stapes velocity, and admittance in response to air-conducted stimuli both before and after the introduction of a dehiscence. 3

Results and Model

After the surgical introduction of a dehiscence there is a low frequency (200Hz3kHz) decrease in cochlear potential, an increase (500Hz-2kHz) in stapes veloc-

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114 ity, and a low frequency (150-750Hz) increase in middle-ear input admittance (Figure 1A). The frequencies in parenthesis describe the regions of statistical significance. These changes are reversible when the dehiscence is patched. A basic mechano-acoustic model of the chinchilla middle- and inner-ear has been developed (Figure IB) which is qualitatively consistent with the observed mechanical and physiological changes associated with dehiscence [4].

Figure 1. A) The effect of SCD on physiological parameters recorded as the dB difference between pre- and post-SCD conditions. The solid lines show a decrease in cochlear potential. The thin dotted line shows an increase in admittance. The thick dashed line shows an increase in stapes velocity. B) A block diagram of the model layout used to predict the effects of SCD on auditory function in chinchilla. ZME — the impedance of the middle ear, ZQRW = the impedance of the cochlea and round window, ZSCD = the impedance through the dehiscent canal. Introducing a dehiscence closes the switch.

4

Discussion

The results obtained from the chinchilla model of SCD are consistent with human patient d a t a as well as the predictions of the 'third-window' hypothesis and the mechano-acoustic model. The mechano-acoustic model can be adapted to predict the effect of SCD in both human temporal bones and patients. Acknowledgments This research has been funded by the NIH and NSF. Special thanks to M. Wood and the Wallace Middle Ear Research Group at MEEI. References 1. 2. 3. 4.

Minor et al, 1998. . Arch. Otol Head Neck Surg 124, 249-258. Minor et al, 2003. . Oto. Neuroto. 24, 270-278. Mikulec et al, 2004. . O t o . Neuroto. 25, 121-129. Rosowski et al, 2004. . Oto. Neurotol. 25, 323-332.

ON THE COUPLING BETWEEN THE INCUS AND THE STAPES W.R.J. FUNNELL, S.J. DANIEL, B. ALSABAH AND H. LIU McGill University, 3775 rue University, Montreal, QC, Hi A 2B4, Canada E-mail: robert.funnell@mcgill. ca There is a thin bony pedicle joining the lenticular plate to the rest of the long process of the incus. We have previously presented a brief review of its anatomy; new histological observations in cat; and a simplified finite-element model of the long process, pedicle, lenticular plate, incudostapedial joint and stapes head in the cat. Low-frequency simulations suggested that there may be more flexibility in the pedicle than in the incudostapedial joint itself. In this paper the modelling work is extended: a 3-D model for the cat is shown which has a more realistic geometry, and a model for the human is presented.

1 Introduction The incudostapedial joint is a synovial joint between the lenticular plate of the incus and the head of the stapes. There is a thin bony pedicle joining the lenticular plate to the rest of the long process of the incus. The pedicle is extremely fine and it is easy to overlook or misinterpret. We have previously presented a brief review of its anatomy; new histological observations in cat; and a simple finite-element model of the long process, pedicle, lenticular plate, incudostapedial joint and stapes head in the cat. Low-frequency simulations suggested that there may be more flexibility in the pedicle than in the incudostapedial joint itself [1]. In this paper a histology-based 3-D reconstruction of the cat lenticular process is presented which has a more realistic geometry than the simplified finite-element model. The modelling work is then extended to the human ear. First, a new 3-D reconstruction for the human lenticular process and stapes head is presented, based on x-ray micro computed tomography (uCT). Second, a finite-element model with simplified geometry is presented, along with simulation results. 2 Methods The 3-D reconstruction for the cat is based on serial sections from a plasticembedded incus of an adult cat. The sections were cut at a thickness of 1 um, and every section was stained with toluidene blue and mounted. These are the same sections on which the dimensions of our previous model [1] were based. The 3-D reconstruction for the human is based on a uCT dataset obtained using a SkyScan 1072 scanner, with an isotropic voxel size of 4.2 um [2]. The 3-D reconstructions for both cat and human were produced using Fie and 7>3, locally developed computer programs for image segmentation and 3-D surface triangulation. The software is available for free downloading [3]. For the

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116 histological images, slide-to-slide alignment was done manually. For both data sets, structures of interest were outlined either manually or semi-automatically. The configuration and material properties for the new finite-element model are the same as those of our previous model for the cat [1]. The dimensions of the model were estimated from the new human 3-D reconstruction. 3 Models and Results Figs. 1 and 2 show 3-D reconstructions of the cat and human lenticular processes, respectively. Fig. 3 shows a preliminary simulation result for the simplified model of the human lenticular process. More bending is apparent in the pedicle than in the joint, similar to our previous finding for the cat.

Fig. 1. Cat reconstruction

Fig. 2. Human reconstruction

Fig. 3. Human simulation results

4 Discussion Because the bony pedicle is very much thinner in one direction than in the other, it may provide hinge-like incudostapedial flexibility, thus controlling the degree of rocking of the stapes and affecting the nature of the input to the cochlea. Acknowledgements This work was supported by the Canadian Institutes of Health Research, the Natural Sciences and Engineering Research Council (Canada), and the Fonds de recherche en sante du Quebec. References 1. Funnell W.R.J., Siah T.H., McKee M.D., Daniel S.J., Decraemer W.F., 2005. On the coupling between the incus and the stapes in the cat. JARO 6, 9-18. 2. Alsabah B., Liu H., Funnell W.R.J., Daniel S.J., Zeitouni A.J., Rappaport, J.M., 2005. Secrets of the lenticular process and incudostapedial joint. Ann. Mtg. Can. Soc. of Otolaryngol. Head & Neck Surgery, St. John's, Newfoundland. 3. Funnell, W.R.J., 2005: AudiLab software. http://audilab.bmed.mcgill.ca/~funnell/AudiLab/sw/

NOVEL OTOACOUSTIC BASELINE MEASUREMENT OF TWO-TONE SUPPRESSION BEHAVIOUR FROM HUMAN EAR-CANAL PRESSURE

E. L. LE PAGE AND N. M. MURRAY OAEricle Laboratory, P.O. Box 6025, Narraweena, NSW2099 Australia E-mail: ericlepage@oaericle. com. au J. D. SEYMOUR National Acoustic Laboratories, 126 Greville Street, Chatswood, 2067 Australia E-mail: John, [email protected]. au We describe extension of otoacoustic emission technique intended to directly register change in cochlear mechanical baseline. A two tone probe/masker experiment is described in human subjects. Instead of just calculating distortion products from the averaged responses, low frequency variation in ear canal pressure is obtained and the pattern of positive and negative summating / adaptive behaviour versus frequency and level of the masker is reminiscent of two-tone suppression contours. The technique largely eliminates middle ear considerations.

1 Introduction Previous work has shown mechanical behaviour in the baseline position of the basilar membrane in guinea pig preparations analogous to, and measured simultaneously with summating potential behaviour measured at the round window, with similar polarity variations with frequencies above and below the best frequency of the place. Mechanical measurements by Flock more recently have observed substantial dc-shifts in the motion of the Hensen cells. Not all measureable position shifts are interpreted as OHC motile behaviour. Transient development of hydrops is now invoked to explain them. The question of whether dc-shifts occur in relation to outer hair cell homeostasis remains. Quadratic distortion products undergo baseline shifts and these have been interpreted as operating point shifts in OHC potentials by Salt and colleagues. Evoked otoacoustic emissions are an important window into cochlear mechanical behaviour and their human characteristics have been explored extensively in terms of distortion products, transient responses and stimulus frequency emissions. Mostly, emissions contain considerable noise, particularly at low frequencies. The working hypothesis here is that much of this measurement noise is indeed due to adaptive OHC response, hydropic response, or both. Significant external noise exists as cardiac pressure pulse in the ear canal. We have investigated whether cochlear summating responses are salvageable by using signal averaging of the ear canal pressure and looking for differential changes and computing linear regressions on each of the segments defined by onsets and offsets.

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2 Methods and results A standard DPOAE probe is sealed in the ear canal. A two-tone masking paradigm is used, e.g. a contant 25 ms probe tone of 3 kHz at 70 dB SPL is repeated at 50ms intervals. A masker tone of 7ms duration is added 9ms after the start of the probe tone. Both bursts employ 1ms rise/fall times. The masker is varied in frequency and level (Fig.l). Each digitally-generated two-tone pair is repeated phase reversed, and the sum and difference computed. The whole sequence is repeated ten times, taking 2 minutes, and the 10 responses averaged to eliminate external noise. Baseline pressure changes are here determined from the rate of the the difference component (Pa/s). For sound levels above the probe tone level, and for an increasingly wide frequency range with higher level, masker onset produces condensation adaptive response; offset produces rarefaction. This is reproducible within each subject, but varies across subjects.

Transition: MASKER ONSET

i 2= 1 0.25 Masker frequency (octaves from probe)

Figure 1. Level and frequency dependence of ear canal baseline pressure with two-tone masking experiment in one human subject. Probe is fixed (centre) while the masker is varied above and below probe by H oct in 1 /12 oct steps. The z-axis dimension is positive or negative rates of summation (baseline dc-shift Pa/s). Mid-gray is baseline invariance i.e. constant mean pressure. Light regions (see masker onset) indicate condensation, dark regions (particularly with offset) is rarefaction shift.

3 Discussion The technique benefits from various measures for noise reduction, particularly the differencing between the pairs which are unlikely to differentially cause stapedius reflex. These responses are not emissions in the audio-frequency sense, but suggest electro-mechanical adaptation in the cochlea at low frequencies likely for a long length of spatial integration. These results add support to previous demonstration "dc-shifts" in direct mechanical measurements. Most intriguing is the suggestion that the contours may indicate a dc-bias origin for two-tone masking effects. References and poster download: www.oaericle.com.au

IS THE SCALA VESTIBULI PRESSURE INFLUENCED BY NON-PISTON LIKE STAPES MOTION COMPONENTS? AN EXPERIMENTAL APPROACH W.F. DECRAEMER University ofantwerp,171Groenenborgerlaan, B-2020 Antwerpen, E-mail: wim. decraemer@. ua. ac. be

.Belgium

S.M. KHANNA, O. DE LA ROCHEFOUCAULD, W. DONG, E.S. OLSON Columbia University, 650 West 168th Street, NY 10032 ,New York, USA E-mail: [email protected] The mode of vibration of the stapes is predommantly piston-like but at higher frequencies, rotations about the long and short footplate axis are also observed. An experiment was performed to verify whether the non-piston components influence the pressure produced in the cochlea. First the pressure in the scala vestibuli behind the footplate was measured using a micro-pressure sensor while a microphone recorded the pressure produced by the sound source in the ear canal. Then the motion of the stapes was measured under different angles and all 3D stapes motion components were calculated. Piston motion and tilt of the footplate could thus be correlated with vestibular pressure in the same ear. With the present experimental data we can also directly calculate individual cochlear input impedances and find the width of the transmission band and the time delay in the middle ear.

1 Introduction We have shown (e.g. Decraemer and Khanna 2003a) that the mode of vibration of the stapes is predominantly piston-like but that at higher frequencies rotations about the long and short footplate axis are also observed. Because the footplate motion produces the pressure wave in the cochlea, we can ask whether the non-piston components influence the pressure produced in the cochlea. To answer this we have measured the 3-D vibration velocity of the stapes along with the scala vestibuli pressure and ear canal pressure in the adult gerbil. 2 Methods and Results Young gerbils with healthy ears were used for this study. The animals were anaesthetized, the external ear canal was cut short and a small plastic tube was cemented in place to affix the sound source. The middle ear cavity was opened and the pressure in the scala vestibuli at a point closely behind the footplate was measured using a micro-pressure sensor (Olson, 1998) while a probe tube microphone simultaneously recorded the pressure produced by the sound source in the earcanal. The motion of the stapes was measured under different viewing angles with a heterodyne interferometer. Assuming rigid body behaviour the 3-D components were calculated (Decraemer and Khanna, 2003a). Using a 3-D model

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of the stapes (based on a microCT scan of the experimental ear (Decraemer et al, 2003b)) the coordinate transform that puts the stapes in an intrinsic reference system was determined so that the piston-like motion and the tilt of the footplate are obtained as the velocity component along the y-axis and rotations about the x and zaxes (Fig.l). The motion components can now be correlated with the fine structure of the scala vestibuli pressure in the same animal.

— omega (10 rad/sperPa) -omega (102 rad/s per Pa)

Fig. 1 shows the SV re EC pressure gain and the 3 motion components that can produce diplacement along the piston axis of the stapes (these 3 curves also normalized to EC pressure). In some frequency regions the pressure gain is smoother than the piston motion component; in other regions they are both smooth, and similar.

phase omega -1000

0.5

1.5 2 2.5 frequency in Hz

3.5

4 x10 4

References 1. Decraemer, W.F., Dirckx, J.J.J., Funnell, W.R.J., 2003, Three-dimensional modeling of the middle-ear ossicular chain using a commercial high-resolution xray CT scanner, J. Assoc. Res. Otolaryngology, 4,250-263. 2. Decraemer, W.F., Khanna, S.M., 2003, Measurement, visualization and quantitative analysis of complete three-dimensional kinematical data sets of human and cat middle ear, Proceedings of the Middle ear mechanics in research and otology, Matsuyama, Japan, 3-10. 3. Olson, E. S., 1998, Observing middle and inner ear mechanics with novel intracochlear pressure sensors, J. Acoust. Soc. Am. 103 (6), 3445-3463.

BIOMECHANICS OF DOLPHIN HEARING: A COMPARISON OF MIDDLE AND INNER EAR STIFFNESS WITH OTHER MAMMALIAN SPECIES B. S. MILLER, S. 0 . NEWBURG, A. ZOSULS, AND D. C. MOUNTAIN Boston University Hearing Research Ctr, 44 Cummington Strt, Boston, MA 02215, USA E-mail: [email protected] D. R. KETTEN Woods Hole Oceangographic Institution, Mailstop 36, Woods Hole, MA 02543, E-mail: [email protected] The purpose of this study was to measure both middle ear stiffness and basilar membrane stiffness for the bottlenose dolphin (Tursiops truncatus) and compare these results with similar measures in other mammalian species. It was found that the point stiffness of the bottlenose dolphin basilar membrane has a gradient from 20 N/m near the base to 1.5 N/m near the apex and the middle ear has a stiffness of 1.37 x 106 N/m. These values are considerably higher than those reported for most terrestrial mammals, yet consistent with species specialized for high-frequency hearing.

1 Introduction Hearing is arguably a principal sense for odontocetes, or toothed whales, and because it takes place underwater, it is reasonable to assume that the odontocete auditory system is highly derived [1]. Understanding the specialized odontocete auditory system could provide insights into hearing in general and may be useful for comparative studies of hearing in other species. A common approach in modeling the auditory periphery is to start with an acoustic power flow model in which the external ear, middle ear, and cochlea are treated as a series of connected acoustical and mechanical systems. Outputs from each system provide inputs for the next. Key parameters in the power flow model are middle ear stiffness, which dominates the middle ear impedance at low frequencies, and basilar membrane volume compliance, which dominates cochlear impedance [2]. 2 Methods Detailed ear preparation and measurement methods for the middle ear stiffness are outlined in Miller et al. [3], Basilar membrane stiffness measurements were similar to those made by Olson and Mountain [4]. All measurements reported here were made using excised tympano-periotic bones of Tursiops truncatus. Samples were

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122 obtained post-mortem from stranded animals in cooperation with normal stranding response procedures and under letters of agreement and research permits issued to Harvard University, Woods Hole Oceanographic Institution, and D.R. Ketten. Figure I

3 Results and Discussion In terrestrial mammals, correlation between middle ear acoustic stiffness and low frequency cutoff of hearing threshold can be expressed according to the function: / c = 1 . 0 2 x 10"6 k°-5i

(1)

• • • Mouse j7]

o. i

"i

'

To * "

Too

Characteristic Frequency (KHz)

where/, is the -20 dB cutoff frequency and k is the acoustic stiffness of the middle ear [3]. The acoustic stiffness of the bottlenose dolphin middle ear was measured to be 1.04xl017 Pa/m3. Using this value in Eq. 1 yields/I of approximately 7.56 KHz, which is close to value of 8 KHz obtained from inspection of the behavioral audiogram. Stiffness gradients along length of basilar membrane in bottlenose dolphin were measured for three ears from three different animals. Point stiffness was converted to volume compliance, following Naidu [5], using basilar membrane dimensions from Wever et al [6]. Fig. 1, a plot of volume compliance vs. characteristic frequency, shows bottlenose dolphin volume compliance to be similar to that of the mouse [7], a terrestrial species capable of high frequency hearing. Estimates of bottlenose dolphin characteristic frequency were based on the behavioral audiogram and cochlear anatomy [6] [8]. References 1. Ketten, D.R., 2000. Cetacean Ears. In: Au, W., Popper, A.S., Fay, R., (Eds.), Hearing by Whales and Dolphins. Springer-Verlag, New York. 2.

Rosowski, J.J., 1994. Outer and Middle Ears. In: Fay, R.R., Popper, A.N., (Eds.), Comparative Hearing: Mammals. Springer-Verlag, New York.

3.

Miller, B.S., Zosuls, A.L., Ketten, D.R., Mountain, D.C., 2005. In press. Middle ear stiffness of the bottlenose dolphin Tursiops truncatus. IEEE J Oceanic Eng

4.

Olson, E.S., Mountain, D.C., 1991. In vivo measurement of basilar membrane stiffness. J Acoust Soc Am 89, 1262-75.

5.

Naidu, R.C., 2001. Mechanical properties of the organ of corti and their significance in cochlear mechanics, Boston University.

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6.

Wever, E.G., McCormick, J.G., Palin, J., Ridgway, S.H., 1971. Cochlea of the dolphin, Tursiops truncatus: the basilar membrane. Proc Natl Acad Sci U S A 68, 2708-11.

7.

Von Bekesy, G., 1960. Experiments in hearing McGraw-Hill, New York.

8.

Johnson, C.S., 1967. Sound detection thresholds in marine mammals. In: Tavolga, W., (Ed.), Marine Bioacoustics. Pergamon, New York. pp. 247260.

II. Hair Cells

AN EXPERIMENTAL PREPARATION OF THE MAMMALIAN COCHLEA THAT DISPLAYS COMPRESSIVE NONLINEARITY IN VITRO A. J. HUDSPETH AND DYLAN K. CHAN Laboratory of Sensory Neuroscience and Howard Hughes Medical Institute, The Rockefeller University, 1230 York Avenue, New York, NY 10021, USA E-mail: [email protected] To delineate the cellular mechanisms underlying the cochlear active process, we have developed an active in vitro preparation of the cochlea from the clawed jird. The amplitude and phase of the active mechanical and electrical responses of this preparation accord with those obtained in vivo. Analysis of the resonant properties of the exposed cochlear segment discloses two principal modes of oscillation: a second-order mode whose resonant frequency is set by the bulk volumetric stiffness of the segment and the fluid mass loading it, and a less prominent traveling-wave mode whose resonant frequency more closely matches the best frequency in vivo.

1 Introduction An active process plays a dominant role in shaping the responsiveness of the mammalian cochlea, especially for low-amplitude stimuli near the characteristic frequency for a particular cochlear location. Throughout the tetrapod vertebrates, this active process is characterized by four features: amplification of inputs, frequency selectivity, compressive nonlinearity, and spontaneous otoacoustic emission [1]. Two mechanisms have been advanced as candidates to explain the active process. Membrane-based electromotility is an attractive possibility, especially in light of its extraordinary frequency responsiveness [2]. Nonetheless, three arguments weigh against this mechanism at present. First, despite several ingenious proposals [3, 4], it remains possible that the operation of electromotility at high frequencies is limited by the hair cell's membrane time constant. Second, whereas the active process is ubiquitous in the ears of tetrapods, electromotility based on the protein prestin [5] appears to be confined to the outer hair cells of mammals. Even if electromotility underlies the mammalian active process, it follows another mechanism must be at work in non-mammalian tetrapods. Finally, despite the wealth of valuable results on the mechanism of electromotility, the process has not been demonstrated to account quantitatively for any of the four hallmark features of the active process. The second candidate for the active process is active hair-bundle motility. This phenomenon has been shown to demonstrate each of the four key features of the active process [6, 7]. The cellular mechanisms thought to underlie active hairbundle motility, Ca2+-dependent reclosure of transduction channels and myosinbased adaptation, occur in mammals [8, 9] as well as in the amphibians and reptiles

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128 in which the phenomena were initially characterized. However, whether hair-bundle motility can operate at the high frequencies characteristic of mammalian audition, up to many tens of kilohertz, remains uncertain. To determine which of the candidate mechanisms underlies the active process in the mammalian cochlea, researchers require an experimental preparation that both displays the macroscopic signatures of the active process and is amenable to interventions that test the roles of electromotility and hair-bundle motility. The present publication describes such a preparation and provides additional features of its operation not included in the initial description [10]. 2 Methods The common or clawed jird, Meriones unguiculatus, is a burrowing rodent found in desert and steppe habitats in Mongolia and adjacent portions of China and Russia. As a member of the murine Subfamily Gerbillinae, this animal is sometimes termed a "gerbil." The anatomical accessibility of the jird's cochlea, which is partially exposed in a large bulla, commends the species for investigations such as ours. Segments of the jird's cochlear partition were isolated and prepared as described [10]. The acoustic properties of the experimental chamber were calibrated with a pressure transducer (8507C-1, Endevco), and cochlear microphonic responses were recorded with extracellular silver-silver chloride electrodes. The mechanical responses of the in 100 vitro preparation were measured by laser Doppler velocimetry E c (501 OFV, Polytec) to detect vertical movement of the E tectorial membrane and by a photodiode projection system to I 10 a. assess radial hair-bundle v> movement of inner hair cells. T3 "5

3 Results The radial hair-bundle movement of an inner hair cell typically exhibits a compressive nonlinearity in response to lowlevel acoustic stimulation (Fig. 1), so the in vitro preparation retains the cochlear active process. To compare the hair-bundle responses to the

1 <2

20

40 60 Sound-pressure level (dB)

80

Figure 1: Compressive nonlinearity of radial hair-bundle displacement in response to acoustic stimuli in the presence of K+-based endolymph and a +80-mV endocochlear potential. The power-law slope {Mack fine) at low stimulus intensities is 0.59, demonstrating a compressively nonlinear response. The dotted line indicates a slope of unity.

129 vertical displacements of the basilar membrane typically recorded in vivo in response to sound pressure delivered to the outer ear, we performed a series of calibration experiments. To measure the pressure applied across the segment of the cochlear partition, we removed the experimental preparation and placed a pressure transducer in its position. The pressure values reported here and in our previous work [10] therefore correspond to sound-pressure levels in the cochlear scalae. Because of the mechanical amplification afforded by the middle ear in vivo, intrascalar sound-pressure levels are about 20 dB greater than those measured in the air. To compare the present results with ordinary sound-pressure levels, then, the reported values should be diminished by 20 dB. Therefore, the nonlinearity that we examine typically occurs for the equivalent of airborne stimuli of 10-50 dB SPL, in good agreement with in vivo results [11]. The weakest stimuli for which we report responses, 30 dB SPL, correspond to approximately 10 dB SPL in vivo. These stimuli evoke root-mean-square inner-hair-cell bundle responses of about 0.5 nm. Measurements in the same preparation reveal that the vertical displacement of the basilar membrane is about 150% of the radial deflection of the hair bundles. The measured bundle responses are therefore comparable to the roughly 1-nm basilarmembrane displacements seen for equivalent levels of stimulation at the base of the living cochlea [11]. The radial displacement of an inner-hair-cell bundle and the vertical velocity of the tectorial membrane immediately adjacent to the bundle were measured in the same preparation. The cochlear microphonic potential was also recorded simultaneously (Fig. 2a). As with the tectorial-membrane and hair-bundle responses, this electrical signal exhibits second-order harmonic behavior, with a resonant frequency and phase lag at resonance that match those of the simultaneously recorded mechanical responses. Overlay plots of the tectorialmembrane, hair-bundle, and microphonic responses together with the pressure stimulus reveal the phase relationships of these four elements (Fig. 2b).

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Figure 2: Responses of the in vitro preparation, (a) Radial hair-bundle displacement (black), vertical tectorial-membrane velocity (orange), and the microphonic potential (green) are shown in response to a 300-3000 Hz, 71-dB SPL acoustic pressure stimulus (red), (b) Overlay plots of the boxed responses in (a) at frequencies below (left), at (middle), and above (right) the 900-Hz resonance demonstrate the phase relationships between the responses. Upward deflections reflect hair-bundle movement toward the modiolus (black), upward tectorial-membrane velocity (orange), positive lower-compartment potential (transduction-channel opening; green), and positive lower-compartment pressure (red). To clarify the phase relationships, the overlaid traces are not to scale.

Because the preparation affords optical access along the full length of the isolated cochlear segment, it was possible to observe the bundle movements of inner hair cells at any position. Stimulating with acoustic frequency sweeps of 300-3000 Hz, we measured the phase of the response with respect to that of the stimulus as a function both of stimulus frequency and of location along the basilar membrane (Fig. 3a,b). A phase lag was noted between the basal and apical ends of the cochlear segment, with a maximum lag of about 60° occurring at a frequency above the resonant frequency of the preparation. This peak in phase difference corresponded with a small resonance in the response at this higher frequency, which was independent of the amount of liquid in the lower compartment and thus of the second-order resonant mode imposed by the experimental system. The response at the basal end of the segment consistently led the apical response in both left and right cochleae, making it unlikely that the phase difference arose as an artifact of the recording chamber. The wave velocity and wavelength along the cochlear segment exhibited broad minima near the second resonant frequency, and their respective values of 4.1 ms"' and 3.7mm were comparable to those recorded in vivo at the characteristic frequency (Fig. 3c,d) [11]. These results suggest that the cochlear segment in the in vitro preparation oscillates in two modes: a dominant secondorder mode whose resonant frequency is dependent upon the bulk volumetric stiffness of the entire basilar membrane and the liquid mass in the lower

131 compartment, and a secondary traveling-wave mode whose best frequency is set by intrinsic properties of the exposed segment. 4 Discussion In our experimental preparation, the tectorial membrane evidently moves in phase a

b

-0.1

£. -0-2 | -0.3 -0.4 1 2 Frequency (kHz) 30 <0

£

I

20 10

9>

1

2

Frequency (kHz)

Figure 3: Traveling-wave motion in the in vitro preparation. (a) The phase of hair-bundle movement at the apical end of the exposed segment with respect to movement at the basal end lags maximally at 1.0-1.4 kHz. (b) The phase of 1.2-kHz hair-bundle movement relative to the -0.4 0 200 400 600 response at the basal end increasingly with Distance from base (urn) lags distance from the basal end of the exposed 30 segment, (c) TravelingE wave velocity is lowest E 20 around 1.1 kHz, the same frequency at which a small resonance in the mechani 10 cal response is seen in Fig. 2. (d) The wavelength also decreases to a minumum around this 1 2 higher resonant frequency. Frequency (kHz)

with the hair bundles of inner hair cells. The tectorial membrane's resonant frequency matches that of the hair bundles, and the tectorial membrane's velocity leads the hair-bundle displacement by n/2 radians throughout the frequency range tested. Upward displacement of the tectorial membrane corresponds to inward movement of the hair bundle. This result, which appears at first glance to contradict the standard model in which outward deflection of the bundle is associated with upward partition movement, is in fact reasonable. Consistent with results obtained with the hemicochlea [12], the reticular lamina in our preparation is displaced radially inwards when the partition moves toward the scala media, whereas the tectorial membrane undergoes insignificant radial movement. An inner hair cell's bundle, being attached to the reticular lamina, would thus appear to be moving inwards as well, whereas its top would be viscously coupled to the tectorial membrane. Thus, the shear between the reticular lamina and the tectorial membrane

132 would induce an outward deflection of the bundle—that is, rotation around its basal insertion—whereas the bundle itself is largely translating inwards. The phase relationship of the microphonic potential to the tectorial-membrane and hair-bundle responses is not entirely consistent, exhibiting a phase lead between zero and TC/2 radians relative to the mechanical displacement. This may reflect three factors. First, the possibility exists that the hair bundles of inner hair cells, being coupled to the tectorial membrane only through a boundary layer of fluid, are in fact viscously coupled to the mechanical movement of the cochlear partition, as observed for low frequencies in vivo [13]. Second, the existence of a traveling wave, however attenuated, means that the microphonic potential represents a weighted average of all hair cells in the preparation, whose mechanical and electrical responses vary in phase. Thus, the phase of a mechanical recording taken at a single location along the exposed cochlear segment is not directly comparable to the phase-averaged microphonic potential. Finally, if there are any additional modes of movement across the radial dimension of the organ of Corti, the inner and outer hair cells may not move exactly in phase, leading to another source of potential phase shift. The microphonic potentials are typically about 100 uV in peak-to-peak magnitude at resonance for bundle deflections near ±300 nm in response to a 71-dB SPL acoustic frequency sweep. Given the 2-kQ transepithelial resistance, these values correspond to a microphonic current of roughly 50 nA. A typical 700um exposed segment has approximately 100 inner hair cells and 300 outer hair cells; a single hair cell would then be estimated to account for about HOpA of transduction current. Considering the +80-mV applied endocochlear potential and the approximately -50-mV resting potential estimated from the transepithelial potential at which the microphonic potential reverses sign [10], this current corresponds to a single-cell conductance of 0.9 nS, which is considerably lower than the saturation values of 9.4 nS obtained in vitro [14] and of 17.3 nS obtained at the apex of the hemicochlea [15]. The considerable discrepancy in estimated single-cell conductance represents in part damage done to the preparation; however, the acoustic stimulus is not saturating, and the microphonic potential is likely to be underestimated owing to the phase dispersion along and perhaps across the organ of Corti. In vivo analysis of the cochlear active process is greatly complicated by the presence of a traveling wave on the cochlear partition. As a result of this mode of movement, different portions of the partition are at any instant responding in quite different ways. As the basilar membrane moves upwards at one position, the hair cells there are depolarized, and their active process—whether driven by membranebased electromotility or by active hair-bundle motility—is of a particular strength and polarity. At the same time, though, the basilar membrane only a few hundred micrometers away is moving downwards, causing hair-cell hyperpolarization and evoking an active response that is different, perhaps even opposite. Because the wavelength of the traveling wave diminishes near the characteristic place for any

133 particular frequency, this problem is most acute where the active process is most vigorous and of the greatest importance in determining cochlear responsiveness. Immediately before the traveling wave collapses, its wavelength is thought to decline to 500 um or so, depending on the characteristic frequency and species [11]. Hair cells only a few tens of diameters apart must then operate in opposition to one another. In the experimental preparation under consideration, we have attempted to simplify the movement by encouraging a segment of the cochlear partition to resonate in a simple, second-order mode. To the extent that the segment of cochlear partition moves in this fashion, the preparation offers the simplification that all of the hair cells function more-or-less in concert. The cochlear microphonic signal, for example, reflects their simultaneous depolarizing and hyperpolarizing responses. More importantly, the active process is likely to operate synchronously throughout the segment. As for any reductionistic modification of a complex biological phenomenon, the simplification that we have achieved is purchased at the price of some distortion in the activities under study. For example, it is likely that the intrinsic kinetics of the active process varies along the tonotopic map. In order to achieve reasonable results in a model of active hair-bundle motility based on Ca2+-dependent reclosure of transduction channels, it is necessary to impose a tonotopic variation in the activation energy of channel gating [16]. Consistent with this expectation, experimental measurements reveal systematic gradients in the rate of channel reclosure along the basilar membrane [17]. It follows that the active process manifested in the present experimental preparation must be somewhat compromised during stimulation at the preparation's resonant frequency, which may not match the segment's intrinsic best frequency. Although the geometrical configuration of the present experimental preparation is meant to favor second-order resonance, the traveling-wave mode of motion is not entirely suppressed. In most of our preparations of the jird's middle cochlear turn, the compliance of the cochlear partition and the mass of entrained perilymph establish a natural frequency of 700-1000 Hz. In many instances, however, measurement of bundle motion at inner hair cells and phase changes along the exposed segment disclose an additional resonance in the range 1200-1400 Hz. Although it is of smaller amplitude than the low-frequency resonance, this highfrequency response probably occurs nearer the cochlear segment's natural frequency in vivo [18]. Future experiments should attempt to match the imposed mechanical resonance to this intrinsic resonance, which may augment the active response.

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Acknowledgments The authors thank the members of our research group for comments on the manuscript. This research was supported by National Institutes of Health grant DC00241. A.J.H. is an Investigator of Howard Hughes Medical Institute. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Manley, G.A., 2001. Evidence for an active process and a cochlear amplifier in nonmammals. J Neurophysiol 86, 541-549. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc Natl Acad Sci USA 96,4420-4425. Dallos, P., Evans, B.M., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science 267, 2006-2009. Weitzel, E.K., Tasker, R., Brownell, W.E., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J Acoust Soc Am 114, 1462-1466. Zheng, J., Shen, W., He, D.Z., Long, K.B., Madison, L.D., Dallos, P., 2000. Prestin is the motor protein of cochlear hair cells. Nature 405, 149-155. Martin, P., Hudspeth, A.J., 1999. Active hair-bundle movements can amplify a hair cell's response to oscillatory mechanical stimuli. Proc Natl Acad Sci USA 96, 14306-14311. Martin, P., Hudspeth, A.J., 2001. Compressive nonlinearity in the hair bundle's active response to mechanical stimulation. Proc Natl Acad Sci USA 98, 14386-14391. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat Neurosci 6, 832-836. Holt, J.R., Corey, D.P., Eatock, R.A., 1997. Mechanoelectrical transduction and adaptation in hair cells of the mouse utricle, a low-frequency vestibular organ. J Neurosci 17, 8739-8748. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8, 149-155. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea. Physiol Rev 81, 1305-1352. Hu, X., Evans, B.N., Dallos, P., 1999. Direct visualization of organ of Corti kinematics in a hemicochlea. J Neurophysiol 82, 2798-2807. Sellick, P.M., Russell, I.J., 1980. Responses of inner hair cells to basilar membrane velocity during low frequency auditory stimulation in the guinea pig cochlea. Hear Res 2, 439-446. Kros, C.J., Riisch, A., Richardson, G.P., 1992. Mechano-electrical transducer currents in hair cells of the cultured neonatal mouse cochlea. Proc R Soc Lond B Biol Sci 249, 185-193.

135 15. 16. 17. 18.

He, D.Z., Jia, S., Dallos, P., 2004. Mechanoelectrical transduction of adult outer hair cells studied in a gerbil hemicochlea. Nature 429, 766-770. Choe, Y., Magnasco, M.O., Hudspeth, A.J., 1998. A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectricaltransduction channels. Proc Natl Acad Sci USA 95, 15321-15326. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2003. Tonotopic variation in the conductance of the hair cell mechanotransducer channel. Neuron 40, 983990. Milller, M., 1996. The cochlear place-frequency map of the adult and developing Mongolian gerbil. Hear Res 94, 148-156.

Comments and Discussion Withnell: In your talk you discussed channel reclosure associated with myosinmediated channel slippage and relaxation of the gating tension. Could such a mechanism play a role in hair-bundle driven amplification, and if so, how would relaxation of the gating tension produce a reversal of bundle direction of motion (or a power-stroke)? Answer: We have established that active hair-bundle motility is driven by myosinlc-mediated adaptation and by Ca2+-dependent channel reclosure, a process that Dr. Gillespie and his colleagues have demonstrated in an accompanying contribution also involves mechanical relaxation of myosin-lc. The cyclic activity of myosin molecules that underlies active hair-bundle motility has been modeled {Proc. Natl. Acad. Sci. USA 97: 12026 [2000]; J. Neurosci. 23: 4533 [2003]), and experiments by Dr. L. Le Goff and Dr. D. Bozovic have recently confirmed that the mechanism operates as proposed (in preparation). During the positive phase of stimulation, when a hair bundle moves towards it tall edge, the opening of transduction channels releases a part of the tension stored in the flexed stereociliary pivots and thereby enhances the forward motion. Slipping adaptation by the myosin motors subsequently releases additional tension and permits channel reclosure. During the negative phase of displacement, by contrast, the myosin molecules use ATP to ascend the stereociliary actin cytoskeleton, thus increasing tip-link tension and repriming the system for another cycle of movement. Zheng: When we are talking about "cochlear amplifier", we usually mean the mechanical input from the OHCs. When we are talking about the "active hair bundle motility", we are supposed to talk about that of the OHCs. However, in your experiment, you measured the hair bundle motion of the IHCs instead of that of the OHCs. We know that IHCs and OHCs behave quite differently, and the link between the motions of the IHCs and OHCs is still not clear. Therefore, it is invalid to use the mechanical responses of the IHCs to address the "active hair bundle motility" of the OHCs. I am curious to know your reasons to do so. Why don't you measure the mechanical motion of the hair bundles of the OHCs directly?

136 Answer: Across a broad range of receptor organs and throughout the tetrapods, the ear's active process is defined by amplification, frequency tuning, compressive nonlinearity, and spontaneous otoacoustic emission. Active hair-bundle motility has been shown to account for all four of those characteristics in the bullfrog's sacculus. Moreover, the present experiments and the accompanying contribution from Dr. Fettiplace and his colleagues establish that hair cells of the mammalian cochlea display active hair-bundle motility and that it contributes to the active process. Because of the low optical contrast of the hair bundles on outer hair cells in our preparation, we elected to measure movement of the bundles on inner hair cells as a means of detecting the compressive nonlinearity diagnostic of the active process. The use of inner hair cells as an assay for the active process by no means implies that these cells mediate amplification. Chadwick: My comment concerns how the magnitude of the bundle stiffness inferred from your gerbil preparation (I think you said 14 mN/m) would affect the shape of the force/displacement relation in your active bundle model. I suspect such a large value will effectively eliminate the negative stiffness region in the force/displacement relation unless you drastically alter the magnitude of the active molecular parameters you determined from the frog. Answer: The magnitude of a hair bundle's gating compliance—which underlies the phenomenon of negative stiffness—is directly proportional to the number of stereocilia in a hair bundle (or more precisely to the number of gating springs, and hence tip links) and to the square of the geometrical gain factor that relates shear at the stereociliary tips to horizontal displacement of a bundle's top. For hair bundles of the frog's sacculus, whose stiffness is around 1 rnN-m"1, there are potentially about 50 tip links interconnecting 60 or so stereocilia; the bundle's geometrical gain factor is 0.14. Detailed morphological data are not available for the hair bundles of outer hair cells in the middle turn of the jird's cochlea, whose stiffness we estimate as 14mN-m_1. From descriptions of the corresponding cochear positions in other rodents, though, we expect each hair bundle to possess about 150 stereocilia with 100 tip links and to display a geometrical gain factor near 0.4. If the gating-spring stiffness and channel-gating distance are constant, we therefore anticipate the maximal gating compliance in the mammalian preparation to be 15-fold that in the frog. If this proves to be the case, the mammalian hair bundles should also demonstrate negative stiffness that can serve as the substrate for an active process mediated by active hair-bundle motility. van der Heijden: The range of deflections over which you observe negative hair bundle stiffness indicates that this is a low-intensity phenomenon. This is clear from your figure 1: compressive growth is confined to a 10 to 20-dB range of SPLs at the low end. At higher SPLs, linearity reigns. Cochlear-mechanical nonlinearity, however, is known to exist over a range of at least 80 dB. Do you agree that negative hair bundle stiffness is unlikely to account for compression, suppression and distortion except at very low sound levels?

137 Answer: The observations reported in the present publication deal with the compressive nonlinearity associated with the ear's active process; negative stiffness is not directly under investigation. Figure 1 demonstrates that, in an excised segment of the middle turn of the jird's cochlea, the magnitude of hair-bundle movements displays power-law scaling with the stimulating pressure. The exponent of 0.7 confirms the presence of compressive nonlinearity, a feature of the active process. The nonlinearity falls well short of that observed in an intact animal, which reaches 0.3 or even less. As you have noted, the dynamic range of the nonlinearity is also restricted in our experiments to a pressure difference across the cochlear partition of about 25-55 dB SPL (Nat. Neurosci. 8: 149 [2005]), which corresponds to 5-35 dB SPL for stimulation in air. Although we are uncertain why the in vitro preparation fails to match the performance of the intact ear, likely causes include damage during dissection, stimulation at a frequency more than one octave below the natural frequency of the cochlear place, experimentation at a temperature of 31 ° rather than 38°, and perhaps an inappropriate ionic environment. In order to address the issue that you have raised, we are attempting to remedy some of these deficiencies in our continuing experiments.

CA2+ DYNAMICS IN AUDITORY AND VESTIBULAR HAIR CELLS: MONTE CARLO SIMULATIONS AND EXPERIMENTAL RESULTS

MARIO M. BORTOLOZZI, ANDREA LELLI AND FABIO MAMMANO Venetian Institute of Molecular Medicine, via G. Orus 2, 35129 Padua - Italy E-mail: [email protected], +39 049 7923231 E-mail: [email protected], +39 049 7923247 We developed a simulation code in the Matlab environment for the study, using the Monte Carlo method, of cellular phenomena involving diffusion, buffering, extrusion and release of Ca2+. In particular we simulated the entry of Ca2+ at individual presynaptic active zones (hotspots) of auditory and vestibular hair cells, where Ca2+ plays a fundamental role in the transduction of mechanical stimuli, due to sound or acceleration, into electrical signals to be sent to the brain. The realistic reconstruction, in three dimensions, of the cellular boundaries and the derivation of the virtual fluorescence ratio AF/F0 (equivalent to the one computed from fluorescence microscopy experiments) allowed us (i) to directly compare simulations to experimental data, (ii) to supply an estimate of the equivalent concentration of Ca2+ reactants (buffers) and (iii) to show how the mass action law hypothesis brakes down because of the local non equilibrium of the system.

1 Introduction Past attempts at understanding Ca2+ dynamics in hair cells have followed either experimental or theoretical lines. Experimental approaches typically combine Ca2+sensitive fluorescent indicators {dyes) and microscopy to produce images of the patterns of fluorescence of a Ca2+ indicator (complexed to Ca2+) following various stimulation protocols [1, 2]. Unfortunately, such optical methods suffer from intrinsic limitations due to the limited spatial resolution. Furthermore, in general, several approximations are utilized in the interpretation of fluorescence imaging data [3]. In this work we have modeled, using the Monte Carlo method, the buffered diffusion of Ca2+ from discrete and localized Ca2+ entry sites (hotspots) following depolarization of hair cell plasma membrane. Monte Carlo simulations, based upon random number generation, have been used successfully to study reaction and diffusion processes in biological systems [4, 5, 6, 7 and 8]. There are several reasons why one should adopt a Monte Carlo approach. First, it permits to construct realistic representations of the relevant cell surfaces, in particular plasma membrane and nuclear membrane. Second, the boundary conditions for the reaction diffusion equations are more easily taken into account, and can be altered with great ease. Third, simulating the dynamics of a relatively small number of molecules by a stochastic approach allowed us to better compare and comprehend experimental fluorescence data of Ca2+ buffered by fluorescent dyes in living hair cells. Which

138

139

may be more appropriate and safer than the solution of the reaction-diffusion differential equations in terms of concentrations [9 and 10]. 2 Methods 2.1 Diffusion equation and random vjalk The concentration C of a set of N identical molecules that start diffusing at time t=0 in nfree, homogeneous and isotropic medium from a point source in the origin of the Cartesian axes, can be derived from Fick's second law as: M

AD 1

NfN

(x^y'+z1) 4Dl

C(x,y,z,t) = ^3/2 ^3/2 (4*Z>0 {AnDty [11] where Mis the number of mols, NA the Avogadro's number and D the diffusion constant (um2 s"1). The Monte Carlo algorithm can be exploited to approximate the Brownian motion of the individual molecules (random vjalk) with arbitrary boundary conditions. In the limit of N=l, the function NAC(x,y,z,At) can be interpret as the occurrence probability, after a time At, of a displacement of a single molecule from the origin to the point of coordinates (x,y,z), i.e. the product of the three independent probabilities Px, Py, Pz of a displacement along the axes x, y, z. These probability distributions are normalized Gaussians with variance a = yJ2Dkt. In our algorithm, molecular motion is not followed at the level of the actual Brownian motion, rather it is described at a much coarser level using N of the order of 10s particles and a time step At of the order of 10"5 s. Figure 1. Cell boundary construction (plasma membrane and nucleus). We assumed generalized cylindrical symmetry for the hair cells, whereby the symmetry axis is a smooth curve belonging to the focal plane. Starting from an image of the hair cell (A) we intended to simulate, we designed the contour of the plasma membrane in the focal plane and constructed a 3D model (B and C) of the membrane from the interpolated 2D contour (A). The interaction between the simulated particles and the cell boundaries was assumed to obey the solution of the unidimensional diffusion equation for a instantaneous point source in a infinite cylinder of infinitesimal thickness [11].

140 2.2

Chemical

reactions

2+

Ca binding reactions are a fundamental mechanism to maintain intracellular Ca 2+ concentration ([Ca 2+ ] ; ) at sub-uM levels. The reactions involving Ca 2+ , a pool of endogenous buffers (B) as well as one exogenous buffer (F, typically, a fluorescent dye), and the mass conservation law were simulated by the following two sets of partial differential equations:

^ ^ - O C a n m - O C a B ] dt (Eq.l) cfCaF] = C[Ca 2 + ],[F]-^ F F [CaF] dt

3[Ca2 dt

5[CaB] 5[CaF]_ dt dt 3[CaB]_ 9[B] dt dt d[CaF] _ 5[F] dt

(Eq.2)

dt

where k^ , k^ and k^ , k^ are, respectively, the binding and unbinding rate constants of Ca 2+ to B and F. Molar concentrations were mapped to number of particles by the use of a mapping factor $ = CVii/«v,i for each species i, which defines the relationship between the number »v,i of simulated particles of the z'-th specie counted within a given volume J 7 and the corresponding concentration Cv>; . Chemical reaction computations (Eqs. 1 and 2) were performed by subdividing the 3-D diffusion space in cubic voxels of side / (comprised between 200 nm and 500 nm) and using a time step Ax = 5-10"7 s. 2.3

Calcium influx

Under whole-cell voltage clamp conditions, hair cells of the frog semicircular canal, stimulated by depolarization, revealed Ca 2+ entry at selected sites (hotspot) located mostly in the lower (synaptic) half of the cell body [12 and 13]. Their mean estimated diameter dn01 is about 276 nm [14], which is very close to the spatial resolution, /, of our simulations. For this reason, we assumed the hotspots to be point sources whose time dependence is dictated by that of the underlying Ca 2+ current. To determine Ca 2+ influx, we fitted [15] experimental current traces to obtain, using the mapping factor %, the mean number «Ca2* (?) of Ca 2+ ions entered through a single hotspot at time t, nc^(t)=

round\

^

V ^FcX

, where Qc^{t) '

"HOT

is

J

the total charge carried by Ca 2+ into the cell, Fc = 9.6485x10 4 C mol"1 is the Faraday constant and « H OT the number of active hotspots present in the cell. The function roundQ was used throughout to approximate the result to the nearest integer number of particles.

141 2.4 Calcium extrusion and storage During the course of a typical Ca2+ transient, various pumps and exchangers remove Ca2+ from the cytoplasm. In hair cells, the hair bundles rely on mobile Ca2+ buffers, the plasma membrane Ca2+-ATPases (PMCAs) and the SERCA pumps of the endoplasmic reticulum to regulate Ca2+ levels [16]. Uptake of Ca2+ due to pumps can be modeled as an instantaneous function of the [Ca2+];, Ca2+

4

l

dt

,,

'

!>*],-

[Ca 2+ ]; + tf M "

[9, 10, 16 and 17]. The parameter y depends to the number of pumps and their maximal turnover rate, KM is their Michaelis constant and the exponent m equals one, for the PMCA pumps, and two for the SERCAs. 2.5 Converting particle counts to simulatedfluorescence signals An estimate of the [Ca2+]( change can be obtained by fluorescence experiments using single wavelength indicators [12, 13] such as Fluo3, Oregon Green 488 BAPTA-1 and many others. At a given wavelength of emission, the measured fluorescence signal F can be expressed by F=Sbnb+S/if (Eq.3), where nb is the number of molecules of dye buffered to Ca2+ and n/ is the number of free dye molecules [3]. In general, Sb and Sf depend of many parameters of the experimental setup. Suppose the dye to be in equilibrium with Ca2+, we can obtain the free Ca2+ concentration change by A[~Ca2+j = AF/F0=(F-F0)/F0

(Eq.4), where F0 is the

2+

mean basal fluorescence signal before Ca enters the cell [3]. Nevertheless, the equilibrium hypothesis underlying Eq.4 breaks down near active zones during Ca2+ influx. In order to compare simulation results to experimental data we defined a = SbISf to obtain, using Eq.3, the relationships: F = Sf(anb + tij-), F0 = Sj-(anbo + rij-0) (Eqs.5 and 6), where nM and np are, respectively, the number of dye molecules bound to Ca2+ and the initial number of free molecules at equilibrium (before Ca2+ enters the cell). In our simulations involving Oregon Green 488 BAPTA-1, we set a=5 (measured on our imaging setups). Defining A as the constant of proportionality between the number n of real molecules and the one N of simulated particles, we obtain, from Eqs.5 and 6, F = Sj-A(aNb + Nf) and F = SfA.(aNb0+Nf0). Leading to the final expression: ArCa 2+ l sAF/FQ= [aNb +Nf- aNb0 -jV/0]/(aj\r60

+ Nf0).

To include in the model the error on AF/F0 due to the poor axial resolution of wide field microscopy, we considered the relationship between the fluorescence intensity, Fz, in the image plane due to a point source and the source distance, z, from the focal plane (z = 0) . In particular, we estimated the ratio a>(z) = F/FZ=Q , by fitting the data of Hiraoka et al. [18] for the case of a 90 urn diameter illumination field.

142

To simulate the operating conditions of the CCD camera used to acquire the fluorescence images, wc integrated numerically the computed fluorescence signal over time intervals of 4.03 ms, corresponding to the actual CCD exposure time. Consecutive integration periods were separated by a delay of 0.1 ms to account for data transfer from the CCD image area to its storage area [19]. 3 Results and Discussion Figure 2. Setting initial conditions for the simulations. The hair cell examined in the following was 25 urn long. The location and the number of the active hotspots were estimated: I) from the experimental Ca"' current entering the cell, considering that each hotspot generated aboul a 45pA current [10 and 13] and, 2) from the pseudo-color movie of the ratio AF/F0 obtained by processing the fluorescence images captured during the experiment with a mean period of 4.03 ms (including 0.1 ms of data transfer), during 50 ms cell depolarization. The simulated Ca2* current (shown as smooth line) was derived by fitting the patch-clamp data and equally distributing Ca2" influx between the ten active hotspots.

Ca2-current fit

0 „. Ml

>

,„

4M

200 220 240 260

280 300

320

340

360 380

400

Time (ms)

For these experiments we used hair cells of the semicircular canals of the frog (crista ampullar is). We carried out several simulations involving different BAPTA total concentrations because we were interested in obtaining an estimate of the basal concentration of the endogenous native Ca2* buffers in hair cells. This is central to the comprehension of intracellular Ca2+ dynamics. The best agreement between experimental and simulated kinetics was obtained using 1.6 raM BAPTA as the equivalent (in the simulations) of the endogenous buffers. This value is the same obtained from experimental results in saccular hair cells [20]. Figure 3 shows how Monte Carlo (unlike PDE methods) correctly reproduces the intrinsic noise features of the AF/Fa signal. We also found that the overwhelming contribution to the speed of the recovery phase of the signal (over the one second time scale of these simulations) is due to the buffers, instead of to the calcium pumps in the plasma membrane and the ER. Note that the concentration of free calcium that reaches the apex of the cell is only about 70 nanomolar starting from a resting concentration of 50 nanomolar. In conclusion, this simulation code can be used as a versatile instrument. Several cellular phenomena involving diffusion, buffering, extrusion and release within cellular staictures can be accurately simulated with using our variant of the Monte Carlo algorithm with acceptable CPU time consumption.

143

Figure 3. Real and simulated hair cell Ca2* dynamics. We simulated about 150,000 particles reacting within voxels of side /=0.5 urn with computational steps of 0.5 us. (A) Fluorescence-ratio (AF/Ft,) pseudo-colour images of the simulated (left) and real cell (right) compared after about 100 ms from the onset of the Ca"' current (Figure 2) at the ten hotspots. The black circles superimposed on the two figures are the regions of interest (ROls) where AF/F0 was measured (panel B), placed approximately in zones corresponding to the location of two selected hotspots. (B) Comparison between virtual (black line) and experimental (red line) fluorescence-ratio AF/F0 from the ROls in A. (C) The mass action law. which predicts proportionality between the signal A/-"//'",, and the free calcium concentration change, brakes down because of the local non equilibrium of the system. To make the point we analyzed pseudo-line scan plots obtained by plotting the lime course of the relevant signal at each pixel along the line shown superimposed on the cell plotted with the white hotspots (Panel D).

Acknowledgements We thank C. D. Ciubotaru (Venetian Institute of Molecular Medicine, Padua, Italy) for help with computer programming and image processing and S. Bastianello (idem) for helpful comments.

144 References 1. Issa, N.P., Hudspeth, A.J., 1994. Clustering of Ca2+ channels and Ca2+activated K+ channels at fluorescently labeled presynaptic active zones of hair cells. Proc Natl Acad Sci U S A 91(16): 7578-82. 2. Tucker, T., Fettiplace, R., 1995. Confocal imaging of calcium microdomains and calcium extrusion in turtle hair cells. Neuron 15(6): 1323-35. 3. Grynkiewicz, G., Poenie, M., et al., 1985. A new generation of Ca2+ indicators with greatly improved fluorescence properties. J Biol Chem 260(6): 3440-50. 4. Saxton, M.J., 1994. Anomalous diffusion due to obstacles: a Monte Carlo study. Biophys J 66(2 Pt 1): 394-401. 5. Saxton, M.J., 1996. Anomalous diffusion due to binding: a Monte Carlo study. Biophys J 70(3): 1250-62. 6. Kruk, P.J., Korn, H., et al., 1997. The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study. Biophys J 73(6): 2874-90. 7. Gil, A., Segura, J., et al., 2000. Monte carlo simulation of 3-D buffered Ca2+ diffusion in neuroendocrine cells. Biophys J 78(1): 13-33. 8. Bennett, M.R., Farnell, L., et al., 2000. The probability of quantal secretion near a single calcium channel of an active zone. Biophys J 78(5): 2201-21. 9. Lumpkin, E.A., Hudspeth, A.J., 1998. Regulation of free Ca2+ concentration in hair-cell stereocilia. JNeurosci 18(16): 6300-18. 10. Wu, Y.C., Tucker, T., et al., 1996. A theoretical study of calcium microdomains in turtle hair cells. Biophys J 71(5): 2256-75. 11. Crank, J., (1975). The Mathematics of Diffusion. London, Oxford University ' Press. 12. Lelli, A., Perin, P., et al., 2003. Presynaptic calcium stores modulate afferent release in vestibular hair cells. J Neurosci 23(17): 6894-903. 13. Rispoli, G., Martini, M., et al., 2001. Dynamics of intracellular calcium in hair cells isolated from the semicircular canal of the frog. Cell Calcium 30(2): 131-40. 14. Roberts, W.M., Jacobs, R.A. , et al., 1990. Colocalization of ion channels involved in frequency selectivity and synaptic transmission at presynaptic active zones of hair cells. J Neurosci 10(11): 3664-84. 15. Rispoli, G., Martini, M., et al., 2000. Ca2+-dependent kinetics of hair cell Ca2+ currents resolved with the use of cesium BAPTA. Neuroreport 11(12): 2769-74. 16. Dumont, R.A., Lins, U., et al., 2001. Plasma membrane Ca2+-ATPase isoform 2a is the PMCA of hair bundles. J Neurosci 21(14): 5066-78. 17. Goldbeter, A., Dupont, G., et al., 1990. Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl Acad Sci U S A 87(4): 1461-5.

145 18. Hiraoka, Y., Sedat, J.W., et al., 1990. Determination of three-dimensional imaging properties of a light microscope system. Partial confocal behavior in epifluorescence microscopy. Biophys J 57(2): 325-33. 19. Mammano, F, Canepari, M, Capello, G, Ijaduola, RB, Cunei, A, Ying, L, Fratnik, F, Colavita, A, 1999. An optical recording system based on a fast CCD sensor for biological imaging. Cell Calcium, 25(2): 115-123. 20. Roberts, W.M., 1993. Spatial calcium buffering in saccular hair cells. Nature 363(6424): 74-6.

E L E C T R O - M E C H A N I C A L W A V E S IN ISOLATED OUTER HAIR CELL

S. CLIFFORD, W.E. BROWNELL* AND R.D. RABBITT Dept. ofBioengineering, Univ. Utah, Salt Lake City, UT, USA E-mail: [email protected] *Bobby R. Alford Department Otorhinolaryngology and Communicative Sciences, Baylor College of Medicine, Houston, TX, USA E-mail: [email protected] Recent in vitro and in vivo data have drawn attention to the presence of high-frequency electro-mechanical resonances in the electrically evoked response of the cochlear partition and analogous resonances in isolated cochlear outer hair cells (OHCs). Resonances in isolated OHCs are similar to those present in damped piezoelectric structures and therefore it has been suggested that the behavior may result from the interplay of electro-mechanical potential energy and mechanical kinetic energy. In OHCs, the total potential energy includes both mechanical and electrical terms associated with the lateral wall while the kinetic energy accounts for the inertia of the moving fluids and tissues entrained by the moving plasma membrane. We applied first principles of physics to derive a model of OHC electromechanics consisting of an electrical cable equation directly coupled to a mechanical wave equation. The model accounts for the voltage-dependent capacitance observed in OHCs by means of a nonlinear piezoelectric coefficient. The model predicts the presence of electromechanical traveling waves that transmit power along the axis of the cell and underlie highfrequency resonance. Findings suggest that the subsurface cisterna (SCC) directs current from the transduction channels to the lateral wall and slows the phase velocity of the traveling wave. Results argue against the common assumption of space-clamp in OHCs under physiological or patch clamp conditions. We supplemented the traveling wave model with an empirical description of transduction current adaptation. Results indicate that the so-called RC paradox isn't paradoxical at all; rather the capacitance of the OHC may work in concert with transduction current adaptation and electro-mechanical wave propagation to achieve a relatively flat frequency response.

1 Introduction Current theories concerned with the sensitivity and frequency selectivity of mammalian hearing involve OHCs functioning as active amplifiers [1], boosting mechanical input to the inner hair cells. Both active hair bundle motion [2] and somatic electromotility [3, 1] are involved The mechanism somatic force production, while not completely understood, is not directly dependent upon ATP [4] and is in part, due to the outer hair cells (OHCs) highly specialized trilaminate lateral wall. It has been speculated that OHC somatic force production requires the cells to maintain cycle-by-cycle membrane potential modulations up very high frequencies well above the whole-cell membrane time constant [5]. One would expect the OHC membrane capacitance to short circuit the cell at high frequencies and prevent voltage driven displacement from occurring—this is known as the RC paradox [6]. Piezoelectric models of the OHC lateral wall are among the numerous attempts that have been made to address the RC paradox [7-14]. Piezoelectric models predict

146

147 experimental results such as whole-cell piezoelectric resonance exhibited by OHC [15] at high frequencies [16-20]. In addition, recent piezoelectric models agree with the relatively flat frequency response generated by cells upon low frequency stimulation in the pipette micro-chamber configuration [21]. OHC electromechanical behavior is consistent with thermodynamic Maxwell reciprocity required of piezoelectric materials [22, 23]. It is also useful to note that this remarkable piezoelectric behavior of OHCs is closely linked to the expression of the membrane-bound protein prestin [24-26]. It has been shown that isolated OHCs exhibit high-frequency electrical resonances as predicted by the piezoelectric models [20]. Resonances in piezoelectric materials arise due to the interaction between mechanical potential and electrical potential energy as well as kinetic energy. These piezoelectric resonances have standing modes of vibration that are established by constructive interference of waves traveling in one direction with waves traveling in the opposite direction [27, 28]. This connection between resonance, wave propagation and the presence of piezoelectric-like resonances in OHCs led us to develop the piezoelectric traveling wave theory of OHC somatic motility. Results suggest three factors that may be essential OHC somatic motility for high-frequency hair bundle motion: 1) an effective RC corner that shifts up with increasing frequency, 2) trasduction current adaptation that increases current with frequency and, 3) electro-mechancial wave propagation along the lateral wall. 2 Methods 2.1 OHC Traveling wave equations An axisymmetric model of the OHC was derived from first principles by treating the lateral wall as a piezoelectric material with constitutive behavior described by Tiersten [27]. A conductance tensor was added to the standard piezoelectric theory to account for membane conductance, and a Boltzmann function to account for strain-dependent saturation of the piezoelectric coefficient and the assocaited OHC voltage dependent capacitance [9, 29, 30]. Under the assumption of axisymmetric deformations, homogeneity, locally constant intracellular volume (for each dx slice of the cell conservation of linear momentum along the axis of the hair cell gives d2u j d2u dV du ni —2T = c —2r - a y— ' *- > dt dx dx dt where x is the axial position along the cell, t is time, u(x,t) is the local axial displacement, and c is the mechanical speed (in the absence of an electric field) along the axis of the cell . The parameter a is proportional to the piezoelectric coefficient, and y is the effective damping coefficient resulting from interaction with both the fluid inside outside the cell. Based on large OHCs from the apical turn of the guinea pig, we estimate c~2.9 m/s, a~88 m2/v-s2, and /-4.5e3 s"1 (at 1

148 kHz). Note if the voltage V is constant or the piezoelectric coefficient a is zero, then Eq. 1 reduces to the classical wave equation. Spatial variation of the membrane potential Fwas modeled using a distributed approach similar to Halter et al. [31]. In this model, it is assumed that current flows from the apical end of the cell along the narrow annular space between the subsurface cisterna (SSC) and the plasma membrane. This assumption has not been validated experimentally but, interestingly, results in an electro-mechanical wave speed consistent with resonance frequencies observed experimentally [19] and reproduces the relatively flat whole cell and force and displacement observed experimentally [21]. Part of the current entering the cell at the cilia is shunted to ground through the piezoelectric element in the lateral wall, while the remaining fraction reaches the base of the cell. From Kirchoff s current and voltage laws, the cable equation governing the membrane potential for the piezoelectric case is A.2—--T

V-/3

= -TJI >

(2)

dx dt dxdt where V(x,t) is the perturbation in the membrane potential, I(x,t) is the injected current (per unit length), A is the classical space constant appearing in the cable equation, x is the classical membrane time constant associated with the zero-strain condition , and 1/ 77 is the membrane conductance per unit length that appears in the cable equation [32]. The above equation reduces to the standard cable equation in the absence of strain (du/dx = 0 ), or when the piezoelectric coefficient is zero p=Q. For the highly resistive lateral wall of large OHCs from the apical turn of the guinea pig cochlea we estimate X = 1.8e-3 m, T = 2 s, /?= 0.28 V-s, and rj=2.65e6 Q. To model the relationship between hair-bundle motion and the transduction current, we used a very simple first-order model that accounts for some of the major properties of transduction current adaptation

*L + ±Ii = G*.

(3)

dt r, dt where / is the transduction current, T is the transduction current adaptation time constant, G, is the transduction current gain and x is the bundle displacement. For 1 kHz, we estimate T ~ 49e-6 s and G, ~ 0.012 Amp/m [33]. For sinusoidal stimuli below 1/z,, adaptation causes the transduction current to increase as the frequency of hair bundle motion is increased. For bundle frequencies higher than (1/T,) this simple model predicts relatively flat current gain and phase. 3 Results and Discussion There are three key features of the piezoelectric traveling wave equations that may have direct relevance to OHC function—particularly at high auditory frequencies where single-compartment models may fail. The first feature (cable equation) leads

149 us to question the concept of space-clamp and frequency-independent RC input properties of OHCs. An infinitely long cable, even in the absence of piezoelectricity (JJ=0), has a frequency dependent input capacitance, and a corner frequency that moves up with increasing frequency. Fig. 1 shows the voltage at x=0 of an infinite cable to an impulse of current injection at (applied at t=0, x=0 for P=0). Notice in the left panel that the voltage decays with multiple relaxation times showing that a single RC model is not appropriate to capture the frequency dependent input impedance. For the cable equation, the input capacitance and conductance both decrease with increasing frequency above (1/T) due to the fact that the length of membrane clamped by the injected current becomes shorter as the frequency is increased. Hence, it is never possible in a simple cable to exceed the corner frequency using current injection at a point (e.g. solid curve in Fig. IB is always above the dotted curve). We hypothesize that OHCs behave in a similar way and that the variation in OHC length along the cochlea optimizes the frequency dependent length constant of the cell with respect to the best place in the cochlea. 100-

B

S

^

10-

_^*^

1 0.1 0.01 - !"•"""'• 0.5

1.0

1.5

Time < t > %,}

"

"

T

S

n

»•'•»'''"'" 1

^

>™T-r-rrmr—T-r-rrc m)

o.i i w Input Frequency ( O) T M)

Fig. 1. Response of an infinite cable to impulse current injection at x=0. Left panel (A) shows nonexponential decay of the voltage at x=0 illustrating multiple relaxation times. Panel B illustrates the apparent corner frequency (1/TM) of the cable as a function of input frequency. Below the cable corner frequency, the cable is "space-clamped" for a finite length corresponding to the DC length constant. Above the cable corner frequency, loss through the membrane reduces the length of the clamped segment and thereby decreases the input capacitance. As a result the corner is never reached. Instead, relative to the input stimulus, the cable appears to become shorter as the frequency is increased.

Results in Fig. 1 indicate that the "effective" size of the cell felt at the transducer may decrease with frequency thus bypassing part of the problem of capacitive shunt by the membrane. The second feature (transduction current adaptation) further builds on this effect. Since the transduction current adapts (Fig. 2A) for maintained hair bundle displacements, the current magnitude will increase with bundle frequency (at least below 1/T,) and that this will also counteract membrane capacitance (Fig. 2B). This is illustrated in Fig. 2 for a simple first-order linear model of transduction current adaptation.

150

1 A

T

-I

0

1 2 Time (n»)

3

-

l

i

l

l

0.1

i

10

100

Frequency 0d\7)

Fig. 2. Panel A shows adaptation of a model outer hair cell transduction current (lower) in response to a step bundle displacement (above). This form of adaptation is a high-pass filter in the frequency domain (B, solid curves) that would be expected to counteract the roll-off in hair-cell receptor potential caused by membrane capacitance (B, dashed curves).

The third key feature of the model is the fact that the piezoelectricity introduces slow electro-mechanical traveling waves. This occurs because piezoelectricity couples mechanical inertia and stiffness to the electrical cable properties. Waves are predicted support cycle-by-cycle function of OHCs somatic electromotility at high auditory frequencies and quantitatively predict high frequency electro-mechanical resonances of isolated cells [19]. Fig. 3 shows voltage and displacement predicted by this model for three cases: A) sinusoidal voltage stimuli (mV) using a pipette microchamber B) sinusoidal current injection (pA) using a patch pipette attached to the base of the cell and C) sinusoidal hair bundle displacement (urn) to induce a modulated transduction current. It is important to note the significant differences in voltage and displacement patterns between these three stimulus types.

151 A. Pipette Microchamber-0.1 kHz

_ Qispiacenwni <• -Voltage

Fig. 3. Pipette microchamber (A), patch pipette (B) and physiological voltage and displacement. Axial displacement (thick solid curves) and intracellular voltage perturbation (dotted curves) vs. distance from the cuticular plate are shown for 100 Hz stimuli. The thin solid and dotted lines indicate envelopes of the waves. Magnitudes are normalized re: peak values. Consistent with axons, space clamp is predicted to occur only at very low stimulus frequencies.

Fig. 4 illustrates high frequency responses to sinusoidal hair bundle displacement (um). Waves traveling down the cell reflect at the boundaries and result in complex patterns of vibrations. The voltage inside the SSC is equal to the voltage in the basal region of the cell, but the voltage between the SSC and PM is not spaced clamped and varies along the length of the cell. Note that dispersive electro-mechanical waves are predicted to travel both up an down the axis of the cell resulting in a combination of standing wave and traveling wave patterns of electro-mechanical vibration. Results lead to the hypothesis that the OHC lateral wall supports relatively slow electro-mechanical traveling waves, and that these waves underlie high-frequency resonances evoked by electrical stimulation of isolated hair cells and of the cochlear partition. Results further lead to the hypothesis that transduction current adaptation and cable properties of OHCs serve to counteract membrane capacitance and act in concert with electro-mechanical wave propagation to allow OHCs to respond cycleby-cycle to hair-bundle displacements at high auditory frequencies.

152 A. Transduction C u r r e n t - 1 0 kHz

<•• Displacement

—"Voltage

Fig. 4. Predicted OHC high-frequency responses. Physiological axial displacement (thick solid curve) and intracellular voltage perturbation (dotted curve) are shown as functions of distance from the apex of the cell (left axes) and time in the stimulus cycle (bottom axis) for two stimulus frequencies (top 10 kHz and bottom 30 kHz). Thin dashed curves show the envelope of the intracellular voltage and thin sold curves show the envelope of axial displacement.

Acknowledgments This work was supported by the National Institutes of Health under DC004928 (Rabbitt) and DC000354 (Brownell). References 1. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 227: 194196. 2. Hudspeth AJ., 2005. How the ear's works work: mechanoelectrical transduction and amplification by hair cells. C R Biol. Feb;328(2): 155-62. 3. Dallos P, Fakler B., 2002. Prestin, a new type of motor protein. Nat Rev Mol Cell Biol. Feb;3(2):104-ll. 4. Ashmore, J.F., 1987. A fast motile response in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. J. Physiol. 388: 323-347. 5. Hudspeth A.J., Logothetis N.K., 2000. Sensory systems. Curr Opin Neurobioly 10:631-41. 6. Housley, G.D., Ashmore, J.F., 1992. Ionic currents of outer hair cells isolated from the guinea-pig cochlea. J. Physiol. (Lond.). 448:73-98 7. Mountain, D.C., Hubbard, A.E., 1994. A piezoelectric model of outer hair cell function. J. Acoust. Soc. Am. 95:350-354. 8. Tolomeo, J.A., Steele, C.R., 1995. Orthotropic piezoelectric properties of the cochlear outer hair cell wall. J. Acoust. Soc. Am. 97:3006-3011.

153 9. Iwasa, K.H., 1993. Effect of stress on the membrane capacitance of the auditory outer hair cell. Biophys. J. 65:492-498. 10. Dallos, P., Hallworth, R., Evans, B.N., 1993.Theory of electrically driven shape changes of cochlear outer hair cells. J.Neurophysiol.70:299-323. 11. Iwasa, K.H., 1994. A membrane model for the fast motility of the outer hair cell. J. Acoust. Soc. Am. 96:2216-2224. 12. Gale, J.E., Ashmore, J.F., 1994. Charge displacement induced by rapid stretch in the basolateral membrane of the guinea-pig outer hair cell. Proc. Roy. Soc. (Lond.) B. Biol. Sci. 255:233-249. 13. Kakehata, S., Santos-Sacchi, J., 1995. Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge. Biophys. J. 68:2190-2197. 14. Iwasa, K.H., 2001. A two-state piezoelectric model for outer hair cell motility. Biophys. J. 81:2495-2506 15. Weitzel, E.K., Tasker, R., et al., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J Acoust Soc Am 114(3): 1462-6. 16. Spector, A.A., Brownell, W.E., et al., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J Acoust Soc Am 113(1): 453-61. 17. Spector, A.A., Popel, A.S., et al., 2003. Piezoelectric properties enhance outer hair cell high-frequency response. Biophysics of the Cochlea: From Molecule to Model. E.D., A.W. Gummer, and M.P. Scherer. Singapore, World Scientific: 152-160. 18. Weitzel, E.K., Tasker, R., et al., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J Acoust Soc Am 114(3): 1462-6. 19. Rabbitt, R.D., Ayliffe, H.E., Christensen, D., Pamarthy, K., Durney, C , Clifford, S., Brownell, W.E., 2005. Evidence of piezoelectric resonance in isolated outer hair cells. Biophys J. 88(3): 2257-65. 20. Dallos, P., Evans, B.N., 1995. High-frequency outer hair cell motility: corrections and addendum. Science. 21. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of high frequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA. 96:4420-4425. 22. Zhao, H.B., Santos-Sacchi, J., 1999. Auditory collusion and a coupled couple of outer hair cells. Nature. 399(6734):359-62. 23. Dong, X.X., Ospeck, M., Iwasa, K.H., 2002. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys J. 82(3): 1254-59 24. Zheng, J., Shen, W., He, D.Z., Long, K.B., Madison, L.D., Dallos, P., 2000. Prestin is the motor protein of cochlear outer hair cells. Nature. 405(6783): 149-55.

154 25. Zheng, J., Madison, L.D., Oliver, D., Fakler, B., Dallos, P., 2002. Prestin, the motor protein of outer hair cells. Audiol Neurootol. 7(1):9-12. 26. Liberman, M.C., Gao, J., He, D.Z., Wu, X., Jia, S., Zuo, J., 2002. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature. 419(6904):300-4. 27. Tiersten, H.F., 1969. Linear Piezoelectric Plate Vibrations. New York, Plenum. 28. Meirovitch, L. 1982. Analytical Methods in Vibrations. New York, Macmillian. 29. Gale, J.E. Ashmore, J.F., 1997. "An intrinsic frequency limit to the cochlear amplifier. Nature 389(6646): 63-6. 30. Santos-Sacchi, J., Navarrete, E., 2002. Voltage dependent changes in specific membrane capacitance caused by prestin, the outer hair cell lateral membrane motor. Plugers Arch 444(1-2): 99-106. 31. Halter, J.A., Kruger, R.P., et al., 1997. The influence of the subsurface cisterna on the electrical properties of the outer hair cell. Neuroreport 8(11): 2517-21. 32. Weiss, T.F., 1996. Cellular Biophysics. Vol. II Electrical Properties, Bradford Books. 33. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R., 2003. Nat Neurosci 6, 832-6. Comments and Questions Grosh: What effect does the mechanical constraint of the electrodes have on the motion and response of the hair cell? Answer: This is an excellent question that relates to experiments where cells are mechanically constrained tightly in a chamber. It is well known that constraining a piezoelectric material reduces the voltage-induced strain and also reduces the component of measured capacitance associated with the piezoelectric change movement. Rigidly constraining a piezoelectric material to completely prevent deformation reduces the measured capacitance to that of the passive electrical permittivity of the material (e.g. the so-called non-linear component of capacitance reduces when the material is constrained). With respect to our outer hair cell microchamber experiments, it is true that some cells fit tightly within the microchamber and were partially constrained. These partially constrained cells would be expected to exhibit a smaller piezoelectric effect relative to those fitting loosely within the microchamber. Indeed, we observed differences between cells consistent with this idea (Biophys. J. 88(3):2257-65. PMID 15613632). It is therefore important to know the mechanical boundary conditions and loads in addition to the electrical currents and voltage when interpreting apparent capacitance of outer hair cells.

"AREA C H A N G E P A R A D O X " IN O U T E R H A I R CELLS' MEMBRANE MOTOR K. H. IWASA Biophysics

Section,

NIDCD,

NIH, 50 South Drive, Bethesda, E-mail: [email protected]

MD 20892-0827

USA

Outer hair cells in the cochlea have motility which directly uses electrical energy available at their plasma membrane. It has been shown that this motility can be reasonably explained by a simple two state model in which two states differ in charge and membrane area but not in the mechanical compliance. The model leads to a biphasic dependence of the axial stiffness analogous of gating compliance. However, the experimentally observed axial compliance monotonically increases with depolarization. Such observation appears to be explained by assuming that a large compliance of the state with smaller membrane area. However, such an assumption leads to incorrect tension dependence of the motor. It is found that this inconsistency is associated with the condition that increased membrane tension reverses the size of membrane areas of the two states. To avoid this paradox, the compliance of the state with smaller membrane area must decrease as membrane tension increases. That means that the axial compliance that is monotonic with respect to voltage can be predicted only if turgor pressure is less than 0.1 kPa, somewhat less than reported estimates.

1

Introduction

The cell body of outer hair cells has voltage dependent motility [1,2,3], which is critical for ear function as demonstrated by the hearing deficiency of mice without normal prestin [4], a protein essential for the motility [5]. This cell motility is associated with charge transfer across the membrane [6,7,8]. These mechanical and electric changes are coupled, satisfying the reciprocal relationship [9]. These observations can be quantitatively described by an 'area motor' model in which charge transfer takes place during conformational transitions between two states that have different membrane areas [10,11]. This model predicts changes in the axial compliance, analogous to 'gating compliance' of mechanotransducer channels [12]. The voltage dependence of the compliance predicted is bell-shaped, analogous to membrane capacitance [11]. The measured axial stiffness, however, has a voltage dependence similar to length changes, which is monotonically decreasing function of the membrane potential [13,14]. The maximum change in the stiffness is several fold, much larger t h a n the relative amplitude of length changes, which is several percent. Based on this observation, it has been argued that length changes are epiphenomena that is accompanied by stiffness changes [14].

155

156 A motile mechanism for outer hair cells based on stiffness changes (stiffness motor) requires large changes in stiffness and t h a t the amplitude is sensitive to turgor pressure [15]. The experimental observations that load-free amplitude is insensitive to applied (positive) turgor pressure and that the voltage dependence shifts linearly with turgor pressure [16,17] contradict the prediction of the stiffness motor. These experiment will be referred to as "pressure experiments." Since the free energy due to area changes and that of stiffness changes are additive, area motor and stiffness motor are, in principle, not exclusive of each other. A model that includes these two terms, which could be called a hybrid model, has been proposed to explain large voltage dependent changes in the axial stiffness [18]. Such a hybrid model, however, is invalid if it cannot explain the "pressure experiments" because these pressure experiments are the very basis for determining the area changes in the motor, an essential step for the model. This self-consistency of hybrid models is examined here.

2

Hybrid Model

Let us approximate the geometry of an outer hair cell with a cylinder of radius r. Then the cell's length and diameter is determined by its lateral membrane. Membrane tension T of the lateral membrane is given by [10],

(1)

*={?"')•

where P is pressure across the cell membrane and / ( = F/2irr) is due to axial force F. The first component is in the axial direction, which is indicated by the index 1, and the second in the circumferential direction, indicated by the index 2. Consider a membrane motor t h a t has two conformations, I and II. The conformation II takes up membrane area An, which is larger than the area Aj of the conformation I. Transitions between these states require transfer of charge Aq. Here area changes has two components corresponding to tension in two directions (membrane tension is anisotropic). The values for compliance of the two states are in general not equal. Let C / and C J J inverse of the elastic moduli of the state i" and of the state II, respectively. The difference A G in the Gibbs free energy in the two states is given by,

A G = A G 0 - qVm - A A • T - ^TT(AnCn

- A7C7)T,

(2)

157 where q is charge transfered and Vm is the membrane potential. Quantities T and T T are membrane tension and its transposed form, respectively. The first term is a constant, the second term is electrical energy difference, and the third term is due to area difference. These three terms are the same as the original 'area motor' model [10]. The last term is due to the difference in the compliance of the two states. Because membrane tension T is anisotropic, area difference A A can be anisotropic. The difference A Atot in the membrane area of the motor when it is subjected to membrane tension T is expressed by, A A W = A A + (A„Cn

- A/CJ)T.

(3)

The first term is area displacement due to conformational transitions. The second term is difference in the elastic displacements in the two states. If An > Ai for T = 0, it would be reasonable to assume t h a t AJJ > Ai still holds for T > 0 even if the compliance of the state I is greater than the state II. We will come back to this issue later. The probability Pu that the motor is in state II is given by,

_

exp[-/3AG] 1 + exp[—pAGJ

where f3 = 1 / ( A : B T ) , fcs being Boltzmann's constant and T is the temperature. The elastic modulus K of the lateral membrane depends on the state of the motor because the motor undergoes changes in its compliance. Let the elastic modulus be K / when PJJ = 0 and K// when Pu = 1. A simple dependence of the elastic moduli on the motor state Pu would be a linear combination, K = KI(1-PII)

+ KIIPII,

(5)

which is assumed in the calculation given below. To solve our equations, a number of additional assumptions are required. One such assumptions is volume constant constraint. Another is a relationship between motor stiffness and membrane stiffness. The former is ei + 2e2 = v, where the volume strain v is a constant, which is related to turgor pressure of the cell, t\ is axial strain, and £2 is circumferential strain. The latter condition can be. C7 = K71

(6)

Cn = K-\

(7)

158

3

E x a m p l e : U n i f o r m Stiffness-Changes

Here the simplest possible model for stiffness changes is examined for illustration. Let us assume that the membrane stiffness changes uniformly, keeping the ratios of stiffness in the two states are constant, i.e. K,

7K77.

(8)

W i t h this assumption the observed stiffness changes correspond to 7 \

0.3 (Fig.

! ) •

Another experimental observation to satisfy is that the voltage-dependence of cell displacement has a linear relationship with applied pressure [17]. However, the "uniform change" model predicts nonlinear shift even if the difference in the stiffness in the two motor states is smaller t h a n the difference required for the voltage dependence of the axial stiffness (Fig. 2). stiff ness(nN/m)

B displacement^ nm)

microchamberpotentialV)

2

-0.2

—

-0.1 0 0.1 0.2 microchamberpotentiaiy)

Figure 1. Effect of reducing stiffness of the compact state on voltage dependences of cell length (A) and the axial stiffness (B). From the top, the values for the stiffness parameter 7 is 1, 0.8, 0.6, 0.4, and 0.3. With decreasing 7, changes of both length and compliance take place at more negative potential. For larger 7, the stiffness is has a minimum, which is due to gating compliance. Load-free condition. Data points are adopted from [14] obtained with a configuration in which the basal end is sucked into a micro-chamber. The membrane potential is more negative than the micro-chamber potential by about 50 mV and changes less steep. Thus the value for q is adjusted to 0.7 e to fit the data. The elastic moduli used are 80% of the values in Table 1 in ref [11]. Other parameter values are not changed.

4

Size Reversal: T h e P a r a d o x

As we have seen earlier that the compact state must be significantly more compliant than the extended state to be able to explain the experimentally observed voltage-dependence of the axial stiffness. For relatively large membrane tension,

159 amplitude axialstrainbypressure 0.06 %05* 0.04 0.03

-0.06

-0.04

-0.02

axial pressure strain

Figure 2. Effect of turgor pressure on the amplitude and voltage-dependence of length changes by electromotility. Axial strain at —75 mV is used for an indicator for turgor pressure. The data points are taken from Fig. 5A in[17]. Volume strain 0.2 gives rise to axial strain —0.08, which approximately corresponds to 0.5 kPa. Values of parameters are in Table 1 except for the volume strain v. A: The amplitude. The prediction of the model (solid line) is not affected by the stiffness ratio 7. B: Voltage dependence of the motor. The membrane potential at which the cell has half-amplitude displacement (mid-point potential) is plotted against axial strain at the reference voltage. The values for 7 is from the top, 1, 0.825, 0.65, 0.475, and 0.3. The data points are taken from Fig. 5A in [17]. Shaded area indicates the range of membrane tension that may correspond to [14]

such a condition could make the membrane area of the compact state larger t h a n that of the extended state. In the following we examine if such a reversal takes place under our experimental conditions. For numerical evaluation, we assumed that the dimension of the motor is 100 nm 2 , corresponding to 10 nm particles, and that the elastic moduli of state II is given in Table 1 in ref [11]. At P = 0 . 5 kPa, the maximum turgor pressure in the experiment shown in Fig. 2, membrane tension stretches the area of state II by 1.8 nm 2 . For 7 = 0 . 3 , the increased area of state I by stretching is 6 nm 2 . Because the membrane area of state II is larger than state I by 3.7 nm 2 at null membrane tension, the state / becomes larger t h a n the state II when P = 0 . 5 kPa. Is such a reversal of the membrane area of the two states due to increased membrane tension physically reasonable? Consider a physical entity such as a protein which has two conformational states, compact and extended. It appears reasonable that the compact state is more compliant because the extended state would be harder to stretch further. However, how can a compact state become larger by being stretched and still remains more compliant? It would be reasonable to assume t h a t increased area strain leads to increased stiffness so that such reversal in size does not happen.

160 In the region where the model encounters a paradox due to applied pressure, it is not surprising that the model is unable to explain the result of pressure experiments [16,17]. The axial stress-strain experiments [14], however, do not impose such large membrane stress and does not lead to size reversal. 5

Discussion

The argument presented above is based on an assumption that changes in motor stiffness is uniform. Instead of assuming a simple relationship Eq. (8), it might be possible to seek stiffness changes that satisfy pressure experiments and axial stiffness experiments as constraints. However, it turns out that models that assumes orthotropic elasticity cannot satisfy all these constraints. This examination therefore indicates that the problem associated with "size paradox" is representative of the problem. Size reversal can be avoided by assuming t h a t the compact state / is softer only for small stress below, say Tc. The stiffness of the compact state must rise quickly with increased membrane tension to prevent size reversal. To be consistent with the pressure experiments, the difference in stiffness of the two motor states can be appreciable only for turgor pressure less than 0.1 kPa (Fig. 2), which is somewhat lower than reported values in vitro. Pressure changes due to membrane potential changes is up to 1 Pa and keeps membrane tension well below Tc. Then the axial stiffness could be a monotonic function of the membrane potential. It should also be noted that voltage-dependent cell motility at turgor pressure less t h a n 0.1 kPa is dominated by area changes. Stiffness changes, if large, cannot be significant in the free energy because membrane tension is low. Thus observed length changes and force generation of outer hair cells cannot be epiphenomena. There is yet another problem. Recall here that area difference has been determined by the motor's dependence on membrane tension over a relatively wide range above Tc. The area difference below Tc must be larger. However, there is no ways of determining the area difference of the motor states because the effect of membrane tension on the motor cannot be used to determine it. References 1. W. Brownell, C. Bader, D. Bertrand, and Y. Ribaupierre. Evoked mechanical responses of isolated outer hair cells. Science, 227:194-196, 1985. 2. B. Kachar, W. E. Brownell, R. Altschuler, and J. Fex. Electrokinetic shape changes of cochlear outer hair cells. Nature, 322:365-368, 1986. 3. J. F . Ashmore. A fast motile response in guinea-pig outer hair cells: the

161

4.

5.

6.

7. 8. 9.

10. 11. 12.

13. 14. 15.

16.

17. 18.

molecular basis of the cochlear amplifier. J. Physiol. (Lond.), 388:323-347, 1987. M. C. Liberman, J. Gao, D. Z. He, X. Wu, S. Jia, and J. Zuo. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature, 419:300-304, 2002. J. Zheng, W. Shen, D. Z.-Z. He, K. B. Long, L. D. Madison, and P. Dallos. Prestin is the motor protein of cochlear outer hair cells. Nature, 405:149155, 2000. J. F. Ashmore. Forward and reverse transduction in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. Neurosci. Res. Suppl., 12:S39-S50, 1990. J. Santos-Sacchi. Reversible inhibition of voltage-dependent outer hair cell motility and capacitance. J. Neurophysioi, 11:3096-3110, 1991. K. H. Iwasa. Effect of stress on the membrane capacitance of the auditory outer hair cell. Biophys. J., 65:492-498, 1993. X. X. Dong, M. Ospeck, and K. H. Iwasa. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys. J., 82:1254-1259, 2002. K. H. Iwasa. A membrane model for the fast motility of the outer hair cell. J. Acoust. Soc. Am., 96:2216-2224, 1994. K. H. Iwasa. A two-state piezoelectric model for outer hair cell motility. Biophys. J., 81:2495-2506, 2001. J. Howard and A. J. Hudspeth. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron, 1:189-199, 1988. D. Z. Z. He and P. Dallos. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc. Natl. Acad. Sci. USA, 96:8223-8228, 1999. D. Z. Z. He and P. Dallos. Properties of voltage-dependent somatic stiffness of cochlear outer hair cells. J. Assoc. Res. Otolaryngol., 1:64-81, 2000. K. H. Iwasa. Mechanisms for the fast motility of the outer hair cell from the cochlea. In E. R. Lewis, G. R. Long, R. F . Lyon, P. M. Narins, C. R. Steele, and E. Hecht-Poinar, editors, Diversity in Auditory Mechanics, pages 580-586. World Scientific, Singapore, 1997. M. Adachi and K. H. Iwasa. Electrically driven motor in the outer hair cell: Effect of a mechanical constraint. Proc. Natl. Acad. Sci. USA, 96:7244-7249, 1999. M. Adachi, M. Sugawara, and K. H. Iwasa. Effect of turgor pressure on outer hair cell motility. J. Acoust. Soc. Am., 108:2299-2306, 2000. N. Deo and K. Grosh. Two state model for outer hair cell stiffness and motility. Biophys. J., 86:3519-3528, 2004.

CHLORIDE AND THE OHC LATERAL MEMBRANE MOTOR

J. SANTOS-SACCHI, L. SONG, J.P. BAI, D. NAVARATNAM Otolaryngology, Neurobiology and Neurology, Yale University School of Medicine, 333 Cedar St, New Haven Ct. 06510, USA E-mail: [email protected] The OHC motor, likely comprised of prestin and other associated proteins intrinsic to the cell's lateral membrane, presents sensitivity to chloride ions. We have been studying the effects of intra and extracellular chloride on many of the biophysical traits of the OHC motor through evaluations of the cell's nonlinear capacitance. Here we review some of our recent observations, including interactions between the motor's tension dependence and CI flux through the lateral membrane. Additionally, we report on our efforts to estimate intracellular CI in intact OHCs, and on our estimates of the motor's chloride sensitivity in intact OHCs. These data are helping us to understand how the cochlea amplifier is managed in vivo. Finally, we illustrate how prestin can be used to identify the presence of the environmental toxin tributyltin that can leach from toxin-treated marine structures, including sonar domes.

1 Introduction Nonlinear amplification in the mammalian organ of Corti relies on anionic interactions with the outer hair cell (OHC) lateral membrane motor, a key component being the integral membrane protein, prestin [1-4]. This anion modulation has been shown for prestin directly, in transfected cells, as well as in native OHCs. Chloride, the most abundant physiological anion, probably plays the major role, though we have shown in the intact OHC that sulfate can also support motor activity as evidenced by robust nonlinear capacitance (NLC)[5], the electrical signature of prestin's voltage-dependence [6;7]. Here we report on the potential effects of intracellular and extracellular CI on OHC motor activity, and show that interactions of the motor and chloride, while substantial, cannot fully account for many of the motor's biophysical traits. 2 Methods OHCs were freshly isolated from the adult guinea pig organ of Corti by sequential enzymatic (dispase 0.5 mg/ml) and mechanical treatment in Ca-free medium. Currents from voltage-clamped cells were recorded using an Axon 200B amplifier, Digidata 1321A (Axon Inst., CA, USA) and the software program jClamp (Scisoft, CT). Solutions (see Figure legends for composition of pipette and extracellular solutions) were delivered to individual cells by Y-tube, during continuous whole bath perfusion with control extracellular solution consisting of NaCl (140mM), CaS0 4 (2 mM), MgS0 4 (1.2 mM) and Hepes (10 mM), pH 7.2, 300 mOsm. Nonlinear membrane capacitance was evaluated using a continuous high-resolution

162

163

(2.56 ms sampling) two-sine voltage stimulus protocol (10 mV peak at both 390.6 and 781.2 Hz), with subsequent FFT-based admittance analysis as fully described previously [8;9]. These high-frequency sinusoids were superimposed on voltage ramps. C-V data were fit with the first derivative of a two-state Boltzmann function and a constant representing the linear capacitance [10], ze

b = exp

•zeyVm-Vpkcm)

(1) kT kT(l + b) V kT J where Qmax is the maximum nonlinear charge moved, Vpkcm is voltage at peak capacitance or half maximal nonlinear charge transfer, Vm is membrane potential, Ciin is linear capacitance, z is apparent valence, e is electron charge, k is Boltzmann's constant, and T is absolute temperature. Cm = Q.

: + C«

3 Results 3.1 One-third ofOHC motor charge movement is insensitive to intracellular CI In order to study the effects of intracellular chloride on OHC motor function, we used the chloride ionophore, tributyltin (TBT) to assure absolute control of chloride on the inner aspect of the lateral membrane. Fig. 1 shows the dosei *, T (8)

E o.

3-

a

(5)

0.06

B > £

100 80 60 -

(12)

*!

*

e>

(6)

" ¥ " "T"

'-*-,,

20

I

Figure 1. OHC motor-Cl dose-response relationship in presence of TBT. Nonlinear charge density, Qsp (A) and Vpkcnl (B) as a function of intracellular sub-plasmalemmal CI concentrations are fitted with logistic Hill function (filled triangles, malate as substitute anion). Each point represents the average (+/se; numbers in parentheses) from recordings with TBT (1 (JVI) present. Qsp and VpkCm were measured after pipette washout reached steady state. Open triangles represent values from 5 mM CI intracellular/extracellular with gluconate as substitute anion.

°

"g. -20 > -40 -

[CI] i n / 0 U ,(mM)/wTBT

response function for chloride ion effects on motor charge movement and Vpkcm. While chloride has continuous, though saturating, effects on Vpkcm, effects of CI

164

E O

Vm ( mV)

Figure 2. Competing effects of Y-tube perfusion pressure and CI flux on NLC. Whole cell recording with 1 mM CI in pipette (malate substitute anion), 140 mM CI outside. Conditions: a, 140 mM perfusion pipette off and away from cell; b, perfusion turned on. Note slight shift of NLC to right; c, tip moved close to ^5o cell. Note increase in NLC but shift to right; d, switch to 1 mM CI perfusion. Note expected shift to right; e, switch back to 140 mM perfusion. Note shift back to left. All traces depict steady state conditions.

on Qsp are absent below about 1 mM CI. After substantiating with TBT that setting equal intra and extracellular levels of chloride affords absolute control of CI activity at the motor's inner aspect, we determined that the Cl-NLC IQ is about 7 mM [4], 3.2 Tension and chloride affects on the motor are independent The motor's nonlinear charge movement and VpicCm are sensitive to tension applied to the membrane that houses prestin [11-16]. An increase in membrane tension typically causes a shift in Vpkcm to the right and a decrease in peak NLC in wholecell voltage clamped OHCs [14], while an increase in CI causes a shift to the left and an increase in NLC [3]. The effects of tension are not driven by CI flux across the lateral membrane even though tension can gate GmetL [3]. Fig. 2 shows that the tension induced by single cell Y-tube perfusion (fluid flow) can overpower the effects of induced CI influx. That is, a rightward shift in Vpkcm occurs when a pipette perfusing 140 mM CI is placed close to the cell (condition c), even though the

0.0 -

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Figure 3. Prestin transfection in CHO cells does not induce Gmc
induced tension might be expected to activate GmetL and CI influx, which typically results in a leftward shift. In fact, the perfusion had increased intracellular CI, since

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a subsequent switch to 1 mM CI perfusion (same flow) causes the expected shift to the right as intracellular levels drop (condition d); the following switch back to 140 mM CI perfusion causes NLC to shift back to negative potentials. These data show that the interpretation of perfusions can be complex, as competing forces of CI and tension may be at play. 3.3 GmetL does not derive from prestin GmetL is a nonselective conductance which resides in the lateral membrane of the OHC, passes CI efficiently, is voltage and tension dependent, and has a bimodal temperature sensitivity, showing a Qio above 4 at physiological temperatures [3]. The many similarities between prestin activity and GmetL led us to suggest that perhaps GmetL arises from prestin, similar to leak conductances arising from the activity of other membrane transporters. We have tested a variety of biophysical perturbations of prestin which do not simultaneously and similarly affect GmetLMost notably, the expression of prestin does not corresponding induce a chloride conductance (Fig. 3), indicating that GmetL is a distinct molecular entity. 3.4 Intracellular chloride is near the Kjfor chloride prestin effects The sensitivity of the OHC motor to CI and the existence of the lateral membrane chloride conductance, GmetL, points to the importance of the transmembrane gradient of CI in driving CI flux. Thus, it is important to determine intracellular CI levels in order to gauge the sensitivity of the motor to changes in CI near its inner aspect. By using the gramicidin patch technique, which ensures that CI levels in the cell remain unperturbed, and the competitive effects of salicylate on motor activity (NLC) we were able to assess OHC CI levels. First we calibrated salicylate effects under

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Figure 4. Salicylate action on the motor can be used to estimate intracellular chloride levels. Salicylate-induced reduction in NLC magnitude differed depending on intracellular CI levels. These differences served as a calibration for the estimation of intact cell CI levels; by comparing the effects of salicylate on cells patched with the gramicidin technique to the calibration, we arrived at an intracellular CI concentration near 10 mM, when extracellular CI was 140 mM.

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standard whole cell conditions at different CI concentrations, and then compared the effects of salicylate on gramicidin patched cells with normal, in vivo, concentrations of CI outside the cell. The effectiveness of salicylate under these conditions matched those obtained with 10 mM CI intracellularly, indicating that, in the intact

166 cell, CI is near 10 mM (Fig. 4). This level is close to the Kj effects of CI on the motor (Fig. 1), where changes in CI have their greatest effects. 3.5 Chloride flux through the OHC membrane via Gmeli is skirted by the marine environmental toxin TBT The sensitivity of the OHC motor to intracellular CI, and the large gradient normally found in intact cells highlights an important homeostatic mechanism that limits CI movements across the OHC membrane. Disruption of this mechanism is predicted to cause cochlear amplifier malfunction. The chemical TBT is an ever present toxin that resides in our waters, originally deriving from boat bottom paint to limit fouling. Though the chemical is marked for worldwide ban by treaty by 2008, it remains in sediment and in the marine food chain. Thus, accumulation in marine mammals can lead to exposure of inner ear tissues. We have shown that levels of as little as 100 nM can disrupt CI levels in OHCs [4]. Here we show that TBT which leaches from sonar dome no-foul material still used on warships can alter motor function in OHCs (Fig. 5). In as little as a 10 min exposure of a 4 gm piece of material to extracellular solutions, subsequent perfusion onto OHCs results in

55 whole cell patch clamp 50

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Control, 1 mM CI in and out 140 mM CI perfusion 140 mM CI rubber without TBT in for 10 minutes 140 mM CI rubber with TBT in for 10 minutes 0

50

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Vm ( mV) Figure 5. TBT that leaches from sonar dome material disrupts CI homeostasis in OHCs. After steady state conditions at 1 mM (gluconate substitition) inside and outside the cell (a), 140 mM extracellular solution was perfused and caused a slight increase and leftward shift of NLC due to CI influx through GmetL (b). Perfusion with that same solution exposed for 10 min to sonar dome material without TBT causes little change (c); however, perfusion with the same solution that was exposed to TBT sonar dome material causes a huge influx of CI indicated by changes in NLC (d).

massive flux of CI across the OHC membrane, as indicated by marked changes in NLC. We have hypothesized that TBT exposure could interfere with marine mammal echolocation, resulting in beaching of whales and dolphins. Save the whales! Support the ban.

167 4 Discussion Recent experiments clearly indicate that CI plays a significant role in controlling OHC motor activity [2-4]. Here we have highlighted some important features of the evolving CI story. Notably, when considering the similarity between intracellular CI levels and the Cl-prestin Kd, the importance of the lateral membrane CI conductance must be considered paramount. Thus, not only does transmembrane CI flux play a significant role in assuring normal cochlear amplification [17], but agents that compromise CI homeostasis are expected to lead to deficits in capabilities that rely on our, and our marine mammal counterparts', acute sense of hearing. Acknowledgments We thank Margaret Mazzucco. Supported by NIH NIDCD grant DC000273 to JSS. References 1. Zheng, J., Shen, W., He, D.Z., Long, K.B., Madison, L.D., Dallos, P., 2000. Prestin is the motor protein of cochlear outer hair cells, Nature, 405 149-155. 2. Oliver, D., He, D.Z., Klocker, N., Ludwig, J., Schulte, U., Waldegger, S., Ruppersberg, J.P., Dallos, P., Fakler, B., 2001. Intracellular anions as the voltage sensor of prestin, the outer hair cell motor protein, Science, 292 2340-2343. 3. Rybalchenko,V., Santos-Sacchi, J., 2003. CI- flux through a non-selective, stretch-sensitive conductance influences the outer hair cell motor of the guinea-pig, J. Physiol, 547 873-891. 4. Song, L., Seeger, A., Santos-Sacchi, J., 2005. On membrane motor activity and chloride flux in the outer hair cell: Lessons learned from the environmental toxin tributyltin, Biophysical Journal, 88 2350-2362. 5. Rybalchenko, V., Santos-Sacchi, J., 2003. Allosteric modulation of the outer hair cell motor protein prestin by chloride. In Gummer, A (Ed.), Biophysics of the Cochlea: From Molecules to Models World Scientific Publishing, Singapore, pp. 116-126. 6. Santos-Sacchi, J., 1990. Fast outer hair cell motility: how fast is fast? In Dallos, P., Geisler, CD., Matthews, JW, Ruggero, MA, Steele, C.R. (Eds.), The Mechanics and Biophysics of Hearing Springer-Verlag, Berlin, pp. 6975. 7. Ashmore, J.F., 1990. Forward and reverse transduction in the mammalian cochlea, Neurosci. Res. Suppl, 12 9-S50. 8. Santos-Sacchi, J., Kakehata,S., Takahashi,S.,1998. Effects of membrane potential on the voltage dependence of motility-related charge in outer hair cells of the guinea-pig, J. Physiol, 510 (Pt 1) 225-235.

168 9. Santos-Sacchi, J.,2004. Determination of cell capacitance using the exact empirical solution of dY/dCm and its phase angle, Biophys. J., 87 714-727. 10. Santos-Sacchi, J., 1991. Reversible inhibition of voltage-dependent outer hair cell motility and capacitance, J. Neurosci., 11 3096-3110. 11. Iwasa, K.H., 1993. Effect of stress on the membrane capacitance of the auditory outer hair cell, Biophys. J., 65 492-498. 12. Gale, J.E., Ashmore, J.F., 1994. Charge displacement induced by rapid stretch in the basolateral membrane of the guinea-pig outer hair cell, Proc. R. Soc. Lond B Biol. Sci., 255 243-249. 13. Zhao, H.B., Santos-Sacchi, J., 1999. Auditory collusion and a coupled couple of outer hair cells, Nature, 399 359-362. 14. Kakehata, S., Santos-Sacchi, J., 1995. Membrane tension directly shifts voltage dependence of outer hair cell motility and associated gating charge, Biophys. J., 68 2190-2197. 15. Santos-Sacchi, J., Shen, W.X., Zheng, J., Dallos, P., 2001. Effects of membrane potential and tension on prestin, the outer hair cell lateral membrane motor protein, Journal of Physiology-London, 531 661-666. 16. Ludwig, J., Oliver, D., Frank, G., Klocker, N., Gummer, A.W., Fakler, B., 2001. Reciprocal electromechanical properties of rat prestin: The motor molecule from rat outer hair cells, Proc. Natl. Acad. Sci. U.S.A, 98 41784183. 17. Nuttall, A.L., Zheng, J., Santos-Sacchi, J., 2005. Modulation of cochlea amplification by tributyltin and salicylate, Assoc. Res. Otolaryngol. Abs., p. 117.

FAST ADAPTATION IN VESTIBULAR HAIR CELLS DEPENDS ON MYOSIN-1C P.G. GILLESPIE, J. D. SCARBOROUGH Oregon Hearing Research Center and Vollum Institute, Oregon Health & Science Portland OR 97239 E-mail: [email protected]

University,

J.A. MERCER McLaughlin Research Institute,

Great Falls MT

59405

E. STAUFFER AND J.R. HOLT Department

ofNeuroscience,

University of Virginia School of Medicine, Virginia 22908

Charlottesville,

Fast adaptation, the rapid termination of transduction current that follows a mechanical stimulus, correlates temporally with hair-bundle force production that could boost bundle displacement in response to weak stimuli. We have presented data in favor of the "release model", which proposes that Ca2+ lengthens a mechanical linkage in the transduction apparatus, reducing gating-spring tension and allowing channels to close. To determine the molecule responsible for fast adaptation, we introduced the Y61G mutation into the Myolc genomic locus using gene targeting. We show here that both fast and slow slipping adaptation are faster in Y61G knock-in hair cells as compared to C57BL/6 control cells. Although these results show that mechanical activity of myosin-lc is required for fast adaptation in vestibular hair cells, additional controls are required to ensure that the differences in adaptation rate are not due to strain differences between the two mouse lines.

1 Introduction Hair cells react to sustained bundle deflections by restoring the open probability of their transduction channels toward the resting state, a process called adaptation [1]. Adaptation has two phases, fast and slow; fast adaptation occurs in 1-10 ms (vestibular hair cells) or 10-1000 us (auditory hair cells), while slow adaptation occurs over 10-100 ms. Slow adaptation occurs when the adaptation motor slips down the cytoskeleton; the resulting bundle movement is opposite that of fast adaptation. To demonstrate the role of the unconventional myosin myosin-lc (Myolc) in slow adaptation, we mutated Tyr-61 of Myolc to Gly (Y61G), then showed that iV6(2-methylbutyl) ADP (NMB-ADP) selectively inhibits the mutant Myolc [2]. We generated a transgenic mouse line that expresses Y61G-Myolc and showed that slow adaptation was blocked by NMB-ADP only when the analog was delivered to mutant hair cells [3]. In the prevalent model for fast adaptation, when Ca 2+ enters an open transduction channel, it forces channels shut, causing a negative bundle movement

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170 [4]. The mechanism of fast adaptation is controversial, however; experiments from the Hudspeth lab suggested that associated with the release of a mechanical element in series with the transduction channel [5, 6]. In addition, recent work from the Fettiplace lab suggests that fast adaptation in cochlear hair cells is correlated with large forces moving the bundle in the positive direction, conflicting with predictions of the channel-reclosure model [7]. These results were consistent with our data suggesting that NMB-ADP inhibits fast adaptation in Y61G knock-in mice [8] An increased rate of fast adaptation in Y61G hair cells compared with C57BL/6 would also support the role of Myolc in fast adaptation. To more thoroughly investigate fast adaptation in the absence of myosin inhibition, we averaged transduction-current records from multiple cells and compared adaptation properties in Y61G and control hair cells. Although the data show that fast and slow positive adaptation are faster in Y61G than in C57BL/6 hair cells, genetic background differences between the two mouse strains calls into question the significance of these results. 2 Methods 2.1 Generation of Y61G knock-in mice We generated the targeting construct using a 6.5 kbp Not I - Pst I fragment of the BamH I genomic clone described previously [3]. Tyrosine-61 was converted to glycine by changing the codon to GGA. The neomycin-resistance positive selection cassette, flanked with loxP sites, was inserted into a Nhe I site located in the large intron between exons 4 and 5. ES cells were electroporated, two positive clones were identified, and one chimeric mouse was generated that transmitted the mutation to subsequent generations. The neo cassette was removed by breeding mice heterozygous for the floxed allele to the Cre deleter mouse. The Y61G mice were backcrossed to C57BL/6J (>10 generations). 2.2 Electrophysiology Recording and stimulation of mouse utricle hair cells in intact epithelia were carried out using methods similar to those previously described [3]. Sensory epithelia were excised from P0-P7 mice in MEM (Invitrogen, Carlsbad, CA) supplemented with 10 mM HEPES, pH 7.4 (Sigma, St. Louis, MO). To remove the otolithic membrane, the tissue was bathed for 20 min in 0.1 mg/ml protease XXIV (Sigma) dissolved in MEM plus 10 mM HEPES pH 7.4. The tissue was mounted onto a glass coverslip and held flat by two glass fibers; the coverslip was mounted in an experimental chamber on a fixed-stage upright microscope (Axioskop FS; Zeiss, Oberkochen, Germany) and viewed with a 63x water-immersion objective with differential interference contrast optics.

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Figure 1. Transduction currents and time-dependent adaptive shift in C57BL/6 (control) and Y61GMyolc hair cells. A,B: transduction currents in response to mechanical displacements of -1000 to +2000 nm (increments of 200 nm) for C57BL/6 (A) or Y61G (B) mouse hair cells. Each current trace is averaged from 8 (C57BL/6; 210± 15 pA) or 13 (Y61G; 199 ± 19 pA) traces. C, D: inferred-shift analysis of positive adaptive shifts calculated from average traces in A and B. C and D are identical except for abscissa scale. C57BL/6 (black) shifts are slower than Y61G (gray) shifts.

Electrophysiological recordings were performed in an artificial perilymph solution that contained (in mM): 137 NaCl, 5.8 KC1, 10 HEPES, 0.7 NaH 2 P0 4 , 1.3 CaCl2, 0.9 MgCl2, and 5.6 D-glucose, vitamins and amino acids as in MEM (Invitrogen), pH 7.4 and 311 mOsm/kg. Recording electrodes were filled with (in mM): 135 KC1, 5 EGTA-KOH, 5 HEPES, 2.5 Na2ATP, 2.5 MgCl2, and 0.1 CaCl2; this solution was pH 7.4 and 284 mOsm/kg. Hair cells were stimulated by drawing the

172 kinocilium into a pipette filled with extracellular solution [3]; transduction currents were recorded as described [8]. Current records were averaged using Clampfit 8.2 (Axon Instruments) and analyzed using a Mathematica 5.1 program as described [8]. Total extent

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Fast extent

Slow t

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0 1000 2000 z Z'~ DiiCtiiC^Srfrfi'^ 0 1000 2000 0 1000 2000 Displacement (nm) Displacement (nm) Figure 2. Dissection of properties of fast and slow adaptation in C57BL/6 (black points andfits)and Y61G (gray points and fits) hair cells using inferred-shift analysis. A-C: total (A), slow (B), and fast (C) extent of adaptation extrapolated to infinite time. D-E: time constants for slow (D) and fast (E) adaptation. Note stimulus-dependent increase in fast adaptation rate. F-G: rates of slow (F) and fast (G) adaptation. Note faster slow and fast adaptation in Y61G hair cells.

173 3 Results 3.1 Average transduction currents and inferred-shift analysis To better compare adaptation kinetics, we averaged transduction-current records from C57BL/6 or Y61G hair cells (Fig. 1A,B). By eye, Y61G currents appeared to adapt slightly faster, although the difference was relatively subtle. To both extract the adaptive shift quantitatively and to separate fast and slow adaptation, we subjected traces in A or B in response to positive bundle deflections to inferred-shift analysis [8, 9]. By deconvolving the current records with the highly nonlinear displacement-response relation, inferred-shift analysis allowed extraction of the shift of this relation with time. After this analysis, the faster adaptation seen in Y61G hair cells was much more apparent, particularly for large displacements at short times (Fig. 1C,D). 3.2 Separation of fast and slow slipping adaptation To measure the contributions of fast and slow adaptation to the inferred-shift traces of Fig. 1C, we fit the time-extent relations with double-exponential functions [8, 10]. This analysis yielded fast and slow extents and time constants (T); the extent divided by the extent yields the initial rate. These parameters are illustrated in Fig. 2. The data were fit as previously described [8]. 4 Discussion Averaging current records as we did here allows for a slightly different biasing of the control and Y61G datasets. In our previous work [8], we carried out the inferred-shift analysis on data from individual cells, then averaged the shift-time records. This latter approach weights all cells identically, as the resulting extenttime relations are independent of the size of the transduction current. In the present analysis, we selected for cells of large current amplitudes. Moreover, the averages will be weighted towards the cells with the largest transduction currents. Because these cells often have the fastest adaptation as well, they may indeed be more representative of endogenous hair cells than are cells with small transduction currents, which may have suffered physical and enzymatic trauma from the dissection. Thus the present analysis allows a different view of the properties of fast and slow adaptation from our previous work, although the fundamental conclusions remain the same [8]. These results revealed that Y61G mice have shortened time constants for both fast and slow adaptation, with little change in the extent of adaptation. The consequence of these changes was to increase the rates of both fast and slow adaptation, albeit over different displacement ranges. Accelerated slow adaptation in Y61G mice was prominent in intermediate displacement ranges (500-

174 1500 nm), while the rate of fast adaptation was larger for displacements above 1500 nm. The time constant for fast adaptation (ifast) in C57BL/6 cells remained at 10-12 ms for all displacements, while it decreased from ~12 ms to <5 ms for Y61G cells. Two interpretations of these data are possible. In the first, we assume that the 10 generations of backcrossing the Y61G mice - generated in 129 strain ES cells has removed any contributions of the parent strain to hair cell transduction. In this interpretation, larger rates of fast and slow adaptation in Y61G mice are due exclusively to the Myolc mutation. We suggest that the Y61G mutation could affect the mechanics of the Myolc protein, allowing a more rapid equilibration to a "released" mechanical state. How would a mutation in the nucleotide-binding site of Myolc affect the motor's mechanical behavior? One possibility is that the Tyr-toGly mutation changes the intrinsic mechanics of the protein, perhaps destabilizing the stiff state. An alternative explanation is that by reducing ADP affinity and hence ADP occupancy [2], the Y61G mutation affects the distribution of Myolc amongst attached states. In particular, as the ADP-bound state is thought to be a stable, force-sustaining state of Myolc [11], increased occupancy of the nucleotidefree state might allow more rapid mechanical transitions. This hypothesis leads to the prediction that any mutation that affects the occupancy of the force-sustaining ADP-bound state would also increase fast adaptation. Mutations that affect this state in Myolb have been identified in "loop 1", a surface loop that interacts with myosin's nucleotide binding site [12]; similar mutations in Myolc should also increase fast adaptation, perhaps more substantially than does the Y61G mutation. A second possibility suggests caution, however, in interpreting these results. It is possible that differences between Y61G mice and C57BL/6 are due to effects of a 129-strain allele of a locus that is linked to the Myolc locus. The 10 backcrosses used would reduce the 129 contribution substantially, but it still would consist of >10 centimorgans (potentially containing a significant number of genes) with a very large variance between animals. In addition, dominant 129 alleles unlinked to Myolc could also contribute. This consideration raises three points. First, even with backcrossing, proper controls for these experiments would be not only C57BL/6 mice, but also 129 mice. Although the C57BL/6 contribution is much larger, 129 genes easily could affect properties we are studying. Second, a better strategy for gene targeting is to maintain the mutation in a single strain, e.g., if the mutation is generated in 129 ES cells, cross the mutant chimera to 129 mice and maintain the mutation on that strain. Finally, the background strain issue is avoided altogether with a strategy like that used for our Y61G experiment where the phenotypic effect is generated within a single cell, such as happens when NMB-ADP inhibits Y61G Myolc. Each cell serves as its own control.

175 Acknowledgments This work was supported by grants R01 DC003279 to J.A. Mercer (P.G. Gillespie. and J.R. Holt, subcontract Pis) and ROl DC002368 to P.G. Gillespie. References 1. Eatock, R.A., 2000. Adaptation in hair cells. Annu. Rev. Neurosci. 23:285314. 2. Gillespie, P.G., Gillespie, S.K., Mercer, J.A., Shah, K., Shokat, K.M., 1999. Engineering of the myosin-ip nucleotide-binding pocket to create selective sensitivity to N(6)-modified ADP analogs. J. Biol. Chem. 274:31373-31381. 3. Holt, J.R., Gillespie, S.K., Provance, D.W., Shah, K., Shokat, K.M., Corey, D.P., Mercer, J.A., Gillespie, P.G., 2002. A chemical-genetic strategy implicates myosin-lc in adaptation by hair cells. Cell. 108:371-381. 4. Cheung, E.L., Corey, D.P., 2005. Ca2+ changes the force sensitivity of the hair-cell transduction channel. Biophys. J. in press. 5. Bozovic, D., Hudspeth, A.J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc. Natl. Acad. Sci. USA. 100:958-963. 6. Martin, P., Bozovic, D., Choe, Y., Hudspeth, A.J., 2003. Spontaneous oscillation by hair bundles of the bullfrog's sacculus. J. Neurosci. 23:45334548. 7. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R. 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat. Neurosci. 6:832-836. 8. Stauffer, E.A., Scarborough, J.D., Hirono, M., Miller, E.D., Shah, K., Mercer, J.A., Holt, J.R., Gillespie P.G., 2005. Fast adaptation in vestibular hair cells requires myosin-lc activity. Neuron. 47:541-553. 9. Shepherd, G.M.G., Corey, D.P., 1994. The extent of adaptation in bullfrog saccular hair cells. J. Neurosci. 14:6217-6229. 10. Hirono, M., Denis, C.S., Richardson, G.P., Gillespie, P.G., 2004. Hair cells require phosphatidylinositol 4,5-bisphosphate for mechanical transduction and adaptation. Neuron. 44:309-320. 11. Batters, C , Arthur, C.P., Lin, A., Porte,r J., Geeves, M.A., Milligan, R.A., Molloy, J.E., Coluccio, L.M., 2004. Myolc is designed for the adaptation response in the inner ear. EMBO J. 23:1433-1440. 12. Clark, R., Ansari, M.A., Dash, S., Geeves M.A., Coluccio, L.M., 2005. Loop 1 of transducer region in mammalian class I myosin, Myolb, modulates actin affinity, ATPase activity, and nucleotide access. J Biol Chem. 280:3093530942.

THE PIEZOELECTRIC OUTER HAIR CELL: BIDIRECTIONAL ENERGY CONVERSION IN MEMBRANES W.E. BROWNELL Baylor College of Medicine, Houston, TX 77030., USA E-mail: [email protected] Membranes show bidirectional energy conversion in that their mechanical strain and electrical polarization are coupled. Changes in transmembrane potential generate mechanical force and membrane deformation results in charge movement. The coefficients for the electromechanical transduction and the mechano-electrical transduction have the same magnitude, satisfying Maxwell reciprocity and suggesting a piezoelectric-like mechanism. Outer hair cell models that include its piezoelectric behavior indicate that charge movement occurs at frequencies that span the mammalian hearing range. Experiments have confirmed the modeling results, including the presence of resonances at high frequencies. Another set of experiments have measured electrically evoked pN forces in long (>10 um) cylinders of cellular membrane having radii <150 nm. Highly curved membrane cylinders are found in all hair cells, specifically in their stereocilia and in the fusion pore that forms when a synaptic vesicle joins the presynaptic membrane. High frequency membrane-based electro-mechanical conversion of the receptor potential may contribute to the stereocilia amplifier motor. It may also contribute to the synaptic amplifier required for assuring the temporal precision of neurotransmitter release. Evolutionary pressures for high frequency amplification may have led to the development of mammalian somatic electromotility through an expansion of both the structure and function of the stereocilia bundle motor down the lateral wall of the primal outer hair cell.

1 Introduction 2 Viscous damping and cochlear amplification The survival benefit of localizing predator or prey results in an evolutionary selection pressure for detecting ever higher frequencies. The liquid environment of vertebrate hearing organs imposes a damping force on the vibration of inner ear structures. Viscous damping is directly proportional to the velocity of the vibrating structures so that the force resisting movement increases proportionally with frequency. The damping force sets limits on the frequency at which inner ear structures can differentially vibrate which, in turn, sets the frequency limits of hearing for a given species. Diverse strategies have been adopted by vertebrate inner ears to mechanically counteract fluid damping and increase the upper limit of hearing. Most of the strategies involve the production of a negative damping force. A bundle motor associated with the mechano-electrical transduction in stereocilia appears to be the negative damping strategy used by early vertebrates. When mammals appeared, they incorporated a somatic motor involving a membrane-based

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177 piezoelectric-like mechanism located in the lateral wall of their cylindrically-shaped outer hair cells (OHCs). 3 The piezoelectric outer hair cell Piezoelectricity is a tight coupling between the electrical polarization and deformation of a material. It is inherently bidirectional - deformation is associated with the production of an electric potential (direct piezoelectricity), and application of an electric potential deforms the material (converse piezoelectricity). Many materials are piezoelectric with some having piezoelectric coefficients of sufficient magnitude to be of use as submarine sonar or clinical ultrasound transducers. Thermodynamic considerations require piezoelectric materials to display Maxwell reciprocity in which the coefficients for the direct and converse effects have the same magnitude. OHCs are piezoelectric-like. Electromotility is equivalent to the converse piezoelectric effect. The direct piezoelectric effect has also been observed in OHCs and the experimental evidence supports Maxwell reciprocity. See Brownell [1] for a review. OHC piezoelectric behavior results in charge movement whenever the cell is deformed [2-4]. Thermodynamic considerations reveal that OHC piezoelectricity can contribute to maintaining electromotility at high frequencies [2]. The all-pass nature of the associated charge movement requires that the OHC plasma membrane be treated as more than a simple leaky capacitor. Because of the importance of sonar, electrical engineers have developed tools for incorporating piezoelectric elements into electrical circuits. An equivalent circuit analysis of the OHC reveals that piezoelectricity not only pushes the low-pass corner frequency to higher values, but also predicts ultrasonic resonances in the OHC lateral wall admittance [3]. Recent experiments on isolated OHCs have confirmed the essential features of the equivalent circuit models including ultrasonic resonances [4]. A biophysics-based analysis of the resonant behavior predicts electro-mechanical wave behavior which has recently been measured along the lateral wall of isolated OHCs [4]. OHC piezoelectricity not only generates the requisite mechanical force, but it also circumvents the frequency limits that are imposed by the passive electrical properties of conventional cellular membranes. OHCs are mechanically loaded in vivo. They are firmly anchored to supporting cells by tight junctions in the reticular lamina. Cochlear fluids and both the tectorial and basilar membranes introduce additional mechanical loads. The OHC is therefore a viscous-damped mechanicallyloaded resonator in contrast to the unloaded or free resonator so far considered in the models of the isolated OHC. The loading and damping would be expected to result in a broadening and weakening of the resonance peak as a function of frequency. The observation of broad mechanical resonances in electrically-evoked organ of Corti vibrations [5; 6] is consistent with this expectation.

178 4 Similarities between the OHC apical pole and its lateral wall When OHC electromotility was discovered, examples of a similar, membranebased, electro-mechanical force transduction mechanism were not apparent in the biological literature. While electromotility was an obvious candidate for the mammalian cochlear amplifier, it was in the uncomfortable position of appearing to be an isolated biological phenomenon. Because evolution is a conservative process where existing mechanisms and molecules undergo slight changes to improve performance, it was likely that other examples of electro-mechanical force transduction would emerge. Hair cells are terminally differentiated epithelial cells whose apical and basal poles differ structurally and functionally. Evidence for membrane-based motile mechanisms in both the apical and basal pole have emerged over the past 20 years. Recent studies have revealed fast stereocilia motor behavior in mammalian inner and outer hair cells [7; 8]. We have previously examined the possible existence of a synaptic amplifier in the basal pole of hair cells that utilizes a membrane-based, bidirectional, electro-mechanical mechanism to ensure precise temporal activation of 8th nerve fibers [9]. The remainder of this section will be devoted to identifying the structural and functional similarities between the OHC apical pole and lateral wall. 4.1 The trilaminate apical pole The hair cell apical pole consists of three layers: 1) the plasma membrane; 2) a cytoskeletal matrix; and 3) the membranous canalicular reticulum (Figure 1 shows the apical pole on an OHC). The plasma membrane conforms to the contours of the cytoskeletal matrix immediately beneath it. Stereocilia are organized around densely packed bundles of F-actin. These bundles have rootlets anchored in the hair cell's cuticular plate. The cuticular plate is composed of F-actin enriched by a number of other cytoskeletal proteins. The apical pole has a third layer immediately basal and adjacent to the cuticular plate. This layer consists of a complex of membranes called the canalicular reticulum, a structure that occurs in ion-transporting epithelia. Membrane-bound organelles located in the hair cell apex have been noted in many early ultrastructural studies. Their presence in living cells is revealed by fluorescent lipid markers, suggesting a role in organizing the apical pole. The three layers of the apical pole span a distance of ~ 1 um. The apical pole is the likely precursor for a similar trilaminate organization in the OHC lateral wall. 4.2 The trilaminate lateral wall The trilaminate organization of the hair cell apical pole appears again in the OHC lateral wall (see insert on the lower right of Figure 1). The OHC is a cylinder with a radius of ~ 4.5 um. The three layers of its lateral wall form three axially concentric cylinders. The thickness of the lateral wall is -100 nm (about 25% the wavelength of visible light and an order of magnitude less than the thickness of the OHC's

179 trilaminate apical pole). The plasma membrane is again the outermost layer. The membrane-bound subsurface cisterna forms the innermost layer. The membranes of Figure 1. Cut away of an outer hair cell highlighting the organization of its apical pole. Inset at upper right is a topdown view of the stereocilia bundle showing the plane of the cut. Stereocilia rootlets do not penetrate the cuticular plate, which is concave and extends to the edges of the cell. Tight junctional complexes are found between the OHC and the supporting cell phalangeal processes. The membranous organelle immediately below the cuticular plate is called the canalicular reticulum. It is contiguous with the lateral wall subsurface cisterna. Inset on the lower right is a high magnification rendering of the lateral wall. Modified from [10].

the subsurface cisterna are continuous with those of the canalicular reticulum. Sandwiched between the membranous layers is a cytoskeletal matrix called the cortical lattice. It is composed of cytoskeletal proteins, two of which (F-actin and spectrin) are found within the cuticular plate. The cortical lattice is organized into microdomains of parallel actin filaments that are oriented, on average, in a circumferential direction. The conformation of the lateral wall plasma membrane is determined in part by its attachment to the actin filaments by means of an unknown cytoskeletal protein that forms "pillars". See Brownell [1; 10] for a more in depth review of these and other trilaminate structures related to biological motility. 4.3 Mechanical force generation by the stereocilia bundle The OHC stereocilia bundle and lateral wall generate active mechanical force using unknown motor mechanisms. The bundle generates force at right angles to the cell's longitudinal axis, parallel to the bundle's axis of symmetry. The lateral wall generates force parallel to the OHC axis. The bundle motor unit is associated with mechanoelectrical transduction so that it is reasonable to assume a single stereocilium represents the fundamental motor unit for the bundle motor. Mechano-electric transduction channels in the stereocilia of many, if not all, hair cells change their conductance with prolonged stimulus. The change is referred to as adaptation and is an electromechanical event. A sustained ionic flux (involving calcium) results in a change in the mechanical force acting on the mechanoelectrical

180 transduction channel. Two types of calcium-dependent adaptation mechanisms have been identified: one with longer (>10 ms) and the other with shorter (<1 ms) time constants [1]. The adaptation of hair cell receptor potentials has been linked with active mechanical movements of the stereocilia bundle, most recently in mammalian hair bundles [7; 8]. A cochlear amplifier based on the stereocilia bundle may have been sufficient to provide negative damping at frequencies reaching the upper limit of reptilian (typically <3 kHz) and avian (<10 kHz) hearing. The mammalian cochlear amplifier reaches frequencies approaching 100 kHz. Recent experimental results suggest that the same membrane-based mechanism may contribute to both the bundle and somatic amplifiers. 4.4 Mechanical force generation by membrane tethers We have been pulling membrane tethers to measure the passive mechanical properties of the OHC membrane. In the course of these experiments we have measured pN level forces generated by the tether membrane in response to electrical stimulation via a whole-cell tight seal patch pipette on the cell body [11]. Tethers are formed by pulling on optically-trapped microspheres after spontaneous attachment to cell membrane. The resulting membranous cylinders are narrow (< 300 nm) and can reach lengths in excess of 60 (am. Depolarizing potentials result in elongation, while hyperpolarization shortens the tethers. We have observed force production at frequencies > 6 kHz [12]. Because the patch-clamp is low-pass, it is likely the tethers respond to higher frequencies. A theoretical analysis suggests the tether response is based on membrane flexoelectricity [13]. Flexoelectricity, as the name implies, is the electricity that results from bending. Membranes also show converse flexoelectricity; both the direct and converse forms satisfy Maxwell reciprocity. The coefficient for both is the same and its value varies with the amount and distribution of phospholipids, integral membrane proteins and membrane-associated proteins. The force generated by a change in transmembrane potential is inversely proportional to the membrane's radius of curvature (in part because curvature affects the distribution of phospholipids and therefore membrane polarization). See Petrov [14; 15] for a review. The magnitude of the forces we have measured from membrane tethers are consistent with the flexoelectric coefficients that have been measured in other biological membranes [13]. Since the geometry and size of the membrane tethers resemble that of a stereocilium, it is possible that a flexoelectric membrane-based force generator contributes to high-frequency bundle forces. Petrov has previously pointed out that direct flexoelectricity could augment mechanoelectrical transduction in stereocilia, and becomes more important at higher frequencies (flexoelectricity is a high-pass phenomenon) [14]. Anvari et al. [12] has shown that the sinusoidal response is proportional to tether length. If stereocilia elongate with depolarization and show similar length dependence, then the bundle would be deflected towards the tallest

181

row. The resulting movement would result in more depolarization and the positive feedback results in the observed negative stiffness [8]. 5 On the origin of the outer hair cell electromotility The motor mechanism underlying OHC electromotility generates forces with gains of at least 50pN/mV at frequencies approaching 100 kHz [1; 16]. Two plausible molecular mechanisms for OHC electromotility have been proposed. One is driven by in-plane conformational changes of a motor protein and the other by out-of-plane flexoelectric bending [17]. Measures of charge movement have led to estimates of motor protein (nominally prestin) density that vary between 5000 to 10,000 elements/um2. This would result in -15-30 million total elements per cell depending on the length of the cell. In the membrane-bending flexoelectric model, the motor unit is a longitudinally oriented ripple with a width of -40 nm or - 25,000 per urn. A 50 um-long cell would thus have >1 million motor units. Even if the bundle motor operates throughout the mammalian frequency range, the bundle motor's net force is limited by the number of motor units which is equal to the number of stereocilia (<300). The number of motor units in the lateral wall is between 103 to 104 times the number of bundle motor units. The increased number of lateral wall motor units allows for high frequency OHC somatic force production. A cochlear amplifier based on the bundle motor alone appears to have reached a limit at around 10 kHz. Increasing the frequency range for hearing another order of magnitude requires the negative damping force underlying the cochlear amplifier to increase by the same amount. The surface area at the apical pole cannot sustain 104 stereocilia. Mammals appear to have found the requisite real estate for their cochlear amplifier by expanding the apical pole along the OHC lateral wall. The fundamental motor unit in the flexoelectric based model for OHC somatic electromotility are circumferential plasma membrane ripples organized by cortical lattice F-actin. If evolution followed the scenario suggested above, the ripples represent a morphed version of the stereocilium motor units of the bundle amplifier. In both cases a voltage-driven change in membrane curvature generates mechanical force. Depolarization leads to bending of the bundle towards the tallest row and to shortening of the soma. Both of which could be working in concert for the high frequency requirements of the mammalian cochlear amplifier. 6 The synaptic amplifier The magnitude of inner hair cell receptor potentials varies with stimulus intensity yet the timing of neural discharge is intensity-invariant for both clicks and best frequency tones. In both mammals and frogs, the preferred phase angle is invariant with sound intensity at best frequency. Temporal invariance in the presence of receptor potentials of increasing magnitude argues for a feedback mechanism

182 resembling that of the cochlear amplifier on basilar-membrane vibrations. OHC mechanical feedback preserves the temporal fine structure of basilar-membrane vibrations throughout a broad range of intensities. Temporal shifts of basilarmembrane vibration zero-crossings and local peaks and troughs would occur in the absence of mechanical feedback, and these shifts are not observed experimentally. We have previously demonstrated on thermodynamic grounds that flexoelectric mechanisms similar to those thought responsible for OHC electromotility could modulate hair-cell afferent synaptic transmission [9]. Our recent experiments on membrane tethers [12] provide experimental evidence that the membrane cylinder that makes up the fusion pore could be modulated by flexoelectric activity. Ruggero and colleagues have recently presented evidence that temporal synchrony of auditory nerve fibers extends beyond frequencies for phase-locking limits to the limits of hearing for the animal [18]. While our results establish that the magnitudes of the forces and fields resulting from membrane flexoelectricity are sufficient to modulate neurotransmitter release, further work is required to experimentally verify our proposal and to extend our findings beyond simple membranes to the more complex membranes of living cells. The manner by which electromechanical coupling in synaptic membranes can explain the precise temporal control required for processing inter-aural temporal cues will require still further analysis. Just as cochlear amplifier models are based on the intrinsic tuning of the basilar membrane, it may be necessary to consider either mechanical or electrical tuning at the synapse. 7 Discussion I have suggested that high frequency membrane-based flexoelectric mechanisms in both the stereocilia bundle and lateral wall could contribute to the mammalian cochlear amplifier. The same mechanism may contribute to a synaptic amplifier active at the primary afferent synapse of the inner hair cell. The flexoelectric coefficient in each case can be adjusted for a specific function by modulating the composition of the membrane. Recent experiments have revealed that changes in the lipid profile modulate stereocilia transduction [19]. The presence of prestin in the lateral wall plasma membrane identifies a specific membrane protein that appears to modify the flexoelectric coefficient. There is a modest increase (2-3X) in force production in direct comparison of membranes with or without prestin, on the other hand there is more than a three order of magnitude increase of charge movement [1]. The strong influence on charge movement most likely reflects prestin's membership in the Slc26A family of anion transporters. There are two reasons why the function of Slc26A transporters might benefit from flexoelectric membrane bending. The first is that membrane bending leads to a differential tension between the leaflets of the bilayer. This could facilitate the conformational changes of the protein. Under this scheme the membrane (which includes a contribution from prestin) acts as the voltage sensor. This scenario provides a rationale for the existence of voltage gated ion channels in single cell organisms in

183 which Slc26A anion transporters are also found. The rapid potential changes associated with voltage gated ion channels could trigger bending and make the transport process independent of thermally driven fluctuations. A second benefit derives from the acoustic wave that is generated by the bending membrane. The resulting nano-sonication would serve to mix the unstirred layer and further facilitate transport. These considerations suggest that the origins of OHC electromotility may be linked to evolutionarily ancient mechanisms associated with membrane transport. The active bending of the stereocilia bundle, somatic electromotility and neurotransmitter release represent three rapid membrane-based mechanical events that are synchronized with the hair-cell receptor potential. Confirmation of a role for membrane flexoelectricity in the bundle, somatic and synaptic amplifiers would provide a unifying biophysical framework for exploring all three phenomena and their role in hearing. How the action of each contributes to the cochlear amplifier and ultimately to the neural code that communicates information about the acoustic environment to the central nervous system presents challenges for future work. Clarification of the role of the many proteins that are known to be involved each of the three processes will require precise structural information and knowledge of their interaction with the membrane. The origin and integration of the well known non-linearities of all three amplifiers, particularly at the threshold of hearing will motivate our research enterprise for years to come. Acknowledgments B. Anvari, B. Farrell, E. Glassinger, C.C. Lane, C.E. Morris, A.G. Petrov, A.S. Popel, F. Qian, R. Rabbitt, R. Raphael, F. Sachs, A.A. Spector, and C. Wei made valuable contributions. Supported by NIDCD grants R01 DC 02775 & DC00354. References 1. Brownell, W.E., 2005. The piezoelectric outer hair cell. In: Eatock, R.A., (Ed.), Vertebrate Hair Cells. Springer, New York. 2. Spector, A.A., Brownell, W.E., Popel, A.S., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J Acoust Soc Am 113, 453-461. 3. Weitzel, E.K., Tasker, R., Brownell, W.E., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J Acoust Soc Am 114, 1462-1466. 4. Clifford, S., Rabbitt, R.D., Brownell, W.E., 2005. Electro-mechanical waves in isolated outer hair cells. In: Nuttall, A.L., (Ed.), Auditory Mechanisms: Processes and Models. World Scientific, London.

184 5. Scherer, M.P., Gummer, A.W., 2004. Vibration pattern of the organ of Corti up to 50 kHz: evidence for resonant electromechanical force. Proc Natl Acad S c i U S A l O l , 17652-17657. 6. Grosh, K., Zheng, J., Zou, Y., de Boer, E., Nuttall, A.L., 2004. Highfrequency electromotile responses in the cochlea. J Acoust Soc Am 115, 2178-2184. 7. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8, 149-155. 8. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880-883. 9. Brownell, W.E., Farrell, B., Raphael, R.M., 2003. Membrane electromechanics at hair cell synapses. In: Gummer, A.W., (Ed.), Biophysics of the Cochlea: From Molecule to Model. World Scientific, Singapore, pp. 169-176. 10. Brownell, W.E., 2002. On the origins of outer hair cell electromotility. In: Berlin, C.I., Hood, L.J., Ricci, A.J., (Eds.), Hair Cell Micromechanics and Otoacoustic Emissions. Delmar Learning, San Diego, pp. 25 - 46. 11. Qian, F., Ermilov, S., Murdock, D., Brownell, W.E., Anvari, B., 2004. Combining optical tweezers and patch clamp for studies of cell membrane electromechanics. Rev. Scientific Instruments 75, 2937-2942. 12. Anvari, B., Qian, F., Pereria, F.A., Brownell, W.E., 2005. Prestin-lacking membranes are capable of high frequency electro-mechanical transduction. In: Nuttall, A.L., (Ed.), Auditory Mechanisms: Processes and Models. World Scientific, London. 13. Glassinger, E., Raphael, R.M., 2005. Theoretical analysis of membrane tether formation from outer hair cells. In: Nuttall, A.L., (Ed.), Auditory Mechanisms: Processes and Models. World Scientific, London. 14. Petrov, A.G., Usherwood, P.N., 1994. Mechanosensitivity of cell membranes. Ion channels, lipid matrix and cytoskeleton. Eur Biophys J 23, 119. 15. Petrov, A.G., 2002. Flexoelectricity of model and living membranes. Biochim Biophys Acta 1561, 1-25. 16. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc Natl Acad Sci U S A 96, 4420-4425. 17. Raphael, R.M., Popel, A.S., Brownell, W.E., 2000. A membrane bending model of outer hair cell electromotility. Biophys J 78, 2844-2862. 18. Recio-Spinoso, A., Temchin, A.N., van Dijk, P., Fan, Y.H., Ruggero, M.A., 2005. Wiener-kernel analysis of responses to noise of chinchilla auditorynerve fibers. J Neurophysiol.

185 19. Hirono, M., Denis, C.S., Richardson, G.P., Gillespie, P.G., 2004. Hair cells require phosphatidylinositol 4,5-bisphosphate for mechanical transduction and adaptation. Neuron 44, 309-320. 20. Cheung E.L.M., Corey D.P., 2005. Ca2+ changes the force sensitivity of the hair-cell transduction channel. In: Nuttall A.L., editor. Auditory Mechanisms: Processes and Models. Singapore: World Scientific.

Comments and Questions Chadwick: You were suggesting that there may be a common membrane mechanism for somatic and hair bundle motility. Could you elaborate further these piezo or flexo motility mechanisms might bend a hair bundle? Answer: I suggest that a membrane based mechanism could make a contribution to active hair bundle motility. The membrane based electromechanical force generation we have been characterizing in membrane tethers [12] resembles the voltage dependent saccular hair bundle "flick" described at this meeting by the Corey lab [20]. In my text, I suggest one possible mechanism for voltage dependent bundle movements that is based on our observation that the axially directed electromechanical force in tethers is directly proportional to tether length. If individual stereocilium show similar length dependence then bending of the bundle would occur that, like the flick, depends on the presence of tip links. An additional contribution to bundle movement may be more directly related to our flexoelectric model of somatic motility [17] and would involve changes in the curvature of stereocilium membranes. If, as in the outer hair cell flexoelectric model, depolarization results in an increase in membrane curvature the radius of individual stereocilium would decrease by less than the thickness of a cellular membrane. When summed over the bundle the cumulative effect would be bundle movement. Allen: What role does prestin play in the membrane bending model of electromotility? Answer: I am very glad you asked this question Jont, since it gives us the opportunity to clarify a few misconceptions about the bending model in the literature. For example, there appears to be a notion out there that the bending model is purely lipid based. I really don't know where this idea came from, since in the original 2000 paper in the Biophysical Journal, we simply developed a phenomenological flexoelectric model and showed that it could fit the electromotility data. There was a free parameter in our fit, which is the product of the number of dipoles (sensors/motors) and the dipole moment on each motor. As this was done before prestin was discovered, we were keeping an open mind and performed two calculations: one assuming the number of dipoles corresponded to the density of lipids in the membrane, and the other assuming the number of dipoles corresponded to the number of particles (now believed to be prestin molecules) in freeze-fracture images. Now I know it was a long paper and we did these on the last

186 pages of the discussion section, but both dipole moments calculation came out reasonable (in retrospect, that for lipids was a little bit on the high side), and so we stated the data did not permit us to make a determination on the mechanism. But we did explicitly point out that a protein conformational change was a possibility, and suggested a few possible mechanisms by which protein conformational changes can lead to membrane bending. So thanks again for asking and allowing us to clarify this misconception.

OUTER HAIR CELL MECHANICS ARE ALTERED BY DEVELOPMENTAL CHANGES IN LATERAL WALL PROTEIN CONTENT H.C. JENSEN-SMITH AND R. HALLWORTH 'Department

of Biomedical Sciences, Creighton University, 1912 California Plaza, Nebraska 68178, USA E-mail: [email protected]

Omaha,

Electromotile length change and force generation by outer hair cells is thought to be essential for a sensitive and sharply tuned mammalian cochlea. Outer hair cell stiffness is in turn important for effective transmission of force to the organ of Corti. Maturation of stiffness in outer hair cells during development may therefore be an important factor in the onset and maturation of hearing. We compared the mechanical properties of developing and adult gerbil outer hair cells using calibrated glass fibers. We found that specific compliance of outer hair cells increased dramatically up to the onset of hearing and decreased after that. We examined F-actin, spectrin and prestin synthesis in developing and adult gerbil outer hair cells. While the F-actin content of the lateral wall decreased progressively during postnatal development, both spectrin and prestin increased close to the onset of hearing. These results strongly support the hypothesis that the cortical lattice and the prestin content of the lateral wall membrane influence outer hair cell mechanical properties.

1 Introduction Cochlear outer hair cells (OHCs) are poised to augment basilar membrane (BM) vibration in the organ of Corti during acoustic stimulation [1]. Contraction and elongation of OHCs in response to membrane potential changes occurring at acoustic frequencies, i.e., electromotility [2], are fundamental for attaining high sensitivity and frequency selectivity in the mammalian cochlea [3-8]. Surrounded by support cells, the OHCs must work against the load imposed by these structures to augment auditory signals. A significant amount of axial stiffness is therefore crucial for the OHC to contract and elongate at acoustic frequencies. The highly specialized OHC lateral wall (LW) is responsible for generating stiffness, force and maintaining a cylindrical cell shape (for review see 9). This unique trilaminated structure is composed of the plasma membrane, cortical lattice (CL) and subsurface cisternae. The prestin rich plasma membrane is attached to the actin-spectrin CL by 'pillars' of unknown origin [10]. The CL is composed of circumferential F-actin filaments cross linked to longitudinal spectrin filaments [11,12]. The subsurface cisternae located beneath the CL consist of varying numbers of complex membrane bound organelles of unknown function. Although it is well known that membrane prestin can directly alter OHC stiffness when electrically stimulated [13], it has been shown that other LW constituents can regulate OHC stiffness in a prestin-independent fashion [14-17]. Several researchers have measured OHC axial stiffness or compliance in mature

187

188 OHCs using a variety of techniques [for review see 17]. Until now, however, the stiffness of the OHC during postnatal development has not been described. 2 Methods Gerbil OHCs were isolated from the day of birth (post natal day 0, P0) and at three day intervals starting at P3. Strips of organ of Corti were placed into a low calcium solution containing 0.5% to 1.0% papain (Calbiochem, La Jolla, CA) for 10 to 20 min. Isolated OHCs were placed in an experimental chamber located on an Olympus 1X70 inverted microscope (Olympus America Inc, Melville, NY) containing 320 mOsm L-15 with 1% BSA, 5 mM TEA, 2 mM CoCl2. Cells with nuclei shifted from the basal pole, or moving granular material in the cytoplasm, were excluded. OHC compliance was measured using calibrated glass fibers using established methods [18, 19]. Specific compliance was calculated by dividing the complaince by the cell length, which was measured from a video screen using a calibrated grid. For quantitative fluorescence, isolated cells were embedded in agarose, fixed, blocked and permeabilized (24 h), and then exposed to either phalloidin-Alexa 568 (Molecular Probes) to detect filamentous actin, or to primary antibodies against spectrin (Sigma) or prestin (kindly provided by J. Zheng, Northwestern University) followed by secondary antibodies coupled to Alexa 488 or 568. A single fluorescence intensity image was generated for each OHC using a Zeiss AxioPlan META NLO multiphoton confocal microscope (Carl Zeiss Jena, Jena, Germany). Each profde was obtained in a single pass without prior exposure to fluorescence illumination. Negative controls were established by omitting the primary antibody. Fluorescence intensity profiles orthogonal to the OHC long axis were obtained at 25%), 50%o and 75% of cell length. The intensity of fluorescence in the lateral wall was obtained as the difference between the peak and the background extracellular fluorescence. For overall analysis of age-related differences in specific compliance or fluorescence, one way analysis of variance (ANOVA) tests were performed. Posthoc Fishers t-tests were then used to compare the mean responses from each age group. Animal care and handling was performed in accordance with protocols approved by the Creighton University Institutional Animal Care and Use Committee.

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3 Results Fig 1 shows the average specific compliance (error bar 1 s.e.m.) of isolated OHCs as a function of developmental age. Specific compliance increased by more than a factor of 2 (from 0.032 to 0.067 km/N/um of length) up to P9. Specific compliance then decreased between P9 and P12 (around the onset on hearing) to close to the P3 value (0.030 km/N/um). The average value of specific compliance did not change significantly in later development. For comparison, the specific compliance of adult guinea pig OHCs is also shown in Fig. 1 (data from [19]). Adult guinea pig OHCs are about 5 times stiffer than mature gerbil OHCs. We examined the potential contributions of the major components of the OHC lateral wall to the changes in specific compliance during development. Fluorescence intensity profiles were obtained from isolated gerbil OHCs. To reduce the effects of bleaching, we used fade-resistant fluorescent labels (Alexa 488 and Alexa 568) and a procedure in which cells were exposed to laser illumination only once and were otherwise kept away from ambient and ultraviolet light. At birth (P0), phalloidin labeled F-actin was particularly strong throughout the OHC LW (Fig. 2B), including the entire basolateral cellular membrane. The intensity of the label in the OHC LW decreased progressively during development such that in late development the intensity was on average about one-third of that observed at P0 (p < 0.001). In contrast, label for spectrin was observed mainly in the cuticular plate (CP) at P0. Label appeared to extend basalward during development such that the entire lateral wall was labeled by P9. The average intensity of the label was constant up to and including P9 (Fig. 2C). The intensity of the label increased substantially between P9 and P12, which suggested that a new round of sysnthesis of spectrin or incorporation into the LW had occurred. The intensity of spectrin label in the LW declined only slightly in the later stages of development. In contrast, label for prestin in the LW was observed in significant quantities only after P6 and reached a nearly-mature level at P12 (Fig. 2D). However, a small but significant increase in the intensity of prestin label was observed after PI2, which

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4 Discussion

If the CL is important for determining OHC mechanical properties, a detectable change in OHC mechanics should occur during CL formation. The striking increase in OHC specific compliance observed between P3 and P9 corresponds closely in time to the elaboration of spectrin in the OHC lateral wall (Fig. 3). It might have been expected that OHC stiffness would increase at the onset of hearing. However OHC deformability increased substantially. The function of this increase is not clear, but our anatomical studies offer an explanation. The incorporation of spectrin in the LW appears to have a significant impact on OHC mechanical properties. This is not surprising as spectrin filaments are thought to be significantly more compliant than F-actin [20]. The CL is the only cytoskeletal structure capable of modifying OHC mechanics during development. We did not observe any other actin or spectrin structures that underwent substantial changes during this time period. Likewise, although

191 microtubules develop during this period [21, 22], they are not connected in such a way as to confer structural rigidity. Other LW structures are also unlikely to mediate the observed changes in OHC mechanics. Weaver and Schweitzer [23] have described a steady increase in cisternae content after the onset of hearing. This increase would be expected to contribute extra stiffness to the LW at that time. The extent and development of the cisternae in earlier development are unknown. Prestin in the LW is also hypothesized to contribute stiffness to the OHC [13]. There is a rapid amplification of prestin expression in the OHC from P6 to P12. The insertion of prestin into the LW corresponds closely to the dramatic decrease in OHC specific compliance from P9 to PI2. This suggests that the large density of prestin in the lateral wall membrane significantly changes the stiffness of the membrane. In contrast, there is also a significant increase in the spectrin content of the CL between P9 and PI2. However, if our inferences from the early stages of development are correct, the further incorporation of spectrin would be expected to increase, not decrease, specific compliance. For effective transmission of force to the organ of Corti, the OHC must have sufficient axial stiffness to work against the load applied by the organ of Corti. A previous report showed that demembranated OHCs, consisting mainly of the CL, are readily deformable and have about one hundredth of the stiffness of intact OHCs [24]. The OHC LW therefore appears to act as a composite material with properties distinct from that of any of its individual components. Our data suggest that both prestin and the OHC CL significantly modify the mechanical properties of intact OHCs.

II

Figure 3. Comparison of developmental progression of specific compliance and the lateral wall proteins actin, spectrin, and prestin.

1* Developmental Age
Acknowledgments This work was supported by NIH NIDCD grant DC02053, NIH NCRR grant RR17417, the Nebraska Center for Cell Biology (NSF-EPSCoR), and a gift from Richard Bellucci, M.D. Heather Jensen-Smith is a Clare Booth Luce Fellow. We thank Alex Bien and Rebecca Van Winkle for experimental and technical assistance, respectively, and Jing Zheng and Peter Dallos for the gift of the prestin antibody.

1. Nobili, R., Mammano, F., Ashmore, J., 1998. How well do we understand the cochlea? Trends Neurosci., 4, 159-167. 2. Brownell, W.E., Bader, C.R., D, de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science, 227, 194196. 3. Ashmore, J.F., 1987. A fast motile response in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. J. Physiol., 388, 323-347. 4. Ruggero, M.A., Rich, N.C., 1991. Furosemide alters organ of corti mechanics: evidence for feedback of outer hair cells upon the basilar membrane. J. Neurosci., 4, 1057-1067. 5. Evans, B.N., Dallos, P., 1993. Stereocilia displacement induced somatic motility of cochlear outer hair cells. Proc. Natl. Acad. Sci. U.S.A., 90, 83478351. 6. Nuttall, A.L., Ren, T., 1995. Electromotile hearing: evidence from basilar membrane motion and otoacoustic emissions. Hear. Res., 92, 170-177. 7. Fridberger, A., Boutet de Monvel, J.B., 2003. Sound-induced differential motion within the hearing organ. Nature Neurosci., 5, 446-448. 8. Liberman, M.C., Gao, J., He, D.Z.-Z., Wu, H., Jia, S., Zuo, J., 2002. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature, 419, 300-304. 9. Brownell, W.E., Spector, A.A., Raphael, R.M., Popel, A.S, 2001. Micro- and nanomechanics of the cochlear outer hair cell. Ann. Rev. Biomed. Eng., 3, 169-194. 10. Flock, A., Flock, B., Ulfendahl, M., 1986. Mechanisms of movement in outer hair cells and a possible structural basis. Arch Otorhinolaryngol., 243, 83-90. 11. Holley, M.A., Ashmore, J.F., 1988. A cytoskeletal spring in cochlear outer hair cells. Nature, 335, 635-637. 12. Wada, H., Usukura, H., Sugawara, M., Katori, Y., Kakehata, S., Ikeda, K., Kobayashi, T., 2003. Relationship between the local stiffness of the outer hair cell along the cell axis and its ultrastructure observed by atomic force microscopy. Hear. Res., 177, 61-70. 13. He, D.Z., Dallos, P., 1999. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc. Natl. Acad. Sci. U.S.A., 96, 8223-8228. 14. Frolenkov, G.I., Mammano, F.; Belyantseva, LA., Coling, D., Kachar, B., 2000. Two distinct Ca(2+)-dependent signaling pathways regulate the motor output of cochlear outer hair cells. J. Neurosci., 20, 5940-5948. 15. Zhang, M., Kalinec, K., Urrutia, R., Billadeau, D.D., Kalinec, F., 2003. ROCK-dependent and ROCK-independent control of cochlear outer hair cell electromotility. J. Biol. Chem., 278, 35644-35650.

193 16. Dallos, P., He, D.Z., Lin, X., Sziklai, I., Mehta, S., Evans, B.N., 1997. Acetylcholine, outer hair cell electromotility, and the cochlear amplifier. J. Neurosci., 15,2212-2226. 17. Zelenskaya, A., Boutet de Monvel, J., Pesen, D., Radmacher, M., Hoh, J.H., Ulfendahl, M., 2005. Evidence for a highly elastic shell-core organization of cochlear outer hair cells by local membrane indentation. Biophys. J., 88, 2982-2993. 18. Hallworth, R., 1997a. Modulation of outer hair cell compliance and force generation by factors known to affect hearing. Hear. Res., 114, 204-212. 19. Hallworth, R., 1997b. Modulation of OHC force generation and stiffness by agents known to affect hearing. In: Diversity in Auditory Mechanics, (E.R. Lewis, P.E. Narins and C.R. Steele, eds.), World Science Publishing, Singapore, pp. 524-530 20. Holley, M.A., Ashmore, J.F., 1990. Spectrin, actin and the structure of the cortical lattice in mammalian cochlear outer hair cells. J. Cell Sci., 96, 283291. 21. Hallworth, R., McCoy, M., Polan-Curtain, J., 2000. Tubulin expression in the developing gerbil organ of Corti. Hear. Res., 139, 31-41. 22. Jensen-Smith, H.C., Eley, J., Steyger, P.S., Luduefia, R.F., Hallworth, R., 2003. Cell type-specific reduction of P tubulin isotypes synthesized in the developing gerbil organ of Corti. J. Neurocytol., 32, 185-197. 23. Weaver, S.P., Schweitzer, L., 1994. Development of gerbil outer hair cells after the onset of cochlear function: An ultrastructural study. Hear. Res., 72, 44-52. 24. Tolomeo, J.A., Steele, C.R., Holley, M.C., 1996. Mechanical properties of the lateral cortex of mammalian auditory outer hair cells. Biophys. J., 71, 421-429.

Comments and Discussion Wada: Our data (shown in our poster entitled "Heat stress-induced changes in the mechanical properties of mouse outer hair cells") shows that the stiffness of OHCs in mice increased after the conditioning by whole-body heat stress. We also observed that the amount of filamentous actin (F-actin) increased after such stress. These two factors showed a proportionality relation with each other, suggesting that the increase of F-actin leads to an increase of stiffness of OHCs. Answer: That corresponds to what we reported - during early development, as the actin content of the lateral wall decreases, the compliance increases. It would be interesting to know what happens to the spectrin content of the lateral wall after heat stress.

O U T E R H A I R CELL M E C H A N I C S R E F O R M U L A T E D W I T H ACOUSTIC VARIABLES J O N T B. ALLEN University of Illinois at Urbana-Champaign, 2061 Beckman Institute for Advanced Science and Technology, 405 North Mathews, Urbana, IL 61801 USA E-mail: jba<§'auditor-ymodels. org P.F. F A H E Y Dept.

of Phys/EE,

University E-mail:

of Scranton, Scranton, [email protected]

PA 18510

USA

The electromechanical properties of the Outer Hair Cell (OHC) have been reformulated in terms of acoustic variables. It is anticipated that the acoustic variable formulation will be more useful for incorporating OHC electromechanics into cochlear micromechanics. For guidance on the interdependency of the acoustic and electrical quantities and to aid physical intuition we also present piezoelectric circuit diagram for the OHC.

1

Introduction

The equations for a cylindrical elastic sheathed outer hair cell are [1]

'\R{Vt-Vz) RPt

=

ez e e ec

'Sl'Jlz 5R/R

hEz 1 kv '8l'Jlz 5R/R (1 - kv2) kv k

(1)

where Vz,t are the external and internal pressures, lz is the length of the cell, 6l'z represents a change in length, with positive values corresponding to increased length, R and 8R represent the radius and change in radius, h is the effective thickness of the cell wall, ez = hEz/(l — kv2), ec — hEc/(l — kv2), 2 e = vhEc/(l — kv ), where Ez > 0 is the axial Young's modulus, v is a Poisson ratio (0 < v < 0.5) for the axial and circumferential directions with v = vzc = vcz, k = Ec/Ez such t h a t 0 < k < 1, in terms of either the circumferential or axial Young's modulus Ez and Ec respectively. If the standard sign convention is followed, 61' and 8R indicate increases in length and radius and the terms involving pressure are signed so that a positive value indicates a tension in the wall of the cell. The physical interpretation of (1) involves the direct stretching in the axial and circumferential directions, and includes the membrane's Poisson coupling stiffness, represented by e. Equation 1 is the two-dimensional Hooke's law for the cell. On the left of the equal sign are the stresses (tensions) on the membrane, expressed in terms of pressure. The force AeVt, where Ae = TTR2, divided by the circumference

194

195 2TTR, is the axial tension, acting from within. Since the internal Vt and external Vz pressure act on opposite sides of the end-cap, their signs must differ. The stress acting in the circumferential direction may be determined by computing the total force in this direction, Vt x 2R x lz, and dividing by the length over which it is applied 21z. The matrix of stiffness coefficients ([e z ,e;e,e c ]) is symmetric due to membrane reciprocity. The axial and radial stresses and strains are coupled by a "Poisson stiffness" e which accounts for the axial shortening of the membrane as the circumference increases. To visualize this it is helpful to think of the membrane surface laid out flat. When e is nonzero, as the membrane is stretched in one direction, it becomes shorter in the other. This Poisson coupling induces a coupling between the cell's endcap and wall areas, leading to a volume rate change difference which we denote the Poisson Volume velocity Vp, elaborated upon in the next section. 2 2.1

Results Change of sign i

i

We next define a new length 51z = —8lz by changing the sign of 51z, so that a positive externally applied pressure Vz gives a positive axial impedance, as required by circuit theory conventions. This transformation leads to ~\R(PX-Vt) RVt

ez -e -e er_

Slz/lz 6R/R

After this transformation, a shortening of the cell corresponds an increasing 2.2

Acoustic

(2) SIz.

variables

Equation 2 must be transformed so t h a t the products of the port variables have units of power. One may work in either mechanical variables [F, 1} or acoustic variables (V,V). Since the cell's turgor pressure Vt is not conveniently represented as a force, it is best to use acoustical variables, which are natural when working with basilar membrane models. The axial volume velocity Vz is obtained by multiplication of lz by the area of the end cap Ae = itR2. Likewise the radial volume velocity Vr is obtained by multiplication of R by the wall area Aw = 2irRlz. These definitions follow from V = AwR + AJz

= Vr-Vz

(3)

where V is the net volume velocity (the time rate of change of the cell volume V = Aelz = AwR/2). A related definition is the Poisson volume velocity Vp =

Vr+Vz.

(4)

196 corresponding to the differential wall and endcap volume velocities resulting from the Poisson coupling stiffness e. Appling these definitions to (2) results in the cell's acoustic impedance matrix

~vz-vt v

t

1

sRV

2ez -e —e

2ec

'Vz Vr.

(5)

where s = iui is the Laplace frequency. In this acoustic-impedance model, the axial volume velocity is into the cell while the radial volume velocity is out of the cell. For example, when e = 0 an increase in the externally applied pressure (6VZ > 0) results in an increase in Vz (i.e., 5VZ > 0), corresponding to a shortening of the cell. 2.3

Physics of the piezoelectric

effect

Warren Mason was the first to show t h a t as a piezoelectric crystal is compressed, the material's bound charge q moves proportionally to the length change 51, namely q ex. 61 [2]. In the same publication Mason provids a summary of his experimental results in terms of an electrical equivalent circuit. If one assumes that the OHC is piezoelectric, then the OHC model may be implemented as shown in Fig. 1, via two transformers. The two volume velocities Vz and Vr give rise to the two currents (charge flows) qz and qr which are integrated by the membrane capacitance Cm, resulting in to voltage vm(t) across the capacitor. Likewise, a change in voltage across the membrane causes a force on the embedded charge, giving rise to two independent strains in the membrane, resulting in a net pressure change (i.e., pr and pz). The transformer relations t h a t relate these efforts (p, v) and flows (q, V) are pz = (j)zVz,

pr = <j)rVr

<jz = (j)zVz,

qr =

(6)

(j)rVr.

Define compliances cz, cr and c shown in Fig. 1 as capacitors, as the reciprocal of stiffnesses (c = 1/fc), kz = 1/cz = (2e* - e)/RV kc = 1/cr EE (ec/2 - e)/RV k = 1/c = -e/RV.

(7)

Having defined the transformers in (6), one may proceed to write down the elastic circuit equations from the circuit diagram 'Vz-Vt' Vt qm

=

kz — k k
—(br

Crr

6Vz SVr Vm

(8)

197

qr-

•*—-qm(t)

•+ Qz

v

+

Cr

n

vz

+ N2 r

Vr(t)

JVi

'-Cm

-

Vz

Vr

vm(t) Vzit)

cz

VP "

Vz{t) - Vt

Figure 1. Circuit diagram corresponding to (8).

The first two rows are the loop pressures while the third row is a nodal equation taken at the top of element Cm. This derivation requires the use of (6) and (4). Equation 8 is related to Eqs. (1-3) of [3]. After some algebra the piezoelectric OHC model impedance matrix is Vz-Pt

{kz -k) + <j>l/Cm k + (j>z(j>r/Cm <j>z/C„ k + (t>zr/Cm (kc - k) + 4>2r/Cm 4>r/Cv 4>z/Cm (j>r/Cm 11Cm

vz Vr

(9)

Via a term-by-term comparison, the OHC impedance matrix elements Zij are defined by the elements of (9). For example z\\ = (kz — k)/s + <j)2zjsCmNote the term s = ito must be introduced in the denominator to transform each stiffness into an impedance. Note that this impedance (stiffness) matrix is positive-symmetric, as required by the electrical circuit representation of Fig. 1. Since every impedance matrix is positive definite, all the codeterminants must be positive. The definition of a positive definite matrix, in this context, requires t h a t the total power Vz(Vz-Vt)

+

VrPt+qmv,

(10)

198 is equal to T

1

(kz -k) + ArlCm 4>Z/Cr, k + (j)z4>r/Cm (kc ~k) + (j)2r/Cm 4>r/Cn

vz

(11) Vr Am Two bulk admittances are relevant to the circuit of Fig. 1, the unconstrained (i.e., Vz = 0) bulk soma admittance a

Am.

Vr-Vz

yv

and the unconstrained membrane Poisson admittance

(12) due to v

vr + vz

y = ^

(13)

The physical interpretation of these two bulk admittances are fundamental. The first represents the net volume velocity of t h e cell per unit pressure. The second represents the proportion of Poisson current Vp through the capacitor labeled c in Fig. 1. This flow depends only on e (not on ez or e c ) (see (7)). When e —> oo, c —» 0 and Vp —> 0. Due to the minus sign in the numerator of (12), yv < yp, for the case of the unconstrained cell. In the in vivo case (i.e., in the constrained cell), yu = 0. Relations for these admittances in terms of the membrane parameters will be evaluated next. This concludes the nontrivial transformation from stress-strain membrane variables to acoustic variables. 2.4

Incorporation

of Iwasa and Chadwick

results

Iwasa and Chadwick (1992) [1] measured t h e relative axial length change 5lz/lz and the relative cell radius change 5R/R, as a function of the soma turgor pressure Vt, for isolated OHCs. These measurements were made under the condition of no applied axial force (Vz = 0), and with vm = 30 mv. Note t h a t the cell's volume changes during this measurement, thus V of (3) represents t h e flow through the pipette. Iwasa and Chadwick found that the relative length Sz and radius Sr change are proportional to the turgor pressure, namely 5z\

5l'Jlz

w GzVt,

5r = SR/R « GrTt. 3

(14) 3

From Fig. 2 of [1], Gr = 0.13 x 10~ [Pa] and -Gz « 0.069 x 10~ . We may rewrite (14) in terms of the acoustic variables (The cell becomes shorter (i.e.,

199 8VZ > 0) with increasing Vt (i.e., SVt > 0) since —Gz > 0.) Vz = -sGzVVt,

Vr =

(15)

2sGrVVt

defined in Fig. 1. From (5) with Vz = 0 one may show that ~ v\j%

^*

— —•^cl \™z^c

RV^^-0

/C^fC

KQK )

nj^fij

K(^fv J — thy

> 0,

(16)

rz=o

and 8Vr

VGr

~rvz/\i^z'^c

2ez

>0.

(17)

e,ec

Vz=0

Also (2Gr + Gz)sV = 0.191 x 10" 3 sV.

yv =

(18)

vz=o Given (4) and (15), Vp = (2Gr - Gz)sVVt

= 0.329 x

l0^3sVVt,

(19)

where Vt is in Pascals, resulting in yp = 0.329 x 10^ 3 sV.

(20)

The product of Vp and Vt represents the Poisson coupled elastic energy. Define 7 = Gr/Gz. From Fig. 1 of [1], 7 = - 1 / 0 . 4 3 = - 2 . 3 2 6 , while from Fig. 2 of [1], 7 = Gr/Gz = —1.884. These two estimates come from different experiments and 6 different cells. An average of these two estimates gives 7 = —2.1. The parameter 7 may be interpreted as the reciprocal of the Poisson ratio of some presumed circumferential tubes around the the cell (like barrel hoops). If 7 is exactly 2, it would imply that the membrane enveloping the OHC conserves volume. (This might represent fluid and other structures trapped between the cisternae and the cell plasma membrane, for example.) The case of incompressible tubes, 7 = —2, is close to the average value of Iwasa and Chadwick (1992) data. Thus (jfr

7 = — « - 2 ± 40%. GZ From this point on we shall assume that 7 = —2.

(21)

200

From (15) — = -27 :

(22)

vz

For the conditions of the Iwasa and Chadwick (1992) experiment, combining (4) with (21) gives Vp = 5VZ. while (3) and (22) give V = 3VZ. 2.5 The in vivo cell At acoustic frequencies, or in the in vivo case when the cell is sealed, V = 0. From (3) Vr = Vz, leading to Vp = 2VZ. Assuming no axial load (Vz = 0), and a constant applied voltage (qm = 0), the ratio of Vr to Vz may be found from (5) 2e, e c /2-

Vz

(23) Kc

Combining (22) and (23) gives kz ~ —4:kc, or equivalently cz « — cr/A. Since both — Gz and Gr were found to be greater that zero (see (16) and (17)) it follows that ezec > e2 and that e > e c /2. Thus from (7), kc < 0. From (23), this is the same as saying that as the turgor pressure in increased, the cell becomes fatter and shorter.

rxr-

-9m(*)

qr~ qz

C™

um(i)

•

Vr ( * ) . +

n

Vr

^z

+ N2

M •+ Vr Cr(V~m)

-W,

Vz Vp,

+

cz{Vm)

(

)Vz(t)

c(Vm)

±J

-T>t

Figure 2. Final circuit diagram with turger pressure as the source. Since the net volume at acoustic frequencies must be zero, Vz = V r , and Vp = 2V z .

Figure 2 shows the configuration of the final curcuit with the membrane compliances shown as voltage dependent, the volume velocity constrained to be

201 zero, as required at acoustic frequencies, with the turger pressure shown as a battery, the acoustic power source of the cell. Since Vz = Vr, and Vp = 2VZ, using the circuit of Fig. 2 one may easily find the turgor pressure and evaluate the axial acoustic impedance of the cell and relate the nonlinear capacitance to the axial loading on the cell. From Eq. 9 p

kc

<prkz —
which shows how the turger pressure depends on both the voltage and the axial pressure. This expression may then be substituted back into Eq. 9, and the results may be simplified, for the intact cell constrained to a constant volume, giving ~5VZ _ qm

1 kz+kT

z+4>r

4>Z+4>T

kz+kr

kz+kr

I Grr

Vz Vm

(24)

This leads to a very simple result. For the OHC to be nonlinear, either kz and or kr must be voltage dependent. Furthermore, this leads to a direct prediction about the voltage dependent nonlinear capacitance, and its relationship to the voltage dependent stiffness and displacement. 3

Conclusion

We have reformulated the OHC constitutive equations in terms of acoustic variables and summarized the electromechanical properties of the OHC with a piezoelectric circuit following Mason's classic model [2]. Future steps will to incorporate OHC NL capacitance along with voltage controlled stiffness results into this scheme. As these data are nonlinear our circuit will necessarily acquire nonlinear voltage-controlled circuit elements. It is our hope that the incorporation of voltage dependent values for ez(Vm), e c (V m ) and e(Vm) will be sufficient to represent all of the nonlinear response of the OHC. We would like to thank Robert Haber for discussions on the form of (1) and on the physical intrepretation of the axial to radial coupling. References 1. Iwasa, K. and Chadwick, R., 1992. Elasticity and active force generation of cochlear outer hair cells orientation. J. Acoust. Soc. Am 92, 3169-3173. 2. Mason, W.P., 1939. A dynamic measurement of the elastic, electric and piezoelectric constants of rochelle salt. Phys. Rev. 52, 775-789. 3. Spector,A., Brownell, W., and Popel, A., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 90, 453-461.

A MODEL OF HIGH-FREQUENCY FORCE GENERATION IN THE CONSTRAINED COCHLEAR OUTER HAIR CELL ZHIJIE LIAO AND ALEKSANDER S. POPEL Johns Hopkins University, Baltimore, Maryland 21205 USA Email: zliao(a),bme. ihu. edu and apopel(a),bme. ihu. edu WILLIAM E. BROWNELL Baylor College of Medicine, Houston, Texas 77030 USA Email: brownell(a),bcm. tmc. edu ALEXANDER A. SPECTOR Johns Hopkins University, Baltimore, Maryland 21205 USA Email: aspector(a).bme.ihu.edu The cochlear outer hair cell (OHC) has a unique property of electromotility, which is critically important for the sensitivity and frequency selectivity during the mammalian hearing process. The underlying mechanism could be better understood by examining the force generated by the OHC as a feedback to vibration of the basilar membrane. In this study, we propose a model to analyze the effect of the constraints imposed on OHC on the cell's high-frequency active force generated in vitro and in vivo. The OHC is modeled as a viscoelastic and piezoelectric cylindrical shell coupled with viscous intracellular and extracellular fluids, and the constraint is represented by a spring with adjustable stiffness. We found that constrained OHC can achieve a much higher corner frequency than free OHC, depending on the stiffness of the constraint. We also analyzed cases in which the stiffness of the constraint was similar to that of the basilar membrane, reticular lamina, and tectorial membrane and found that the force per unit transmembrane potential generated by the OHC can be constant up to several tens of kHz.

1 Introduction The cochlear outer hair cell (OHC) plays a key role in the amplification and frequency discrimination during the mammalian hearing process. Through the mechanism termed electromotility [1], the OHC is capable of changing its length in response to changes in the cell's transmembrane potential. Because the OHC is constrained in the cochlear structure, such a change in somatic length generates a force that is fed back to the vibrating basilar membrane (BM). As a consequence, the movement of the BM is adjusted to enhance sensitivity and frequency selectivity. The force generated by OHCs is of critical importance and has already been studied in both experiments and models. A number of studies have been developed for low-frequency conditions. Hallworth [2] has used a suction pipette to hold the basal end of the OHC and measured the force that was generated by the cell and

202

203

applied to a glass fiber against the OHC apical end. Iwasa and Adachi [3] chose the whole-cell voltage-clamp technique to examine force generation. Hallworth [2], Iwasa and Adachi [3], and Spector et al. [4] had developed models to analyze the OHC active force. Frank et al. [5] have applied the microchamber setup [6] and, for the first time, measured the OHC high-frequency active force generation. They also demonstrated that the force generated by OHC could be constant up to tens of kHz. Tolomeo and Steele [7] have developed a dynamic model of OHC vibrating under the action of mechanical and electrical stimuli and interacting with the intracellular and extracellular viscous fluids. Ratnanather et al. [8] had considered both the viscosity of the fluids and that of the cell wall. In this study, we have modeled the constrained OHC as a circular cylinder held by a micropipette (microchamber) and attached to a spring at the other end. The viscous intracellular and extracellular fluids and the viscoelastic and piezoelectric cell's lateral wall are coupled. By choosing to make the stiffness of the spring equal to that of the glass fiber or to that of the cochlear components, we were able, respectively, to model experimental conditions or make predictions regarding the OHC active force production in vivo. We found that a constrained OHC could achieve a much higher corner frequency than a free OHC, and that the force per unit transmembrane potential in vivo could be constant up to a few tens of kHz. Our model can provide the effective inertial and viscous properties of the cell-and-fluids system for dynamic models of OHC with lumped parameters. Also, this model describing OHC as a local amplifier can be incorporated into a global cochlear model that considers the cochlear hydrodynamics and frequency modulation of the receptor potential. Finally, the proposed approach can lead to a better understanding of the mechanics underlying OHC high-frequency electromotility.

2 Model As shown in Fig. 1, the total traction exerted on the cell wall surface is determined by the intracellular and extracellular fluids: "cell

= 5

ext

_

"int

'

W

where gcell is the total traction exerted on the cell wall surface, and o ext and 6 int are, respectively, the tractions due to the cell's wall interaction with the extracellular and intracellular fluids. The constitutive equations for the cell wall that include the orthotropic elastic, viscous and piezoelectric components [7, 8] take the form, \N

n

uv

_

dux dx + ur r

c

~92"/

n -v dxdt -rj

dur

yjt _

204

Here Nx and Ng and are the components of the stress resultant (i.e., the product of the stress and cell wall thickness) generated in the cell wall; the subscripts r, x and 9 indicate the radial, axial and circumferential directions, respectively; Cs are the stiffness moduli; ux and ug are two components of the displacement; 77 is the cell wall viscosity; / is time; V is the transmembrane potential change; and ex and eg are two coefficients that determine the production of the local active stress resultant per unit transmembrane potential [9, 10].

Figure 1. In vivo the outer hair cell (OHC) is sandwiched between tectorial membrane and basilar membrane (a). Such system can be modeled as a cylindrical shell, interacting with surrounding viscous fluids and constrained by two springs (b). In vitro the microchamber is used to measure high-frequency OHC force generation by attaching a fiber to the cell end (c). For simplicity, only the excluded part of cell is considered, and the cell holding point at the orifice of the microchamber can be treated as the fixed boundary condition (d).

The movement of intracellular and extracellular fluids is governed by linearized Navier-Stokes equations [7]. The closed end of the cylindrical cell is treated as an oscillating rigid plate immersed in the fluid that will add extra hydrodynamic resistance to the cell wall; also, additional terms associated with the effect of the constraint (spring) are factored into the equation. The stress (resultant) and displacement can be expressed as the Fourier series in the cell's wall and fluid domains. Then, the Fourier series are substituted into the governing equations for the corresponding domains, and the respective boundary conditions are taken into account. As a result of these derivations, the solution in terms of the Fourier coefficients of the cell wall displacement is obtained as follows: u ecu = L' c cel i+k fluid +k elld +k spring J (—opiez) > (3) were fl u and g are, respectively, the vectors of the Fourier coefficients of the cell wall displacement and the stress due to electrical stimulation of the cell. Also, kceii, kfiuid, kend and kspring are the matrices that determine the stiffness associated with the cell wall, fluids, closed end, and constraint, respectively. Finally, the cell end displacement wend can be calculated from the displacement coefficients vector n , and the force acting on the constraint is obtained as "cell' * end

° ^constr ^end

t

\^)

205 where kmnstr is the stiffness of the cell constraint, represented by a spring attached at the cell's end. The force .Fend is equal to the active force generated by the cell as a result of its electrical stimulation. We compute this force and present our results in terms of force per unit transmembrane potential. The use of active force per unit transmembrane potential allows us to analyze the effect of the constraints in vivo separately from the effect of high-frequency changes in the receptor potential. The elastic moduli and coefficients of the electromotile response for the cell wall are chosen as Cn = 0.096 N/m, Cu = 0.16 N/m, C22 = 0.3 N/m, and ex = 0.0029 N/Vm, e9 = 0.0018 N/Vm [4, 9, 10]. We also choose 1 x 10-7 Ns/m for the cell wall (surface) viscosity and 6 x 10"3 Ns/m2 and 1 x 10~3 Ns/m2 for the intracellular and extracellular (volume) fluid viscosity, respectively. 3 Results and Discussion Our model results agreed well with and were validated by the low-frequency force measured by Hallworth [2] and Iwasa and Adachi [3]. Fig. 2 shows the force magnitude, displacement, and phase shift for various levels of stiffness of the constraint (spring). To simulate both experimental and physiological conditions, we included sets of four curves in which the dashed lines correspond to the stiffness of the fiber in the experiment by Frank et al. [4], and the solid, dotted, and dashed-dotted lines correspond to the stiffness of the cochlear membranes constraining the OHC in vivo. The fiber stiffness in the experiment by Frank et al. [4] was equal to 0.17 N/m. In vivo, OHCs are constrained by the underlying BM and the overlying tectorial membrane ™ and reticular lamina (RL). Thus, we have estimated the effects of these three components of the cochlea. The stiffness of the BM in the basal turn of the cochlea was estimated as 1.25 N/m [11], and this case is illustrated by the solid lines in Fig.2. Zwislocki et al. [12] had estimated the stiffness of the TM as 0.05 N/m. Recently, Scherer and Gummer [13] have probed the organ of Corti along the RL (the TM was removed). The upper and lower limits of the obtained stiffness were equal, respectively, to 0.2 N/m and 0.05 N/m. Assuming that the stiffness of the OHCs underlying the RL in Scherer and Gummer's [13] experiment was much smaller than that of the RL, we attribute the stiffness they measured to the RL. Thus, the dotted and dashed-dotted lines in Fig. 2 correspond, respectively, to the upper and lower limits of the stiffness of the RL. The dashed-dotted lines also represent the case in which the stiffness of the constraint is equal to that of the TM.

206

(A) :

(B)

V v. v V. v.

\ £ = 0.20N/m fc = 0.17N/m £ = 0.05N/m

\

^ \ \ : \ V:

k: loading stiffness Cell length = 30 urn

£ = 1.25 N/m k = 0.20 N/m * - 0 . 1 7 N/m fc = 0.05 N/m t = 0 N/m

A: loading stifthess Cell length = 30 fim

10'

Frequency (Hz)

Frequency (Hz)

(C)

\

k = 1.25 N/m k = 0.20 N/m k -0.17 N/m k = 0.05 N/m k = 0 N/m

k: loading stiffness Cell length = 30 urn

Figure 2. Modeling the high-frequency force generation. (A) force (per unit transmembrane potential); (B) displacement; (C) phase. 1.25 N/m is the stiffness of the basilar membrane in the basal turn [11], while 0.20 and 0.05 N/m are the upper and lower limits of stiffness of the reticular lamina located at the positions of OHCs [13]. 0.05 N/m is also the stiffness of tectorial membrane [12]. The loading stiffness used in the experiment of Frank et al. [4] is 0.17 N/m. The near-isometric force can be constant at -60 pN/mV up to 100 kHz, if the BM stiffness is chosen.

Frequency (Hz)

The results presented in Fig. 2 demonstrate the importance of the effect of the imposed constraints on the active force produced by the OHC. A more constrained cell had a longer range of constant active force: the ranges of constant active forces reached 30 kHz when the constraint stiffness is 0.17 N/m as used in the experiment by Frank et al. [4], and the force reaches 100kHz when the constraint stiffness was equal to that of the BM (1.25 N/m). In terms of estimating the active force production by the OHC in vivo, we can reasonably predict that the physiological case lies somewhere between the cases corresponding to the stiffness of the BM and that of the RL. Therefore, our results indicate that the active force produced by the OHC under physiological conditions is, probably, constant up to a few tens of kHz. An accurate prediction of the active force production in vivo will require a more complete model of the constraints imposed on OHC in which the characteristic stiffness of all three components (the BM, TM, and RL) is explicitly considered. Nevertheless, our finding that the constrained OHC has a greater (up to tens of kHz) range of a constant active force is consistent with the cochlear frequency map. Indeed, the basal (high-frequency) area

207

of the cochlea associated the cochlear amplifier has a much greater stiffness in the BM that imposes constraints on OHCs in this area. Several factors could have contributed to the longer active force plateau under conditions of higher stiffness of the constraint. One of them is that the higher the stiffness of the constraint, the smaller the movement of the cell (Fig. 2B). Thus, the losses associated with the interaction with the two surrounding fluids and with the relative motion of the components of the cell composite wall become reduced for highly constrained cells. This condition results in a greater roll-off frequency for the force. Another factor is related to the increase in the total stiffness of the system (cell + spring) that also results in an increase in the roll-off frequency. As we have already mentioned, we computed the active force per unit the cell transmembrane potential, and the total force will be equal to the product of the obtained force per unit transmembrane potential and the receptor potential. Thus, the frequency dependence of the total active force generated by the OHC in vivo will be determined by a combination of mechanical factors, which are associated with cell vibration, and the electrical (piezoelectric) properties of the cell membrane shaping the receptor potential. 4 Conclusions A model of the OHC active force generation under high-frequency conditions is proposed. It is shown that OHC is capable of generating a constant force per unit transmembrane potential of up to tens of kHz, depending on the constraint stiffness. The greater the stiffness of the constraint, the broader the frequency range of the constant active force produced by the cell. The proposed approach can be used to provide the effective dynamic properties of the cell+fluid system explicitly relating them to the viscosity and mass of the fluid involved in cell vibration as well as to the viscosity on the cell wall. The developed model can serve as an OHC-associated module in global models of the cochlea. Acknowledgments This work was supported by research grants DC02775 and DC00354 from the National Institute of Deafness and Other Communication Disorders (NIH). References 1. Brownell, W.E., Bader, CD., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 224, 194196.

208

2. Hallworth, R., 1995. Passive compliance and active force generation in the guinea pig outer hair cell. J. Neurophysiol. 74, 2319-2328. 3. Iwasa, K.H., Adachi, M., 1997. Force generation in the outer hair cell of the cochlea. Biophys. J. 73, 546-555. 4. Spector, A.A., Brownell, W.E., Popel, A.S., 1999. Nonlinear active force generation by cochlear outer hair cell. J. Acoust. Soc. Am. 105, 2414-2420. 5. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA. 96,4420-4425. 6. Dallos, P., Hallworth, R., Evans, B.N., 1993. Theory of electrically driven shape changes of cochlear outer hair cells. J. Neurophysiol. 70, 299-323. 7. Tolomeo, J.A., Steele, CD., 1998. A dynamic model of outer hair cell motility including intracellular and extracellular viscosity. J. Acoust. Soc. Am. 103, 524-534. 8. Ratnanather, J.T., Spector, A.A., Popel, A.S., Brownell, W.E., 1997. Is the outer hair cell wall viscoelastic? In: Lewis, E.R., Long, G.R., Lyon, R.F., Narins, P.M., Steele, C.R., Hecht-Poinar, E. (Eds.), Diversity in Auditory Mechanics. World Scientific, Singapore, pp. 601-607. 9. Spector, A.A., Brownell, W.E., Popel, A.S., 1998. Estimation of elastic moduli and bending stiffness of the anisotropic outer hair cell wall. J. Acoust. Soc. Am. 103, 1007-1011. 10. Spector, A.A., Jean, R.P., 2003. Elastic moduli of the piezoelectric cochlear outer hair cell membrane. Experimental Mechanics 43, 355-360. 11. Gummer, A.W., Johnstone, B.M., Armstrong, N.J., 1981. Direct measurement of basilar membrane stiffness in the guinea pig. J. Acoust. Soc. Am. 70, 1298-1309. 12. Zwislocki, J.J., Cefaratti, J.K., 1989. Tectorial membrane II: Stiffness measurements in vivo. Hearing Res. 42, 211-227. 13. Scherer, M.M., Gummer, A.W., 2004. Impedance analysis of the organ of Corti with magnetically actuated probes. Biophys. J. 87, 1378-1391. Comments and Discussion Chadwick: How do you reconcile your result of increasing the plateau region of the hair cell response with increasing stiffness of the hair cell constraint, with those of Mammano who suggests the softness of Deiters' cells help to increase the plateau region? Answer: It seems that the question stemmed from a misinterpretation of Mammano's statement that was not about Deiters' cell softness but rather about the viscosity of that cell. The estimates of Deiters' cell stiffness by Tolomeo, Steele, and Holley show that Deiters' cells are very stiff with the point stiffness about 20 times greater than that of the basilar membrane. These data on Deiters' cell stiffness

209 were used in our modeling to predict the active force plateau region under physiological conditions. We appreciate the stimulating question. Gummer: Thank you for bringing to our attention that the bandwidth of the electromotile response is increased by elastic loading of the cell. However, there is a major difference between your model results and our experimental results (Frank et al, 1999); namely, for "unloaded" cells, we found bandwidths about a decade larger than your model values (for a 30-um cell, 35 kHz instead of your value of 5 kHz in Fig. 2B). Also, the measured asymptotic high-frequency slope was -12 dB/oct, instead of the -6 dB/oct reported here. What could be the sources of these discrepancies? Answer: Our estimate of the frequency slope of the electromotility curve in Fig. 2A in Frank et al. (1999) is about -8 dB/octave, which is similar to our data in Fig. 2 of our paper published in this proceedings. However, the estimate of the corner frequency of electromotility in our model result is indeed smaller than that in Frank et. al. (1999). Several factors, such as the holding potential and viscosities of cell wall and internal fluids, could contribute to this difference. To fully understand the observed discrepancy, an additional analysis is required. Thank you for your thorough analysis of our modeling results and for the stimulating questions.

THEORETICAL ANALYSIS OF MEMBRANE TETHER FORMATION FROM OUTER HAIR CELLS

E. GLASSINGER AND R. M. RAPHAEL Rice University, MS-142, PO Box 1892, Houston, TX, 77251-1892, E-mail: [email protected]

USA

The mechanical properties of cellular membranes can be studied by forming a long, thin, bilayer tube (a tether) from the membrane surface. Recent experiments on human embryonic kidney and outer hair cells (OHCs) have demonstrated that the force needed to maintain a tether at a given length depends upon the transmembrane potential. Since the OHC tether force is highly sensitive to the holding potential, these results suggest that the unique electromechanical properties of the OHC membrane contribute to the voltage response of the tether. Here we develop a theoretical framework to analyze how two proposed mechanisms of OHC electromotility, piezoelectricity and flexoelectricity, affect tether conformation. While both forms of coupling are predicted to lead to experimentaly observable changes in tether force, piezoelectric coupling is predicted to cause an increase in tether force with depolarization while flexoelectric coupling is predicted to lead to a decrease in force. The results of this analysis indicate tether experiments can provide insight into electromechanical behavior of the OHC membrane.

1 Introduction Since membranes are fundamental components of many basic cellular processes, understanding how they respond to changes in mechanical, chemical and electrical environments is an essential and crucial step towards characterizing the cellular basis of both normal and disease states. One method to study the properties of cellular membranes is to extract a thin bilayer tube, termed a tether, from the membrane surface. This tube can be formed by using an optical or magnetic force transducer to pull an attached bead away from the membrane surface. Analyses of tether experiments have provided measurements of the local bending stiffness of both synthetic and cellular membranes [1, 2]. In addition, analyses have helped to correlate changes in cellular function with changes in tension and membranecytoskeletal adhesion energy [3]. Recent tether experiments on voltage-clamped outer hair cells have demonstrated that the force required to maintain a tether formed from both outer hair cells (OHCs) and human embryonic kidney cells (HEKs) is sensitive to the transmembrane potential [4, 5]. The greater force gains measured for tethers formed from OHCs suggest that the unique electromechanical properties of the membranes of these cells contribute to the voltage sensitivity of the tether force. The normal electromechanical response of the OHC membrane is believed necessary for the remarkable frequency discrimination and sensitivity of mammalian hearing [6]. These cells amplify the fluid vibrations of the cochlea by transducing electrical energy into mechanical energy. In mammals, this response

210

211

depends upon the expression of the integral membrane protein prestin [7]. Determining how prestin transduces electrical into mechanical energy will provide fundamental insights into the underlying mechanism of the cochlear amplifier. A number of theories suggest prestin functions as a piezoelectric type motor in which its conformational changes lead to changes in membrane tension and/ or strain [8, 9]. Macroscale analysis of the whole cell deformation provides a linear piezoelectric coupling coefficient on the order of 10"12 C/m [9]. Another model proposes that instead of expanding membrane area, prestin changes the membrane curvature [10]. The theory is based upon flexoelectricity, a form of electromechanical coupling observed in both synthetic and native membranes [11]. In this analysis, we consider theoretically how these modes of electromechanical coupling affect the conformations of tethers formed from cellular membranes. This work extends current thermodynamic models of tether formation to account for energies of both active area and curvature changes and provides a theoretical framework upon which the proposed mechanisms of electromotility can be evaluated. 2 Models and Results 2.1 Thermodynamic analysis of membrane electromechanics Equilibrium tether conformations can be predicted by determining the stability points of the extended energy variational, 9 0 = 8G-dW [12]. For isothermal deformations, G is the electric Gibbs energy and W accounts for the external mechanical and electrical loads applied to the tether. The electric Gibbs energy is obtained by integrating the electric Gibbs energy density G over the membrane area. Equilibrium membrane conformations satisfy: dG - dW = 0 . When required, solutions are obtained numerically using a variant of the Newton-Raphson method in which the step size is adjusted by bisection to ensure the error is reduced for each iteration [13]. 2.2 Thermodynamic analysis of tether equilibrium The thermodynamic analysis of tether conformation is extended from a model developed by Hochmuth et al. to interpret the behavior of tethers formed from cellular membranes [2]. In this section, an overview of this model is provided. Since most cells have a complex geometry, the cellular membrane is approximated as a flat, semi-infinite disc of radius rd,o [2]. The tether shape is parameterized as a cylinder of length Lt and radius Rt. Under the assumption that tether formation does not cause area dilation, the decrease in area of the membrane disc (-AAd) equals the change in tether area [2].

212 The work to form a tether is done by the tether force F and the far-field tension T of the membrane disk: W=FLt + TAAd. The energy density (J/m2) of the tether is the sum of the local bending energy and the membrane-cytoskeletal adhesion energy density y: G=

-kcc2+y.

R,

(1)

iz

=»-~F

Figure 1: Schematic of tether formation from a semi-infinite disc. For this model, the change in area of the disc (jtTd2OTd!02) equals the tether

Here kc is the local area 2-ER,L,. bending stiffness of the membrane and c is the sum of the two principal curvatures of the membrane. For the geometry of this model, the curvature is the inverse of the tether radius, 1/R,. For a tether of area 2nR,Lh the energy is: nKL

'- + 2nR,Lty. R.

(2)

Equilibrium tether conformations can be predicted by minimizing the following expression with respect to R, and Lt: nk L
(3)

Minimizing Eq. 3 provides relations for the tether force in terms of R, and the apparent tension Ta where Ta=T + y: F=

27ikc

and

F = 2n^2kcTa

(4)

Since the tether force depends upon the far-field membrane tension and the bending energy, voltage induced changes in either will alter the tether force. 3 Flexoelectric coupling Direct coupling between curvature and the electric field alters the bending energy of the membrane. The flexoelectric coupling energy density is -fcE where/is the flexoelectric coupling

-50 0 50 Membrane Potential (mV)

Figure 2: Predicted equilibrium tether force for flexoelectric coupling. The results are plotted for Ta = 3.0 x ICC4 N/m and fc= 2.7 x 10-" J - a typical value for a red blood cell membrane [16].

213 coefficient. For a tether of area 2nR,Lt, the coupling energy is -2nfELt. Inserting this energy into Eq. 3 provides two equations which account for the flexoelectric contribution to the tether force: F =

^fKL_2;rjE

and

F = 2jr^2kcTa -InfE.

(5)

R

t

The transmembrane potential is related to the electric field E under the boundary condition E = V/h where h is the thickness of the membrane (~5 nm). The predicted tether force dependence on flexoelectric coupling is given in Figure 2. 3.1 Electrically induced changes in membrane tension Piezoelectric coupling can change area strain and/or membrane tension. Linear coupling alters tension via the general constitutive relation Tt = QEJ - e,F, where Cy are the generalized orthotropic moduli, e, are the components of the material strain, and e, are the piezoelectric coupling coefficients. To determine how applied fields affect the tension of the plasma membrane, the electrically-induced deformation of the whole cell is considered. Following previous mechanical analyses of the voltage driven deformation of the OHC, the cell is modeled as a thin cylindrical shell [9, 14]. The equilibrium conformation is determined using the approach outlined in the membrane electromechanics section. For an orthotropic cylinder of length / and radius r, the energy expression is: (I-I)2 ® = Cu7rr0^L l

+

C22xlo±

o

(r-rf °J- +

2xCl2{r-ra)(l-l0)

r

„

•

• 2*e,r0 (/-/„) K -2xe e l 0 {r-ro)V-

AP(xr2l-

(6)

V0)

The first five terms account for the electromechanical energy of the cylindrical shell [9, 14]. The last term accounts for the pressure-volume work where the constant V0 is the cell volume at zero pressure. The tension changes are analyzed under two distinct experimental conditions: constant volume and constant pressure. For the constant volume case, the constraint nr2! = Vm is introduced. The constant Vm is the volume of the cell where E = 0. Differentiating Eq. 6 with respect to r and / provides two relations that can be solved to determine the equilibrium conformation for an applied voltage. The tension for a given conformation can be calculated using the constitutive equations for the longitudinal and circumferential tensions: T

z = Cnsz + Cn£e ~ ezE

and

T

e = Cnse + Cn£z ~ eeE •

(7)

The predicted tension changes depend upon the whether the pressure or cell volume is fixed. To determine how these tension changes affect the tether force, the average of Tz and Tg is substituted into Eq. 4. For a constant pressure condition, little

214

change in tether force is predicted. For the constant volume condition though, the tether force increases with depolarization (Figure 3). (A)

100 r 90

%

80

S

70

1

60

H 50 40 '

'

-100

'

•

•

-50 0 50 Membrane Potential (mV)

'

100

™

-100

-50 0 50 Membrane Potential (mV)

100

Figure 3: Voltage dependence of the force to maintain a tether from a cylindrical linear piezoelectric shell under either constant internal pressure of 40 Pa (A) or a constant volume constraint (B). Elastic and coupling coefficients are from [17]: Cn = 0.016 N/m, Cn = 0.029 N/m, C,2 = 0.056 N/m, ez = -0.001 C/m2 , ee = -0.0013 C/m2. The force is plotted for a hypothetical cell where P = 40 Pa, /„ = 60 um, ra = 5 um, Vm = 1.01 Vaandkc = 2.7 x 10"19 [16].

4 Discussion Previous theoretical analyses of tether equilibrium have determined that the tether force depends upon the apparent far-field membrane tension as well as the energy required to bend the membrane into the highly curved tether geometry. Consequently, voltage-induced changes in either the tension or bending energy will affect the tether force. To understand the voltage-dependence of the tether response, the contributions of both piezoelectric and flexoelectric coupling are considered in this analysis. The extent which piezoelectric coupling affects the tether force depends upon the experimental conditions. If a constant pressure is applied to the cell and the volume is free to change, then little change in tether force is predicted for a linear piezoelectric continuum. If the volume is constrained instead of the pressure, then significant changes in tether force are predicted (Figure 3). Thus, if prestin operates as an area motor, then under appropriate experimental conditions, the tether force should be sensitive to the holding potential. In addition to piezoelectricity, other factors also contribute to the apparent membrane tension. The apparent tension is the sum of the membrane tension, the membrane-cytoskeletal adhesion energy and surface osmotic pressure. All three of these factors theoretically may be influenced by the transmembrane potential. While the shell analysis provides a reasonable estimation of the membrane tension, the underlying cytoskeletal architecture also affects membrane tension. An applied field may alter how the cytoskeleton contributes to the membrane tension. However,

215 given the cytoskeleton likely provides a supportive rather than active role in fast electromotility, the cytoskeletal contribution to the voltage-dependence of the apparent membrane tension should be smaller than that of the membrane. Voltagedependent changes in protein conformation or interfacial composition could affect the membrane-cytoskeletal adhesion energy and consequently, the tether force. The magnitude of this effect may be assessed by measuring the voltage-dependence of the tether force for cells in which the cytoskeleton has been digested enzymatically. The tether force is sensitive to the bending energy as well as the membrane tension. Full interpretation of prestin's contribution to the tether force, though, requires knowledge of whether or not the protein enters the tether. Although labeled integral membrane proteins are present in tethers formed from red blood cells [15], the presence of prestin in tethers formed from either OHCs or HEKs has not been established. The values of coupling coefficients determined from both the nanoscale bending and piezoelectric models of OHC motility can lead to experimentally measurable changes in tether force. The predicted trends, however, are opposite in direction. The tether force decreases with depolarization for coefficients obtained from the nanoscale bending model and increases with depolarization for piezoelectric coefficients. Preliminary experimental data on the voltage sensitivity of the tether force matches the trends predicted for flexoelectric coupling and is consistent with the coupling coefficient derived from the nanoscale bending model of electromotility (10~19 C) (Qian, F and Anvari, B, unpublished results). These results motivate further investigations to determine the underlying mechanism of voltage sensitivity of the tether force. Acknowledgments We would like to thank Drs. Brownell, Qian and Anvari for their insights and valuable discussions regarding the development of this analysis. This work was supported by NSF-IGERT Grant DGE-0114264. References 1. Waugh, R.E., et al., 1992. Local and nonlocal curvature elasticity in bilayer membranes by tether formation from lecithin vesicles. Biophys J, 61(4):97482. 2. Hochmuth, R.M., et al., 1996. Deformation and flow of membrane into tethers extracted from neuronal growth cones. Biophys J, 70(l):358-69. 3. Sheetz, M.P., 2001. Cell control by membrane-cytoskeleton adhesion. Nat Rev Mol Cell Biol, 2(5):392-6.

216 4. Qian, F., et al., 2004. Combining optical tweezers and patch clamp for studies of cell membrane electromechanics. Review of Scientific Instruments, 75:2937-2942. 5. Anvari, B., et al., 2005, Prestin-lacking membranes are capable of high frequency electro-mechanical transduction, in Auditory Mechanisms: Processes and Models, A.L. Nuttall, Editor. World Scientific. 6. Brownell, W.E., et al., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science, 227(4683): 194-6. 7. Zheng, J., et al., 2000. Prestin is the motor protein of cochlear outer hair cells. Nature, 405(6783): 149-55. 8. Hallworth, R., B.N. Evans, Dallos, P., 1993. The location and mechanism of electromotility in guinea pig outer hair cells. J Neurophysiol, 70(2):549-58. 9. Tolomeo, J.A., C.R. Steele, 1995. Orthotopic piezoelectric properties of the cochlear outer hair cell wall. J Acoust Soc Am, 97(5 Pt 1):3006-11. 10. Raphael, R.M., A.S. Popel, W.E. Brownell, 2000. A membrane bending model of outer hair cell electromotility. Biophys J, 78(6):2844-62. 11. Petrov, A., 2001. Flexoelectricity of model and living membranes. Biochimica et Biophysica Acta, 85535:1-25. 12. Benjeddou, A., 2000. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Computers & Structures, 76(l-3):347363. 13. Garg, S.C., 1977. UTIAS Report: Numerical Methods for the Minimization of Functionals: Comparison and Extension, in UTIAS Report. University of Toronto, Institute for Aerospace Studies, 266. 14. Spector, A.A., Jean, R.P., 2004. Modes and balance of energy in the piezoelectric cochlear outer hair cell wall. Journal of Biomechanical Engineering-Transactions of the Asme, 126(1): 17-25. 15. Berk, D.A., Hochmuth, R.M., 1992. Lateral mobility of integral proteins in red blood cell tethers. Biophys J, 61(1):9-18. 16. Waugh, R.E., Bauserman, R.G., 1995. Physical measurements of bilayerskeletal separation forces. Ann Biomed Eng,. 23(3):308-21. 17. Tolomeo, J.A., Steele, C.R. 1995. Orthotopic piezoelectric properties of the cochlear outer hair cell wall. J Acoust Soc Am, 97(5 Pt 1):3006-11.

Comments and Discussion Chadwick: Can you explain why both leaflets of a membrane are in tension in the bending model of membrane force generation? Why doesn't bending induce tension in the stretched leaflet and compression in the compressed leaflet resulting in no net force? Raphael: This is an excellent question, which takes into account the bilayer nature of the membrane, and you are correct that bending will induce differential dilations

217 in the two leaflets, which lead to a tension differential. This effect is known as the "nonlocal" contribution to the bending energy, because it can relax over the surface of a membrane by molecular diffusion. However, the geometry of the tether (two membranes drawn into a narrow cylinder) imposes a constant differential density field, with the magnitude of the differential tension directly proportional to the tether length. In fact, tether formation at long tether lengths provided the first measurements of the nonlocal bending stiffness (Raphael and Waugh, 1996). Our analysis only considered the local bending energy, which reflects the energy needed for curvature deformation of both monolayers. In a paper we have in press, we show that the nonlocal contribution is small for the tether lengths currently investigated. However, we should note in passing that voltage-dependent nonlocal effects, conceivably mediated by surface charge effects, could be a mechanism for nanoscale bending. Answer: Thanks for the analysis aimed at a distinction between the "in-plane" (piezoelectric-like) and "out-of-plane" (flexoelectric-like) modes of the motor activity. In your analysis, however, the body of the tether can only be flexoelectric, and the piezoelectric mechanism contributes via the far field only. What is the rational for that? If you did any estimates of the piezoelectric effect of the membrane of the tether body, what parameters could you use? The piezoelectric coefficients associated with the force production are combinations of the active (motor-related) strains and passive stiffness. Thus, such coefficients for the body of the tether could be very different from those estimated for the whole wall and used in your analysis of the far field. Raphael: This question raises an excellent point. Our rational for neglecting flexoelectricity in the cell body is that the curvature of the tether will dominate the tether response. Clearly, we need to consider piezoelectricity in the cell body, since it can communicate with the tether by tension. In a paper we have in press in Physical Review E, piezoelectric effects are considered in both the far-field membrane as well as in the tether. In this manuscript, we varied the piezocoefficient by three orders of magnitude (10-12 C/m -10-9 C/m), and found the voltage response of the tether to be small. This analysis was for pure lipid vesicles aspirated into pipettes. As you note, the piezoelectric properties of the membrane in the tether may differ from those of the lateral wall complex, but since the tether area is much smaller than that of the cellular membrane, our intuition is the contribution to the tether force should be small.

N O N L I N E A R R E S P O N S E S I N PRESTIN K N O C K O U T M I C E : IMPLICATIONS FOR COCHLEAR FUNCTION

M.A. CHEATHAM, K.H. HUYNH, AND P. DALLOS Northwestern

University, 2240 Campus Drive, Evanston IL 60208-3550 E-mail: m-cheatham(a).northwestern. edu

USA

Construction of pseudotransducer functions in prestin knockout (KO) mice reveal that the outer hair cell (OHC) transducer appears to function normally, which allows one to study nonlinearities in mice that do not show frequency selectivity or amplification. Measurement of harmonic distortion indicates that the second harmonic exceeds the third in homozygotes and their controls. In addition, intermodulation distortion shows that the cubic difference tone (CDT), 2fl-f2, is -20 dB down from fl in both KO and wildtype (WT) mice. However, in contrast to controls where the cubic exceeds the quadratic difference tone (QDT, f2-fl), f2-fl and 2fl-f2 are similar in magnitude for KO mice. Because KO mice also exhibit two-tone suppression, these results support the idea that cochlear nonlinearity persists in the absence of low thresholds and sharp tuning and that the hair cell transducer is the primary source of cochlear distortion.

1 Introduction Previous reports indicate that mice lacking prestin lose their sensitivity [1,2] and frequency selectivity [2], the two hallmarks of cochlear amplification. In order to evaluate the relationship between the active process and cochlear nonlinearity, we examined distortion products in prestin knockout mice and their controls. Although knockouts exhibit distortion product otoacoustic emissions [3] and responses at 2flf2 in the cochlear microphonic (CM) [2, 3], additional information is required to quantify the relative levels of even- versus odd-order components generated in response to both single- and two-tone inputs. We also provide the first measurements of two-tone suppression in mice lacking OHC motor function. 2 Methods Prestin KO mice were produced commercially on a mixed 129S1/C57BL6 background [4]. Cochlear potentials were recorded on F6/F7 generation mice between 4 and 7 weeks of age using a round window electrode in animals anesthetized with Sodium Pentobarbital. CM measurements were obtained from fast Fourier transforms of averaged response waveforms collected with a 49.9 kHz lowpass filter to minimize aliasing. In addition, offline examination of averaged response waveforms allowed peak positive and peak negative CM potentials to be documented and plotted as a function of peak sound pressure. This procedure is based on that used originally by Russell and Sellick [5] for inner hair cell receptor

218

219 potentials. Construction of these CM pseudotransducer functions [6-8] provides a means to monitor mechano-electrical transduction. In other words, the method produces an estimate of the shape of the transfer function relating sound pressure at the tympanic membrane to hair cell receptor currents based on the gross CM. Additional details are found in a previous publication [3]. 3 Results 3.1 Pseudotransducer functions Because the cochlear microphonic (CM) reflects summed receptor currents produced by a spatially distributed array of OHCs [9], this gross ac potential provides information about OHC function. Hence, the status of the OHC transducer was assessed by constructing CM pseudotransducer functions for wildtype (+/+) and knockout (-/-) mice. This method provides a relatively simple way of documenting changes in hair cell transduction due to cochlear disruptions, including the loss of prestin. The pseudotransducer functions in Fig. 1 were collected at 6 kHz, which is a very low frequency for the mouse cochlea. This choice was made in order to minimize the effect of OHC loss at the base of the cochlea in homozygotes [10]. In addition, the use of a low frequency input assures that most of the contributing hair cells respond on the tails of their tuning curves. This behavior assures that the functions are reasonable representations of the OHC transducer with less influence by amplification in controls, thereby facilitating comparisons. Data in the top panel indicate that responses in homozygotes are smaller than those in wildtype controls. The reduced sensitivity is indicated by the relatively shallow slopes of their pseudotransducer functions. In contrast, wildtype mice (solid lines) show steep slopes around the origin, consistent with their greater sensitivity. In the bottom panel, the functions are normalized by plotting all values relative to the largest positive response, which is given a value of 1.0. This manipulation partially compensates for the reduced sensitivity seen in homozygotes and better reveals the shape of the functions, which are similar in the two genotypes, i.e., both are asymmetrical in the negative, hyperpolarizing direction.

220

Figure 1. The top panel shows pseudotransducer functions at 6 kHz for wildtype and knockout mice. The latter are plotted with dashed lines. In the bottom panel, the results are normalized to the largest positive value. Solid lines designate wildtype mice.

Peak Sound Pressure (Pa)

The direction of asymmetry is also revealed in the averaged response waveforms, shown in Fig. 2 for 6 kHz at 84 dB. The response from a wildtype mouse, shown at the top, has a dc shift in the negative direction, i.e., a negative summating potential (SP). The waveform at the bottom is from a knockout mouse whose asymmetry is also in the hyperpolarizing direction. A negative SP at low frequencies is consistent with normal OHC transducer function. For example, inputs well below best frequency generate negative, hyperpolarizing dc receptor potentials in OHCs, while IHCs produce only positive, depolarizing responses [11-13]. In addition, no negative SP is recorded in Kanamycin-treated guinea pigs with OHC loss at the base of the cochlea [14], Hence, OHCs are thought to be the sole generators of the negative SP. Although not shown here, a positive SP was observed at high stimulus frequencies for both genotypes. The bipolar nature of the SP response is a normal feature of cochlear electrophysiology [15].

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Sound Pessure Level (dB SPL)

CM input-output functions were measured at 12 kHz in both wildtype and homozygous mice. An example from each genotype is shown at the top of Fig. 3. In each case, the second harmonic at 24 kHz is larger than the third at 36 kHz. The lower panels show the magnitude of even- and odd-order components measured relative to the fundamental. In both cases, the relative distortion levels in KO mice are similar to those in wildtype controls. 3.3 Intermodulation distortion Intermodulation distortion was also measured for a primary pair with fl at 10 kHz; f2 at 12.2 kHz. The top panels in Fig. 4 show input-output functions for fl alone along with functions for the cubic difference tone, 2fl-f2 at 7.8 kHz (squares) and for the quadratic difference tone, f2-fl at 2.2 kHz (open triangles). CM magnitude is plotted as a function of the level of f2, which is 14 dB less intense than fl. In contrast to the response pattern in the wildtype control, f2-fl is larger than 2fl-f2 in the knockout. Relative levels of distortion are provided in the lower panels for both the cubic and the quadratic difference tones. As noted earlier for prestin KO mice on the 129S6/C57BL6 background [2, 3], the levels of 2fl-f2 measured relative to fl alone are similar for wildtype and homozygous mice, again implicating normal forward transduction. However, for f2-fl, the relative levels of the quadratic difference tone are higher than in wildtype mice by -15 dB.

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3.4 Two-tone suppression Because intermodulation distortion is generated using two partially overlapping pure tones, it is possible to measure each primary alone and in combination with its partner, thereby providing a measure of suppression. Figure 5 shows spectra for f2 alone (dashed lines) and for fl and f2 together. The latter analysis reveals a profusion of difference tones, as well as a measurement of £2 in the presence of f1. Because fl is 14 dB greater than f2, the lower-frequency primary suppresses the higher by 6 dB in the control and by 4 dB in the KO. As indicated in Fig. 4, the QDT is larger in homozygotes. Although KO mice display mutual suppression between primaries, we do not imply that all aspects of suppression are demonstrated or even expected in mice lacking prestin. In fact, the interactions demonstrated in Fig. 5 very likely originate in the OHC transducer.

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4 Discussion Results in this report are similar to those obtained previously on the prestin KO mouse (129S6/C57BL6) developed by Jian Zuo and colleagues at St. Jude Children's Research Hospital [1-3]. Although not shown here, we demonstrated before that the commercially generated KO suffers a frequency-dependent shift of -50 dB in compound action potential thresholds and a loss of sharp tuning [4]. Immunocytochemistry, using our C-terminal prestin antibody, also shows the absence of protein, as do western blots. In spite of the loss of amplification, the relative magnitudes of both second and third harmonics are similar in wildtype and homozygous mice. This result, along with wildtype-like pseudotransducer functions recorded in KOs, suggests that the OHC transducer is functioning normally in mice lacking prestin (see also He et al. in this volume). The presence of a negative SP, as well as two-tone suppression and intermodulation distortion, is also consistent with normal OHC transducer function [16, 17]. Hence, this animal model is unusual because most other manipulations designed to damage OHCs produce a change in forward transduction, which then reduces the drive for reverse transduction [3]. When evaluating the intermodulation distortion, it is assumed that the CM reflects local mechanics and not the repropagated components that dominate mechanical and single unit responses in normal animals [18]. That said, the data in Figs. 4 and 5 reveal that the CDT is the largest difference tone observed in wildtype controls. In contrast, f2-fl and 2fl-f2 are relatively similar in magnitude in mice lacking prestin protein. A possible explanation is as follows. For the parameters used in this study, the QDT at 2.2 kHz is well below fl at 10 kHz, while the CDT at 7.8 kHz is just slightly below fl. Because of this frequency difference, the QDT should be attenuated more than the CDT due to narrow-band filtering at the generation site in normal animals. However, in prestin KO mice lacking frequency

224

selectivity, this differential attenuation does not exist. Hence, the QDT is commensurate with the CDT in mice lacking prestin. Taken together, our results demonstrate that Prestin KO mice generate nonlinear responses including harmonic and intermodulation distortion, bipolar summating potentials and two-tone suppression. In other words, cochlear nonlinearities persists in the absence of amplification and frequency selectivity. These results are consistent with the idea that the OHC transducer, i.e., forward transduction, is the source for the vast majority of cochlear nonlinearities [17, 19]. Acknowledgments Work supported by the NIDCD Grant #DC00089 and by the Hugh Rnowles Center. We thank J.H. Siegel and M.A. Ruggero for comments on the manuscript.

References 1. Liberman, M.C., Gao, J., He, D.Z., Wu, X., Jia, S., Zuo, J., 2002. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature 419, 300-4. 2. Cheatham, M.A., Huynh, K.H., Gao, J., Zuo, J., Dallos, P., 2004. Cochlear function in Prestin knockout mice. J. Physiol. 560, 821-30. 3. Liberman, M.C., Zuo, J., Guinan, J.J., Jr., 2004. Otoacoustic emissions without somatic motility: can stereocilia mechanics drive the mammalian cochlea? J. Acoust. Soc. Am. 116, 1649-55. 4. Huynh, K.H., Cheatham, M.A., Zheng, J., Dallos, P., 2005. Characterizing a second prestin knockout mouse derived from the 129S1 strain. Abs. Assoc. Res. Otolaryngol., 229. 5. Russell, I.J., Sellick, P.M., 1978. Intracellular studies of hair cells in the guinea pig cochlea. J. Physiol. 284, 261-290. 6. Legan, P.K., Lukashkina, V.A., Goodyear, R.J., KOssl, M., Russell, I.J., Richardson, G.P., 2000. A targeted deletion in alpha-tectorin reveals that the tectorial membrane is required for the gain and timing of cochlear feedback. Neuron 28, 273-85. 7. Patuzzi, R., Moleirinho, A., 1998. Automatic monitoring of mechanoelectrical transduction in the guinea pig cochlea. Hear. Res. 125, 1-16. 8. Bian, L., Chertoff, M.E., 1998. Differentiation of cochlear pathophysiology in ears damaged by salicylate or a pure tone using a nonlinear systems identification technique. J. Acoust. Soc. Am. 104, 2261-71.

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9. Dallos, P., Cheatham, M.A., 1976. Production of cochlear potentials by inner and outer hair cells. J. Acoust. Soc. Am. 60, 510-2. 10. Wu, X., Gao, J., Guo, Y., Zuo, J., 2004. Hearing threshold elevation precedes hair-cell loss in prestin knockout mice. Brain Res. Mol. Brain Res. 126, 30-7. 11. Russell, I.J., Sellick, P.M., 1983. Low-frequency characteristics of intracellularly recorded receptor-potentials in guinea pig cochlear hair cells. J. Physiol. 338, 179-206. 12. Cody, A.R., Russell, I.J., 1987. The response of hair cells in the basal turn of the guinea-pig cochlea to tones. J. Physiol. 383, 551-69. 13. Dallos, P., 1986. Neurobiology of cochlear inner and outer hair cells: intracellular recordings. Hear Res 22, 185-98. 14. Dallos, P., Wang, C.Y., 1974. Bioelectric correlates of kanamycin intoxication. Audiology 13, 277-89. 15. Dallos, P., Schoeny, Z.G., Cheatham, M.A., 1972. Cochlear summating potentials. Descriptive aspects. Acta Otolaryngol Suppl 302, 1-46. 16. Patuzzi, R.B., Yates, G.K., Johnstone, B.M. 1989. Outer hair cell receptor current and sensorineural hearing loss. Hear. Res. 42,47-72. 17. Jaramillo, F., Markin, V.S., Hudspeth, A.J., 1993. Auditory illusions and the single hair cell. Nature 364, 527-9. 18. Dallos, P., Cheatham, M.A., 1974. Cochlear microphonic correlates of cubic difference tones. In: Zwicker, E., Terhardt, E., (Eds.), Fact and Models in Hearing. Springer-Verlag, New York. pp. 312-322. 19. Patuzzi, R.B., Yates, G.K., Johnstone, B.M., 1989. Outer hair cell receptor current and sensorineural hearing loss. Hear Res 42,47-72.

MECHANICAL IMPEDANCE SPECTROSCOPY ON ISOLATED CELLS

M.P. SCHERER, Z. FARKAS AND A.W. GUMMER Department

Otolaryngology, University Tuebingen, E-mail: [email protected]

Germany

Cells isolated from the organ of Corti were held in the microchamber configuration and their mechanical impedance was measured in a broad frequency range (0.48-50 kHz). This was achieved with a more sensitive version of a previously presented method employing magnetically actuated probes. Preliminary data suggest that axially loaded outer hair cells exhibit a purely viscoelastic impedance composed of a spring and a frequency dependent damper. The spring constant compares with known values.

1 Introduction Knowing the dynamic mechanical properties of cells isolated from the organ of Corti is of fundamental importance for understanding and modeling the cochlear amplifier. Recently, we developed a technique for measuring the mechanical impedance of biological samples in a broad frequency range [1]. Briefly, a calibrated magnetic force cantilever immersed in the bath is vibrated by an external magnetic field. The vibration velocity at the tip of the cantilever is measured by an interferometer. From the velocity difference with and without contact to the sample cell, the cell impedance can be inferred. Here, we present the application of an improved version of this method to isolated cells from the organ of Corti. 2 Results and Discussion Fig. 1 shows the measured impedance spectrum of an OHC. Noise increases at low frequencies, because the stiffness-dominated impedance of the cantilever is large for low frequencies and, consequently, displacement amplitudes are smaller than for high frequencies. Remaining negative, the imaginary part tends to zero for high frequencies and can be described by the impedance of a spring. Although some of the low-frequency points in the real part are noisy, the damping appears to decrease with frequency and always remains positive. While the reactive part dominates at low frequencies, both reactive and resistive parts are of similar magnitude above 1.5 kHz. No mechanical resonance appears in this spectrum. Stiffness values matched previous data [2-4]. The absence of a resonance is in agreement with the calculation of Tolomeo and Steele [5]. The inertia of the fluid seems to play no role in this frequency range - a finding that is in agreement with the impedance of the whole organ [1]. These promising results encourage further improvement of our measurement technique. In principle, a variety of cells can be investigated in various orientations by holding them onto a suction capillary.

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Acknowledgments Supported by the Deutsche Forschungsgemeinschaft Gul94/5-l (M.P.S.) and by the EC, Marie Curie Training Site HEARING (QLG3-CT-2001-60009) (Z.F.). References 1. 2.

3. 4. 5.

Scherer, M.P., Gummer, A.W., 2004. Impedance analysis of the organ of corti with magnetically actuated probes. Biophys. J. 87,1378-1391. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA 96, 4420-4425. Hallworth, R., 1995. Passive compliance and active force generation in the guinea pig outer hair cell. J. Neurophysiol. 74, 2319-2328. Iwasa, K.H., Adachi, M., 1997. Force generation in the outer hair cell of the cochlea. Biophys. J. 73, 546-555. Tolomeo, J.A., Steele, C.R., 1998. A dynamic model of outer hair cell motility including intracellular and extracellular fluid viscosity. J. Acoust. Soc. Am. 103, 524-534.

H E A T STRESS-INDUCED C H A N G E S IN THE M E C H A N I C A L PROPERTIES OF MOUSE OUTER HAIR CELLS M. MURAKOSHI, K. IIDA, S. KUMANO AND H. WADA Depertment of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai 980-8579, Japan E-mail: [email protected] N. YOSHIDA AND T. KOBAYASHI Depertment of Otorhinolaryngology - Head and Neck Surgery, Tohoku Graduate School of Medicine, 1-1 Seiryo-machi, Sendai 980-8675,

University Japan

Overexposure to intense sound damages outer hair cells (OHCs) and causes the loss of cochlear amplification, resulting in permanent hearing loss. However, OHCs are protected from such exposure by prior sublethal conditioning. Although the protective mechanisms is thought to be based on the modification of the cell structure which reduces the mechanical damage of cells, it is not clear whether the cell structure becomes more flexible or more rigid by such modification. In this study, therefore, the mechanical properties of OHCs in mice with/without heat stress were measured by atomic force microscopy (AFM). As a result, it was found that conditioning by heat stress causes an increase of Young's modulus of OHCs in mice 3-12 h after heat stress.

1 Introduction High sensitivity, wide dynamic range and sharp frequency selectivity of mammalian hearing are realized by electromotility of outer hair cells (OHCs). Thus, OHCs play an essential role in the mammalian auditory system. Unfortunately, however, they are susceptible to external stimuli. It has been elucidated that OHCs can be protected from traumatic sound exposure by prior sublethal conditioning, such as nontraumatic sound exposure, heat stress, ischemia and physical restraint. One possible protective mechanism is modification of the cell structure to reduce the mechanical damage of cells, such modification leading to changes in the mechanical properties of OHCs. However, it is unclear how these properties of OHCs change due to such conditioning. In the present study, therefore, the mechanical properties of OHCs in mice with/without heat stress were investigated. 2 Methods The care and use of the animals in this study were approved by the Institutional Animal Care and Use Committee of Tohoku University, Sendai, Japan. CBA/JNCrj strain male mice, aged 10-12 weeks (25-30 g), were divided into a control group and an anesthesia + heat group. In the latter group, the animals were anesthetized and were placed in an aluminum boat floating in a hot water bath maintained at 46.5°C to raise the rectal temperature up to 41.5°C. It was maintained at that temperature for 15 min. The cochleae were detached from the animals 3, 6, 12, 24 and 48 h after 15-min heat stress. The organ of Corti was then dissected form the cochlea and OHCs were isolated by incubation with an enzymatic digestion medium and subsequent gentle trituration of the dissected tissue. Finally, Young's modulus

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of the OHC was measured by an indentation test using an AFM (NVB100, Olympus). 3 Results and Discussion As shown in Fig. 1, Young's modulus of the mouse OHCs increased by 3 h after heat stress and reached a peak at 6 h, and then began to decrease 12 h after such stress, although it was still greater than that of the control group. Young's modulus returned to the preconditioning level at 24 h. One possible speculation is that F-actin, which is a primary component of the cytoskeleton of the OHCs and strongly contributes to their mechanical properties, may be modulated according to the cellular response caused by heat stress. Polymerization and depolymerization of F- Figure 1. The mean and standard deviation actin is controlled by heat shock proteins of Young's moduli of the OHCs obtained for the control group and the anesthesia + (HSPs) [1] and the amount of such proteins is heat groups. The asterisks show statistically elevated by whole-body heat stress in the significant difference from the control group cochlea [2]. Moreover, the amount of F-actin (P < 0.05 by Student's Mest). of the OHCs increases by exposure to conditioning noise [3]. It is understandable that the increase of F-actin leads to an increase of Young's modulus of the OHCs. Acknowledgments This work was supported by Grant-in-Aid for Scientific Research on Priority Areas 15086202 from the Ministry of Education, Culture, Sports, Science and Technology of Japan, by a Health and Labour Science Research Grant from the Ministry of Health, Labour and Welfare of Japan, by a grant from the Human Frontier Science Program and by a 21st Century COE Program Special Research Grant of the "Future Medical Engineering Based on Bio-nanotechnology." References 1.

2.

Lavoie, J.N., Hickey, E., Weber, L.A., Landry, J., 1993. Modulation of actin microfilament dynamics and fluid phase pinocytosis by phosphorylation of heat shock protein 27. J. Biol. Chem. 268,24210-24214. Yoshida, N., Kristiansen, A., Liberman, M.C., 1999. Heat stress and protection from permanent acoustic injury in mice. J. Neurosci. 19, 1011610124.

230

3.

Hu, B.H., Henderson, D., 1997. Changes in F-actin labeling in the outer hair cell and the Deiters cell in the chinchilla cochlea following noise exposure. Hear. Res. 110,209-218.

FREQUENCY DEPENDENCE OF ADMITTANCE AND CONDUCTANCE OF THE OUTER HAIR CELL B. FARRELL f , R. UGRINOV 1 AND W. E. BROWNELL* *Institute of Solid State Physics, Bulgarian Academy of Sciences, Sofia, Bulgaria and Baylor College of Medicine, Houston, TX, USA E-mail: [email protected] and brownelKalbcm. tmc. edu

f

1 Results Outer hair cells, OHCs isolated from cochlea of guinea pig were voltage clamped in whole-cell mode in solutions that contain K and Ca channel blockers. Membrane conductance, G was measured at DC with a voltage pulse protocol (Figure 1A) and found to depend upon DC potential (Figure 1C). 1/G was maximum close to zero volts at 460 (±52) Mf2 and decreased monotonically to 180 (±20) and 85 (±10) MQ at negative and positive holding potentials, respectively. Admittance, Y was measured with a dual-sinusoidal stimulus while the holding potential was ramped from -0.16 to 0.16 V (Figure 2C, [1]). Unlike G measured at DC, the capacitance, Cm dominates the real part, Re(Y) at all frequencies, only at < 100 Hz and at extreme voltages does G and Re(Y) merge (Figure 2C and inset). This demonstrates that G of OHC must be measured at DC and cannot be calculated from measured Y as suggested by Santos-Sacchi et al. [1]. C

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Figure 2. A. Measured (dotted line) and calculated (solid line) Cm, where lines represent values determined at different frequencies. Lines represent in decreasing magnitude 0.25f, 0.5f, l.Of, 2.0f, 4.0f and 8.0f Hz where f: 195.625 Hz. B. Comparing phase of Y for OHC at peak C, (solid triangles) and at 0.1 V (solid squares), with that obtained for model circuits with similar capacitors (open diamonds 51 pF and open circles 30 pF), where Rm: 200 MQ and series resistance, Rs : 4 Mfi. Open triangles: gain of OHC capacitance. C. Real (Y) of OHC. Lines represent frequencies outlined in A in increasing order from bottom to top of plot. Inset compares Re(Y) (solid lines) with G determined at DC (circles). Rs for OHC recording, was 4.3 MQ

Measured capacitance, Im(Y)/(27if) (Im(Y): imaginary part of Y) approaches the calculated capacitance, Cm [1] at frequencies < l/(27tRmCm), about 6-50 Hz for the cell shown in Figure 2A. The gain of the calculated Cm decreases from 1.2 at 0.5f Hz to 0.9 at 8.0f Hz (f=195.625 Hz), because of the roll-off induced by Rs (Figure 2B). The maximum phase of Y occurs between 0.25f and 0.5f for peak Cm, and at l.Of for minimum OHC Cm. The optimum frequency to measure Cm of OHC is at a frequency when gain is maximum and noise is minimum, and is around 200 Hz where f = l/(2nV(RmRs)Cm) and phase(Y) is maximum for lowest Cm (Figure 2A and B). Acknowledgments Supported by NIDCD research grants R01 DC 02775 and DC00354. References 1.

Santos-Sacchi J., Kakehata S., Takahashi S., 1998. Effects of membrane potential on the voltage dependence of motility-related charge in outer hair cells of the guinea-pig. J. Physiol. 510: 225-35.

MODELING OUTER HAIR CELL HIGH-FREQUENCY ELECTROMOTILITY IN MICROCHAMBER EXPERIMENT ZHIJIE LIAO AND ALEKSANDER S. POPEL Johns Hopkins University, Baltimore, Maryland 21205 USA Email: [email protected] and [email protected] WILLIAM E. BROWNELL Baylor College of Medicine, Houston, Texas 77030 USA Email: [email protected] ALEXANDER A. SPECTOR Johns Hopkins University, Baltimore, Maryland 21205 USA Email: [email protected] 1 Introduction and Methods Cochlear outer hair cells (OHC) are critically important for the amplification and sharp frequency selectivity of the mammalian ear [1]. The microchamber experiment has been an effective tool to analyze the OHC high-frequency performance [2-4]. In this study, we simulate the OHC electromotility in the microchamber. Our model considers the inertial and viscous properties of fluids inside and outside the cell as well as the viscoelastic and piezoelectric properties of the cell composite membrane [5]. The final solution to calculate OHC motile response was obtained in terms of Fourier series [6]. 2 Results and Discussion Fig. 1 displays the OHC electromotility in two extreme conditions: no-slip condition (OHC can not at all move in and out of the microchamber orifice) or full-slip condition (OHC can move freely through the microchamber orifice without any imposed friction). For low frequencies, the no-slip condition results in an electromotile response twice as great as that in the full-slip condition, but this difference reduces at high frequencies. Dallos et al. [2, 3] reported electromotility range 0.92 ~ 4.74 nm/mV for the 55 ~ 72 um cells. These experimental results are in good agreement with our model predictions (1.3 ~ 2.7 nm/mV) for the 60 um cell. Frank et al. [4] obtained smaller cell length changes (0.25 nm/mV), and the reason for that may come from the fact that the set point is not at the steepest part of OHC electromechanical transduction curve. Fig. 2 shows that indeed by shifting setpoint potential to more hyperpolarization our model results can be made closer to Frank's results [4]. By assuming the coefficients (ex and eg) that determine the production of the local active stress resultant per unit transmembrane potential is

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proportional to the slope of the electromechanical transduction curve, we found that, if the set-point potential shifts 100 mV toward higher polarization, the predicted cell displacement amplitude reduces to 0.25 - 0.5 nm/mV depending on the chosen boundary condition at the cell-pipette interface. q = 0.5 Applied voltage : 1 mV Cell length : 60 mm Cell wall viscosity: 1 x 10" Ns/m External fluid viscosity : 1 x 10" Ns/m2

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1 ' \ I1 11 \ \ 1 1 \ 1 ' \ 1 1 \ 1 I ^— ... 1 . . . . 1 Applied voltage (mV)

Fig. 2. Estimation of set-point in Frank's et al. experiment [4], The electromechanical transduction function curve comes from Dallos et. al. [2]. Two points are selected to calculate electromechanical responses.

3 Conclusions We propose a model of high-frequency electromotility of outer hair cell generated in the microchamber experiment. The model can both reconcile the existing results of different groups and better understand the high-frequency performance of the cell. References

6.

Brownell, W.E., Bader, CD., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 224, 194196. Dallos, P., Hallworth, R., Evans, B.N., 1993. Theory of electrically driven shape changes of cochlear outer hair cells. J. Neurophysiol. 70, 299-323. Dallos, P., Evans, B. N., 1995. High frequency motility of outer hair cells and the cochlear amplifier. Science. 267, 2006-2009. Frank, G., Hemmert, W., Gummer, A.W., 1999. Limiting dynamics of highfrequency electromechanical transduction of outer hair cells. Proc. Natl. Acad. Sci. USA. 96, 4420^1425. Spector, A.A., Brownell, W.E., Popel, A.S., 1999. Nonlinear active force generation by cochlear outer hair cell. J. Acoust. Soc. Am. 105, 2414-2420. Tolomeo, J.A., Steele, CD., 1998. A dynamic model of outer hair cell motility including intracellular and extracellular viscosity. J. Acoust. Soc. Am. 103, 524-534.

CHLORPROMAZINE AND FORCE RELAXATION IN THE COCHLEAR OUTER HAIR CELL PLASMA MEMBRANE - AN OPTICAL TWEEZERS STUDY D.R. MURDOCK, S. ERMILOV, AND B. ANVARI Rice University, Department

of Bioengineering, 6100 Main Street, Houston TX 77005, USA E-mail: [email protected]

A.A. SPECTOR AND A.S. POPEL Johns Hopkins University, Department of Biomedical Engineering, Street, Baltimore MD 21218, USA

3400 North

Charles

W.E. BROWNELL Baylor College of Medicine, Bobby R. Alford Department of Otorhinolaryngology Communicative Sciences, One Baylor Plaza, Houston TX 77030, USA

and

The cationic amphipath chlorpromazine (CPZ) is postulated to selectively partition into the inner leaflet of the plasma membranes and modulate the electromotile behavior of cochlear outer hair cells (OHCs). We used an optical tweezers system to characterize the mechanical properties of OHCs plasma membrane (PM) through the formation and analysis of membrane tethers in the presence and absence of CPZ. We observed characteristic force relaxation when the tethers were formed and maintained at a constant length for extended periods. This relaxation process was modeled using a 2nd order Kelvin body that provided stiffness, membrane viscosity-related measurements, and relaxation time constants, which collectively indicated an overall biphasic nature of relaxation. Our results with CPZ strengthen the hypothesis linking the drug's effect to reducing the mechanical interaction between PM and cytoskeleton.

1 Introduction The mammalian outer hair cell (OHC) is a cylindrical epithelial cell that is essential for normal hearing [1]. Chlorpromazine (CPZ) is a cationic amphipath that is postulated to preferentially partition into the inner leaflet of the OHC phospholipid bilayer and shifts the electromotile response curve in OHCs [2]. We formed and then analyzed OHC membrane tethers using a viscoelastic model in order to better understand the mechanism by which CPZ affects cochlear function. 2 Methods Optical tweezers provide an advanced technique for precise micromanipulation and force measurements. A microsphere manipulated with the optical trap was moved away from the cell forming a thin strand (tether) of membrane material. Membrane tethers exhibited force relaxation with time when held at a constant length (Fig.

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1A). A 2nd Order Generalized Kelvin model (Fig. IB) was selected to model this behavior in order to obtain salient information related to mechanical properties of the membrane tether. Calculated parameters included stiffness values (/i), coefficients of friction (77), force relaxation times ( r ) , and equilibrum force (Feq). 90 I

A

•

Force Data

—

Kelvin Model Fit

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www

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Figure 1. A: Force relaxation in OHC membrane tether. B: 2nd order generalized Kelvin body used to model tethering force data.

3 Results and Discussion Upon 0.1 mM CPZ application, the first relaxation time remained virtually unchanged from the NES values while the second relaxation time decreased by -50% (p <0.05) under the same conditions, suggesting an area specific effect of the drug. Equilibrium force (Feq) decreased by -40% (p < 0.001) and 31% (p<0.05) in OHCs treated with 0.1 mM and 0.05 mM CPZ, respectively. These results suggest that CPZ may weaken the connection between the PM and the underlying cytoskeleton. We propose that CPZ's demonstrated effect on the OHC voltagedisplacement function may involve a change in lateral wall mechanical properties. Acknowledgments We thank Feng Qian and Cindy Shope for their invaluable technical expertise. References 1.

2.

Brownell,W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science. 227, 194196. Oghalai, J.S., 2004. Chlorpromazine inhibits cochlear function in guinea pigs: Hear. Res. 198, 59-68.

ESTIMATION OF THE FORCE GENERATED BY THE OUTER HAIR CELL MOTILITY AND THE PHASE OF THE NEURAL EXCITATION RELATIVE TO THE BASILAR MEMBRANE MOTION: THEORETICAL CONSIDERATIONS M. ANDOH, C. NAKAJIMA AND H. WADA Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aoba-yama, Sendai 980-8579, Japan E-mail: andoh@wadalab. mech. tohoku. ac.jp To clarify the mechanics of the cochlea, the investigation of the outer hair cell motility in the organ of Corti is crucial. In this study, a finite-element model of the organ of Corti of the gerbil cochlea including the OHCs was constructed, and the magnitude of the force generated by the OHC motility was estimated. Consequently, the maximum value of the force generated by the OHC motility was obtained to be 150 nN. The phase of the neural excitation relative to the basilar membrane motion was then estimated, and it was found that the OHC motility did not affect the phase of the neural excitation.

1 Introduction When the organ of Corti (OC), which sits on the basilar membrane (BM), vibrates, it is conventionally thought that the hair bundles of the inner hair cell (IHC) and the outer hair cell (OHC) are deflected due to the shear motion between the tectorial membrane (TM) and the reticular lamina (RL). The IHC excites auditory nerves when its hair bundle deflects toward the tallest stereocilium and the OHC changes its length in response to the deflection of its hair bundle. A force generated by the OHC motility amplifies the OC vibration. However, due to experimental difficulties, it is difficult to ascertain the magnitude of the force generated by the OHC motility, as well as the phase of the neural excitation relative to the BM motion. In this study, a finite-element model of the OC of the gerbil cochlea was constructed and used to estimate such factors. 2 Methods A model of the OC of the gerbil cochlea (Fig. 1) was constructed based on the measurement data [1]. The characteristic frequency (CF, the most effective stimulus frequency) of this location is approximately 16 kHz. The mechanical properties assigned to this model were determined based on previous reports. A model of the lymph fluid surrounding the OC and one of the lymph fluid in the sub-TM space, which is a space between the TM and RL, were also constructed to consider the influence of the lymph fluid on the vibration of the OC and that of the hair bundle of the IHC. To analyze the dynamic behavior of the OC, a custom-made linear finite-element code was used.

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Figure 1. Model of the OC discretized with finite elements. The number of nodes is 1274 and the number of elements is 2139. Scale bar represents 50 um. The model of the lymph fluid surrounding the OC is not shown, and the model of the lymph fluid in the sub-TM space is shown within the model of the OC.

3 Results and Discussion 3.1 Cochlear amplification caused by the outer hair cell To obtain the experimentally obtained gain of the velocity of the BM vibration generated by the OHC motility [2], the maximum value of the force generated by the OHC motility was estimated to be 150 nN. Figure 2 shows the gain of the velocity of the BM vibration with the OHC motility relative to that without it. The numerically obtained gain is similar to that of the experimental data for each stimulus intensity. 3.2 Neural excitation relative to the basilar membrane motion Figure 3 shows the phase of the neural excitation relative to the BM motion with the OHC motility. Comparison of this phase with the phase without the OHC motility [3] shows these two phases to be the same. This indicates that the OHC motility does not affect the phase of the neural excitation relative to the BM motion although it amplifies the vibration of the OC. Numerical results Experimental data (Ren and Nuttall [2])

40 60 80 Pressure (dB SPL)

100

Figure 2. Gain of the velocity of the BM vibration with the OHC motility relative to that without it for stimulus intensities from 20 dB SPL to 100 dB SPL at CF.

0.1

1

10

30

Frequency (kHz}

Figure 3. Phase of the neural excitation relative to the BM motion with the OHC motility.

Acknowledgments This work was supported by a grant from the Human Frontier Science Program, by a Health and Labour Science Research Grant from the Ministry of Health, Labour and Welfare of Japan, by Grant-in-Aid for Scientific Research (B) (2) 13557142 and Grant-in-Aid for Scientific Research on Priority Areas 15086202 from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and by a 21st Century COE Program Special Research Grant of the "Future Medical Engineering Based on Bio-nanotechnology."

239

References 1. 2. 3.

Edge R.M., Evans B.N., Pearce M., Richter C.-P., Hu X., Dallos P., 1998. Morphology of the unfixed cochlea. Hear. Res. 124, 1-16. Ren T., Nuttall A.L., 2001. Basilar membrane vibration in the basal turn of the sensitive gerbil cochlea. Hear. Res. 151, 48-60. Andoh M., Nakajima C , Wada H., 2005. Phase of neural excitation relative to basilar membrane motion in the organ of Corti: Theoretical considerations. J. Acoust. Soc. Am. In press.

QUANTIFICATION OF CALCIUM BUFFERS IN VARIOUS SUBCELLULAR LOCATIONS IN RAT INNER AND OUTER HAIR CELLS S. MAHENDRASINGAM1, R. FETTIPLACE1,2, AND CM. HACKNEY1'2

'School of Life Sciences, Keele University, Staffs. ST5 5BG, U.K and 2Department of Physiology, University of Wisconsin-Madison Medical School, WI53706, USA. E-mail: [email protected] Calcium buffers help shape and localize cytoplasmic Ca2+ transients in excitable cells. We have measured the concentrations of calbindin-D28k, calretinin, parvalbumin-a and parvalbumin-p, four endogenous calcium-buffering proteins in rat cochlear hair cells during development. In hearing animals, the inner hair cells (IHCs) have a tenth of the calcium buffering capacity provided by these proteins compared with the outer hair cells (OHCs) where the cell body contains levels equivalent to more than 5 mM calcium-binding sites. Overall, buffer concentrations decrease in IHCs and increase in OHCs during cochlear maturation.

1 Introduction Calcium is a key signal in hair cells where it regulates both mechanotransduction and neurotransmitter release. Endogenous calcium buffers help ensure the spatial and temporal separation of calcium signalling pathways. Here we have investigated the concentrations of the main diffusible buffers in rat cochlear hair cells before and after the onset of hearing (post-natal day 12). 2 Methods Cochleas from young rats (postnatal days 7, 16 & 26) were fixed and embedded in LR-White resin. Ultrathin sections were incubated overnight at 4°C in polyclonal antibodies to calbindin-D28k and calretinin (Chemicon), parvalbumin-a and parvalbumi-P (SWant) or a monoclonal antibody to PV-P (a gift from Dr MT Henzl, University of Missouri) followed by an appropriate secondary antibody conjugated to 15 nm gold particles. To determine the concentration of the buffers, measured amounts of each protein were dissolved in 10% bovine serum albumin in phosphate buffer and fixed like the cochleas to solidify the gel and embedded in the same resin. Sections were cut and labelled in the same drops of antibody solution as cochlear sections and the concentrations of each buffer in the cytoplasm calculated from the comparative gold densities as determined by transmission electron microscopy. The concentrations in the OHCs were similar in the three rows of cells so these are given as averages across the rows in Fig. 1. Labelling densities in the stereocilia and nuclei were also compared with the cytoplasm.

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3 Results and Discussion The sum of the calcium buffer concentrations decreased in IHCs and increased in OHCs as the cells developed their distinct adult properties during cochlear maturation. The most striking finding was that PV-P occurs at millimolar concentrations in the cytoplasm of OHCs and, at most, micromolar concentrations in IHCs in post-hearing rats (Fig. 1). Calretinin occurred at concentrations of no more than 20 - 50 uM in both cell types but, unlike the other proteins, was found at a significantly higher level in the nuclei than in the cytoplasm of at all stages perhaps suggesting a role in Ca 2+ signalling. All the buffers were largely excluded from the stereocilia compared with the cuticular plate (not shown) perhaps to permit fast unbuffered Ca 2+ regulation of the mechanotransducer channels. A

Inner hair cell

B

Outer hair cell

Figure 1. Graphs showing the concentration of the three highest level buffers against age. A: Inner hair cells. B: Outer hair cells averaged across all three rows. Bars = standard errors of the mean.

The results suggest that Ca 2+ has separate roles in the two types of hair cell, reflecting their different functions in auditory transduction. The high concentration of calcium buffer in OHCs is similar only to that in skeletal muscle and poses an important question as to the role of Ca 2+ in their function. Ca 2+ is employed in IHCs primarily for fast phase-locked synaptic transmission whereas Ca 2+ may be involved in regulating the OHCs motor role in cochlear amplification. Acknowledgments Supported by grants from the University of Wisconsin-Madison to CMH and RF and NIDCD ROl DC 01362 to RF.

III. Stereocilia

SIGNAL TRANSFORMATION BY MECHANOTRANSDUCER CHANNELS OF MAMMALIAN OUTER HAIR CELLS R. FETTIPLACE Department of Physiology, University of Wisconsin Medical School, Madison, WI 53706, USA. E-mail: [email protected] A.C. CRAWFORD Department of Physiology, Cambridge University, Cambridge CB2 3EG, UK. E-mail: acl51@cam .ac.uk H.J. KENNEDY Department

of Physiology, University of Bristol, Bristol BS8 1TD, UK. E-mail:[email protected]

To understand and model the contribution of outer hair cells to cochlear function, a full knowledge of both forward and reverse transduction is needed. To determine the limitations imposed by forward transduction, we have characterized mechanotransducer (MET) currents and hair bundle mechanics of outer hair cells in isolated coils of neonatal rats. In response to step deflections of the hair bundle, MET currents activated and then rapidly adapted with a sub-millisecond time constant that depended on extracellular calcium and cochlear location. The adaptation time constant imposed a first order high-pass filter at a corner frequency that, when corrected to in vivo conditions, was similar to the cell's characteristic frequency. Hair bundle mechanics determined by stimulation with a flexible fiber, exhibited a pronounced non-linearity that developed with the same time course as fast adaptation. We propose that the MET channels will high-pass filter the input signal and provide positive mechanical feedback to augment motion of the tectorial membrane. The time course of the feedback varies with cochlear location.

1 Introduction Outer hair cells play a central role in the amplification and frequency tuning of the mammalian cochlea [1]. Their contribution to the cochlear amplifier requires both forward transduction through vibration of their stereociliary bundles opening MET channels, and reverse transduction involving force generation by contractions of the cell body [2], possibly aided by active movements of the hair bundle [3]. Understanding the signals that drive the amplifier requires a detailed knowledge of the properties of the MET channels. Much information about forward transduction has been derived from in vivo recordings of cochlear microphonics and receptor potentials [4] supplemented by studies of MET currents in various isolated preparations [4, 5]. Despite these extensive data, there is a lack of information about the kinetic limitations imposed by mechanotransduction. Here we summarize recent measurements of MET currents in single voltage-clamped OHCs using a rapid piezoelectric stimulator to deflect the hair bundles [6]. This approach also enabled

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us to examine the mechanical properties of the hair bundle and search for active bundle-driven force generation. 2 Methods Experiments were performed on first and second row outer hair cells (OHCs) in isolated apical and middle turns of the rat organ of Corti as described previously [6]. Rats (P6 - PI2) were killed using procedures approved by the Animal Care Committee of the University of Wisconsin. Excised apical and middle turns were fixed in an experimental chamber on a Zeiss Axioskop FS microscope and viewed through a 40X LWD water-immersion objective. The chamber was perfused with artificial perilymph (composition in mM: 154 NaCl, 6 KC1, 1.5 CaCl2, 2 Napyruvate, 10 glucose and 10 Na-HEPES, pH 7.4) at room temperature, 19-23 degrees C. The endolymphatic surface of the organ of Corti was independently perfused through a 100-um pipette with a perilymph-like solution with normal (1.5 mM) or reduced CaCl2 (0.02 mM, buffered with 4 mm HEDTA). Cells were wholecell voltage-clamped at -84 mV with borosilicate patch electrodes connected to an Axopatch 200A amplifier. Electrodes were filled with an intracellular solution of composition in mM: 142 CsCl, 3.5 MgCl2, 1 EGTA, 5 Na2ATP, 0.5 Na2GTP and 10 CsHEPES pH 7.2. Recording time constants with up to 80% series-resistance compensation were between 10 and 50 us. Hair bundles were deflected by motion of a glass probe driven by a piezoelectric stack actuator (Physik Instrumente). For displacement clamp experiments, the probe was impelled axially and its tip was fire-polished to ~3 urn in diameter to fit into the V-shaped hair bundle of the OHC. The actuator was driven with voltage steps filtered with an 8-pole Bessel filter set at 5-10 kHz. The resulting displacement of the probe had a rise time of 40-80 u,s. Force steps were delivered with a calibrated flexible glass fiber (~30 um in length; stiffness, 1 - 3 mN/m) introduced along the axis of the cochlea. The fiber tip was coated with a bead of Sylgard (~3um diameter) that also fit into the V-shaped hair bundle of the OHC. The time course of motion of the fiber was monitored by positioning the image of the edge of the Sylgard bead onto a pair of photodiodes (Centronics LD 25) at 400X total magnification. The photodiodes were mounted on a piezoelectric bimorph deflections of which were used to calibrate the photocurrent throughout the recording. To measure bundle mechanics, the voltage step to the piezoelectric stack was filtered at 1.5 - 2 kHz, the displacement of the fiber tip when not attached to the bundle having a rise time of 0.15- 0.2 ms. The speed of the fiber was limited by the filtering of the voltage command applied to the piezoelectric stack and not by viscous drag on the fiber or bead. For constructing force-displacement plots, the first reading of bundle motion was taken at a time (denoted by t = 0) corresponding to the peak of the low-level MET current. The current reached a peak 0.3 ms after the start of the response, which was approximately three times the equivalent time

247

constant of the filter settings (0.08 to 0.16 ms). Excluding the first 0.3 ms of response ensured that viscous drag did not contaminate the time course of the bundle motion. 3 Results 3.1 Tonotopic variations in outer hair cell MET current In response to a displacement step of the hair bundle, MET currents activated with a time course indistinguishable from that of the stimulus but then rapidly adapted with a sub-millisecond time constant, the peak current being graded with displacements of a few tenths of a micron (Fig. 1). The current developed with a time constant of less than 50 ixs, which was probably limited by the time course of the displacement step. A similar conclusion about the activation kinetics of MET channels in mammals was reached from the spectral composition of current noise [7]. These measurements showed that the half-power frequency attributable to the channel kinetics exceeded the 2.5 kHz frequency of the recording filter. Lowering extracellular Ca2+ to 0.02 mM had two distinct effects: to increase the current amplitude, attributable to relief of channel block by Ca2+, and to slow adaptation. Both amplitude and adaptation time constant in low and high Ca2+ varied tonotopically. Recordings were made at two locations with fractional distances along the basilar membrane from the apex of 0.2 and 0.5, corresponding to characteristic frequencies of 4 kHz and 14 kHz respectively [8]. Recordings at each position showed that the peak MET current was approximately twice as large and the adaptation time constant twice as fast at the high-frequency compared to the low-frequency location. The maximum MET currents in high Ca2+ for the two positions were 1.36 ± 0.12 nA (high CF; n = 5) compared to 0.78 ± 0.13 nA (low CF; n = 5). The corresponding values for the adaptation time constant were 45 ± 6 (is (high CF) and 83 ± 8 fis (low CF). When the extracellular Ca2+ was reduced to 0.02 mM, the concentration found in rat endolymph [9], the peak current increased by about 50 per cent at each position and the adaptation time constant slowed about two-fold. Nevertheless, the differences in maximum current and adaptation between the two positions were retained (Fig. 2). One other consequence of lowering external Ca2+ was to increase the fraction of current activated at rest to between 10 and 40 per cent of the maximum (n =5). These results are consistent with adaptation being controlled by Ca2+ entry through the MET channels. If the larger maximum current at higher CF largely reflects a bigger MET-channel unitary conductance, as reported in turtle hair cells [10], it follows that adaptation is faster at the higher CF because of greater Ca2+ influx. Our results agree with He et al., [5] who found an increase in the amplitude of the OHC MET currents along the tonotopic axis of the gerbil hemi-cochlea.

248

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3.2 Mechanical properties ofOHC hair bundles To examine hair bundle mechanics, stimuli were delivered with a glass fiber more flexible than the bundle and the resulting bundle displacement was monitored by imaging the fiber tip (the Sylgard bead) on a pair of photodiodes [11]. For technical reasons, only the low frequency cochlea position was assayed and the driving voltage to the piezoelectric actuator was slowed by filtering at 1.5 - 2 kHz. Nevertheless, MET currents in response to flexible-fiber stimulation showed the same fast onset and adaptation as seen with the stiff probe. The force delivered could be calculated from the difference in displacement of the two ends of the fiber scaled by the fiber's stiffness. Force-displacement relationships of hair bundles in

249 twelve out of fifteen cells studied were very non-linear and became increasingly compliant over the range where the MET channels were gated (Fig. 3). Furthermore, the non-linearity developed with a time course similar to fast adaptation of the MET current. This type of behavior was first reported in nonmammalian vertebrates where it was attributed to the 'gating compliance', a decrease in stiffness associated with opening of the MET channels [12]. Nonlinearities in hair bundle mechanics, probably of similar origin, have also been seen in the mammalian cochlea but were not linked to adaptation [13]. The results were analyzed in terms of the gating-spring model which predicts a relationship between the applied force (Fg) and bundle displacement (X) given by: FB=X-Ks-A-Po(X)+F0

(1)

where Ks is the passive linear stiffness, p0 is the probability of opening of the MET channels, and A and F0 are constants. The negative term in eqn. (1) signifies an active component in which channel gating generates a force in the same direction as the imposed displacement, causing hair bundle stiffness to decrease with channel opening to reach a minimum when/>0 is ~0.5 (ref. 15). Fits of eqn. (1) to the results deviated from the gating-spring model in that the constant A increased as adaptation progressed. A further difference is that A was much larger than expected from the gating spring model. In that model, A is the product of the number of MET channels and the single-channel gating force, less than 30 pN for OHC's [14], whereas values 20 to 100-fold larger were needed for the fits in Fig. 3C. Nevertheless, the results are still consistent with force production being linked to the probability of opening of the MET channels. In some OHCs the force-displacement relationship possessed a negative slope region but in five cells more extreme behavior was observed: for a range of stimuli, the displacement of the end of the flexible fiber attached to the hair bundle exceeded that of the end cemented to the piezoelectric device thus, the forcedisplacement relationship became negative as adaptation progressed, indicating that the hair bundle is doing work on the fibre. Maximum force generation, estimated as the difference between steady state and instantaneous force-displacement plots at fixed displacement, was 517 ± 96 pN.

250

200

400

Displacement (roil)

Figure 3. Mechanical properties of OHC hair bundle. A. Average MET currents (top) in a PI 1 rat OHC in response to stimulation with a flexible fiber, stiffness Movements of end of fiber attached to piezo (middle) and of the hair bundle (bottom). B. Peak MET current (7) scaled to its maximum value (Imax, 0.37 nA) plotted against displacement at peak of current. C. Force-displacement plots at different times (t) after the peak of the current: t = 0 (filled circles), 0.07ms, 0.27 ms, 0.47 ms, 0.67 ms, 3.9 ms, 8 ms (filled triangles). Smooth curves are fits to eqn. 1 using p 0 (X) relation from B. and Ks = 3 mN/m.

3.3 Calcium dependence of bundle mechnanics If force generation by the bundle reflects gating and adaptation of the MET channel, it should be susceptible to altering extracellular Ca2+. Lowering Ca2+ reversibly reduced the hair bundle mechanical non-linearity and slowed its onset. To determine the time course of force production, the change in force between the instantaneous relation (t = 0, measured at the peak current) and the plots at subsequent times were measured at a fixed displacement corresponding to the point at which the compliance was maximal. This analysis in four cells indicated that bundle force develops with the same time course as fast adaptation. For example, in one cell force production occurred with time constants of 0.3 ms (1.5 mM Ca2+) and 0.6 ms (0.02 mM Ca2+) which were similar to those of fast adaptation under the same conditions: 0.28 ms (1.5 mM Ca2+) and 0.68 ms (0.02 mM Ca2+). (The adaptation time constants measured with the flexible fiber were slower than those reported above probably because the stimulus onset was slower due to the voltage command to the piezoelectric device being filtered at a lower corner frequency, 1.5 kHz compared to at least 5 kHz with the stiff probe). These observations provide evidence that OHC hair bundles can generate force of substantial magnitude (> 500 pN) on a sub-millisecond time scale similar to that of fast adaptation. It is presently unclear what process might underlie force production of such speed and magnitude. A mechanism attributable to the MET channels implies either ten times more channels per stereocilium or intrinsic properties different from those in sub-

251 mammalian vertebrates. Alternative sites for force generation include the stereociliary rootlets or the apical surface of the cell, though either site would require signal transmission from the MET channels at the tips of the stereocilia. 4 Discussion We have measured the properties of outer hair cell MET channels in isolated preparations derived from immature rats and exposed to conditions different from those in the intact cochlea. Our limited evidence on the lack of variation in maximum current and adaptation time constant with age suggests that our results may approximate those in animals with fully developed hearing [6]. However several corrections are needed to extrapolate to in vivo conditions. These include the presence of an endolymph with K+ as the major cation, an endolymphatic potential of 80 mV, and a higher temperature. Each of these factors will increase the amplitude of the transducer current and the rate of adaptation. Our previous extrapolations [6] indicate that the current amplitudes will be about 4-fold larger, 6 - 9 nA, and that the adaptation time constants will be 8-fold faster. Other things being equal, correcting the measured values in 0.02 mM Ca2+ (Fig. 2) imply adaptation time constants, xA, in vivo of 30 us at the low-frequency position and 11 (is at the high-frequency position. These time constants are equivalent to a halfpower frequency (l/2TtxA) of the high-pass filter of 5.3 kHz and 14.5 kHz at the two cochlear locations, which are very similar to the estimated CFs of 4 kHz and 14 kHz respectively. These corrections are necessarily approximate but suggest a correspondence of the adaptation time constants to the hair cell CF. If active force generation by the hair bundles has a parallel time course to fast adaptation, then it too will have kinetics that are matched to the CF. However, it is not yet possible to make force measurements on hair bundles at the microsecond speed needed to rigorously test this assertion. Nevertheless, the predicted speed of fast adaptation suggests that the hair bundle motor may provide positive mechanical feedback at stimulation frequencies of tens of kilohertz. The hair bundle motor could therefore supplement force generation by the somatic motor at high frequencies, or may even constitute the major mechanism of cochlear amplification [15, 16]. Acknowledgments This work was supported by grant ROl DC 01362 to RF from the NIDCD. References 1. Dallos, P., 1992. The active cochlea. J. Neurosci. 12,4575-4585.

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2. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 194196. 3. Kennedy H.J., Crawford A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification.Nature 433:880-3. 4. Kros, C.J., 1996. Physiology of mammalian cochlear hair cells. In: Dallos, P., Popper, A.N., Fay, R.R. (Eds.) The Cochlea. Springer, New York, pp 318-385. 5. He, D.Z.Z., Jia, S., Dallos, P., 2004. Mechanoelectrical transduction of adult outer hair cells studied in a gerbil cochlea. Nature 429, 766-770. 6. Kennedy, H.J., Evans, M.G., Crawford, A.C., Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat. Neurosci. 6, 832-836. 7. van Netten S.M., Dinklo, T., Marcotti, W., Kros, C.J., 2003. Channel gating forces govern accuracy of mechano-electrical transduction in hair cells. Proc. Natl. Acad. Sci. USA 100, 15510-15515. 8. Muller, M., 1991. Frequency representation in the rat cochlea. Hear. Res. 51, 247-254. 9. Bosher, S.K., Warren, R.L., 1978. Very low calcium content of cochlear endolymph, an extracellular fluid. Nature 273, 377-378. 10. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2003. Tonotopic variation in the conductance of the hair cell mechanotransducer channel. Neuron 40, 983-90. 11. Crawford, A.C., Fettiplace, R., 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. 12. Howard, J., Hudspeth, A.J., 1988. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron 1, 189-199. 13. Russell, I.J., Kossl, M., Richardson, G.P., 1992. Nonlinear mechanical responses of mouse cochlear hair bundles. Proc. R. Soc. Lond. B. 250, 217227. 14. van Netten, S.M., Kros C.J., 2000. Gating energies and forces of the mammalian hair cell transducer channel and related hair bundle mechanics. Proc. R. Soc. Lond. B. 267, 1915-1923. 15. Fettiplace, R., Ricci, A.J., Hackney, CM., 2001. Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169-175. 16. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro .Nat Neurosci. 8, 149-55.

253 Comments and Discussion Gummer: According to your force-displacement curves, displacements of several hundred nanometers are required before the hair-bundle is able to exert force on the stimulus fiber. Although you explained that the very fast adaptation process possibly causes "smearing" of measured 10- functions, the required displacement amplitudes are up to two orders of magnitude greater than cochlea-amplified basilar-membrane amplitudes (typically, 0.3 nm at 0 dB SPL). That is, could the active hair-bundle mechanics reported here be simply a high-intensity phenomenon, and therefore, largely irrelevant for cochlear amplification? Answer: Force generation in Fig. 3 of our chapter occurs for hair bundle displacements covering the gating range of the mechanotransducer channels as is expected for the active process. However, the current-displacement (I-x) relationships measured with a flexible fiber are broader than determined with a rigid probe, probably due to the unavoidably slow onset of the stimulus, slower even than the fast adaptation time constant - less than 0.1 ms. During bundle stimulation with a flexible fiber, the mechanotransducer channels will become adapted during the stimulus onset, and the I-x curve will be shifted positive. The measured I-x curve will then be the sum of unshifted and shifted curves, the net effect being to broaden the I-x relationship. To both overcome this problem and measure the true speed of force generation will require developing an even faster method of delivering force steps to the hair bundle.

STEREOCILIARY VIBRATION IN THE GUINEA PIG C O C H L E A

A. FRIDBERGER, I. TOMO, M. ULFENDAHL AND J. BOUTET DE MONVEL Center for Hearing and Communication Research, Department of Clinical Neuroscience, KarolinskaInstitutet, M1.00-ONH, Karolinska Universitetssjukhuset, 17176Stockholm E-mail: anders.fridberger@cfh. ki.se Using a novel technique for rapid time-resolved confocal microscopy, we acquired image sequences showing the sound-evoked motion of inner and outer hair cell stereocilia bundles in the apical, low-frequency regions of the guinea pig cochlea. Motion of structures of interest was analyzed by optical flow computation. Sound stimulation at 80 - 100 dB SPL and 200 Hz led to deflection of both inner and outer hair cell stereocilia. The deflection was linearly related to the displacement of the reticular lamina. However, deflection was smaller for inner hair cell stereocilia. Phase differences were also found: deflection of inner hair cell stereocilia led that of the outer hair cell by 44 degrees on average. It was previously shown that apical inner hair cells have 10 - 16 dB larger AC receptor potentials than outer hair cells (Russell & Sellick, 1983; Dallos, 1985). Our results suggest that inner hair cells are equipped with transducer channels of higher conductance or higher density than are the outer hair cells. In view of the tiny deflection that inner hair cells are supposed to detect, it might also be that active processes acting at the level of their stereocilia are necessary near threshold.

1 Introduction Outer hair cell (OHC) stereocilia are firmly embedded into the gelatinous tectorial membrane. This connection causes OHC stereocilia to deflect in response to the organ's vibrations. Inner hair cell (IHC) stereocilia do not appear to be attached to the tectorial membrane, and the mechanism by which they deflect is therefore less obvious. Electrophysiological recordings suggested that IHC stereocilia motion is driven by fluid interaction in the tiny space between the tectorial membrane and the reticular lamina [1]. This would imply that IHC bundle deflection is proportional to the velocity of the organ of Corti, while in OHCs deflection is proportional to the organ's displacement. Here we present a detailed account of stereocilia motion in the apical region of the guinea pig cochlea in excised temporal bone preparations. Images were acquired by a modified confocal microscope and analyzed using optical flow analysis. 2 Methods 2.1 Preparation and Sound Stimulation Pigmented guinea pigs were decapitated and the temporal bone attached to a holder, with the external auditory meatus facing a loudspeaker. An important difference from our previous studies [2-4] was that the preparation was immersed in an endolymph-like solution. Reissner's membrane was ruptured using a fine needle.

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255 Thereafter, the dye RH795 was added to the perfusion medium (12.5 ug/ml; Molecular Probes). Due to the opening in Reissner's membrane, this dye stained stereocilia on both inner and outer hair cells. Because the preparation was immersed in an endolymph-like solution and perfused with normal medium, the hair cell's natural ionic environment was preserved. The preparation was mounted on a laser scanning confocal microscope and visualized at a pixel size of 110 nm. Sound stimulation was applied at 200 Hz, close to the expected best frequency for this cochlear region. Stimulus levels ranged between 88 and 110 dB re 20 uPa. Due to the immersion of the preparation and opening of the apical turn, the stimulus level is reduced. Under these experimental conditions, organ of Corti vibrations are generally thought to be unaffected by OHC motility. Passive mechanical processes are crucial for organ function, being predominant in the living animal at these sound intensities. 2.2 Time-resolved confocal imaging The phase relation between each image pixel and the sound stimulus was tracked by sampling the voltage waveform driving the loudspeaker. Pixels having similar phases were collected, forming an image of the preparation at a given phase of the stimulus. 2.3 Analysis of hair bundle motion Stereocilia displacements during a full cycle of motion were analyzed by a wavelet differential optical flow algorithm [4]. The optical flow of the resampled and smoothed image sequence was computed. A significant increase in accuracy was obtained compared to our previous studies [2-4], displacements on the order of a few nanometers being estimated with a magnitude error less than 10%. 3 Results 3.1 Stereocilia motion Figure 1A shows two OHCs imaged during sound stimulation. The reticular lamina and the hair bundles rotated in phase with the stimulus, making the cilia to deflect, showing a pivoting motion from base to tip. Figure IB displays the trajectories of these two points. The main axis of motion at the base of the hair bundles matched the long axis of the cilia. A small radial motion component gave the trajectory the shape of an elongated ellipse. The trajectory of the tip of the bundle was also an elongated ellipse, but its orientation was different from that of the base. This difference led to a deflection of the hair bundle directly in phase with the displacement of the reticular lamina. This deflection was computed by simply subtracting the tip and base trajectories. As the cells moved downward, the OHC bundle deflected 28 nm to the left, for a total base displacement of 95 nm. Thus, displacement of the organ of Corti toward scala tympani resulted in deflection in the

256 inhibitory direction. The pattern of OHC bundle trajectories remained very similar at higher sound intensities. Notably the trajectories' orientations were almost the same at all intensities. We also measured the bundles' angular deflection, defined as the angle formed between the two extreme positions of the stereocilia. For stimulus levels between 92 and 110 dB SPL, OHC deflection angles were between 0.130.88°. Figure 1C shows an IHC in the same preparation and at the same location as the OHCs seen in Figure 1 A. The displacements of the IHC bundle tip and base were about 30% smaller than those of the OHCs at equal stimulus level (maximum displacement at the base of 66 nm). The deflection amplitude of the IHC bundle was 14 nm, about half that of the OHC. As a result, the angular deflection of the IHC bundle were in the range 0.08-0.54°, about 40% smaller than the values found for the OHCs. Angular deflections of 25 pairs of IHCs and OHCs were measured from 4 preparations. Each pair referred to an IHC and an OHC at the same location in the cochlea. In all cases, the OHCs showed larger stereocilia deflections than IHCs. The mean angular deflections for the applied range of sound intensities was 0.49° ± 0.30° and 0.97° + 0.60° for IHCs and OHCs, respectively. This difference was significant when assessed according to Student's t-test for paired variables Defle&tan

Base 0

20

40

60

X Displacement (nm)

Deflection

Figure 1. A) Confocal image showing two OHCs during sound stimulation at 200 Hz and 98 dB SPL. Scale bar, 3 um. B) Motion at the base and the tip of the hair bundle. Deflection was computed as the vector difference between the trajectories. C) Confocal image of an IHC at the same location as the cells in panel A. D) Motion at the tip, base and the computed deflection of the hair bundle.

X Displacement (nm)

(pO.00001). The standard deviations reflect variation caused by different vibration amplitudes in different IHC-OHC pairs, rather than measurement errors. The slopes

257 of the regression lines (stereocilia angular deflection versus reticular lamina displacement) were not significantly different for IHCs and OHCs (0.35° / 100 nm for OHCs and 0.41° /100 nm for IHCs). 3.2 Phase relations OHC bundle deflection was in phase with the reticular lamina displacement, as the minima (and maxima) of both recordings occurred at the same instants. Using Fourier transformation, we found that IHC cilia deflection led reticular lamina displacement by 44° on average. 3.3 Apparent pivot axes of the stereocilia We analyzed the apparent pivot axes of the tips and bases of the stereocilia by the least-squares method described in [2, 3]. Results are illustrated in Figure 2. The bundle bases of the IHC and of the first row OHC rotated around similar axes located in the region of the IHC base or lower. The pivot axis of the second row OHC bundle base was found closer to the reticular lamina, near the head of the pillar cells. Although the pivot axes of the tip and base of the IHC bundle were significantly different, both were found below the reticular lamina in the same directions (the corresponding trajectories being nearly parallel). Both parts of the IHC bundle thus moved in similar ways, following the rotation of the reticular lamina. By contrast, the trajectories of the OHC stereocilia had different orientations from tip to base. The pivot axes of the OHC bundle tips were found in a direction nearly parallel to the reticular lamina, somewhere above the head of the pillar cells. 4 Discussion Figure 2. Pivot analysis of hair cell stereocilia motion. Sound intensity in this case was 104 dB SPL. Estimated pivot axes are positioned in a schematic drawing of the organ of Corti. Circles: OHC bundle bases (rows 1 and 2). Crosses: OHC bundle tips. Diamond: IHC bundle base. Star: IHC bundle tip. The lines show the directions perpendicular to the trajectories of the corresponding cilia bases or tips.

258 4.1 Pattern of cilia deflection for outer hair cells The observed trajectories of the OHC cilia bases and tips are consistent with a model of OHC bundle deflection driven by the opposing rotations of the reticular lamina and the tectorial membrane. An important difference with classical models [5] is that the motion of the organ of Corti is far from being rigid, which was seen even at the level of a single hair bundle. The apparent center of rotation of the tips was closer from the hair cells than naively expected from the point of attachment of the tectorial membrane. This pattern was observed consistently in many experiments. If significant, the observed difference might have several origins. The most natural one would be the presence of deformations in the tectorial membrane, but it could also reflect a relative shallowness in the coupling between the OHC cilia and the tectorial membrane. 4.2 Pattern of stereocilia deflection for inner hair cells Our data provide direct evidence that deflection of IHC stereocilia occurs by a different mechanism than the one at work in OHCs. Our results are consistent with a model of IHC cilia deflection driven by fluid interactions, as expected from their lack of attachment with the tectorial membrane. IHC stereocilia deflection was found to lead the displacement of the reticular lamina by 44°, a figure representative of most our experiments, and close to previous estimates obtained from electrophysiological studies (65 - 80° measured by Dallos [6]; and -50°, observed at 86 dB SPL by Dallos and Cheatham [7]). A model of IHC bundle deflection driven purely by fluid velocity, as frequently assumed, would correspond to a phase lead of 90°. Our smaller phase lead estimate rather suggests that the IHC bundles responded to a combination of velocity and displacement. This feature is not unexpected in realistic models of hair bundle deflection driven by hydrodynamic forces [8]. It seems also likely that interaction with the Hensen stripe could affect the fluid flow around IHC cilia [9]. 4.3 Small amplitude of IHC bundle deflection In typical experiments, the deflection of OHC stereocilia had an amplitude about twice that of IHC stereocilia (when observed at the same location in the cochlea). At least two natural explanations for this may be mentioned. Clearly, attachment of stereocilia to the tectorial membrane should help stimulate the OHC bundles, resulting in a more effective deflection. In addition, OHCs show larger amplitudes of vibration in response to sound than do the IHCs, the latter being located closer to the overall pivot axis of the organ of Corti [2,3 and figure 2], In this view, the fact that reticular lamina displacement and angular cilia deflection were near proportional with similar slopes for IHCs and OHCs is of interest. This creates an issue when considering the induced receptor currents. Electrophysiological

259 measurements indicate that receptor potentials in IHCs are about 4 times larger than in OHCs [6,10]. Taking account of the hair cells' impedances (estimated in Dallos' recordings [6]), receptor currents are found to be about twice larger in IHCs than in OHCs, in vivo. Comparing with our results, this means that IHCs are about 4 times more effective to convert deflection into a receptor current than are the OHCs. If the hair bundles of IHCs and OHCs have similar mechanical properties, this would seem to imply a difference in the transduction channels themselves (e.g. higher conductance, larger number, or higher opening sensitivity of IHC transduction channels). References 1.

2.

3. 4.

5.

6. 7. 8. 9. 10.

Dallos P., Billone M.C., Durrant J.D., Wang C.-Y., Raynor S., 1972. Cochlear inner and outer hair cells: Functional differences. Science 177:356 -358. Fridberger A., Boutet de Monvel J., Ulfendahl M., 2002 Internal shearing within the hearing organ evoked by basilar membrane motion. J Neurosci 22:9850-57. Fridberger A., Boutet de Monvel J., 2003. Sound-induced differential motion within the hearing organ. Nature Neurosci 6:446-48. Fridberger A., Widengren J., Boutet de Monvel J., 2004. Measuring hearing organ vibration patterns with confocal microscopy and optical flow. Biophys. J. 86, 535-43. Rhode W.S., Geisler CD., 1967. Model of the displacement between opposing points on the tectorial membrane and reticular lamina. J Acoust Soc Am. 42: 185-190. Dallos P., 1985. Response characteristics of mammalian cochlear hair cells. J Neurosci 5:1591-1608. Cheatham M.A., Dallos P. 1998. The level dependence of response phase: Observations from cochlear hair cells. J Acoust Soc Am 104: 356 - 69. Freeman M., Weiss T., 1990. Hydrodynamic forces on hair bundles at low frequencies. Hear Res 48:17-30. Steele C.R., Puria S., 2005. Forces on inner hair cell cilia, in press. Russell I.J., Sellick P.M., 1983. Low-frequency characteristics of intracellularly recorded receptor potentials in guinea-pig cochlear hair cells. J Physiol. 338:179-206.

Comments and Discussion Gummer: I am happy to see that you are also proposing fluid amplification in the subtectorial space as a possible mechanism for stimulating IHC stereocilia (see Gummer et al., this volume). Since this mechanism requires an intact tectorial

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membrane (TM), which could be compromised by opening Reissner's membrane, please state whether: i) the TM is intact, ii) the OHC stereocilia are embedded in the TM, and iii) the proximity of Hensen's stripe to the IHC stereocilia. Answer: Tectorial membrane integrity was assessed after completion of the measurements by staining it with ConA/Alexa488. The tectorial membrane retained its normal size, position and relation to both outer and inner hair cell stereocilia. Hensen's stripe was located close to the hair bundle but I do not have a measurement of the distance right now. The image showed during the talk is representative of our experiments and indicates that Hensen's stripe is very close to the stereocilia. Aranyosi: Your measurements show that the reticular lamina undergoes elliptical motion. We also saw elliptical trajectories of motion in the alligator lizard cochlea, and showed that (1) such motion could be explained by a rigid body model, and (2) this model exhibited two modes of motion — a translation in the transverse direction, and a rotation centered near the neural side of the basilar membrane. Can your elliptical trajectories be explained by rigid body motion, and if so, do you see evidence of multiple modes of motion of the organ of Corti? Answer: I did not have time to mention this during the talk, but the data, which is shown in the manuscript submitted to this meeting, indicates that the motion is far from being rigid. Different structures within the organ have different centers of rotation (see also Fridberger et al., J Neuroscience (2002); Fridberger and Boutet de Monvel, Nature Neuroscience (2003); Fridberger et al., Biophysical J (2004)). Guinan: I noticed that in your plot of IHC stereocilia phase, the two points with the lowest amplitudes had much different phases than the other points. This is reminiscent of the level-dependent phase jumps seen in auditory nerve firing by many people. Is the level difference you see in IHC stereocilia phase significant? And, if so, do you know of a methodological reason for it, or is it telling us that there is a change with sound level in the vibrational mode of the organ of Corti so that IHC stereocilia are driven with a different phase at different levels? Answer: We have seen reversals of the phase in some preparations, but we have not explored the phenomenon in a systematic way. The parallel to the auditory nerve recordings is interesting and I hope that we will be able to say more about this in the future.

THE COCHLEAR AMPLIFIER: IS IT HAIR BUNDLE MOTION OF OUTER HAIR CELLS? 'SHUPING JIA, 2JIAN ZUO, 3PETER DALLOS, '*DAVID Z.Z. HE 'Department of Biomedical Sciences, Creighton University, Omaha, NE 681752St. Jude Children Research Hospital, Memphis, TN 381053Auditory Physiology Laboratory, Northwestern University, Evanston, IL 60208 Cochlear outer hair cells (OHCs) are involved in a mechanical feedback loop in which the fast somatic motility of OHCs is required for cochlear amplification. Alternatively, amplification is thought to arise from active hair bundle movements similar to that in non-mammalian hair cells. We measured the voltage-evoked hair bundle motions in the gerbil cochlea to determine if such movements are also present in mammalian OHCs. The OHCs displayed a large hair bundle movement that was not based on mechanotransducer channels but originated in somatic motility. Significantly, bundle movements were able to generate radial motion of the tectorial membrane in situ. This result implies that the motility-associated hair bundle motion may be part of the cochlear amplifier.

1 Introduction It is generally believed that mechanical amplification by hair cells is necessary to enhance the sensitivity and frequency selectivity of hearing. In the mammalian cochlea OHCs function as the key elements in a mechanical feedback loop that most likely involves OHCs, organ of Corti micromechanics and the tectorial membrane (TM), with inner hair cells (IHCs) responding to the output of the feedback loop (7,2). OHCs exhibit a voltage-dependent length change termed electromotility (3). This somatic motility is thought to underlie cochlear amplification in mammals (/4). The alternative view is that the amplification arises from active hair bundle motion, a phenomenon that has been observed in non-mammalian hair cells (5,6). In order to further study if hair bundle movements are responsible for amplification in mammalian OHCs, we evaluated voltage-evoked hair bundle activity in the cochlea of gerbils and prestin knockout mice (4). 2 Results Sensory epithelia were dissected from the cochleae of adult gerbils and prestin knockout mice. The resulting coil preparation was bathed in artificial perilymph and mounted on the stage of a Leica upright microscope with a 63x water-immersion objective. Under bright-field illumination at high magnification, the hair bundles behaved as light pipes (7) and appeared as bright V-shaped lines (Fig. 1A). To measure bundle motion, the magnified (l,260x) image of the edge of the hair bundle was projected onto a photodiode through a rectangular slit. The photodiode-based

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system, mounted on the photo-port of the Leica microscope, had a 3-dB cutoff frequency of 1,100 Hz and was capable of measuring motion down to ~5 nm with moderate averaging and low-pass filtering. Before the voltage-evoked bundle motion was measured, we recorded mechanotransducer currents to verify that the mechanotransducer apparatus in the stereocilia was not damaged. Fig. IB shows an example of such recording from an apical turn gerbil OHC. The hair bundle was deflected by a fluid jet (with pipette tip diameter of 10 urn) positioned 20-30 um away from the bundle. Transducer currents were recorded at the holding potential of-70 mV in the voltage-clamp mode. Large transducer current was observed (Fig. IB). The size of the current is comparable to previous studies in mammalian OHCs (8-10). To determine bundle motions, sinusoidal voltage bursts (102 Hz) were applied to the OHCs through the patch electrode. The voltage command varied the membrane potential from -100 to -40 mV from a holding potential of -70 mV. Examples of the voltage-evoked hair bundle movements are shown in Fig. 1C. Bundle motion is asymmetrical with depolarization evoking larger bundle motions in the direction toward the tallest stereocilia than hyperpolarization does in the opposite direction. The direction of bundle motion during membrane potential change is consistent with that seen in turtle hair cells (7,11), but is of opposite polarity to that seen in bullfrog saccular hair cells (12,13). Fig. 1. A. Hair bundles of OHCs under high magnification (63x water-immersion objective) with bright field illumination. Double-headed arrow indicates the direction of bundle motion. Scale bar represents 10 um. B. Mechanotransducer currents recorded from an apical turn gerbil OHC from the coil preparation. The bundle was deflected by an oscillating stream from a fluid jet positioned -20-30 um away from the bundle. The response shown is the average of 3 trials. The voltage command (102 Hz) to drive the water jet is presented at the bottom of the panel. Inward current is plotted downward. C. Voltage-evoked bundle motions of a gerbil OHC at two different Jims Iflisj Time<msj extracellular calcium concentrations. The 102 Hz voltage command varied the membrane potential from 100 to ~W) mV around the holding potential of -70 mV. Positive bundle motion (toward tall cilia) is plotted upward in this and all subsequent figures. D. Bundle motion before and after 100 uM streptomycin was perfused to the OHC stereociliary region. The responses in C and D were the averages of 100 trials. The scale bar in C also applies to the responses in D.

Hair cells of several non-mammalian species display an active hair bundle motion in response to changes in membrane potential (7, 11-13). The active motion, intimately associated with mechanotransducer channels, is secondary to alteration of calcium influx in the stereocilia and is, therefore, dependent on the extracellular calcium concentration (7,11). We sought to determine whether the bundle motion observed in OHCs also operates on a similar basis. Bundle motion was examined

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when the extracellular calcium concentration was altered. Fig. IC shows an example when the extracellular calcium was reduced to 5 uM. Robust voltageevoked bundle motion was still observed. Streptomycin is known to block mechanotransducer channels (8) and eliminate active and spontaneous bundle motion (7,13). We perfused 100 uM streptomycin to the ciliary area to see whether it blocked the voltage-evoked bundle motion in OHCs. As shown in Fig. ID, the bundle motion was not affected by streptomycin. Collectively, these results suggest that the observed bundle motion in OHCs is different from the voltage-evoked bundle motion seen in non-mammalian hair cells. As an alternative to motility derived from mechanotransducer processes, it is possible that bundle motion arises as some consequence of somatic motility. To demonstrate that the observed hair bundle motion is associated with somatic motility, we examined the voltage-evoked bundle motion in neonatal gerbils. Studies have shown that the onset of OHC motility occurs around 6-8 days after birth (14) while mechanotransducer channels are known to be mature at birth (8,9). Voltage-evoked bundle motions of apical turn OHCs were measured from developing gerbils at 4, 8, and 12 days after birth (DAB). Fig. 2A shows some examples of the responses measured from those preparations. At 4 DAB when electromotility had not yet developed, no voltage-evoked bundle motion was detected (n=10), although large transducer currents could be measured (data not shown). At 8 DAB, we observed small bundle motion in 1 of 8 cells examined. At 12 DAB when all OHCs exhibit electromotility (14), voltage-evoked bundle motion was detected in all 7 cells studied, with a magnitude of approximately 72% of that of the adult OHCs with the same voltage stimulation. The fact the development of bundle movements correlates with the development of somatic motility suggests that the voltage-evoked bundle motion is related to somatic motility. We examined the voltage-evoked bundle motion in prestin (75) knockout mice (4). Such measurements are important to determine whether there is any small transducer channel-based bundle motion that is overshadowed by the dominant motility-associated bundle motion. These mice have normal morphology of the hair bundles and normal mechanotransducer functions (4,16) with no OHC somatic motility. We measured transducer currents first to confirm that their mechanotransducer channels are functional. Fig. 2B shows an example of the transducer current recorded from an apical turn OHC of the prestin knockout mouse. As shown, large asymmetrical transducer current was observed. We measured the voltage-evoked bundle motion from the OHCs of prestin-null mice. No voltage-evoked bundle motion was seen in any of the 11 cells examined (Fig. 2C). In contrast, when the voltage-evoked bundle motion was measured from OHCs of wild-type mice, large bundle motions were seen for all cells studied. We also measured the voltage-evoked bundle motion with the ciliary area perfused with endolymph-like solution to mimic the in vivo chemical condition in 5 additional prestin-null OHCs. No voltage-evoked bundle motions were observed in any of the

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5 cells examined. This confirms that the voltage-evoked bundle motion is indeed associated with somatic motility. Fig. 2. A. Voltage-evoked bundle motions measured from 4-, 8-, and 12-day-old gerbil OHCs. The stimulus waveform and voltage command is the same as shown in Fig. 1C. B. Mechanotransducer currents recorded BCWB from an apical turn OHC of prestin knockout mouse. C. Lack of voltage-evoked bundle motion from the prestin knockout mouse OHC. D. Bundle motions of an apical turn gerbil OHC as a function of voltage levels (from a holding potential of -70 mV). Steadystate response from D was fitted with a second-order Boltzmann function (solid line) and plotted in the bottom panel. Slope function (dashed line) was obtained as the derivative of the Boltzmann function. The series resistance was 75% compensated. Because membrane conductances were blocked, the uncompensated voltage error (not corrected in the plot) was less than 4 mV at the largest voltage levels. '""vuHg* t£v)" f£jo»ty{Hij """ E. Motility-associated bundle motions evoked by a series of voltage bursts with different frequencies (frequency is shown on the top of the response waveforms). The peak-to-peak response was measured and plotted as a function of frequency in the bottom panel. 4 DAS

Subsequently, we examined bundle motion as a function of membrane potential (input-output function). Fig. 2D shows an example of the response measured from an apical turn gerbil OHC when the membrane potential was stepped from the holding potential of -70 mV. The responses were asymmetrical and nonlinear with saturation in both directions, similar to that seen in OHC somatic motility (77). We fitted the response with a second-order Boltzmann function, and the maximum sensitivity calculated from the derivative of this function was ~5 nm/mV (Fig. 2D). The maximum peak-to-peak response observed in the example was 567 nm. The largest peak-to-peak response observed among 6 cells examined was 832 nm. We also examined the frequency response of the voltage-evoked bundle motion between 50 and 1,000 Hz using sinusoidal voltage bursts. An example is shown in Fig. 2E. Apparently, large bundle motions were still present at 1,000 Hz. The frequency response of the bundle motion was similar to that of OHC somatic motility measured under whole-cell voltage-clamp condition (18). The TM is an important element of the mechanical feedback loop and its role in mechanoelectrical transduction, frequency tuning, and cochlear amplification has been demonstrated (19-21). The most direct path for OHC bundle motion to influence input to IHCs is through the TM. We questioned whether hair bundle motion could generate a radial TM motion. For this purpose, the gerbil hemicochlea (22) was used to examine TM radial motion driven by OHC bundle motion. Hemicochleae (Fig. 3A) were prepared from 25 to 30 day old gerbils. Whole-cell recordings were made from the upper basal turn where OHC mechanotransducer currents were previously recorded (70). The cells were current-clamped to a level

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that would result in a membrane potential of approximately -70 mV. Current (100 Hz sinusoid, 100 to 300 uA) bursts generated by a modified battery-powered stimulator (Isostim A320, WPI) created a diverging electrical field between the stimulating pipette (tip diameter of 4 um) positioned 50-60 urn away from the OHCs and the indifferent earth in the bath. This focal electrical stimulation depolarizes and hyperpolarizes OHCs near the electrode (23). Fig. 3C shows an example of simultaneous recordings of radial motion of the TM and the membranevoltage response of an OHC. As shown, the focal electrical stimuli resulted in a net membrane potential change of 18 mV (peak-to-peak) and produced a radial TM motion of ~10 nm (peak-to-peak). Depolarization (hyperpolarization) resulted in TM motion toward the spiral ligament (modiolus). While the voltage response of the OHC was nearly symmetrical, TM motion was asymmetrical, with both ac and dc components. This asymmetry resembles that of the bundle motion considered above and may originate from the asymmetry of OHC somatic motility (77). To confirm that the TM motion was the result of bundle motion, we measured TM motion in preparations where the TM was detached from the hair bundles of OHCs. As expected, no TM motion was detected (Fig. 3D) in any of 15 such preparations examined. We also observed radial TM motion when 100 mV sinusoidal voltage was applied to one OHC under the whole-cell voltage-clamp condition (data not shown) This again confirms that the TM motion was the result of bundle motion. Fig. 3. A. Hemicochlea from a 30-day-old gerbil. The square represents the area where the TM motion was measured using a photodiode-based technique. The white double-headed arrows indicate directions of the TM motion measured. Small black arrow indicates the Hensen's stripe on the underside of the TM. B. Hensen's stripe and IHC bundle at high magnification. Bars in A and B represent 10 urn. C. Simultaneous recordings of TM radial motion and membrane potential changes of an OHC from the upper basal turn of a 28-day-old gerbil hemicochlea. Current f S f — < ^ — — — ^] fmttftmm vsftage response (100 Hz sinusoid, bottom trace in B) was •ss3 (%m*Kinjected c« -^" injected through another pipette positioned ~50 um away from the cell under recording to depolarize and hyperpolarize it. Upward deflection in the trace represents the movement of the TM toward the spiral ligament. D. TM motion and membrane voltage response measured from another hemicochlea when the TM was detached from the hair bundles No TM motion was observed. The responses are the averages of 200 trials. 'VfflSMh.

3 Discussion This work demonstrates significant ciliary rotation evoked by OHC electromotility. Yet, in the absence of electromotility, ciliary rotation, presumably related to the

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mechanotransducer channels, is below the resolution limit of our system. The motility-associated bundle motion is large (over 800 nm), approximately ten times (20 dB) larger than the transducer-channel based bundle motions observed in nonmammalian hair cells (7,12,13). Voltage-evoked bundle motion of IHCs was reported in a recent study (24) using a two-chamber preparation. The motilityassociated response possibly overshadows transducer channel-based mechanisms in OHCs. It is not fully established how OHC length changes result in bundle motion. However, tilting of the cuticular plate during motility has been reported to occur at high frequencies (up to 15 kHz) in coil preparations (25). Rotation of the reticular lamina as a result of OHC motility was also seen in situ (23). It is, therefore, likely that rotation of the reticular lamina along its fulcrum at the pillar heads and possibly tilting of the cuticular plate within the reticular lamina during OHC length change can produce bundle motions. OHC somatic motility has been proposed to be responsible for cochlear amplification in mammals. However, it is yet to be fully determined how active somatic movements of OHCs excite IHCs. Obviously, coupling OHC motility to basilar membrane and reticular lamina movements in an appropriate phase would boost their displacements. In addition, the bundle motion associated with OHC somatic motility provides a possibility for OHC motility to boost the input to IHCs. Because movement of the bundle is able to produce radial motion of the TM, this motion could amplify mechanical input to the IHC by increasing fluid motion in the TM-reticular lamina gap. It is such fluid flow that stimulates the freestanding IHC cilia (27). It is conceivable that fluid-pumping by Hensen's stripe (see Fig. 3B) onto the closely apposed IHC cilia is the excitatory mechanism. The ' V or ' W shaped staircase structure of the OHC stereocilia is well suited for promoting mechanical coupling between the TM and reticular lamina, which can transfer the motilitydriven hair bundle motion into the radial motion of the TM. It is, therefore, conceivable that the motility-associated hair bundle motion may be part of cochlear amplification in mammals. Under this scheme, OHC somatic motility not only boosts basilar membrane vibration but also drives the hair bundle motion, which is able to produce the radial motion of TM. The force produced by OHC hair bundles can further enhance the radial motion of the TM. Since the bundle and TM motions are both associated with somatic motility of OHCs, this scheme is in line with studies using prestin-knockout mice (4,16), which support motility-based amplification as the dominant mechanism in the mammalian cochlea. The principal argument against somatic motility as the amplifier is that the lowpass filter characteristics of OHC membrane attenuate receptor potentials at high frequencies. However, it has been proposed that extracellular potential changes within the organ of Corti could drive OHC motility at high frequencies (28). Recent measurements of basilar membrane vibration and extracellular potentials provide evidence that those extracellular potentials can indeed drive OHC motors at high frequencies (29). Furthermore, theoretical modeling also indicates that the

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piezoelectric property of OHCs can significantly increase the frequency response of OHCs (30). References 1. Dallos, P., Fakler, B., 2002. Prestin, a new type of motor protein. Nat. Rev. Mol. Cell Biol. 3, 104 2. Santos-Sacchi, J., 2003. New tunes from Corti's organ: the outer hair cell boogie rules. Curr. Opin. Neurobiol. 13,459 3. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses in isolated cochlear outer hair cells. Science 227, 194 4. Liberman, M.C., et al., 2002. Prestin is required for outer hair cell electromotility and the cochlear amplifier. Nature 419, 300 5. Hudspeth, A.J., 1997. Mechanical amplification of stimuli by hair cells.Curr. Opin. Neurobiol. 7,480 6. Fettiplace, R., Ricci, A.J., Hackney, CM., 2001. Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169 7. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2000. Active hair bundle motion linked to fast transducer adaptation in auditory hair cells. J. Neurosci. 20, 7131 8. Kros, C.J., Rusch, A., Richardson, G.P., 1992. Mechano-electrical transducer currents in hair cells of the cultured neonatal mouse cochlea. Proc. R. Soc. Lond. B. Biol. Sci. 249, 185 9. Kennedy, H.J., Evans, M.G., Crawford, A.C, Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nature Neurosci. 6, 832 10. He, D.Z.Z., Jia, S.P., Dallos, P., 2004. Mechanoelectrical transduction of outer hair cells studied in a gerbil hemicochlea. Nature 429, 766 11. Crawford, A.C, Fettiplace, R. 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359 12. Assad, J.A., Hacohen, N., Corey, D.P., 1989. Voltage dependence of adaptation and active bundle movement in bullfrog saccular hair cells. Proc. Natl. Acad. Sci. USA. 86, 2918 13. Bozovic, D., Hudspeth, A.J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc. Natl. Acad. Sci. USA 100, 958 14. He, D.Z.Z., Evans, B.N., Dallos, P., 1994. First appearance and development of electromotility in neonatal gerbil outer hair cells. Hear. Res. 78, 77 15. J. Zheng et al., 2000, Prestin is the motor protein of cochlear outer hair cells. Nature 405,149 16. Cheatham, M.A., Huynh, K.H., Gao, J., Zuo, J., Dallos, P., 2004. Cochlear function in prestin knockout mice. J. Physiol. 560, 821 17. Santos-Sacchi, J., 1989. Asymmetry in voltage-dependent movements of isolated outer hair cells from the organ of Corti. J. Neurosci. 9, 2954

268 18. Santos-Sacchi, J., 1992. On the frequency limit and phase of outer hair cell motility: effects of the membrane filter. J. Neurosci. 12, 1906 19. Legan, P.K., et al., 2000. A targeted deletion in alpha-tectorin reveals that the tectorial membrane is required for the gain and timing of cochlear feedback. Neuron 28, 273 20. Lukashkin, A.N., et al., 2004. Role of the tectorial membrane revealed by otoacoustic emissions recorded from wild-type and transgenic Tecta (deltaENT/deltaENT) mice. J. Neurophysiol. 91, 163 21. Gummer, A.W., Hemmert, W., Zenner, H.P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning. Proc. Natl. Acad. Sci. USA 93, 8727 22. Hu, X.T., Evans, B.N., Dallos, P., 1999. Direct visualization of organ of Corti kinematics in a hemicochlea. J. Neurophysiol. 82, 2798 23. Mammano, F., Ashmore, J.F., 1994. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature 365, 838 24. Chan, D.K., Hudspeth, A.J., 2005. Ca(2+) current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat. Neurosci. 8,149 25. Reuter, G., Gitter, A.H., Thurm, U., Zenner, H.P., 1992. High frequency radial movements of the reticular lamina induced by outer hair cell motility. Hear. Res. 60, 236 26. Dallos, P., Billone, M.C., Durrant, J.D, Wang, C.-y., Raynor, S., 1972. Cochlear inner and outer hair cells: functional differences. Science 177, 356358 27. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880 28. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science 267,2006 29. Fridberger, A., et al., 2004. Organ of Corti potentials and the motion of the basilar membrane. J. Neurosci. 24, 10057 30. Spector, A.A., Brownell, W.E., Popel, A.S., 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 113,453 Comments and Discussion Chan: Very nice work. My question relates to the discrepant results regarding voltage-evoked movement of hair bundles- whereas both Fettiplace and myself have observed voltage-evoked bundle movement that is sensitive to transduction-channel block (by streptomycin or amiloride), you do not find such a streptomycin-sensitive. Is it possible that this discrepancy is related to the bias of the transducer channel? Your transducer-current traces suggest a resting open probability of only a few percent, whereas Fettiplace's results place the transducer closer to 10-20%, and my

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microphonic recordings place the transducer near 50%, which is typically observed in vivo in OHCs at high frequencies. Answer: I could not explain the discrepancy between my data and those of Fettiplace. In our preparation, only 5% of transducer channels were open. The preparation is essentially the same as that used by Fettiplace et al. I would assume that more channels are open in vivo (as you have showed) with the tectorial membrane attached. It is not clear whether more channels operating at rest would contribute to bundle motion. The V-shaped structure of the stereocilia certainly is not very well suited for the ciliary rotation. The direction of tip-links is also not unidirectional. Anyway, we are using an isolated cochlear preparation and hopefully, this preparation will provide some answers.

PRESTIN-LACKING MEMBRANES ARE CAPABLE OF HIGH FREQUENCY ELECTRO-MECHANICAL TRANSDUCTION

B. ANVARI AND F. QIAN Department

of Bioengineering, 6100 Main St., MS-142, Rice University, Houston TX 77005, USA E-mail: anvari(a),rice.edu, E-mail: fensqian(a),rice.edu F. A. PEREIRA

Hufflngton Center on Aging, Department of Otorhinolaryngology & Communicative Science, Department of Molecular and Cellular Biology, One Baylor Plaza, Houston TX 77030, USA E-mail: foereira(a),bcm. tmc. edu W. E. BROWNELL Department

of Otorhinolaryngology & Communicative Sciences, One Baylor Plaza, TX 77030, USA E-mail: brownell(a),bcm. tmc.edu

Houston

Using a novel experimental technique that combines optical trapping with patch-clamp and fluorescence photometry, we provide preliminary evidence that native biological membranes are capable of electrically-induced piconewton level force generation in the absence of specialized transmembrane proteins such as prestin. Force generation is dependent on membrane tension and the transmembrane electrical potential. Salicylate diminishes and prestin enhances force generation.

1 Introduction Mammalian outer hair cells (OHCs) within the organ of Corti are specialized sensory cells with force generating capabilities [1]. Recently, an OHC transmembrane protein, prestin, has been discovered [2]. When prestin is expressed in non-auditory mammalian cells it endows the transfected cells with electromotility [2], and voltage-dependent non-linear capacitance (NLC) [3], which serves as a reliable "signature" of electromotility [3]. Atomic force microscopy experiments have demonstrated that upon electrical stimulation of rat prestin-transfected human embryonic kidney (HEK) cells in a microchamber configuration, forces up to a stimulus frequency of 20 kHz are generated [4], Conversely, mechanical stimulation of the cells shifted the voltage-dependence of the NLC. The preponderance of these experimental results clearly establishes that prestin enhances native motility and imparts NLC to cells, and suggest that prestin contributes to the mechanism responsible for OHC electromotility. In this paper, we report measurements of electrically-induced forces by prestin-lacking membranes and outer hair cells.

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271 2 Methods We have designed and constructed a system that combines optical tweezers with patch-clamp and fluorescence photometry techniques [5]. With this system, optical tweezers are used to form a plasma membrane tether from a patch-clamped cell while fluorescence photometry is used to measure electrically-induced forces by membranes. We form membrane tethers by trapping a fluorescent sulfate-derivatized polystyrene microsphere (typically 4.0 um in diameter) and bringing it in contact with the cell. The cell is subsequently moved away from the trapped microsphere using a piezoelectric translator (PZT) to form a membrane tether linking the trapped microsphere to the cell. Patch pipettes with typical resistances of 2-4 MQ are pulled from borosilicate capillary tubes, and placed near an optically-trapped microsphere. After a seal with resistance of >1GQ is formed, a voltage pulse or gentle suction is applied to break the membrane patch in order to enter the whole cell patch configuration. The light from a Xenon source is used for fluorescence excitation of the trapped microsphere. The fluorescent emission from the microsphere is focused onto a quadrant photodetector (QPD). Light from a halogen source is used for visualization of the cells by a CCD camera. We use the dynamic displacement of the trapped fluorescent microsphere from the trapping center in response to force application as a technique to obtain timeresolved force measurements. Specifically, as the tether is elongated by movement of the PZT, the trapped microsphere is displaced from its trapping center to cause a change in the fluorescence intensity projected onto the QPD surface, generating a continuous voltage signal on each quadrant. Calibration of the transverse microsphere displacement is performed using the displacement of a coverslip-adherent microsphere, positioned at the same focal plane as a trapped particle, to known transverse distances with the PZT, and recording the change in QPD differential voltage signal, as described in our previous work [6]. To calibrate for the transverse trapping force, a solution is flown (by moving the PZT) through a trapped particle within the chamber at a known velocity, and the drag force acting on the spherical microsphere is calculated from Stokes' law [6]. Outer hair cells were obtained from the cochlea of Albino guinea pigs within four hours of the animal sacrifice. Both cochlea were dissected from temporal bones, and placed into the normal extracellular solution (NES). After 5 min of incubation, OHCs were harvested using a microsyringe and placed in a poly-Dlysine coated sample chamber with 1.5 ml of NES.

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(a)

Human embryonic kidney (HEK) cells were used as models to investigate force generation in the absence of prestin. Cultured HEK cells were incubated into the sample chamber for 2 hours. After the cells became adherent to the bottom of the sample chamber, the culture medium was substituted with 1.5 ml of an NES solution.

(b)

3 Results Examples of tethering force measurements from a giant unilamellar lipid vesicle (GULV), a wildtype HEK cell, and an OHC under nonvoltage clamped conditions are shown in Figure 1. The magnitude of the peak value, (c) which represents the tether formation force, was the least (=40pN) for the GULV, and greatest (=120pN) for the OHC, with an intermediate value (=70pN) for the HEK cell. The larger value of the force required to pull tethers from the OHC reflects the influence of the underlying cortical lattice, which is absent Figure 1. Tethering force profiles for: (a) GULV, (b) wildtype HEK, and in the GULV and HEK cells. The steady state (c) OHC without voltage-clamping. force values showed a similar trend with the lowest value (=20pN) for the GULV, an intermediate value (~25pN) for the HEK cell, and the greatest value (=50pN) for the OHC, an indication of increased membrane tension with a progression in membrane-cytoskeleton complexity. We carried out experiments aimed at investigating the membrane mechanical response to high frequency sinusoidal electrical excitation (Figure 2). Using Fourier analysis of the temporal force measurements, we observed that both OHC and wildtype HEK cell membranes were capable of producing a force in response to lOOmV peak-to-peak electrical excitation at 3.1kHz. Note that the attenuations caused by the low-pass filtering of patch-clamp amplifier leave the possibility that membranes may respond to much higher electrical excitation frequencies. These results confirm the ability of membranes to generate mechanical force in response to changes in high frequency transmembrane potential even in the absence of specialized membrane proteins such as prestin, while the presence of prestin in the OHC enhances the amplitude of the generated force.

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When carrying out the experiments at various holding potentials, we discovered that the amplitude of force generation was voltage-dependent at both low and high frequency electrical excitations (Figure 3). Results (normalized to the response at zero holding potential) from membrane tethers formed from HEK cells (w=7) demonstrate a reduction by an approximate UBU f i l l

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factor of three in electrically-induced force generation as the membrane becomes increasingly depolarized at 1kHz sinusoidal excitation frequency (±20mV peak-to-peak). Results from membrane tethers formed from two OHCs show a similar trend at lower excitation frequency of 6Hz (±20mV peak-topeak). We also carried out experiments using wildtype HEK cells where membrane tethers were pulled to various lengths to effectively induce changes in the membrane tension, and measured the electrically-induced force generation in response to 1kHz sinusoidal

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excitation (±100mV) at holding potential of -40mV. Results demonstrate that force generation increases with changes in membrane tension as the tether length is increased (Figure 4).

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Early experiments have suggested that salicylate (Sal) induces extra negative surface potential to membranes [7], presumably by partitioning its benzene ring into the lipids. We observed a nearly two-fold decrease in the amplitude of the electrically-induced force generation by membrane tethers formed from wildtype HEK cells in the presence of lOmM extracellular Sal (Figure 5) when compared with the results in the absence of Sal (Figure 2).

Figure 5. Electrically-induced force generation from wildtype HEK membrane tethers in presence of lOmM Sal.

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4 Discussion Although the exact mechanism for our observed electrically-induced force generation by membranes is not known (let alone its enhancement by prestin), the process may be viewed as generation of mechanical stresses that result from changes in membrane surface area (piezoelectric phenomenon) [8,9], or curvature (flexoelectric phenomenon) [10-12]. Flexoelectricity may be attributed to changes in the lipid surface charge equilibrium associated with the charged head groups of phospholipids: curving the membrane causes an effective displacement of electric charges across the whole membrane (e.g., excess of negative charges over the expanded outer surface and deficiency over the compressed inner surface), which results in a large electric dipole (or more generally, multipoles) [13]. Converse flexoelectric effect may be attributed to the Lippman equation [14] that equates the surface charge to the negative derivative of the interfacial tension with respect to the electrostatic potential. The mobile charges within the lipid membranes are attracted to the charges supplied by an external voltage source. These mobile charges repel each other laterally, creating a local pressure and changing the net interfacial

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tension. In a membrane bilayer, it is this differential tension between the two interfaces that can induce curvature changes [15]. Therefore, membrane surface charge and membrane tension are two key physical properties whose effects on force generation need to be understood. The fact that our previous results [16] have not indicated a significant difference in the mechanical (as opposed to electromechanical) characteristics of membranes, and yet, we observe a decrease in force generation in presence of Sal in wildtype HEK cells, which lack prestin, tends to suggest that a motor-like mechanism may exist within the membrane itself whose origin may be traced to charge properties of the lipids. Our preliminary results with Sal are not only consistent with the hypothesis of Sal-induced inhibition of electromotility with Sal acting as a chloride competitor [17], but also provide the additional information that membranes themselves may possess a motor-like ability that is impaired by Sal. Recently, other investigators have reported that hair bundles of mammalian hair cells are capable of force production [18,19]. Our observation of electricallyinduced force generation by prestin-lacking membranes is consistent with these studies. We are motivated by our preliminary studies, which suggest an enhancement of a native membrane-based motor mechanism by prestin, to explore which particular structural features of prestin as well as its interaction with the membrane may contribute to the overall electrically-induced force generation. While it is reasonable to expect that presence of specific proteins within the membrane will alter the intrinsic membrane electrical polarization resulting from the charged lipid head groups, it remains unknown as to what prestin domains will induce the greatest effect. To address these issues, we plan to use prestin-transfected HEK cells, mutated prestins, and other protein members of the SLC26A family to which prestin belongs in our future studies. Acknowledgements This study was supported in part by a grant (R01-DC02775) from the National Institute of Deafness and Other Communication Disorder at the National Institutes of Health. References 1. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 1946. 2. Zheng, J., Shen, W., He, D.Z., Long, K.B., Madison, L.D., Dallos, P., 2000. Prestin is the motor protein of cochlear outer hair cells. Nature 405, 149-55. 3. Santos-Sacchi, J., Dilger, J.P., 1988. Whole cell currents and mechanical responses of isolated outer hair cells. Hear Res 35, 143-50.

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4. Ludwig, J., Oliver, D., Frank, G., Kleocker, N., Gummer, A.W., Fakler, B., 2001. Reciprocal electromechanical properties of rat prestin: the motor molecule from rat outer hair cells. Proc Natl Acad Sci U S A 98, 4178-83. 5. Qian, F., Ermilov, S., Murdock, D., Brownell, W.E., Anvari, B., 2004. Combining optical tweezers and patch clamp for studies of cell membrane electromechanics. Rev Sci Instrum 75, 2937-2942. 6. Ermilov, S., Anvari, B., 2004. Dynamic measurements of transverse optical trapping force in biological applications. Ann Biomed Eng 32, 1016-26. 7. McLaughlin, S., 1973. Salicylate and phospholipid bilayer membranes. Nature 243, 234-236. 8. Dong, X.X., Ospeck, M., Iwasa, K.H., 2002. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys J 82, 1254-9. 9. Spector, A.A., Jean, R.P., 2004. Modes and balance of energy in the piezoelectric cochlear outer hair cell wall. J Biomech Eng 126, 17-25. 10. Petrov, A.G., 2002. Flexoelectricity of model and living membranes. Biochim Biophys Acta 1561, 1-25. 11. Raphael, R.M., Popel, A.S., Brownell, W.E., 2000. A membrane bending model of outer hair cell electromotility. Biophys J 78, 2844-62. 12. Glassinger, E., Raphael, R. M., 2005. Theoretical analysis of membrane tether formation from outer hair cells. In: Nuttall, A.L. (Ed.), Auditory Mechanisms: Processes and Models. World Scientific, London. 13. Todorov, A.T., Petrov, A.G., Fendler, J.H., 1994. Flexoelectricity of charged and dipolar lipid membranes studies by stroboscopic interferometry. Langmuir 10, 2344-2350. 14. Brett, C.M.A., Brett, A.M.O., 1993. Electrochemistry principles, methods, and applications. Oxford Scientific Publications, Oxford. 15. Zhang, P.C, Akeleshian, A.K., Sachs, F., 2001. Voltage induced membrane movement. Nature 413, 428-432. 16. Ermilov, S., Brownell, W.E., Anvari, B., 2004. Effect of salicylate on outer hair cell plasma membrane viscoelasticity: studies using optical tweezers. In: Cartwright, A.N., (Ed.), Nanophotonics and Biomedical Applications, SPIE International Symposium on Biomedical Optics. SPIE, San Jose, CA. 5331, 136-142. 17. Oliver, D., He, D.Z., Kleocker, N., Ludwig, J., Schulte, U., Waldegger, S., Ruppersberg, J.P., Dallos, P., Fakler, B., 2001. Intracellular anions as the voltage sensor of prestin, the outer hair cell motor protein. Science 292, 2340-3. 18. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880-883. 19. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8, 149-155.

Ca z+ CHANGES THE FORCE SENSITIVITY OF THE HAIR-CELL TRANSDUCTION CHANNEL1 E. L. M. CHEUNG 2 AND D. P. COREY Howard Hughes Medical Institute and Department of Neurobiology, Harvard Medical School, Boston, MA 02115, USA E-mail: [email protected] The mechanically gated transduction channels of vertebrate hair cells tend to close in ~1 ms following their activation by hair bundle deflection. This fast adaptation is correlated with a quick negative movement of the bundle (a "twitch"), which can exert force and may mediate an active mechanical amplification of sound stimuli in hearing organs. We used an optical trap to deflect bullfrog hair bundles and to measure bundle movement while controlling Ca2+ entry with voltage clamp. The twitch elicited by repolarization of the cell varied with force applied to the bundle, going to zero where channels were all open or closed. The force dependence is quantitatively consistent with a model in which a Ca2+-bound channel requires ~3 pN more force to open, and rules out other models for the site of Ca2+ action.

1 Introduction The extraordinarily high sensitivity and sharp frequency tuning of vertebrate hearing require the presence of an active mechanical amplification, a process that apparently resides within the mechanosensitive hair cells themselves [1,2]. By selectively increasing the vibration of the basilar membrane on which hair cells ride, this "cochlear amplifier" contributes up to 50 dB of gain to the acoustic signal [3]. Two different mechanisms have been proposed to underlie the cochlear amplifier: a shortening of cochlear outer hair cells driven by depolarization ("electromotility") [4,5], and a quick negative movement of the hair cells' mechanosensitive stereocilia caused by Ca2+ entry through transduction channels ("fast adaptation") [6,7,8]. In fast adaptation, Ca2+ entering through transduction channels at the tips of stereocilia is thought to bind directly to the channels or to associated components of the transduction apparatus, thereby promoting channel closure and rapidly reducing the receptor current. When they close, the channels exert a small force on the filamentous linkages between stereocilia and move the bundle of stereocilia by a few nanometers (the "twitch") [6]. Bundles pushing back against the overlying tectorial membrane, if in phase with the stimulus, might then amplify the mechanical stimulus [9,10]. Since fast adaptation has been observed in a variety of species and hair cell organs, the hair bundle-based mechanism is attractive for non-mammalian hearing organs, which lack electromotility but have cochlear amplification qualitatively similar to that found in mammals [11]. This mechanism is also attractive for the mammalian cochlea: because fast adaptation is

2

This chapter is excerpted from a paper to be published in the Biophysical Journal Present address: Depts. of Biological Sciences and Applied Physics, Stanford University

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278 associated with ion entry through transduction channels rather than with the subsequent receptor potential, it might operate at higher speeds. Several Ca2+-dependent mechanisms for fast adaptation have been proposed: First, Ca2+ could bind directly to the transduction channel to stabilize the closed state and thereby shift the P0(F) relation [6,8]. Second, Ca2+ could bind to an intracellular elastic "reclosure element" in series with the channel, reducing its spring constant, and the reduced tension would allow channels to close [12]. Third, Ca2+ could bind to a "release element" in series with the channel so as to lengthen it by a fixed distance, releasing tension in an elastic element and again allowing closure [13]. To distinguish among these three potential mechanisms, we made simultaneous electrical and mechanical measurements of fast adaptation in single bullfrog hair cells. Receptor currents were recorded and Ca2+ entry was controlled using wholecell patch clamp techniques, while a gradient force optical trap was used to apply forces to hair bundles and to measure force- and Ca2+-dependent bundle movements. We found that fast adaptation is only consistent with a model in which Ca2+ directly promotes channel closure, and in which channels altered by Ca2+ binding require 3.4 + 0.8 pN more force to open. 2 Methods Physiology. Single hair cells were dissociated from the saccule of adult bullfrogs (Rana catesbeiana). The bath contained (in mM) 120 Na+, 2 K+, 5 Cs+, 4 Ca2+, 135 CI", 3 Dextrose, and 5 HEPES at pH= 7.27. In some experiments, external solution was exchanged with one containing 0.1 Ca2+, or with 0.1 Ca2+ and 0.2 mM gentamicin. Pipettes contained 105 Cs+, 3 Mg2+, 111 CI", 3 NaATP, 1 BAPTA, 5 HEPES, pH=7.25. Whole cell patch clamp recordings were made using conventional patch clamp techniques with acquisition and analysis programs written in Lab View 5.1. The acquisition program generated the voltage and twodimensional mechanical commands synchronously via two hardware-connected A/D boards. Optical trap. An optical trap was constructed using a Nd:YAG laser on an inverted microscope with a high-numerical-aperture microscope objective. The Nd:YAG beam was deflected with a two-dimensional acousto-optic deflection (AOD) system and bead movements were detected with a HeNe laser following the design of Visscher and Block [14]. Single latex beads (2.0 p.m) in external solution were trapped and calibrated, and then attached to the kinociliary bulb of a hair cell using the trap to press it against the bulb. The displacement of every bead was calibrated and recorded with step displacements of the trap prior to attaching it to the bundle. A gigaseal was then established. Care was taken to keep the pipette away from the detection beam path.

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3 Results 3.1 Movement of a hair bundle in response to force steps We dissociated hair cells from bullfrog sacculi, and used the whole-cell patch clamp method to control transmembrane voltage and record receptor current. Force steps were generated by step displacements of the infrared beam; their rise time was about 15 us, so the bundle-deflection risetime (200-400 us) was limited only by the viscous drag on the bead and bundle. Positive force steps, which deflect a bundle towards its kinocilium, elicited rapidly activating transduction currents which saturated with 100-150 nm bundle deflection (Fig. 1A). The activation curve (Fig. IB) was comparable to those measured with fast stimulators in bullfrog and turtle [6,8,15]. We also observed a typical gating compliance [6]. From fits to the current and the compliance in 7 cells, we found an average of 23 ± 3 channels, a gating spring stiffness of 0.75 mN/m and a gate swing of 2.5 ± 0.5 nm (channels at each end of the tip link, mean ± SE). 3.2 Movement evoked by depolarization By changing Ca2+ influx through open transduction channels and thus changing the forces produced by the fast and slow adaptation processes, voltage alone can produce movement of a hair bundle [16,17,18,10]. In response to a depolarizing voltage step, we found that a freestanding hair bundle moved in three distinct phases. The slowest phase occurred in tens of milliseconds and was negative-going; it is thought to be the mechanical correlate of slow adaptation and is attributed to the myosin-lc motor complex climbing up the actin cores of stereocilia [18,19,8,20]. The middle phase was positive-going and took place in a few milliseconds, the same timescale as fast adaptation; it is thought to be a voltageinduced twitch corresponding to the relaxation in tip link tension when channels open after Ca2+ unbinds from some intracellular element [21,15,10]. The fastest phase was a negative movement with depolarization, which we term the "flick." This movement was previously observed in turtle hair cells, where it was described as being linearly voltage-dependent and occurring as fast as the voltage clamp could depolarize the cell [21] The "flick:" a fast, voltage-dependent movement. We found that the flick is nonlinear with voltage, saturating at large positive potentials (data not shown). It is apparently not a Ca2+-dependent process, nor does it require any ion influx through transduction channels. On the other hand, the flick seems to require both intact and taut tip links, suggesting a voltage-dependent conformational change of some component of the transduction apparatus. The flick is not altered by force-dependent channel gating, although it might still involve a voltage-dependent conformational change of the channel.

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Figure 1. Mechanical and electrical responses to a family of force steps (A) Receptor current with two phases of adaptation. (B) Peak receptor current as a function of deflection. (C) Bundle movement with two phases of adaptation. The bundle movement corresponding to A showed a fast deflection followed by a slow relaxation for large deflections. For small positive deflections, an additional small and rapid negative movement occurred at the same timescale as the fast phase of adaptation (arrow). (D) Force vs. deflection; force measured at the peak of the receptor current. (E) Amplitudes of fast and slow adaptation with increasing deflection. The fast phase of I(X) shift (o) showed near-complete adaptation for small steps but declined for larger steps, whereas the slower phase (•) was negligible for small steps, and rose to -80% for larger steps. (F) Instantaneous stiffness of the bundle as a function of bundle deflection. The stiffness showed the characteristic dip near the center of the I(X) curve due to gating compliance.

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The "twitch:" a mechanical correlate of fast adaptation. We found that fast adaptation of the mechanosensitive current was slowed either by reducing external Ca2+ or by depolarizing the cell to reduce Ca2+ influx. Depolarizing the cell to -60 or -40 mV, which reduces Ca2+ influx through transduction channels, also slowed the twitch commensurately. Our observations support the idea [12,21,15] that the twitch is a mechanical correlate of fast adaptation and that it follows from Ca2+ entry through transduction channels. Next, we wanted to determine where Ca2+ acts to mediate this twitch. To measure in detail the mechanical correlates of Ca2+ action, we again controlled Ca2+ entry by changing the membrane potential but focused on the second phase of bundle movement (the twitch). For a depolarization to +60 mV, a freestanding bundle exhibited a negative, sub-millisecond flick, and a slower positive twitch (Fig. 2A). A repolarizing step back to -80 mV produced flick and twitch in the reverse directions. We measured the amplitude of the twitch following the flick (arrows, Fig. 2A). The "off twitch for depolarization (in which Ca2+ is expected to unbind) had the same magnitude as the "on" twitch for repolarization (Fig. 2B), suggesting that the twitch involves a reversible binding reaction with a fixed mechanical correlate. When we reduced Ca2+ in the external solution, reducing

281 fast adaptation in the receptor current, we reduced the voltage-induced twitch in both directions—further evidence that the voltage-induced twitch is generated by the same mechanism as the deflection-induced twitch (data not shown). 3.3 Predicting the force dependence of repolarization twitch To understand the twitch quantitatively, we first asked how Ca2+ binding would affect the position-force relation of a hair bundle. We began with a simplified mechanical model which treats the bundle as a stereocilia pivot spring (stiffness ks) in parallel with the transduction complex. The transduction channel is in series with an elastic gating spring (stiffness kg) and in series with the myosin motor mediating slow adaptation. This simple model can account for the gating compliance illustrated in Fig. IF and for slow adaptation. Ca2+ might act on any of these •. ••„ -30 ^ >»# elements to cause a movement of the V bundle. First, Ca2+ V * might bind to the transduction channel to change the relationship between force and open probability. Second, Ca2+ might bind to an internal elastic element that is the Figure 2. Movement produced by repolarization to allow Ca2+ influx, gating spring or in varying force bias on a hair bundle. The negative movement was largest series with it, to over the range where force activates the channels, (see text) change its stiffness. Finally, Ca2+ could bind to an internal element that changes conformation to lengthen slightly. With certain parameters, in particular if the gating swing is large and the gating spring is stiff, all three models can produce qualitatively similar negative bundle movements over some range of force steps. If the gating swing is small or the gating spring soft, however, only the first model can produce a twitch. For any parameters, the three models can clearly be distinguished if the twitch upon Ca2+ entry is measured over a range of applied force.

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3.4 Measuring the force dependence of the twitch We deflected bundles with a series of force steps while Ca2+ influx into the stereocilia was halted by a depolarization to +40 mV. After 6 ms, the cell was hyperpolarized to -120 mV to allow Ca2+ entry, and we measured the resulting movement (Fig. 2C). We measured bundle movement from the peak of the flick to the plateau of the twitch, but before much movement from slow adaptation had occurred (Fig. 2C, inset). These data were compared with predictions of the three different models. For each cell, the relevant parameters could be measured from data as in Fig. 1, leaving just one free parameter for fitting. In the third model (Axg), we could vary the change in gating spring setpoint upon Ca2+ binding. Fig. 2D shows the best fit, with Axg=-0.29 nm (a shortening with Ca2+), and fits with Axg at twice and half that value. In the second model (Akg), we varied the change in spring stiffness upon Ca2+ binding. Fig. 2E shows the best fit, with AKg=+35.1 uN/m (a stiffening with Ca2+) and twice and half that value. In the first (AP0), we could vary the shift of the P0(f) curve upon Ca2+ binding. Fig. 2F shows a fit with Af0=1.5 pN ( corresponding to lowered open probability with Ca2+). A similar fit to the voltage-dependent twitch was done for six other cells. In all seven cases the AP0 model fit the data well and the other two models did not. Finally, we can determine the effect of Ca2+ on channel sensitivity. The P0(F) curve shifted to the right due to Ca2+ binding, indicating that a single channel with Ca2+ bound requires 3.4 + 0.8 pN more force along the tip link axis to open. 4 Discussion It has long been recognized that Ca2+ entering through hair-cell transduction channels binds within nanometers to promote closure of the channel. Our measurements, tested by three models, strongly suggest how: that Ca2+ shifts the force dependence of activation such that 3-4 pN more force, equivalent to 1-2 kT, is needed to open a Ca2+-bound channel. It has been proposed that such a mechanism may mediate frequency tuning in auditory organs [6], and a model incorporating such a mechanism produces amplification of bundle movement for small stimuli of appropriate frequency [7]. Thus, understanding the site of Ca2+ action narrows the search for the cochlear amplifier in molecular terms. Because the amplifier exhibits tonotopic variation in frequency in most auditory organs, this also narrows the search for a variable element underlying tonotopy.

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Acknowledgments We thank Steven M. Block for advice on construction of the optical trap and Lynda Stevens for administrative assistance. Supported by NIDCD grant DC00304 (to DPC). DPC is an Investigator of the Howard Hughes Medical Institute. References 1. Dallos, P., Harris, D., 1978. Properties of auditory nerve responses in absence of outer hair cells. J Neurophysiol 41:365-383. 2. Brown, M.C., Nuttall, A.L., Masta, R.I., 1983. Intracellular recordings from cochlear inner hair cells: effects of stimulation of the crossed olivocochlear efferents. Science 222:69-72. 3. Overstreet, E.H., 3 rd , Temchin, A.N., Ruggero, M.A., 2002. Basilar membrane vibrations near the round window of the gerbil cochlea. J Assoc Res Otolaryngol 3:351-361. 4. Brownell, W.E., Bader, C.R., Bertrand, D., de Ribaupierre, Y., 1985. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227:194196. 5. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science 267:2006-2009. 6. Howard, J., Hudspeth, A.J., 1988. Compliance of the hair bundle associated with gating of mechanoelectrical transduction channels in the bullfrog's saccular hair cell. Neuron 1:189-199. 7. Choe, Y., Magnasco, M.O., Hudspeth, A.J., 1998. A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectricaltransduction channels. Proc Natl Acad Sci U S A 95:15321-15326. 8. Wu, Y.C., Ricci, A.J., Fettiplace, R., 1999. Two components of transducer adaptation in auditory hair cells. J Neurophysiol 82:2171-2181. 9. Hudspeth, A.J., Choe, Y., Mehta, A.D., Martin, P., 2000. Putting ion channels to work: mechanoelectrical transduction, adaptation, and amplification by hair cells. Proc Natl Acad Sci U S A . 97:11765-11772. 10. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat Neurosci 8:149-155. 11. Manley, G.A,. 2001. Evidence for an active process and a cochlear amplifier in nonmammals. J Neurophysiol 86:541-549. 12. Bozovic, D., Hudspeth, A. J., 2003. Hair-bundle movements elicited by transepithelial electrical stimulation of hair cells in the sacculus of the bullfrog. Proc Natl Acad Sci U S A 100:958-963. 13. Gillespie, P.G., Corey, D.P., 1997. Myosin and adaptation by hair cells. Neuron 19:955-958. 14. Visscher, K., Block, S.M., 1998. Versatile optical traps with feedback control. Methods Enzymol. 298:460-489.

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15. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2002. Mechanisms of active hair bundle motion in auditory hair cells. J Neurosci 22:44-52. 16. Crawford, A.C., Evans, M.G., Fettiplace, R., 1989. Activation and adaptation of transducer currents in turtle hair cells. J Physiol (Lond) 419:405-434. 17. Assad, J.A., Hacohen, N., Corey, D.P., 1989. Voltage dependence of adaptation and active bundle movement in bullfrog saccular hair cells. Proc. Nat. Acad. Sci., USA 86:2918-2922. 18. Assad, J.A., Corey, D.P., 1992. An active motor model for adaptation by vertebrate hair cells. J. Neurosci. 12:3291-3309. 19. Gillespie, P.G., Wagner, M.C., Hudspeth, A. J., 1993. Identification of a 120 kd hair-bundle myosin located near stereociliary tips. Neuron 11:581-594. 20. Holt, J.R., Gillespie, S.K., Provance, D.W., Shah, K., Shokat, K.M., Corey, D.P., Mercer, J.A., Gillespie, P.G., 2002. A chemical-genetic strategy implicates myosin-lc in adaptation by hair cells. Cell 108:371-381. 21. Ricci, A.J., Crawford, A.C., Fettiplace, R., 2000. Active hair bundle motion linked to fast transducer adaptation in auditory hair cells. J Neurosci 20:7131-7142. 22. Benser, M.E., Marquis, R.E., Hudspeth, A.J., 1996. Rapid, active hair bundle movements in hair cells from the bullfrog's sacculus. J Neurosci 16:56295643. Comments and Discussion Brownell: I have two questions related to the fast, voltage dependent bundle "flick". 1) We have demonstrated at this meeting that membranes generate electromechanical force even in the absence of specialized proteins such as prestin (Anvari et al.). This force, like the flick, is greatest for hyperpolarizing potentials and becomes smaller as the holding potential is depolarized. We have not yet tested the calcium dependence of prestin free tethers but we know calcium is not required for outer hair cell electromotility. We have previously calculated that a change in membrane curvature can quantitatively account for the length changes observed outer hair cell electromotility with membrane depolarization resulting in a decrease in the radius of curvature (Raphael et al., 2000). If stereocilia membranes were to undergo comparable depolarization induced reductions in radius, the cumulative effect would be to move the bundle in the negative direction. Given the similarities, can you identify a compelling reason why electromechanical force generated by the stereocilia membrane might not contribute to the flick? 2) At the risk of answering my own question I wonder if you have looked at the effect of salicylate on the flick? If a membrane based electromechanical force were responsible we would expect to see a reduction in flick magnitude with increasing salicylate concentrations. Answer: An intriguing feature of the flick movement is that it requires taut tip links. The flick is abolished by cutting the tip links with BAPTA, or by negative

285 bundles deflections that would relax the tip links. Consequently, we should look for a mechanism that changes tip-link tension. In the membrane curvature model, depolarization increases curvature. If stereocilia have wavy membranes (and good rapid-freeze deep-etch images suggest they don't; Kachar et al., 2000), then depolarization might cause the membrane to tighten around the actin cores of stereocilia, pushing fluid into the cell body. If the actin cores cannot resist the tightening force, the stereocilia might shorten. However we might expect that stereocilia would shorten proportionally, so that at the level of a tip link the taller stereocilium of a pair would shorten by the same amount as the shorter of a pair, producing no change in tip-link tension. Thus it seems unlikely that membrane curvature could produce the flick movement. A way to test it would be to try salicylate, which we have not done.

HAIR BUNDLE MECHANICS AT HIGH FREQUENCIES: A TEST OF SERIES OR PARALLEL TRANSDUCTION K.D. KARAVITAKI AND D.P. COREY Department of Neurobiology and Howard Hughes Medical Institute, Harvard Medical School, Boston, Massachusetts 02115, US E-mail: [email protected] Propagation of stimuli across the stereocilia within a hair bundle affects the gating of transduction channels. Tip links and lateral links are the two most probable candidates in providing the mechanical connection between the stereocilia. To distinguish between the two we measured the movement of individual stereocilia when pulling on the tallest stereocilium of a bundle. Hair cells were isolated and their hair bundles were displaced using a glass pipette attached to the kinocilium and driven by a piezoelectric bimorph. The stimuli were sinusoids with frequencies at 20 Hz and 700 Hz. The motion of the bundle was visualized using stroboscopic video microscopy and was quantified using cross correlation methods. Our data suggest that the bundle moves as a unit and that adjacent stereocilia bend at their bases and touch at their tips. We argue that this motion is consistent with the lateral links being involved in the propagation of stimuli across the bundle and with transduction channels being mechanically in parallel.

1 Introduction When the tip of a hair bundle is deflected by the force of a sensory stimulus, the stereocilia move as a unit and produce a shearing displacement between adjacent tips (reviewed in [1]). The resulting stimulus could be applied to transduction channels in two different ways: First, if tip links provide the main connection between stereocilia, then the tallest stereocilium of a column pulls on the next, which pulls on the next. The transduction channels are mechanically in series, and the opening of one channel reduces the force on others of the series (negative cooperativity). Second, if stereocilia are primarily held together by lateral links, then transduction channels are mechanically in parallel. The opening of one channel increases force on other channels, making them more likely to open (positive cooperativity). How the opening and Ca2+ -dependent closing of transduction channels affects cochlear mechanics depends critically on which model, or how much of each model, dominates the mechanics. To distinguish beteween these models we measured the movement of individual stereocilia when pulling on the kinocillium of a bundle using low and high frequency stimuli. Preliminary data show that the hair bundle moves as a unit and that individual stereocilia do not bend or splay during stimulation. The implications from such findings are discussed.

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287 2 Methods Isolated hair cells from the bullfrog sacculus were dissociated as described in Assad et al. [2]. Briefly, sacculi were surgically exposed and bathed for about 14-15 min (depending on the size of the frog) in oxygenated perilymph-like solution (120 mM NaCl, 2 mM KCl, 0.1 mM CaCl2, 3 mM Dextrose, 5 mM Hepes, pH -7.3) containing 1 mM EGTA and ImM MgCl2 used to lower the free Ca2+ concentration. Sacculi were subsequently removed from the frog and dissected to remove the otoconia from their apical surface. The otolithic membrane was removed after treating the sacculi with 50 \xglml protease XXIV(Sigma Chemicals) for 22 min. Hair cells were flicked out of the sacculus and allowed to settle onto a petri dish with a clean glass bottom containing the oxygenated perilymph-like solution. We used cells that had settled on their sides so that we could image their hair bundles along their excitation axis. The hair bundles were displaced using a glass pipette attached by suction to the kinocilium and driven by a piezoelectric bimorph. The stimuli were sinusoids with frequencies at 20 Hz and 700 Hz and peak amplitude ranging from 250-300 nm. Hair cells were visualized with a 63x water immersion objective with an additional 5x magnification and modified DIC optics. The resolution of the images was about 30nm/pixel. Illumination was via a high power light emmiting diode (LED) (Luxeon, 5-Watt Star, A.p ~ 505 nm) positioned onto the field diaphragm. A CCD camera (Hamamatsu, C2400) was mounted on the phototube of the microscope (Zeiss, Axioskop) and was connected to an image processor (Hamamatsu, Argus). Hair bundle motion was visualized by strobing the LED at eight equally spaced phases during the stimulus period. Acquisition programs were written in LabView 6.1 (National Instruments) and generated the voltages that controlled the bimorph and the current source driving the LED, via a National Instruments A/D board. Resulting images (Fig. 1A) were used to create animations of the observed motion. Images were interpolated and high passed filtered. Features of interest (like the edge of individual stereocilia) were selected (Fig. IB) and cross correlation metheods were used to quantify their motion. 3 Results 3.1 Stereocilia motion is sinusoidal and varies with height relative to the base In Figure 2 we plot the timecourse of displacement of the tallest stereocilium in the focal plane at different heights along its length for a 20 Hz stimulus frequency. The magnitude of the displacement increased with height relative to the insertion point of the stereocilium. This trend was the same for the 700 Hz stimulus. For each displacement we also show the resulting fitted sine waveform calculated using the magnitude of the primary frequency component at 20 Hz. We will subsequently use the magnitude of the fitted waveforms to understand the motion of the stereocilia.

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Figure 1. (A) Hair bundle image showing the glass probe attached to the kinocilium. Scale bar: 2 urn (B) Same image as in (A), high pass filtered, showing the extractions of interest. Extractions bl-b9 were used to correct for drift and rocking of the bundle while stimulation. The dots at the base of each stereocilium indicate the estimated pivot points. Figure 2. Displacement of the tallest stereocilium at 20 Hz.. Symbols result from our correlation analysis while the corresponding lines result from fitting the data points with a sine wave. Different symbols correspond to extractions from different heights along the bundle as indicated in Figure 1.

3.2 Stereocilia displacement is proportional to their height To understand the displacement profile of each stereocilium we plotted the Time (msec) magnitude of motion at different heights relative to its insertion point (Fig. 3). At each point along the length of the stereocilium the displacement was proportional to the height and was fitted well with a straight line. Results were similar for different stereocilia within the hair bundle for both stimulus frequencies. Within experimental error, stereocilia move as rigid rods, pivoting at their bases, even at higher frequency.

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Figure 3. Peak displacement of individual stereocilia measured at different heights above their pivot points. Linear fits are shown for each set of data. Top row 20 Hz stimulus, bottom row 700 Hz stimulus. All data are from the bundle shown in Figure 1.

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3.3 Displacement of adjacent stereocilia, at the same height, is similar We plotted the displacement magnitude of adjacent stereocilia and observed that, each moved by the same amount when measured at the same height (Fig. 4). For both stimulus frequencies the displacement magnitude of short stereocilia had a maximum deviation of about 25nm relative to the tallest stereocilium measured along the same height.

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We have used isolated hair cells from the bullfrog sacculus to understand the motion of the hair bundle in response to low and high frequency sinusoidal stimuli. We recorded from cells within 2.5 hours following animal decapitation. Cells that had any of the: swollen soma, broken stereocilia, missing kinocillia were not used. Although the stiffness of the hair bundles were not measured in these experiments,

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other investigators have shown that similar enzymatic protocols preserved the stiffness of the bundle within 10% of its original value [3]. We also expect that due to our enzymatic treatment ankle links will be absent in our hair bundles [4, 5, 6]. Our preliminary data show that the magnitude of stereocilia displacement is proportional to their height for both low and high stimulus frequencies. The stereocilia appear to move as rigid rods that pivot at their insertion points (pivot points). Previous investigators have shown that hair bundle stiffness decreases as the inverse square of the distance relative to its pivot point [7, 8]. Such stiffness profile is consistent with the stereocilia moving as rigid rods that pivot at their insertion point. Similar results have been obtained by Corey et al. [9] using very low frequency stimuli. Recently, Cotton and Grant [10, 11, 12] suggested that different stereocilia within the same hair bundle move differently depending on their location relative to the kinociliary axis of symmetry. Our experiments so far have not shown such differences. Displacement of adjacent stereocilia is similar when measured at the same height, and there is no evidence that the bundle is splaying during our stimuli. Corey et al. [9] used a simple geometrical model of the hair bundle, and assuming that individual stereocilia bend only at their insertion point and that they touch at their tips found that the front and the back edge of the hair bundle move the same distance when measured at the same height. They also demonstrated the same result experimentally using low frequency stimuli. Similar modeling data have been obtained by Jacobs and Hudspeth [5]. Our experimental data combined with the above mentioned modeling studies appear to support the idea that the bundle moves as a unit and that adjacent stereocilia bend at their bases and touch at their tips. Our data suggest that when the hair bundle from the bullfrog saculus is deflected, all the stereocilia within the bundle receive the same stimulus. If tip links were to provide the main connection between stereocilia the shortest stereocilium would be deflected by a smaller amount due to the serial opening of the transduction channels. On the other hand lateral links connecting adjacent rows of stereocilia appear more likely to effectively propagate the stimulus forces across the hair bundle. The involvement of lateral links in the propagation of the stimulus within a bundle has been previously hypothesized [1, 5, 13, 14]. If that is the case then transduction channels appear to be mechanically in parallel resulting in positive cooperativity which might be required to explain negative hair bundle stiffness [15]. Acknowledgments This work was supported by the Howard Hughes Medical Institute (HHMI). D.P.C. is an investigator and K.D.K. is a research associate of the HHMI.

291 References 1. Howard, J., Roberts, W.M., Hudspeth, A.J., 1988. Mechanoelectrical transduction by hair cells. Ann. Rev. Biophys. Chem. 17, 99-124. 2. Assad, J.A., Shepherd, G.M.G., Corey, D.P., 1991. Tip-link integrity and mechanical transduction in vertebrate hair cells. Neuron 7, 985-994. 3. Bashtanov, M. E., Goodyear, R.J., Richardson, G.P., Russell, I.J., 2004. The mechanical properties of chick (Gallus domesticus) sensory hair bundles: relative contributions of structures sensitive to calcium chelation and subilisin treatment. J. Phyiol. 559, 287-299. 4. Hudspeth, A.J., Corey, D.P., 1977. Sensitivity, polarity, and conductance change in the response of vertebrate hair cells to controlled mechanical stimuli. Proc. Natl. Acad. Sci. USA. 74, 2407-2411. 5. Jacobs, R.A., Hudspeth, A.J., 1990. Ultrastructural correlates of mechanoelectrical transduction in hair cells of the bullfrog's internal ear. Cold Spring Harbor Symp. Quant. Biol. 55, 547-561. 6. Goodyear, R.J., Marcotti, W., Kros, C.J., Richardson, G.P., 2005. Development and properties of stereociliary link types in hair cells of the mouse cochlea. J. Comp. Neurol. 485, 75-85. 7. Crawford, A.C., Fettiplace, R., 1985. The mechanical properties of ciliary bundles of turtle cochlear hair cells. J. Physiol. 364, 359-379. 8. Howard, J., Ashmore, J.F.,1986. Stiffness of sensory hair bundles in the sacculus of the frog. Hear. Res. 23, 93-104. 9. Corey, D.P., Hacohen, N., Huang, P.L., Assad, A.J.,1989. Hair cell stereocilia bend at their bases and touch at their tips. Soc. Neurosci. Abstr. 15,208. 10. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: I. Single stereocilium. Hear. Res. 197, 96-104. 11. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: II. Simplified bundle models. Hear. Res. 197, 105-111. 12. Cotton, J., Grant, W., 2004. Computational models of hair cell bundle mechanics: III. 3-D utricular bundles. Hear. Res. 197, 112-130. 13. Pickles, J.O., Comis, S.D., Osborne, M.P., 1984. Cross-links between stereocilia in the guinea pig organ of Corti, and their possible relation to sensory transduction. Hear. Res. 15, 103-112. 14. Pickles, J. O., 1993. A model for the mechanics of the stereociliar bundle on acousticolateral hair cells. Hear. Res. 68, 159-172. 15. Iwasa, K.H., Ehrenstein, G., 2002. Cooperative interaction as the physical basis of the negative stiffness in hair cell stereocilia. J. Acoust. Soc. Am. I l l , 2208-2212. Also see Erratum on J. Acoust. Soc. Am. 112, 2193.

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Comments and Discussion Aranyosi: You showed that disassociating the tip links with BAPTA had no effect on the lack of splay of hair bundles, implying that the side and/or ankle links hold the bundle together. Measurements from Hudspeth's group, among others, show that the tip links contribute significantly to the overall stiffness of the hair bundle, implying that bundle deflections are resisted primarily by the tip links. How do you reconcile these two observations? Answer: This question illuminates an interesting dichotomy between stiffness to bundle deflections and stiffness that holds the bundle together. We found that stereocilia don't separate by more than a few nanometers when deflected over the full activation range, suggesting that side links provide considerable stiffness to prevent stereocilia separation. At the same time, they allow relative shear of stereocilia tips over many nanometers (20 nm over the activation range and more than 200 nm for some of the largest deflections we gave). Thus the side links mediate a kind of sliding adhesion that prevents separation of stereocilia membranes but allows them to slide relative to one another. Side links therefore don't resist the deflection of stereocilia and don't contribute to deflection stiffness. Deflection stiffness in our measurements is contributed in roughly equal measure by the gating springs and the pivot stiffness of stereocilia. In chick hair cells (Bashtanov et al., 2004) the shaft connectors also contribute significantly to deflection stiffness.

HAIR CELL TRANSDUCER CHANNEL PROPERTIES AND ACCURACY OF COCHLEAR SIGNAL-PROCESSING C. J.W. MEULENBERG AND S. M. VAN NETTEN Department

of Neurobiophysics, University of Groningen, Nijenborgh 4, 9747 AG, Groningen, The Netherlands E-mail: c.j. w. meulenberg@rug. nl s.m. van. netten@rug. nl

Mechanically activated transducer channels in cochlear outer hair cells (OHC's) transduce sound encoded mechanical signals into electrical signals. Entry of extracellular Ca2+ through these channels modulates transduction by reducing their open probability, a phenomenon called adaptation [1]. Analysis of the mechanical and electrical characteristics of the transducer channels in OHC's has shown that the transducer channel's open probability can be adequately described by a differentially activating two-state model [2], Also a direct relationship was demonstrated between the gating spring stiffness (Ks) and the accuracy (amia = 2kT/[Ks-D~\ = 5.4 nm, where D is the distance between the engaging positions of the closed and open conformational state) with which hair bundle position can be detected as a result of intrinsic channel stochastics. In combination with an assumed Ca2+-dependent gating spring stiffness [e.g. 3], we predict on the basis of the two-state model that at endolymphatic Ca2+ concentrations (~ 20 uM) an improved accuracy (CT„,;„ ~ 3 nm) can be attained at the equilibrium position of the hair bundle.

Experimental data on mouse OHC's recorded in 1.3 mM extracellular Ca2+ (Figure 1, squares) were taken as reference and a differentially activating two-state model was used to generate fits (Figure 1, solid lines) [2]. Decreasing the energy gap, As, with 1.5 kT, shifts the current-displacement curve in the negative direction, which is associated with lowering the extracellular Ca2+ concentration (dashed lines A, B). It does not affect the operational range, nor the accuracy. With a As of 5 kT opposite effects are observed (dotted lines A, B). In rat OHC's, altering the extracellular Ca2+ concentration from 1.5 mM to the endolymphatic Ca2+ concentration (~ 20 uM) shifts the operational range about 20% in the negative direction (atpoptn = 0.5) and causes a doubling of the hair bundle's passive stiffness, which could possibly be due to an increased Ks [3]. Modelling an almost doubled Ks (12.9 uN/m; dashed line C, D) we observe a similar relative shift, a decrease of the (instantaneous) operational range and an improved accuracy, amin, to about 3 nm at the hair bundle's resting position (X= 0). Decreasing Ks to 5 uN/m (dotted lines C, D) shifts the current-displacement curve in the positive direction, broadens the operational range and degrades the accuracy. Under normal endolymph conditions a Ca2+-dependent Ks might therefore cause a hair cell to have an optimal accuracy at the hair bundle's resting position. The associated limited operational range may be effectively extended by the dynamical effects of Ca2+-dependent adaptation, so as to combine a suitable operational range with a high signal-to-noise ratio of cochlear signal processing.

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Figure 1. Hair cell transducer current (A, C) and accuracy (B, D) as function of hair-bundle displacement (X), together with modelled effects of changing the (deactivated) state energy difference (Ae) and the gating spring stiffness (Ks). Fits of the two-state gating-spring model (solid lines) to measured data (squares) are taken from [2] with Ks = 7.2 (xN/m; As= 3.5 kT; Ncb = 66; X0 = -33 nm; D = 26 nm; so that Omin = 5.4 nm. A and B show the effects of changing As; dashed line As =2 kT, dotted line As= 5 kT. C and D show the effects of Ks; dashed line Ks~ 12.9 nN/m, dotted line Ks = 5 |iN/m.

References 1. Eatock, R.A., Corey, D.P., and Hudspeth, A.J., 1987. Adaptation of mechanoelectrical transduction in hair cells of the bullfrog's sacculus. J. Neurosci. 7,2821-2836. 2. van Netten, S.M., Dinklo, T., Marcotti, W., Kros, C.J., 2003. Channel gating forces govern accuracy of mechano-electrical transduction in hair cells. Proc. Natl. Acad. Sci. USA. 100, 15510-15515. 3. Kennedy, H.J., Crawford, A.C., Fertiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature 433, 880-883.

Ca2+ PERMEABILITY OF THE HAIR BUNDLE OF THE MAMMALIAN COCHLEA C. HARASZTOSI, B. MTJLLER AND A. W. GUMMER Department Otolaryngology, University Tuebingen, Elfriede-Aulhorn-Strasse 5, 72076 Tuebingen, Germany, E-mail: csaba.harasztosi@ uni-tuebingen.de Although experimental and theoretical information about intracellular concentration of Ca2+ in the stereocilia of lower vertebrates is available, there is only few information about mammalian systems. The aim of the present experiments was to investigate the origin of mechanically evoked Ca2+ signals in the hair bundle of outer hair cells (OHC).

1 Methods OHCs were mechanically isolated from the adult guinea-pig cochlea. Ca2+ transients were evoked by deflection of the stereocilia using a fluid-jet stimulator. To facilitate Ca2+ entry into the hair bundle, Ca2+ concentration in the fluid-jet solution was 4 mM (extracellular 100 uM). Intracellular Ca2+ changes were monitored using the acetoxymethyl ester form of the fluo-3 dye and the fluorescence signals were detected by a confocal laser scanning microscope. 2 Results 2.1 Average Ca + signals in the hair bundle The time course of the onset of the average intracellular Ca2+ transient in the hair bundle was exponential; the average time constant (T) was 0.26±0.19 s. Application of the open transduction-channel blocker dihydrostreptomycin (DHSM, 100 \\M) caused the speed of the Ca2+ elevation to become significantly slower, x=2.14±1.36 s; this change was partially reversible (x=0.75±0.24 s) after washout. Application of DHSM did not influence the steady-state amplitude of the average Ca2+ transients. The decay of the intracellular Ca2+ signal after removal of the fluidjet stimulus was also exponential; the time constant was 3.15±1.31 s. 2.2 Local effect of DHSM The local effect of DHSM can be seen in Fig. 1 as a decreased slope of the onset of the signal. The first column demonstrates the average intracellular Ca2+ transient while the second indicates the local effect of DHSM. In the DHSM row, the time delay between the basal and apical signals was eliminated by the drug. This effect of DHSM showed reversibility, plotted in the third row, labeled "Washout".

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Figure 1. In the schematic drawing of the stereocilia, the rectangles indicate the regions of interest (ROI), the area where the signal was collected for analysis. In the left column, ROI was chosen for the whole hair bundle, while in the right column the apical S»i» and basal signals were separated. In the DHSM row of the right column, the time delay between the basal and apical signals was eliminated by the ^ a S t y e a drug.

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3 Discussion An interpretation of the observed fluorescence pattern is that Ca2+ can enter stereocilia through the transduction channels and also through the membrane by a transduction channel independent pathway(s). The result of the DHSM experiment is that Ca2+ entry through transduction channels is faster than through other pathways. The observation that the fluorescence started to increase first at the tip region of the middle row of stereocilia implies that Ca2+ entered first through transduction channels, which are supposed to be in that location. The result that DHSM preferentially blocked Ca2+ entry in the middle of the hair bundle, also supports the hypothesis that transduction channels are located far from the tip of the tallest stereocilia. Acknowledgments We would like to thank Serena Preyer for helpful discussions and Anne Seeger for her technical support.

IV. Emissions

COMPARATIVE MECHANISMS OF AUDITORY FUNCTION: GROUND SOUND DETECTION BY GOLDEN MOLES P. M. NARINS Depts. of Physiological Science and Ecology & Evolutionary Biology, UCLA, Los Angeles CA 90095, USA E-mail: pnarins&Mcla. edu The Namib Desert golden mole, Eremitalpa granti namibensis, is a nocturnal, surfaceforaging mammal, possessing a massively hypertrophied malleus which presumably confers low-frequency, substrate-vibration sensitivity through inertial bone conduction. When foraging, E. g. namibensis typically moves between sand mounds topped with dune grass which contain most of the living biomass in the Namib Desert. We have observed that foraging trail segments between visited mounds appear remarkably straight, suggesting sensory-guided foraging behavior. Foraging trails are punctuated with characteristic sand disturbances in which the animal "head dips" under the sand. The function of this behavior is not known but it is thought that it may be used to obtain a seismic "fix" on the next mound to be visited. Geophone recordings on the mounds reveal spectral peaks centered at ca. 300 Hz ca. 15 dB greater in amplitude than those from the flats. Seismic playback experiments suggest that in the absence of olfactory cues, golden moles are able to locate food sources solely using vibrations generated by the wind blowing the dune grass on the mounds. Morever, the mallei of the golden moles in the genera Chrysochloris and Eremitalpa are massively hypertrophied. In fact, out of the 117 species for which data are available, these golden moles have the greatest ossicular mass relative to body size (Mason, 2001). Laser Doppler vibrometric measurements of the malleus head in response to seismic stimuli reveals peak sensitivity to frequencies below 300 Hz. Functionally, they appear to be low-frequency specialists, and it is likely that golden moles hear through substrate conduction (Supported by NIH Grant DC00222).

1 Introduction Golden moles are blind, noctural, surfacing-foraging mammals that live in subSaharan Africa south of a line from Uganda in the east to Cameroon in the west. Mitochondrial DNA analysis has recently placed the golden moles (family Chrysochloridae) in the Afrotheria clade, a group composed of seemingly disparate taxa that share a common evolutionary origin in Africa [1], although this view has been recently challenged [2]. Mason and others [3-6] have noted that some genera of golden moles possess extraordinarily hypertrophied mallei. Fielden and her colleagues discovered that these small, blind animals hunt at night for small insects, spiders and even lizards located in sand mounds or hummocks topped with dune grass [7]. Challenged to produce an adaptive explanation for their remarkable ossicles, we (a) initiated an investigation of the foraging behavior of these animals in the Namib Desert [8], (b) completed a seismic playback study in the field to determine the cues necessary to attract the moles [9], (c) are involved in a modeling effort to understand the

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coupling of the ear to the skull [6, 10], and see Mason [11-13], and (d) are carrying out a functional study of the ossicular motion in response to seismic stimuli [10,16]. In this paper, I review the present state of our knowledge about the use of seismic cues by the golden mole in foraging, and relate this to the functional anatomy of its highly specialized middle ear. Models have been proposed that suggest that the golden mole middle ear may function as an inertial motion detector. Evidence for this view is presented as well as preliminary measurements of the modes of ossicular vibration in response to substrate-borne vibration. 2 Field Recordings 2.1 Seismic measurements Foraging trails of individual golden moles were examined over as long a distance as possible in the linear dune fields of the Namib Desert in Gobabeb, Namibia. Along the trails, the moles visit mounds or hummocks which are located at the base of the slip-face of the giant linear dunes. These mounds are topped with live dune grass; they have been shown to contain 99% of the living biomass in the Namib Desert [7], and represent rich food sources for the golden moles. Foraging trails consisted of a) footprints, b) small depressions indicating head-dipping behavior in which the animal stops forward motion and buries his head beneath the sand, and c) extended disturbances in the sand indicating sandswimming in which the animal moves just beneath the surface of the sand. All trail features were mapped including the locations of head-dipping and sandswimming events. We used calibrated geophones to measure substrate velocities of both mounds and the desert flats; from these, power spectra were calculated. To obtain relaible geophone readings, it was necessary to couple the geophones physically and firmly to the substrate; combining the output of an array of three orthogonally-oriented geophones provided the resulting velocity vector at the surface. 2.2 Results We found that encounters with food patches were statistically non-random, suggesting that foraging in this species is sensory-guided. Peak velocity amplitude of a typical hummock is -5 dB re 1 \ivnls at a frequency of ca. 300 Hz, whereas the peak velocity amplitudes of the desert flat measured far from any hummock are typically 15-20 dB lower than the hummocks, and at a frequency of ca. 120 Hz (Fig. 1). Peak hummock velocities were significantly above the noise floor at distances on the order of 20m, longer than any inter-hummock path segment we observed for any mole. This suggests their potential use by the moles as seismic beacons for localizing concentrated prey sources. Geophone measurements made directly on or near the mounds revealed seismic signals emanating from the movements of the prey items themselves, principally

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dune termites. These signals are typically short-duration, click-like pulses exhibiting broadband power spectra with spectral peaks below 50 Hz. Thus, foraging by the Namib Desert golden mole involves a two-stage seismic detection system in which the first stage consists of localizing prey-containing mounds at relatively long distances (approaching 20 m), whereas the second stage involves detection of prey movements near the mound.

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Distances between adjacent head-dips were significantly smaller within 0.5m of a mound than they were at >0.5m from a mound (p < 0.05, Mest, «=6) [8]. These results may be considered the spatial analog of the hunting bat's terminal buzz in which echolocation pulses are produced at very high rates as the bat closes in on its prey, presumably to increase temporal resolution in the last phases of prey capture.

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3 Field Playback Studies 3.1 Setup To determine the cues that are used by golden moles to localize the hummocks, we hypothesized that the wind blowing the dune grass sets the hummocks into resonance, producing the tone-like vibrations that travel as surface waves detectable by our geophones. To test this directly, we made gcophone recordings at the base of a hummock of the substrate vibrations made by wind blowing the dune grass. We then buried eight seismic sources (Clarke Synthesis transducers, model TST 229 F4 ABS) in a circle of radius 5m, and activated three adjacent transducers with the geophone recordings. We placed one geophone at the center of the arena and adjusted the playback level of each source to be ca. 0.0001 cm/s (rms vertical velocity) at the geophone. In addition, we plotted the surface velocity values at 32 points to visualize the vibrational field within the arena (Fig. 2). Once the sources were activated, we placed a golden mole in the center of the arena, released it and observed its sandswimming trajectory as it moved toward the edge of the arena (»=9). Motion trajectories were mapped and the exit points for each mole tested were noted. Between trials, the sand in and around the arena was raked thoroughly and swept smooth to eliminate residual olfactory and tactile cues.

Figure 2. Schematic view of the circular test arena (radius: 5m) for seismic playback experiments in the Namib Desert. Three of the eight vibration transducers (2,3,4) are simultaneously activated with a seismic recording of wind blowing the dune grass (see text); the remaining five transducers arc silent. Individual mole trajectories are shown. The linear scale bar indicates velocities in multiples of 0.05 mm/s; the numbers in the arena indicate contour lines with the same units.

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3.2 Results All nine sandswimming moles exited the hemi-arena containing the active sources (Fig. 2). Moreover, the two surface-walking moles were not attracted to the active seismic sources. These preliminary results support the hypothesis that in the absence of olfactory cues, these blind, nocturnal golden moles use seismic signals generated by the wind moving the dune grass-hummock complex to home in on the hummocks, and thus to locate food sources [9, 14]. 4 Modeling Efforts 4.1 Background When the log of the malleus plus incus mass is plotted against log body mass for 49 mammalian species, the ossicles that lie most significantly above the regression line through the data points are those of several golden mole species [5]. The hypertrophied mallei of the golden moles are extraordinary not only for their increased mass, but also for the displacement of the ossicular center of mass from the rotatory axis (Fig. 3a). This latter feature results in the malleus acting as an inertial motion sensor. 4.2 Model and Interpretation A simple mechanical model of the golden mole middle ear is shown in Fig. 3b. This model exhibits the first order properties of the Chrysochloris ossicles shown in Fig. 3a. The large mass of the ossicles, together with their relatively loose ligamentar suspension, is expected to bias the peak mechanical response of the malleus toward low frequencies [5], a prediction borne out by recent measurements [10]. It is of note that the model in Fig. 3b is also an excellent approximation of a mechanical analogy for a velocity sensor, i.e., a geophone. In this context, headdipping behavior may be viewed as a means of coupling the animal's skull to the substrate to ensure proper operation of its geophone-like middle ears.

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Rotary axis

Figure 3. Inertial motion detection in the Cape Golden Mole, Chrysochloris asiatica. See text for explanation, (a) Ossicles of Chrysochloris (b) Mechanical analogy. (After [12], Reprinted with permission.)

5 Seismic Response of the Middle Ear Chrysochloris has a distinctly club-shaped malleus (Fig. 3a, 4a); this is likely an adaptation for sensing both airborne and substrate-borne stimuli [10,16]. 5.1 Methods The skull of Chrysochloris was attached to a metal plate with acrylic resin. The superior portion of the malleus head was exposed for either vertical or lateral measurements with the scanning laser Doppler vibrometer (SLDV/Polytec PSV300). For seismic stimulation the metal plate was driven either vertically (figure not shown) or laterally (Fig. 4b) by a vibration exciter (B&K 4809). The stimulus was a periodic chirp of vibration sweeping from 15-600 Hz with a calibrated amplitude of 100 (im/s (±20%) over this frequency range. The 20-40 points measured by the SLDV were restricted to the distal portion of the malleus head (Fig. 4a).

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Figure 4. (a) Schematic diagram of middle ear ossicles of C. asialica. The grid indicates the points scanned during the motion analysis. APM = anterior process of the malleus, LPI = lenticular process of the incus, SPI = short process of the incus, (b) head of C. asialica mounted on metal plate being driven laterally; motion visualization with SLDV showing z-axis translation, (c) LPI motion reconstruction using each component separately (e.g., Iz, tox, coy) or all components together (all).

Motion reconstruction was carried for the lenticular process of the incus (Fig. 4c). For lateral stimulation, the malleus showed a resonance peak between 100-200 Hz. Although the rotational motions were greatest around the x-axis, followed by the yaxis, the motion at the LPI is best approximated by the translational component, ft. 6 Discussion The results of this ongoing study are consistent with the hypothesis that golden moles use a two-stage seismic detection system to locate prey in the Namib Desert. In the first stage, the animal localizes the sand mounds topped with dune grass by sensing at a distance the vibrations generated by the wind-blown dune grass. In the second stage, the substrate vibrations generated by prey item movements are detected at close range. For both stages, the detection involves head-dipping behavior, which acts to couple the animal's skull firmly to the substrate, thus

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enabling it to sense the propagated surface waves. Seismic playback experiments demonstrated that a pure vibrational stimulus generated by wind blowing the dune grass is attractive to the moles. Initial scanning laser Doppler measurements of the malleus motion in response to lateral seismic stimuli suggest that it does indeed act as an inertial motion sensor. Responses to vibrational stimuli in the vertical plane as well as to airborne sound are underway [16]. Acknowledgments G. Bronner, J.U.M. Jarvis, E.R. Lewis, M.J. Mason, and J. O'Riain collaborated on the field work in Namibia, U. Willi carried out the laser measurements of the middle ear ossicles, and S.W.F. Meenderink assisted with the preparation of Figure 2. Supported by NIH grant no. DC00222. References 1. Springer, M.S., Cleven, G.C., Madsen, O., de Jong, W.W., Waddell, V.G, Amrine, H.M., Stanhope, M.J., 1997. Endemic African mammals shake the phylogenetic tree. Nature 388, 61-64. 2. Zack, S.P., Penkrot, T.A., Bloch, J.I., Rose, K., 2005. Affinities of 'hyopsodontids' to elephant shrews and a Holarctic origin of Afrotheria. Nature 434,497-501. 3. Forster Cooper, C. 1928. On the ear region of certain of the Chrysochloridae. Philos. Trans. R. Soc. Lond. B 216, 265-283. 4. von Mayer, A., O'Brien, G., Sarmiento, E.E., 1995. Functional and systematic implications of the ear in golden moles. J. Zool. Lond. 236, 417430. 5. Mason, M.J., 2001. Middle ear structures in fossorial mammals: a comparison with non-fossorial species. J. Zool. Lond. 255, 467-486. 6. Mason, M.J., Narins, P.M., 2002. Seismic sensitivity in the Desert Golden Mole {Eremitalpa granti): A review. J. Comp. Pscychol. 116, 158-163. 7. Fielden, L.J., Perrin, M.R., Hickman, G.C., 1990. Feeding ecology and foraging behaviour of the Namib Desert golden mole, Eremitalpa granti namibensis (Chrysochloridae). J. Zool. Lond. 220, 367-389. 8. Narins, P.M., Lewis, E.R., Jarvis, J.U.M., O'Riain, J , 1997. The use of seismic signals by fossorial Southern African mammals: A neuroethological gold mine. Brain Res. Bulletin 44, 641-646. 9. Narins, P.M., Lewis, E.R., 2004. Ground sounds: seismic detection in the golden mole. Abstr. 147th meeting of the Acoustical Society of America, J. Acoust. Soc. Am. 115, 2555.

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10. Willi, U., Bronner, G., Narins, P.M., 2005. The multimodal middle ear of the Cape Golden mole {Chrysochloris asiatica). Abstr. 28th ARO Res. Mtg. 320321. 11. Mason, M.J., 2003a. Morphology of the middle ear of golden moles (Chrysochloridae). J. Zool. Lond. 260, 391-403. 12. Mason, M.J., 2003b. Bone conduction and seismic sensitivity in golden moles (Chrysochloridae). J. Zool. Lond. 260, 405-413. 13. Mason, M.J., 2004. Functional morphology of the middle ear in Chlorotalpa golden moles (Mammalia, Chrysochloridae): Predictions from three models. J. Morphol. 261, 162-174. 14. Lewis, E.R., Narins, P.M., Jarvis, J.U.M., Bronner, G., Mason, M.J., 2005. Catch the whisper of the wind: possible uses of microseismic cues for navigation by the Namib golden mole. In preparation. 15. Mason, M.J., Narins, P.M., 2001. Seismic signal use by fossorial mammals. Amer. Zool. 41, 1171-1184. 16. Willi, U., Bronner, G., Narins, P.M., 2005. Ossicular differentiation of airborne and seismic stimuli in the Cape Golden mole {Chrysochloris asiatica). In preparation.

DPOAE MICRO- AND MACROSTRUCTURE: THEIR ORIGIN AND SIGNIFICANCE DAVID T. KEMP UCL Centre for Auditory Research, UCL EAR Institute, 332 Grays' Inn Road London WC1X 8EE, UK E-mail: emission(a),dircon. co. uk PAUL F. TOOMAN Institute of Laryngology and Otology, UCL EAR Institute. Now atAudiology Services Department, Milton Keynes General Hospital, Milton Keynes, UK. E-mail: Paul. Tooman&.mkeeneral. nhs. uk DPOAE amplitude variations with frequency can be due to interference between place and wave fixed components. When these components are separated other structure remains on a scale of one octave for wave-fixed DPOAE and on a scale of approx 1/5 octave or 400Hz at 3kHz in place-fixed DPOAE. Quasi-periodic peaks and valleys occur in both 2f,-f2 and 2f2-fi place-fixed emissions at specific DPOAE frequencies irrespective of the ratio of f2/fl and hence irrespective of the stimulus configuration on the basilar membrane. We present data and statistics on this structure from 12 human subjects and discuss its origin. Various hypotheses for the structure are discussed and assessed against the data including; a second DPOAE place fixed source, basal reflection standing waves, periodicity in cochlear refection and coherent reflection filtering. The experimental evidence best supports a coherent reflection filtering origin.

1 Introduction OAEs have the potential to inform us about the functional status of outer hair cells but this potential cannot be fully realized without a good understanding of the mechanisms of emission specifcally their inherent frequency dependance and their interactions. Interference between emissions from different mechanisms with different propagation times and also standing wave interference due to multiple internal reflection introduce great complexity into emission spectra. This presents a challenge to cochlear modelers and limits the practical interpretation of OAE data. Understanding of OAE complexity is steadily increasing. Kemp[l] identified place-fixed and wave-fixed DPOAE emission components on the basis of their different observed group delays observed with iso-f2/f 1 ratio sweeps, and associated these with irregularity based and nonlinear reflection based sources respectively. Zweig and Shera [2] described a coherent reflection mechanism for place-fixed emissions in which the waves within a broad and tall traveling wave peak filtered dense spatial cochlear irregularities resulting in a traveling wave reflector accounting well for place-fixed OAE group delay characteristics. Shera and Guinan [3] emphasized that the low latency wave-fixed DP component required only nonlinear mechanical interaction between the primaries to create a reverse DP

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Figure 1 From [5]. Two human DPOAE intensity 'maps' for sidebands 2f,-f2 (upper half of each map) and 2f2-fi (lower half of each map) plotted for DP frequency against primary frequency ratio C/fl. The top map (a) shows total DP intensity, the bottom map (b) shows only the slow 'place fixed' DPOAE separated out by editing the inverse Fourier transform of iso-primary-ratio frequency sweeps. Total DP data (a) shows a horizontal band around £2/fl=1.2 which represents the condition of optimum emission of wave fixed 2frf2. No such condition exists for the emission of 2f2-f, which instead exhibits vertical (i.e. DP frequency dependant) banding in both maps. The placed fixed-only map (b) shows that vertical banding in 2f2-fi continues across the fl=f2 line into the 2f,-f2 structure. Primary levels were 70,70dBSPL

traveling wave whereas place-fixed emissions required only linear 'reflection' of an apical traveling DP or stimulus frequency wave at irregularities Recently Ren [4] has revived suggestions of a third DP emission mechanism viz. a direct pressure wave transmission from source to middle ear. Knight and Kemp [5] mapped human DPOAE intensity with primary frequency ratio against DP frequency and then separated the wave and place fixed components to observe their individual frequency structures (figure 1). The strong horizontal band of 2f,-f2 emission seen around £2/fl~1.2 in figure la is typical the wave-fixed DP component. It has a broad frequency structure on a scale of about an octave plus evidence of other structures on a scale of 100-200Hz probably due to interference with the underlying place fixed component. The 2f2-fi emission shows quasi-

310 periodic structure on a scale of 400Hz. This structure can also be traced in the placefixed only 2fi-f2map (lb) especially at low f2/fl ratios. Kemp and Knight [6] noted that wave-fixed DP emission occurs only for 2frf2 and other lower sidebands. This is because i) the traveling wave phase gradient of f2 is always steeper than that of fl if £2>f1 and ii) the two gradients have opposing influences on the phase of 2frf2, 3fi-2f2 etc. The lower frequency DP source's spatial phase (cp) gradient can therefore be less than that of fl and f2 and even change sign. At some f2/fl ratio the gradient will most closely match that of a true 2f]-f2 reverse traveling wave. DP traveling waves from the greatest number of DP source elements under the f2 envelope will then arrive coherently at the base leading to the strongest wave fixed DPOAE emission. At some smaller f2/fl the DP source phase gradient will become flat across an extended region and this might possibly couple more effectively to a pressure wave directly moving the oval and round windows with minimal delay, perhaps interfering with the wave-fixed traveling wave emission over a broad frequency scale. For even smaller f2/fl (<1.1) the spatial DP phase distribution must approach that of an apically traveling DP wave causing most 2frf2 DP energy to propagate apically to its frequency place where it can be reflected back to create a DP place-fixed emission of high latency. All three emissions routes could interfere in the ear canal creating a complex frequency structure. As with stimulus frequency emissions multiple reflections could also occur as the DPOAE re-enters the cochlear by reflection from the middle ear and then reflects out again. In figure lb, where slow wave-fixed emissions are removed, the frequency structure of 2frf2 remains complex. In contrast the DP component 2f2-fj exhibits a simpler structure; a quasiperiodic modulation with a period of about 400Hz in both general and place fixed maps. Knight and Kemp [5] found no evidence of (fast) wave-fixed 2f2-fi emission. It is not possible for this upper frequency intermodulation DP to create a strong wave fixed traveling wave because the DP source phase (2cp2-f 1. Some 2f2-fi DP energy will propagate apically to its frequency place where place-fixed (reflection) emission could occur as for 2frf2. Probably more DP 2f2-fj energy is generated under the f2 envelope between the 2f2-fj and f2 places. A 2f2-f( traveling wave is not supported in this region but the DP source phase gradient that exists will be steeper than that of f2. We wondered if this evanescent wave could combine with spatially matching components of irregularities to transmit some of this 2f2-fi energy directly back to the middle ear creating a second place-fixed OAE with a delay equal to the just the forward stimulus delay. We wanted to know if the ~400Hz periodicity seen in 2f2-fi DPOAE was the result of interference between two 2f2-fi sources, or whether it could be attributed to a periodicity in the place-fixed reflection source, or to statistical fluctuations as in the coherent filter reflector after Zweig and Shera [2]. The aim of this study was to quantify the macrostructure seen in 2f2-f] and small ratio 2frf2 and to try to objectively determine its origin.

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2 Methods Recordings of the amplitude and phase of 2frf2 and 2f2-f!. were made in 12 normally hearing human subjects ears with primaries of LI = L2 = 75dBSPL and

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Figure 2 (a) Top. DP intensity (dBSPL) and phase (degrees) from a typical subject KG right. All 12 subjects ears showed a comparable structure of rounded peaks and some deep notches with high correlation between 2f,-f2 and 2f2-fi data. Phase data showed a linear downward trend with inflections across some notch frequencies. The mean common inter-notch interval was 390Hz (s.e. 16Hz) across the 2-4kHz range and 380Hz(s.e.40Hz) across l-2kHz. (b) Lower panel above. Analysis of the inter-peak intervals (lower left) and the lOdB peak bandwidths (lower right) in a 2-4kHz range for all 12 subjects. The 400Hz dominant structural scale is consistent with the Knight and Kemp data[5].

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Figure 3 Left. Correlation was seen in most subjects between peaks in their 12ms sweep TEOAE spectrum and their close primary DP macrostructure. Left is the best example. The short sweep time was designed to exclude the build up of internal TEOAE reflections.

small f2/fl ratios of-1.01 to avoid wave fixed contamination. Measurement steps were 12Hz with 10s of data per point. Subjects were all examined from 2-4kHz, and

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some at l-2kHz and other stimulus levels. In two subjects DP recordings were made with pneumatic pressure applied to the sealed ear canal. Nonlinear transient evoked OAEs spectra were also recorded using 84dBpe clicks at 12ms intervals. The project was conducted with the approval of the Ethical Committee of the Royal Free Hospital, London. 3 Results Figure 2a is a typical example of data showing a quasi-periodic modulation of DPOAE intensity as a function of DP frequency for both 2f2-fi and for 2frf2 at small f2/fl. Correlated inflexions of phase can be seen. Figure 2b shows the statistics of the inter-peak interval and the lOdB bandwidth of the peaks for 12 subjects. The dominant structure scale is well defined at around 400Hz or 1/5 octave. Substantial similarities were found between this frequency spectrum structure and that of TEOAEs in most subjects as in figure 3. Pneumatic pressure was applied during DPOAE measurement in 2 subjects. It is known that changes in middle ear impedance can change spontaneous emission frequencies and shift SFOAE microstructure. Only 100mmH2O was applied so as not to greatly change middle ear conduction and hence internal stimulus levels but no significant change in the frequency of DP notches frequency was observed. The most likely origin of this structure is interference. It is easy to calculate what pattern would be expected from interference between two signals of identical frequency but dissimilar levels and latencies as a function of frequency. (Figure 4a.). The interference pattern matches the experimental data. The group latency of the dominant component can be deduced from the mean phase slope (-dcp/dco)

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DPOASd«lay ms

Figure 4 (a) Left: Computer simulated interference notches for a simple two-source model. The delay of the dominant component determines the linear phase gradient (faint line). The presence of a secondary component in this case V% amplitude of greater delay causes amplitude notches and inflexions in the resultant phase gradient (bold line). The inter-component delay determines the inter-notch interval Af Right (b). Experimental data showing intercomponent delay (ie 1/notch interval) versus total component delay for each of 12 subjects.

313 whereas the relative time delay At between the notional interfering components can be inferred from the inter-notch interval AF, dA=l/AF Hz. The relative amplitudes of the two components determines the depth of notch. Equal intensity gives an infinitely deep notch and a 180° peak-to-peak biphasic phase jump. These decline systematically in magnitude as the components are made unequal. We measured the mean phase gradients, notch depth and local phase transitions in our experimental data together with the inter-notch frequency interval. Notch depths averaged around lOdB indicating interference between components with amplitudes within about 50% of each other. Phase transitions where scattered between +-180° indicating interference is occurring, although this was only weakly correlated with notch depth. From the inter-notch frequency interval we obtained a notional inter-component time difference of 2-3ms. We found this to be inversely correlated (figure 4b) with the overall group latency of the DPOAEs obtained from the phase gradient of each ear, figure 4b, which ranged from 2.5 to4.5ms. This means that the greater the DPOAE latency the smaller the absolute inter-component time difference and therefore the greater the inter-notch frequency. 4 Discussion Human place-fixed DPOAEs show typically a 1/5 octave intensity modulation with DP frequency (Af ~400Hz around 3kHz)- most clearly seen in the 2f2-fi component at over a wide range of f2/fl ratios at these higher stimulus levels. We considered if the structure could be some kind of multiple reflection self interference involving the middle ear. In that case we would expect the inter-peak interval Af » 1/T where T is the DP latency. Ears with greater latency emissions would show more dense frequency structure. Instead we found Af « 2/T. We also found an inverse relationship with greater latency emissions showing LESS dense frequency structure (larger Af in figure 4b). We found no evidence for middle ear reflection involvement and no evidence that standing waves were involved. We considered if interference was taking place between two independent emission sources eg a reverse travelling wave and a direct pressure wave emission. In this case of independent sources we would expect little or no correlation between Af and the mean latency. In fact we saw (figure 4b) a clear negative correlation with ears having greater DP latency emissions showing less dense frequency structure, ie the interfering components have less time difference the greater the latency of the emission. The quasi-periodic place fixed DP frequency structure in question is emissionfrequency based and very little affected by stimulus frequencies, or ratios, intensities or emission generation mode (e.g. 2frf2, 2f2-fi or TEOAE). This points to a robust characteristic of the place fixed 'reflector' itself and/or of the transmission route back to the middle ear for place-fixed OAEs. Periodic spacial modulation of the reflection mechanism on a scale of 400Hz (~lmm) could explain

314 the structure without interference but the clear signs of interference seen argue against this. Zweig and Shera's [5] coherent reflection model for place fixed emissions predicts OAE intensity fluctuations with frequency due to interference between reflected components from within the 'tall broad' traveling wave peak- a consequence of coherent filtering. Our observation that human ears with longer OAE latencies have broader DP frequency structure is consistent with the idea that that higher OAE latency corresponds to a narrower bandwidth of the coherent reflection filter, ie in ears with higher OAE latency the traveling wave peak is broader and/or of more uniform wavelength. In conclusion our search for evidence of interference between different discrete DP sources proved negative and although the periodicity of DP structure can be surprisingly uniform - the relation found between latency and peak separation points to an origin in the characteristics of the coherent filter responsible for the creation of the retrograde traveling wave. References 1. 2. 3. 4. 5. 6.

Kemp, D.T., 1986. Otoacoustic emissions, travelling waves and cochlear mechanisms. Hear. Res., 22:95-104. Zwieg, G., Shera, CA. 1995. The origin of periodicity in the spectrum of evoked otoacoustic emissions. JASA 98, 2018-2047. Shera, C.A., Guinnan, J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms JASA 105 782-798. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat. Neurosci. 7,333-334. Knight, R.D., Kemp, D.T., 2001. Wave and place fixed DPOAE maps of the human ear. JASA 109, 1513-1525. Kemp, D.T., Knight, R.D., 1999. Virtual DP reflectors explains DPOAE wave and place fixed dichotomy. Assoc Res Otolaryngol; 22nd Midwinter Research Meeting A.

PHYSICAL MECHANISMS OF OAE GENERATION AND PROPAGATION: THE HYDRODYNAMIC APPROACH A. VETESNfK Department Otolaryngology,

University Tuebingen, Elfriede-Aulhorn-Strasse Tuebingen, Germany E-mail: ales, [email protected]

5, 72076

R. NOBILI Department of Physics "G. Galilei", University of Padova, ViaMarzolo8, Italy E-mail: rnobili @padova. infn. it

35131 Padova,

A. W. GUMMER Department Otolaryngology,

University Tuebingen, Elfriede-Aulhorn-Strasse Tuebingen, Germany E-mail: [email protected]

5, 72076

To help elucidate how otoacoustic emissions (OAEs) originate at and propagate from certain cochlear sites to the middle ear, we extend a previous theoretical investigation [1]. Using simplified ID and 2D linear cochlea models, we try to explain the rationale that stands behind our key assumption, namely the instantaneous hydrodynamic coupling between stapes and basilar membrane (BM) and among BM portions. We argue that, because of the mathematical peculiarities of the undamped cochlea model and of doubtful implications about group velocity in the damped case, a physical interpretation of the WKB method is far from being clear and conclusive. By contrast, a faithful representation of fluid coupling in terms of Green's functions reveals an instantaneous longitudinal interaction between BM segments, which can be characterized as a sort of space delayed damping. To exemplify the range of our view, a frequency-domain simulation of the mechanisms underlying the generation of distortion products in a nonlinear hydrodynamic cochlea model is reported.

1

Introduction

The most commonly accepted explanation of the phenomenon of OAEs as a byproduct of cochlear dynamics is that the active cochlea mechanism gives rise to pressure difference waves traveling backwards along the BM to the stapes. Feeding back via the middle-ear ossicles, these are detected as a sound in the ear canal. Only recently, the art of experimental technique has reached a point where it is possible to measure the BM vibration at OAE frequencies as a function of longitudinal location [2]. Reported data indicate the failure of the backward-traveling theory, leaving the impression of a conceptual gap in our understanding of cochlea mechanics. In a previous theoretical investigation [1], the instantaneous hydrodynamic coupling between the stapes and the BM, as well as among BM portions, was instead postulated and the existence of the backward-traveling wave was excluded. 315

316 Interestingly, this study was criticized for certain misconceptions of cochlea mechanics [3]. In response to this critique, we advance here a few considerations on the expected behavior of the one-dimensional linear cochlea model, which indicates certain difficulties with a straightforward physical interpretation of the WKB approximation. Our analysis extends to a two dimensional box model showing that a faithful representation of fluid coupling by the Green's functions is only consistent with an instantaneous longitudinal coupling between BM segments. Finally, we report an example of our frequency domain simulations showing how the instantaneous coupling work in distortion product generation. 2

A physical interpretation of the WKB approximation

Here and in the following, only steady-state BM responses to tones of radian frequency to will be considered. In the long-wavelength approximation of the box cochlea model, as described for instance in [4], the modified pressure difference Pd(x,to) between the scalae at the BM coordinate x, i.e. the pressure difference due to the BM motion alone, can be described by a second order differential equation plus boundary conditions (BCs) at the stapes (x = 0) and helicotrema (x = L), respectively d2Pd{x,uj) + dxPd(x,v)\x=0

X2(x,u>)Pd(x,cu)=0, = - 2 p w 2 , Pd(x)\x=L

= 0,

where Z(x,ui) = k(x) -to2m

+ iUJ h(x),

X(X,LO) = \JQ{UJ)/Z(X,LO)

= A r (x, w)

Q(OJ) =

(2pw2)/H,

+i\i(x,uj).

Here m, h(x) and k(x) are respectively BM mass, BM viscosity and BM stiffness per unit BM length; H the height of the cochlear canal and p the cochlear fluid density. It is well-known that an approximate solution of Eq.l can be obtained by means of the eikonal WKB approximation as a sum of two wave component, namely Pd(x,Lo) = \(x,co)-V2[a1(u)e-lf°X{S'")dS

+ a2(Lo)elf°X{s'Uj)d*]

,

(3)

where a\ (u) and a2 (u>) are complex constants determined by the above BCs. Because of both the abrupt fall to zero of the wave profile beyond the site XCF of characteristic frequency (CF) and the BC at the helicotrema, the amplitude of the backward TW component [factor of a2 in Eq.3], is very small compared to the forward one [factor of a\ in the same equation]. Under this assumption, the BM displacement can be safely assumed to be represented as Z(x,u>) = a 1 H Q - 1 M A 3 / 2 ( x , W ) e - j r A ^ ^ .

(4) 2

As an asymptotic expansion, the WKB method simplifies the effect of d in Eq.l by assuming that only the phase variation Q(x, w) = f^ X(x, u))dx is significant in

317 the leading term of the expansion. The amplitude A(x,u) = \(x,w)~1/2 is then determined by balancing the subsequent terms of the expansion, which leads to the so-called transport equation dx(dxQ(x, w) A2(x, w)) — 0. In the framework of the variational formalism for Hamiltonian systems, the transport equation is known as the conservation of energy flow or of wave action. It seems therefore irrefutable that the success of WKB approximation implies that the group velocity vg(x,u)

= [^A(x,w)]" 1 = LUQ(OJ)/{\3(x,w)[k{x)

+ IOJh(x)/2}}

,

(5)

defines the energy transport along the BM. According to Lighthill [5], for Z(x, tu) real, i.e. for h(x) = 0, the averaged BM energy is given by (E(x,w)) =

l/2k{x)\Z(x,w)\2.

Evidently, the product^ (a;, to) (E(x,u)) is a simple constant. At the resonance point xr, however, where w = yjk{xr)/m, Eq.l is singular. It is not clear, therefore, whether the WKB method is also valid in this case. For Z(x,u>) = fcoe~ax — u2m, where UQ and a are real positive constants, the real solution of Eq.l, which is an hypergeometric function, was found either for x < xr or for x > xr [6]. The authors noted that the complex solution (traveling wave) for x < xr derived in [7] corresponds to the case of "<5-function absorption", i.e. h(x) = S(x — xr). It should be mentioned, however, that the boundary conditions were ignored in those studies. Because of the peculiar property of hypergeometric function parameters (a + b = c), we leave this interesting boundary value problem untouched. According to [8], for a complex Z(x, ui) the quantity that remains constant under the "wave action" is the energy-like term E(x,u>)tt?A{x,w)[k(x)+iwh{x)l2] U(x,uJ)=a1(u;)Q~\u;)\3/2(x,u),

, W

indeed dx[E(x,L>)vg(x,w)] = 0. However, it is hardly acceptable to identify E(x, ui) with a total BM energy. Firstly, E(x, UJ) is a complex function without clear physical meaning, secondly a contribution of Ai (x, u) to the BM amplitude was overlooked. From the above arguments, it seems that the success of the WKB method relies rather on a favorable mathematical property of A(x, to) than on physical properties of TW phenomena.

318

3

Power balance and conservation of fluid volume

The exact equation of a two-dimensional box model is described by an integral equation [-u2m(x)+iujh(x)+k(x)]£(x,u)

=

W2GS{X)+UJ2

/

G(x,x)£,(x, to) dx , (7)

Jo

where Gs{x) and G(x,x) represent the effective parts of the Green's functions (Gs(x, y) and G(x, x, y, y) considered solely for y=0)[4]. The former accounts for the stapes-BM coupling and the later for the BM-BM hydrodynamic coupling. Formally, G(x,x) can be split into a long-range part Go(x,x) corresponding to the boundary value problem defined in Eq.l and a short-range or singular part Gp(x,x) related to the logarithmic singularity. G{x, x) was derived under the assumption that inward stapes motion causes downward BM motion. Hence, because of the mentioned abrupt fall of the TW at XCF, the fluid volume comprehensively displaced by the TW along the BM interval between the stapes and XCF equals the fluid displaced by the stapes, i.e. / £(x,uj)dx = -H, (8) Jo Fig.lC represents the real part of the left hand side integral of Eq.8 evaluated as a function of distance from the stapes. The integral is completed between the base and the first wavelength; dashed line represents the total fluid volume. From the standpoint of Eq.7, therefore, TW is viewed as a set of "hydrodynamic circuits" coupling scalae. For the TW, as a steady wave, the stapes should balance power dissipated by the BM damping over a whole cycle. The global BM power balance equation can be written as f

GF

h(x)\£(x,to)\2

dx = SR{W J

CF

Gs{x)\i{x,Lo)\el^x^-K/2UxY

(9)

As Gs{x) is defined by a simple linear function, referring to Eq.8, it is apparent that the effective action of the stapes takes place within the first "hydrodynamic circuit". The local power balance equation can be obtained by multiplying Eq.7 by the complex conjugate of the BM velocity and then taking its real part. It can be written as h{x) Ux,u)\2=u[{Ps{x,u))

+ {P0(x,o})) +

(PP(X,LJ))],

(10)

where {....) is the time average; subscripts 5, 0 and P indicate that the quantities are related to the stapes, the long-range part and a short-range part of the Green's function, respectively. In Fig.lA,B amplitudes and phases of a TW are compared for an exact box model (solid line) and its long-wavelength approximation (dashed line). The term

319 Gp(x, x), whose absence is responsible for this disparity, behaves predominantly in Eq.7 as a small additional mass term. Fig.ID illustrates how significantly Gp(x, x) contributes to the local power balance defined by Eq.10. This can be explained as follows. Because the amplitude and phase responses near the stapes have a relatively small slope (dashed and solid lines are almost indistinguishable near x = 0), Gp(x,x) can be treated as 5(x — x) of magnitude equal to the area underlying the Gp(x,x) profile, i.e. it contributes to Eq.7 by an additional mass term Am « (2 H)/3. However, when the TW peak is approached, both TW amplitude and phase changes are sufficiently abrupt to alter the integration over the restricted area of the influence of the logarithmic singularity. As a consequence, Am progressively decreases so as to become negligible at XQF of a 1-D model. It would be surprising if this procedure would lead to a purely real Am. Indeed, Fig.l indicates that Am should be considered as a mass ± damping term. We refer to this as the space delay damping in contrast to the slow-feedback time-delayed stiffness introduced by Zweig [9]. Obviously it represents a kind of an instantaneous spatial interaction.

ratio

l«x,eo)|

A

1l. SL

1*

- X(x,ta)

, • •i

/'< 9t[f|{y,
Local Power Balance

D

fjh ,'AI .-^y i'\ \ >

Figure 1. Conservation of fluid mass and power balance in a box model. A,B: TW amplitudes and phases for a box model (solid lines) and a 1-D model (dashed lines), the input frequency F=1500 Hz. C: Conservation of fluid mass. Real part of the left hand side integral of Eq.8 evaluated as a function of distance from stapes. D: Local power balance. Solid line h(x)\£,(x,uj)\2. Dotted line w[{Ps(x,u)) + (P0{x,u))]. Dot-dashed line ui{Pp(x,uj)): note remarkable sink-source shape.

\i 0

4

1 2 3 Distance from stapes [cm]

0

1 2 3 Distance from stapes [cm]

Frequency-domain simulations of OAEs

Simulations were carried out on a nonlinear hydrodynamic model of the human cochlea ([1],[10]). To achieve physically realistic boundary condition at the stapes the middle ear was modeled as a two-port system with parameters published in [11]. Model equations were solved in the frequency domain by means of the recursive algorithm [10]. The convergence of the procedure was verified by computation of

320

steady-state responses of the model in the time domain. Numerical integration was performed by Matlab's implementation of an explicit Runge-Kutta method. The systematic change in amplitude of distortion-product OAEs (DPOAEs) as a function of the primary frequency ratio /1//2 was faithfully reproduced in an agreement with the experimental data. In our simulations, the main source of the 2/i — j ^ distortion product (DP) was the site of the $1 amplitude fall. An impact of the cochlear amplifier (CA) gain on the amplitude of both DP at CF place \£{XCF,UDP)\ and DPOAE was investigated. From our simulations, it turns out that \£(XCF, LODP)\ is far more sensitive than DPOAE and directly linked to CA gain before saturation of \£(XCF,UDP)\ is achieved. DPOAE are more sensitive for low- to mid-level primaries (i.e. < 60 dB SPL). 5

Discussion

In the framework of hydrodynamic modeling sketched above, OAEs are effectively related to the mutual interaction of the stapes and the first "hydrodynamic circuit". And local BM responses are projected into this communication instantaneously via the Green's function. This might be considered as an extremely cumbersome way to describe the process of interference of forward and backward TWs. However, the space delay damping introduced above is an example of how peculiar the energy communication within the cochlea can be. This suggests that only experiments based on a thorough study of cochlea hydrodynamics can improve our understanding of OAEs. One-to-one mapping seems to be patently simplistic. Acknowledgments A.V. is supported by the Marie Curie Intra-European Fellowship EARPOST. References 1. Nobili, R., Vetesnik, A., Turicchia, L. and Mammano, E, 2003. Otoacoustic Emissions from Residual Oscillations of the Cochlear Basilar Membrane in a Human Ear Model. JARO 4,478-494. 2. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat. Neurosci. 7, 333-334. 3. Shera, C.A., Tubis, A. and Talmadge, C.L., 2004. Do forward- and backwardtraveling waves occur within the cochlea? Countering the critique of Nobili et al. JARO 5, 349-359. 4. Sondhi, M.M., 1978. Method for computing motion in a two-dimensional cochlear model. J. Acoust. Soc. Am. 63, 1468-1477. 5. Lighthill, J., 1981. Energy flow in the cochlea. J.Fluid Mech. 106, 149-213.

321 6. Kok, L.P. and van Haeringen, H., 1979. Reflections on "Reflection on reflection". Internal report, 148, Inst, of Theoretical Physics-Univ. of Groningen. 7. de Boer, E. and MacKay, R., 1980. Reflection on reflection. J. Acoust. Soc. Am. 67, 882-890. 8. de Boer, E. and Viergever, M.A., 1984. Wave propagation and dispersion in the cochlea. Hearing Res. 13, 101-112. 9. Zweig, G., 1991. Finding the impedance of the organ of Corti. J. Acoust. Soc. Am. 89, 1229-1254. 10. Nobili, R. and Mammano E, 1996. Biophysics of the cochlea II: Stationary nonlinear phenomenology. J. Acoust. Soc. Am. 99, 2244-2254. 11. Puria, S., 2003. Measurements of human middle ear forward and reverse acoustics: Implications for otoacoustic emissions. J. Acoust. Soc. Am. 113,27732789.

MEASURING COCHLEAR DELAYS USING OTOACOUSTIC EMISSIONS R.H. WITHNELL Department

of Speech and Hearing Sciences, Indiana University, 200 South Jordan Bloomington, IN47405, USA E-mail: rwithnel&indiana.edu

Avenue,

Otoacoustic emissions provide unambiguous evidence that the cochlea supports energy propagation both towards, and away from, the stapes. It is generally accepted that energy propagation away from the stapes involves a traveling wave mechanism. The mechanism by which energy propagates back to the stapes remains controversial. Examination of the mode by which energy propagates back to the stapes has been done by interpreting otoacoustic emission delay times and comparing these delay times with basilar membrane measured cochlear delay times. However, cochlear delay times inferred from basilar membrane measurements represent a measurement from a spatially confined region on the basilar membrane that is fixed in position whereas otoacoustic emissions generally represent measurement from a more spatially distributed region of the cochlea. Further complicating matters, otoacoustic emissions appear to have a complex origin that confounds estimates of cochlear delay based on the phase derivative. Here, signal onset delay is reported for otoacoustic emissions arising from different mechanisms (SFOAE versus DPOAE), matched for stimulus frequency. Comparison of signal onset delay for the two emissions argues for a bi-directional traveling wave mechanism i.e., energy propagates back to the stapes as a traveling wave rather than an acoustic compression wave.

1 Introduction The mechanics of cochlear function has been examined using a variety of experimental techniques, including basilar membrane (BM) recordings, hydrodynamical measurements, auditory nerve (AN) recordings, and otoacoustic emission measurements. Each has contributed to our understanding of cochlear mechanical function but each has limitations that circumvent unequivocal interpretation and it is not clear how these measures relate to each other. BM recordings represent a local view of cochlear mechanics, being spatially confined, from which 'panoramic' function can only be inferred [1]. They also represent an invasive procedure that may alter cochlear mechanical function (particularly if the cochlea is not sealed prior to making recordings). AN recordings, from which cochlear mechanical function has been inferred, is qualified by BM motion being half-wave rectified at the inner hair cell, and substantial variance in the data measurements e.g., [2]. Hydrodynamical measurements e.g., [3], have provided seemingly accurate measures of middle ear delay times but, as a measure of cochlear function, are qualified by the large opening in the cochlea that is required to make such measurements possible, and the unknown effect of the presence in-situ of a relatively large transducer on cochlear mechanics. Otoacoustic emissions (OAEs) provide unambiguous evidence that the cochlea supports energy propagation both towards, and away from, the stapes, but are qualified by the

322

323

complexity of their generation [4-6] and questions regarding the dominant mode of energy propagation back to the stapes [7]. Measurement of cochlear delay provides valuable insight into the mechanics of cochlear function e.g., how does cochlear tuning relate to cochlear travel times i.e., are cochlear filters minimum phase, what effect does cochlear mechanical amplification have on cochlear travel times, and how does energy predominantly propagate to and from the stapes? BM measurements, limited to the first and fourth cochlear turns, provide cochlear delay times (calculated from the phase gradient as stimulus frequency is swept but measurement is restricted to a spatially confined region of the cochlea) that shows substantial inter-subject variation. Such measurements are thought to be related to single-unit AN recordings but are presumably only analogous to OAE measures of delay at low stimulus levels [6]. The mechanics of the cochlea is spatially distributed and so BM and AN recordings provide only a very limited view of such mechanics. OAEs provide a non-invasive view of cochlear mechanical function that is possibly more representative of the spatially distributed nature of mechanical cochlear function, subject to a complete understanding of the complexity of their generation. In this paper, measurement of cochlear delay is reported in terms of signal onset delay for OAEs arising from different generation mechanisms. Group delay has previously been found to be representative of BM estimates of cochlear delay only at low stimulus levels [6], and even then subject to considerable inter-subject variation of delay that has been attributed to variation in the cochlear irregularity from which such low-stimulus level OAEs are thought be reflected [8]. Signal onset delay should provide a direct measure of the actual physical delay of an OAE in the time domain, independent of the mechanism of generation. 2 Methods DPOAEs (2frf2 OAE) and SFOAEs (stimulus frequency = f2) were recorded from anesthetized Albino guinea pigs with signal generation and response acquisition computer-controlled using custom software and a sound card. DPOAEs were evoked using a pulsed-tone paradigm [9] with one of the stimulus tones (f{) presented continuously while the other tone (f2) was pulsed on for 103.5 ms in every 250 ms with ~ 2.5 ms rise and fall times and 98.5 ms duration. Stimulus frequency ratio was fixed at 1.2, with f2 = 5400 to 11340 Hz (540 Hz step-size) and stimulus level ~ 74dB pSPL; stimulus level was based on a constant voltage delivered to the loudspeaker with probe tube corrections made post-hoc and so L2 ranged from 70 to 78 dB pSPL with 0 < Li/L2 < 10 dB. SFOAEs were evoked by ~ 33.5 ms tonebursts with 3 ms rise and fall times and 27.5 ms duration. Stimulus frequency varied between 5400 and 10150 Hz. Stimulus level was ~ 70 dB pSPL (65 to 72 dB pSPL). The OAE was extracted from averaged the ear canal sound pressure recording using

324

the nonlinear differential extraction technique [10] with a stimulus level ratio of 6 dB. The stimulus tone and OAE were extracted using narrow band filtering of the time domain signal about the center-frequency of each component of interest. Using Matlab, each ear canal sound pressure recording (or the nonlinear derived SFOAE) was filtered using the filtfilt function (performs zero-phase digital filtering by processing the input data in both the forward and reverse directions). The filter used was a band-pass, linear phase FIR digital filter (Hamming window) with a bandwidth of 200 Hz and a filter order of 200. Signal onset was defined as the point in time at which the absolute value of the Hilbert transform of the signal equals 10% of the peak amplitude. OAE delay was quantified in terms of signal onset delay i.e., OAE onset minus signal onset. Figure 1. Example f> stimulus and 2fpf2 OAE in top panel and an abbreviated section in time in the bottom panel showing the signal onset based on 10% of the peak amplitude. The upper panel shows the absolute value of the Hilbert transform of the f2 stimulus and 2frf2 OAE, each plotted against a different y-axis scale. The bottom panel emphasizes the region of these waveforms at signal onset, the horizontal dashed line representing 10% of the peak amplitude for the stimulus and OAE.

q E n $ 0.02

1 0 0.18

0.00M

|

seconds

Figure 1 provides an example of the f2 stimulus and 2frf2 OAE obtained (magnitude of the Hilbert transform of the time domain waveform) in panel (a) and illustrates the signal onset in panel (b) where the time axis has been abbreviated to concentrate on the region of stimulus and OAE onset.

325 3 Results Figure 2 shows signal onset delay versus stimulus frequency for the 2frf2 OAE and the corresponding SFOAE, matched in frequency to the f2 stimulus. The 2frf2 OAE is expected to arise predominantly from the f2 region [11,12] from a nonlinear distortion mechanism [9,13]. The SFOAE at 10% of the peak amplitude is expected to be dominated by a place-fixed reflection mechanism (stimulus level was approximately 70 dB pSPL; for the signal onset definition of 10% of the peak amplitude, this corresponds to an effective stimulus level of approximately 50 dB pSPL, a stimulus level that should produce an SFOAE dominated by a linear coherent reflection mechanism). For both the 2fi-f2 OAE, generated by a nonlinear distortion mechanism, and the SFOAE, generated by a place-fixed reflection mechanism, considerable scatter is present in the data, confounding obtaining a fit to the data. To facilitate curve-fitting while removing the effect of data outliers, data is shown from the 10th to 90th percentile of signal onset delay values obtained for each of the OAEs, with curves fitted to this data set. Each data set was fit with a 6th order polynomial. It was expected that a power law (x a (f/1000)b) would best describe cochlear delay versus frequency [8], but the scatter in the data and the data being measured over only a one octave range presumably obfuscates such a relationship. The scatter in the data for SFOAE has previously been shown to not be a construct of noise but rather, it has been suggested, comes from "intrinsic variations in emission phase that are correlated with variations in emission frequency" [8] i.e., a construct of variation in cochlear reflectance. The delay values obtained by Shera & Guinan [8] were calculated from the first derivative of the phase with respect to frequency and not directly from the time domain. Here, the scatter is also evident in SFOAE time domain measurements, illustrating that variations in cochlear reflectance directly affect SFOAE travel times1. Comparison of the 6th order polynomial fitted to each of the data sets reveals that there is a substantial difference in delay between the fitted curves i.e., the SFOAE signal onset delay is substantially longer than the 2frf2 OAE signal onset delay. A bidirectional traveling wave mechanism with energy propagating along the BM predicts that tsfoae ~ 2 *x2 « 2(xdpoae - xdp), where xdp « 0.1 *T2

(1)

i.e., SFOAE delay will be approximately equal to twice the forward travel time (x2) of the f2 stimulus, and also approximately equal to twice the delay of the 2frf2 OAE (tdpoae), where the 2frf2 energy originating from the f2 region is arising in its long wave region (f2/fi = 1.2).

My thanks to Christopher Shera for pointing out that the scatter in physical SFOAE delays could be attributed to variation in cochlear reflectance.

326

Figure 2. SFOAE signal onset delay (stimulus frequency = f2), dark triangles, and 2frf2 OAE signal onset delay, light squares, versus f2 frequency. There is negligible overlap in the data sets, although both show considerable scatter, with SFOAE signal onset delay considerably longer than 2fi-f2 OAE signal onset delay.

1.5

0.5

10 kHz

In contrast, an acoustic compression wave mechanism for the reverse propagation of energy would mean that the reverse travel time would be negligible and ^sfoae ~ ^2 ~ ^dpoae " ^dp

(2)

where f2/ft = 1.2 for the DPOAE. Figure 2 is clearly not consistent with an acoustic compression wave mechanism. Significant variability in signal onset delays obtained for both the 2fi-f2 OAE and SFOAE introduce a complexity that precludes the data satisfying equation 1 quantitatively but certainly, the discrepancy between the SFOAE and 2fi-f2 OAE signal onset delays argues for a bi-directional traveling wave mechanism along the BM. Preliminary analysis of the effect of noise on the estimate of OAE signal onset suggests that noise does not contribute to the observed scatter in the delays. The effect of noise was quantified using synthetic tonebursts and adding Gaussian noise with an amplitude range determined by measured signal to noise ratios for the OAEs; the synthetic signals with the added noise were then analyzed in exactly the same was as the OAEs. 4 Discussion The hydrodynamics of the cochlea provides for energy transport away from the stapes in one of two forms: an acoustic compression wave (fast wave) and via an inertially mediated bulk fluid flow (slow wave) that produces a pressure difference across the basilar membrane [14,15]. Sensory transduction is mediated by the latter or slow wave, the graded mechanical properties of the BM providing a spatial tuning with each frequency mapped to a different cochlear location. It was originally believed that there was a preferential direction for the propagation of energy along the cochlear partition toward the helicotrema [16,17]. However, with the discovery of OAEs [18] it was clear that the cochlea supported the propagation of energy in both directions. Essentially all models of cochlear function assume that

327

this propagation of energy in both directions involves a traveling wave mechanism i.e., spatial filtering associated with the mechanical properties of the BM (stiffness and mass) will influence energy propagation equally in both directions. Recently, Ren [7] reported no evidence for reverse traveling waves from BM measurements, and stapes vibration that preceded BM vibration. In contrast to all previous studies of BM vibration, Ren [7] was able to measure from not one cochlear location but rather longitudinally over about 1mm. Ren measured the intermodulation distortion product 2frf2 phase for stimulus frequency ratios (f2/fi) ranging from 1.05 to 1.2 and found in all cases a negative slope i.e., the data indicated only forward traveling waves for 2frf2. Ren concluded, based on the lack of evidence for a reverse traveling wave, that energy propagates back to the stapes nearly instantaneously as an acoustic compression wave. However, this interpretation, while persuasive, is not unequivocal. Ren's findings do not exclude the possibility that the 2frf2 forward traveling wave dominance is a construct of stimulus frequency ratio and that at higher stimulus frequency ratios, a 2frf2 reverse traveling wave would dominate [19]. The current data, while showing considerable variability, argue against a compression wave being the dominant mode of energy propagation back to the stapes (in guinea pig). References 1.

2.

3. 4. 5.

6.

7. 8.

Patuzzi, R.B. 1996. Cochlear macromechanics and micromechanics, in The Cochlea (pp. 186-257), Dallos, P., Popper, A.N., Fay, R.R. (Eds), Springer, New York. Gummer, A.W., Johnstone, B.M. 1984. Group delay measurement from the spiral ganglion cells in the basal turn of the guinea pig cochlea, J. Acoust. Soc. Am. 76, 1388-1400. Olson, E.S., 1999. Direct measurement of intra-cochlear pressure waves. Nature. 402, 526-529. Zweig, G., Shera, C.A., 1995. The origin of periodicity in the spectrum of evoked otoacoustic emissions. J. Acoust. Soc. Am. 98, 2018-2047. Talmadge, C.L., Tubis, A., Long, G.R., Piskorski, P., 1998. Modelling otoacoustic emission and hearing threshold fine structures. J. Acoust. Soc. Am. 104,1517-1543. Goodman, S.S., Withnell, R.H., De Boer, E., Lilly, D.J. & Nuttall, A.L. 2004. Cochlear delays measured with amplitude-modulated tone-burst evoked OAEs,Hear. Res. 188, 57-69. Ren, T. 2004 Reverse propagation of sound in the gerbil cochlea. Nature Neuroscience, 7, 333-334. Shera, C.A., Guinan, J.J., 2003. Stimulus-frequency-emission group delay: A test of coherent reflection filtering and a window on cochlear tuning. J. Acoust. Soc. Am. 113, 2762-2772.

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9. Talmadge, C.L., Long, G.R., Tubis, A., Dhar, S., 1999. Experimental confirmation of the two-source interference model for the fine structure of distortion product otoacoustic emissions. J. Acoust. Soc. Am. 105, 275-292. 10. Kemp, D.T., Ryan, S., Bray, P. 1990. A guide to the effective use of otoacoustic emissions, Ear Hear. 11, 93-105. 11. Withnell, R.H., Shaffer, L.A., Talmadge, C.L. 2003. Generation of DPOAEs in the guinea pig. Hear. Res. 178, 106-117. 12. Schneider, S., Prijs, V.F., Schoonhoven, R. 2003. Amplitude and phase of distortion product otoacoustic emissions in the guinea pig in an (fl ,f2) area study. J. Acoust. Soc. Am. 113, 3285-3296. 13. Kalluri R., Shera, C.A. 2001. Distortion-product source unmixing: A test of the two-mechanism model for DPOAE generation. J. Acoust. Soc. Am. 109, 622-637. 14. Lighthill, J. 1991. Biomechanics of hearing sensitivity. J. Vibr. & Acoust. 113, 1-13. 15. Yates, G.K. 1995. Cochlear structure and function, in Hearing, Moore, B.C.J. (Ed.), Academic Press. 16. Zwislocki, J. 1953. Wave motion in the cochlea caused by bone conduction. J. Acoust. Soc. Am. 25, 986-989. 17. Bekesy, G. 1960. Experiments in Hearing. McGraw-Hill Book Company, USA. 18. Kemp, D.T., 1978. Stimulated acoustic emissions from within the human auditory system. J. Acoust. Soc. Am. 64, 1386-1391. 19. Shera, C.A. 2003. Wave interference in the generation of reflection- and distortion- source OAEs. Biophysics of the Cochlea: From Molecule to Model, pp.43 9-449. World Scientific, Singapore.

Comments and Discussion Ruggero: In contrast with the opinion expressed in your contribution, work in my laboratory has demonstrated that a comparison of group delays of basilar-membrane vibrations and stimulus-frequency otoacoustic emissions permits to evaluate a popular theory of the origin of otoacoustic emissions (the "theory of coherent reflection filtering" of Zweig and Shera). Specifically, our paper (Siegel et al., JASA, October 2005, now in press) contradicts a key prediction of that theory and thus invalidates it. Answer: The results I presented here are consistent with the CRF theory and contradict the conclusion of your paper (Siegel et al., JASA, October 2005, In press). Your paper does not invalidate the CRF theory but rather questions it. In examining experimentally the CRF theory, we need to understand the limitations of all of the paradigms used for data acquisition for the experiments performed in relation to this theory.

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Ruggero: I do not agree with your statement that "group delay has ... been found to be representative of BM estimates of cochlear delay only at low stimulus levels". Please see the appropriate sections of my review with Luis Robles (Physiological Reviews, 2001). Answer: With respect to your second comment, you have misquoted me. I stated that SFOAE estimates of group delay calculated from the phase gradient are only comparable with BM estimates of group delay at low stimulus levels. SFOAE estimates of group delay based on the phase gradient are confounded at higher stimulus levels by the contribution to the phase from emission generated by a wavefixed mechanism (see Goodman et al., 2003, 2004). Ruggero: Please provide some justification for that statement. Ruggero: Re: contradictions and invalidations: the in-press paper on SFOAEs by Siegel et al. (JASA October 2005) falsifies the theory of coherent reflection filtering because it invalidates one of its "key predictions", namely the delay prediction. [A "key prediction (of the CRF theory) is that reflection-source-emission group delay is determined by the group delay of the basilar-membrane (BM) transfer function at its peak". More precisely, the CRF theory predicts that, for low stimulus levels, "the SFOAE group delay is approximately equal to twice the group delay of the BM mechanical transfer function, evaluated at the cochlear location with CF equal to the stimulus frequency".] Note that the preceding two sentences, from the Siegel et al. paper, are direct quotes from (Shera and Guinan, 2003). Re "misquotation": I have not misquoted you. The statement that "...group delay has been ... found to be representative of BM estimates of cochlear delay only at low stimulus levels" is a verbatim quote from your Preliminary Manuscript for the Portland MOH Meeting (see lines 23-27 of page 259). Answer: Yes, there is an error of omission and "OAE" should precede "group delay" in the sentence. If you read on further in the same sentence it is clear that I am referring to OAEs. I presumed that your original question referred to my talk in which no such error of omission was made and the statement was as given in my previous response. Siegel: It is hard to see how your measurements test the CRF theory, particularly what quantitative predictions of onset delays would emerge from a model incorporating both nonlinearity and coherent reflection, with the stimulus conditions and methods you use. Your measurements may be relevant, but the only way to know would be to simulate them using a real model. Your choice of a fairly high level for LI in your pulsed f2 DPOAE paradigm almost certainly reduces the gain of the cochlear amplifier for f2 with a corresponding reduction of the near-CF group delay at the f2 place. It is also uncertain where the DPOAE detected at onset originates within the generation region, since ramping f2 on presumably results in a time-varying excitation pattern that shifts toward the base as the amplitude of f2 increases. So it cannot be readily determined whether the first

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observable DPOAE originates near the f2 place with some particular propagation delay, or further basal, where the propagation delays are shorter. In contrast, your nonlinear SFOAE extraction paradigm guarantees that the SFOAE generated first by the lowest-level excitation as the tone is ramped on will be missed, since this method removes any linear component of the response, whether that might be the stimulus pressure or the low-level (quasilinear) part of the emission itself. This will artificially lengthen the onset delay by an unknown time. The combined effect of the two paradigms should be to underestimate the SFOAE delay reduce the onset delay of the DPOAE in the direction of the relatively larger SFOAE delays indicated by your data. Interpreting the SFOAE delay is further complicated by the possible contribution of a nonlinear reflection component, as suggested by Tahnadge and colleagues. Our paper in press demonstrates failure of the delay prediction of the CRF theory as originally proposed. This does not address the reflection mechanism itself, but only the mode of propagation to the stapes. The discrepancy is not in the SFOAE group delay data cited as evidence for the CRF theory, but in what we believe to be comparisons with unrepresentative values of basilar membrane group delay at CF. It is logical to reject a theory based on the failure of a key prediction. But a modified version of the CRF theory may produce SFOAE delays in better agreement with more direct measures of group delay at CF. Answer: Two-tone suppression and nonlinearity are two sides of the same coin, unavoidable in any examination of cochlear function. It does not follow that twotone suppression necessarily contaminates using emissions to measure cochlear travel times, although it is indeed a caveat (the same caveat that applies to SFOAE measurements such as those reported in Siegel et al in JASA (in-press) where the emission was extracted using a suppression paradigm). Your comments concerning the DPOAE measurements, unsubstantiated as they are by either experiment or a realistic time domain nonlinear cochlear model that includes two-tone suppression effects, are difficult to respond to. It is indeed true that the nonlinear extraction paradigm will not produce the earliest part of the ramp of an SFOAE evoked by a tone-burst where the effective stimulus level is sufficiently low that the growth of the emission is effectively linear. But, the definition of signal onset used in this manuscript was 10% of the peak amplitude of the f2 signal, or approximately 50 dB pSPL. Cleary a qualifier to the data presented here (and presented in more detail in Withnell et al, 2005, in-press) is how well this definition corresponds to the actual physical delay. And indeed, the SFOAE, unlike the DPOAE, cannot be extracted using Fourier analysis, the method of extraction (suppression, nonlinear derived technique) not necessarily extracting the whole emission. It is worth noting that comparison of the SFOAE average group delay extracted using a nonlinear extraction technique with a 6 dB stimulus ratio (Goodman et. al., 2004) with that of the average group delay for an SFOAE extracted using the Brass & Kemp suppression paradigm (Shera and Guinan, 2003)

331 shows the group delays matched for stimulus frequency and level to be essentially the same. Further, the average group delay reported by Shera and Guinan (2003) for the SFOAE (extracted in the same way as Siegel et. al. (in-press)) with a stimulus level of 40 dB SPL is 1.1 to 1.4 ms, a value that agrees well with the signal onset delays of 1 to 1.3 ms reported here with a stimulus level of 47 dB SPL (50 dB pSPL) (in a quasi-linear, dispersive system the signal onset delay is equivalent to the group delay provided the input signal is sufficiently narrow-band). The signal onset delay comparison presented here between the SFOAE and the 2flf2 OAE suggests a bi-directional slow wave mechanism but the variability in the data qualifies this interpretation. This variability, common to both types of OAE, has been explored further (Withnell et. al., 2005, in-press), but additional studies are necessary to understand its origin.

DISTORTION P R O D U C T OTOACOUSTIC EMISSIONS IN THE AMPHIBIAN EAR

P I M VAN D I J K Dept. of Otorhinolaryngology, University Medical Centre School of Behavioral and Cognitive Neurosciences, University The Netherlands E-mail: [email protected]

Groningen of Groningen

SEBASTIAAN W . F . MEENDERINK Dept. of Otorhinolaryngology, University Hospital Maastricht Institute Brain and Behaviour, Univeristy of Maastricht The Netherlands E-mail: [email protected]. nl By comparing the range of emission frequencies with that of neural characteristic frequencies of the amphibian and basilar papillae, the emission generation site may be inferred. Spontaneous otoacoustic emissions in the amphibian ear seem to originate from the amphibian papilla. In contrast, distortion product otoacoustic emission are presumably generated by both the amphibian and the basilar papillae. Distortion products from the amphibian papilla are very sensitive to ischemia; distortion products from the basilar papilla are less sensitive. These results suggest that the basilar papilla may not include an active amplifier. In support of this hypothesis, we show that distortion products from the basilar papilla show only a weak temperature dependence. These emissions are possibly independent of metabolic rate. The basilar papilla in frogs may be the only passive vertebrate hearing organ. In contrast, emissions from the amphibian papilla are clearly temperature dependent, consistent with active auditory processing.

1

Introduction

T h e frog inner ear includes two hearing organs with high sensitivity t o airborne sound: the amphibian papilla (AP) and the basilar papilla (BP). In b o t h papillae, the hair cells are on a relatively stiff support; there is no flexible basilar membrane. The hair cells in the A P and the B P are covered by a tectorial membrane, which presumably serves to direct acoustic energy from the inner fluids t o t h e hair cells and may be a substrate for mechanical tuning [1]. There are a number of important differences between these two papillae. The A P is larger, with 1100 to 1200 hair cells, versus only about 100 hair cells in t h e B P (numbers for Rana catesbeiana; reviewed in [2]). In contrast t o t h e inner and outer hair cells in the mammalian inner ear, neither papilla holds hair cells with obvious functional or anatomic specializations. The A P has a tonotopic organization with low and high frequencies exciting rostral and caudal neurons, respectively

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333 [3]. In contrast, in the B P of an individual frogs the majority of neurons have nearly identical tuning properties [4], with a characteristic frequency above the highest characteristic frequency of the AP. Thus, the two papillae function as complementary hearing organs, with the A P being a frequency analyzer with highest sensitivity to relative low-frequencies while the BP seems to function as a single auditory filter, tuned to the highest frequencies in the frog's hearing range. Otoacoustic emissions from the amphibian ear were first described by Palmer and Wilson [5]. This showed t h a t otoacoustic emissions can be generated in an ear without a basilar membrane and without sensory cells similar to mammalian outer hair cells. The best documented emissions from the amphibian ear are spontaneous otoacoustic emissions (SOAEs) and distortion product otoacoustic emissions (DPOAEs). Fig. 1 compares neural characteristic frequencies to the frequency ranges for which these two types of otoacoustic emissions have been detected. DPOAEs can be detected in the range of characteristic frequencies of both the A P and the BP. In Rana pipiens, the D P gram displays a notch near the frequency-separation of the AP and the BP. Presumably, near this notch D P O A E components from the AP and the B P interfere. In Hyla cinerea, relatively few neurons are tuned to frequencies between 1200 and 3000 Hz. In this gap interval, no D P O A E s were detectable. By comparing the distribution of neural characteristic frequencies (panels A and B) to the frequency ranges of DPOAE-generation (panels C and D), we concluded that both the A P and the B P generate distortion products. DPOAEs from the A P and the B P differ with respect to several properties. For low stimulus levels (<70 dB SPL), input-output functions of DPOAEs from the A P have rather shallow slopes ( < 1 d B / d B ) , similar to those in other vertebrate species. In contrast, DPOAEs from the BP grow much more steeply (2-3 d B / d B ) [7]. In addition, DPOAEs from the AP are more vulnerable to disruption of the normal physiology: ceasing the oxygen supply t o the inner ear abolishes low-level DPOAEs in the A P within 6 minutes. In contrast, in the B P the decay takes place over approximately half an hour [11]. In contrast to DPOAEs, SOAEs seem to originate from the AP only. In both ranid and hylid frogs, the range of SOAE frequencies (see Fig. 1, panels E and F) approximately corresponds t o the upper octave of the amphibian papilla (see panels A and B). Remarkably, the highest SOAE frequencies somewhat exceed the highest characteristic frequencies from the AP, but this may be due to differences in the body temperature at which the measurements were taken. These results may imply that the B P functions as a passive hearing organ, without the ability to generate SOAEs and with DPOAEs resulting from a passive nonlinear response. If true, DPOAEs from the B P may not depend on

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1000 2000 3000 Primary frequency f^ (Hz)

SOAE frequency (Hz)

Li

1000 2000 3000 SOAE frequency (Hz)

Figure 1. Comparison between neural characteristic frequencies and emissions frequencies for ranid (left column of panels) and hylid (right column) frogs. (A) Distribution of characteristic frequencies in Rana pipiens [4]. (B) Distribution of characteristic frequencies in Hyla cinerea [6]. In panel (A) and (B) the vertical dashed line indicates the boundary between AP and BP neurons. This boundary is also shown in the other panels. (C) Example of a DP-gram measured in Rana pipiens [7]. The noise floor in these measurements was at about -25 dB SPL. (D) Example of a DP-gram measured in Hyla cinerea [8]. The horizontal dash-dot line indicates the approximate noise floor of these measurements at -5 dB SPL. (E) Distribution of spontaneous otoacoustic emission (SOAE) frequencies in ranid frogs. Data from Rana esculenta [9] and Rana pipiens [10] were combined. (F) Distribution of SOAE frequencies in hylid frogs. Data from Hyla cinerea, Hyla chrysoscelis and Hyla versicolor were combined [10].

metabolism and may be nearly insensitive to temperature. This would put the frog basilar papilla in a unique position among vertebrates: it may be the only vertebrate hearing organ without active feedback.

335 2

Material and M e t h o d s

Distortion products otoacoustic emissions were recorded from nine ears of 5 frogs, Rana pipiens pipiens. The animals were anaesthetized with an intramuscular injection of a pentobarbital sodium solution (diluted Nembutal; effective dosage 30 A*g/kg body weight). Emissions were recorded using a Bruel & Kjaer condenser microphone, model 4179. Pure tone stimuli were played through two E-A-RTONE 3A speakers. Custom-built software controlled Tucker Davis System 3 hardware for stimulus generation and response registration. The frog body temperature was controlled using a custom-built waterbath and measured with a small K-type thermocouple, placed in the frog's oral cavity. 3

Results

The effect of changing body temperature was different for D P O A E s generated by high-level stimuli (> 80 dB SPL) as compared to emissions generated by low-level stimuli (< 70 dB SPL). The high-level emissions did not consistently depend on temperature, both for the amphibian and the basilar papilla. In contrast, low-level emissions from the AP consistently and reversibly decreased in amplitude when the body temperature was reduced (average rate of change 6.2 [s.d. 3.7] dB/10°C). For low-level DPOAEs from the basilar papilla the effect of body temperature was significantly less (average rate 2.9 [s.d.4.6] dB/10°C). Fig. 2 displays an example for one frog; these data were obtained in a single experiment, with emissions from the AP and B P recorded in parallel. 4

Discussion

These results underline the important differences between the AP and the BP in frogs. The small temperature dependence of DPOAEs from the BP may imply that their generation does not require energy from metabolism. They may have been generated by passive nonlinear reflection. In contrast, DPOAEs from the AP clearly depend on temperature; their generation presumably involves an active biological mechanism. The conclusion that the AP is active and the BP passive is supported by the absence of spontaneous otoacoustic emissions in the frequency range of the B P (see Fig. 1) and the relatively slow decay of D P O A E amplitudes when the oxygen supply is interrupted [11]. The frog B P may be the only vertebrate hearing organ which does not rely on active mechanical feedback. Remarkably, hearing in the AP and BP frequency ranges show similar sensitivity. How can the B P be sensitive without an active mechanism? In contrast

336 Amphibian papilla

Basilar papilla :25..28 dB SPL

m :22..25 m 19..22 m 16..19

T=21°C7o

13.. 16 10..13 :7..10 :4..7

5

%o

Stimulus level L, [dB SPLJ

60 ~ 70 so Stimulus level L| [dB SPL]

1..4

:-2..1 •5..-2 :-8..-5 11..-8 14..-11

T=12°C70

17..-14

60 70 Stimulus level L, [dB SPL]

50

60 70 80 Stimulus level L, [dB SPL]

Figure 2. Temperature dependence of the amplitude of DPOAEs. All measurements were taken from a single subject. Each panel displays the dependence of the amplitude of the distortion component at 2/2 - /1 on the levels L% and L2 of the stimulus tones. The emission response level is illustrated by the graylevel code. The arrows indicate the phase of the distortion product, relative to the phase at the highest stimulus levels (upper right in each panel). (A) / j = 8 1 4 Hz, h/fi=l.l, body temperature 21 °C, (B) / i = 1 6 0 6 Hz, / 2 / / i = l . l , body temperature 21 °C, (C) same as panel (A), but at body temperature 12 °C, (D) same as panel (B), but at temperature 12 °C. These results show that in the amphibian papilla, DPOAEs in response to low-level stimuli disappear as a result of cooling. In contrast, low stimulus level DPOAEs from the BP exhibit a minor temperature dependence.

to other vertebrate hearing epithelia, the mechanics of the BP does not support a tonotopic organization; within each subject, neurons contacting the BP have virtually identical tuning curves [4]. Possibly, the coupling of hair cells into a single auditory filter reduces noise in the basilar papilla. The insensitivity to temperature may be useful for the ectothermic frog. It provides the frog with consistent spectral information, regardless of ambient temperature.

337 Acknowledgments This work was supported by the Netherlands Organization for Scientific Research (NWO) and the Heinsius Houbolt Foundation. References 1. S. Authier, G. A. Manley, A model of the frequency tuning in the basilar papilla of the Tokay gecko, Gekko gecko, Hear. Res. 82 (1995) 1-13. 2. J. H. Fox, Morphological correlates of auditory sensitivity in anuran amphibians, Brain Behav. Evol. 45 (1995) 327-338. 3. E. R. Lewis, E. L. Leverenz, H. Koyama, The tonotopic organization of the bullfrog amphibian papilla, an auditory organ lacking a basilar membrane, J. Comp. Physiol. 145 (1982) 437-445. 4. D. A. Ronken, Spike discharge properties t h a t are related to the characteristic frequency of single units in the frog auditory nerve, J. Acoust. Soc. Am. 90 (1991) 2428-2440. 5. A. R. Palmer, J. Wilson, Spontaneous and evoked otoacoustic emissions in the frog Rana esculenta, J. Physiol. 324 (1982) 66P. 6. R. R. Capranica, A. J. M. Moffat, Neurobehavioural correlates of sound communication in anurans, in: J. P. Ewert, R. R. Capranica, D. J. Ingle (Eds.), Advances in vertebrate neuroethology, Plenum, New York, 1983, pp. 701-730. 7. S. W. F. Meenderink, P. Van Dijk, Level dependence of distortion product otoacoustic emissions in the leopard frog, Rana pipiens pipiens, Hear. Res. 192 (2004) 107-118. 8. P. Van Dijk, G. A. Manley, Distortion product otoacoustic emissions in the tree frog Hyla cinerea, Hear. Res. 153 (2001) 14-22. 9. P. Van Dijk, H. P. Wit, J. M. Segenhout, Spontaneous otoacoustic emissions in the European edible frog (Rana esculenta): Spectral details and temperature dependence, Hear. Res. 42 (1989) 273-282. 10. P. Van Dijk, P. M. Narins, J. Wang, Spontaneous otoacoustic emissions in seven frog species, Hear. Res. 101 (1996) 102-112. 11. P. Van Dijk, P. M. Narins, M. J. Mason, Physiological vulnerability of distortion product otoacoustic emissions from the amphibian ear, J. Acoust. Soc Am. 114 (2003) 2044-2048.

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Comments and Discussion de Boer: In view of the specific frequency regions of the BP and the AP, can you give us an idea of the frequency spectra of mating and communication calls of these animals? Answer: The mating call of Rana pipiens has frequency components in the range from a few 100 Hz to about 3500 Hz, with the main components below 2000 Hz [1]. Other communication calls of this species are in the same frequency range. In Hyla cinerea, the mating call has components around 1000 Hz and in the range from 3000 to 4000 Hz, with relatively little acoustic energy near 2000 Hz [2,3]. A comparison of these frequency ranges to the data in Fig. 1 of our paper shows, that for Rana pipiens and Hyla cinerea communication calls approximately match the frequency ranges of their amphibian and basilar papillae.

[1] A. S. Feng, J. C. Hall, D. M. Moffat, 1990. Neural basis of sound pattern recognition in anurans. Prog. Neurobiol. 34, 313-329. [2] H. C. Gerhardt, 1974. The significance of some spectral features in mating call recognition in the green treefrog (Hyla cinerea). J. Exp. Biol. 61, 229-241. [3] R. R. Capranica and A. J. Moffat, 1983. Neurobehvioral correlates of sound communication in anurans. In: J.-P. Ewert, R. R. Capranica, D. J. Ingle (Eds.), Advances in vertebrate neuroethology, Plenum, New York, pp. 701-730.

CALCIUM WAVES, CONNEXIN PERMEABILITY DEFECTS AND HEREDITARY DEAFNESS VALERIA PIAZZA 1 *, MARTINA BELTRAMELLO 1 *, FELIKSAS BUKAUSKAS 2 , TULLIO POZZAN 1 AND FABIO M A M M A N O ' 3 Venetian Institute of Molecular Medicine, via Orus, 2 - 35129 Padova,

Italy

'Department ofNeuroscience, Kennedy Center, Albert Einstein College of Medicine, Morris Park Ave., Bronx, NY, 1046 department

of Physics, University of Padova, via Marzolo 8, 35132 Padova, E-mail: fabio. mammano@unipd. it

1300

Italy

The complex deafness locus DFNBl contains GJB2, the gene encoding connexin 26 (Cx26) and GJB6, encoding Cx30, the two most abundant connexins in the inner ear (Petit et al., 2001). These connexins may form heteromeric/heterotypic channels in the gap junctions that interconnect cochlear supporting cells. By showing that a specific defect of Cx26 affects metabolic coupling mediated by IP3 we have recently offered a mechanistic explanation for the pathogenesis of deafness due to connexin mutations [1]. Abnormal or impaired connexin function has been linked to several other diseases, including skin disease, peripheral neuropathies, and cataracts [7], thus our data may have a more general impact. Gap junction blockade impairs the spreading of Ca2+ waves and the formation of a functional (glial-like) syncytium in cochlear supporting cells. Wave propagation necessitates also a regenerative mechanism mediated by P2Y receptors [6] and this may constitute a fundamental mechanism by which supporting cells co-ordinate their responses following activation of sensory hair cells by sound.

1 Introduction Early onset forms of hereditary hearing impairment in humans are monogenic in origin. Thirty-seven genes responsible for isolated hearing impairment in humans are known to date. Mutations in one of them, underlying the DFNBl form of deafness, have been found to be responsible for about half of all cases of human deafness in countries surrounding the Mediterranean Sea. DFNB1 is thus almost as frequent as cystic fibrosis. DFNBl can be caused by mutations in the GjB2 gene (121011), which encodes the gap junction protein connexin-26 (Cx26) or by GjB6 (604418), which encodes connexin-30 (Cx30). In the cochlea, Cx26 and Cx30 proteins exhibit overlapping expression patterns [13] (Fig. 1) that define two main communication compartments: an epithelial network, comprising supporting cells and adjacent epithelial cells, and a connective network.

These authors contributed equally to this work

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340

In principle, conncxin mutations might affect cell function in a number of ways; for instance, by altering protein expression levels, their trafficking and targeting to the plasma membrane, as well as the control of biophysical properties of the junctional channel (e.g., voltage and/or chemical-gating or channel permeability to second messengers) [9]. Recently, the ubiquitous second messenger IP3 has been implicated in the propagation of intercellular Ca2+ waves through cochlear support cells following mechanical stimulation of hair cells [6]. Figure. 1 Connexins in (he organ of Corli. (A) Confocal section through an organotypic culture of the organ of Corti labeled with an antibody against conncxin 26 (Cx26); scale bar, 40 um (B) Double labeling with antibodies against Cx26 and Cx30; scr, sensory cell region. (C) effect of gap junction inhibitors, carbenoxolone (Cbx) and CO2 on junctional conductance. Inset: fluorescence (top) and bright field image (bottom) of the a Hansen's cell pair loaded in situ with Oregon green 488 BAPTA-1 though the patch-clamp pipettes.

Models of Ca2+ waves that involve the production of IP3 are based on the diffusion of IP3 from a stimulated cell through gap junction channels into neighboring cells where it elicits Ca2+ release from intracellular stores [15,16]. The question then arises as to whether, and to what extent, the intercellular diffusion of IP3 does occur in the supporting cells of the organ of Corti and whether this is of functional significance. 2 Methods 2.1 HeLa cell culture and transfection A clone of HeLa cells essentially devoid of connexins [5] was provided by Dr. Klaus Willecke (University of Bonn, Germany) and cultured according to standard procedures. Cells grown to ~80% confluence on culture plates were transfected with plasmid DNA using Lipofectamine Plus 2000 (Invitrogen, Carlsbad, CA). Original Cx26 and Cx30 constructs were obtained from Dr Roberto Bruzzone (Institute Pasteur, Paris, France). The Cx coding sequences were cut out of the multiple cloning sites (MCSs) and ligated into the MCSs of pECFP-Nl and pEYFP-Nl vectors (BD Biosciences, Palo Alto, CA) to create fluorescent fusion proteins after transfections [21.

341 2.2 Organ cultures and immunofluorescence Cochleas were dissected from postnatal day 1-2 Sprague-Dawley rat pups in ice cold HEPES-buffered (10 mM, pH 7.2) HBSS and placed onto glass coverslips or MatTek dishes coated with lOug/ml CellTak (Collaborative Biomedical Products, Bedford, MA, USA), as previously described [6]. The experimental protocol for animal use was approved by the Institutional Animal Care and Use Committee of Padova University. Cultures were incubated in DMEM/F12 and maintained at 37°C for 1-2 days. Monoclonal antibodies against Cx26 and Cx30 (Zymed Laboratories, S. San Francisco, CA), were used for labeling of cochlear cultures. No crossreactions were observed between the two antibodies. 2.3 Electrophysiology and imaging For electrophysiological recordings, cultures were transferred to an experimental chamber mounted on the stage of an upright microscope (BX61, Olympus Optical Corporation, Tokyo, Japan) equipped with an infinity-corrected water-immersion objective (60x, 0.90 NA, LUMPlanFl, Olympus). Dual patch clamp recordings, fluorescence imaging, intracellular delivery of IP3 or fluorescent tracers were performed as previously described [1,2,6]. 2.4 IP} permeability estimate The total permeability, Pj, was obtained from measurements performed in pairs of transfected HeLa cells by dividing the flux, reaching the acceptor cell (cell 2) by the concentration difference, between donor (cell 1) and acceptor [18]. As a first-order approximation, concentration changes were estimated from the imaging data assuming rough proportionality between Ca2+ signals and IP3 concentration. The average IP3 permeability coefficient, pu was derived by dividing F, by the estimated number of open channels nu = gj I y, where y is single channel conductance [17]. For each frame in a sequence, gj was derived from the dual whole cell patch clamp data acquired simultaneously to the imaging data. All results are given as mean + S.D., unless otherwise stated. 3 Results For the first set of experiments we exploited organotypic cultures of rat cochlea. Delivery of IP3 via the patch pipette to a single supporting (Hensen's) cell in the organ of Corti, loaded with fura-2-AM and bathed in suramin, resulted in the rapid elevation of the [Ca2+]; in the patched cell. Ca2+ signals propagated to the nearest neighbors within 10 s, and declined thereafter. Omission of IP3 from the patch pipette resulted in no signal propagation. The previous experiments were repeated in organ cultures briefly superfused in medium saturated with 100% C0 2 to block gap junction channels. A few seconds after achieving the whole-cell configuration, with IP3 in the patch pipette, the acidifying extracellular medium was washed out. The

342 Figurc.2 Effect of C02 on intercellular communication among supporting cells of the organ of Corti. (A) Cell I was contacted by a patch pipette (outlined) loaded with 500 uM IP3. (B) Fura-2 ratio changes, AR, from the corresponding regions of interest in (A); intracellular delivery of IP3 started 30 s after the onset of the recording, while the culture was exposed to C02 (solid black bar) to block gap junction channels. During washout (empty bar) the 1.5 ml chamber was superfused with normal extracellular saline, flowing at 2 ml/min. (C) Selected frames from the sequence in (B) captured at the times shown, measured from the onset of IP3 delivery. Letters in square brackets in (C) and below the arrowheads in (B) are matched. Suramin was omitted on purpose to allow paracrine propagation of the stimulus. Note spread of the Ca2+ rise to cells at distances >60 urn from the patch-clamped cell 2-3 min after washout. Scale bars, 20 uni.

4 4

.2+1

[Ca ]; elevation remained confined to the patched cell for approximately one minute and thereafter began to spread to the neighboring eeils. Suramin was left out during these recordings, to allow for the paracrine effect of released ATP, and, consistently, the spread at later times reached well beyond the nearest neighbors (Fig.2). The spreading of the Ca + signal beyond the nearest neighbors observed upon C0 2 removal may reflect opening of connexin hemichannels that can release ATP [8]. Indeed in the presence of suramin, the Ca + rise remained limited to the nearest neighbor cells (not shown). Finally, delivering IP3 to a single Hensen's cell in a naive organ culture elicited a transient [Ca2*]; elevation in the patched cell, followed by a complex pattern of oscillations in the surrounding cells. The characteristics of these signals resembled those elicited by mechanical damage or by extracellular application of ATP [6]. Altogether these data suggest that the underlying mechanisms are the same: cell-to-cell diffusion of IP3 across gap junctions, release of ATP in the extracellular medium (endolymph, in vivo), activation of P2Y receptors at the endolymphatic side, ensuing in the regenerative propagation of intercellular Ca2+ waves and oscillations. For the second set of experiments, communication incompetent HeLa cells [5] were transiently transfected with human Cx26 constructs (hCx26) tagged with either one of two GFP mutants, CFP and YFP, at their C terminal end [2] (Fig.3, A).

343 Figure 3. IP3 permeability measurement in pairs of transfected HcLa cells expressing hCx26. (A) Differential interference contrast (DIC) image merged with the fluorescence image of the same field illuminated at 500 nm showing a small cluster of HcLa cells, two of which are positive for transfection with hCx2x tagged with YFP; scale bar, 15 urn. (B) False color images sampling the lime course of fura-2 fluorescence ratio changes, AR, at the times shown following intracellular delivery of IP3 first to cell 1 (at time t=5s, frames [a-c]) and, later, also to cell 2 (frame [d]); three color-coded ROls used in the computations are superimposed on frame [a]; scale bar, 10 urn. (C) Top, traces from the corresponding ROIs in (B), located on the two sides of the gap junction (traces n. I 5 10 TWO) and 2) and over the entire cell 2 (trace n.3); vertical arrows point at the onset of IP3 delivery to cell 1 (wc I) and cell 2 (we II); arrowheads, labeled a-d, mark acquisition times of the corresponding frames in (B). Bottom, junctional conductance (gj) monitored during image acquisition. (D) Voltage steps applied to cell 1 (A
iM-.J

UUli M

In control double patch clamp experiments, electrical coupling between untransfected HeLa cell pairs was null (g, = 0). We found null g, also in pairs transfected with the recessive deafness mutant V95M of Cx26, indicating that the mutation prevents the formation of functional channels despite assembling into junctional plaques. Instead, the g,- of V84L mutant transfectants was 45±15 nS, (n=13), i.e. slightly greater than that of the wt hCx26 (31+13 nS, n=9). Similar results (as far as V84L is concerned) were obtained in the paired oocyte assay [4] and, given the similarity in the expression pattern, altogether suggest that the V84L mutation does not affect the conductance of single gap junction channels. In the experiment of Fig.3, (B-E) we used fura-2 to monitor intracellular calcium concentration ([Ca21];) following delivery of IP3 to a cell in a pair transfected either with wt hCx26 and bathed in suramin (200 uM). During intracellular delivery of IP3 (100 uM) to wt hCx26 transfectants, [Ca2+]j elevated rapidly in the patched cell, followed by [Ca2+]j elevations in the coupled cell. In V84L transfectants, the average [Ca2l]j elevation in the patched cell was unaffected whereas [Ca2+]j elevations in the coupled cell were greatly diminished , suggesting a potential defect of permeability to IP3. No propagation of the Ca2' signal was ever

344

observed in control untransfected cells. As expected, the V95M mutant was characterized by complete blockade of the IP3-induced [Ca2+]j rise in the acceptor cell, paralleled by null electrical conductance. In V84L transfectants, the defect of IP3 transfer was quantified by combining single channel recordings (Fig.3, F) and Ca2+ imaging experiments to estimate the IP3 permeability coefficient, pu (see Methods [18]). The pu of homotypic V84L mutant gap junction channels was 8.3%+3.5% (n=13, p<10"5 Student /-test) of the wt hCx26 control (n=13, p<10"3 Student /-test) [1]. 4 Discussion IP3 permeability defects may translate in a deafness phenotype by interfering with sensory transduction, a process requiring transfer of K+ across the hair cells [10], which is sensed by the supporting cells [11]. K+ spatial buffering by cochlear supporting cells likely requires a coordinated activity. Indeed it has been suggested that the activation of Ca2+ dependent Cl-K co-transport systems in the supporting cells may be essential in maintaining the ionic balance of the cochlear fluids, with alteration in K+ levels leading to excitotoxic death of the hair cells [3,11]. In conclusion: i) the negligible effect of the V84L mutation on unitary conductance and its dramatic effect on IP3 transfer indicate that the exchange of two neutral aminoacids can produce structural changes that are critical for some, but not all channel functions; ii) metabolic communication, e.g. diffusion of IP3 and possibly of other second messengers across gap junctions appears essential for sound perception. Acknowledgements Supported by grants from the Telethon Foundation, (Project n. GGP02043), Ministero dell'Universita e Ricerca Scientifica (MIUR, FIRB n. RBAU01Z2Z8, PRIN-COFIN 2002067312002) to F.M., Centro di Eccellenza (co-ordinator, T.P.) and the Italian Health Ministry. References 1.

2.

Beltramello, M., Piazza, V., Bukauskas, F.F., Pozzan, T., Mammano, F., 2005. Impaired permeability to Ins (1,4,5)P3 in a mutant connexin underlies recessive hereditary deafness. Nat Cell Biol 7, 63-9. Beltramello, M., Bicego, M., Piazza, V., Ciubotaru, CD., Mammano, F., D'Andrea, P., 2003. Permeability and gating properties of human connexins 26 and 30 expressed in HeLa cells. Biochem Biophys Res Commun 305, 1024-33.

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3. Boettger, T., Hubner, C.A., Maier, H., Rust, M.B., Beck, F.X., Jentsch, T.J., 2002. Deafness and renal tubular acidosis in mice lacking the K-Cl cotransporter Kcc4. Nature 416, 874-8. 4. Bruzzone, R., Veronesi, V., Gomes, D., Bicego, M., Duval, N., Marlin, S., Petit, C , D'Andrea, P., White, T.W., 2003. Loss-of-function and residual channel activity of connexin26 mutations associated with non-syndromic deafness. FEBS Lett 533, 79-88. 5. Elfgang, C , Eckert, R., Lichtenberg-Frate, H., Butterweck, A., Traub, O., Klein, R.A., Hulser, D.F., Willecke, K., 1995. Specific permeability and selective formation of gap junction channels in connexin-transfected HeLa cells. J Cell Biol 129, 805-17. 6. Gale, J.E., Piazza, V., Ciubotaru, CD., Mammano, F., 2004. A mechanism for sensing noise damage in the inner ear. Curr Biol 14, 526-9. 7. Gerido, D.A., White, T.W., 2004. Connexin disorders of the ear, skin, and lens. Biochim Biophys Acta 1662, 159-70. 8. Goodenough, D.A., Paul, D.L., 2003. Beyond the gap: functions of unpaired connexon channels. Nat Rev Mol Cell Biol 4, 285-94. 9. Harris, A.L., 2001. Emerging issues of connexin channels: biophysics fills the gap. Q Rev Biophys 34, 325-472. 10. Jentsch, T.J., 2000. Neuronal KCNQ potassium channels: physiology and role in disease. Nat Rev Neurosci 1, 21-30. 11. Lagostena, L., Ashmore, J.F., Kachar, B., Mammano, F., 2001a. Purinergic control of intercellular communication between Hensen's cells of the guineapig cochlea. J Physiol 531, 693-706. 12. Lagostena, L., Cicuttin, A., Inda, J., Kachar, B., Mammano, F., 2001b. Frequency dependence of electrical coupling in Deiters' cells of the guinea pig cochlea. Cell Commun Adhes 8, 393-9. 13. Lautermann, J., ten Cate, W.J., Altenhoff, P., Grummer, R., Traub, O., Frank, H., Jahnke, K., Winterhager, E., 1998. Expression of the gap-junction connexins 26 and 30 in the rat cochlea. Cell Tissue Res 294, 415-20. 14. Petit, C , Levilliers, J., Hardelin, J.P., 2001. Molecular genetics of hearing loss. Annu Rev Genet 35, 589-646. 15. Sneyd, J., Charles, A.C., Sanderson, M.J., 1994. A model for the propagation of intercellular calcium waves. Am J Physiol 266, C293-302. 16. Sneyd, J., Wetton, B.T., Charles, A.C., Sanderson, M.J., 1995. Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a twodimensional model. Am J Physiol 268, C1537-45. 17. Verselis, V., White, R.L., Spray, D.C., Bennett, M.V., 1986. Gap junctional conductance and permeability are linearly related. Science 234, 461-4. 18. Verselis, V.K., Veenstra, R., 2000. Gap junction channels: Permeability and voltage gating. In: Hertzberg, E.L., (Ed.), Gap Junctions, Vol. 30. JAI Press Inc., Stamford, CT. pp. 129-193.

R E S O N A N T M O D E S O F O A E IN T H E I N V E S T I G A T I O N O F H E A R I N G

W.W. JEDRZEJCZAK, K.J. BLINOWSKA AND P.J. DURKA Department

of Biomedical Physics, Institute of Experimental Hoza 69, 00-681 Warszawa, Poland E-mail:

Physics, Warsaw University, ul. wiedrz(a)fuw.edu.pl

W. KONOPKA Department

of Otolaryngology, Medical University, ul. Zeromskiego 113, 90-549 Lodz, Poland E-mail: konopka(a),achilles. warn, lodz.pl

Transiently evoked otoacoustic emissions - TEOAEs (tones and broadband stimuli) - were analyzed by means of an adaptive approximations method based on the Matching Pursuit (MP) algorithm. This method is an iterative, nonlinear procedure which decomposes a signal into a sum of known waveforms of well defined frequencies, latencies, time-spans and amplitudes. It provides high resolution energy distributions in the time-frequency space. The MP method allows for direct and accurate determination of component latency, since that is one of the parameters returned by the procedure. It was found that the parameters of components identified by the MP method - amplitude, latency and time-span - are affected in case of hearing disturbance caused by noise. The MP method made it possible to identify the resonant modes that appear for a given subject, with the same frequencies and latencies for different stimulation frequencies. The same resonant modes were also identified in responses to click stimuli. The method of adaptive approximations opens new possibilities in the field of investigation of hearing mechanisms and offers new tools for diagnosis of hearing disturbances.

1 Introduction Transiently evoked otoacoustic emissions (TEOAEs) elicited by a click - a short, broadband stimulus - are one of the standard procedures in hearing tests. The response which follows this stimulus consists of several components of different frequencies and latencies. The use of a broadband signal allows for an assessment of functioning of the major part of the cochlea. However, in order to study properties of the response in narrower frequency bands, tone-burst stimuli are used. It was shown by Probst et al. [1] that the spectra of the summed responses to different frequency tones are similar to those evoked by a click. These results were later extended to hearing impaired patients by Probst et al. [2] and Prieve et al. [3]. These studies imply that, if one can uncover a method that extracts single frequency components from click-evoked TEOAEs, there is, in fact, no need to use tone-burst stimuli. In recent studies of OAE, continuous wavelet transform (WT) [4] or discrete WT [5] was used. However due to its poor frequency resolution wavelet transform systematically underestimates the slope of the latency-frequency relation. The method proposed by us, Matching Pursuit (MP), is free of the limitation of WT, which binds inversely time and frequency bands; moreover, the MP method

346

347

allows for decomposition of the OAE signal into its basic components described by means of well defined frequencies, latencies, amplitudes, and time-spans. 2 Methods 2.1

Matching Pursuit

The method of adaptive approximations is based on the decomposition of the signal into basic waveforms (also called atoms) from a very large and redundant dictionary of functions. Finding an optimal approximation of a signal by selecting functions from a very large and redundant set is a computationally intractable problem, therefore sub-optimal solutions are applied. The waveforms are fitted in an iterative procedure, starting with the atom giving the highest product with the signal, which means that it accounts for the largest part of the signal energy. Then the next atoms are fitted to the residues. This method is called Matching Pursuit (MP), and was described in detail in Jedrzejczak et al. [6]. We use a dictionary of Gabor functions, given by the formula: gr(t) = K(y,(t>)e

{ s

- > cos(m(t-u)+)

C1)

The components of the signal are described by the following parameters: frequency co, latency u, time-span s, amplitude K{y,(f) and phase <j). We have used a Gabor dictionary consisting of 106 atoms. It was shown in Jedrzejczak et al. [6] that Gabor functions approximate the signal of otoacoustic emissions very well. The idea of the method is illustrated in Fig.l. 2.2

Experimental procedures

Two data sets were analyzed. In both cases, otoacoustic emissions were recorded using the ILO 292 Echoport system designed by Otodynamics. Responses to 260 repetitions of stimuli were averaged with the "nonlinear" mode of stimulation. The acquisition window had a standard onset at 2.5 ms with a cosine rise/fall of 2.26 ms and flat top up to 20.5 ms.

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10 time [ms| Figure 1. Illustration of the MP method. At the top the OAE signal; below its time-frequency representation (energy in shades of gray), found in the iterative MP decomposition into 66 atoms (99.5 % of energy). At the left: spectrum obtained by summation of the time-frequency distribution in time. At the bottom of the picture the 5 highest energy atoms found by the iterative procedure are shown. Their time-frequency representations and corresponding spectral peaks are connected by lines.

The first data set consisted of the OAE recordings from 12 young (20-25 years) adult men. In pure tone audiometry the hearing thresholds were 10-15 dB. For all these subjects, the responses to a click stimulus and a set of tone bursts stimuli of 5 frequencies (1000, 1414, 2000, 2828 and 4000 Hz) and of half-octave bands were measured. The tone-burst stimuli were constructed to cover the same frequency band (850 to 4750 Hz) as the click stimulus. The second experiment concerned the influence of noise on OAE. Two datasets of click evoked OAEs from 124 ears were recorded. The first dataset was measured from 62 ears of male personnel who serviced aircraft (aged 24-51), thus these individuals were regularly exposed to jet engine noises. The second set, used as the control group, consisted of 62 ears from age-matched males. These subjects were laryngologically healthy with hearing thresholds of 10-15 dB HL. The subjects exposed to aircraft noise had threshold levels that were in average 6.6 dB higher. The protocol of the experiments was approved by the board of human experimentation. 3 Results 3.1

Click and tone-burst evoked OAE

Tone and click evoked OAE were decomposed by means of the MP algorithm and the parameters of the components were found. In most cases the basic features of

349

the click evoked OAE are reproduced by the first 15 waveforms, which account for 95% of the energy of the signal. When the components of the signal are known, it is straightforward to construct the time-frequency distribution of the energy density (Figures 2 and 3). The time-frequency (t-f) representations of the tone evoked OAE are presented in Fig. 2. Usually the atom of the highest energy was closest to the frequency of the stimulation. It can be observed that the frequency of the tone stimulus is not exactly reproduced in OAE and the response depends on the individual features of the subject's cochlea. Namely for each subject there are some privileged frequencies, which appear to a higher or lower degree for different frequencies of the stimulus. E.g. in Fig. 2 a component of frequency of around 2 kHz appears at stimulation frequencies of 1414, 2000 and 2828 Hz. 1000 Hz

1414 Hz

2000 Hz

2828 Hz

4000 Hz

6 5 14 dSSk

cr 2 P

0

0 0 20 0 20 0 10 20 10 20 0 10 20 °0~ 10 10 time [ms] time [ms] time [ms] time [ms] time [ms]

Figure 2. Time-frequency distributions of energy for an OAE signal evoked by tone burst stimuli (from 1000 to 4000Hz) for one subject. Frequency of the stimulation is given above the maps.

In Fig. 3, showing energy distribution of click evoked OAE in t-f space, the centers of the atoms for click and tones evoked OAE are shown together. We can observe that the centers of tone evoked OAE tend to be shifted toward longer latencies. This could have been expected from the fact that the stimuli in the case of bursts were applied with some delay. We can conjecture that the click evoked response is the superposition of the tone responses, which indicates the linearity of the mechanisms for the applied level of stimuli.

350

4

8 12 time [ms]

16

20

Figure 3. Time-frequency distribution of energy obtained by means of the MP decomposition of click evoked OAE. White dots indicate t-f centers of the main atoms of click evoked OAE. Dark dots mark the positions of the strongest atoms of responses to tone bursts.

In Fig. 4 a histogram of time spans of resonant modes is shown. It has a bimodal character. It seems that there are some short-time resonant modes as well as long-time resonant modes. The second ones are connected with spontaneous OAE. A 30

B 6 5

,_,

20

>> g3 d-2 &

10

""1 0

0

2

4

6 8 10 12 14 16 18 t ime -sp an [ms]

0

(

10 time [ms]

Figure 4. A: Histogram of the time-spans (durations) of atoms that can be considered as resonant modes. Cases with long duration represent synchronized spontaneous activity (SSOAE). B: Example of energy distribution in t-f space of TEOAE with SSOAE activity (components of long duration).

3.2

Ears influenced by noise

In order to make statistical comparisons, atoms were grouped in half-octave frequency bands. Only the highest energy components for each subject in each band were selected for further analysis. Frequency-latency dependence as shown in Fig. 5A is logarithmic, which is a consequence of the cochlear structure. For the band up to 1414 Hz, there were no significant changes in the exposed group, but for higher frequencies, there was a significant shift towards longer latencies.

351 The time span parameter proved to be the least influenced by exposure of subjects to jet-engine noise. In Fig. 5B the trend can be observed that in all bands the duration of components of TEOAEs from ears exposed to noise was longer than in the non-exposed case. However, the difference between the two datasets was found to be statistically significant only for the 2000 Hz and 2379 quarter-octave band. B • -e• ^

X 3

•*-

6 5

exposed , norma!

4

•

• * -

'N*

-

exposed . normal

.

X 3

i e - ^a>» •e< •*• H3H

• O

•*.

mm<

(4»^SH"4

M3»

ien ""KWH

M

8 10 12 14 1S1B20 latency (msj

2

3 4 5 6 7 8 910 time span [ms]

Figure 5. A: Quarter-octave average latencies of waveforms fitted to the TEOAE signals for non-exposed (circle) and exposed subjects (rectangle). B: Quarter-octave average time-span (durations in time) of waveforms fitted to the TEOAE signals for non-exposed (circle) and exposed subjects (rectangle).

4 Discussion Application of adaptive approximations by the MP algorithm allowed for identification of OAE intrinsic components, which eluded conventional methods of signal analysis. This was possible because of the high time-frequency resolution of MP and the parametric description of the components by parameters with a clear meaning, namely: their latencies, frequencies, time spans and energy (or amplitude). Usually most of the energy of the signal is described by a few components only. Comparison of t-f energy distributions for tone and click stimuli revealed that the MP decomposition into components gives practically the response to the individual tones. An advantage of the MP approach is that from one measurement of click evoked OAE, responses to particular tones may be extracted. In earlier OAE works, which used filtration to determine latency (Prieve et al. [3]), no significant differences between latency in OAEs of normal and impaired ears were found. This outcome was probably due to a poor resolution and a high bias of the filtration method. In their study of a group affected by impulsive noise, Sisto and Moleti [5] detected, by wavelet method, a shift towards longer latencies in the frequency range from 1-2 kHz with no changes in the 4.4 kHz band. The results of the present work show shifts in frequencies higher than 2 kHz. Changes in latencies observed here for the higher frequency region are compatible with the

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decreasing amplitude and also with the fact that the cochlear structures responsible for high-frequency perception are more prone to damage. The time-span of a component is a parameter not available in the other analysis methods. For healthy subjects, it had values from 2 ms for 4 kHz, to 4.5 ms for 1 kHz. We have also observed components with very long time-spans that are possibly connected with synchronized spontaneous activity. Acknowledgment This work was partly supported by a grant of the Polish Ministry of Scientific Research and Information Technology no. 3 Tl IE 003 28. References 1. Probst, R., Coats, A.C., Martin, G.K. and Lonsbury-Martin, B.L., 1986. Spontaneous, click-, and toneburst-evoked otoacoustic emissions from normal ears. Hear. Res. 21, 261-275. 2. Probst, R., Lonsbury-Martin, B.L., Martin, G.K., Coats, A.C., 1987. Otoacoustic emissions in ears with hearing loss. Am. J. Otolaryngol. 8, 7381. 3. Prieve, B.A., Gorga, M.P., Neely, S.T., 1996. Click- and tone-burst-evoked otoacoustic emissions in normal-hearing and hearing-impaired ears. J. Acoust. Soc. Am. 99, 3077-3086. 4. Tognola, G., Grandori, F., Ravazzani. P., 1997. Time-frequency distributions of click-evoked otoacoustic emissions. Hear. Res. 106, 112-122. 5. Sisto, R., Moleti, A., 2002. On the frequency dependence of the otoacoustic emission latency in hypoacoustic and normal ears. J. Acoust. Soc. Am. I l l , 297-308. 6. Jedrzejczak W.W., Blinowska K.J. Konopka W., Grzanka A., Durka P.J., 2004. Identification of otoacoustic emission components by means of adaptive approximations. J. Acoust. Soc. Am. 115, 2148-2158. Comments and Discussion Guinan: Does your method produce unique results? If not, then how do you interpret the different results you get from the same data? Answer: Yes, the method produces unique results, if the set of waveforms used to fit to the signal (called dictionary) is big enough to cover all frequency and time positions of signal features. In our case the dictionary was big enough - 106 waveforms. de Boer: In my youth I occupied myself with radioactive decay. The procedure to analyze a given decay function went as follows. You approximated the given function by an exponential function, as well as you could. Then you subtracted that

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function. The remainder was again approximated by an exponential function, with a different coefficient, etc. That procedure, known as 'peeling', often diverged. Your procedure resembles it. How do you protect yourself against divergence? Answer: It was proven in Mallat and Zhang (Matching pursuits with timefrequency dictionaries. IEEE Trans. Signal Process. 1993, 41, 3397-3415) that if dictionary (set of waveforms used to fit to the signal) is dense enough in respect to analyzed signal then Matching Pursuit procedure always converges to this signal.

D P O A E FINE S T R U C T U R E C H A N G E S AT H I G H E R STIMULUS LEVELS - E V I D E N C E FOR A N O N L I N E A R REFLECTION COMPONENT G. R. L O N G Speech and hearing Program, Graduate Center, City University Fifth Ave, New York, 10016, USA E-mail: glongQgc. cuny.edu

of New York,

365

C. L. T A L M A D G E National

Center for Physical Acoustics, University of Mississippi, Mississippi 38677, USA E-mail: [email protected]

University,

The effects of changes in primary level on DPOAE are evaluated using frequencymodulated primaries (log frequency sweeps), which maintain a constant frequency ratio. We use 8s/octave sweeps to evaluate the DPOAE fine structure, and 2s/octave sweeps to evaluate the generator component alone. Using this procedure we have obtained data over a wide range of levels in one session, permitting evaluation of changes in the relative level of components with level. The fine structure spacing and phase of DPOAE at higher primary levels are consistent with the development of a nonlinear reflection component from the distortion product region as hypothesized in Talmadge et al., (2000).

1

Introduction

The most commonly investigated distortion product otoacoustic emission (DPOAE) is 2/i — fa, which is produced when two tones of frequencies fa and fa (where fa > fa) are introduced to the ear. Whenever DPOAEs are measured with sufficiently fine frequency resolution, stable pseudo-periodic fluctuations in the level and phase of the D P O A E with frequency are observed. Much current research and models [1] support the claim that this fine structure is generated by the interaction of two components having different phase variations with frequency. The distortion is thought to be generated near the fa tonotopic frequency, leading to a wave-fixed component with a corresponding slow phase change with 2fa — fa frequency for fixed primary ratio fa/fa- This "generator component" is thought to be primarily dependent on the nonlinear properties of the cochlea and thus is also referred to as the "nonlinear component." Part of this generated energy travels basally towards the oval window, while the rest travels apically to the 2 fa — fa tonotopic location, where a fraction of this apically traveling component is then reflected back basally. The amount

354

355 reflected depends on the properties of the basilar membrane and is thus place fixed, and consequently the phase of the reflected component changes rapidly with frequency. There are thus two principal D P O A E components at the oval window: One having a short latency and slowly-varying phase with frequency, and the other having a longer latency and rapidly-varying phase. (Note that additional components are expected resulting from multiple internal reflection [5].) The combined signal amplitude at the oval window (and in the ear canal) will be enhanced when the two primary components are in phase and reduced when they are out of phase, resulting in the observed D P O A E fine structure. The relative amplitudes of the two components depends on level, and thus the fine structure pattern also depends on stimulus level [1]. Some models [2] suggest that additional components might be generated at higher stimulus levels. At low distortion levels, the reflection from the characteristic region depend linearly on level, but at higher levels a nonlinear reflection is predicted t h a t is wave fixed, and thus has phase t h a t varies only slowly with frequency. Furthermore as the stimulus levels are increased, the traveling wave broadens, potentially giving rise to distortion from more basal regions of the traveling wave [3]. Much clinical and basic research using D P O A E s assumes t h a t the signal in the ear canal is associated with activity from the overlap region alone. A better understanding of the properties of the two components is essential. In order to evaluate the two (or potentially more) components we need high frequency resolution measures of D P O A E amplitude and phase. We have developed a more efficient procedure that frequency modulates (log or linear sweeps) the two primaries keeping / 2 / / 1 constant. Depending on the sweep rate and the analysis one can either obtain accurate representation of the D P O A E fine structure or the generator component uncontaminated with the reflection component [4]. In this paper we use this procedure to evaluate changes in the D P O A E fine stucture with level. 2

Methods

The effects of changes in primary level on D P O A E are evaluated using frequencymodulated primaries (log frequency sweeps) which maintain a constant frequency ratio. We used 8s/octave sweeps, and 2s/octave sweeps. Using this procedure we obtained data over a wide range of levels (L 2 =25—75 dB SPL. L i = 3 9 d B + 0 . 4 L2l equal level primaries were used for L2 above 65 dB SPL) and frequencies (/ 2 sweeping from 1000-4000, / 2 / / i = 1 . 2 2 ) in one session. Five members of Ph.D. program at the Graduate Center CUNY (2 males and 2 females) served as subjects. They were seated in a reclining chair in a double-walled IAC booth. All conditions were collected in a single session. C W

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has no spontaneous emissions, JL has one very small one, MH has a little larger one at low frequencies, the last two subjects MM and M W have several low level (below -5 dB SPL) SOAE. Custom programs for Mac computers (Mac OS X) controlled a Motu 828 D / A converter and wrote the data to disk for offline analysis. Two ER2 tube

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phones were connected to an ER10 microphone which was inserted in the ear canal. Before being digitized using the Motu 828, the signal from the microphone •was preamplified by the Etymotic preamplifier and then amplified and filtered (300-10,000Hz) by a Stanford SR560 low noise amplifier under computer control. Sweeps with identical stimulus conditions (direction and duration) were av-

358 eraged to reduce the noise floor, or subtracted to estimate the noise floor. Sweeps with high noise levels were eliminated as long as a minimum of 8 sweeps could be averaged. Up and down sweeps were obtained to ensure that the rate of sweep did not effect the data and to provide an indication of the singal to noise ratio. In in interest of clarity we only present the upsweeps in this paper. At high levels the two curves are essentially identical. At lower D P O A E levels the sweeps vary somewhat a due to noise contamination. Sequential least-squares fit (LSF) analyses were used to extract the levels of the primaries and DPOAE. Overlapping Hann-windowed segments of data were LSF to in-phase and quadrature swept-tone components to obtain the amplitude and phase of the D P O A E .

3

Results

The fine structure obtained with the 8s/octave sweeps (2 octave taking 16s) differs greatly from subject to subject as can be seen in Figure 1. In all subjects the depth of the original fine structure decreases with increasing level, there are some small changes in the fine structure at lower levels but all showed major changes in the pattern at the highest level tested (L\ — Li = 75). A second wider fine structure appears this level at some frequencies in 2 subjects JL and MM. Examination of the phase from the same sweeps (Figure 2) reveals that the generator component is dominant at all levels for C W (the phase slope is always gradual. In all other subjects, the slope increases at low stimulus levels indicating that the reflection component becomes dominant at this level at some frequencies. Note that phase slope is reversed at the highest stimulus levels for JL. This coincides with the change to the wider fine structure in Figure 1, No fine structure is seen at higher primary levels when sweeping at 2s/octave (4s for 2 octaves) (Figure 3). At lower levels a wider fine structure similar to that seen for stimulus frequency OAEs is seen. It is is often associated with SOAEs. When the generator component was extracted from the 8s/octave sweeps using filtering in the time domain [5], the pattern was very similar to the 2s/octave sweeps. At higher primary levels the wider structure in JL is attenuated, but still visible. An Inverse Fourier Analysis of JL's d a t a reveals that their is an additional component with negative group delay. This component is there at all levels, but becomes equivalent in magnitude to the generator component near 70 dB SPL. In order to ensure that the effect did not stem from the sweeping primaries we established that the pattern of D P O A E fine structure was essentially identical when measured with more conventional procedures.

359

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4

Discussion

The large individual differences in D P O A E fine structure with level can be better evaluated by the combination of the 8s/octave and 2s/octave sweeps. The 2s/octave sweeps provide a rapid tool for evaluating the generator component uncontaminated by the reflection component. The phase properties at the high-

360 est stimulus levels for JL were predicted for stimulus frequency OAE [2] when reflectance on the basilar membrane or the oval window is large. It is possible that the middle ear reflex is starting to impact the D P O A E fine structure at the higher levels by changing the amount reflected back into the inner ear at the oval window. Alternatively, the pattern seen is consistent with Mills [3] claim that there are two components one near the narrow traveling wave maximum and the other stemming from the more basal passive component. The negative group delay does not reflect negative travel time. Group delay gives an estimate of latency in a linear system, when a single filter is being tested. The cochlear is nonlinear and frequency dispersive (the filter changes with frequency). A nonlinear reflection would generate short group delays, but the travel time would still be twice the round trip travel time. The group delay would thus not represent travel time, but would reflect the underlying processes. Acknowledgments This research was supported in part by PSC CUNY and the National Institute on Disability and Rehabilitation Research, US D O E Rehabilitation Engineering Research Center - Hearing Enhancement. Changmo Jeung, Monica Wagner, and Marcin Wroblewski helped with the data collection and analysis. References 1. Mauermann, M., Kollmeier. B„ 2005. Distortion product otoacoustic emission (DPOAE) i n p u t / o u t p u t functions and the influence of the second D P O A E source.. J. Acoust. Soc. Am. 116, 2199-2212. 2. Talmadge, C.L., Tubis, A., Long, G.R., Tong, C , 2002. Multiple internal reflections in the cochlea and their effect on D P O A E fine structure. J. Acoust. Soc. Am 108, 2911-2932. 3. Mills, D,M., 1997. Interpretation of distortion product otoacoustic emission measurements. I. Two stimulus tones. J. Acoust. Soc. Am. 102, 413-429. 4. Long, G.R., Talmadge, C.L., Lee, J., 2004. Using sweeping tones to evaluate D P O A E fine structure.. ARO Abstr. 27, 102-102. 5. Dhar, S, Talmadge, C.L., Long, G.R., Tubis, A., 2002. Multiple internal reflections in the cochlea and their effect on D P O A E fine structure. J. Acoust. Soc. Am 112, 2882-2892.

THE BIOPHYSICAL ORIGIN OF OTOACOUSTIC EMISSIONS JONATHAN H. SIEGEL Northwestern University, Dept. of Communication Sciences and Disorders, 2240 Campus Drive, Evanston, II 60208, USA E-mail: i-siezel(a),northwestern. edu While studied extensively since their discovery by Kemp in the late seventies, the cellular basis of the phenomenon of otoacoustic emission remains unknown. Data from experiments in humans, chinchillas and Mongolian gerbils was used to test the hypothesis that otoacoustic emissions originate in the hair cell transduction apparatus. Specifically, a double Boltzmann model of the transducer predicts that emissions generated by a single tone (stimulus frequency otoacoustic emissions - SFOAE) should be measurable at stimulus levels 20 or more dB below neural threshold, but sufficient to modulate the activity of enough transduction channels to produce a macroscopically observable result. On the other hand, for a fixed lowlevel probe tone that evokes SFOAE, it should only be possible to demonstrate the presence of emission by using a suppressor tone large enough to drive the transducer into its nonlinear range, approximately where the suppressor level reaches neural threshold. This result should be independent of suppressor frequency. Both predictions were confirmed experimentally in all three species. The threshold suppressor level was consistently near the threshold of the compound neural response monitored with an extracochlear electrode, even for suppressors more than an octave higher than the frequency of a low-level (30 dB SPL) probe tone. Cochlear microphonic responses were always detected at the lowest levels demonstrating SFOAE. The hair cell transducer appears to be the site of interaction between the probe and suppressor tones for all suppressor frequencies, consistent with a single suppression mechanism. Nonlinear interactions demonstrated in SFOAE and CM between widely separated tones do not appear to have a correlate in the basilar membrane, suggesting that, at least under some conditions, pressure waves can be initiated directly from forces produced by the hair bundle.

1 Introduction Recent reports indicate that otoacoustic emissions originate in the hair cell transducer under conditions in which the cochlear amplifier is rendered inoperative [1-3]. Interest in the transducer is further heightened by the recent evidence that the cochlear amplifier resides in the hair bundle [4, 5]. It is not known to what extent the transducer contributes to otoacoustic emissions at low levels in normal ears. Stimulus-frequency otoacoustic emissions (SFOAE), which appear to be tones emitted by the ear in response to a tone, can be measured at levels near threshold [6]. To separate the SFOAE from the stimulus tone (probe) that evokes it, it is common to use a second moderately-intense (suppressor) tone to selectively remove the SFOAE. If the suppressor completely removes the SFOAE, then the residual, calculated as the vector change in the probe response when the suppressor is added to the stimulus [7,8], provides an accurate measure of the emission. If the suppression is less than total, then the residual does not accurately represent the

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SFOAE. The part of the emission that is not suppressed may be erroneously considered part of the stimulus. Since the hair cell transducer has been implicated in the generation of otoacoustic emissions, it is of interest to explore the behavior of two-tone interactions in a computational model of the transducer and in experimental data. Experiments measured two-tone interactions in SFOAE and in the cochlear microphonic (CM) recorded from the round window. The CM is known to represent the summed receptor currents from hair cells [9], so similar two-tone behavior in SFOAE and CM would be expected if the transducer was the site of interaction of the stimuli for both phenomena. Measurements at near-threshold stimulus levels were used to simplify interpretations by restricting the cochlear region of interaction. 2 Methods These experiments were performed in anesthetized, tracheotomized chinchillas with body temperature maintained by a heating pad. The cartilaginous part of the ear canal and pinna and the lateral portion of the bony meatus are removed to allow optimal coupling of an Etymotic ER-10B+ otoacoustic emission probe. The bulla is opened to place a silver ball electrode on the round window to record CM and the compound action potential. Both middle ear muscles are severed from the ossicular chain. Animal procedures were approved by Northwestern Univeristy's IACUC. We measured stimulus frequency otoacoustic emissions using a variant of the commonly used suppression/vector subtraction method [7, 8, 10, 11]. The magnitude and phase of the residuals were expressed as the equivalent level and phase of a stimulus tone that would have produced the observed change in the ear canal pressure [10]. We simultaneously measured analogous suppression of the cochlear microphonic potentials in the same animals using the second A/D input of the sound card. Data were collected using Emav [12]. 3 Models and Results 3.1 Transducer model: Effect of bias The transducer model is a second-order Boltzmann fit to experimentallymeasured transducer functions [13, 14]:

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where g(t) is the conductance of the transducer, gmax is the maximum conductance, xse, is the offset from the normal operating point of the transducer function and x(t)) is the waveform of the input signal. Units of displacement are nanometers.

363

At the normal resting position (operating point) of the hair bundle (xset = 0), a small fraction of the transducer current is activated, due to transduction channels active at rest (Figure 1A). Deflections in the excitatory direction (positive) open more channels, while inhibitory deflections (negative) reduce the resting current by closing channels that were open at the resting position. The solid curve is the normal situation, while the dashed curve represents the addition of a static negative bias to the normal operating point. Figure IB depicts the output amplitude at the probe frequency for single tone excitation as a function of increasing input level. If the transducer set point is shifted to the right (xset= -50), the output amplitude is decreased significantly at low input levels, but grows rapidly to meet the response for the normal set point as the input amplitude is raised. The two curves exhibit relatively linear growth for input displacements below 15 nm. Figure 1. Basic character-istics of the hair cell trans-ducer. A: Displace-ment vs conductance plots for the normal set point and with the function displaced by 50 nm. B: Amplitude from the transducer of the response to a single tone for the two operating points depicted in A.

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Figure 2 quantifies suppression of the probe tone in the transducer model for two paradigms. In the first, the suppressor tone is held at a relatively high fixed level and the response to the probe tone is depicted as a function of increasing level (thin solid curves). The measure of the output at the probe frequency is not the suppressed output itself, but the change from the unsuppressed response to the probe tone, directly analogous to the "residual" SFOAE at the probe frequency measured using a suppressor tone to separate the stimulus from the emission. The response to the probe in the absence of a suppressor is depicted as the thick solid line. For suppressors above about 50 dB re 1 nm, the amplitude of the residual is almost exactly the same as that of the response to the probe by itself, indicating essentially complete suppression of the probe. For fixed suppressor levels below 50 dB re 1 nm, the residual underestimates the actual probe response with an error that is constant (in dB) with decreasing probe level. In the same way, incomplete suppression of an SFOAE yields an inaccurate estimate of the emission.

364 true probe response

Figure 2. Dependence of the amplitude of the residual in the transducer model as a function of the level of either the probe (thin solid lines) or suppressor (dashed line) with the other tone fixed in level as indicated. The response of the probe when presented alone is indicated by the thick solid line. For a sufficiently strong fixed suppressor (Ls = 60 dB) the residual accurately measures the probe response. If the suppressor level is lowered (i.e., Ls = 40 dB) the residual underestimates the true probe response. 0

20 40 Probe or Suppressor Level (dB re 1 nm)

60

In the second paradigm, the probe tone is fixed in level and the suppressor level is varied (dashed curve). The transducer model predicts that the residual will always be detected at a lower level in the first paradigm than in the second. This behavior can be understood by considering that the sum of the two tones must drive the transducer out of its "quasi-linear" range for suppression to occur. As long as the fixed suppressor tone amplitude is large enough to do this on its own, residuals at the probe frequency can be detected at levels far below those at which the probe drives the transducer into nonlinearity by itself. A shift in operating point similar to that shown in Figure 1 reduces the difference in thresholds for the two paradigms. 3.3

Experimental verification of model predictions

The SFOAE and CM data both conformed to the major predictions of the transducer model. The SFOAE residual measured in response to a 4 kHz, 30 dB probe tone with a fixed 60 dB SPL suppressor and varied probe level was consis-tently detected at probe levels close to 20 dB lower than the threshold for suppres-sion for the fixed probe conditions (Figure 3). This was the case both for suppressor tones near the frequency of the probe or more than an octave higher (interaction region likely basal to that of the cochlear amplifier for the probe). The appearance of the residual above the noise floor was at similar stimulus levels for both paradigms and for both the SFOAE and CM. The threshold for suppression with fixed probes was not strongly dependent on probe level, as long as the residual was clearly detected above the noise floor for suppressors near 60 dB SPL (not shown). Unlike the SFOAE, the CM can be observed directly without using a suppressor to separate the stimulus from the response. The CM residual with fixed suppressor was displaced below the CM at the probe frequency for both the 3.9 kHz and 10 kHz suppressors, demonstrating that the CM was not completely suppressed even by the most intense suppressors used (70 dB SPL (not shown)). The two curves were closer for the 10 kHz suppressor, probably resulting from the spatial weighting of the round window electrode favoring nearby CM generators. Virtually identical results (not shown) confirm these predictions in Mongolian gerbils and humans.

365

0

20 40 60 Probe or Suppressor Sound Pressure Level (dB)

0

20 40 60 Probe or Suppressor Sound Pressure Level (dB)

Figure 3. Two-tone interactions measured in a chinchilla. A: SFOAE suppression conforms to the predictions of the transducer model with no shift in operating point. The residual is always seen at lower levels with the fixed suppressor paradigm (thick curves) than for the fixed probe paradigm (thin curves). This is true both for a suppressor near the probe frequency (3.9 kHz, solid curves) and for a suppressor more than an octave above the probe frequency (10 kHz, dashed curves). B: Similar behavior is seen in the suppression of the CM. The probe alone CM (Lp varied) is consistently larger than the CM residual, indicating incomplete suppression.

With a fixed 4 kHz, 30 dB SPL probe, the threshold for suppression for suppressors near or above the probe frequency was typically within 5 dB of CAP threshold at the suppressor frequency (data not shown). The CM at the suppressor frequency was consistently observed at levels typically 20 dB below the threshold for suppression. 4 Discussion A second-order Boltzmann model of the hair cell transducer accounts for several features of two-tone suppression measured in SFOAE and CM. The suppression data indicate that the transducers in the living intact cochlea operate at set points in which a significant fraction of the transducer conductance is active at the resting position of the hair bundle. Surprisingly small vibrations of the basilar membrane appear capable of exciting hair cells sufficiently to contribute to SFOAE. For example, for the chinchilla, a 4 kHz, 30 dB SPL tone produces an rms displacement of about 0.3 nm at the 9.5 kHz place (Ruggero, private communication). This same displacement would be reached in a sensitive cochlea at around -10 dB SPL for a tone at CF. The suppressor evokes a CM above the noise floor around this same SPL and begins to suppress the 4 kHz probe near 20 dB SPL, corresponding to a displacement of about 5 nm. Since the round window CM presumably underestimates the level at which hair cell transducer currents become significant, it therefore appears that the 4 kHz

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probe tone evokes transducer activity at the place of the 10 kHz suppressor. We never demonstrated an SFOAE using a suppressor in which the probe tone would not have generated a CM "signal". It is reasonable to propose that the SFOAE is also a (suppressible) signal at even the lowest levels at which it is demonstrated. No suppression of the response to the 4 kHz tone should be evident in the basilar membrane vibrations at the 10 kHz place under these conditions [15], so hair bundle forces may create a pressure wave that contributes to SFOAE even near threshold. It has been proposed that the suppressor acts in two fundamentally different ways: it may remove SFOAE sources (signals) at the probe frequency that are actually present, or it may induce "...mechanical perturbations and/or sources of nonlinear distortion that would not otherwise be present..." [16]. However, in our measurements, it is plausible that the suppressor always removes a signal. Since CM suppression was not complete even at 70 dB suppressor levels, it appears likely that SFOAE suppression is also incomplete. If so, then it may be nearly impossible to completely suppress the SFOAE with suppressor tones that do not persistent and possibly pathological effects, even for probe tones as low as 30 dB SPL. It is difficult to know how much of the SFOAE goes undetected with suppressors commonly used to measure emissions. The range of stimulus levels over which the SFOAE can be considered a linear phenomenon appears to be confined to levels near and below CAP threshold. Nonlinear distortion is therefore likely to contribute significantly to SFOAE over most of their measurable range, not only at relatively high stimulus levels [17, 18]. Acknowledgments Supported by NIH grant DC-00419 and Northwestern University. References 1.

2.

3.

4.

Mom, T., Bonfils, P., Gilain, L., Avan, P., 2001. Origin of cubic difference tones generated by high-intensity stimuli: effect of ischemia and auditory fatigue on the gerbil cochlea. J. Acoust. Soc. Am. 110:1477-1488. Liberman, M.C., Zuo, J., Guinan, Jr., J.J., 2004. Otoacoustic emissions without somatic motility: Can stereocilia mechanics drive the mammalian cochlea? J. Acoust. Soc. Am. 116:1649-1655. Carvalho, S., Mom, T., Gilain, L., Avan, P., 2004. Frequency specificity of distortion-product otoacoustic emissions produced by high-level tones despite inefficient cochlear electromechanical feedback. J. Acoust. Soc. Am. 116:1639-1648. Chan, D.K., Hudspeth, A.J., 2005. Ca2+ current-driven nonlinear amplification by the mammalian cochlea in vitro. Nature Neurosci. 8:149-155.

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5. Kennedy, H.J., Crawford, A.C., Fettiplace, R., 2005. Force generation by mammalian hair bundles supports a role in cochlear amplification. Nature. 433: 880-883. 6. Schairer, K.S., Fitzpatrick, D., Keefe, D.H., 2003. Input-output functions for stimulus-frequency otoacoustic emissions in normal-hearing adult ears. J Acoust Soc Am. 114: 944-66. 7. Brass, D., Kemp, D.T., 1993. Suppression of stimulus frequency otoacoustic emissions J Acoust Soc Am 93:920-39. 8. Shera, C.A., Guinan Jr., J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: a taxonomy for mammalian OAEs. J Acoust Soc Am 105:782-98. 9. Dallos, P., 1973. The Auditory Periphery. Academic Press, New York. 10. Guinan, J.J., 1990. Changes in stimulus frequency otoacoustic emissions produced by two-tone suppression and efferent stimulation in cats. In: P. Dallos, CD. Geisler, J.W. Matthews, M.A. Ruggero and C.R. Steele (Eds.), The Mechanics and Biophysics of Hearing, Springer, Berlin, pp. 170-177. 11. Dreisbach, L.E., Chen, W., Siegel, J.H., 1998. Stimulus-frequency otoacoustic emissions measured at low- and high-frequencies in untrained human subjects. Assoc. Res. Otolaryngol Abs. 21:349. 12. Neely, S.T., Liu, Z., 1993. EMAV: Otoacoustic emission averager. Tech Memo No. 17 (Boys Town National Research Hospital, Omaha). 13. Kros, C.J., Lennan, G.W.T., Richardson, G.P., 1995. Voltage dependence of transducer currents in outer hair cells of neonatal mice. In: Active Hearing. A. Flock (Ed.) Elsevier Science, Oxford, pp. 113-125. 14. Lukashkin, A.N., Russell, I.J., 1998. A descriptive model of the receptor potential nonlinearities generated by the hair cell mechanoelectrical transducer. J. Acoust. Soc. Am. 103:973-980. 15. Rhode, W.S., Recio, A., 2001. Multicomponent stimulus interactions observed in basilar-membrane vibration in the basal region of the chinchilla cochlea. J. Acoust. Soc. Am. 110:3140-3154. 16. Shera, C.A., Tubis, A., Talmadge, C.L., Guinan Jr. J.J., 2004. The dual effect of "suppressor" tones on stimulus-frequency otoacoustic emissions. Assoc. Res. Otolaryngol Abs. 27:181. 17. Goodman, S.S.; Withnell, R.H., Shera, C.A., 2003. The origin of SFOAE microstructure in the guinea pig. Hear. Res. 183:7-17. 18. Talmadge, C.L., Tubis, A, Long, G.R., Tong, C , 2000. Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure. J Acoust Soc Am 108:2911-2932.

368 Comments and Discussion Siegel: Jont Allen offers a valid reason to calibrate the source impedance of an otoacoustic emission probe to allow separation of the stimulus from the emission. I worry about the practicality of this approach. There is some finite error in estimating the source impedance (it is a quantity derived from pressure measurements). It is not known whether these errors are sufficiently large to give misleading results regarding otoacoustic emissions, whatever that might mean. The problem is knowing with confidence that a reliable measure has been made. I calibrate the pressure response of my otoacoustic emission probe carefully and have good reason to trust the levels it reports to within 1 dB over the frequency range of measurements. Since the quantity I measure is pressure, that is an appropriate calibration, regardless of the theoretical advantages in estimating emission power.

SPONTANEOUS OTOACOUSTIC EMISSIONS IN LIZARDS, AIR PRESSURE EFFECTS ON THEM AND THE QUESTION OF POINT SOURCES AND GLOBAL STANDING WAVES GEOFFREY A. MANLEY Lehrstuhlfur

Zoologie der Technischen Universitat Miinchen, Lichtenbergstrasse Garching, Germany. Email: geoffrey. manlev(3),wzw. turn, de

4, 85747

Shera [1] proposed that pressure effects on the middle ear provide a model for distinguishing between a point-source and a global standing-wave model of SOAE generation. A point source is supposed to be insensitive to changes in the boundary conditions for oscillation, whereas a standing wave would be influenced. Changing middle-ear pressure in humans alters both frequency and amplitude of SOAE, supporting Shera's assumption that mammalian SOAE originate through global standing waves. Lizards are highly reliable generators of SOAE, but their hearing organ differs from that of mammals in size, structure and micromechanics. Thus they provide a good system in which to continue to examine ideas about the generation of spontaneous emissions. In lizards, both negative and positive pressure changes were produced in the ear canal by adding or withdrawing air. Increases in pressure led to no or only small changes in frequency and amplitude, whereas pressure drops led to a fall or rise in SOAE frequency of up to several percent and to amplitude loss. These changes were observed over much smaller pressure ranges than those necessary in humans. The question is discussed as to whether such data permit a clear distinction of the nature of the emission source.

1 Introduction Unlike laboratory mammals, lizards are very reliable producers of spontaneous otoacoustic emissions (SOAE [2,3,4]). SOAE in non-mammalian papillae are generated by the transduction channels of the hair-cell stereovillar bundles [3] and new evidence points to the involvement of channels in mammalian active processes as well [5,6]. The patterns of lizard SOAE spectra correlate with the specific anatomy of the auditory papilla, especially with the presence or absence of a continuous tectorial structure. Papillae with continuous tectorial structures tend to be large with many hair cells and produce few, large-amplitude spectral peaks. In contrast, papillae without a tectorial membrane or with a salletal tectorial structure tend to produce a larger number of peaks of smaller amplitude [7,8]. These lizard data suggest that morphological features are important in the patterning of SOAE spectra. This is compatible with the idea that SOAE arise from point or localized sources in the hearing organ that, for some reason, emit more strongly than other regions, but also with the idea that impedance irregularities permit only particular standing-wave patterns. Humans, uniquely among mammals, have significant numbers of SOAE peaks and these are spaced at both regular and irregular frequency intervals [9]. One possible 'point-source' explanation for such spectral patterns, in which the local properties of the papilla determine the spectral

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SOAE pattern, is morphological irregularity of the organ of Corti, especially apically, where the coiling is tighter [10]. Recent modeling work, however, suggests that the frequency patterning of SOAE spectra in humans is due to standing waves in the cochlea, set up between the active organ of Corti and reflection from the footplate of the stapes [1]. Such models assume that all hair cells of the cochlea are active and emit sound energy. Constructive interference of waves with particular path lengths to and from the middle ear would result in standing waves measurable as SOAE peaks, whereas destructive interference would obscure the presence of an active papilla at that frequency [1]. Irregular peak spacing in SOAE spectra is supposed to be due to impedance discontinuities. Although such models provide no explanation for the extreme rarity of SOAE in most laboratory mammals, they do model the common patterns of SOAE as reported by early workers (e.g., [11]). Since discussion of these distinctions has suffered from agreed definitions of the sources of SOAE, the following is offered: A point source is a localized group of hair cells that have sufficient spontaneous activity at a common frequency that part of the emitted energy is measurable in the ear canal. All the energy in point-source SOAE (PS-SOAE) derives from these local hair cells. The amplitude, however, will be sensitive to the impedance it sees - for example of the stapes footplate. In contrast, global standing-wave SOAE (GSW-SOAE) do not arise from a localized group of hair cells and even hair cells whose best response frequency is different may contribute energy to the signal. The SOAE signal derives from the funneling of energy by the particularities of standing-wave conditions in a given cochlear area: In the absence of a standing wave, no SOAE is observed. The relatively long path length leads to stable, narrow GSW-SOAE peaks. Experiments altering the properties of the middle-ear interface to the cochlea, such as changes in the relative air pressure across the tympanic membrane, are supposed by Shera [1] to provide a means of distinguishing between the pointsource and global standing-wave models of SOAE patterning. Whereas a point source should not be influenced by the properties of the middle-ear interface, global standing waves should be. Changes in middle-ear pressure have long been known to affect SOAE in humans [e.g., 9]. To provide a broader basis to continue the discussion of SOAE origins, this paper describes preliminary data on the effects of pressure changes on SOAE peak frequencies and amplitudes in two lizard species. 2 Methods The following two lizard species were used: Gerrhosaurus major (Gerrhosauridae, n=2) and Cordylus cordylus (Cordylidae, n=4). Both species have a salletal tectorial structure over the high-frequency region of the papilla and SOAE lie between 1 kHz and 5kHz. The length of their basilar papillae is about 600um in Cordylus and 1.4mm in Gerrhosaurus (estimated from [12]). Animals in a sound-attenuating chamber were anesthetized with isoflurane (Rhodia), placed on a thermal blanket to

371

control body temperature and their eardrums were checked for cleanliness. Their temperature was monitored by a tiny thermistor. A microphone (Etymotic ER-10B) in a coupler was sealed to the skin with Vaseline™. The coupler was attached by an air-tight joint to a tube with a 50ml airfilled syringe outside the acoustically-shielded chamber. Using the syringe, pressure changes were effected by adding or withdrawing air in 1 or 2mBar steps and measured using a hand-held pressure monitor (Greisinger GMH 3150) with a resolution of O.lmBar. Since larger positive pressures often led to leakage at the seal, measurements were begun using negative pressures. The microphone signal was amplified and either FFT analysed (Stanford SR760) or fed into a computer interface for analysis using Labview™ software. Up to 200 spectra were averaged (Harming window, frequency range up to 6 kHz). Pressure-induced changes were measured using narrowed frequency bandwidth and spectra were stored for each pressure step. Data files were later analysed using a spreadsheet program. Measurement sets were usually repeated up to three times. SOAE were identified in the zero-pressure-difference spectra and their frequency and amplitude determined at all pressure steps where they were still visible. Small pressure steps were necessary to reliably identify individual peaks. Changes in frequency were expressed in percent, amplitudes in dB relative to the values at zero pressure difference. Temperature also influences the SOAE frequencies [2,4], so measurements were only made when the body temperature was stable (±0.2°C). 3 Results In both species, small changes in air pressure led to frequency shifts and a drop in the amplitudes of SOAE peaks (Figs. 1, 2). After changes of maximally 10 to 15 mBar, the SOAE peaks were no longer visible. Pressure affected the SOAE in different ways: (a) In all cases, amplitudes were rarely increased and all decreased to the noise level during large frequency shifts. (b) Frequencies sometimes changed very little, they increased (from 1 to 3% in Gerrhosaurus, Fig. 2) or decreased (by maximally 5% in Cordylus). In general, the changes in frequency were larger for decreased than for increased air pressures. (c) In cases where several SOAE were observed in one ear, the air-pressure effects were larger for low-frequency SOAE and smaller for higher-frequency SOAE. (d) A relatively strong hysteresis was usually observed (e.g., Fig. 1). (e) Repeating the measurement series usually led to smaller values of shifts in later measurements, even if the repeat measurements were separated by several days.

372

With changes in air pressure, the two species showed, on average, frequency

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Figure 1: Spectra from the ear of Gerrhosaurus major measured during stepped changes in air pressure outside the eardrum from zero (top trace, through negative pressures down to -7 mBar, then back to zero and to positive pressures of maximally +8 mBar (bottom trace). Three to four SOAE peaks are visible.

shifts of opposite sign. The shifts were often small and even within the data from one species, cases of shifts of the opposite sign were observed. In all cases, larger frequency shifts were accompanied by a loss of SOAE amplitude (Fig. 2).

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Figure 2: The effects of changes in air pressure on (left) three SOAE from Cordylus of frequencies between 2.578 and 3.852kHz and (right) five Gerrhosaurus SOAE from between 3.203 and 4.078 kHz. The data from Cordylus represent three repeats of the measurements. In each column, the upper panel illustrates the changes in SOAE center frequencies and the middle panel changes in SOAE amplitudes as a function of pressure difference to ambient. In the lowest panels, amplitude changes are shown as a function of the corresponding frequency shifts only for those cases in which the pressure was changed from zero and up to the first reversal of pressure.

4 Discussion The frequencies of lizard SOAE are temperature sensitive, but in species that have a salletal tectorial membrane, shifts with temperature are small [7]. In the present data, a temperature stability of ±0.2°C would have reduced resulting frequency changes to 0.2%. The shifts seen were much larger (>5%).

374

In humans, pressure-induced frequency shifts of SOAE were towards higher frequencies for both positive and negative pressures [11,13]. In the lizards, the effects of positive pressure were absent or small, but the effects of negative pressure could be of either sign. In some lizard data not shown here, a small negative pressure induced a large drop in frequency, which increased again upon greater negative pressures. Thus in this respect there is much greater variability of pressure effects on lizard SOAE. In comparison to the human data, however, the effects on lizard SOAE were achieved using much smaller pressure differences of 10 to 15 mBar. In humans, the pressure sensitivity of the frequency shifts seen in the range reported here (2.0 to 4.0kHz) was on average 0.33Hz/hPa [13], whereas in Cordylus it was nearer 10Hz/ hPa, or 30 times more seneitive. This difference correlates with the general frequency instability of lizard SOAE in comparison to those of humans [4,7]. Lizard SOAE have much larger bandwidths and external tones can shift SOAE frequencies by more than 400Hz. The high sensitivity for pressure changes and some of the variability seen may be explained by the fact that in lizards, the tympanic membrane and middle-ear ossicle are not obviously pre-tensioned and even a small change in air pressure may move the eardrum to a new position. In spite of these differences, there were clearly parallel effects to those seen in humans: (a) Where ears displayed several SOAE peaks, frequency changes were larger for the lower-frequency peaks, as in human data [13]. For SOAE above 4kHz, any effects were very small indeed, (b) Changes in frequency become larger and amplitudes become smaller, the greater the pressure difference applied. Thus lizard SOAE are affected by air pressure applied to the middle ear. The simplest explanation of these data would be to assume that in lizards also (as suggested by Shera [1]), global standing waves influence the frequencies at which SOAE can be measured. However, Shera [1] set up a dichotomy between mammalian and non-mammalian emissions, suggesting that in mammals, global standing waves are responsible for all but "atypical" emissions, whereas in nonmammals, "the point-source mechanism may predominate in species, such as frogs, lizards, and birds, in which spontaneous cellular oscillations have been observed". Perhaps all hair cells are capable of spontaneous oscillations, based on one or more of several active mechanisms. To propose that an active bundle mechanism underlies SOAE generation is not necessarily to propose a point-source "model". It is not productive to consider one active bundle or hair cell as a point source, instead, the localization of the energy source (see Introduction) may provide a useful definition. It is not important which cellular active mechanisms drive SOAE, but it is important to find out what determines at which frequencies this activity is measurable in the ear canal. On the definition used here, both PS-SOAE and GSWSOAE can contribute to SOAE patterning both in mammals and non-mammals. Reasons for the very common occurrence of SOAE in all lizards might be that (a) the hair-cell mosaic is normally not as strictly ordered as in mammals; (b) the emitting hair-cell areas of lizard papillae (>lkHz) mainly consist of

375 oppositely-oriented (and thus out-of-phase in their activity [16]) hair-cell populations whose relative size varies somewhat from place to place; (c) tectorial sallets provide a natural grouping of hair cells and (d) the unique anatomies of their papillae offer many plausible impedance discontinuities [7,8,15,17]. Unfortunately, we know far too little about the lizard middle ear and cochlea to easily interpret the present data. If standing waves are present in the tiny cochleae of lizards, then the feedback should be at least ten times as fast as in humans. This is compatible with (a) the known frequency instability of lizard emissions (i.e. their broad bandwidth [2,4]) and (b) with the fact that the time delays seen in interactions between different SOAE in lizard cochleae are extremely short (0.1ms, [14]), being about ten times shorter than in humans. On the other hand, there are substantial differences between the systematic shifts seen in human SOAE and the present lizard SOAE, in the direction and magnitudes of the frequency shifts between similar species and even with one species. Perhaps data from additional species will help elucidate what is happening. Acknowledgements Supported by a grant from the DFG (MA 871/10-1/2). I thank Carl Cristel, Kathrin Pfliiger and Laura Schebelle for assistance with the measurements and Pim van Dijk for patient and continuing discussions of these phenomena and for valuable comments on an earlier version of the manuscript. References 1.

Shera, C.A., 2003. Mammalian spontaneous otoacoustic emissions are amplitude-stabilized cochlear standing waves, J. Acoust. Soc. Amer. 114, 244-262. 2. Koppl, C , 1995. Otoacoustic emissions as an indicator for active cochlear mechanics: A primitive property of vertebrate auditory organs. In: Manley, G.A., Klump, G.M., Koppl, C, Fasti, H. and Oeckinghaus, H. (Eds.), Advances in hearing research. World Scientific, Singapore, pp. 207-216. 3. Manley, G.A., 2001. Evidence for an active process and a cochlear amplifier in non-mammals. J. Neurophysiol. 86, 541-549. 4. Manley, G.A., 2000. Otoacoustic emissions in lizards. In: Auditory Worlds: Sensory Analysis and Perception in Animals and Man. Wiley-VCH, Weinheim, pp. 93-102 5. Kennedy, H.J., Evans, M., Crawford, A.C., Fettiplace, R., 2003. Fast adaptation of mechanoelectrical transducer channels in mammalian cochlear hair cells. Nat. Neurosci. 6, 832-836.

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6. Chan D.K., Hudspeth, A.J., 2005. Ca(2+) current-driven nonlinear amplification by the mammalian cochlea in vitro. Nat. Neurosci. 8, 149-155. 7. Manley, G.A., 1997. Diversity in hearing-organ structure and the characteristics of spontaneous otoacoustic emissions in lizards. In: Lewis, E., Long, G., Lyon, R., Narins, P., Steele, C. (Eds.), Diversity in Auditory Mechanics. World Scientific Publishing Co., Singapore, pp. 32-38. 8. Manley, G.A., 2004. The lizard basilar papilla and its evolution. In: Evolution of the Vertebrate Auditory System, Manley, G., Popper, A., Fay, R. (Eds.) Springer. New York, pp. 200-223. 9. Zwicker, E., Schloth, E., 1984. Interrelation of different oto-acoustic emissions, J. Acoust. Soc. Amer. 75, 1148-1154. 10. Manley, G.A., 1983. Frequency spacing of acoustic emissions: a possible explanation. In: Webster W R, Aitken L M (Eds), Mechanisms of Hearing. Melbourne, Australia, pp. 36-39. 11. Schloth, E., Zwicker, E., 1983. Mechanical and acoustical influences on spontaneous otoacoustic emissions, Hear. Res. 11, 285-293. 12. Wever E.G., 1978. The Reptile Ear. Princeton Univ Press, Princeton N.J. 13. Hauser, R., Probst R., and Harris, F.P., 1993. Effects of atmospheric pressure variation on spontaneous, transiently evoked, and distortion product otoacoustic emissions in normal human ears, Hear. Res. 69, 133-145. 14. van Dijk, P., Manley, G.A., Gallo, L., 1998. Correlated amplitude fluctuations of spontaneous otoacoustic emissions in five lizard species. J. Acoust. Soc. Amer. 104, 1559-1564. 15. Manley, G.A., 1990. Peripheral Hearing Mechanisms in Reptiles and Birds, Heidelberg, Springer 1990. 16. Manley, G.A., Kirk, D., Koppl, C , Yates, G.K. (2001) In-vivo evidence for a cochlear amplifier in the hair-cell bundle of lizards. Proc. Nat. Acad. Sci. USA. 98,2826-2831. 17. Manley, G.A., 2002. Evolution of structure and function of the hearing organ of lizards. J. Neurobiol. 53, 202-211.

DEVELOPMENT OF MICROMECHANICALLY-RELEVANT HAIR-CELL PROPERTIES: LATE MATURATION OF HAIR-CELL ORIENTATION IN THE BASILAR PAPILLA OF BIRDS C. KOPPL, A. ACHENBACH, T. SAGMEISTER AND L. SCHEBELLE Lehrstuhlfur

Zoologie, Technische Universitat Miinchen, Lichtenbergstrasse4, 85747 Garching, Germany E-mail: Christine.Koeppl@wzw. turn, de

The non-uniform, but highly precise patterns of hair-cell orientation in the basilar papilla of birds makes this organ an attractive model for studying the developmental mechanisms that determine hair-cell polarity. We show here that, consistent with earlier observations on the chicken, the final maturation of the hair-cell orientation pattern in the basilar papilla of the barn owl, an altricial bird, occurs late in development, after the onset of hearing. This raises the question whether hair-cell polarity is entirely governed by internal signals or whether normal stimulation and function of hair cells might be necessary for final adjustment.

1

Introduction

The morphological polarity of hair cells, defining their axis of optimal mechanical sensitivity, is not uniform in the basilar papilla of birds. Instead, the hair-cell orientation deviates in a complex and well-known pattern from a strictly radial orientation (review in [1]). These deviations are most pronounced across the apical, low-frequency regions of the papilla. Several authors speculated that the regular, but non-uniform arrangement reflects the micromechanical stimulation pattern mediated by the tectorial membrane [2, 3]. It was even suggested that the tectorial membrane may, at certain developmental stages, excert an orienting force on the hair-cell bundles [4]. The developmental regulation of hair-cell polarity is currently a subject of great interest, with efforts being concentrated on identifying the molecular signals involved (review in [5]). Studies on the mammalian cochlea, where all hair cells are uniformly and radially oriented, suggest an early developmental determination and several candidate genes may be involved [5]. Most other hair-cell organs, however, show a more complex orientation pattern, the avian basilar papilla arguably being the most sophisticated example. Here, it is known that the development of hair-cell orientation passes through a stage of nearly uniform, radial orientation, before the mature pattern gradually emerges, suggesting a second phase of orienting signals. We studied the development of the basilar papilla in barn owls, altricial birds that hatch in an immature state with very restricted sensory capabilities. Auditory function, as assessed by evoked-potential recordings from the round window, develops entirely posthatching [6]. We were therefore interested to see whether the hair-cell orientation pattern in the owl is mature before hatching and the onset of

377

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hearing or whether there is a significant posthatching period of maturation which leaves open the possibility of a functional adjustment. 2

Methods

Basilar papillae of barn owls (Tyto alba) aged between hatching and two months old and from one 6 year old adult, and of chickens (Gallus gallus, egg-layer breeds)

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379 aged between El8 and PI9, were prepared for SEM using standard methods. Samples of hair cells were analyzed in strips of papilla, located at up to 9 equidistant positions from apex to base. For each hair cell, the angle between the axis of the stereovillar height gradient and the neural edge of the papilla was determined, as well as the precise location of the hair cell across the papilla. To quantify the change in orientation angle with the position of the hair cell across the papilla, two linear regressions were fitted. The point where the two regressions met defined the maximal angular deviation from radial and the cross-sectional position of this maximal angular deviation (example in Fig. 1). 3 3.1

Results Barn owl

Within the first two weeks after hatching, systematic changes in hair-cell orientation across the basilar papilla were rarely observed. Hair cells were, on average, oriented radially and the variance in orientation angles was reduced significantly between the late embryo and P l l . In owls aged three weeks and older, systematic changes in hair-cell orientation across the basilar papilla were consistently observed. However, the orientation angles initially were less extreme and the changes correspondingly more gradual than in the mature papilla. Between P20 and P40, there was a rapid development towards adult values of slopes and maximal angular deviations from radial (Fig. 2). Consistent with previous observations [7], the deviations from a radial orientation were more pronounced in the apical, low-frequency regions of the basilar papilla. However, small but systematic changes in hair-cell orientation across the papilla were also observed at far basal locations and appeared to follow a similar developmental course. Final maturation of the hair-cell orientation pattern approximately coincided with the attainment of mature response thresholds of the CAP [6].

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3.2

Chicken

The development of hair-cell orientation has been documented in detail for the embryonic chicken basilar papilla [4]. These data suggested that there may still be a significant post-hatching component in the development of apical papillar regions, however, this age bracket had not been studied in detail. We therefore reinvestigated the hair-cell orientation in late embryos (El8) and post-hatching chickens aged up to 19 days. At El8, we found the maximal hair-cell orientation angles were already mature. There was no further increase in posthatching chickens. Cotanche and Corwin [4] reported that the orientation angles actually overshoot slightly before returning to the mature value. We saw a similar weak trend at mid-papillar locations (50 and 60%) within the age bracket studied. The clearest change, however, occurred in the apical regions (up to 40% from the apical end). Here, the location of the hair cells oriented most deviantly from radial still shifted towards the neural edge of the papilla (Fig. 3). This happened around hatching. The hair-cell orientation pattern appeared mature in all aspects by P4.

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4

Discussion

We confirm here for the altricial barn owl a similar sequence for the development of hair-cell orientation as had previously been shown for the precocial chicken [4]. In addition, we extend the observations on the chicken to include the final, subtle adjustments in hair-cell orientation that occur around hatching. The following sequence emerges as the typical development for the avian basilar papilla. In a first phase of development, the variance in hair-cell orientation decreases until all hair cells at a particular longitudinal position are oriented on average radially. In a second phase of development, a systematic change in hair-cell orientation across the basilar papilla emerges, during which orientation angles gradually increase until a position-specific mature angle is achieved. In the mature state, the deviation from a radial orientation is maximal near the apical, low-frequency end of the papilla and minimal near the basal, high-frequency end. While the first phase of this orientation development occurs early and before the onset of hearing function, the second phase clearly overlaps with functional development. In the precocial chicken, the second phase of hair-cell orientation development begins at about E l l [4], hearing at physiological levels (<100dB SPL) at about El5 [8]. In the altricial barn owl, the second phase of hair-cell orientation development only starts at 2-3 weeks after hatching, even after the onset of hearing

382

[6]. This raises the question whether hair-cell orientation is entirely governed by internal signals or whether normal stimulation and function of hair cells might be necessary for final adjustment. Experiments are currently underway to test this. Acknowledgments Supported by the Deutsche Forschungsgemeinschaft (Heisenberg fellowship to CK and grant KO 1143/11). References 1. Gleich, O., Manley, G.A., 2000. The hearing organ of birds and crocodilia. In: Dooling, R.J., Fay, R.R., Popper, A.N. (Eds), Comparative Hearing: Birds and Reptiles. Springer Verlag, New York, pp. 70-138. 2. Tilney, M.S., Tilney, L.G., DeRosier, D.J., 1987. The distribution of hair cell bundle lengths and orientations suggests an unexpected pattern of hair cell stimulation in the chick cochlea. Hear. Res. 25, 141-151. 3. Manley, G.A., 1995. The avian hearing organ: a status report. In: Manley, G.A., Klump, G. M., Koppl, C , Fasti, H., Oeckinghaus, H. (Eds.), Advances in Hearing Research. World Scientific Publishing, Singapore, pp. 219-229. 4. Cotanche, D.A., Corwin, J.T., 1991. Stereociliary bundles reorient during hair cell development and regeneration in the chick cochlea. Hear. Res. 52, 379402. 5. Barald, K.F., Kelley, M.W., 2004. From placode to polarization: new tunes in inner ear development. Development 131, 4119-4130. 6. Koppl, C , Nickel, R., 2004. Prolonged maturation of cochlear function in the barn owl after hatching. Abstr. 27th Midwinter Meetg. ARO. 7. Fischer, F.P., Koppl, C , Manley, G.A., 1988. The basilar papilla of the barn owl Tyto alba: A quantitative morphological SEM analysis. Hear. Res. 34, 87102. 8. Saunders, J.C., Coles, R.B., Gates, G.R., 1973. The development of auditory evoked responses in the cochlea and cochlear nuclei of the chick. Brain Res. 63, 59-74.

383 Comments and Discussion Brownell: Fibrils in the mammalian tectorial membrane are oriented along the axis of symmetry of the outer hair cell stereocilia bundles. Have you noticed a comparable relation between the orientation of avian tectorial membrane fibers and the stereociliar bundle orientation that you have reported? Answer: We have not investigated this in any detail; in fact, the only time we observe the tectorial membrane microscopically is in its fixed (and therefore distorted) state, when taking it off to expose the hair-cell surfaces for the SEM. In these instances, the tectorial membrane showed a matrix-like structure, but no clear striation in the radial direction or in register with the underlying hair-cell bundle orientation. It has also been shown by others that the avian tectorial membrane has a different molecular composition to that of its mammalian counterpart. A striking difference is the absence in birds of the collagen fibrils that underlie the unique striated-sheet matrix in mammals (Goodyear and Richardson, 2002, J.Neurobiol. 53:212-227).

PREDICTION FOR AUDIOGRAMS AND OTOACOUSTIC EMISSIONS M. FURST AND Y. HALMUT School of Electrical Engineering, Faculty ofEngineering, Tel-Aviv University Tel-Aviv 69978, Israel E-mail: [email protected] Transient evoked otoacoustic emissions (TEOAE) are simulated by a cochlear model with embedded outer hair cells (OHC). TEOAE were produced due to the nonuniform behavior of the OHC gain. Normal audiograms are related with TEOAE. Abnormal audiograms are obtained with increasing nonuniformity and TEOAE abolishment

1 Introduction Recently, we developed an one-dimensional inner ear model which incorporated an outer hair cell model, which control each other through cochlear partition movement and pressure [1]. The aim of this paper is to include the external and middle ears to the inner ear model [2] in order to predict Oto Acoustic Emissions (OAEs). 2 Model Formulation In order to include the external and middle ears to the model, the boundary conditions of the inner ear model [1] should be modified. The outer and middle ears are modeled by a simple mechanical model [2]. The input signal (P ) simulates the ear via a speaker that is placed in the sealed ear canal. The pressure in the ear canal ( P ) is thus obtained by: Pec{t)=Pi„{t)-TeJow{t)

(1)

where t,ow is the oval window displacement, and Y ec is a constant derived from the middle ear and ear canal mechanical properties [2]. The oval window displacement is derived by solving the differential equation: (0+ ^owYow^ow (0"*" ^ow^ow^ow (^

) = P(o,t) + r„epln(t) (2) where
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window [2]. Solving equation [1] along with Eq. (2) and (3) yields a solution of the ear activity, including the basilar membrane motion and the ear canal pressure (Eq. (1)). 3 Simulation Results TEOAE can be produced by the model only when we introduce nonuniformity in one of the mechanical parameters. We chose to test the nonuniformity of the OHC gain. Fig 1 represents 2 examples of simulated TEOAE, when the stimulus was a 100 usee long rectangular wave. The mean OHC gain was 0.5 with std of io~6 . The simulated TEOAEs resemble measured TEOAEs, and demonstrate the possible cause for OAE variability. The average power spectrum of the simulated TEOAE is a band-pass between 2 and 5 kHz. It contains frequencies that are mostly influenced by the OHCs, but it does not include frequencies below 2 kHz. Two examples of OAE recorded by the model

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References Furst M., Cohen A., 2004. Integration of outer hair cell activity in a onedimentional cochlear model. J. Acoust. Soc. Am. 115,2185 - 2192. Talmadge, C.L., Tubis, A., Long, G.L., Piskorski, P.,1998. Modeling otoacoustic emission and hearing threshold fine structure. J. Acoust. Soc. Am. 104, 1517-1543.

A R E CLICK-EVOKED A N D STIMULUS-FREQUENCY OAES GENERATED BY THE SAME MECHANISM? R A D H A K A L L U R I A N D C H R I S T O P H E R A. S H E R A Eaton-Peabody

Laboratory,

Boston,

MA 02114,

USA;

Speech and Hearing Biosciences and Technology Program, Harvard-MIT Division Health Sciences and Technology, Cambridge, MA 02139 USA E-mail: [email protected]

of

We measured click-evoked and stimulus-frequency otoacoustic emission input-output transfer functions (XCE a n d Tgp) over a broad range of stimulus intensities in humans. T C E a n d Tgp are similar in overall magnitude, spectral structure, and phase at all intensities studied. The strong similarity between TQE a n d T S F supports the hypothesis [6,4] that human CEOAEs and SFOAEs are generated by the same mechanism.

It is commonly believed that, whereas stimulus-frequency otoacoustic emissions (SFOAEs) arise by linear-reflection mechanisms [6], click-evoked emissions (CEOAEs) arise by nonlinear-distortion mechanisms [5]. These conclusions are complicated by species differences and are in disagreement with coherentreflection models which predict that both SFOAEs and CEOAEs arise by the same linear-reflection mechanism. Differences in OAE generating mechanisms should manifest as differences in the spectral and phase characteristics of the emissions [6]. The experiments presented here test the predicted relationship between CEOAEs and SFOAEs by measuring and appropriately comparing the two emission types in the same human subject (N = 4). To make a meaningful comparison between emissions evoked by two very different stimuli, we compute the CEOAE and SFOAE "transfer functions", XCE and TSF, respectively. TQE and TSF are obtained by dividing the frequency response of the corresponding OAE by t h a t of the stimulus. Click-evoked OAEs were measured using both the nonlinear derived technique [2] and the linear windowing technique [1] at stimulus levels ranging from 35 — 80 peak-equivalent dB SPL (corresponding to approximately 15 — 60 dB SPL, estimated using emission growth functions). SFOAEs were measured using an acoustic suppression paradigm with probe levels ranging from 10 — 40 dB SPL and with a fixed suppressor level (55 dB SPL). In agreement with linear-reflection models, TQE and T S F share a similar spectral shape, phase behavior, and dependence on stimulus level. Both transfer functions exhibit the same spectral landmarks (i.e., peaks and notches) and their phase-vs-frequency functions are almost identical (Fig. 1). The observed

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387 a g r e e m e n t b e t w e e n T Q E a n d T s p : (1) d i s a g r e e s w i t h t h e m o d e l of N o b i l i a n d collegues [3], a n d (2) s u p p o r t s t h e h y p o t h e s i s t h a t h u m a n C E O A E s a n d S F O A E s a r e g e n e r a t e d b y t h e s a m e linear-reflection m e c h a n i s m a t low a n d m o d e r a t e s o u n d levels [6,4].

Figure 1. Comparison of CEOAE (shaded symbols) and SFOAE (open symbols) transfer function magnitudes (left panel) and phases (right panel) in one subject. Comparisons are shown at two stimulus levels. At 20 dB SPL, the transfer functions are approximately independent of level. The results are similar in all four subjects.

References 1. K e m p , D. T., 1978. Stimulated acoustic emissions from within t h e h u m a n auditory system. J. Acoust. Soc. A m . 64, 1386-1391. 2. K e m p D. T., 1990. A guide to t h e effective use of otoacoustic emissions. Ear Hear. 11, 93-105. 3. Nobili, R., Vetesnik, A., Turichchia, L. and M a m m a n o , F., 2003. Otoacoustic emissions from residual oscillations of t h e cochlear basilar membrane in a h u m a n ear model. J. Assoc. Res. Otolaryngol. 4(4), 478-494. 4. Talmadge, C. L., Tubis, A., Long, G. R. and Piskorski, R , 1998. Modeling otoacoustic emission and hearing threshold fine structures. J. Acoust. Soc. A m . 104(3), 1517-1543. 5. Yates, G. K. and Withnell, R. H., 1999. T h e role of intermodulation distortion in transient-evoked otoacoustic emissions. Hear. Res. 136(1-2), 49-64. 6. Zweig, G. and Shera, C. A., 1995. T h e origin of periodicity in t h e spectrum of evoked otoacoustic emissions. J. Acoust. Soc. Am. 98, 2018-2047.

A C O M P A R A T I V E S T U D Y OF E V O K E D OTOACOUSTIC EMISSIONS IN GECKOS A N D H U M A N S C H R I S T O P H E R B E R G E V I N A N D D E N N I S M. F R E E M A N Research Laboratory of Electronics, MIT, Cambridge MA 02139, E-mail: [email protected] and [email protected]

USA

C H R I S T O P H E R A. S H E R A Eaton-Peabody Laboratory, Boston MA 02114, E-mail: shera@epl. meei. harvard, edu

USA

Models of otoacoustic emission (OAE) generation mechanisms often attribute important features of OAEs to waves traveling along the cochlear partition. Since the lizard basilar papilla manifests no obvious analog of the mammalian traveling wave, detailed characterization of lizard OAEs offers an important opportunity to test and extend our knowledge of emission mechanisms. We report otoacoustic measurements (DPOAEs and SFOAEs) in the ears of adult leopard geckos (Eublepharis macularius) and humans. We compare and contrast the properties of gecko and human OAEs and discuss their implications for mechanisms of OAE generation.

1

Motivation

Current theories for otoacoustic emission (OAE) generation suggest that basilarmembrane (BM) traveling waves play a key role in the underlying mechanism(s) [1]. However, OAEs have been observed in non-mammals where traveling waves have not been measured. Do mammalian and non-mammalian OAEs therefore arise by fundamentally different mechanisms? Understanding any differences in their generation can provide powerful insight into the underlying inner ear physiology. 2

OAE Comparison

We performed a systematic comparison of SFOAEs and DPOAEs in both leopard geckos (Euhlepharus macularius) and humans (Homo sapiens sapiens) using the same measurement system, stimulus paradigms, and animals/subjects. Table 1 summarizes our major findings to date. Although the evoked OAEs from the two species have many qualitiative similarities, 1 they also manifest large quantitative differences. Our comparisons raise many questions, including: •'Spontaneous emissions have been reported in both humans and geckos [2].

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389 Human

SFOAE

DPOAE

Gecko

• Levels typically 0-10 dB SPL

• Levels similar to or larger than humans (0-20 dB SPL) over entire range of hearing (0.2—5 kHz)

• Magnitude punctuated by numerous deep notches with corresponding phase jumps • Long phase-gradient delays (4-9 ms)

• Occasional magnitude notches and phase jumps • Short phase-gradient delays (0.5-2 ms)

• Modest levels (~0 dB SPL)

• Large levels (~20 dB SPL)

• Few measurable high-order DPs

• Many measurable high-order DPs

• Significant differences in delay for 2 / 1 - / 2 (short), 2 / 2 - / 1 (long), and SFOAE (longest)

• Similar phase-gradient delays for lower- and upper-sideband DPOAEs; all are shorter than the SFOAE delay

Table 1. Comparison between human and gecko OAEs. SFOAE stimulus parameters: {LP,LS} = {40,55} dB SPL; fa = / p + 40 Hz. DPOAE stimulus parameters: {LP,LB} = {65,65} dB SPL; fixed / 2 / / 1 ratio.

• Is cochlear nonlinearity much stronger in the gecko t h a n in the human? And/or are human D P O A E s more highly filtered (e.g., by traveling waves) after generation? • W h a t accounts for the different phase-gradient delays seen in gecko vs human OAEs? Acknowledgments We thank AJ Aranyosi and John Guinan for insightful discussions. Supported by grants R O l DC003687 (CAS), R O l DC0023821 (DMF), and T32 DC00038 (SHBT training grant) from the NIDCD. References 1. Shera, C.A. and Guinan, J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: A taxonomy for mammalian OAEs. J. Acoust. Soc. Am. 105, 782-798. 2. Manley G.A., Gallo L., and Koppl O , 1996. Spontaneous otoacoustic emissions in two gecko species, Gekko gecko and Eublepharis macularius. J. Acoust. Soc. Am. 99, 1588-1603.

V. Cochlear Models

COCHLEAR ACTIVITY IN PERSPECTIVE EGBERT DE BOER Academic Medical Center, University of Amsterdam, E-mail: e. d. boer(a),hccnet. nl

The

Netherlands

In the years 1970-1980 it gradually became known that the live cochlea shows, for high frequencies and low stimulation levels, a mechanical response that in its peak is as frequencyselective as primary auditory nerve fibers, and demonstrates a comparable degree of nonlinearity. It proved impossible to simulate these properties, in particular the selectivity, with a "normal", i.e., "passive" cochlear model. Accordingly, "active" models of cochlear mechanics were developed. In most of these the basilar membrane (in fact, the organ of Corti) is assumed to be capable of augmenting (amplifying) the power of the cochlear wave. This must occur "locally", i.e., over a restricted region of the length of the basilar membrane (BM), while in other regions the generated power is dissipated, thus rendering the model stable. The power-amplifying elements are generally believed to be outer hair cells (OHCs). Nonlinear transduction in these cells can explain many, possibly all, nonlinearities found in BM responses. With the "inverse solution" method as developed by this author, local activity can be quantitatively determined and analyzed from experimentally obtained BM response data a most fruitful interaction between experiment and theory. Nonlinearity can be studied as well with this method. Cochlear activity can be viewed from many angles, from many perspectives. A number of these are described in this paper. More questions can be formulated and only few of them can be addressed in this paper. A most fundamental question remains: How does the "local" character of activity arise? Several theories have been put forward. One involves a secondary resonance in the organ of Corti. It will be suggested that this leads to a conflict with data on impulse responses. Spatial integration (including both feed-forward and feed-backward) provides another possibility, but this type of model does not seem universal. In summary, only few of our perspectives in cochlear activity have yet reached their horizons.

O ye 11 tak' the High Road and I '11 tak' the Low Road, And I'll be in Scotland afore ye. But me and my true love will never meet again, On the bonnie, bonnie banks o' Loch Lomond. 1 The high road and the low road - A useful perspective In the words of Sheldon Glashow [1], the Low Road is the path from the laboratory to the blackboard, from experiment to theory, the traditional path science has been following since the Renaissance. In great contrast, the High Road tries to avoid the morass of mundane experimental data. The ancient Greeks took it, they never bothered about doing experiments to test their theories. Since Galileo Galilei (and his predecessors) we think we do better now. The concept of 'cochlear activity' has oscillated between these two roads as we will see. We will start with experiments, taking the Low Road. From 1970 on, the extreme fragility and vulnerability of the cochlea had become most noteworthy [2,

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3, 4, 5, 6, 7, 8]. In point of fact, the mechanical response of the live, viable cochlea stimulated by weak sounds proved to be much more frequency-selective than that of the cochlea post-mortem. Although explaining the response of the dead organ was relatively easy -Zwislocki ([9]) succeeded as early as 1948! - this was not the case for the viable cochlea as measured by Rhode. In 1980 Kim et al. ([10]) made a daring proposal: in order to simulate "Rhode's ante-mortem observations" a model should be used in which the cochlear wave was 'actively' amplified on its way to the peak. A typical example of the High Road: no verification of individual assumptions was in sight, the hypothesis just came 'out of the blue'. In technical terms the hypothesis was based on a (linear) model with the following properties: 1. the cochlea operates as a simple mechanical structure with two long channels filled with an ideal fluid, separated by the 'cochlear partition' comprising the basilar membrane (BM) and the organ of Corti, 2. the mechanics of the 'cochlear partition' is linear and can be represented by the BM mechanical impedance, the complex quotient of pressure and velocity. 3. the real part of the BM impedance is negative over a finite segment of the BM length, basally from the place of largest response, in this segment the power of the cochlear wave will be amplified. We call the property described in item (3) 'activity'. Adding and removing activity produced all the observed differences between the two responses. A few years later de Boer ([11]) showed mathematically that in a short-wave model, given the essential properties of the in vivo response of the viable cochlea to a low-level stimulus, only an active model can simulate that response. Unlike Kim's hypothesis, de Boer's elaboration is an example of climbing the ladder from the Low Road to the High Road: firmly based on and starting from a specific type of measured response and going up toward theory. Related endeavors to climb the ladder from the Low to the High Road were undertaken [12, 13, 14, 15]. We should especially stress at this point that the resulting BM impedance has a negative real part only over a limited segment of the BM's length. The excess power is dissipated in the regions where the BM is not active, thus making the model stable. In summary, it has been shown that it is impossible to construct a cochlear model - of the type outlined in 1) and 2) above - that simulates the measured mechanical response of the viable cochlea, and that is passive (i.e., not locally active). In later years several locally active, more elaborate and specific, models of the cochlea have been described [e.g., 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. In the same period the pronounced nonlinearity of the cochlea became more and more dominant - starting with Rhode ([3]). In fact, almost all nonlinearities that were known from neural responses were found in mechanical BM responses [16, 17], see also the excellent review paper by Robles and Ruggero ([18]), and could be attributed to the nonlinear mechanics of the cochlea, more specifically to the nonlinear properties of the active elements.

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Since otoacoustic emissions were discovered by Kemp ([19]), almost all types of cochlear nonlinearity were found in these responses, too. The study of otoacoustic emissions is extremely important, especially because it opens a noninvasive window into the human cochlea. Actually, the discovery of spontaneous otoacoustic emissions (SOAEs), see Wilson ([20]), has strengthened the idea that in the cochlea acoustic power can be generated, although there still is no definite proof that the same mechanism is involved in the two processes. The physiological counterpart of a spontaneous otoacoustic emission, a spontaneous 15-kHz oscillation of the basilar membrane, has been described recently [21] - this finding is bringing such a proof nearer. Yet the principle of activity should still be considered as a hypothesis.

basilar

Figure 1. Idealized three-dimensional model of the cochlea. The basilar membrane is narrower than the width of the model. Fluid can move in three dimensions, x, y and z; x is the direction along the length of the basilar membrane (BM). In front: location of stapes (x = 0) and round window. In back: helicotrema (x = L).

396 BMresponse,expar. 1911!

Figure 2. Upper panel. Response of the guinea-pig cochlea in two conditions: a viable cochlea (solid lines) stimulated with 20 dB SPL per octave and post-mortem (dashed lines) stimulated with 100 dB per octave. Amplitude and phase are referred to the response at the stapes. Responses have been converted from the frequency (J) to the location (x) domain. Location 0 is the location of the stapes. Best frequency is around 17 kHz, hence a model length of 6 mm is sufficient. Lower panel: the corresponding BM impedance functions (real and imaginary parts), solid lines correspond to the viable cochlea and dashed lines to the post-mortem case. For the post-mortem condition the functions are more or less monotonic. For the viable cochlea the real part of the impedance (thick solid line) shows a pronounced 'swing' toward negative values, signifying 'local activity'.

2 Modeling techniques in perspective Modeling of the (linear) cochlea can be done in three forms: A) Given a model, and all its parameters (in particular, the BM impedance), it is possible to compute the response. This constitutes the 'forward solution', and is a typical example of the High Road. B) It is given that the model, of a certain structure, has to have a certain, known, response, and the problem is to find the set of parameters that is required to produce that response. The 'inverse solution' is used for this purpose, it starts in the Low Road and leads upwards: from the Low to the High Road. The main result is the BM impedance. C) After completion of the inverse solution, the response is re-computed with the set of parameters, determined by the inverse solution, inserted. This step will be referred to as 'resynthesis'. In this case the ladder from the High Road to the Low Road is descended. Ideally, resynthesis would yield the same response as is

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used as input to the inverse solution, but several intricacies of the inverse solution method may prevent this from being exactly true. 3 My perspective on a nonlinear cochlea - Acquisition of data Prior to executing the inverse solution, it is necessary to consider some very general questions on 'procedure' and 'strategy'. The cochlea is a frequency-dependent nonlinear system. How should we go about analyzing it in a very general sense? The most common types of stimulus lead to undefined states of nonlinearity. For instance, when we observe the response of the BM to a tone of constant level, the degree of nonlinearity depends on the frequency. Furthermore, when using a click stimulus, the degree of nonlinearity depends on time, and this is different in different regions of the cochlea. I have indicated one way of action to avoid this dilemma [34]. It involves stimulation with wide-band noise to ensure that all along the length of the BM the degree of nonlinearity is (approximately) constant. In order to apply the underlying theorem (called the EQ-NL theorem), it is compulsory to use in an experiment a wide-band acoustical random-noise stimulus and to measure the 'response' as the input-output cross-correlation function (input is the motion of the stapes, output the motion of the BM). From this cross-correlation function modeling of the cochlea - all three forms - can be done within the theory of linear systems, and the resulting parameters have a precisely determined meaning with respect to the actual nonlinear system, the cochlea. In particular, consider the BM impedance as determined by the inverse solution. When a linear model - called the 'comparison model' - is provided with that BM impedance, the response of that comparison model will accurately correspond to the actual response to wide-band noise, in the form of the input-output cross-correlation function - measured in the nonlinear cochlea. In our work we have consistently applied this stimulus-analysis method (e.g., [15]). To execute this procedure a number of distinct steps are necessary. We start with the cross-correlation spectrum, i.e., the Fourier Transform of the measured cross-correlation function. That spectrum is a function of frequency valid for one location, and it has to be converted to a function of location, valid for one frequency (usually the best frequency, BF, is chosen for this frequency). Generally, the regular mapping ('scaling') of frequency to place of the cochlea is used (for more technical details see [14]). Second, a specific cochlear model must be selected. We have almost always used a model of which the geometry is constant over the full length of the model. See Figure 1. The model has been made three-dimensional in order to accommodate 'long' as well as 'short' waves (see [35]) - a two-dimensional model would have sufficed but a three-dimensional model (in which the BM is narrower than the width of the model and the fluid displaced by the BM can thus move in three directions) is more realistic. With the 'inverse solution' the BM impedance function is computed, as a function of location (x) for the same fixed value of the frequency (/). By (inversely) scaling place to frequency the computed impedance

398 function can be converted to other frequencies. Using this transformation in resynthesis (method C) it is even possible to compute and analyze the associated resynthesized impulse response [15]. 4 The inverse solution - My perspective on activity and nonlinearity A typical example of observed responses and BM impedance functions derived from the inverse solution is given in Figure 2. The data have been acquired by using wide-band noise as described above, the level indicated is the level in the highest octave, around 17 kHz, in dB SPL. The abscissa shows distance from stapes. The upper panel shows two amplitude and phase response functions for two conditions. The solid lines show the response of the live and viable cochlea to a stimulus of 20 dB SPL per octave. The finely dashed lines show the response post-mortem, obtained with a 100-dB stimulus. All responses are referred to the response of the stapes to noise of the same level. The lower panel shows the BM impedance derived with the inverse-solution method from the two conditions. The abscissa is the same as in the upper panel, and the ordinate scale is compressed for large positive and negative values - so as to show details of small as well as large values. Again, solid lines depict the impedance of the viable cochlea, dashed lines that of the post-mortem cochlea. To start with the latter, the real part is positive throughout the entire x-region meaning that the power of the wave as it is started at the stapes is continually absorbed. The imaginary part of the impedance is monotonically decreasing and negative. This is equivalent to the impedance of a stiffness that decreases with increasing x which feature agrees with what is conventionally supposed to be the case in the cochlea. The real part of the impedance of the viable cochlea shows a most specific pattern, this function (thick solid line) makes a 'swing' from positive values near the stapes location to negative values and back to positive values. Negative values mean, of course, 'activity', in the active region the BM and its associated structures amplify the cochlear wave. Amplification ceases at the rightmost zero-crossing, and it is not surprising that the peak of the response (upper panel) is near this zerocrossing location. Note, again, that activity is local, the active region extends over a limited region of the abscissa. We checked that this result corresponds to a stable system. We should stress in passing that the tuning of the viable cochlea apparently occurs via the real part of the impedance, and not via an interplay between stiffness and mass. Going back once more to the post-mortem case, we note the same feature: the imaginary part of the post-mortem impedance does not show a tendency to cross the zero line: there is no clear effect of a mass component. In this case, again, tuning is due to an interplay between damping and stiffness. It is a curious fact that the first more or less 'complete' model of the cochlea (Zwislocki [9]) had just damping and stiffness as its main mechanical parameters. At present we consider this property as typical of short-wave behavior [35].

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It is repeated that the property of 'local activity' has directly been derived from experimental data on movements of the basilar membrane in a living animal, thus climbing from the Low to the High Road. Figure 2 confirms and strengthens the adhoc hypothesis of Kim et al. ([10]). The difference between the viable and the dead cochlea is mainly shown by the behavior of the real part of the BM impedance presence and absence of local activity. There are subtle differences in the imaginary part as well, but to conserve space we must refrain from discussing these in detail. It should be well realized at this point that it is the difference of the two impedances in this figure that is produced by the 'active' mechanism. It is generally assumed that outer hair cells (OHCs) are closely involved in this process. This notion becomes important as we shall see presently. When the cochlea is stimulated by louder sounds, it is driven into nonlinearity. We have found that variation of the stimulus level corresponds to a gradual transition between the two impedances shown in Fig. 2. Our interpretation is that the transduction function of OHCs (the function that relates the stereociliary displacement to the locally generated pressure) is curved so that with stronger stimulation the active mechanism is partially saturated. With this assumption the variations of the response with stimulus level can be simulated not only qualitatively but quantitatively [15]. 5 A negative perspective: What if it is not true? It has been stated earlier: it is impossible to use a passive cochlear model to simulate responses as found experimentally from a viable cochlea. Could we really do without activity? In an ingenious experiment it has been attempted to directly estimate the gain of the cochlear amplifier. The experiment was designed and performed by Allen and Fahey ([36]), it involved recording of 1) otoacoustic emissions (OAEs) in the external ear canal, along with 2) measuring the response of a primary auditory neuron, in an anesthetized cat. The acoustical stimulus was a pair of pure tones, with frequencies f and f2 , with f2 > f\, and the distortion-product frequency / D P = 2f - f2 was chosen equal to the characteristic frequency (CF) of the auditory neuron under study. The frequency / D p was kept constant while the ratio f21 f\ of the frequencies f and f2 was varied over as wide a range as possible. From the source of the DP two waves can be imagined to emerge, one going basally and giving rise to an OAE (along pathway #1) in the ear canal and the other apically, exciting the neuron (along pathway #2). When the ratio f2 If was varied, different amounts of amplification were expected to occur in these two pathways, and these differences should be measurable. Space does not permit a more complete description, suffice it to state the conclusion from the experiment: no substantial amplification was apparent. A very puzzling and intriguing result. With a different technique, using solely otoacoustic emissions, the essential elements of

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the Allen-Fahey experiment were repeated by Shera and Guinan ([37]). The conclusions were similar; again a puzzling result. Our own study [38], in which we used the movements of the BM as the monitor of the DP at its proper location, produced entirely comparable results. Part of the negative result of the Allen-Fahey experiment has been resolved in recent years, formulated in terms of the usual locally-active model of operation of the cochlea. It has been argued that the retrograde DP wave (pathway #1) going to the stapes is appreciably reduced in magnitude - in its source - by wave interference when the two primary frequencies approach each other (Shera [39]). This DP wave is composed of wavelets, each originating from a different location, and these wavelets tend to annihilate when they propagate backward. The interference effect is especially pronounced when the frequencies f and _/~2 a r e close together. Such an amplitude reduction only occurs in the DP wave toward the stapes (pathway #1) and does not take place in the forward-going wave (pathway #2) toward the location tuned to the DP frequency: A fundamental asymmetry. Actual power gain computations in cochlear models directly derived from data show that the amount of amplification is quite moderate, generally, it remains below 20 dB [40], hence wave interference would need to reduce the amplitude by less than a factor of 100 (10 squared) to hide all effects of cochlear amplification in the Allen-Fahey type of experiment. What if the cochlea is not locally active? Researchers who have expressed this opinion have never been able to explain why and how mechanical measurements of BM motion invariably have demonstrated i), a high degree of tuning of the viable cochlea at low stimulus intensities, ii), the typical nonlinear pattern of tuning, peak-frequency shifting and amplitude compression for higher intensities, iii), great loss of tuning and lowering of the best frequency in the post-mortem cochlea, and iv), a number of nonlinear effects. If there would be no local activity, the cochlea should operate according to a mechanism that differs completely and fundamentally from the one we have summarized above and which has been used by almost all researchers in cochlear mechanics. I have no inkling of how this could be achieved. In addition, we cannot deny the validity of our and others' inverse solutions which all invariably point to a locally active cochlea. No, we cannot do without activity. We have 'to live with an active cochlea' (in the most literal sense). 6 'Tuning of activity' in perspective A most intriguing - and as yet unsolved - question is how the local aspect of activity is achieved by the cochlea. 'Local' means here that for each frequency there is a specific spatial region along the length of the basilar membrane in which activity is present. Translated from space to frequency it means that at each location the active mechanism is frequency-selective: it is a filter. What type of filter? Attempts to isolate it have led to an amazing, and still disputed, conclusion: the filter involved in activity tuning appears to be non-causal [41, 42]. Of course, such a

401 conclusion must be - and has been - considered with much skepticism. However, in models with 'feed-forward' [43, 28], OHCs (supposedly the active elements) receive input from locations where the cochlear wave arrives earlier. In such models it is to be expected that the local impedance (local pressure divided by local velocity) is non-causal. Further on, we will consider this theme some more. The filtering aspect of the activity mechanism has often been solved by assuming that there is a second resonance at work. That resonator should reside in the tectorial-membrane complex, take its mass mainly from the tectorial membrane and its stiffness from that of this membrane and the arrays of OHC stereocilia embedded in it. Starting with Neely and Kim ([22]), many models have included such a second-resonance principle, and it has proven of great value. A word of caution - in a perspective view - is necessary here. Experiments tell us that the timing of zero-crossings of impulse responses is nearly invariant under variations of stimulus intensity [44, 45, 46]. With their locally-active model of the cochlea in which the effective BM impedance is modified - via saturation - in a predictable manner by variations in stimulus level, de Boer and Nuttall ([15]) could accurately reproduce near-invariance of timing, but in the Neely-Kim model [22] this proved impossible. Later research by Shera ([47]) has elucidated the reason for this: the pole-zero pattern involved in internal filtering of the cochlea has to obey certain laws for near-invariance to hold. A second resonance of which the importance varies with stimulus level tends to disrupt this property. Whether this is universally true remains to be seen (personal communication: Karl Grosh). 7 'Spatial convolution' in perspective Non-causality in the active component of the BM impedance still forms a somewhat mysterious feature. In a model which derives its spatial tuning from feed-forward (that is, a model in which the OHCs as the 'active' elements receive an input from more basal locations than their own) this would not be too surprising. However, such a model (for instance, [28]) is not realistic in other respects. In a perspective view on modeling of the locally-active cochlea, it is important as well as instructive to dwell on this subject some more. We have studied a generalization of the principle of 'feed-forward'. Let us assume that at each location x the input to the amplifying elements (OHCs) is a weighted average of the BM velocity, averaged over space to the left ('feed-forward') as well as to the right of x ('feed-backward', a term not to be confused with 'feedback'...). The combination can be called "spatial convolution". Estimating the coefficients involved in spatial convolution is another example of going from the Low Road to the High Road: we start from data and arrive at a model. We have found that the spatial-convolution principle - without any intermediate filtering - could produce in several experiments a surprisingly good simulation of the low-level response [42]. This was, however, not the case in all experiments. In a further study [48] it was shown that in the 'successful' cases near-invariance of timing in impulse responses could also be simulated very well. In

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these cases descending from the High Road to the Low Road has again been rewarding. 8 Perspectives of (coherent) reflection We should not forego to mention one further aspect of activity, wave reflection, and, specifically, 'coherent reflection'. In a perfectly smooth cochlea virtually no reflection of waves occurs. From a region in which there are spatial irregularities in the cochlea, however, reflection of waves can be expected. The 'rules' under which these are relatively prominent, i.e., where 'coherent reflection' occurs, have been formulated by Zweig and Shera ([49]). One of the conditions is that there has to be a region of appreciable amplification in the cochlea, flanked by steep slopes. This condition is obviously fulfilled in a cochlea with local activity. When coherent reflection is especially strong, the retrograde wave can be reflected again by the stapes, it is amplified and adds to the primary wave and so can cause spontaneous oscillations to occur. There often will occur multiple spontaneous oscillations, this property has been observed regularly in spontaneous otoacoustic emissions (SOAEs), and the same tendency has been found in spontaneous mechanical BM oscillations [21]. This feature has also been adequately explained by the theory of coherent reflection. We mentioned earlier that in a perfectly smooth - and linear - cochlea no reflection of waves takes place. When we consider nonlinearity, however, this is different. Wherever a nonlinear process takes place, distortion-product waves are created that can propagate in two directions. We have seen this already in the case of the DP from a two-component stimulus. Among the distortion products is also a wave with the same frequency as the primary stimulus. A nonlinear 'reflection' as caused by this wave has curious properties. Reflections like this one have been named 'wave-fixed' reflections, and have been described for the first time by Kemp and Brown ([50]) - note that this was a paper in the proceedings of the first symposium of the present series! In point of fact, wave-fixed reflection is closely interwoven with scaling of frequency and location in the cochlea. In contrast, coherent reflection is typically 'location-bound', or 'place-fixed'. Of late, both types of reflection were summarized by Shera and Guinan ([51]). Recently the notion of reflection in the cochlea has become confounded. Ren ([52]) reported that in his experiments on mechanical movements of the BM with two-tone stimulation (frequencies /j and / 2 ) n e c °uld not observe evidence of a backward-traveling wave associated with the distortion product (DP) with frequency 2/j — fi- He suggests that it is a compression wave that travels backward. In his review of reverse propagation of this component Ruggero ([53]) noted a preponderance of data indicating that the DP is transmitted to the stapes with a far larger speed than either of the primary-tone waves. Further study is

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necessary because these data conflict with what we have concluded earlier about wave interference of reverse-propagating waves. 9 Multiple propagation modes - A new perspective? In the commonly used model of the cochlea (see Section I) two fluid-filled channels surround the cochlear partition. In reality, the organ of Corti is considerably more complex than a simple membrane, and more detailed features of it have been taken into account in modeling. In one variation the organ of Corti is considered as a separate channel in which fluid can move longitudinally [26, 13]). Because of the high damping that such fluid movements would incur, it is difficult to visualize actual power amplification to take place inside this channel. If cochlear activity is due to somatic motility of outer hair cells, it should be realized that an isovolumetric elongation of an OHC produces a local volume change in the organ of Corti, the reticular lamina and the basilar membrane being pushed away from one another. A three-channel model should take this effect into account. The organ of Corti is not the only channel in the longitudinal direction. There is another one, the Inner Spiral Sulcus, and its function has been invoked to explain how OHCs could ever be able to exert forces on the BM without being visibly anchored on their apical side to the outer walls of the cochlea [24]. If that hypothesis is true, a still more realistic model of the cochlea should contain four instead of three fluid channels! In the view of the author, there may be new perspectives in these directions. A different type of differential movement in the organ of Corti could occur in the radial direction. Although such radial movements would not be coupled to the predominantly longitudinal fluid movements in the main channel(s), they may well be important for the micromechanics of the organ of Corti. 10 A perspective view on Hopf bifurcations In the past few years a different type of active cochlear model has been considered. It is a collective model; it is assumed to consist of a (large) number of 'Hopf oscillators (a form of Van der Pol oscillators) that are all kept at or very close to their points of instability. The model as a whole would display generic properties, universal properties that are associated with 'Hopf bifurcations' and belong to a very general theory of nonlinear systems [54]. The study of such a model is highly intriguing, to say the least. However, I do not think that the cochlea can operate this way. One of my main objections is: all these oscillators would operate in the amplitude region of Brownian motion, and I do not see how each oscillator would ever receive a sufficiently stable and smooth control signal to keep its operating point close to the bifurcation point. Actually, for a single oscillator this view is challenged by at least one paper in this Symposium [55]. Assuming the oscillators to be fundamentally

404

unstable leads to other problems. The oscillators would be mutually coupled by the cochlear fluid, and could give rise to chaotic behavior. If, at higher stimulus levels, the oscillators would become entrained with the stimulus, they would soon display a degree of tuning that is lower than that of the same oscillators in a dead cochlea. This is so because the nonlinearity in the 'Hopf oscillators is expansive. For a quadratic nonlinearity, as it is usually considered (analogously to the Van der Pol oscillator), the resulting input-output characteristic has a slope of j ^ , for another type of nonlinearity it could be different. In contrast, the 'oscillators' that I and others derive from the inverse solution have completely different properties. These 'oscillators' have a central 'active' region surrounded by 'passive' regions in which all power generated is dissipated. Furthermore, they have been given a realistic saturating nonlinearity (the 'Hopf oscillators have an expanding nonlinearity and I do not know of any physiological mechanism with such a property). As a result, the input-output function of 'our' type of oscillator model is realistic. 11 A perspective of problems Hence, I believe we have to come back to our simpler kind of models, although all problems of these are far from being solved. Let me list a few (some of these are definitely inter-related): a) b) c) d) e) f) g) h) i) j) k) m) n)

How are OHCs anchored at their apex? Is there a (mechanical) role to be played by the Internal Spiral Sulcus? How is the Reticular Lamina hinged? And the Tectorial Membrane? How important is the dynamics of the fluid in the channel formed by the Organ of Corn? How important are additional (longitudinal) modes of wave propagation? How important are additional (transversal) modes of vibration of the Organ of Corti? What (mechanical) part is played by the Tectorial Membrane? Does it act as a (well-damped) resonator? How large is the damping in the sub-tectorial space? Can it support a 'resonance' or is it too large? How do OHCs produce activity, by somatic motility or via stereociliary mechanics? How is the intrinsic electrical low-pass filtering of OHCs overcome? How does reciprocal mechanics of transducer channels operate? How can stiffness variations of OHCs be transmitted? Are these variations observable by our type of analysis? Is it really possible to explain all nonlinearities of the cochlea with one principle, a nonlinear transduction function of the OHCs? Why is activity more pronounced in the high-frequency than in the lowfrequency region?

405

o) How is 'tuning' of activity actually achieved, is spatial convolution involved or not? p) Adaptation plays a dominant role in molecular biology of hair cells and sensory gates. Why don't we find (more) evidence of it in cochlear mechanics? q) How can we understand the role of efferent stimulation (both biochemical and mechanical)? r) Do we understand sufficiently well how Inner Hair Cells (IHCs) are stimulated? s) What is the part played in cochlear mechanics by compression waves? This list is far from exhaustive. We could go on, almost indefinitely. Space does not permit embarking on any of these topics. The choice as to what should be the most important topics to be treated in this paper has been entirely my own, and I have tried to put these into a general translucent perspective, using the ladder from the Low Road to the High Road and back to the Low Road as a guide. Further perspectives, not all opaque, can be opened and I think that a synthesis may well be within reach. Because of the many uncertainties and unsolved questions related to activity, there certainly is a future in cochlear modeling, of the locally active cochlea in particular. And thus, in the future, we will be able to describe active cochlear models in a wider perspective. Acknowledgments The list of people I wish to thank for collaboration with me, and for their friendship, is long. Here is an excerpt. I am especially grateful to all authors mentioned in the reference list for their influence on my understanding, to Alfred (Fred) L. Nuttall, for providing me with the opportunity for continuing my study of hearing over many years after my retirement, and, in particular, for making it possible to combine theory with experiment, to Fred's wife, Bonnie, for being the most wonderful hostess you can imagine, to Jiefu (Jeff) Zheng for his excellent contributions to the experiments and his superb experimental skill, to Edward Porsov who wrought miracles with the computers, to Tianying Ren for his eternal creativity, to Yuan Zou and Ning Hu for their contributions to data acquisition and processing, further, to Bob Masta, Dave Dolan, Gary Dootz and Meng He Guo for their contributions in the pioneering days of this research in Ann Arbor, Michigan, and, finally, to all members of the Portland (Oregon) "Nuttall Lab" for their participation in discussions and their continuing friendship. References 1.

Glashow, S.L., 1988. Interactions. Warner Books, New York.

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2. Russell, I.J., Sellick, P.M., 1978. Intracellular studies of hair cells in the mammalian cochlea. J. Physiol. 284, 261-290. 3. Rhode, W.S., 1971. Observations of the vibration of the basilar membrane in squirrel monkeys using the Mossbauer technique. J. Acoust. Soc. Am. 49, 1218-1231. 4. Rhode, W.S., 1978. Some observations on cochlear mechanics. J. Acoust. Soc. Am. 64, 158-176. 5. Sellick, P.M., Patuzzi, R., Johnstone, B.M., 1982. Measurement of basilar membrane motion in the guinea pig using the Mossbauer technique. J. Acoust. Soc. Am. 72, 131-141. 6. Robles, L., Ruggero, M.A., Rich, N., 1986a. Mossbauer measurements of the mechanical response to single-tone and two-tone stimuli at the base of the chinchilla cochlea. In: Peripheral Auditory Mechanisms, edited by J.B. Allen, J.L. Hall, A. Hubbard, S.T, and Neely, A. Tubis. (Springer, Berlin), pp. 121127. 7. Robles L., Ruggero, M.A., Rich, N.C., 1986b. Basilar membrane mechanics at the base of the chinchilla cochlea. I. Input-output functions, tuning curves, and response phases. J. Acoust. Soc. Am. 80, 1364-1374. 8. Nuttall, A.L., Dolan, D.F., Avinash, G., 1990. Measurements of basilar membrane tuning and distortion with laser doppler velocimetry. In The Mechanics and Biophysics of Hearing, edited by P. Dallos, C. D. Geisler, J. W. Matthews, M. A. Ruggero, and C. R. Steele (Springer, Berlin), pp. 288295. 9. Zwislocki, J., 1948. Theorie der Schneckenmechanik: Qualitative und quantitative analyse. Acta Oto-Laryngol., suppl. 72. 10. Kim, D.O., Neely, S.T, Molnar, C.E, Matthews, J.W., 1980. An active cochlear model with negative damping in the partition: Comparison with Rhode's ante- and post-mortem observations. In: Psychophysical, Physiological and Behavioural Studies in Hearing, edited by G. v.d. Brink and F.A. Bilsen (Delft University Press, Delft, Netherlands), pp. 7-14. 11. de Boer, E , 1983. No sharpening? A challenge for cochlear mechanics. J. Acoust. Soc. Am. 73, 567-573. 12. Zweig, G , 1991. Finding the impedance of the organ of Corti. J. Acoust. Soc. Am. 89, 1229-1254. 13. Dimitriades, E.K, Chadwick, R.S, 1999. Solution of the inverse problem for a linear cochlear model: A tonotopic cochlear amplifier. J. Acoust. Soc. Am. 106, 1880-1892. 14. de Boer, E , Nuttall, A.L, 1999. The "inverse problem" solved for a threedimensional model of the cochlea. III. Brushing-up the solution method. J. Acoust. Soc. Am. 105, 3410-3420. 15. de Boer, E , Nuttall, A.L, 2000. The mechanical waveform of the basilar membrane. III. Intensity effects. J. Acoust. Soc. Am. 107, 1497-1507.

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16. Cooper, N., Rhode, W.S., 1993. Two-tone suppression and distortion production on the basilar membrane in the hook region of cat and guinea pig cochleae. Hear. Res. 66, 31-45. 17. Robles, L., Ruggero, M.A., Rich, N.C., 1997. Two-tone distortion on the basilar membrane of the chinchilla. J. Neurophysiol. 77, 2385-2399. 18. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea (review paper). Physiol. Rev. 81, 1305-1352. 19. Kemp, D.T., 1978. Stimulated acoustic emission from within the human auditory system. J. Acoust. Soc. Am. 64,1386-1391. 20. Wilson, J.P., 1980. Evidence for a cochlear origin for acoustic re-emission, threshold fine-structure and tonal tinnitus. Hearing Res. 2, 233-252. 21. Nuttall, A.L., Grosh, K., Zheng, J., de Boer, E., Zou, Y., Ren, T. 2004. Spontaneous basilar membrane oscillation and otoacoustic emission at 15 kHz in a guinea pig. J. Assoc. Research Otolaryng. (JARO) 5, 337-349. 22. Neely, S.T., and Kim, D.O., 1986. A model for active elements in cochlear biomechanics. J. Acoust. Soc. Am. 79, 1472-1480. 23. Geisler, CD., 1993. A realizable cochlear model using feedback from motile outer hair cells. Hear. Res. 68, 253-262. 24. de Boer, E., 1993. The sulcus connection. On a mode of participation of outer hair cells in cochlear mechanics. J. Acoust. Soc. Am. 93, 2845-2859. 25. Mammano, F., Nobili, R., 1993. Biophysics of the cochlea: Linear approximation. J. Acoust. Soc. Am. 93, 3320-3332. 26. Hubbard, A. E. 1993. A traveling wave-amplifier model of the cochlea, Science 259, 68-71. 27. Neely, S.T., 1993. A model of cochlear mechanics with outer hair cell motility, J. Acoust. Soc. Am. 94, 137-146. 28. Geisler, CD., Sang, C , 1995. A cochlear model using feed-forward outerhair-cell forces. Hear. Res. 86, 132-146. 29. Chadwick, R.S., Dimitriades, E.K., Iwasa, K.H., 1996. Active control of waves in a cochlear model with subpartitions. Proc. Natl. Acad. Sci. USA 93, 2564-2569. 30. Fukazawa, T., 1997. A model of cochlear micromechanics. Hear. Res. 113, 182-190. 31. Chadwick, R.S., 199). "Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions," Proc. Natl. Acad. Sci. USA 95, 14594-14599. 32. Steele, C.R., Lim, K.-M., 1999. Cochlear model with three-dimensional fluid, inner sulcus and feed-forward mechanism. Audiology and NeuroOtology 4,197-203. 33. Lim K.-M., Steele, C.R., 2002. A three-dimensional nonlinear active cochlear model analyzed by the WKB-numeric method. Hearing Research, 170, 190205.

408 34. de Boer, E., 1997. Connecting frequency selectivity and nonlinearity for models of the cochlea, Audit. Neurosci. 3, 377-388. 35. Lighthill, M.J., 1981. Energy flow in the cochlea. J. Fluid Mech. 106, 149-213. 36. Allen, J.B., Fahey, P.F., 1992. Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane. J. Acoust. Soc. Am. 92, 178-188. 37. Shera, C.A., Guinan, J.J., 1997. Measuring cochlear amplification and nonlinearity using distortion-product otoacoustic emissions as a calibrated intracochlear sound source, ARO Midwinter Meeting Abstracts, nr. 51. 38. de Boer, E., Nuttall, A.L., Hu, N., Zou, Y., Zheng, J., 2005. The Allen-Fahey experiment extended. J. Acoust. Soc. Am. 117, 1260-1267. 39. Shera, C.A., 2003. Wave interference in the generation of reflection- and distortion-source emissions. In: Biophysics of the cochlea: from molecule to model, edited by A.W. Gummer, E. Dalhoff, M. Nowotny, and M. P. Scherer (World Scientific, Singapore), pp. 439-454. 40. de Boer, E., Nuttall, A.L., 200). Power gain of the "Cochlear Amplifier". In: Physiological and psychological bases of auditory function, edited by D.J. Breebaart, A.J.M. Houtsma, A. Kohlrausch, V.F. Prijs, and R. Schoonhoven (Shaker, Maastricht), pp. 1-7. 41. de Boer, E., Nuttall, A.L., 1997. On cochlear cross-correlation functions: connecting nonlinearity and 'activity'. In: Diversity in Auditory Mechanisms, edited by E. R. Lewis, G. R. Long, R. F. Lyon, P. M. Narins, C. R. Steele, and E. Hecht-Poinar (World Scientific, Singapore), pp. 291-297. 42. de Boer, E., Nuttall, A.L., 2003a. Properties of amplifying elements in the cochlea. In Biophysics of the Cochlea: From Molecules to Model, edited by A.W. Gummer, E. Dalhoff, M. Nowotny, M.P. Scherer (World Scientific, Singapore), pp. 331-342. 43. Steele, C.R., Baker, G., Tolomeo, J., Zetes, D., 1993. Electromechanical models of the outer hair cell, in Biophysics of Hair-Cell Sensory Systems, ed. H. Duifhuis, J.W. Horst, P. van Dijk and S.M. van Netten (World Scientific, Singapore), pp. 207-214. 44. Robles, L., Rhode, W.S., Geisler, CD., 1976. Transient response of the basilar membrane measured in squirrel monkeys using the Mossbauer effect. J. Acoust. Soc. Am. 59, 926-939. 45. Ruggero, M.A., Rich, N.C., Recio, A., 1992. Basilar membrane responses to clicks. In Auditory physiology and perception, edited by Y. Cazals, L. Demany and K. Horner (Pergamon, London), pp. 85-91. 46. Recio, A., Rich, N.C., Narayan, S.S., Ruggero, M.A., 1998. Basilarmembrane responses to clicks at the base of the chinchilla cochlea. J. Acoust. Soc. Am. 103,1872-1989.

409 47. Shera, C.A., 2001. Intensity-invariance of fine time structures in basilarmembrane click responses: Implications for cochlear mechanics. J. Acoust. Soc.Am. 110,332-348. 48. de Boer, E., Nuttall, A.L., 2003b. Filtering in the cochlear amplifier? ARO Midwinter Meeting abstracts 26, p. 25-26, # 98. 49. Zweig, G., Shera, C. A., 1995. The origin of periodicity in the spectrum of evoked otoacoustic emissions, J. Acoust. Soc. Am. 98,2018-2047. 50. Kemp, D.T., Brown, A.M., 1983. An integrated view of cochlear mechanical nonlinearities observable from the ear canal. In: Mechanics of Hearing, edited by E. de Boer and M.A. Viergever (Delft University Press, Delft, Netherlands), pp. 75-82. 51. Shera, C.A., Guinan, J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: A taxonomy for mammalian OAEs. J. Acoust. Soc. Am. 105, 782-798. 52. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nature Neurosci. 7, 333-334. 53. Ruggero, M.A., 2004. Comparison of group delay of 2fx-f2 distortion product otoacoustic emissions and cochlear travel times. Acoust. Res. Letters Online (Acoust. Soc. Am.) 5, 143-147. 54. Jiilicher, F., Camalet, S., Prost, J., Duke, T.A.J., 2003. Active amplification by critical oscillations. In: Biophysics of the cochlea: from molecule to model, edited by A.W. Gummer, E. Dalhoff, M. Nowotny, and M. P. Scherer (World Scientific, Singapore), pp. 16-23. 55. Martin, P., Nadrowski, B., Jiilicher, F., 2005. Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity. This symposium, paper 1088. Comments and Discussion Neeley: You emphasized the local nature of active processes in cochlea; however the non-local nature of the resulting amplification is also an important feature of cochlear mechanics. As you know, the local activity feeds energy into the traveling wave and produces maximum amplification at a more apical place. This feature distinguishes the cochlear amplifier from amplification in nonmammals. Have you considered how amplification in nonmammals differs from your models of the cochlear amplifier? Answer: When the activity is local, so is the amplification. At the point where activity ceases, the model ceases to amplify, and the response reaches a maximum at approximately the same location. My inverse method can only be applied to a cochlea that scales frequency to location as a result of stiffness varying with location. Therefore, I cannot apply my method to responses of animals that do not have a basilar membrane or, if they do, do not demonstrate some form of traveling wave.

A M E C H A N I C A L - E L E C T R I C A L - A C O U S T I C MODEL OF T H E COCHLEA KARL GROSH, NIRANJAN DEO, AND LEI CHENG Department of Mechanical Engineering, Ann Arbor, MI 48109. Email:

University of Michigan [email protected]

SRIPRIYA RAMAMOORTHY Bose Corporation,

Framingham,

MA

The coupling of the mechanical and the electrical response of the cochlea is well known. Acoustical stimulation gives rise to the cochlear microphonic while electrical stimulation of the cochlea elicits both basilar membrane motion and otoacoustic emissions. Disruption of the resting electrical environment, through efferent stimulation, artificial injection of current, and a variety of other means is known to affect hearing sensitivity and the mechanical response of the cochlea to stimulus. The key missing element in most models is the explicit coupling of the electrical domain to the mechanical degrees of freedom. By modeling this coupling, predictions of both mechanical forces and transducer currents may be made enabling comparisons and analysis of electro-physiological experiments. A mechanical-electrical—acoustic model of the cochlea is presented whose key components are micro—electro—mechanical coupling of the cochlear structures, a two-duct acoustic model with structural—acoustic coupling at the basilar membrane (BM), and a global electrical circuit to model conductances in the different scalae. Predictions of the cochlear microphonic, other cochlear potentials, BM velocity and otoacoustic emissions in response to pure acoustic input and bipolar electrical stimulation are presented. Model simulations show that including three dimensional fluid effects improves BM response characteristics. A tectorial membrane shear mode resonance is shown to provide amplification to the BM at the characteristic frequency of a location. This project is funded by NIH NIDCD R01 04084.

1

Introduction

The electrical environment in the cochlea plays a key role in the active enhancement of the basilar membrane (BM) response. In addition, the potentials measured in the cochlea provide an indirect measure of the functioning of the cochlea. It is critical to model the electrical environment in the cochlea to develop a more predictive model which enables the study of intra-cochlear potentials such as the cochlear microphonic. Here we present a model of a cochlea which includes the electrical pathways and micro-mechanics of the organ of Corti (OoC). The OoC model includes outer hair cell (OHC) motility and the dependence of stereocilia conductance on its displacement. Acoustic or electrical stimulation can be used as input to the model. Model predictions for acoustic and electrical excitations are shown and compared with experimental results. The role of a second resonance in the OoC ensemble is discussed. 410

411

V**?t&>*

Middle Ear

Basilar Membrane

Figure 1. (a) Model schematic, (b) Micromechanical model for the organ of Corti structures.

2 2.1

Model Description Duct geometry and organ of Corti model

The cochlea is modeled as a two duct fluid-filled chamber with the basilar membrane (BM) in the center separating the two chambers (see Fig. 1). The fluid interacts directly only with the BM; other micro-structures interact with the fluid indirectly via BM. The fluid is assumed to be inviscid and compressible; fluid viscosity is heuristically accounted for via BM and TM viscous damping. The fluid pressure is governed by the Helmholtz equation. For emissions, a middle ear model [1] is connected to the oval window. The OoC kinematics are based on a study by Dallos [2]. The micromechanical model includes first mode of BM motion, bending and shear modes of the tectorial membrane (TM), and OHC activity. The stereocilia, Deiter cells, and pillar cells are modeled as rigid links. The micro-mechanical model has three independent degrees of freedom (BM displacement, TM displacement parallel to the reticular lamina [RL], TM bending perpendicular to RL). The motions of the other structures (for e.g. stereocilia deflection, OHC strain) can be solved for in terms of these three quantities. The equations of motion for the micro-model are obtained using Lagrange's method. 2.2

Electrical pathways and electro-mechanical coupling

The electrical pathways in the scala media, scala vestibuli, and scala tympani are modeled using one dimensional cables to simulate the spread of current along the cochlea. Fig. 2 shows the local circuit at each crosssection along the length, with the three cables (SV, ST, and SM) passing through each radial cross-section. The governing equations for the electrical degrees of freedom are derived using Kirchhoff's laws for the circuit shown above. Two of the current sources, Is\ and Is2, are current due to the variable stereocilia conductance and current due to OHC electromotility, respectively (see below). An external current source and sink (ISPRC) c a n b e used to represent a bipolar sinusoidal current input.

412

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T h e electrical degrees of freedom couple to the mechanical domain through t h e OHCs and the stereocilia. T h e stereocilia conductance varies with its deflection as GA = G°A + GAust, where GA = 1/RaO is the conductance of the stereocilia when there is no sound input, ust is t h e stereocilia displacement, and GA is the conductance to displacement slope about ust = 0. T h e linearized fluctuating current is Ist = G°AV + (Vsm Vohc)GAust. T h e second t e r m is treated as an equivalent current source {Isi = (Vsm Vohc)GAuat, see Fig. 2). T h e linearized expressions relating O H C strain and transmembrane voltage

to the OHC force and current are Fohc = Kohc U0hc + £3 ohc lohc = 4>ohc/Zm — lUJtz U0hc ,

(1)

where Foh0 is the force exerted by the O H C on the B M and the RL, u0hc is t h e change in OHC length, €3 is t h e electromechanical coupling coefficient, Zm is the net basolateral impedance of the O H C given by 1/Zm = 1/Rm — itoCm (see Fig. 2),
Model Predictions

T h e model is solved in the frequency domain using a finite element discretization in length (a;) and height (z), and mode shapes for the fluid in t h e width (y) dimension. T h e following results have been obtained using the first five symmetric fluid modes in the y direction and a uniform 1041x41 mesh in the x-z plane.

413 3.1

Response to acoustic input BM response re Stapes (active versus passive)

BM Phase re Stapes

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—

Active x=0.5cm Passive x=0.5cm Active x=l .0cm Passive x= 1.0cm 5

10

15

Frequency (kHz)

Frequency (kHz)

F i g u r e 3. B M d i s p l a c e m e n t m a g n i t u d e a n d p h a s e a t x = 0 . 5 c m a n d a t x = 1 . 0 c m ( l e n g t h of B M = 2.5 c m ) , n o r m a l i z e d t o s t a p e s d i s p l a c e m e n t for a c o u s t i c i n p u t .

BM response re Stapes

Fig. 3 illustrates frequency response - - - Passive 1 mode • - -Passive 5 modes of BM motion for acoustic input with Active 1 mode and without activity. Activity is conActive 5 modes trolled by changing the conductivity of stereocilia channels (zero for the passive model). The model achieves around a half-octave shift in frequency and 25dB gain for basal locations. Spatial plots also agree qual0.002 0.004 0.006 0.0 Distance from stapes (m) itatively with experimental findings. Fig. 4 shows spatial response of the F i g u r e 4. Effect of fluid m o d e s o n m o d e l BM and the effect of fluid modes on response (acoustic input). passive and active response. A key feature to note is the slow spatial cut off of the passive one-mode (or 2-d) fluid model and the overly sharp response of the active 2-d model. Including additional modes accurately models added fluid mass loading on the BM and enhances passive cutoff, more closely matching experiments. 3.2

Cochlear potentials in response to acoustic input

Figure 5a shows A.C. potentials (OHC intracellular potential in main figure, ST potential and SM potential as insets) in mV in response to acoustic input of 40dB at 18.4 kHz (40 dB SPL input corresponds to nearly 0.0001 nm stapes displacement at 10 kHz; estimated from Nuttall [3]). Figure 5b shows the phase difference between ST potential and BM displacement at x=0.46cm (best frequency of 18kHz). The predicted phase matches the experimental results of Fridberger et al. [4]. The model predicts that the magnitude of the ST

414 potential is not as sharp as BM displacement (not shown), while experimental result shows similar tuning for ST and BM (see inset).

X (cm)

Frequency (kHz)

Figure 5. (a) Alternating potentials in response to acoustic stimuli at 18.4kHz; Inset plots have same axes and units (mV and cm). Thin dashed line shows OHC voltage envelope. (b) Phase difference between ST potential and BM at x=0.46cm. Solid line is model result while stars represent experimental data from Fridberger et al., 2004. Normalized BM and ST magnitudes from the experiment are shown as inset.

3.3

Response to electrical input

Figs. 6 and 7 show BM velocity response at the current injection site (CIS) (x=0.5cm) when subjected to a 35/xA bipolar current stimulus and acoustic input, for the model (fig. 6) and experiment (fig. 7, from Grosh et al. [5]). The inset figure in the modeling plot corresponds to response at a slightly apical location (x=0.55cm). Note the similarity in the phase of the theoretical predictions with the experiment (fig. 7). The model prediction of the BM amplitude shows more peaks at excitation location than seen in the experiment, although the BM response at a location more apical shows a double peak similar to experiments. 4

Discussion

The mechanical-electrical-acoustical model described here is based on experimentally observed and hypothesized geometrical and physical parameters. It includes full three dimensional fluid effects, linearized OHC activity, and dependence of stereocilia conductance on its deflection. A single model is used to simulate the BM response to both acoustic and electric excitation without any change in material properties. Experimental results indicate that the BM response to bipolar stimulus typically exhibits one or two peaks [5]. The model shows more spectral fluctuation at the location of current injection than experimental results.

415 BM displacement

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The discrepancy could be due to either the uncertainty of the recording location in the experiment or due to incorrect representation of the current spread in the model. The multiple peaks in the model arise due to the existence of the TM shear resonance mode in addition to the BM resonance and the constructive and destructive interference of backward propagating and reflected waves. Analysis of the model shows that the active peak seen in acoustic stimuli corresponds to the resonance mode dominated by TM shear properties while the passive peak corresponds to the BM dominated mode. The BM mode is not prominent in the acoustic response of the active cochlea as the TM mode response dominates that of the BM mode.

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The one parameter in this model which is not completely in tune with experimental observations so far, is the stereocilia conductance to displacement slope. Experimental data on transducer currents indicate maximum currents up to 2.5nA [6] which after corrections for temperature, endolymphatic potential and other factors [7] can be estimated to be up to 15nA. This translates to a maximum estimated in vivo conductance to displacement slope of 12 S/cm 2 , while a value of around 85 S/cm 2 has been used in the model . Force gen-

eration by the stereocilia, not presently in the model, could account for this discrepancy. Other effects that could be important are the feed-forward mechanism of outer hair cells [8], and fluid flow effects in the sulcus and through the RL-TM gap. Future work is aimed at eliminating these deficiencies in the model and on including OHC nonlinearity and stereocilia force generation in the model. Acknowledgments This work was supported by National Institutes of Health Grant No. NIDCD R01-04084. References 1. Zwislocki J., 1963. Analysis of the middle-ear function, part ii: Guineapig ear. J. Acous. Soc. Am. 35, 1034-1040. 2. Dallos P., 2003. Organ of Corti Kinematics. J. Assoc. Res. Otolaryngol. 4, 416-421. 3. Nuttall A.L., 1998. Measurements of the guinea-pig middle-ear transfer characteristic. J. Acous. Soc. Am. 56, 416-421. 4. Fridberger A., de Monvel J.B., Zheng J.F., Hu N., Zou Y., Ren T.Y., Nuttall A., 2004. Organ of Corti potentials and the motion of the basilar membrane. J. Neurosci. 24, 10057-10063. 5. Grosh K., Zheng J.F., Zou Y., de Boer E., Nuttall A.L., 2004. Highfrequency electromotile responses in the cochlea. J. Acous. Soc. Am. 115, 2178-2184. 6. He D.Z.Z., Jia S.P., Dallos P., 2004. Mechanoelectrical transduction of adult outer hair cells studied in a gerbil hemicochlea. Nature 429, 766770. 7. Fettiplace R., 2004. Estimate on in vivo transducer current in stereocilia of gerbils. Personal communication. 8. Steele C.R., Lim K.M., 1999. Cochlear model with three-dimensional fluid, inner sulcus and feed-forward mechanism. Audiol. Neuro-Otol. 4, 197-203.

COCHLEAR COILING AND LOW-FREQUENCY HEARING R. S. CHADWICK 1 , D. MANOUSSAKI 2 , E. K. DIMITRIADIS 3 , B. SHOELSON 1 'Section on Auditory Mechanics, NIDCD, Bethesda, MD 20892, 2Dept. Mathematics, Vanderbilt University, Nashville, TN 37240, 3DBEPS/OD, N1H, Bethesda, MD 20892 USA E-mail: [email protected] D. R. KETTEN, J. ARRUDA, J. T. O'MALLEY Dept. Otology and Laryngology, Harvard Medical School, Boston MA 02114, and Woods Hole Oceanographic Institution, Woods Hole, MA, 02543 USA Surface gravity waves in a spiral channel can be used as an analogue for cochlear macromechanics (Manoussaki et al. [1]). We found that in a vertical-walled channel with uniform cross section, as a low-frequency wave propagates inward from larger to smaller spiral radii, the wave amplitude near the outside wall grows while the amplitude near the inside wall decreases. This relative amplitude change induces a radial tilt of the free surface, the magnitude of which increases in inverse proportion to the spiral radius. The tilt, which can be interpreted in terms of energy redistribution, can be explained by a "whispering gallery effect," can develop dynamically on the cochlear partition and, by contributing to the bending of apical stereocilia (Cai et al. [2]), can augment low-frequency hearing by as much as 20 dB. We therefore hypothesized that cochlear spiral radii ratios (largest/smallest) could account for interspecies differences in low-frequency hearing. Preliminary analyses of spiral parameters obtained from published data on mammalian species, as well as from histological sections and 3D CT scans of the cochleae of low-frequency baleen whales and high-frequency dolphins and porpoises, tend to support our hypothesis: species with good low-frequency hearing have larger spiral ratios than do those with poor low-frequency hearing.

1 Introduction The search for the functional significance of cochlear coiling has attracted researchers in fields ranging from evolutionary biology and comparative physiology to auditory mechanics. Lieberstein [3] argued that coiling was an evolutionary adaptation required by small mammals to hear low-frequency sounds. This idea has been given some credence by West [4], who correlated features of cochlear coiling with behavioral audiograms in small ground-dwelling mammals. However, in studies of coiling by cochlear mechanicists, coiling effects have generally been found to be negligible. Huxley [5] provides a notable exception by suggesting that coiling can mechanically isolate adjacent sections along the cochlear partition and provide a sharper resonance effect.

417

418 2 Methods 2.1 Cochlear macromechanics In Manoussaki et al. [1] we used the WKB method to study the propagation of surface gravity waves in a spiral vertical-walled channel of uniform cross section, so as to isolate the effect of curvature. We show that there is an analogy between surface gravity waves and the classical impedance formulation of cochlear mechanics when we neglect damping of both the surface gravity waves and the cochlear partition, since they have different dependencies on frequency. We restrict the frequency to be below the lowest characteristic frequency in the cochlear impedance model to enable the modeled cochlear wave to reach the apex. In the channel all waves will reach the apex; however, we must restrict input frequencies to values sufficiently low to suppress higher-order modes across the width of the channel. Under these conditions pg (fluid density times gravity) plays the role of spring K and mass M on the cochlear partition, such that pg = {K-Mco2)l2. In this context the factor of 1/2 arises because of the reduction of two fluid layers in the cochlear model to one in the channel. 2.2

Ray tracing

We simulated a spiral channel in which the paths of surface waves are represented by rays. The vertical sidewalls are modeled as ideal mirrors; that is, impinging rays undergo specular reflection at an angle equal to the angle of incidence relative to the normal to the side wall. We calculated the paths of 100 equally spaced rays entering the outer turn of the channel, tangent to the walls. The rays are traced as they propagate toward the innermost point of the spiral, where the deviation from a uniform distribution gives a measure of energy-density redistribution across the channel. 2.3

Histology

Ears were fixed in 10% neutral buffered formalin and decalcified in 0.27 M ethylene-diamine-tetra-acetate (EDTA) containing 1% formalin. After decalcification, specimens were dehydrated in a graded series of ethanols from 50% through 100%, embedded in celloidin, and hardened. The celloidin-embedded tissue blocks were sectioned at 20 microns, and every tenth section was stained with hematoxylin and eosin and mounted on sealed glass slides for examination by light microscopy. 2.4

CT scans

Fresh, frozen, or formalin-fixed ears were examined using a Siemens Volume Zoom Helical CT scanner. Scan data were obtained at 0.5- to 1-mm increments with an ultra-high bone protocol and imaged at 0.1-mm slice thicknesses in coronal and transaxial planes. Three-dimensional views of the inner ear membranous labyrinth

419 and associated neural canals were obtained by segmenting related X-ray attenuations. 2.5

Spiral parameters

The calculation of the ratio of maximum to minimum radii of a cochlea is very sensitive to the location of its center. To facilitate comparisons across species, it is necessary to establish an objective, repeatable method for determining the mathematical center of the cochlear spiral. Using mid-modiolar CT sections to estimate the basilar membrane (BM) position relative to the scalae media-vestibuli margins, we first traced and extracted the x-y- coordinates of the border of the BM on a top orthogonal image of the 3D CT scan. We made an initial guess of the center by fitting a circle to a small number of points at the spiral apex, and used this guess as the center of a grid of coordinates generated to represent possible best-fit centers. For each point in this grid, we computed R and 9 along the length of the traced curve, and we fit the data to a nonlinear spiral model of the form R(0) = /?0(exp(-/?<9)- 0.6-bd1) The mean squared error was determined for each fit, and the grid point that minimized the error was selected as the computational center. The estimated BM location curve and the computed center were then overlaid on the image of the cochlea, from which we determined the ratio of the maximum and minimum distances to the best-fit center. 3 Results 3.1

Cochlear macromechanics: surface gravity-wave analogue

In a straight channel, or in one of constant curvature, we expect waves to propagate uniformly without change. However, Manoussaki et al. [1] found a surprising result when the channel has non-uniform curvature: for waves propagating in a direction of increasing curvature (decreasing radius of curvature), the amplitude on the outside wall amplifies, while the amplitude on the inside wall decreases. This results in an increasing radial tilt of the free surface (Fig.l). Thus the increase in curvature seems to induce a passive mechanical amplification of tilt while preserving the constancy of energy flow along the cross section of the channel or cochlear duct. Manoussaki et al. [1] found a simple relation that quantifies the radial tilt: At]^l/Rm, where the difference in wave amplitude on the outside and inside walls is Afj, and Rm is the distance from the center of the spiral to the midline of the channel or cochlear partition. Thus if Rm decreases by a factor of 10 from base to apex, as it does in some species (Table 1), the tilt increases by a factor of ten. If this tilt is a signal that can be sensed by the neurosensory cells in the cochlear partition, curvature in this species could account for a passive amplification of 20 dB. In a

420

separate study of the effect of curvature on cochlear micromechanics, Cai et al. [2] showed that the tilt effect persists in a model with structural elements in the organ of Corti and a circular cross section: curvature significantly improves the shearing efficiency of apical outer hair cell stereocilia bundles. These results lead us to the hypothesis that cochlear curvature improves low-frequency hearing sensitivity, and that mammalian species with good low-frequency hearing should have higher maximum/minimum spiral radii ratios than those with poor low-frequency hearing sensitivity.

Figure 1. Radial tilt of the wave amplitude. On the left, the the wave amplitude is shown for the spiral channel. On the right the same is shown graphically in a straight box to illustrate the amplification of tilt more clearly. The outside wall is denoted by rw = 0.5, and the inside wall is at rw = -0.5. The wave enters the channel at rm = 25, and travels inward to r„ = 3.7.

3.2

Mechanism of radial tilt: the whispering gallery effect

What then is a simple, intuitive explanation of both the free surface tilt and its amplification as the wave propagates towards the spiral center? Concerning first the tilt itself, we can adopt the geometric optics argument that Rayleigh [6] used to explain the phenomenon of the Whispering Gallery in London's St. Paul's Cathedral, where whispers travel large distances along a curved wall. Rayleigh showed that a pencil of rays emanating from a source toward a nearby concave boundary, would, after any number of reflections, be confined near the boundary. In other words, disturbances tend to cling to a concave boundary. The same line of reasoning can be used to demonstrate that disturbances are dispersed by a convex boundary. In the present problem of surface gravity waves propagating in a curved, vertical-walled channel, the concave boundary is the outer wall, the convex boundary is the inner wall, and the source of disturbances is the walls themselves. Any redistribution of rays shows the redistribution of energy density across the channel. Wave energy density is related to wave amplitude, so that wave energy redistribution results in a radial tilt of the free surface, increasing from inside to the outside (Manoussaki et al. [1]). This is illustrated in the geometric ray tracing of Fig. 2, in which rays entering

421

the channel at the outer opening (arrows) cling to the outer wall as they propagate to the center. Figure 2. Ray tracing analysis shows that spiral walls redistribute rays toward the outer wall at the center of the spiral. This illustrates the whispering gallery effect.

3.3

Analyses of cochlear spirals for different

species

Table 1. Radii ratios and low-frequency thresholds. Spiral center estimated from inner turn of von Bekesy's cochlear partition spiral diagrams [7]. I-ow-frequcncy hearing thresholds are from West [4J.

species Rmax/Rmin Hz

man 10 30

cow 10 20

elephant 7.5 15

guinea pig 7.4 40

rat 4.3 400

mouse 4.0 800

Table 2. Radii ratios and low-frequency thresholds for some marine mammals. Spiral centers were estimated from complete spiral fits to Ketten's basilar membrane spiral diagrams that were reconstructed from histological sections [8]. Low-frequency hearing thresholds are from Ketten [8].

species

humpback whale

bottlenose dolphin

Rmax/Rmin Hz

8.3 20

5.5 200

harbor porpoise 2.6 500

Table 3. Radii ratios and low-frequency thresholds for some marine mammals. Spiral centers were estimated from spiral fits to curves estimating the location of the basilar membrane on the orthogonal projections of the C r scans based on mid-modiolar CT sections. Low-frequency hearing thresholds are from Ketten [8].

species

blue whale Rmax/Rmin 4.8 Hz 12

Northern right 8.1 15

bottlenose dolphin 5.0 200

harbor porpoise 4.5 500

422

Figure 3. Top orthogonal projections of CT scans. Upper left, blue whale; upper right. Northern right whale; lower left, bottlenose dolphin; lower right, harbor porpoise. Estimated BM location from midmodiolar sections (yellow curve); best-fit spiral center (red dot). Radii ratios arc given in Table 3.

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423

4 Discussion The idea that cochlear curvature was an adaptation by mammals to improve lowfrequency hearing sensitivity is given more credence in this present work. We have elucidated a physical principle of radial redistribution of wave-energy density by the spiral geometry, which can be interpreted as a whispering gallery effect. The principle is demonstrated three ways: a) radial tilt of a surface gravity wave analogue of cochlear macromechanics; b) improved apical outer hair cell bundle bending efficiency due to curvature in a complex wave propagation model that includes the organ of Corti and tectorial membrane; and c) an elementary ray tracing analysis in a spiral channel. The effect grows in proportion to the ratio of maximum to minimum spiral radii. This leads to the hypothesis that the larger this ratio, the lower the low-frequency threshold of a particular species. Tables 1-3 and Fig. 4 demonstrate the trends, which generally support the hypothesis, using three different methods of data analysis. Further work is required to understand differences in estimated radii ratios of the same species using different methods. The obvious deviation of the blue whale seen in Fig. 4 begs further investigation. Also, the spiral radius ratio is not the sole determinant of the frequency hearing sensitivity, and clearly more work is required to establish the roles of different factors. The source of material for this paper is from a manuscript submitted to Nature. References 1. 2. 3.

4.

5. 6. 7. 8.

Manoussaki, D., Dimitriadis, E.K., Chadwick, R.S., 2005. Travelling waves in a spiral channel, (in revision). Cai, H., Chadwick, R.S ., Manoussaki, D.,2005. Wave propagation in a complex cochlear micromechanics model with curvature, (this volume). Lieberstein, H.M., 1972. The basilar membrane as a uniformly loaded plate clamped on two spiral boundaries in a plane or on two helical-spiral boundaries: relevance of the species record. Math. Biosci. 13, 139-148. West, CD., 1985. Relationship of the spiral turns of the cochlea and the length of the basilar membrane to the range of audible frequencies of ground dwelling mammals. J. Acoust. Soc. Am. 77, 1091-1101. Huxley, A.F., 1969. Is resonance possible in the cochlea after all? Nature 221,935-940. Rayleigh, L., 1964. Theory of Sound. Vol. II., Dover Publications, New York. von Bekesy, G., 1960. Experiments in Hearing. McGraw-Hill, New York. Ketten, D.R., 2000. Cetacean ears. In: Au, W.W. L., Popper, A.N., Fay, R. R. (Eds.), Hearing by Whales and Dolphins. Springer-Verlag, New York, pp. 43-108.

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Comments and Discussion Brownell: Your transepithelium electrical stimulation data show a conspicuous resonance between the acoustic resonance and the upper limit of outer hair cell electromechanical force production. Your models do not yet simulate this behavior. Rabbitt et al (2005) have measured an electrical resonance in isolated OHCs from the low frequency region of the cochlea. This resonance frequency would be expected to increase inversely to OHC length (Weitzel et al. 2003). What would you have to add to your model to simulate your data? Answer: For frequencies below 25 kHz at this location (the 18 kHz CF location), the multi-peaked response at and just below the CF for this location is often seen in experimental data (although there are animal dependent differences in the details of the response, see Grosh et al. (2004)). Our models are able to replicate the qualitative and quantitative nature of this electromotile response (see Fig. 6 and inset) where we do show a pronounced dip in the frequency response at a frequency below the CF. Since our model of the OHC is piezoelectric, one could label this a low frequency piezoelectric resonance effect. We attribute the multi-peaked nature of the response in this region to the local resonant behavior of the cochlear partition (including the OHCs) and to wave propagation effects (from the excitation region to the stapes and back). These lower frequency responses were the focus of this study. We are beginning to examine the ability of our model to predict the response at the higher frequencies, far above CF. In principle; we would not have to add any more physics to our model to replicate the high frequency resonance seen in the experimental data. The OHCs in our model have a place dependent length (and therefore stiffness) along with the place varying dependencies of the other properties, so we would expect to see place dependent high frequency resonances and anti-resonances. We may need to include a more detailed model of the OHCs or higher order kinematics (i.e., modes) of the organ of Corti structure to accurately replicate the high frequency response. We haven't attempted detailed simulations of isolated OHCs - this is however, planned.

MULTI-SCALE MODEL OF THE ORGAN OF CORTI: IHC TIP LINK TENSION CHARLES R. STEELE Stanford University, Mechanical Engineering, Durand Building, Room 262, Stanford, CA 94305, USA E-mail: [email protected] SUNIL PURIA Stanford University, Mechanical Engineering, Durand Building, Room 262, Stanford, CA 94305, USA Stanford University, Otolaryngology-Head and Neck Surgery, Stanford, CA 94305 E-mail:

[email protected]

The capability for the accurate and efficient computation of the three-dimensional elastic features of the organ of Corti has been available for some time. Our recent work has been on the inclusion of the viscous fluid. Novel measurements from various laboratories provide the opportunity to refocus on the elastic properties. The current detailed model for the organ of Corti is reasonably consistent with these diverse measurements in guinea pig. The individual rows of IHC cilia with tip links and the Hensen stripe are included. The results for low frequency show a phase of tip link tension similar to auditory nerve measurements. For high amplitudes for the guinea pig base, because of the near contact with the Hensen stripe, the excitation changes polarity, similar to the peak-splitting neural behavior sometimes observed.

1 Introduction The auditory nerve threshold is close to the basilar membrane (BM) response, as shown in one cochlea by Narayan, et al. [1]. However the complex arrangement of the organ of Corti (OC) makes it likely that the actual excitation of the cilia of the inner hair cells (IHC) does not merely follow the motion of the BM. Hence there is interest in developing more detailed simulation of the OC, such as in [2], [3] and [4]. The study [2] was motivated by the measurements of the inner hair cell (IHC) response by Cheatham and Dallos [5] in the upper turns of the guinea pig (GP) cochlea and the eighth nerve and (BM) responses in the base of the chinchilla by Ruggero, et al. [6]. The IHC at the apex behaves as might be expected, with a maximum excitation when the BM is between maximum displacement and velocity toward scala vestibuli (SV). However, the neural recordings at the base indicate excitation with velocity toward scala tympani (ST). The finding in [2] is that the phase of IHC excitation, related to the tension in the tip link of the tallest cilium of the IHC, can be anything, particularly depending on the elastic properties of the TM. However, at the GP base, with TM elastic properties given by the measurements in [7] and [8], the excitation occurs for BM displacement and

425

426

velocity toward SV, consistent with [6], while at the apex, the excitation is for BM displacement and velocity toward ST, consistent with [5]. The present effort is a continuation of [2] with a focus on a thorough reevaluation of the recent experimental results on geometry and stiffness to improve the model. Secondly, the nonlinear solution for the full OC model is developed. The significant nonlinearities considered are (1) the buckling instability of the inner and outer pillar cells and the Dieter rods and (2) the nonlinear flow of fluid between the Hensen stripe and the IHC cilia. 2 Methods Our approach is described in some detail in [2]. A close view of the IHC cilia is in Figure 1. The compatibility of pressure and displacement in the fluid and on the walls provides the system of equations in terms of the compliance and permeability matrices. Currently this is reduced to a system of 10th order. From this the linear, steady-state response for many different frequencies can be calculated in one second of laptop computer time. (MSB DAM COM

0.W2 0.08

, f j ' TM I v I „"i ^. — ••- _ - / ^*rs HS i *TSSr*Toir~""roi» ua"

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Figure 1. Close view of IHC cilia for GP apex. The Hensen stripe (HS) is the triangle attached to the TM above. Dashed and solid lines show undeformed and deformed configurations, with the tip of the IHC cilia near the HS. The static pressure loading is toward ST, greatly amplified. The radial and axial distances are in mm.

For the nonlinear effect of fluid flow between the tip of the IHC cilia and the TM and Hensen stripe, only a few terms in the permeability matrix need be modified. The nonlinear 10th order system is solved using the forward integration function NDSolve in Mathematica. This requires around one minute for a given problem to compute several cycles of response. The full OC model is tuned to satisfy the anatomy in [9], [10], [11], [12] , and [13], the stiffness measured in [14], [15], [16], [17], [18], [7], [19] , [20], and [21], the BM shape [22] and [23], the quasi-static motion measured in [24], and the dynamic response measured in [25], [26], and [13]. 3 Results We have achieved reasonable satisfaction of these goals using one set of parameters, with one exception. For the GP apex, either the TM and/or the OHC

427

cilia must be softer than that indicated by the recent measurements. For the GP base, all works well. An interesting aspect is that the BM beam model of Hornera, et al. [23] has the Cooper [22] deformation shape under a uniform pressure loading. However, for point loading, the response of the beam model is nothing like that found by Miller [14] or in gerbil by Olson and Mountain [20] and Edge, et al. [21]. For the point load, the outer pillar stiffens the BM substantially. This provides good information on the axial stiffness of the pillar heads and the RL. The axial stiffness is significant for the local point load but not for the pressure loading, for which all the neighboring sections of the OC will move together. The measurements of Fridberger, et al. [24] show a pronounced nonlinear effect. The quasi-static pressure towards ST causes a much larger displacement of the upper portion of the OC than pressure towards SV. The pressure is not known, but may be around 0.5 Pa. The linear solution for this pressure indicates that buckling of the inner pillars occurs for the pressure towards ST, and buckling of the outer pillars and the Deiter rods for pressure towards SV. The displacements of many points of the OC are compared to the measurements. The general agreement supports the notion of the buckling. It is possible that such buckling could occur for acoustic stimulation at rather high levels. It seems that either the TM or the cilia must be soft for the moderately good agreement of the BM shape and the agreement at the individual points. The calculated phase is similar to [27] at the apex. The results for the force in the tip link of the IHC cilia for the GP base at different intensities are in Figure 2. The input is a pressure difference between ST and SV, which varies sinusoidally. The phase of the pressure difference is shown by the purely sinusoidal curve in each plot. The positive maximum corresponds to maximum pressure toward SV, which causes shear on the OHC cilia in the excitatory direction. The solution is for the initial condition of zero displacement of all elements at time zero. It can be seen that what appears to be a nearly steady-state response is achieved in these few cycles. An expanded view for very small time shows that all displacements do start with zero as prescribed; there exist very short time response modes. For low pressure, the response agrees closely with the linear steady-state solution. The maximum tension in the tip link for this frequency is nearly 180° out of phase with the pressure, i.e., for pressure toward SV. For pressure of 30 Pa (124 dB-SPL), Figure 2 (a), a small nonlinear effect appears as a distortion of the response curve consisting of a small plateau. For a slight increase in pressure to 35 Pa (b), the plateau becomes a small secondary peak. For another step in pressure to 40 Pa (c), the secondary peak becomes positive. Thus there are two peaks of maximum tip link tension in each cycle. For another step to 50 Pa (d), the secondary peak becomes dominant. This secondary peak is almost in phase with the driving pressure. So for a change in pressure corresponding to about 5 dB, there is a shift in the phase of the excitation of 180°. For a middle ear pressure gain from the ear canal to SV of 30 dB, this shift in phase would correspond to about 95 dB-SPL,

428

close to the transition level reported in [6]. What we do not see is the second shift back in phase occurring at about 30 dB higher pressure, as seen in the auditory nerve [6]. The calculations show only an increase in the relative size of the secondary peak. Note that the out-of-phase peak stays about constant in (a-e), while the in-phase peak grows in amplitude.

(a) 30 Pa (123.5 dB-SPL)

(b) 35 Pa (124.8 dB-SPL)

(c) 40 Pa (126 dB-SPL)

(e) 60 Pa (129.5 dB-SPL)

(f) Gap at 60 Pa

torceTlpLInk IS

I

8.5 0.01

0.02

0.03

(d) 50 Pa (128 dB-SPL)

0.M

Figure 2. Nonlinear solution for the GP base with initial gaps between the tip of IHC cilium and HS and TM of 7% (20 nm) at 100 Hz. (a) At the pressure difference ST-SV of 30 Pa the excitatory force in the tip link is out-of-phase with the pressure, but the negative portion acquires a secondary step that is in-phase. (b) At 35 Pa, the negative step becomes a small peak, (c) At 40 Pa, the secondary peak becomes positive, (d) At 50 Pa, the secondary peak becomes the dominant excitatory force, (e) At 60 Pa, the secondary peak becomes larger, (f) The gap between the Hensen stripe and the cilium tip shows that the secondary peak occurs when the tip comes into close contact. This offers an explanation for the 180° change in phase measured in auditory nerve fibers at 80 dB-SPL (in the ear canal) by Ruggero, et al. [6]. Also the presence of the two excitatory peaks within the cycle (c-e) suggests a reason for the "peak splitting" observed in auditory nerve fibers [28], [29].

The change in the gap between the tip of the IHC tall cilium and the Hensen stripe is shown in Figure 2 (f) for high pressure. The initial gap for these calculations is about 20 nm. So the gap is nearly shut with the value of- 20 nm, for almost half of the cycle in (f). Of course, the gap is never totally closed, since infinite force would be required. 4 Discussion For low frequency there is phase locking of the auditory nerve fibers. The present full OC model indicates IHC excitation, assumed to be proportional to the tension in the tip link connected to the tallest cilium, that is generally between BM displacement and velocity toward SV at the GP apex. This is consistent with the intracellular recordings [5] and measurements of the relative rotation of IHC and OHC cilia [13]. At the GP base, the phase of excitation is for BM motion toward

429 ST, which is consistent with the direct measurements [6]. The reason for this phase difference is that the fluid region under the TM and between the IHC and OHC cilia tends to open for BM motion toward ST. This causes fluid to flow in from the inner sulcus, bending the IHC cilia in the excitatory direction. In the apex, this is not so significant since the TM adapts more readily. The quasi static measurements [24] were a surprise. The upper portion of the OC has substantial displacement for positive pressure in SV causing displacement of the BM toward ST, but hardly moves for positive pressure in ST. The explanation, consistent with the element stiffness properties, is that buckling of the inner pillars occurs with positive pressure in SV, and buckling of the outer pillars and the Deiter rods occurs with positive pressure in ST. This provides a severe test that the present elastic model passes reasonably well. It remains to be explored, to see if this phenomenon is significant in the auditory range at different locations in the cochlea. Another interesting mechanical nonlinearity is caused by the small gap between the cilia of the IHC and the Hensen stripe and TM. The actual initial gap will probably never be determined. Consequently in [2], various values for this were assumed and some effect was found on the phase and amplitude of IHC excitation in the linear calculation of response. The present nonlinear calculation shows an interesting effect of the amplitude of pressure on phase. For high pressure, corresponding to about 90 dB-SPL, the phase of the IHC excitation switches 180°. This is quite similar to the auditory nerve behavior [6]. Furthermore the intensity levels at which peak splitting develops, given in 1 dB steps in [28], look similar to the development of the two positive peaks in Figure 2. The negative peaks are most likely not realistic, since a buckling instability of the tip link could occur for very little compressive force. Such sharp negative peaks are not seen in the IHC recordings [30]. The neural behavior is variable [29], and the peak splitting and change in phase are not found in the GP base in [31]. However, it seems that the present calculations, based on the observation of the Hensen stripe near the IHC cilia in [12] and reinforced in [13], support completely the notion that the Hensen stripe plays a crucial role in the excitation of the IHC. The suggestion is made by Zwislocki [32] that there must be some mechanical nonlinear coupling between the TM and the OC. Cody and Mountain [30] provide further evidence for this. The present results appear to offer strong indication that the mysterious nonlinearity is simply due to the restricted fluid flow between the tip of the IHC and the Hensen stripe.

Acknowledgments This work was supported by Grant RGP0051 from the Human Frontier Science Program.

1. Narayan, S.S., Temchin, A.N., Recio, A., Ruggero, M.A., 1998. Frequency tuning of basilar membrane and auditory nerve fibers in the same cochleae. Science 282, 1882-4. 2. Steele, C.R., Puria, S., 2005. Force on inner hair cell cilia. Int. J. Solids Struct, in press. 3. Cai, H., Chadwick, R., 2002. Radial structure of traveling waves in the inner ear. SIAM J. Appl. Math. (USA) 63, 1105-20. 4. Andoh, M., Wada, H., 2003. Dynamic characteristics of the force generated by the outer hair cell motility in the organ of Corti - (Theoretical consideration). JSME Int. J. Ser. C-Mech. Syst. Mach. Elem. Manuf. 46, 1256-1265. 5. Cheatham, M.A., Dallos, P., 1999. Response phase: a view from the inner hair cell. J Acoust Soc Am 105, 799-810. 6. Ruggero, M.A., Narayan, S.S., Temchin, A.N., Recio, A., 2000. Mechanical bases of frequency tuning and neural excitation at the base of the cochlea: comparison of basilar-membrane vibrations and auditory-nerve-fiber responses in chinchilla. Proc Natl Acad Sci U S A 97, 11744-50. 7. Shoelson, B., Dimitriadis, E.K., Cai, H., Kachar, B., Chadwick, R.S., 2004. Evidence and implications of inhomogeneity in tectorial membrane elasticity. Biophys J 87, 2768-77. 8. Freeman, D.M., Abnet, C.C., Hemmert, W., Tsai, B.S., Weiss, T.F., 2003. Dynamic material properties of the tectorial membrane: a summary. Hear Res 180, 1-10. 9 Kelly, J.P., 1989. Cellular organization of the guinea pig's cochlea. Acta Otolaryngol Suppl 467, 97-112. 10. Zetes, D.E., J.A.Tolomeo, Holley, M.C., 2004. Mapping the mechanical properties of cytoskeletal structures in the mammalian inner ear. manuscript. 11. Cabezudo, L.M., 1978. The ultrastructure of the basilar membrane in the cat. Acta Otolaryngol Suppl 86, 160-175. 12. Edge, R.M., Evans, B.N., Pearce, M., Richter, C.P., Hu, X., Dallos, P., 1998. Morphology of the unfixed cochlea. Hear Res 124, 1-16. 13. Fridberger, A., Tomo, I., Ulfandahl, M., Boulet de Monvel, J., 2005. Imaging hair cell transduction during sound stimulation: dynamic behavior of mammalian stereocilia. manuscript. 14. Miller, C.E., 1983. Structural implications of basilar membrane compliance. J. Acoust. Soc. Am. 77, 1465-1474. 15. Tolomeo, J.A., Holley, M.C., 1997. Mechanics of microtubule bundles in pillar cells from the inner ear. Biophys J 73, 2241-7.

431 16. Scherer, M.P., Gummer, A.W., 2004. Impedance analysis of the organ of Corti with magnetically actuated probes. Biophys J 87, 1378-91. 17. Steele, C.R., Scherer, M.P., Chandrasekaran, C , Chandrasekaran, C , Gummer, A.W., 2005. An analytic model for the mechanical point impedance of the organ of Corti. Poster ARO. 18. Abnet, C.C., Freeman, D.M., 2000. Deformations of the isolated mouse tectorial membrane produced by oscillatory forces. Hear Res 144, 29-46. 19. Langer, M.G., Fink, S., Koitschev, A., Rexhausen, U., Horber, J.K., Ruppersberg, J.P., 2001. Lateral mechanical coupling of stereocilia in cochlear hair bundles. Biophys J 80, 2608-21. 20. Olson, E.S., Mountain, D.C., 1994. Mapping the cochlear partition's stiffness to its cellular architecture. J Acoust Soc Am 95, 395-400. 21. Emadi, G., Richter, C.P., Dallos, P., 2004. Stiffness of the gerbil basilar membrane: radial and longitudinal variations. J Neurophysiol 91, 474-88. 22. Cooper, N.P., 2000. Radial variation in the vibrations of the cochlear partition. In: Wada, H., Takasaka, T., Ikeda, K., Ohyama, K., Koike, T., (Eds.), Recent Developments in Auditory Mechanics. World Scientific, Tohoku, Japan, pp. 109-115. 23. Hornera, M., Champneys, A.G.H.N.C, 2004. Mathematical modeling of the radial profile of basilar membrane vibrations in the inner ear. J. Acoust. Soc. Am. 116,1025-1034. 24. Fridberger, A., Boutet de Monvel, J., Ulfendahl, M., 2002. Internal shearing within the hearing organ evoked by basilar membrane motion. J Neurosci 22, 9850-7. 25. Khanna, S.M., Ulfendahl, M., Flock, A., 1989. Modes of cellular vibration in the organ of Corti. Acta Otolaryngol Suppl 467, 183-8. 26. Hemmert, W., Zenner, H.P., Gummer, A.W., 2000. Three-dimensional motion of the organ of Corti. Biophys J 78, 2285-97. 27. Fridberger, A., de Monvel, J.B., Zheng, J., Hu, N., Zou, Y., Ren, T., Nuttall, A., 2004. Organ of Corti potentials and the motion of the basilar membrane. J Neurosci 24, 10057-63. 28. Kiang, N.Y., 1990. Curious oddments of auditory-nerve studies. Hear Res 49, 1-16. 29. Cai, Y., Geisler, CD., 1996. Temporal patterns of the responses of auditorynerve fibers to low-frequency tones. Hear Res 96, 83-93. 30. Cody, A.R., Mountain, D.C., 1989. Low-frequency responses of inner hair cells: evidence for a mechanical origin of peak splitting. Hear Res 41, 89-99. 31. Wada, H., Takeda, A., Kawase, T., 2002. Timing of neural excitation in relation to basilar membrane motion in the basal region of the guinea pig cochlea during the presentation of low-frequency acoustic stimulation. Hear Res 165, 165-76.

432

32. Zwislocki, J.J., 1986. Are nonlinearities observed in firing rates of auditorynerve afferents reflections of a nonlinear coupling between the tectorial membrane and the organ of Corti? Hear Res 22, 217-21. Comments and Discussion Gummer: Your model is extremely useful because it is predictive. Here I might mention that your theoretical finding of acoustically driven transversal expansion and contraction of the subtectorial space was found independent of our experimental finding that such motion can be elicited by intracochlear electrical stimulation (Nowotny and Gummer, submitted). Which parameters in your model determine this motion? Answer: Generally, the opening of the gap in LI (between the TM and RM and IHC and OHCl) occurs for any mechanical loading toward ST and is fairly insensitive to the elastic parameters. I plan to calculate directly the situation of OHC electrical excitation in your experiment, which shows the gap so clearly.

A MICROMECHANICAL MODEL FOR FAST COCHLEAR AMPLIFICATION WITH SLOW OUTER HAIR CELLS TIMOTHY K. L U 1 2 , SERHII ZHAK 1 , PETER DALLOS 3 , RAHUL SARPESHKAR 1 Analog VLSI and Biological Systems Group, Research Lab of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Ave. Rm. 38-276, Cambridge, MA 02139, USA. Harvard-MIT

Division of Health Sciences and Technology, 77 Massachusetts 219, Cambridge, MA 02139, USA.

Ave. Rm. E25-

Auditory Physiology Laboratory, Departments of Neurobiology and Physiology and Communication Sciences and Disorders, Northwestern University, Evanston, IL 60208, USA. E-mail: [email protected] Recent experimental evidence has demonstrated that somatic outer hair cell (OHC) motility is important for amplification in the mammalian cochlea [1,2]. However, under the 'somatic electromotility' theory, the transmembrane potential that is responsible for driving the somatic OHC force is subject to low-pass filtering by the electrical RC time constant of the OHC membrane [3], Numerous mechanisms have been proposed to compensate for the attenuation of the membrane potential by the low membrane time constant at high frequencies [3,4-10]. We present a micromechanical model derived from an engineering-based analysis of cochlear mechanics and experimental data. Our model does not require novel compensatory mechanisms and demonstrates that adequate OHC gain with negative feedback significantly extends closed-loop system bandwidth and increases resonant gain. The OHC gain-bandwidth product, not just bandwidth, determines if high-frequency amplification is possible. Thus, fast cochlear amplification is possible with slow OHCs simply due to in situ feedback dynamics, though our model does not preclude other compensatory mechanisms.

1 Introduction In engineered systems, the performance of mechanical systems is often limited by the speed of motors. Negative feedback rather than positive feedback is commonly used to compensate for slow mechanical response times and to achieve desired closed-loop system characteristics. Negative feedback with gain results in faster dynamics because the active component generates a large input drive that brings the output to the desired level more quickly. Feedback makes closed-loop dynamics differ from that predicted from open-loop time constants. A common form of negative feedback, tachometer feedback, controls the velocity output of a slow motor by feeding the motor velocity back into the input with gain K (Fig. la).

433

434

X(s»

~>

,

Y(s)

1 ts+1

r-

K

Tachometer Gain

0 -

~ - Closed Loop K = 10 { Closed Loop K = 100 | ....... Open Loop K = 0 !

,(......~™_.,r„^

-20

"•^

-SO

^

^

\

io Frequency {radfs}

Gain Block

Resonant Block

-\ r^

X<s)

-"

-20 •-40

'

Y(s)

1 — 1

•Er*s*+^S*t

-

•«—»»,.......

-

**

"*

— Closed Loop K ^ = 1 | Closed Loop K ^ * 10 ( .,,,,,, Open Loop Kohe ~ 10 I I

\ t

\

>

,

N,. *\ >^ N^ x, ***

-45 -90

~ \

-135 -180

to Frequency (raoVs)

-

Figure 1. Negative feedback alters a system's closedloop response from its openloop characteristics. a, Tachometer feedback senses the motor's angular velocity (Y(s)) and feeds it back into the input. Higher tachometer gain, K, reduces the effect of the slow motor time constant (r). System dynamics are described in the s-plane (5 =jco,j = V-l, and co = 2iif). b, Closedloop Bode plots {Y(s)/X(s)) for (a) show that as the gain increases from K = 10 (dashed line, green) to K = 100 (solid line, blue), the frequency limit imposed by the time constant is pushed to higher frequencies compared with no negative feedback, where K = 0 (dotted line, black), c, Negative feedback with a resonant system plus a gain block with a slow time constant represents the essence of what allows fast amplification with slow OHCs. d, Closed-loop Bode plots (Y(s)/X(s)) for (c) show that increasing the gain from Kohc = 1 (dashed line, green) to Kohc = 10 (solid line, blue) increases the resonant gain and pushes the time constant frequency limit to higher frequencies. The open-loop case with Kotlc = 10 without negative feedback (dotted line, black) has the highest D.C. gain but rolls off earlier due to the time constant and has a lower resonant gain compared with the closed-loop K0/,c = 10 case.

435

In the closed-loop, larger tachometer gains push the frequency limit to higher frequencies (Fig. lb). The closed-loop time constant is a factor l+K less than that of the motor itself so the closed-loop bandwidth is (l+K) higher than the open-loop and the D.C. gain is reduced by (l+K). The product of gain and bandwidth is constant so gain can be traded for bandwidth and vice versa. As shown above, the critical figure of merit is the gain-bandwidth product and a system's ability to function at high frequencies is not solely determined by its open-loop bandwidth characteristics. For example, operational amplifiers typically have open-loop bandwidths of 10 Hz, gains of 105, and are used in negativefeedback configurations to achieve bandwidths of 106 Hz and gains of 1. By analogy, if OHCs have sufficient gain, they can operate at high frequencies despite their slow open-loop membrane time constants. The extraordinarily high OHC piezoelectric coefficient suggests that OHCs have adequate gain [11]. Negative feedback can also increase the gain of resonant systems in configurations such as in Fig. lc. The frequency response (Fig. Id) shows that larger gains, Kohc, push the frequency limit of the slow time constant to higher frequencies while sharpening the resonant peak and increasing its gain. The topology of Fig. lc captures the essence of what allows fast cochlear amplification despite slow OHCs. 2 Methods Our model is based on a simple mechanical analysis of one local section at the base of the cochlea. Based on experimental observations, we assumed that the tectorial membrane-reticular lamina (TM-RL) complex and basilar membrane (BM) are separate resonant subsystems [10,12-14] coupled by the passive OHC somatic stiffness and the OHC force generator [15]. The two resonator model is shown in Fig. 2. Upwards RL displacement (Xri) causes tilting of the sterocilia, which opens up ion channels to allow current into the cell causing depolarization. The OHC force generator, which is positive for contraction, is:

°hc~

rs+1

s-(rs+1)

K

'

The variable kv is the D.C. RL-displacement-tovoltage gain, kj is the D.C. voltage-to-force gain is given by kf, and r is the OHC membrane RC time constant.

JL L_l

Rrt

1

^ «"„1

Figure 2. Organ of Corti micromechanical model. The variable R is damping, k is stiffness, M is mass, F is force, X is displacement, and U is velocity.

436 Figure 3. Block digram representaton of micromechnical model. The membrane voltage is vm. The mechanical impedances, Zr/, Zbm, and Zohc, can be derived directly from Fig. 2. The dotted feedback path represents the negative feedback effect from the OHC force on the RL to the RL velocity. The solid feedback path represents the positive feedback effect from the OHC force on the BM to the RL velocity.

Fig. 3 shows a block diagram that describes the feedback dynamics of this topology. The total net force carried by the RL is FrI = Zrt -Uri. This force en be decomposed into a force, Fr!>ext, arising from the sum of external sources, such as within the organ of Corti, from fluid pressure, or from applied forces, as well as a force, Frii0hc, that arises from the OHC force generator. In our model, forces are positive in the upwards direction by convention. Since a positive Fohc pulls down on the RL but pulls up on the BM, Frii0hc, can be described by two separate feedback loops, one resulting from the effect ofFohc at the RL and the other resulting from the effect of Fohc at the BM. The dotted feedback loop in Fig. 3 represents the former effect and the solid feedback loop represents the latter effect. Due to the other mechanical impedances in the system, only a fraction of the OHC force generator, Fohc, is transmitted back to the RL. A positive RL displacement leads to a positive Fohc, which causes the RL to be pulled down, which tends to decrease the positive RL displacement; therefore, the dotted feedback loop exhibits negative feedback. However, a positive Fohc also causes the BM to be pulled upwards, which tends to push the RL up and increase the positive RL displacement; therefore, the solid feedback loop exhibits positive feedback. Fn,,,«Xl

u rt

+/->. Ml

f*

z,

1 M-1,0 he

•

>

vm

K s-(ts+1}

I

''

F«jtw

^•nf^tm

z*

Haw

^D^OIK

^"MBJAMW,

K

Figure 4. Simplified version of the block diagram in Figure 3. Although Figure 3 shows both postive and negative feedback paths, combining both paths demonstrates that the overall feedback loop is always negative.

From Fig. 3, it appears that this system involves both positive and negative feedback since the effect of the OHC force at the RL and at the BM operates in

437

different directions. However, by combining the dotted feedback loop and solid negative feedback loop in Fig. 3, we can obtain a simplified block diagram that clearly demonstrates the negative feedback inherent in this topology (Fig. 4). The loop transmission is the multiplicative product around the loop in Fig. 4 [16]: _

KK *-bm S(TS +1) ZrlZbm +Z,Zohc + ZbmZohc

Since the parameters in the expression above are positive at D.C., the loop transmission or return ratio of the active OHC force generator is negative at D.C and there is negative feedback inherent in the system irrespective of parameter magnitude [16]. The loop gain (the absolute value of the loop transmission) is increased by the fact that the RL stiffness is less than that of the BM [13] so the intrinsic parameters of the cochlea tend to increase the negative feedback. We used parameters from the basal end of the cochlea (characteristic frequency, CF, = 43.6 kHz [19]) converted appropriately for volume velocities and pressures assuming an 18 um long by 30 um wide section with six OHCs [17,18]: Name K-bm

Mbm

Meaning BM stiffness (25 um probe) BM mass

Units N/m kg

Ref. [14]

N-s/m

—

N/m

[13]

kg

-

N-s/m

-

18 4

mN/m mV/nm

0.3

nN/mV

[201 [7,2122] [23]

0.305

ms

[211

Value 5.5 kbm

(2%-CFf Qbm Rbm

BM quality factor BM damping

6 {kbm-Mbni)

n

^bm

hi

RL stiffness (with 25 um probe)

Mrl

RLmass

Qrl Rri

RL quality factor RL damping

^bm

6 0-2W 6m 4

&k'-u'f ^ohc

K kf T

Single OHC stiffness Single OHC D.C. RLdisplacement-to-voltage ratio Single OHC D.C. voltage-toforce gain OHC membrane time constant

438

3 Results Simulations demonstrate that in analogy to the system in Fig. lc, higher OHC gains (ky) reduce mid-frequency roll-off of the OHC membrane potential (Fig. 5). The closed-loop pole due to the membrane time constant is increased from the open-loop 522 Hz to 4.7 kHz, which is a substantial speedup but is still a factor of 9.3 less than CF. However, the resonant gain at CF is increased with higher OHC gains, further compensating for the OHC time constant, and increasing the membrane potential at CF to almost the same level as it is at D.C. Decreasing the OHC gain by a factor of 10 (dotted line, green) in Fig. 5 results in a 2.5 dB drop in the resonant membrane potential at CF, raises the low-frequency asymptote, and changes the "tip-to-tail" ratio from -3.5 to -20 dB. The OHC force is actually 22.5 dB higher in the highgain case in Fig. 5 (solid line, blue) compared with the low-gain case since both the membrane voltage and ^are greater in the high-gain case. Figure 5. Bode magnitude plot of the transfer function from FrLext to the OHC membrane voltage, vm, based on the block diagram in Fig. 3. The high gain case (k/= 0.3 nN/mV) is shown in the solid blue line compared with the low gain case (k/ = 0.03 nN/mV), which is the dashed green line. fc, w 0.3 nwmv kl*Q.03nNtmV

it?

10*

4 Discussion We have shown that in engineered systems, slow motor time constants can be sped up with electrical amplification in a closed-loop negative feedback system. Analogously, the in situ micromechanical functional anatomy of the cochlea sets up a negative-feedback system that allows the slow OHC time constant to be compensated by the OHC gain. With negative feedback, OHC gain can be traded for bandwidth, allowing the OHC membrane potential to be extended without attenuation past the intrinsic membrane time constant. In addition, the resonant gain due to the resonant TM-RL and BM is increased by negative feedback, helping to further compensate for the OHC membrane time constant. Negative feedback around the BM was suggested by Mountain et al. [24] but in our model, it is negative feedback around the RL that is crucial for OHC speedup. To verify that our model is biologically realistic, we have also constructed a traveling-wave model of the cochlea with realistic parameters and compared the results to experimental data.

439 This model is beyond the scope of this paper but reveals that a good match to cochlear frequency-response curves with reasonable parameters is possible. Thus, the intrinsic architecture of the organ of Corti coupled with sufficient OHC gain and negative feedback is sufficient to extend the OHC bandwidth and generate adequate force at high frequencies. Therefore, no novel mechanisms are necessary. Nonetheless, our model is not mutually exclusive with other compensatory mechanisms that may act synergistically to allow high-frequency OHC somatic electromotility and amplification. Acknowledgments We are grateful for discussions with W. E. Brownell. T.K.L is a HHMI Predoctoral Fellow. This work is also supported in part by a CAREER award from the NSF, a Packard award, and an ONR Young Investigator award. References 1. Liberman, M.C., Gao, J., He, D.Z., Wu, X., Jia, S., Zuo, J., 2002. Prestin is required for electromotility of the outer hair cell and for the cochlear amplifier. Nature. 419, 300-304. 2. Cheatham, M.A., Huynh, K.H., Gao, J., Zuo, J., Dallos, P., 2004. Cochlear function in Prestin knockout mice. J. Physiol. 560, 821-830. 3. Santos-Sacchi, J., 2003. New tunes from Corti's organ: the outer hair cell boogie rules. Curr. Opin. Neurobiol. 13, 459-468. 4. Mountain, D.C., Hubbard, A.E., 1994. A piezoelectric model of outer hair cell function. J. Acoust. Soc. Am. 95, 350-354. 5. Dallos, P., Evans, B.N., 1995. High-frequency motility of outer hair cells and the cochlear amplifier. Science. 267, 2006-2009. 6. Nobili, R., Mammano, F., 1996. Biophysics of the cochlea. II: Stationary nonlinear phenomenology. J. Acoust. Soc. Am. 99, 2244-2255. 7. Ospeck, M., Dong, X.X., Iwasa, K.H., 2003. Limiting frequency of the cochlear amplifier based on electromotility of outer hair cells. Biophys. J. 84, 739-749. 8. Spector, A.A., Brownell, W.E., Popel, A.S. 2003. Effect of outer hair cell piezoelectricity on high-frequency receptor potentials. J. Acoust. Soc. Am. 113,453-461. 9. Weitzel, E.K., Tasker, R., Brownell, W.E., 2003. Outer hair cell piezoelectricity: frequency response enhancement and resonance behavior. J. Acoust. Soc. Am. 114, 1462-1466. 10. Zwislocki, J.J., Kletsky, E.J., 1979. Tectorial membrane: a possible effect on frequency analysis in the cochlear. Science. 204, 639-641.

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11. Dong, X.X., Ospeck, M., Iwasa, K.H., 2002. Piezoelectric reciprocal relationship of the membrane motor in the cochlear outer hair cell. Biophys. J. 82, 1254-1259. 12. Allen, J.B., 1980. Cochlear micromechanics - a physical model of transduction. J. Acoust. Soc. Am. 68, 1660-1670. 13. Mammano, F., Ashmore, J.F., 1993. Reverse transduction measured in the isolated cochlea by laser Michelson interferometry. Nature. 365, 838-841. 14. Gummer, A.W., Hemmert, W., Zenner, H.P., 1996. Resonant tectorial membrane motion in the inner ear: its crucial role in frequency tuning. Proc. Natl. Acad. Sci. U.S.A. 93, 8727-8732. 15. Markin, V.S., Hudspeth, A.J., 1995. Modeling the active process of the cochlea: phase relations, amplification, and spontaneous oscillation. Biophys. J. 69, 138-174. 16. Bode, H.W., 1945. Network Analysis and Feedback Amplifier Design. D. van Nostrand, Princeton, NJ. 17. Fernandez, C , 1952. Dimensions of the Cochlea (Guinea Pig). J. Acoust. Soc. Am. 24, 519-523. 18. Nilsen, K.E., Russell, I. J., 2000. The spatial and temporal representation of a tone on the guinea pig basilar membrane. Proc. Natl. Acad. Sci. U.S.A. 97, 11751-11758. 19. Greenwood, D.D., 1990. A cochlear frequency-position function for several species~29 years later. J. Acoust. Soc. Am. 87,2592-2605. 20. He, D.Z., Dallos, P., 1999. Somatic stiffness of cochlear outer hair cells is voltage-dependent. Proc. Natl. Acad. Sci. U.S.A. 96, 8223-8228. 21. Housley, G.D., Ashmore, J.F., 1992. Ionic currents of outer hair cells isolated from the guinea-pig cochlea. J. Physiol. 448, 73-98. 22. Kros, C.J., 1996. Physiology of mammalian cochlear hair cells. In: Dallos, P., Popper, A.N., Fay, R.R. (Eds.), The Cochlea. Springer-Verlag, Berlin, pp. 328-330. 23. Scherer, M.P., Gummer, A.W., 2004. Vibration pattern of the organ of Corti up to 50 kHz: Evidence for resonant electromechanical force. Proc. Natl. Acad. Sci. U.S.A. 101, 17652-17657. 24. Mountain, D.C., Hubbard, A.E., McMullen, T.A., 1983. Electromechanical Processes in the Cochlea. In: deBoer, E., Viergever, M. (Eds.), Mechanics of Hearing. Delft Univ. Press, the Netherlands, pp. 119-126. Comments and Discussion Gummer: Your negative feedback model at the reticular lamina (RL) as a solution to the time-constant problem is very convincing. We know from the theoretical work of de Boer, Steele and others that the inertia of the basilar membrane (BM) is negligible, and from the experiments of Scherer and Gummer (Biophhys. J. 87, 1378-1391, 2004) that the inertia of the RL is also negligible. Does your model work if the inertial components of the BM and RL impedances are zero?

441 Answer: Yes, our model will still lead to speedup and increase in resonant gain with negative feedback if there is no inertial mass at the BM and RL. However, more OHC gain is needed to get the same speedup and the same increase in resonant gain. This is because, in the no-mass case, the open-loop singularities do not start off as complex singularities but instead reside on the real axis. So, more OHC gain is needed to move these singularities off the real axis into the complex plane. This possibility needs more investigation. However, a big increase in the required OHC gain is highly unlikely. As an aside, I also want to clarify that the RL mass in our model is meant to represent the mass of the TM-RL complex as a whole

THE COCHLEA BOX MODEL ONCE AGAIN: IMPROVEMENTS A N D N E W RESULTS R. NOBILI Department

of Physics

"G.Galilei", Via Marzolo 8, 35131 Padova, E-mail: [email protected]

ITALY

A. V E T E S N I K Universitats-Hals-Nasen-Ohrenklinik, Sektion Physiologische Kommunikation, Elfriede-Aulhorn Str. 5, 72076 Tubingen, E-mail: ales. vetesnik@uni-tuebingen. de

Akustik Und GERMANY

The hydrodynamic box model of the cochlea is revisited for the purpose of studying in detail the approximate scaling law that governs the tonotopic arrangement of its frequency-domain solutions. The law differs significantly from that derived by Sondhi in 1978, commonly known as "approximate shift-invariance", which suffers from an inaccuracy in the representation of the hydrodynamic coupling. Despite the absence of a similar scaling law in real mammalian cochleas, the results here presented may be significant in the perspective that a covariance law of a more general type should hold for real cochleas. To support this possibility, an argument related to the problem of cochlear amplifier-gain stabilization is advanced.

1

Introduction

It is assumed to be known t h a t the hydrodynamic box-model of the cochlea (Fig.lA) is governed by an equation of the form m£{x,t)

+ h(x)£{x,t)

+ k{x)£(x,t)

= -Gs(x)ti(t)-

/ G(x,x) £(x, t)dx , (1) Jo where £{x,t) is the displacement of a basilar membrane (BM) segment at BM position x and time t, dots standing for partial time derivatives; L is the length of the BM; m, h(x) and k(x) are respectively BM mass, BM viscosity and BM stiffness per unit BM length; cr{t) is the stapes displacement. Gs{x) and G(x,x) are the effective Green's functions accounting for the stapes-BM and the BMBM hydrodynamic couplings respectively. These depend uniquely on the fluid density p and the details of the cochlea geometry, i.e., in our case, L, the BM height H and the BM width W. Eq. (1) can be solved by numerical methods provided that m,k(x),h(x), p, L, H, W are known. We assume for these the standard values and profiles proposed by Allen in 1977 [1]: l . m = 0.05 g/cm,

442

443

2. k(x) = fco exp(—2ax), with fc0 = 109 g/(cm sec2), a = 1.7 cm" 1 . 3. /i(x) = ho exp(—ax), with ho = 300 g/(cm sec), 4. p = 1 g/cm 3 , L = 3.5 cm, if = 0.1 cm, W = 1 cm. The choice of an exponentially decreasing profile for k(x) is suggested by the fact that in most mammalian cochleas the BM responses to tones map tonotopically the interval of audible frequencies with an approximately exponentially decreasing profile. By contrast, there is no biologically plausible reason for assuming h(x) proportional to fc(x)1/2. But, as will be apparent in the next, this choice is crucial in order for the waveforms elicited by tones to vary regularly with frequency along the BM according to a well-approximated scaling law.

Figure 1. Cochlear box-model geometry. A: 3-dimensional model of the uncoiled cochlea showing a basilar membrane (BM) segment moving upwards. Horizontal arrows represent opposite displacements of oval and round windows. B : 2-dimensional representation showing stream lines as generated by a point-like source-sink pair. C: 2-dimensional model unfolded to a rectangle of length 1L and height H. The source-sink pair splits into a point-like source and a point-like sink symmetrically located with respect to x = 0.

Flattening the box model to a 2-dimensional [x, y] representation, as sketched in Fig.l, we find Gs(x) = 2p(L — x) and G(x + iy,x) as an analytic function defined on the upper complex semi-plane with logarithmic source and sink singularities at x + iy = L — x and x + iy = L + x respectively. Were this semi-plane unbounded, we would find G(x,x) = (P/TT) ln(|a; — x\/\x + x — 2L|). Actually, the mirroring effect of the rectangle boundaries forces the analytic function to be doubly periodic [3]. Thus we find instead ,_,, , p, isnfCfa; — L)|ml — snfC(x — L)|ml I G(a\x) = - l n —p—7 -~J— f~r,——~—(• , K ' 7T I sn[C(.x - L)\ m) + sn[C(x - L)\m]\

(2)

where sn(z\m) is the first Jacobi elliptic function of complex argument z and modulus m [4]. m is determined by the condition that the complete elliptic

,„.

444 integral of first kind K(m) = J"0 (1 —TOsin 2 B)~xl2 d0 satisfies the equality K{m)/K{\ - m) = L/H and C = K(m)/L. K(m) and K{1 - m) are indeed the quarter-periods of sn(z\m) along the real and the imaginary axis respectively. W i t h the assumed box-model parameters, m turns out to be very close to 1, namely m « 1 — 16exp(—TTL/H) = 1 —16exp(—357r). Correspondingly K(l — TO) is virtually equal to n/2 and C can be safely replaced by n/2H. 2

T h e b o x m o d e l in t h e h y p e r b o l i c a p p r o x i m a t i o n

Equation (1) can be rearranged and Fourier-transformed so as to read

I

L

G(x, x) rj(x, xo) dx + Z(x — x0) r](x, XO) = 2p(x — L) a(xo),

(3)

where r](x,XQ), &(xo) and XQ are respectively related to the Fourier transforms £„(x), Ou of £(;r, t), a(t) and t h e radian frequency LO by t h e equations rj(x, XQ) = £,u(x), O-(XQ) = &U and ^/fco/TOexp(—axo) = u>. We have then Z(x — XQ) = TO{1 — exp[2a(a;o — x)]

, exp[a(a;o — x)]} . (4) VTOfco Thus XQ becomes both a translational parameter for Z and the BM position where the real part of Z vanishes. Eq. (3) can be solved by numerical methods so as to obtain the repertoire of waveforms as elicited by tones of various frequencies. For XQ < L the waveform amplitudes fall down rapidly towards XQ and are virtually zero for x > XQ. Because of fluid incompressibility, these solutions, which will be called typical, satisfy the zero fluid-volume displacement equation I

rj(x,xo)dx=

Jo

/

r)(x,xo) dx = — H<J{XQ) .

(5)

Jo

Using the (undocumented) hyperbolic approximation sn(a;|TO) « tanh(:r) ta,nh(x — nL/2H), which holds for 0 < x < L with an error w 16exp(—357r), Eq. (2) becomes 1 G(x,x)

=G0(x,x)

G0(x, x) = j;[2L-{x

+ P(x-x) + x)-\x-

+ A(x + x) + B{x + x), x\], P{x -x)

where

(6)

= =¥ ln[l - e x p ( - ^ ) ] ,

1 In Sondhi's treatment [3] the approximation sn(x|m) ra tanh(x) was instead used, which led the author to overlook the term B in Eq. (6). Unfortunately, all mathematical manuals known to the Authors report this as an excellent approximation for m close to 1 without specifying that also the condition x < K(m) = L/2 must be satisfied. Actually, this approximation ignores the periodic structure of the elliptic function with quarter-period K(m) along the real axis. Consequently, the hyperbolic approximation of G(x, x) lacks the images of the source-sink pairs mirrored by the basal sides of the cochlear box.

445

A{x

3

+ x) = f ln[l - e x p ( - ^ 2 L - ^ + s ' ) ) ] , B{x + x) = =& ln[l -

e x

p(-^)].

T h e t h i n - c a n a l a p p r o x i m a t i o n satisfies a n e x a c t scaling law

For H —> 0, the singular terms A, B, P in Eq. (6) vanish and G(x, x) = GQ(X,X). The equalities dxG(x,x) = -2p6(x - x)/H, <9 2 G(x,x) = -2p<5(x - x)/H, with dx t h e partial derivative after x, 0(x) t h e Heaviside step function and S(x) t h e Dirac delta function, then hold. From derivatives of Eq.s (1) after x, using t h e above equalities and integrating over x, we obtain the following equation system d2x[Z{x - xQ) r?(x, x 0 )] = (2p/H) r?(x, x0), dx[Z(x-x0)ri(x,xo)}x=o

= 2p,

T](L,X0)

(7) = 0,

(8)

which has t h e form of a second order differential equation plus boundary conditions. Since these equations are invariant with respect t o the translations x —> x + a, Xo —» XQ + a, their solutions take t h e exact scale-covariant form rj(x,xo) = S(XQ)((X — xo), with S(XQ) a suitable scale factor. As Eq. (5) states that typical BM oscillations elicited by equal amplitude tones must displace equal amounts of fluid, we have s(x 0 ) / C(x — xo) dx = s(x 0 ) / C(x — x'Q)dx = — H a(x0), Jo Jo which can be used t o determine S(XQ). T h e origin of t h e scaling law is thus explained. Integrating the first of Eq.s (8) in a neighborhood of x = 0 we find T](X,XQ) « c(x 0 )(x —x 0 )/Z(x —xo) for some 0 < x < e L t h e coefficients of Y+ and Y_ become comparable at x = L. In these conditions, the second of Eq. (8) can be satisfied only if the coefficient of t h e regressive component YL is non negligible, which can be interpreted as a wave-reflection phenomenon occurring at t h e BM apex.

446

— Exact solution {G matrix inversion) — Thin-canal approximation (Go matrix inversion)

___-,--

'"" "\

ij

"

'

""

ia^felffiEFI

Figure 2. Waveform amplitudes and phases from 0.12 to 22 kHz in 9 steps. Solid lines (1): Exact hydrodynamic model; the waveforms follow a well-approximated scaling law. Dashed lines (2): Thin-canal approximation; the waveforms follow an exact scaling law.

Fractional distance from stapes

4

T h e w e l l - a p p r o x i m a t e d scaling law of t h e e x a c t b o x m o d e l

Differentiate Eq.(3) after x then after XQ, with
+ dXo)r)(x,x0)dx 77(0, x0)/H

+ Z(x - x0)(dx

+ dXo)r](x,

x0)

+ 2 J0 B(x + x)dST](x, x0)dx .

(9)

If the integral in the right hand side (r.h.s) is suppressed, we get the incomplete equation already found by Sondhi [3]. An exact scaling law can then be derived considering that the incomplete equation implies t h a t (dx + dxo)ri(x,xo) is the solution of the cochlear equation elicited by a tone of amplitude 77(0, XQ)/H. As this solution is exactly rj(x,xo)r)(0,xo)/H, we can write the partial differential equation (dx + dXo)r)(x,Xo) = ri(0,x0)ri(x:xo)/H, the solution of which is x r)(x + Ax, xQ + Ax) = r](x, x0) exp f*°+ r](0, \)/Hd\ , with Ax the integration parameter. This formula describes the scaling properties of solutions with characteristic frequency sites differing by Ax and frequencies in direct ratio e x p ( - a A a ; ) . The profile of this scaling law is represented by the dotted line in Fig.3. The discrepancy in the basal region of the BM is patent, meaning t h a t the second term in the r.h.s. of Eq. (9) cannot be ignored. Precisely this term, which cannot be written as c(x0) rj(x, x0), is responsible for scale covariance breaking. To take control of the degree of breaking we put

(dx + dX0)ri{x, x0) = [v(0, xQ)/H

+ C(x0)} r](x, x0) + f3(x, x0)

(10)

447 Figure 3. Solutions of equation (3) with a(xo) = 1 and frequencies ranging from 120 Hz (at apex) to 13 kHz (at base). The small circles on the phase curves represent the maximum amplitude sites. Note the scale change of the amplitude profiles and the corresponding upward shifts of the phase profiles. D o t t e d line (S): the scaling law according to Sondhi (1978); Dashed line ( N & V ) : the approximate scaling law computed by the Authors.

Waveform amplitudes at various frequencies [kHz]

S

0

0.5

1

1.5

2

2.5

3

3.5

Basilar membrane position [cm]

and try to determine C(x0) so that the scaling-breaking term (3{x, xn) be as small as possible. This requirement is fulfilled if /3 and r) are functionally orthogonal, i.e. J0 rf(x, XQ)P(X, x0)dx = 0, where upperstar indicates complex conjugation. Combining Eq.s (10), (5), (9) we obtain C(x0) — H~x JQ f3(x,x0)dx and JQ\G(X,X)

- Gs(x)/HW(x,x0)dx

+ Z(x - x0)/3(x,x0)

=

2 Jo B(x + x)dxr](x,x0)dx,

(11)

to be solved in the functional space orthogonal to r/(x,xo)- Surprisingly enough, numerical solutions of Eq. (11) showed that (3{x, x0) is appreciably different from zero only in the limited interval [ 0 , X B ] adjacent to the BM base in which B(x) differs appreciably from zero. Consequently, the equation (dx + dXo) r)(x, xo) « [77(0, XQ)/H + C(xo)] T)(x, XQ) holds with excellent approximation for x > XB and can therefore be integrated giving the well-approximated scaling law •q(x + Ax, x0 + Ax) « r){x, x0) exp f*°+Ax[r){0,

X)/H + C(X)]dX.

Note that, 77(0, A) and C(A) being complex functions of A, t h e scale transformation affects both t h e amplitude and t h e phase of t h e waveforms. These scaling properties can b e equivalently represented by t h e relationships SLJ Su; v*^

*^UJ J ^ Stj> ^^z \X

X^i J ,

yX: A w , X^ji S> XB ) ,

I J

where £ w (ir), £ui'{x) are any two solutions of Eq. (3) and s„ = e x p { -

fto{%{0,

X)/H + C(X)}dX} .

The dashed lines in Fig.3 describe the scaling law computed from Eq. (11) by an iterative integration procedure up to t h e second order of approximation.

448 5

Discussion

Since the real mammalian cochleas do not exhibit the scaling properties of the box model, the subject here presented might be considered only an academic exercise. It is worth noticing, however, t h a t Eq. (12) belongs to a family of more general covariance laws of the form sUJ(x)S,u>[ru(x)} w sul>(x)^UJi[ru,i(x))], where ru (x) is a local transformation of x depending upon u> but more general than a translation, and sUJ(x) is a complex coefficient possibly depending also on x. This formula correlates not only waveforms of different size and phase but also of different height/width ratio. The real cochlea geometry departs appreciably from that of the box model for at least one good reason: BM tapering and spiral canal tunneling allow the human cochlea t o cover the acoustic frequency range with a base-to-apex BM stiffness ratio one order of magnitude less t h a n that of the corresponding box model. If the geometry changes, the Green's functions also change in an approximately locally covariant way. But, in order for the entire cochlear equation to change the same way, the BM stiffness and viscosity profiles must change in particular ways. Whether this happens to some extent is not known presently, but a reason for suspecting this arises quite naturally from the problem of assuring a smooth cochlear amplifier gain (CAG) profile. Previous studies of the Authors [2] on a realistic model of the human cochlea with « 60 dB nonlinear gain over a wide frequency range showed that, due to long-range interactions, even the slightest local perturbation of a cochlear parameter caused severe instabilities. To restore gain uniformity without causing spontaneous oscillations, the CAG profile had to be suitably corrected over an appreciable neighborhood of the perturbation site. What natural supervising device might be able to perform this sort of distributed control in a bounded amount of time? Here we advance the hypothesis t h a t the local covariance of the waveforms favors the cochlear amplifier stabilization by means of locally feedback processes. References 1. Allen,J.B. (1977) Two-dimensional cochlear fluid model: New results J.Acoust.Soc.Am. 49:110-119. 2. Nobili, R., Vetesnik, A., Turicchia, L. and Mammano, F. (2003) Otoacoustic emissions from residual oscillations of the cochlear basilar membrane in a human ear model. J.Ass.Res. Otolaryngol. 4:478-494. 3. Sondhi,M.M. (1978) Method for computing motion in a two-dimensional cochlear model. J.Acoust.Soc.Am. 63:1468-1477. 4. Whittaker,E.T. and Watson,G.N. (1935) A Course of Modern Analysis, The University Press, Cambridge.

FOUR C O U N T E R - A R G U M E N T S FOR SLOW-WAVE OAEs CHRISTOPHER A. SHERA Eaton-Peabody Laboratory, Boston, MA 02114, USA email: shera@epl. meei. harvard, edu ARNOLD TUBIS Institute for Nonlinear Science, La Jolla, CA 92093, USA email: [email protected] CARRICK L. TALMADGE National Center for Physical Acoustics, University, MI 38677, USA email: [email protected]

1

Introduction

A recent paper [6] presents measurements of basilar-membrane (BM) motion to argue against the slow-wave model of OAEs, in which emissions propagate back to the stapes primarily via transverse pressure-difference waves (often simply called "reverse-traveling waves"). The experimental evidence adduced against slow-wave D P O A E s is two-fold: (1) group-delay measurements indicate that the stapes vibrates earlier than the BM at the distortion-product (DP) frequency and (2) longitudinal measurements of BM phase find no evidence for reversetraveling waves. These two experimental results, interpreted using the schematic illustrated in the bottom panel of Fig. 1, have been taken to confirm the suggestion [13,8] t h a t the reverse propagation of OAEs occurs via fast compressional (i.e., sound) waves [6]. The diagram posits that DP fast waves generated near X2 propagate nearly instantaneously t o the stapes, where the asymmetric movements of the oval and round windows create a slow (pressure-difference) wave t h a t propagates to Xdp, driving the transverse motion of the BM en route. Here, we present two pairs of counter-arguments against these claims [6]. The first pair critique the evidence against slows waves outlined above; the second pair argue t h a t the fast-wave model contradicts other well established facts of OAE phenomenology, thereby countering the conclusion t h a t compression waves play the dominant role in the production of otoacoustic emissions. 2

Counter-Argument

#1

The group-delay argument against slow waves fails when the DPs are generated near the point of measurement rather than remotely. The group-delay argument

449

450

nonlinear distortion and slow-wave generation

coherent reflection

nonlinear distortion and fast-wave generation fast-wave generation

Distance from stapes -

Figure 1. Schematic illustrating the generation of slow-wave (top) and fastwave (bottom) lower-sideband DPs. The panels show wave phase lag (increasing downward) vs cochlear location. In each case, slow waves (solid lines) at / i and /2 produce nonlinear distortion near X2, creating either slow or fast (dashed line) waves at f^p. Reverse waves travel to the stapes, where the fast wave creates a slow forward wave that then drives the BM at f^p. In the top panel, distortion near X2 also creates a forward wave that is partially reflected near £dp- In the bottom panel, the slow wave launched from the stapes creates a fast reverse wave near xa p . Empty boxes in the lower panel indicate unknown biophysical mechanisms. For simplicity, the diagram ignores multiple internal reflections. Adapted from [10,6].

against slow waves [6] follows from the contradiction between the group-delay data and the predictions of the schematic diagram shown in the top panel of Fig. 1. T h e argument hinges on a crucial feature of the diagram: Namely, t h a t the region of strong distortion that generates the / d p wave (denoted D in the diagram) is localized at some distance from the stapes. In other words, the argument assumes that the distortion measured in the motion of the stapes did not originate close to the stapes but has propagated to the point of measurement from a remote generation site located elsewhere in the cochlea. Although this assumption presumably holds under many experimental conditions, no evidence of its validity has been presented for the measurements in question [6]. On the contrary, given the relatively high levels of stimulation ( ~ 7 0 d B SPL) and the proximity of X2 to the base ( ~ 2 n n n ) , it seems likely that the DP generation "site" encompasses a considerable stretch of the basal turn of the cochlea. W h a t does the slow-wave framework predict when measurements are made inside the region of strong distortion, D ? Under such circumstances, the framework indicates that D P measurements are typically dominated not by propagated distortion, but by distortion generated close to the point of measurement. Group-delay data of the sort reported in [6] then reveal nothing about D P propagation delays or the relative time ordering of events at the D P frequency within the cochlea. Rather, group-delay measurements reflect changes in the output

451 of the local D P source, whose phase varies as the local phases of the primary tones change with frequency. When fi is fixed, as it was in the measurements [6], the framework predicts that the phase of a locally generated DP varies with the phase of the f\ wave at the site of generation. Measurements of BM transfer functions at two different points in the cochlea show that phase slopes at any given frequency below C F are shallower at the more basal location [7], and similar results presumably apply to intracochlear pressures that drive the stapes [3]. Viewed in this way, the finding that group delays controlled by the f\ wave are smaller at the stapes t h a n they are near x-i is thus entirely consistent with the predictions of the slow-wave framework. The observation t h a t the group-delay data can be explained within the slowwave framework obviates the need to postulate novel biophysical mechanisms to account for the results. Since the generation of compressional (sound) waves requires the vibration of a sound source (OHC somata? hair bundles?), the fastwave interpretation of the group-delay d a t a evidently requires t h a t the vibrating sound source be both (i) strongly coupled to the BM in one direction, since its vibration is presumed to be driven by forward-traveling BM waves at f\ and fi\ and (ii) weakly coupled to the BM in the other direction, since BM motion at /d p occurs significantly after stapes motion (i.e., only after the fast wave has generated a forward-traveling slow wave at the stapes). These two conflicting requirements appear difficult to reconcile with cochlear biophysics. Current understanding of the cochlear amplifier, for example, makes it hard to imagine synchronous volume changes in the hair cells, as proposed by Wilson [13], that are not also accompanied by forces t h a t couple strongly into the transverse motion of the BM. 1 3

Counter-Argument

#2

The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather than remotely. At the DP frequency, the measured BM phase vs position data have negative slopes, as expected for forward- but not reverse-traveling waves. Curiously, three of the four longitudinal measurements presented as evidence against slow waves (see Fig. l a - c in [6]) were made at BM locations largely apical to X2, the presumed center of the 1 One theoretical possibility is that the cochlear amplifier (CA) operates not by generating forces that couple into BM motion locally near the OHC, but by generating compressional waves that couple into BM motion at the stapes via the impedance asymmetry between the cochlear windows. However, without considerable ad hoc manipulation this model for the CA cannot be made to amplify forward-traveling waves except at certain special locations in the cochlea determined by round-trip phase shifts, (de Boer [personal communication] has independently analyzed this model for the CA and uncovered other deficiencies.)

452 region of D P generation. Since both the slow- and fast-wave frameworks predict forward-traveling / d p waves in the region X2 < x < xap, the measurements cannot distinguish the two alternatives. The fourth measurement (Fig. Id) was made basal to #2, but its interpretation suffers from the same limitation as the group-delay data: The argument breaks down when applied inside the region D of strong distortion, where local rather than propagated distortion dominates the measurement. 2 The phase of the local distortion follows t h a t of the D P source, which has the form <j>src(x) = 2cpi(x) - (fa(x) + constant,

(1)

where <j>i(x) is the phase of the / i wave, etc. Since the measurements indicate t h a t STC(x) defined above has a negative slope, the experimental results again appear consistent with the predictions of the slow-wave framework. 4

Interlude

Counter-arguments # 1 and # 2 indicate that recent measurements claimed to refute the existence of slow-wave OAEs [6] fail to provide compelling tests of the slow-wave model. The failure of an argument, however, does not imply t h a t its conclusion is incorrect: It remains possible t h a t slow-wave OAEs really are negligible or non-existent and that fast-wave mechanisms dominate the production of otoacoustic emissions, as claimed. To address this possibility, counter-arguments # 3 and # 4 discuss two additional OAE measurements. Both measurements contradict simple predictions of the fast-wave model but have natural explanations in the slow-wave framework. 5

Counter-Argument

#3

The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and upper-sideband DPOAEs. In the fast-wave model, DPs couple directly to the stapes via compressional waves whose propagation is unaffected by the properties of the BM. Once they couple into the fluids, fastwave DPs—unlike their slow-wave counterparts—undergo no BM-related filtering prior to their appearance in the ear canal. It therefore makes no difference whether fast-wave DPs are generated at cochlear locations whose CFs are above or below their own frequency. The fast-wave model thus indicates that both lower- and upper-sideband DPs are generated in the overlap region near X2 by identical "wave-fixed" mechanisms. As a consequence, the model predicts that 2 Even if the experiments [6] had established that the measurements were dominated by propagated rather than local distortion, interpretation of the data would still be enormously complicated by wave reflection from the stapes.

453 both D P O A E types should manifest nearly constant phase when measured using frequency-scaled stimuli (fixed fij f \ ) . This prediction of the fast-wave model is contradicted by experiment: Whereas the phase of lower-sideband DPOAEs (e.g., 2 / i — / 2 ) at near-optimal primary ratios remains almost constant (as predicted), the phase of upper-sideband DPOAEs (2/2 — /1) varies rapidly with frequency [4].3 The different phase gradients of lower- and upper-sideband DPOAEs can, however, be understood in the slow-wave framework. When DPs couple into BM pressure-difference waves they become subject to filtering by the BM. For lower-sideband DPs, the overlap region near x% is basal to the BM cutoff for / d p waves, and DPs generated in this region propagate freely. At near-optimal ratios, the multiple reverse-traveling D P wavelets created in the distortion region D combine coherently to produce a large reverse-traveling wave whose phase behavior is "wave-fixed." For upper-sideband DPs, however, the region near X2 is apical to the BM cutoff for / d p waves, and D P s generated in this region are strongly attenuated. As a result, place-fixed mechanisms at XdP become dominant [4], For example, upper-sideband DPs generated at x < x&p create slow waves propagating in both directions. Because of phase interactions among the wavelets arising from the distributed DP source, those wavelets initially traveling toward the stapes tend to cancel one another out, whereas those traveling toward XdP tend to reinforce one another. The result is a forward-traveling slow wave, which—as with any forward-traveling wave—undergoes partial coherent reflection near its characteristic place. Since the dominant reverse-traveling wave is generated by scattering off "place-fixed" perturbations, upper-sideband DPOAEs (like SFOAEs) have a rapidly rotating phase. 6

Counter-Argument

#4

The fast-wave model cannot account for the results of experiments performed using the Allen-Fahey paradigm. The Allen-Fahey paradigm [1] consists of measuring the ear-canal D P O A E as a function of r = / 2 / / 1 while the intracochlear DP response is held constant at Xdp (e.g., by monitoring the response of an auditory-nerve fiber tuned to /dp). Aside from possible suppressive effects, the predictions of the fast-wave model can be deduced immediately from the bottom panel of Fig. 1. Fixing the DP response at XdP is equivalent to fixing the fast wave at the stapes, which is equivalent to fixing the D P O A E in the ear canal. How does suppression modify this prediction? As r decreases towards 1, the primaries draw closer to XdP and their suppressive action reduces the response to 3

Although characteristic of mammalian DPOAEs, striking differences between the phasegradient delays of upper- and lower-sideband DPOAEs are not found in the frog [5].

454 the DP at x&p. To maintain the constant response mandated by the paradigm, the D P source output must be increased (e.g., by boosting the levels of the primary tones). When the source output is increased, the fast-wave pressure at the stapes and the D P O A E in the ear canal both increase correspondingly. For the Allen-Fahey paradigm, the fast-wave model therefore predicts t h a t the ear-canal DPOAE will increase at close ratios. This prediction, however, is contradicted by experiment: Studies performed using the Allen-Fahey paradigm all find t h a t the ratio of ear-canal to intracochlear DPs falls as r —> 1 [1,9,2]. The results of Allen-Fahey and related experiments can, however, be understood in the slow-wave framework, where they reflect changes in the effective directionality of the waves radiated from the distortion-source region [11]. Slowwave calculations explain the Allen-Fahey experiment by showing that at close ratios the distortion region D radiates much more strongly toward Xdp t h a n it does back toward the stapes. As a result, and despite the countervailing effects of suppression, fixing the response at x,ip causes the corresponding ear-canal D P O A E to fall as r —• 1. [Note t h a t in the top panel of Fig. 1 the forward- and reverse D P waves emanating from D need not maintain the same amplitude ratio at all values of r; contrast this with the bottom panel, where the ratio of reverse fast wave to forward slow wave is determined, independent of r, by impedance relationships at the stapes.] 7

Conclusion

The counter-arguments presented here indicate t h a t recent tests of the slowwave model [6] provide no convincing evidence against slow-wave OAEs. Furthermore, slow-wave OAEs appear necessary to account for varied aspects of OAE phenomenology well established in the literature. Although our counterarguments support the slow-wave model, they must not be construed to suggest t h a t fast-wave OAEs do not exist; absence of evidence is not evidence of absence. Indeed, we take the totalitarian view of physical law t h a t everything not forbidden is mandatory, and we therefore fully expect that both slow- and fastwave OAEs occur in the normal cochlea. The problem, then, becomes one of establishing the relative contributions of the two (or more?) emission modes and understanding their physical and physiological determinants. In principle, there need be no universal answer to these questions: The dominant OAE mode may vary with species and order (e.g., from amphibians to mammals), with cochlear location (e.g., from base to apex), and with stimulus or other experimental parameters. We have provided examples illustrating the importance of slow-wave contributions to the generation of mammalian OAEs; the role played by fast waves remains to be elucidated.

455 Acknowledgments Supported by grants from the NIDCD, National Institutes of Health. We thank Nigel Cooper, Paul Fahey, and Tianying Ren for helpful discussions. References 1. Allen, J.B. and Fahey, P.F., 1992. Using acoustic distortion products to measure the cochlear amplifier gain on the basilar membrane. J. Acoust. Soc. Am. 92, 178-188. 2. de Boer, E., Nuttall, A.L., Hu, N., Zou, Y., and Zheng, J., 2005. The Allen-Fahey experiment extended. J. Acoust. Soc. Am. 107, 1260-1266. 3. Dong, W. and Olson, E.S., 2005. Two-tone distortion in intracochlear pressure. J. Acoust. Soc. Am. 117, 2999-3015. 4. Knight, R.D. and Kemp, D.T., 2001. Wave and place fixed D P O A E maps of the human ear. J. Acoust. Soc. Am. 109, 1513-1525. 5. Meenderink, S.W.F., Narins, P.M., and van Dijk, P., 2005. Detailed / i , / 2 area study of distortion product otoacoustic emissions in the frog. J. Assoc. Res. Otolaryngol. 6, 28-36. 6. Ren, T., 2004. Reverse propagation of sound in the gerbil cochlea. Nat. Neurosci. 7, 333-334. 7. Rhode, W.S., 1978. Some observations on cochlear mechanics. J. Acoust. Soc. Am. 64, 158-176. 8. Ruggero, M.A., 2004. Comparison of group delays of 2 / i — / 2 distortion product otoacoustic emissions and cochlear travel times. Acoust. Res. Lett. Online 5, 143-147. 9. Shera, C.A. and Guinan, J.J., 1997. Measuring cochlear amplification and nonlinearity using distortion-product otoacoustic emissions as a calibrated intracochlear sound source. Assoc. Res. Otolaryngol. Abs. 20, 51. 10. Shera, C.A. and Guinan, J.J., 1999. Evoked otoacoustic emissions arise by two fundamentally different mechanisms: A taxonomy for mammalian OAEs. J. Acoust. Soc. Am. 105, 782-798. 11. Shera, C.A., 2003. Wave interference in the generation of reflection- and distortion-source emissions. In: Gummer, A.W. (Eds.), Biophysics of the Cochlea: From Molecules to Models, World Scientific, Singapore, pp. 439453. 12. Talmadge, C.L., Tubis, A., Long, G.R., and Piskorski, P., 1998. Modeling otoacoustic emission and hearing threshold fine structures. J. Acoust. Soc. Am. 104, 1517-1543. 13. Wilson, J.P., 1980. Model for cochlear echoes and tinnitus based on an observed electrical correlate. Hear. Res. 2, 527-532.

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C o m m e n t s and Discussion T i a n y i n g R e n : The purpose of the following comments is not to defend the cochlear compression wave theory. Instead, they try to clarify a few points for helping our thinking of the D P O A E . Counter-Argument # 1 reads, in brief: The group-delay argument against slow waves fails when the DPs are generated near the point of the measurement rather than remotely. The longitudinal pattern of basilar membrane vibration measured at the same location as for the emission measurement in the gerbil shows a normal forward travel delay (Ren, 2002, PNAS, 99:17101-6). If the backward traveling wave is symmetrical to the forward wave it should show the same delay, which was not shown by the data. Counter-Argument # 2 reads: The longitudinal BM-phase argument against slow waves fails when the measured DPs are generated locally rather t h a n remotely. Since the measured region of the basilar membrane responses to tones goes from 8 to 24 kHz (Ren, 2002, PNAS, 99:17101-6), the phase curve near the basal end should have revealed the backward traveling wave, if it exists. In Fig. Id (Ren, 2004, Nat. Neurosci., 7:333-4) the observed location is clearly out of the D P generation site because the basilar membrane response to a 12 kHz tone is linear at the 17 kHz BM location. Most importantly, the 2 / i — fi phase calculated based on the j \ and $2 phases of BM vibration is different from the measured 2 / i — /2 phase, which demonstrates that the measured phase data are not dominated by the locally generated DP. Counter-Argument # 3 reads: The fast-wave model cannot account for the dramatically different phase-gradient delays manifest by lower- and uppersideband DPOAEs. T h e reverse propagation of the upper-sideband DPOAEs is different from t h a t of lower-sideband emissions. Although the slow-wave model can explain the fast phase change of the upper-sideband emission, the alternative interpretation based on the fast-wave model remains plausible, since the observed emission delay can be caused by the cochlear filter rather than by a backward traveling wave (Avan et al., 1998, Eur. J. Neurosci., 10:1764-70; Ruggero, 2004, ARLO, 5:143-7). R e p l y : Thank you for your thoughtful comments. 1. Model calculations indicate that relationships between the spatial patterns of BM phase produced by single tones (e.g., those reported in your PNAS paper) and the slopes of 2 / i — ji phase-vs-frequency functions (i.e., D P phase-gradient delays) measured on the BM, at the stapes, or in the ear canal are neither always straightforward nor intuitive. We therefore suggest caution when interpreting both experimental and numerical results, espe-

457 daily when the effective DP generation site is distributed over a relatively broad region of the cochlea a n d / o r reflection from the stapes occurs. 2. Measurements of distortion in single-tone responses are not the most sensitive indicators of the intermodulation distortion produced by two tones, especially when the total distortion is small compared to the primaries (the BM DPs in Fig. Id are 20 dB or more below the primary tones). When local distortion dominates the measured response slow-wave theory indicates that the 2 / i — fa DP phase is only approximately equal to 2<j>\{x) — 4>2(x); even though local distortion makes the controlling contribution, it is not the only component of the response. The main point of our first two counter-arguments is t h a t the slow-wave model can account for the salient features of the data t h a t have been used to argue against slow-wave mechanisms. 3. As pointed out elsewhere (e.g., Koshigoe and Tubis, 1982, JASA, 71:11941200; de Boer, 1997, JASA, 102:3810-3813; Shera et al., 2000, JASA, 108:2933-48), most of the so-called filter build-up cannot be separated from the travel time because the amplitude of the wave builds up while it is traveling. Tubis et al. (2000, JASA, 108:1772-85) demonstrated t h a t the cochlear filter—defined as the contribution to the BM mechanical transfer function arising from the "resonant denominator" in the W K B expression— gives only small contributions to the D P O A E phase derivatives in an active model. Even if it were possible to separate "travel time" from "filter buildup time" in some other meaningful way, it's not clear to what alternative interpretation you refer. Although slow-wave theory indicates t h a t the "reverse propagation of the upper-sideband D P O A E s is different from that of lower-sideband emissions," the same is not true in simple fast-wave models, in which fast-wave DPs propagate as compressional waves unaffected by the filtering (or other) properties of the BM (e.g., Wilson, 1980, Hear. Res., 2:527-32; Shera et al., 2005, ARO Abs., 28:657).

THE EVOLUTION OF MULTI-COMPARTMENT COCHLEAR MODELS

A.E. HUBBARD AND S. LU ECE Department

and Hearing Research Center, Boston University, Boston USA E-mail: [email protected] J. SPISAK AND D.C. MOUNTAIN

Biomedical Engineering

and Hearing Research Center, Boston University, Boston, USA

A major goal in cochlear modeling is to account for the functional mechanism of the cochlear amplifier (CA). Although numerous hypotheses have been presented, many are based on addons to the fundamental one-dimensional model, which assumes only the basilar membrane between two fluid-filled channels, scala vestibuli and scala tympani. Another class of models assumes more than two wave propagation channels (modes), and we call them multicompartmental models, a concept that originated with de Boer [1, 2, and 3]. Using a multicompartmental formulation, we put forward the hypothesis that the CA function is due to a combination of forces on the reticular lamina and the basilar membrane coming from both local hair cells and from a pressure wave that propagates in the fluid-filled spaces between the reticular lamina and the basilar membrane. A generic version of the model has been used to match data from various species. An improved model with parameters based on anatomical data from the gerbil can better match physiological data from the gerbil. A more advanced model that separates arcuate and pectinate regions of the basilar membrane shows the phase angle of the response of the arcuate region to low-frequency probe tones reverses at about midway down the cochlea. Overall, the models provide an explanation of how the CA might work.

1 Introduction How can cochlear outer hair cells (OHC) produce amplification if they have seemingly nothing to push against [1]? It was an enigma to the field of auditory science, a necessary riddle to be solved, since virtually all investigators believed OHCs underlay the cochlear amplifier. In one attempt to solve the riddle, de Boer assumed that the OHC stood between the reticular lamina (RL) and the basilar membrane (BM), pushing equally and oppositely on each, thus implying that if RL and BM could move differently, there could be fluid flow within the organ of Corti (OC). Unfortunately, simplifying assumptions would make a fait accompli the conclusion there was no way such a model could work in an energy-efficient, natural world, de Boer also explored a cylindrical version of the sandwich model and rejected it also [2]. A model in which waves propagated down the spiral sulcus, also failed to explain the cochlear amplifier [3], let alone matching experimental data. Quite to the contrary, matching experimental data was what a multicompartment model, called the traveling-wave amplifier model (TWAMP), did well [4]. It replicated the high and not narrow peaks, characteristic of the BM motion scaled by stapes motion found experimentally, as well as the corresponding phase

458

459 angle data. Although the TWAMP was a multicompartmental model, the model's additional compartment could not be unambiguously identified as an anatomical compartment in the cochlea. Chadwick et al [5] explored a model that had four fluid compartments, the fourth being the subtectorial fluid space. They could produce a gain of around 35 dB using forces on the order of 1 nN per OHC, but the peaks were not sharp enough to match physiological data. We built a multicompartmental model that assumed only somatic OHC motility [6] and found it could match highgain (low SPL) physiological data quite well using OHC force generation ~ 0.085 nN/nm RL deflection per OHC in the base down to -0.012 nNnm in the apex. In this paper, we elaborate two improved versions of that multicompartmental model. A third improvement on the model is in preliminary stages, and is reported in this book in a separate article. 2 Methods A hydromechanical drawing of the basic model is depicted in Figure 1. Over an incremental length along the cochlea, (one of 400 model sections) the biological cochlea has approximately ten OHCs embodied schematically as three OHCs in the cartoon. SV and ST are longitudinal compartments containing fluid. Between the RL and BM, which are modeled as resonant spring-mass-damper structures, is the fluid-filled space that we call the organ of Corti (OC) space. The OC compartment is the third compartment of the multicompartmental model. The RL resonance in all models to follow was on the order Figure 1. Inset: A stylized drawing of the cross-section of a three-compartment model The three compartments are SV, ST, and OC. OHCs push equally and oppositely against the RL and BM, which are resonant structures. Main figure: An electrical analog circuit for one section of the model. 400 sections with varying parameters comprise the entire model. OHC force, is represented as a pressure, since the force acts over an incremental area in the model. It is comprised of an active component that is proportional to the movement of the RL and a passive component. This assumes a rigid tectorial membrane and hair bundle deflection proportional to RL deflection. The "helper" circuit calculates passive opposition to OHC length change.

of a half-octave below the resonance of the BM. In all models explored, the impedance of the RL was on the order of l/10th to l/5th that of the BM. To assign the spring-mass-damper properties of the BM, we used a compliance map [7] and

460

chose the mass element to produce the tuned frequency required by the Greenwood function [8] for a gerbil. We embodied the cartoon shown in Figure 1 (inset) in an electrical impedance analog circuit. We calculated the circuit responses using either TSpice or a Cadence analog simulator, Spectre. We often checked the correspondence between the two simulators, especially in the case of unexpected outcomes. 3 Models and Results 3.1

The basic model with generic parameters

The basic model was able to replicate well the BM/Stapes ratio (magnitude and phase) for the chinchilla [9] using model parameters that were chosen, using a frequency-to-place map that was appropriate for the gerbil. Since the data were from a chinchilla, a model location was chosen so that the tuned frequencies of model and data matched. 3.2

The model using parameters more appropriate to the gerbil

The basic model was changed to incorporate the dimensions of the cochlear scalae as well as the approximate cross-section of the fluid-filled region between the RL and the BM. Both cochlear model fluid inertia and viscosity were estimated. Moreover, the point stiffness data taken from the gerbil were used to estimate the BM compliance values. We also switched the target data to be that obtained from the gerbil [10]. The model performance is co-plotted with the data in Figure 2. The model does a reasonable job in replicating the data. Although it is difficult to put a quantitative measure on goodness of fit, the model tuned to the gerbil does qualitatively somewhat worse than the generic compared to chinchilla data. 10

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The BM was divided into arcuate (AZ) and pectinate (PZ) zones. Fluid was allowed to flow radially between AZ and PZ. We estimated the viscous passage between the Spaces of Neul, through the spaces between the pillars, into the tunnel of Corti. Thus, in addition to the longitudinal fluid compartment over the PZ region, another similar compartment was located over the AZ. The impedance of the AZ was made l/10th that of the PZ. This change greatly improved the phase angle comparison between the PZ phases of the model and the physiological data (see Figure 3), but the comparison between the PZ gains did not compare so well in the region beyond the best frequency. ©ain Pto* tor 30dB Input a t % J m m from ttw &as«

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However, another surprising result emerged from this exploration of the multicompartmental model with both AZ and PZ. The phase angle of the AZ pressure response to low-frequency tones reversed polarity about half-way down the cochlea. This could be significant, because it has for decades been known that the phase angle of the response to low-frequency tones (in the "tails" of the tuning curve) of neurons at various locations down the cochlea reverses, about half-way [11] down the cochlea. Figure 4 shows the phase of neural responses to lowfrequently probe tones, as a function of the best frequency (BF), which amounts to the spatial location down/up the cochlea alongside the model's AZ pressure phase angle.

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4 Disc ussion How can a multicompartmental model in which the OHCs seemingly have nothing to push against work? Part of the answer is that the RL and BM are not in phase when the CA shows highest gain [6]. Thus RL and BM are essentially pushing off each other by way of the OHC connection. Since RL and BM are not in phase, there must be OC fluid flow. Thus, (Figure 5) there is also a traveling pressure wave in the OC, in addition to the pressure waves in SV, and ST. The real drive to the BM comes from the difference between the OC and ST pressure plus the force produced by the OHCs. This force is calculated as a pressure, because in each incremental piece of model there is an implied area of the BM. The various pressures drive the BM in different regions along the BM. The classical pressure difference [12, 13], P-, which is Psv - Pst, drives the BM in the more basal locations. However, as the waves approach the peak region of the velocity on the BM, the OHC forces become more significant than P-. This occurs about 1 mm basal to the peak. Up until this point, the OC to ST pressure difference has been negligible. However about Vi mm basal from the peak of the response on the BM, both the OHC forces and the OC pressure drive the BM comparably, and this action is continued on the apical side of the peak. Well past the peak and on the order of 30 dB down from the peak pressures, the P- wave, which contributed nothing to the BM velocity in the amplification region, is again dominant. Whatever phase lag was attained by the velocity response of the BM when the OC pressure and OHC forces were dominant, now will be wrapped to the nearest cycle of the phase of the velocity that results with P- driving the impedances of the BM and RL (see Fig. 1), thus creating a phase plateau many cycles down from the actual phase ofP-.

463

Figure 5. Left panel: Magnitudes of model pressure differences and OHC force calculated as a pressure. Right panel: Phase angle of the pressure and force responses.

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For an architecture that was once thought doomed to fail [1], the multicompartmental models actually show astonishing promise for explaining the CA, as well as fitting physiological data. It was surprising that the generic multicompartmental model fit chinchilla BM/Stapes ratio data so well. The model with "gerbil" parameters does a comparable job fitting gerbil magnitude data, although the phase angles are, arguably, not as good. To the contrary, the multicompartment model that includes the differentiation between AZ and PZ does well on phase, but the magnitude somewhat misses its mark. However BM motion data are in conflict with the AZ/PZ model's prediction that the AZ and PZ move out of phase [14]. The interesting reversal of the phase angle of the tunnel of Corti pressure that occurs about half-way down the cochlea found in the AZ/PZ model for low frequency probe tones has support from data from the auditory nerve. It leads one to speculate that the AZ pressure directly drives the inner hair cells at low frequency, a theory which we put forward in another article in this book. Acknowledgments We acknowledge the support of NIDCD.

1. de Boer, E., 1990. Wave-propagation modes and boundary conditions for the Ulfendahl-Flock-Khanna preparation. In: Mechanics and Biophysics of Hearing, ed. by P. Dallos, CD. Geisler, J.W. Matthews, M. Ruggero and C.R. Steele, Springer-Verlag, New York, 333-339. 2. de Boer, E., 1990. Can shape deformations of organ of Corti influence the traveling wave in the cochlea? Hear Res 44: 83-92. 3. de Boer, E., 1993. The sulcus connection. On a mode of participation of outer hair cells in cochlear mechanics. J. Acoust Soc Am 93:2845-2859. 4. Hubbard, A.E,. 1993. A traveling wave amplifier model of cochlear. Science, vol. 259, 68-71. 5. Chadwick, R.S., Dimitriadis, E.K. and Iwasa, K., 1996. Active control of waves in a cochlear model with subpartitions. PNAS 93(6): 2564-2569. 6. Hubbard, A.E., Yang, Z., Shatz, L., Mountain, D.C., 2000. Multi-mode cochlear models. In Recent developments in Auditory Mechanics, ed. by H. Wada, T. Takasaka, K. Ikeda, K. Ohyama and T.Koike, World Scientific, Singapore, 167-173. 7. Naidu, R.C., 2001. Mechanical properties of the organ of Corti and their significance in cochlear mechanics, PHD thesis of Boston University. 8. Muller, M., 1996. The cochlear place-frequency map of the adult and developing Mongolian gerbil. Hear Res. 94:148-56. 9. Ruggero, M. A., Rich, N.C., Robles, L., and Shivapuja, B.G., 1990. Middle ear response in the chinchilla and its relationship to mechanics at the base of the cochlea. J Acoust Soc Am 89: 1612-1629. 10. Ren, T. and Nuttall, A., 2001. Basilar membrane vibration in the basal turn of the sensitive gerbil cochlea. Hear Res 151:48-60. 11. Ruggero, M. and Rich, N., 1983. Chinchilla auditory-nerve response to lowfrequency tones. J Acoust Soc Am 73:2096-2108. 12. Peterson, B.P. and Bogert, L.C., 1950. A dynamic theory of cochlea. J Acoust Soc Am 22:369-381. 13. Zwislocki, J.J., 1950. Theory of the acoustical action of the cochlea. J Acoust Soc Am 22:778-784. 14. Cooper, N.P., 2000. Radial variation in the vibrations of the cochlear partition. In Recent developments in Auditory Mechanics, ed. by H. Wada, T. Takasaka, K. Ikeda, K. Ohyama and T.Koike, World Scientific, Singapore, 109-115.

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Comments and Discussion Gummer: What are the dominant components of the impedances of the reticular lamina (RL) and organ of Corti (OC); for example, mainly viscoleastic for the RL, inertial for the OC? Olson: You show pressure predictions. How does your predicted ST pressure close to the BM compare with measurements of ST pressure close to the BM, e.g., Olson, Nature, 1999? Answer: The model we showed in the meeting was one-dimensional. Therefore, we cannot mimic Dr. Olsen's data as a function of distance from the basilar membrane. The model result, as viewed in the spatial domain and assuming frequency maps into distance along the basilar membrane, is similar to Dr. Olsen's result obtained farthest away from the basilar membrane in scala tympani. The pressure increases from near the oval window, peaks slightly around best place, drops a few dB andremains fixed to the end of the cochlea. There are some "wiggles" just apicalfrom the best place, which might correspond to dips in the actual pressure measurements, which were made at a fixed place, sweeping frequency.

W H A T STIMULATES THE INNER HAIR CELLS?

D. C. MOUNTAIN AND A. E. HUBBARD Boston University Hearing Research Center 44 Cummington St., Boston, MA, 02215, USA E-mail: [email protected], [email protected] We have recently proposed that the cochlear amplifier is a fluid pump driven by outer hair cell (OHC) somatic motility [1,2]. According to this hypothesis, the OHCs pump fluid into the tunnel of Corti (TOC) creating a second type of traveling wave that we call the organ of Corti (OC) wave. It is the OC-wave and not the classical traveling wave that is amplified by the OHCs according to the fluid-pump hypothesis. The question remains, however, how does the motion of the OC-wave get coupled to the inner hair cell (IHC) stereocilia? We hypothesize that the organ of Corti pressure distends the tissue in the IHC region leading to deflection of the IHC hair bundle. This hypothesis is supported by the observation that low-frequency IHC receptor potentials can be quite distorted and that the onset of distortion correlates with saturation of the OHC receptor current. We present a model based on the fluid pump hypothesis that replicates many features of the experimentally observed distortion in the IHC receptor potential.

1 Introduction Inner hair cell and auditory nerve responses to low-frequency tones can exhibit large phase shifts and complex response waveforms with increasing stimulus level [3-8]. These complex responses are also present in the IHC membrane conductance change, suggesting that they are also present in the mechanical stimulus to the IHCs, even when the stimulus frequency is well below the characteristic frequency of the measurement location. In contrast, the comparable basilar membrane (BM) responses are much less complex, exhibiting sinusoidal waveforms and only small phase shifts [9,10]. Figure 1 summarizes the low-frequency IHC transmembrane waveform measured by Cody and Mountain [8, 11] in the basal turn of the guinea pig cochlea. The positive peaks of the responses are much narrower and pointed than would be expected if the stimulus to the IHC was a sinusoid. To reconcile the discrepancy between the IHC and BM responses, Mountain and Cody [11] proposed that the OHCs stimulated the IHCs directly via somatic motility. This hypothesis was supported by the fact that the distortion in the IHC receptor potential correlated with saturation of the OHC receptor current as measured using the cochlear microphonic. Using this hypothesis, they developed a phenomenological model that could reproduce the IHC waveform distortion by assuming that the mechanical stimulus to the IHCs resembled a high-pass filtered version of the OHC receptor potential. The question remains, however, what is the mechanism by which OHC somatic motility could stimulate IHC mechano-transduction? To address this question, we

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have developed a simple model for OHC motility and its effect on TOC pressure. The model predicts that the TOC pressure waveform is a high-pass filtered version of the OHC receptor current and that the pressure waveform is distorted in a manner consistent with the distortion observed experimentally in IHC receptor potentials [8]. 2 Methods Our fluid-pump hypothesis for the cochlear amplifier [1,2] assumes that, when the OHCs contract, the reticular lamina is pulled towards the basilar membrane (BM) and fluid is forced out of the OHC region, through the outer pillar cells and into the tunnel of Corti. The result is that the BM is influenced by three different forces (Figure 2): the pressure difference across the organ of Corti, the direct force from the OHCs, and an indirect influence from the OHCs via the pressure change within the organ of Corti. We now add to this hypothesis the concept that it is the pressure within the organ that leads to stimulation of the IHCs.

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To test our hypothesis, we developed a simple, lumped-element, model of OHC motility that included a 3-state Boltzmann model (fit to the data from [12]) for the apical tension-gated conductance and a linearized 2-state Boltzmann model for the OHC voltage-dependent length change. The input to the model was OHC hairbundle displacement and the output of the model was IHC receptor potential. The rate of OHC length change was assumed to be directly proportional to the displacement current produced by charge movement associated with shape changes in the transmembrane-protein prestin. The rate of fluid transfer from the spaces of Nuel around the OHCs to the TOC was assumed to be directly proportional to the rate of OHC contraction. In previous modeling efforts [2], we treated the TOC as an elastic tube but since this study is focused on low-frequency responses, we modeled the TOC as a resistive impedance. The IHC model was the same as used previously [11]. For both the OHC and IHC model, the apical conductance, GA, was computed using equation (1) with the parameters listed in Table 1.

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469

3 Results Figure 3 illustrates the results from the model for a single frequency (125 Hz). The upper panels show the hair bundle displacements for the OHC and IHC respectively. This stimulus level was chosen so as to saturate the OHC apical conductance (middle panel). The resulting OHC receptor potential is a smoothed square wave. The hair-bundle displacement waveform produced by the IHC (top panel) is radically different from that produced by the OHC. This is because the pressure waveform in the organ of Corti follows the OHC displacement current due to the prestin rather than the OHC membrane potential. The IHC transducer halfwave rectifies the hair bundle displacement waveform (middle panel) and the membrane time constant smoothes the receptor current to produce the receptor potential waveform shown in the lower panel.

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Figure 4 illustrates the model responses to the stimulus frequencies and levels used for the experimental results illustrated in Figure 1. The peak-to-peak amplitudes for the model results are quite similar to those for the experimental results and the model waveforms show the peaked shape that is found in the experimental data. A detailed comparison of the OHC and IHC model waveforms to the experimental data suggest that the differences between model and experimental waveforms are largely due to inaccuracies in the OHC model (Figure 5). The model waveforms are somewhat more asymmetric than the waveforms measured experimentally. Also, the present model did not include the passive nonlinearity that was included in the Mountain and Cody model [11]. Experience with the previous

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Time (ms) Figure 4. Simulated IHC receptor potentials for the same stimulus conditions as Figure 1.

model indicates that the addition of this nonlinearity would improve the agreement between model and experiment for the high-intensity 125 Hz stimuli. 4 Discussion The similarity between the model predictions and actual IHC receptor potential waveforms supports the hypothesis that the OHCs act as a fluid pumping system and that the resulting pressure changes inside the organ of Corti are converted to hair bundle motion at the IHCs. How this conversion could take place has not yet been resolved. The IHC soma and surrounding tissue appear to be compliant so it may be that the pressure causes deflections of the IHC with respect to the tectorial membrane. Support for this concept comes from imaging experiments in excised cochlea where IHC hair bundle displacement has been observed in response to OHC contractions [13].

471 125H2

125 Hz

Figure 5. A comparison of the scala media cochlear micophonic (left column) to the simulated OHC receptor potential. For low-frequency stimuli, the cochlear microphonic waveform is assumed to have the same shape as the OHC receptor potential, but inverted.

Acknowledgments This work was funded by NIDCD References 1,

Karavitaki, D.D., Mountain, D.C., 2003 Is the cochlear amplifier a fluid pump? In: Biophysics of the Cochlea: from Molecule to Model. A.W.

472

2.

3. 4.

5. 6.

7.

8.

9.

10.

11. 12.

13.

Gummer, E. Dalhoff, M. Nowotny, M. Scherer (Eds.). World Scientific, Singapore, 310-311. Hubbard, A.E., Mountain, D.C., Chen, F., 2003. Time-domain responses from a nonlinear sandwich model of the cochlea. In: Biophysics of the Cochlea: from Molecule to Model. A.W. Gummer, E. Dalhoff, M. Nowotny, M. Scherer (Eds.). World Scientific, Singapore, 351-357. Kiang, N.Y.S., Moxon, E.C., 1972. Physiological considerations in artificial stimulation of the inner ear. Ann. Otol. Rhinol. Laryngol. 81, 714-730. Sokolich, W.G., Hamernik, R.P., Zwislocki, J.J., Schmiedt, R.A., 1976. Inferred response polarities of cochlear hair cells. J. Acoust. Soc Am 59, 963974. Ruggero, M.A., Rich, N.C., 1983. Chinchilla auditory nerve responses to low frequency tones. J. Acoust. Soc. Am. 73, 2096-2108. Russell, I.J., Sellick, P.M., 1983. Low frequency characteristics of intracellularly recorded receptor potentials in mammalian hair cells. J. Physiol. (Lond.) 338, 179-206. Dallos, P., Cheatham, M.A., Oesterle, E., 1986. Harmonic components in hair cell responses. In: Moore, C.J., Patterson, R.D. (Eds.), Auditory Frequency Selectivity. Plenum, London, 73-80. Cody, A.R., Mountain, D.C. 1989. Low frequency responses of inner hair cells: Evidence for a mechanical origin of peak splitting. Hear Res, 41, 89100. Cooper, N.P., Rhode, W.S., 1992. Basilar mechanics in the hook region of cat and guinea-pig cochleae: Sharp tuning and nonlinearity in the absence of baseline position shifts. Hear Res 63, 163-190. Ruggero, M.A., Rich, N.C., Recio, A., Shyamla Narayan, S., Robles, L., 1997. Basilar-membrane responses to tones at the base of the chinchilla cochlea. J. Acoust Soc Am 101, 2151-2163. Mountain, D.C, Cody, A.R., 1999. Multiple modes of inner hair cell stimulation. Hear Res 132, 1-14. Russell, I.J., Cody, A.R., Richardson, G.P., 1986. The responses of inner and outer hair cells in the basal turn of the guinea pig cochlea and in the mouse cochlea grown in vivo. Hear Res 22, 199-216. Karavitaki, K.D., Mountain, D.C, Cody, A.R. 1997. Electrically-evoked micromechanical movements from the apical turn of the gerbil cochlea. In: Diversity in Auditory Mechanics ER Lewis, GR Long, RF Lyon, PM Narins, CR Steele, and E Hecht Poinar eds, World Scientific Publishing, pp. 392 398.

Comments and Discussion Gummer: Could it be that the fluid flow that you reported within the organ of Corti is due to buckling of the pillar cells? Buckling has been described experimentally by Fridberger and theoretically by Steele (see Steele and Puria, this volume).

473

Answer: We have never seen any evidence of pillar cell buckling in our excised cochlear preparation. The pillar cells appear to be quite rigid and exhibit radial displacements that are 20% or less than those observed for the base of the neighboring outer hair cells (Karavitaki, K.D., Doctoral Dissertation, MIT, 2002). We normally work with stimulus conditions where the maximum outer hair cell displacements are a few hundred nanometers. This is in contrast to Fridberger et al. (J. Neurosci. 22:9850-9857, 2002) who used displacements up to -10 micrometers. It is conceivable that there could species or place differences. Most of our work on fluid flow in the tunnel of Corti was focused on the 4 kHz region of the gerbil cochlea while the Fridberger et al. data were from the 200 Hz region of the guinea pig cochlea. We have looked at pillar cell motion in the 400 Hz region of the gerbil cochlea and see no sign of buckling.

ACTIVE HAIR-BUNDLE MOTILITY HARNESSES NOISE TO O P E R A T E N E A R A N O P T I M U M OF M E C H A N O S E N S I T I V I T Y

P. M A R T I N Laboratoire Physico-Chimie Curie, Unite Mixte de recherche 168 du GNRS Institut Curie recherche, 26, rue d'Ulm, 75248 Paris cedex 05, France E-mail: [email protected] B. N A D R O W S K I Max Planck Institut fur Physik komplexer Systeme Nothnitzerstr. 38, 01187 Dresden, Germany E-mail: [email protected] F. JTJLICHER Max Planck Institut fur Physik komplexer Systeme Nothnitzerstr. 38, 01187 Dresden, Germany E-mail: [email protected] The ear relies on nonlinear amplification to enhance its sensitivity and frequency selectivity. In the bullfrog's sacculus, a hair cell can mobilize active oscillatory movements of its hair bundle to amplify its response to faint stimuli. Hair-bundle oscillations can result from an interplay between a region of negative stiffness in the bundle's force-displacement relation and the Ca 2 +-regulated activity of molecular motors. Within the framework of this simple model, we calculate a state diagram which describes the possible dynamical states of the hair bundle in the absence of fluctuations. Taking different sources of fluctuations into account, we find conditions that yield response functions and spontaneous noisy movements of the hair bundle in quantitative agreement with experiments. We show that fluctuations restrict the bundle's sensitivity and frequency selectivity but find that a hair bundle studied experimentally operates near an optimum of mechanosensitivity in our state diagram.

1

Introduction

T h e mechanosensory hair cells of t h e vertebrate ear amplify their inputs to enhance sensitivity and frequency selectivity to weak oscillatory stimuli (reviewed in [1]). Although the cellular mechanisms t h a t mediate this active process have remained elusive, in vitro [2] as well as in vivo [3] experiments have revealed t h a t the mechanosensory organelle of the hair cell - the hair bundle - can generate active oscillatory movements. When mechanically stimulated near its frequency of spontaneous oscillation, a hair bundle displays a compressive nonlinearity t h a t demonstrates amplified responses to faint stimuli [4]. It has been noticed t h a t this behavior resembles t h a t of dynamical systems t h a t operate in the vicinity

474

475 of an oscillatory instability, a Hopf bifurcation (ref. [4] and references therein). Hair-bundle oscillations are noisy [5]. Noise blurs the distinction between active oscillations and fluctuations and thus conceals the bifurcation between oscillatory and non-oscillatory states. We present here a theoretical description of the effects of fluctuations on active hair-bundle motility. 2 2.1

Models and Results Active Hair-Bundle

Mechanics

Active hair-bundle oscillations are most convincingly explained by an interplay between a region of negative stiffness in the bundle's force-displacement relation and the Ca2+-regulated activity of the molecular motors t h a t mediate mechanical adaptation [6]. This interplay can be described by two coupled equations: XX = -Kgs(X-Xa-DP0)-KspX \aXa

= KSS(X

+ Fe^ + r,

- Xa - DP0) - 7 / m « ( l - SP0) + na

,

(1) .

(2)

Eq. 1 describes the dynamics of the hair-bundle position X. The hair bundle is subjected to friction, characterized by the coefficient A, as well as to the elastic forces —KspX and — KgsY, where Ksp and Kgs are the stiffness of stereociliary pivots and t h a t of the gating springs, respectively, and to the external force i^extThe open probability of transduction channels is P0. Channel opening reduces the gating-spring extension by a distance D. Active hair-bundle movements result from forces exerted by a collection of molecular motors within the hair bundle. By adjusting the gating-spring extension, these motors mediate mechanical adaptation to sustained stimuli (reviewed in [7]). The variable Xa can be interpreted as the position of the motor collection. Eq. 2 describes the mechanics and the dynamics of these motors by a linear force-velocity relation of the form \adXa/dt = — FQ + Fmot, where Aa characterizes the slope of the force-velocity relation. In the hair bundle, the motors experience an elastic force Fmot = KgsY. At stall, these motors produce an average force Fo = 7 / m a x ( l — SP0) , where 7 ~ 1/7 is a geometric projection factor, / m a x is the maximum force t h a t the motors can produce and S represents the strength of Ca2+ feedback on the motor activity [8]. This last parameter is expected to be proportional to the Ca2+ concentration in endolymph [6]. Here we assumed that calcium dynamics at the motor site is much faster t h a n hair-bundle oscillations. Active force production by the motors corresponds to motors climbing up the stereocilia, i.e. dXa/dt < 0. In a two-state model for channel gating, the open probability can be written as

P

°

=

1 + Ae-<*-**)/«

'

(3)

476 where A = expQAG + (KgsD2)/(2N)]/kBT) accounts for the intrinsic energy difference A G between the open and the closed states of a transduction channel and 6 = NkBT/(KgsD). 2.2

State Diagram in the Absence of Noise

To explore the dynamic behaviors of the system described by Eqns. 1-2, we first ignore the effects of fluctuations and assume Fext = 0. Steady states satisfy dX/dt = 0 and dXa/dt = 0. Linear stability analysis of these steady states reveals conditions for stability as well as for oscillatory instabilities t h a t lead to spontaneous oscillations via a Hopf bifurcation. The state diagram exhibits different regimes (Fig. 1). If the force / m a x is small, the motors are not strong enough to pull transduction channels open. In this case, the system is monostable with most of the channels closed. Increasing / m a x leads to channel opening. For intermediate forces and weak C a 2 + feedbacks, the system is bistable, i.e. open and closed channels coexist. For strong C a 2 + feedbacks, however, the motors can't sustain the forces required to maintain the channels open. Spontaneous oscillations occur in a region of both intermediate forces and feedback strengths. Note that there is no oscillation in the absence of C a 2 + feedback, i.e. for S = 0.

c

~ ^ - v 1

.1.6.

\0,6

MC ^

1

•3,9

^m"

0.5

Ml!,

/•

i •

:\

200

MO I

400

600

Figure 1. State diagram of a hair bundle. Lines of equal open probability of the transduction channels (dotted lines) are superimposed and are each indexed by the corresponding value. The hair bundle can be monostable with transduction channels mostly closed (MC) or mostly open (MO), bistable (BI) or oscillatory (grey area).

f

max(PN>

2.3

Effects of

Fluctuations

Noise terms TJ, r/a in Eqns. 1-2 formally take into account the effects of various sources of fluctuations on X and Xa, respectively. Noise terms are zero on average. Their strengths are characterized by autocorrelation functions, respectively < rj(t)r)(0) > and < ria(t)rja(0) >. We assume t h a t different noise sources are uncorrelated and that noise is Gaussian.

477 Assuming that the motors are deactivated ( / = 0), we first discuss thermal contributions to the noise. The noise term 77 in Eq. 1 then results from brownian motion of fluid molecules which collide with the hair bundle and from thermal transitions between open and closed states of the transduction channels. By changing the gating-spring extension, this channel clatter generates fluctuating forces on the stereocilia. The fluctuation-dissipation theorem implies t h a t < r)(t)r](0) > = 2kBT\S(t). The friction coefficient A = A^ + Ac results from two contributions: A^ ~ 1.3 1 0 _ 7 N - s - m - 1 accounts for hydrodynamic friction, which depends on bundle geometry and fluid viscosity [9], whereas Ac results from channel clatter. The contribution Ac can be estimated from the autocorrelation function of the force r\0 that results from stochastic opening and closing of N transduction channels < Vc(t)Vc(0) >^ D2Kl,P0(l-Po)N-1e-^r'

~

2D2K2ssP0(l-P0)N-1Tc6(t)

(4) Assuming t h a t < r]c(t)r]c(0) > ~ 2kBTXc5(t), we define a hair bundle friction AC which is associated to channel opening and closing. Using Eq. 4, we estimate KISD2P0(1-P0)TC

Using typical parameter values (see Table 1 in ref. [10]) our estimate reveals that channel clatter dominates friction and A ~ 3 1 0 _ 6 N - s - m _ 1 . The noise strength resulting from stochastic motor action can also be estimated. Measurements of the initial adaptation rate as a function of the magnitude of step stimuli [8] imply that Aa ~ 1.3 1 0 - 5 N - s - m - 1 . The stochastic activity of motors generates an active contribution r\m to r\a with < r,m(t)vm(0)

> - l2Nap{l

- p)/ 2 e-l*l/ T - * 2Nal2p{\

- p)fra6(t)

.

(6)

Each motor can produce a force / and has a probability p to be bound. Here we have assumed that the Na motors fluctuate independently and t h a t relevant time scales for a hair-bundle oscillation are longer than r a which is the characteristic time of force production by the motors. This noise strength can be described by introducing an effective temperature Tm defined by < rjm(i)rjm(0) >~ 2kBTm\aS{t). With / ~ lpN, ra ~ 10ms and p ~ 0.05, we find Tm/T ~ ^ a 7 2 p ( l - p)f2Ta/{kBT\a) ~ 0.5. Writing < Tfc,(t)jja(0) > = 2kBTa\aS(t), we thus get Ta ~ 1.5T. 2.4

Linear and Nonlinear Response

Functions

Stochastic simulations of Eqns. 1-2 allow us to calculate linear and nonlinear response functions of the model in the presence of periodic force stimuli [10]. The

478 only free parameters are the Ca 2 + -feedback strength S and the maximal motor force / m ax- Along a line of constant open probability P0 = 0.5, the characteristic frequency of spontaneous oscillations varies between a few Hertz and about 50Hz in the range / m a x = 330 — 800pN within which a peak was detected in the spectral density of spontaneous movements. We elected the value of the motor force / m a x — 352pN (see o in Fig. 1) at which the linear response function had the same shape as t h a t observed experimentally [5]. At this operating point, the system displayed noisy spontaneous oscillations X(t) that are similar to the hair-bundle oscillations observed in the bullfrog's sacculus [5,10]. The calculated linear response function xo as a function of frequency agrees quantitatively with the experimental observations [5]. At the characteristic frequency of the spontaneous oscillations, the sensitivity of the system to mechanical stimulation exhibits the three regimes observed experimentally [4] as a function of the stimulus amplitude (Fig. 2 C ) : a linear regime of maximal sensitivity |Xo| = 8.5km-N _ 1 at u> = LOQ for small stimuli, a compressive nonlinearity for intermediate stimuli and a linear behavior of low sensitivity for large stimuli. The maximal sensitivity as well as the breadth of the nonlinear region are in quantitative agreement with experiments. An important parameter t h a t influenced the system's maximal sensitivity is the stiffness of the load to which the hair bundle is coupled. For / m a x — 352pN, power spectra of spontaneous oscillations and response functions were not significantly affected by varying P0 in the range 0.2-0.8. Agreement between simulations and experiments thus did not qualify a particular value of P0.

10 15 20 25 Frequency (Hz) 5 10 15 20 25 Frequency (Hz) 1

10 100 Force (pN)

Figure 2. Response functions calculated from stochastic simulation of Eqns. 1-2 in presence of a periodic stimulus force. (A) Real part x'o °f the linear response function. (B) Imaginary part x'o °f * n e l i n e a r response. (C) nonlinear response function at a fixed frequency (8Hz) near that of the system's spontaneous oscillations.

479 3

Discussion

We have presented a physical description of active hair-bundle motility that emphasizes the role played by fluctuations. The mechanical properties of oscillatory hair bundles in the presence of a periodic stimulus force can be described quantitatively only if fluctuations are taken into account. In the absence of fluctuations, an operating point on the line of Hopf bifurcations in the state diagram would result in diverging sensitivity, infinite frequency selectivity and a compressive nonlinearity over many decades of stimulus magnitudes. This situation is ideal for detecting oscillatory stimuli [11,12,13]. As exemplified by our analysis, fluctuations restrict the system's sensitivity and frequency selectivity to oscillatory stimuli as well as the range of stimulus magnitudes over which the compressive nonlinearity of the bundle's response occurs. Despite fluctuations, a single hair bundle amplifies its response to small stimuli and, correspondingly, the characteristic compressive nonlinearity t h a t arises near a Hopf bifurcation remains. One can define the gain of the amplificatory process as the ratio of the sensitivity at resonance to small stimuli and t h a t to intense stimuli. Both experiments and simulations indicate t h a t active hair-bundle motility provides a gain of about ten. Our theoretical analysis demonstrates t h a t significant amplification happens inside the area of the state diagram where the noiseless system oscillates [10]. Interestingly, the global optimum of mechanosensitivity is obtained at an operating point located near the center of the oscillatory region in the state diagram (see A in Fig.l), thus far from the line of Hopf bifurcations of the noiseless system. Furthermore, the sensitivity is largest if the open probability of the transduction channels is 0.5. The ability of a single hair bundle to detect oscillatory stimuli using critical oscillations is limited by fluctuations which conceal the critical point. This limitation could be overcome if an ensemble of hair cells with similar characteristic frequencies were mechanically coupled, as they probably are in an intact organ. Acknowledgments This work was supported in part by the Human Frontier Science Program Grant RPG51/2003. References 1. Hudspeth, A. J., 1997. Mechanical amplification of stimuli by hair cells. Curr. Opin. Neurobiol. 7, 480-486. 2. Martin, P. , Hudspeth, A. J., 1999. Active hair-bundle movements can

480

3.

4.

5.

6.

7. 8.

9.

10.

11.

12. 13.

amplify a hair cell's response to oscillatory mechanical stimuli. Proc. Natl. Acad. Sci. USA 96, 14306-14311. Manley, G. A. , Kirk, D. L. , Koppl, C. , Yates, G. K., 2001. In vivo evidence for a cochlear amplifier in the hair-cell bundle of lizards. Proc. Natl. Acad. Sci. USA 98, 2826-2831. Martin, P. , Hudspeth, A. J., 2001. Compressive nonlinearity in the hair bundle's active response to mechanical stimulation. Proc. Natl. Acad. Sci. USA 98, 14386-14391. Martin, P. , Hudspeth, A. J., Jiilicher, F., 2001. Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process. Proc. Natl. Acad. Sci. USA 98, 14380-14385. Martin, P. , Bozovic, D. , Choe, Y., Hudspeth, A. J., 2003. Spontaneous oscillation by hair bundles of the bullfrog's sacculus. J Neurosci 23, 45334548. Hudspeth, A. J. , Gillespie, P. G., 1994. Pulling springs to tune transduction: adaptation by hair cells. Neuron 12, 1-9. Hacohen, N. , Assad, J. A. , Smith, W. J., Corey, D. P., 1989. Regulation of tension on hair-cell transduction channels: displacement and calcium dependence. J. Neurosci. 9, 3988-3997. Denk, W. , Webb, W. W. , Hudspeth, A. J., 1989. Mechanical properties of sensory hair bundles are reflected in their brownian motion measured with a laser differential interferometer. Proc. Natl. Acad. Sci USA 86, 5371-5375. Nadrowski, B. , Martin, P. , Jiilicher, F., 2004. Active hair-bundle motility harnesses noise to operate near an optimum of mechanosensitivity. Proc. Natl. Acad. Sci. USA 101, 12195-12200. Choe, Y. , Magnasco, M. O., Hudspeth, A. J., 1998. A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectricaltransduction channels. Proc. Natl. Acad. Sci. USA 95, 15321-15326. Camalet, S., Duke, T., Jiilicher, F. and Prost, J., 2000). Proc. Natl. Acad. Sci. USA 97, 3183-3188. Eguiluz, V. M., Ospeck, M., Choe, Y., Hudspeth, A. J. and Magnasco, M. O., 2000.Phys. Rev. Lett. 84, 5232-5235.

481 Comments and Discussion M. van der Heijden: The dynamical range of the mechanisms you describe is limited to 20 dB or so at the lower end. Of course, one could invoke "shifts in the operating point" to extend the dynamical range. But that seems to serve no practical purpose. Compression on the BM extends to very high sound levels, but you don't need ears to perceive such loud sounds. There exists no noise problem at 85 dB SPL - if anything those poor hair bundles should be protected against the destructive effects of the acoustic power. Do you really think that the reaction forces of these tiny transducer channels operate over a dynamic range of 80 dB, that is, a 100,000,000-fold power range? Answer: In the absence of noise, a dynamical system that operates near an oscillatory instability becomes arbitrarily sensitive as the magnitude of the sinusoidal stimulus becomes smaller (provided that the system is stimulated at the characteristic frequency of the instability). If there were no noise, it would thus be no problem to get a dynamic range of 80 dB with the mechanism that produces active hair-bundle oscillations. Fluctuations restrict the range of the compressive nonlinearity by limiting the sensitivity to LOW stimuli but have no effect for intense stimuli. With fluctuations included, there is no operating point that yields the essential compressive nonlinearity, which characterizes the noiseless system. In fact, we suggest that the oscillatory hair bundles that we have studied operate near an optimum of mechanosensitivity; hence one would NOT observe a dramatic extension of the dynamical range by shifting the operating point. In an intact organ in vivo, the limiting effects of noise might be circumvented if the hair-bundle oscillator were coupled to other oscillators of similar characteristic frequencies, either within the same hair cell or in neighboring hair cells. B. Brownell: What effect would a change in temperature have in your model and do your experiments show the predicted effect? Answer: All our experiments have been done at room temperature and we have thus not tested the effect of temperature on a bundle's sensitivity to oscillatory stimuli. R. Chadwick: Does a hair-bundle need to be in the oscillatory portion of the state diagram in order to exert an active force? Answer: A hair bundle that operates in the stable regions of the state diagram (Fig 1) can indeed exert active forces in response to an external stimulus. Within the framework of our model, an external stimulus (a step force for instance) evokes an active movement of molecular motors that affects the tension in elastic gating springs, in turn producing a force on the hair bundle. Our analysis shows, however, that, in the presence of noise, the system is more sensitive to small oscillatory stimuli if it operates within the oscillatory region of the state diagram.

WAVE PROPAGATION B Y CRITICAL OSCILLATORS D. A N D O R A N D T. D U K E Cavendish

Laboratory,

Madingley

Road, Cambridge

CB3 OHE, UK

A. SIMHA A N D F . J U L I C H E R Max Planck Institute

for the Physics of Complex Systems, Dresden, Germany

Nothnitzerstr.

38,

01187

Waves propagating along the basilar membrane are amplified by an active nonlinear process. The general aspects of the active amplification of periodic signals can be discussed in the framework of critical oscillators. Here, we show how the concepts of a traveling wave and of critical oscillators can be combined to describe the main features of nonlinear wave propagation, energy flow and reflections in the cochlea.

1

Introduction

The cochlea acts as a spatial frequency analyzer which exhibits resonant vibrations at characteristic frequencies that vary with position along the basilar membrane (BM) [1]. These vibrations are monitored by sensory hair cells [2]. This feature of the cochlea can be represented by a transmission line of resonant elements which naturally accounts for the propagation of waves along the basilar membrane which reach a peak amplitude near a position where the characteristic frequency matches the stimulus frequency [3,4,5,6,7]. Active processes in the cochlea play a role in the amplification of weak signals [8,2]. The signatures of these active processes are an increased sharpness of frequency filtering, the occurrence of oto-acoustic emissions and nonlinearities [9,10,11,12,13]. All these signatures are physiologically vulnerable, pointing to an origin of these phenomena in dynamic cellular processes. The compressive nonlinear nature of the active process permits the ear to operate over a large dynamic range of 120 dB, by amplifying weak signals more than strong ones. This nonlinear response of the basilar membrane is thus relevant even for weak stimuli and is connected with interference effects between different frequencies in complex sounds, leading to the generation of distortion products and combination tones [14]. The active nature of the cochlear response has been addressed in previous theoretical work [15,16,17,18,19]. The nonlinear amplification of weak periodic stimuli by active processes can be described generically in the framework of critical oscillators [20,21]. A resonant system generally operates linearly at small stimulus intensities. If a nonlinear response is required in order to amplify weak signals, the system must approach an oscillating instability. Active dynamic

482

483 systems often exhibit such instabilities or Hopf bifurcations where spontaneous oscillations appear. In the vicinity of this critical point, compressive nonlinearities become important and are unavoidable. Their properties are generic, i.e. they appear robustly in a way which is independent of many details of the molecular and cellular processes which underly the oscillating instability. Operation of the system at the oscillating side of the instability, however, compromises signal amplification and detection since spontaneous oscillatory behaviors of the active system interfere with the incoming signal. The ideal point of operation is therefore the critical point itself, where weak signals are most strongly amplified while strong stimuli only induce a behavior which resembles a passive response. The observation of active nonlinear processes even for weak stimulus amplitudes thus indicates t h a t the cochlea contains dynamical systems which operate in the vicinity of a Hopf bifurcation [22,20,21]. Self-regulation mechanisms could play a role to ensure operation of oscillators sufficiently close to the critical point t h a t nonlinearities can become beneficial for the detection of weak signals [20]. The strength of the concept of critical oscillators is that it can capture many important features of hearing. In particular the nonlinear response, the generation of distortion products and the active process are taken into account in a concise and general way which is robust and applicable despite the complexity and the diversity of underlying cellular processes. It thus provides a physical scenario which can clarify general principles that underly signal amplification. In order to discuss the cochlear response and the associated wave propagation, it is therefore useful to combine the concept of critical oscillators with the wave physics in the cochlea. This leads to a simplified description of cochlear vibrations as nonlinear waves which result from the coupling of critical oscillators with varying characteristic frequencies as a function of position and which are coupled hydro dynamically. Here, we briefly outline the features of these nonlinear waves and argue that this framework is ideally suited to discuss nonlinear effects, energy flow and pumping of these waves as well as nonlinear wave reflections in the cochlea. 2

C o c h l e a r waves

The basic physics of cochlear waves may be described most succinctly by a one-dimensional model [3,4,5,6,7]. The BM separates the cochlear duct into two channels which are connected at the apex by a small aperture, the helicotrema. A sound stimulus impinging on the oval window, at the base of the cochlea, causes changes in the pressures Pi(x,t) and P2(x,t) in both channels. Here t is the time and x is the position along the cochlea, with the oval window at x = 0 and the helicotrema at x = L. The pressure gradients induce longitudinal currents

484 Ji{x,t) and J2(x,t), which flow in opposite directions in t h e two channels. We define the relative current j = J\ — J2 and the pressure difference p = Pi — P2. The balance of pressure gradients and inertial forces in the fluid together with the fluid incompressibility and viscosity leads to a relation for the BM motion and the pressure gradients 2pb%h + ndth = dx [bWxP\

.

(1)

Here, h(x, t) is the height profile of the BM, characterizing local displacements; b and I denote the width and height of the cochlear channels, respectively. T h e damping coefficient r\ is proportional to the fluid viscosity. T h e pressure difference p acts to deform the BM. If the response is passive (e.g. in the dead cochlea), close to the basal end, it takes the simple form p = Kh. 3

Critical oscillators

In the active cochlea, the passive response is amplified by a force-generating system. This system comprises a set of mechanical oscillators which are supported on the BM, and which are positioned in such a way t h a t they can drive its motion. The characteristic frequency u>r(x) of the oscillators is a function of position along the membrane. We assume here, that active elements do not oscillate spontaneously but that they operate in the vicinity of a critical point. If the BM contains such critical oscillators, its deformation h in response to pressure differences across the membrane p has characteristic properties as a function of frequency and amplitude, and nonlinear amplification occurs. This can be discussed most easily for a single, isolated oscillator. Its characteristic response to a periodic stimulus pressure p(t) = pe~luJt + c.c. at frequency u> with Fourier amplitude p can be expressed in a general form as [20] p = A(u)h + B\h\2h + 0(h5)

.

(2)

Here, h is the Fourier amplitude of the resulting periodic vibration h(x, t) ~ h(x)e~lbjt + c.c. and A and B are complex coefficients. This expression follows from a systematic expansion in the oscillation amplitude h (comparable to a Landau expansion of t h e free energy of thermodynamic systems near a critical point) and is valid near a Hopf bifurcation. Further away from the bifurcation on the non-oscillating side, the nonlinearities become unimportant while away from the bifurcation on the oscillating side higher order terms can become relevant. Proximity to an oscillatory instability thus automatically provides for nonlinearities which are inherently linked to the active process and thus are not related to the passive nonlinearities properties of the material which

485 appear for large deformations. Note, t h a t for critical oscillators, the dominant nonlinearity is cubic. The linear response function A(LJ) = A'(u>) + iA" (u>) is a complex coefficient with real part A' and imaginary part A". For a critical oscillator, it vanishes at the characteristic frequency, A(u>r) = 0. Thus, at this particular frequency, the response becomes essentially nonlinear for small amplitudes. The shape of the resonance, for nearby frequencies, is described by A(u) ~ a(u> — ur) close to the characteristic frequency tur, where a is a complex number. Furthermore, by its definition as a linear response function, A obeys A(u>) = A*(—u>). As a consequence, A'(0) = K is the passive stiffness of the system and A"(G) = 0. The real and imaginary parts of A(w) thus have the general form as displayed in Fig. 1.

Figure 1. Schematic representation of the real and imaginary parts of the linear response function A(co) = A' + iA" of a critical oscillator with frequency uir.

4

A c t i v e nonlinear traveling waves

We describe the basilar membrane by Eq. (1) using Eq. (2) for the local mechanical response properties. Motivated by the observed variation of the characteristic frequency along the BM, we assume t h a t the position dependence of characteristic frequencies is given by ujr(x) = u>oe~x^d.We thus obtain a nonlinear wave equation for the BM deformation. In frequency representation, it reads [19] -2pbuj2h

- iuT]h = dx \bldx (A{x,uj)h

+ B\h\2h\]

.

(3)

The complex solutions of this equation h{x) = H(x)et^x^ describe the amplitude H and the phase 0 of the BM displacement elicited by a periodic stimulus with incoming sound pressure p(x = 0,t) = p(0)e l w t . For simplicity, we take the coefficient B, describing the nonlinearity close to resonance, to be a purely

486

imaginary constant, B = i/3. This simple choice ensures that Eq. (2) has no spontaneously oscillating solution for p = 0. Examples for solutions to the wave equation are displayed in Fig. 2 The wave equation Eq. (3) describes traveling waves which are linear for small vibration amplitudes h at locations far from the resonance point xr where u> = ujr(xr). As the wave enters at x = 0, it encounters oscillators which locally have a high characteristic frequency as compared to the wave frequency to < u>r. Consequently, the imaginary part A"{LO) < 0 and energy is pumped into the wave by the active process (see Fig. 1). This pumping of the wave can cancel or even overcome the effects of viscous friction and thus enhance wave propagation and energy flow, but is not related to any unstable behavior of the wave.

Figure 2. Nonlinear active traveling waves for three different stimulus frequencies ( / = 370 Hz, 1.3 kHz and 4.6 kHz) and two different sound pressure levels (40 dB and 80 dB). Note that the waveform depends on stimulus intensity.

As the wave propagates towards the apex, its wavelength diminishes and its amplitude builds up, until it approaches the place of resonance. In the immediate vicinity of the characteristic place, \A\ becomes small while h increases. Thus the cubic term in Eq. (3) rapidly becomes more important than the linear term. This leads to a strongly nonlinear BM response. The wave peaks at x = xp < xr, where the response displays the characteristic nonlinearity of critical oscillators, h(xp) ~ p(xp) 1 / 3 . However, the vibration amplitude as a function of sound pressure level at a fixed position can exhibit responses which are not simple power laws. At positions beyond the characteristic place, x > xr, A' becomes negative and consequently the wave number q ~ uj/yA' becomes imaginary, indicating the breakdown of wave propagation. The wave is thus reflected from the characteristic place and the BM displacement decays very sharply for x > xr.

487 5

Discussion

Critical oscillators provide a general framework for the description of active amplification of sounds by cellular processes. While this description does not provide insights into the specific active processes which underly mechanical amplification on the cellular and molecular levels, it captures the general features in a simple and physically consistent way. The nonlinear wave equation which we present here provides a simple theoretical description of the nonlinear and active nature of the cochlear amplifier [19]. This framework can be extended to describe the BM motion elicited by stimuli containing multiple frequencies, by considering the generic nonlinear coupling of frequency components by critical oscillators [14]. The suppression of the response to one tone by the presence of a second tone, and the generation and wave-like propagation of distortion products, are natural consequences of this description. Furthermore, the flow of energy in the wave, as well as the pumping of the wave by active processes, can be clearly defined in this framework, taking into account nonlinear effects and energy supply by the active systems. The nonlinear wave described here has similarities to a laser cavity [23]; wave reflections along the basilar membrane and especially at the characteristic place lead to interesting and nonlinear reflection phenomena which will be discussed elsewhere. It has been suggested t h a t oto-acoustic emissions are related to modes in the cochlea which result from constructive interference of forward and backward traveling waves. Such modes also occur naturally in our nonlinear active wave description. Therefore, the framework of critical oscillators coupled hydrodynamically on the basilar membrane is consistent with the interpretation of oto-acoustic emissions as active wave resonances in the cochlea discussed in Ref. [23]. References 1. G. von Bekesy, Experiments in Hearing (McGraw Hill, New York 1960). 2. P. Dallos, A.N. Popper & R.R. Fay (Eds.), The Cochlea (Springer, New York 1996). 3. J. Zwislocki, Theorie der Schneckenmechanik: qualitative und quantitative Analyse, Acta Otolaryngol, suppl. 72 (1948). 4. G. Zweig, Basliar membrane motion, Cold Spring Harbor Symp. Quant. Biol. 40, 619-633 (1976). 5. E. de Boer, Auditory physics. Physical principles in hearing theory: I, Phys. Rep. 62, 87-174 (1980). 6. J. Lighthill, Energy flow in the cochlea, J. Fluid. Mech. 106, 149-213 (1981).

488 7. G. Zweig, Finding the impedance of the organ of Corti, J. Acoust. Soc. Am. 89, 1229-1254 (1991). 8. T. Gold, Hearing II. T h e physical basis of the action of the cochlea, Proc. Roy. Soc. B 135, 492-498 (1948). 9. D.T. Kemp, Evidence of mechanical nonlinearity and frequency selective wave amplification in the cochlea, J. Arch. Otorhinolaryngol. 224, 37-45 (1979). 10. W.S. Rhode, Observations of the vibration of the basliar membrane in squirrel monkeys using the Mossbauer technique. J. Acoust. Soc. Am. 4 9 , 1218+ (1971). 11. M.A. Ruggero et al, Basilar-membrane responses to tones at the base of the chinchilla cochlea, J. Acoust. Soc. Am. 101, 2151-2163 (1997). 12. I.J. Russel & K.E. Nilsen, The location of the cochlear amplifier: Spatial representation of a single tone on the guinea pig basilar membrane, Proc. Natl. Acad. Sci. USA 94, 2660-2664 (1997). 13. L. Robles & M.A. Ruggero, Mechanics of the mammalian cochlea, Physiol. Rev. 8 1 , 1305-1352 (2001). 14. Physical basis of two-tone interference in hearing, F. Julicher, D. Andor & T. Duke, Proc. Natl. Acad. Sci. USA 98, 9080-9085 (2001). 15. H. Duifuis et. al., in Peripheral Auditory Mechanisms, edited by J.B. Allen et. al. (Springer, Berlin 1985). 16. W h a t type of force does the cochlear amplifier produce? P.J. Kolston, E. de Boer, M.A. Viergever & G.F. Smoorenburg J. Acoust. Soc. Am. 88, 1794-1801 (1990). 17. E. de Boer, chap. 5 in Ref. 1 & references therein. 18. M.O. Magnasco, A wave traveling over a hopf Instability shapes the cochlear tuning curve, Phys. Rev. Lett. 90, 058101, (2003). 19. T. Duke and F. Julicher, Active traveling wave in the cochlea, Phys. Rev. Lett. 90, 158101 (2003). 20. S. Camalet, T. Duke, F. Julicher & J. Prost, Auditory sensitivity provided by self-tuned critical oscillations of hair cells, Proc. Natl. Acad. Sci. (USA) 97, 3183-3188 (2000). 21. V.M. Eguiluz et. al., Essential nonlinearities in hearing, Phys. Rev. Lett. 84, 5232-5235 (2000). 22. Y. Choe, M.O. Magnasco & A.J. Hudspeth, A model for amplification of hair-bundle motion by cyclical binding of C a 2 + to mechanoelectricaltransduction channels, Proc. Natl. Acad. Sci. USA 9 5 , 15321-15326 (1998). 23. C.A. Shera, Mammalian spontaneous otoacoustic emissions are amplitudestabilized cochlear standing waves, J. Acoust. Soc. Am. 114, 244-262 (2003).

M E C H A N I C A L E N E R G Y CONTRIBUTED BY MOTILE N E U R O N S IN T H E DROSOPHILA EAR

M. C. GOPFERT AND J. T. ALBERT Volkswagen-Foundation

Research Group, Institute of Zoology, University of Cologne, Weyertal 119, 50923 Cologne, Germany E-mail: [email protected], [email protected]

In the fruit fly Drosophila melanogaster, hearing is based on dedicated mechanosensory neurons transducing vibrations of the distal part of the antenna. Examination of this receiver's vibrations in wild-type flies and mechanosensory mutants had shown that the auditory mechanosensory neurons are motile and give rise to key characteristics that define the cochlear amplifier of vertebrates, including nonlinear compression and self-sustained oscillations, the mechanical equivalent of spontaneous otoacoustic emissions. Violations of the equipartition theorem now have confirmed that the neurons exhibit power gain, lifting the fluctuations of the receiver above thermal noise. By opposing damping, this neural energy contribution boosts the sensitivity and frequency-selectivity of the fly's antennal ear.

1 Introduction Spontaneous otoacoustic emissions, nonlinear compression, amplification, and frequency selectivity are the four essential characteristics that define the cochlear amplifier of vertebrates [1-4]. At least two of these criteria are met by the ear of the fly. In Drosophila, the distal part of the antenna serves as a sound receiver, vibrations of which are transduced by the chordotonal sensory neurons of Johnston's organ in the antenna's base (Fig. 1) [5,6]. As shown by laser Doppler vibrometric measurements, this antennal receiver nonlinearly alters its tuning with the intensity of sound, twitches spontaneously, and occasionally performs largeamplitude self-sustained oscillations [6-8]. These oscillations, which are the presumptive mechanical analogue of spontaneous otoacoustic emissions, reliably occur when the physiological condition of the animal deteriorates, e.g. after thoracic injection of dimethyl-sulphoxide (DMSO) [7,8]. Mutant analyses revealed that these oscillations as well as the receiver's twitches and nonlinearity are introduced by the sensory neurons of Johnston's organ: mechanosensory mutations such a tilB2, btv5PI, and nompA2, which specifically affect the mechanosensory neurons, linearize the receiver's response and abolish its twitches and oscillations [7,8]. Demonstrating the neurons' ability to mechanically drive the antennal receiver, these findings suggest that the fly's neurons -analogous to the motile hair cells of vertebratesprovide active mechanical amplification to boost the sensitivity of the ear. The benchmark of active amplification is power gain; more energy comes out of an amplifier than is initially fed in. Hence, establishing active amplification requires the demonstration of power gain, which, in strict terms, must be based on violations of fundamental principles of thermodynamics, the equipartition or the

489

490 fluctuation-dissipation theorem. Violations of the fluctuation-dissipation theorem have demonstrated power gain for isolated vertebrate hair cells [9]. Violations of the equipartition theorem, in turn, have documented the ability of the fly's auditory neurons to exhibit power gain inside the ear [10]. This latter work, the identification of neural energy contributions in the Drosophila auditory mechanics, is the topic of this chapter.

Figure 1. Confocal images of the fly's antennal ear. Pseudo-brighl-ficld image (left) dcpicling the three antcnnal segments (1-3) and the arista and corresponding confocal section (right) showing the mechanosensory and olfactory sensory neurons in the 2"'1 and 3"1 antennal segments, respectively. Neurons are labeled by the targeted expression of UAS-mCD8-GFP using the driver line Cha-GAL4. Arrows highlight the mechanosensory neurons of Johnston's organ, which mediate hearing.

2 Methods 2.1 Flies Oregon R was used as WT strain. The nompA2, btv5PI, and MB2 mechanosensory mutants were kindly provided by Maurice Kernan and Dan Eberl. The respective genetic backgrounds, en bw (for nompA2), w; FRT,0A FRf'3 (for btv5PI) and y w (for MB2) were used as controls. 2.2 Measurements and data analysis All mechanical measurements were performed in the absence of external stimulation. Using a Polytec PSV-400 scanning laser Doppler vibrometer, we measured the amplitude of the receiver's vibration velocity, XI, near the tip of the

491

arista (Fig. 1). After Fourier transformation, the spectral velocities, X(&>) , were converted into spectral displacements, \X(a>)\ with X(&>) = X(ft/)/#>, and subsequently squared, yielding the power spectral density, X (cd)\, of the receiver's displacement (Fig.2). Power spectra were fitted with the function of a forceddamped harmonic oscillator (Fig. 2), 2

/I m 2

2

2

FQ

2

X (co) 2

(«0 -« )

+

(-^)

(1) 2

where F 0 is the force acting on the oscillator, m the oscillator's apparent mass, (OQ the natural angular frequency, and Q the quality factor, with Q = ma>01 y and / denoting the damping constant. By integrating the fit function between zero and infinity, we obtained the fluctuation power, i.e. the mean square amplitude, X2 )of the receiver's displacement. The analysis presented is based on the receiver fluctuations in 20 animals per strain. 3 Results At thermal equilibrium, the fluctuations of a passive oscillator will obey the equipartition theorem, 1/2K( X2 \ = \l2kBT

with K = KS, where K is the

effective stiffness, K$ is the spring constant, kB is the Boltzmann constant, and T the absolute temperature. We used the equipartion theorem to deduce K from the receiver's fluctuation power, K = kBT I X2

Notably, the effective stiffness

obtained by this calibration equals the spring constant provided the system is passive. I the system is active, however, the effective stiffness will be smaller than the spring constant, reflecting the increase in fluctuation power (and energy) caused by the action of the additional force. In either case, the mean total energy of the system, E, can be written as E = (KS/K)-kBT, yielding an energy gain, AE, of AE = ((KS IK) — X) • kBT. Hence, provided that both K and Kg are known, active energy contributions can be separated from thermal fluctuations. For a simple harmonic oscillator, Ks can be deduced from the natural frequency, Ks = mco . We calibrated this relation using dead WT flies, the receivers of which can be expected to solely display thermal noise. Given a natural

492

frequency of 798 Hz, a fluctuation power of 0.3x10"16 m2, and Ks = K = 132 uN/m, we obtain a mass of 5.2 ng. Hence, provided the mass is constant, the receiver's spring constant is given as Ks = 5.2 • 10" a>0 . We used this relation to derive Ks from the natural frequency.

100

300 /(Hz)

100

1000

300 /(Hz)

1000

10-14-

I

u 10-ieJ X -% 10-18 10-22 100 C

1000

10-16

^\ll

WT SO NWI

>< 300 /(Hz)

JVI

10-20-

m-22100

\

N

300

1000

/(Hz)

100

300

1000

/(Hz)

Figure 2. Power spectra of the receiver's fluctuations. Example data showing the measured spectrum (thin trace) and the fitted harmonic oscillator model (thick trance) for one animal per strain.

To test the impact of non-neural energy contributions such as the activity of muscles, we examined the receiver's fluctuations in live mutants with defective mechanosensory neurons. Three different mutants with distinct natural frequencies of the receiver were examined (tilB2, btv5P1, nompA2, Fig. 2, 3). For all three mutants, we found K = KS, E = \kBT, and A £ = 0 . These results confirm that (i) the relation is valid, that (ii) the receivers of live flies with defective neurons are passive, that (iii) non-neural energy sources do not contribute to the receiver's

493

fluctuations and (iv) that the mass is constant; even the disconnection of the neurons from the receiver, as found in nompA2 mutants [12], does not affect the receiver's apparent mass. dead WT

100

live mutants

300

f„< Hz )

live WT & controls

1000

100

300

1000

f„(Hz) . WT SO

300 /"(Hz)

1000

Figure 3. Effective stiffness of the receiver as a function of the natural frequency. The straight line depicts the spring constant as deduced from the data of dead WT flies (Ks= 5.2- l(T9
For live WT and control flies with intact mechanosensory neurons, our analysis revealed an effective stiffness considerably lower than the spring constant, documenting a breakdown of the equipartition theorem and, thus, the existence of power gain. For WT flies, we found Ks/K=5.6, which corresponds to E=5.6kgT and AE = 4.6kBT = 19ZJ. Larger energy contributions occurred during self-sustained oscillations as induced by DMSO. Under these conditions, our analysis yielded KS = 50AK, E=50.lkBT, and AE = 49.lkBT =200zJ. This additional energy, which is absent in flies with defective mechanosensory neurons, reflects the mean total energy the neurons add to the receiver's fluctuations.

494

Neural energy contributions associated with reductions in damping (Fig.4). In live flies with intact neurons, the damping constant of the receiver was significantly lower than in dead WT flies (WT live: y=\.2nNm~ s, WT dead: y = 28.4nNm~ s, Fig. 4). Even lower damping constants were found during self-sustained oscillations (y = 0.0lnNm~ s). These figures suggest that the neurons actively oppose damping. This notion is supported by a negative correlation between energy and damping, whereby the receiver's damping constant drops inversely with the squared mean energy of the receiver's fluctuations (Fig.4).

dead WT & ! mutants

100

300

1000

# Hz >

1

10

100

E{kBT)

Figure 4. Damping effects. Damping constant of the antennal receiver as a function of the natural frequency (left) and the fluctuation energy (right). Lines depict the damping constant of the antennal receivers in dead flies (left panel) and a power function fitted to the data (right panel). The latter fit function is described by y = 3 • 10"8 E2 (r2=0.97, p<0.001).

Conclusions We have described a non-invasive approach to identify violations of the equipartition-theorem in the mechanics of an intact ear. The method is based on two premises, inter-individual comparability and constancy of the mass, which both are validated by experimental results. We find that the mechanosensory neurons in the ear of Drosophila melanogaster expend energy to boost the vibrations that enter the ear. This result suggests active amplification as a general scheme in hearing. Acknowledgments We thank D. Eberl and M. Kernan for providing mechanosensory mutants and A. D. L. Humphris, D. Robert, and O. Hendrich, who participated in the research covered

495 by this review. Supported by the Volkswagen-Foundation (Grant 1/78 147, to M.C.G.). References 1. Manley, G.A., 2001. Evidence for an active process and a cochlear amplifier in nonmammals. J. Neurophysiol. 86, 541-549. 2. Robles, L., Ruggero, M.A., 2001. Mechanics of the mammalian cochlea. Physiol. Rev. 81,1305-1352. 3. Gopfert, M.C., Robert D., 2001. Active auditory mechanics in mosquitoes. Proc. R. Soc. Lond. B 268, 453-457. 4. Martin, P., Juhcher, F., Hudspeth, A. J., 2003. The contribution of transduction channels and adaptation motors to the hair cell's active process. In: Biophysics of the Cochlea: from Molecules to Models (ed. Gummer, A.W.). Singapore, World Scientific, p. 3-13. 5. Gopfert, M.C., Robert, D., 2001. Turning the key on Drosophila audition. Nature 411,908. 6. Gopfert, M.C., Robert, D., 2002. The mechanical basis of Drosophila audition. J. Exp. Biol. 205, 1199-1208. 7. Gopfert, M.C., Robert, D., 2003. Motion generation by Drosophila mechanosensory neurons. Proc. Natl. Acad. Sci. USA 100, 5514-5519. 8. Gopfert, M.C., Robert, D., 2003. Micromechanics of Drosophila audition. In: The Biophysics of the Cochlea - From Molecule to Model (ed. Gummer, A.W). pp. 300-307. Singapore: World Scientific. 9. Martin, P., Hudspeth, A.J., Juhcher, F. (2001). Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process. Proc. Natl. Acad. Sci. USA 98,14380-14385. 10. Gopfert, M.C., Humphris, A.D.L., Albert, J.T., Robert, D., Hendrich, O., 2005. Power gain exhibited by motile mechanosensory neurons in Drosophila ears. Proc. Natl. Acad. Sci. USA 102, 325-330. 11. Chung, Y.D., Zhu, J., Han, Y.-G., Kernan, M.J., 2001. nompA encodes a PNS-specific, ZP domain protein required to connect mechanosensory dendrites to sensory structures. Neuron 29, 415-428.

SHORT-WAVELENGTH INTERACTIONS BETWEEN OHCs: A "SQUIRTING" WAVE MODEL OF THE COCHLEAR AMPLIFIER ANDREW BELL Research School of Biological Sciences, The Australian National University, Canberra, ACT 0200, Australia E-mail: [email protected] The geometry and physical properties of the subtectorial space are well-suited to propagation of symmetric Lloyd-Redwood waves or "squirting" waves [1]. Here I analytically model squirting wave interaction in an array of 62 outer hair cells in 3 rows and find that it can lead to a sharply tuned standing-wave resonance - essentially a narrow-band cochlear amplifier.

1 Introduction "Squirting" waves arise when a thin liquid layer is sandwiched between two deformable plates [1]. These conditions reflect those in the subtectorial space, so that outer hair cell length changes could produce squirting waves of short wavelength and high dispersion. Calculated wavelengths appear comparable to the spacing between the outer hair cell rows, so that positive feedback could occur between the body of one OHC (considered as a motor) and the stereocilia of its neighbour (a sensor). The associated high dispersion (c cc/ 2/3 ) means that a spacing between OHCl and OHC3, graded longitudinally from 50 to 20 um, could accommodate standing waves from 20 Hz to 20 kHz. The suggestion is that the cochlear amplifier might be a standing-wave resonance. Could feedback interaction between the 3 rows of OHCs produce its characteristic high gain and sharp tuning? 2 Methods and Results An array of 62 OHCs in 3 rows was considered (Fig. 1A) in which each electromotile cell simultaneously launched a circular squirting waves which then deflected neighbouring OHC stereocilia in an amplifying process that led to further OHC motion and another circular squirting wave. This positive feedback process was modeled analytically based on wave equations and feedback circuits (Fig. IB). It was assumed that (1) The wavefronts expand in a uniform medium without boundaries and the OHCs act as point sources and detectors. (2) At 1 kHz, the interrow spacing of the OHCs was half a wavelength (15 um). (3) Each cell in a given row, because of symmetry, behaved identically. Adding up the wavefronts at the IHC position produced high gain and sharp tuning provided the gain of stereocilia deflection to cell length was sufficient (Fig. 1C).

496

497 t ?IHC

A

"fro,

B

OHC1

—*

; b/2 .

,

. t •. '•!•' '• * I—• ° ' \ '• —j

b/2

i

j

i

HC1

•*' / ' .

.

[ [

.

0HC2

tr°2! OHC2

I

OHC3 .

0HC3

1

0

AV(i*ABlK8-i

N

5=0.2 5= 0.2 y=1

•Q-°3J ,

E E «

AP= 2.28 A0=2.2 A0=2.1 A0=2.O v

- - Wfrequency (Hz)

Figure 1. Squirting wave feedback between OHCs. A: Each cell is the source of a circular squirting wave (here, just one depicted), a = 10 urn, b = d = 30 um. B: Feedback paths between OHCs, where K is the attenuation (magnitude and phase) between neighbouring rows and ris that between OHC1 and OHC3. Input to all cells is an initial stimulus V; outputs Ou 02, and 0 3 for each row. Outputs affect response of neighbouring cells via A: and r, which are functions of cell-to-cell spacing, where K= X/cn, r = 2r n , and n is +10, the number of cells on either side (i.e., longitudinally) able to perceptibly interact. Other factors are Ap, the combined electromotility gain (wave amplitude to membrane potential to cell motion); y, an exponential wave-attenuation constant; and S, the asymmetry in OHC2's response sensitivity to OHC1 compared to OHC3 (because of the ' V of the stereocilia). C: The frequency response of the system, as summed at the IHC position, in which A/} was adjusted to be just below oscillation threshold. Inset displays the derived feedback equations governing the output of each cell prior to summation.

3 Discussion Given simple squirting wave interactions between OHCs, a sharply tuned standing wave resonance is possible. This result accords with other modeling studies [2] and confirms that a radial standing wave could underlie the cochlear amplifier. Acknowledgements This work was supported by an ANU PhD Scholarship and by a grant from the German Research Council, SFB 430, to A. W. Gummer. References 1.

2.

Bell, A., Fletcher, N.H., 2004. The cochlear amplifier as a standing wave: "squirting" waves between rows of outer hair cells? J. Acoust. Soc. Am. 116, 1016-1024. Elliott, S.J., Pierzycki, R., Lineton, B., 2005. Incorporation of an active feedback loop into the "squirting wave" model of the cochlear amplifier. Proceedings, Twelfth International Congress on Sound and Vibration, Lisbon, Portugal, 11-14 July.

WAVE PROPAGATION IN A COMPLEX COCHLEAR MICROMECHANICS MODEL WITH CURVATURE H. CAI AND R. S. CHAD WICK Section on Auditory Mecahnics, NIH/NIDCD, Bldg.10, Rm.5D49, Bethesda, MD 20892, USA E-mail:[email protected], chadwick®helix.nih.gov D. MANOUSSAKI Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA E-mail: daphne @ math, vanderbilt. edu We use our recently developed hybrid analytical/finite-element approach to investigate the significance of curvature in cochlear micromechanics. The new computational model includes the detailed cellular structures within the organ of Corti, the interactions between the cochlear partition and fluid, as well as the coiling effects of the cochlear geometry. Gorverning equations are formulated in a curvilinear coordinate system. We develop an iterative algorithm to solve a fluid-solid interaction eigenvalue problem. We find that the cochlear curvature greatly increases the apical shear gain of the cochlear partition, which is a measure of the bending efficiency of the outer hair cell stereocilia.

1

Introduction

The mammalian cochlea has a snail-like shape. Does the cochlear spiral play a functional role in sound transduction? To answer this question, we extend our recently developed hybrid analytical/numerical approach to include the curvature effects in a complex micromechanics model. Simulations are performed in the apical region of a guinea-pig cochlea, where the curvature is greatest. The effects of cochlear curvature on the function of the cochlea are analyzed by comparing the simulation results with those of our straightened cochlea model [1,2]. 2

Methods

To study the curvature effects, we use a curvilinear coordinate system that incorporates r, the radial distance from the modiolar axis, s, the arc length along the coiled cochlear duct, and z, the distance along the modiolar axis. We use the WKB approximation method to treat the propagation of the traveling wave along the coiled cochlear duct, and use the finite element analysis in the cross section, where we solve a fluid-solid structure interaction eigenvalue problem using an iterative algorithm. The cochlear fluid is viscous and incompressible whose dynamics satisfies the linearized Navier-Stokes equation. The basilar membrane (BM) is modeled as a clamped annular spiral plate whose deflection is calculated by the

498

499

Green's function method. The organ of Corti (OC) and the tectorial membrane (TM) are modeled as Voigt solids using linear elasticity theory. 3 Results and Discussion We calculate the detailed relative motions within the cochlear partition (CP), from which we compute the shear gain (SG) of the cochlea (Fig. 1). SG is defined as the ratio of shearing displacement of the TM and the top of the OC to the BM deflection.

3 2.5

Rmin=0.01 cm

•

• • • 0

c o

o Rmin=0.02 > cm ' Straight model 0.8

model

°-

<*i

Rmin = 0.02cm

a

Emin=0.01 cm -50

0.4

o.e

1

Figure 1. The amplitude (upper) and phase (lower) of the shear gain (SG) at the apex of the cochlea. SG is a complex number whose phase represents the timing difference between the deflections of the OHC stereocilia and the BM. Curvature improves greatly the shear gain. At 1 kHz, the coiled model (Rmj„ = 0.01 cm) gives a shear gain of -2.7, against -0.96 in the straight model, a more than 180% of increase in amplitude. The SG phase changes sign in straight and coiled models. In the coiled model, the motions of the CP correlate in such a manner that when the BM deflects toward the scala vestibuli, the shearing movement between the TM and the OC bends the OHC stereocilia in the excitatory direction.

08

Frequency (kHz)

While most macro- and micromechanics cochlear models have failed to show any signficant effect of cohlear coiling, we find that, at the apex, it greatly improves the shear gain of the CP. References 1. Cai, H., Chadwick, R.S., 2003. Radial structure of traveling waves in the inner ear. SIAM J. Appl. Math. 63, 1105-1120. 2. Cai, H., Shoelson, B., Chadwick, R.S., 2004. Evidence of tectorial membrane radial motion in a propagating mode of a complex cochlear model. Proc. Natl Acad. Sci. USA. 101, 6243-6248.

A 'TWIN-ENGINE' MODEL OF LEVEL-DEPENDENT COCHLEAR MOTION

A. J. A R A N Y O S I Massachusetts

Institute of Technology, Cambridge, E-mail: [email protected]

MA,

USA

Incorporating two nonlinear negative damping elements into a simple fourth-order system accounts for many aspects of the basilar membrane (BM) response to both clicks and tones over a wide range of sound levels.

Responses of the BM to acoustic clicks have multiple components: an initial time delay, a slow rise in the oscillation frequency, and a long-lasting oscillation at the best frequency (BF) of the measurement location [1,2]. The first two components can be attributed to the delay and dispersion of the traveling wave, respectively. The persistent oscillation presumably reflects the effective local impedance of the cochlea. One prominent feature of this oscillation is the presence of multiple lobes, between which the oscillation amplitude falls to zero and reverses phase. Such lobes have been used to support a time-delay feedback model of cochlear impedance [3], but can also be explained by the interaction of a coupled pair of resonators. Equations describing such a pair are Fin(t) + mcx2(t) + kcx2(t) = m1x\(t) + \bx - gi(xi)]ii(t) + kxxi(t) bcXtit) = m2x2(t) + [b2 - g2{x2)]x2{t) + k2x2(t),

(1) (2)

where Fjn(t) is the driving force, X\(t) and x2{t) are the positions of the two resonators, the m,i,bi,ki,i = 1,2 terms are the mass, damping, and stiffness of the two resonators, the mc, bc, kc terms are cross-coupling constants, and gt(xi) is a nonlinear velocity-dependent term in each resonator, defined as the derivative of a Boltzmann function. The unique feature of this system is the presence of two velocity-dependent elements, resulting in a 'twin-engine' system. Figure 1 demonstrates responses of this system to clicks (1A) and tones (IB) at multiple input levels, as well as compressive nonlinear growth (1C). With two nonlinear elements, the model responses to click and tone stimuli were nonlinear over a 60 dB range of input levels. When only the second resonator contained an nonlinear element (i.e., <7i(xi) = 0), with parameters tuned to match low-level click responses, the system continued oscillating for nearly as long at high click levels as at low levels. Moreover, the compressive nonlinearity extended over only 30 dB. This model shows that a fourth-order system is sufficient to account for many properties of the BM response to clicks, if the system contains two nonlinear

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100

200

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-

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Figure 1. Velocity ±2(4) of the model. A. Response to clicks. The velocity has multiple lobes, with the phase of oscillation reversing between lobes. At higher levels, the response peak shifts earlier in time and later lobes become relatively smaller. The timing of the zero-crossings is level-invariant. B . Response to tones vs. frequency at several input levels. The model is sharply tuned at low levels, and the tuning becomes broader as the level is increased. C. Response to tones vs. level. At the best frequency (solid line), the response is compressively linear with a slope of about 1/3 (dotted line) over a 60 dB range of intensities. Away from that frequency (dashed line), the response grows linearly with level.

negative damping terms. A possible physical interpretation of this model is for the two resonators to represent the TM-hair bundle complex and the BM-organ of Corti complex, respectively. Such an explanation could support the intriguing possibility that both somatic motility and bundle motility of outer hair cells contribute to cochlear function. References 1. E. deBoer and A. L. Nuttall. The mechanical waveform of the basilar membrane. I. frequency modulations ("glides") in impulse responses and crosscorrelation functions. J Acoust Soc Am, 101:3583-3592, 1997. 2. A. Recio, N. C. Rich, S. S. Narayan, and M. A. Ruggero. Basilar-membrane responses to clicks at the base of the chinchilla cochlea. J Acoust Soc Am, 103(4) :1972-1989, 1998. 3. G. Zweig. Cellular cooperation in cochlear mechanics. In A. W. Gummer, editor, Biophysics of the Cochlea: From Molecules to Models, pages 315-330. World Scientific, Singapore, 2003.

A HYDRO-MECHANICAL, BIOMIMETIC COCHLEA: EXPERIMENTS AND MODELS

F. CHEN Oregon Hearing Research Center, Oregon Health & Secience University, 3181 SW Sam Jackson Park Road, Portland, OR 97239, USA E-mail: [email protected] H. I. COHEN Department

of Physiology and Biophysics, Boston

University

D. C. MOUNTAIN AND A. ZOSULS Department

of Biomedical Engineering, Boston

University

A. E. HUBBARD Department

of Electrical and Computer Engineering, Boston University, 8 St. Mary Street Boston MA 02215, USA E-mail: [email protected]

The mammalian cochlea performs a remarkable signal processing function that maps the frequency of the incoming signal into different spatial locations along its length. A hydromechanical model was built to mimic the biological cochlea. Companion computational models of the mechanical devices were also implemented. The measured results from the artificial cochlea (ACochlea) demonstrate the cochlear-like features. Experimental data were compared with simulation results. The simulation results from both artificial basilar membrane (ABM) and ACochlear computational models exhibit the same trends as their experimental counterpart. Using the model as an analytic tool, the behavior of the devices was investigated. We determined that the ABM is under high tension, which degrades the frequency response of both ABM and ACochlea.

1 Introduction Although several groups have tried to build a mechanical device to mimic cochlear signal processing functionality [1,2,3], none of them has fully demonstrated cochlear-like features in their device. In this presentation, we describe the construction and characterization of a hydro-mechanical artificial cochlea (ACochlea). The Acochlea was constructed by implementing a fluid channel on one side of the artificial basilar membrane (ABM). The ABM was made by depositing copper beams with progressively increasing length on a soft polymer substrate. Measured results from our Acochlea show passive cochlea-like features: slow traveling wave, sharp high-frequency roll-off, and frequency selectivity.

502

503 2 Methods and Results A hydro-mechanical model was built to mimic the biological cochlea. The ABM was made by depositing copper beams with progressively increasing length on a soft polymer substrate. A fluid channel was implemented on one side of the ABM. The ABM and the fluid channel mimic the hydro-mechanical structure of the mammalian cochlea. Measurements were performed on both the ABM (without the fluid channel) and the Acochlea. Figure 1 shows the measurement on Beam #6, #16 and #26 of a 32-beam Acochlea. Beam Imputes Responsn

Beam Frequency Response

(a)

(b)

Figure 1. Displacement measured on beams along the ACochlea made up of the ABM with cuts on the membrane between beams, (a) Time domain response. Slow cochlea-like traveling waves are demonstrated, (b) Magnitude of the ratio of the beam displacement spectrum and the driver displacement spectrum. A sharp high-frequency roll-off is shown in each right-side panel.

Acknowledgements This work was funded by DARPA contract N00014-00-C-0314. References 1. 2.

3.

White, R. D. and Grosh, K., 2005. "Microengineered hydromechanical cochlear model." Proc Natl Acad Sci 102(5): 1296-1301. Wittbrodt, M. J., Steele, C , et al., 2004. Fluid structure interaction in a physical model of the human cochlea. 148th Meeting of the Acoustical Society of America, San Diego, California. Hemmert, W., et al., 2002. A life-sized, hydrodynamical, micromechanical inner ear. Conference of Biophysics of the Cochlea: from Molecule to Model, Titisee Germany, World Scientific.

SIX EXPERIMENTS ON A 1-D NONLINEAR WAVE-DIGITAL FILTER MODELING OF HUMAN CLICK-EVOKED EMISSION DATA E.L.LEPAGE OAEricleLaboratory, P.O. Box 6025, Narraweena, NSW2099 E-mail: ericlepage@oaericle. com.au

Australia

A. OLOFSSON Unit of Technical & Experimental Audiology, Section of Ear-Nose-Throat-Hearing Department of Clinical Neuro Science, Karolinska Institutet, Stockholm, Sweden E-mail: [email protected] We use a 1-D discrete time domain linear model using the Fettweiss [1] wave-digital filter approach. The model, comprised of 350 segments, is used to gain insight into observed characteristics of a database of 12000 human click-evoked otoacoustic emissions (CEOAE). Its properties are explored by considering various percentages of total OHC activity and time constants of the passive and active mechanics and adaptation effect. The experiments conducted are 1) Variation of time constants to see how CEOAE latency is affected, 2) Influence of aging upon emission strength, 3) Influence of decline in OHC function upon the tonotopic map and the effect of bounding values of stiffness change; the effects of 4) small punctate "lesions" of down-graded OHC activity, 5) large regions of OHC loss and 6) The effect of varying the curvature or 'warp' of the frequency-place map [2].

1 Introduction and methods Otoacoustic emissions vary widely across human subjects. Any type of response will not necessarily have a unique cochlear origin. Our study looks for classes of response due to specific perturbations in parameters of a 1-dimensional wave-digital filter model implemented as a Matlab™ mex file by one of us (AO). The pressure at the first segment represents both acoustic input and resulting CEOAE response. Each segment of the model (Fig.l) provides for forward transduction by the OHC, stiffness variation, resistance tapered to lower values towards the apex, mechanical feedback to the basilar membrane proportional to OHC membrane potential and a lower limit on decrease in stiffness. The one experiment reported here involves varying the 1-pole high-pass filter time-constant (Tdc-disp ms), plus charging and release time-constants of the low-pass filter (Tcharge and Trelease ms respectively). Other key parameters expressed as percentages were the 'kick' provided by the OHC (Rohc) and the minimum stiffness limit (Clim). The latency of modelgenerated CEOAE were computed after varying these parameters in five nested loops (243 combinations) looking for a model explanation for the extent of latency variation with age similar to that observed in a large clinical study [3].

504

505 2 Results The CEOAEs produced by the model had latency versus frequency fitted in identical fashion to the Osspfscenwnt Comparing TF analysis 12000 records with 1-D DWF m o * l values clinically obtained 20: 1 — Fern Neonate as a function of age. FemAgeSO — Male Neonate Two of the cases of the — Male AfleSO — Mode) Fast model were chosen for Model S o w best agreement with mean data from neonates and 80 year old males and females. It would seem that neonatal responses have corresponding model values which indicate faster, higher level OHC U . 4 M g,/B » « J B -DUOS Reft^ve *tHftve«* activity (see table), while Figure 1. Shows on the left the part of the model for one section that controls stiffness, with best matches of 3 time constants (ms) and the shorter latency data model parameters Clim and Rohc (both fractions of unity) to match from older subjects clinical data showing aging effect upon click-evoked otoacoustic correspond to increased emission latency (model fits in dotted, dash-dotted lines). time constants and decreased stiffness, not inconsistent with general expectation.

3 Conclusion The experiment described is one of six showing that even a 1-D computation model may provide significant insight into OAE variations encountered in a large clinical study of otoacoustic emissions records. References 1. 2. 3.

Fettweiss, A., 1971. Digital filter structures related to classical filter networks. Arch. Elek. Ubertragungst, 25, 79-89. LePage, EX., 2003. The mammalian cochlear map is optimally warped. J. Acoust.Soc.Am. 114(2), 896-906. Murray, N.M. and LePage, E.L., 2004. Ageing effect in click-evoked otoacoustic emissions and pure tone audiometry in groups with different types of noise-exposure. Noise and Health, Submitted for Publication.

Poster download: www.oaericle.com.au

MEASUREMENTS AND MODELS OF HUMAN INNER-EAR FUNCTION WITH SUPERIOR SEMICIRCULAR CANAL DEHISCENCE M.E. RAVICZ 1 , W. CHIEN 1 ' 2 , J.E. SONGER 1 ' 3 , S.N. MERCHANT 1 ' 2 ' 3 , AND J.J. ROSOWSKI 1 ' 2 ' 3 1

2

Eaton-Peabody

Department

3

Lab., Mass. Eye & Ear Infirmary, 243 Charles St., Boston MA 02114 mike_ravicz@meei. harvard, edu

of Otology and Laryngology,

Harvard Medical School, Boston MA 02115

Speech and Hearing Bioscience and Technology Program, Harvard-MIT Science and Technology, Cambridge MA 02139

Division of Health

We tested the hypothesis that hearing loss in superior semicircular canal dehiscence (SCD) syndrome is due to a "third cochlear window". SCD in human temporal bones produced a fluid motion in the dehiscence, a reduction in round window velocity comparable to the lowfrequency hearing loss seen in SCD patients, and an increase in stapes velocity; all these results support the "third window" hypothesis. A functionally- and anatomically-based model predicts the temporal bone results.

1 Introduction and Methods Superior semicircular canal dehiscence (SCD) syndrome is a recently-described condition in which patients experience a constellation of vestibular and auditory symptoms including sound- and/or pressure-induced vertigo (Tullio's phenomenon) and a 0-50 dB low-frequency conductive hearing loss [1]. The defining feature of SCD is a dehiscence (opening) in the bony labyrinth that normally separates the superior semicircular canal from the cranial cavity. The cause of the hearing loss has been hypothesized as a shunting of acoustical energy away from the cochlea and through the dehiscence, which acts as a "third cochlear window" [2]. In this study, sound-induced velocities of the round window (Vrw) and stapes (Vs) were measured with a laser-Doppler vibrometer in eight fresh cadaveric temporal bones in three conditions: (1) intact; (2) with a 1-2.5 mm2 dehiscence in the superior semicircular canal - the velocity of the fluid in the dehiscence (Vscd) was also measured; and (3) with the SCD patched. 2 Results and Model 2.1

Effects of SCD on Vscd, Vrw, and Vs

With a dehiscence of at least 1 mm2, Vscd was 20-50 dB above the measurement noise floor. The magnitude of Vrw decreased below 2 kHz: by ~5 dB between 0.5 and 2 kHz, by 16 dB on average at 150 Hz (Fig. 1). Vrw phase increased by as

506

507 much as 0.2 period below 2 kHz. Vs magnitude increased by 3-5 dB on average below 4 kHz; the change in Vs phase was not significant. Patching the dehiscence returned Vrw and Vs approximately to their intact values. 2.2

Model predictions of changes in Vrw and Vs

Experimental results are consistent with predictions of a functionally- and anatomicallybased model of the inner ear that includes an SCD as a third cochlear window. The model assumes that the inner ear is a rigid-walled space filled with incompressible fluids, so the net volume velocity of the two normal cochlear windows (oval and round) is zero. In the model, an SCD (1) produces a fluid volume velocity in the SCD nearly equal to Vs; (2) decreases round-window volume velocity as fluid volume velocity is shunted through the SCD; and (3) increases stapes volume velocity by decreasing inner-ear input impedance (Fig. 1).

1000 FREQUENCY (Hz)

Figure 1. Mean changes in Vrw and Vs magnitude (top) and phase (bottom) observed (solid) and predicted (dashed).

3 Discussion Our temporal-bone measurements and model results are consistent with the lowfrequency conductive hearing loss and increased umbo velocity frequently seen in SCD patients [2,3]. Acknowledgments Funded by NIH / NIDCD and the Silverstein Young Investigator Award. References For references and a copy of the poster, visit http://epl.meei.harvard.edUi

A NEW MULTICOMPARTMENTS MODEL OF THE COCHLEA

SHAN LU, JOHN SPISAK, DAVID C. MOUNTAIN AND ALLYN E. HUBBARD Boston University College of Engineering, 8 Saint Mary's Street, Boston, MA 02215, USA E-mail: [email protected], [email protected] [email protected] A hydromechanical multicompartment cochlear model employing outer hair cell (OHC) force generation creates a slow traveling pressure wave inside the organ of Corti, which is principally responsible for enhanced response of the basilar membrane. This model has been shown generally to mimic physiological data using physiologically realistic parameters. NIH supported this work.

1 Introduction It is commonly assumed that outer hair cell (OHC) voltage-dependent length changes observed in vitro form the basis for the cochlear amplifier in vivo. OHC contractions would be expected to pull the reticular lamina (RL) and basilar membrane (BM) together, squeezing fluid of the organ of Corti (OC) and producing flow in the longitudinal direction. Figure 1 shows the analogous electric circuit of our new model, which includes both hydromechanical as well as an eletroanatomical components. The tension-gated conductance change in the apical part of the OHC senses the motion of the RL. This, in turn, produces a potential change in the lateral wall of the OHC. The voltage change feeds back into the OHC active force generator.

Figure 1. Electroanatomical model with connections to hydrodynamic model.

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Figure 2 compares the model's cochlear microphonic (CM) response with lowfrequency CM responses recorded in scala media of the third-turn in the gerbil cochlea. The dashed lines are model results. The additional data points (doted lines with "+" in 400Hz and 800Hz figures) are from a model whose volume compliance was increased by a factor of two. The BM/stapes velocity ratio result computed using the model also fits experimental data to a modest degree. References 1.

2.

Hubbard, A.E., Chen, F., Mountain., D.C., 2002. A new, realistic multimode theory of the cochlear amplifier, 2002 Midwinter Meeting of the Association for Research in Otolaryngology, 1222. Naidu, R.C., Mountain, D.C., 1998. Measurements of the stiffness map challenge abasic tenet of cochlear theories. Hear Res 124: 124-131.

A 3D FINITE ELEMENT M O D E L OF THE GERBIL COCHLEA WITH FULL FLUID-STRUCTURE INTERACTION

G.D. BUSTARD, D.C. MOUNTAIN AND A.E. HUBBARD Hearing Research Center, BostonUniversity, 44 Cummington Street, Boston MA 02215 E-mail :gbustard@bu. edu A 3D finite-element model of the gerbil cochlea was built, based on a simplified cochlear partition and a viscous fluid field, with fully coupled fluid-structure interaction. A first model, designed to match experimental measurements of point stiffness, generated traveling waves with phase accumulation in line with experimental results but failed to recreate the expected passive frequency-place map of gerbil. Cochlear input impedance was also higher than previously calculated values based on measurementsin Gerbil. In a second model, the stiffness map used as a parameter set was altered to bring the frequency-place map of the model in line with the known function. However, this change further increased cochlear input impedance suggesting that models of this type are unable to account for the full range of experimental measures of the passive gerbil cochlea.

1 Model The underlying mechanics of cochlear tuning, even in the passive cochlea, remain poorly understood. Analytic models are capable of reproducing the traveling wave, but invoke assumptions that make it difficult to relate the models to measurable properties. A 3D finite-element model of the gerbil cochlea was built, based on a simplified cochlear partition and a viscous fluid field, with fluid-structure interaction represented in a realistic way. The two models have one boundary in common at which traction forces and displacements are shared. The solid phase was built of 3D elements and represents a transversely orthotopic plate with material parameters varying from base to apex. The model was excited with pure tones. The commercial package ADINA [1] was used to build the model and run the simulations. 2 Results Mountain and Naidu [2] used a force probe in an in vitro cochlea preparation to measure the point stiffness of the CP as a function of location from the cochlear base. These experiments were recreated as simulations using the finite element model, and in the first model tested, termed Model 1, the material parameters of the CP were chosen such that the model results matched the experimental point stiffness data. Model 1 generated traveling waves with phase accumulation in line with experimental results[3], but predicted a basal best frequency lower than that expected from the passive frequency place map of gerbil [4] and an apical BF

510

511 higher than expected, shown in Figure 1A. Cochlear input impedance was higher than the observed values in Gerbil [5], shown in Figure IB. In a second model, the stiffness map used as a parameter set was altered to bring the frequency-place map of the model in line with the known function. However, this change further increased cochlear input impedance suggesting that models of this type are unable to account for the fall range of experimental measures of the passive gerbil cochlea. 100

• TW peaks in Model 1 tests - TW peaks in Model 2 tests - Gerbil passive FPM 0.1

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Figure 1 A) Frequency-place map of models 1 and 2 vs. expected passive FPM of gerbil. B) Cochlear input impedance Z,„ of FE models vs. results of Overstreet et al [5]

References 1. ADINA R&D, Inc., Watertown MA, U.S.A. 2. Naidu, R., 2000. Mechanical properties of the organ of Corti and their significance in cochlear mechanics. PhD dissertation, College of Engineering, Boston University. 3. Mountain, D.C., Nakajima, H.H., Rafee, S., Hubbard, A.E., 1999. Forward and reverse traveling waves in the gerbil cochlea. In: Wada, H., Takasaka, T., Ikeda, K., Ohyama, K., Koike, T. (Eds), Recent Developments in Auditory Mechanics. World Scientific, Singapore. 4. Muller, M., 1996. The cochlear place-frequency map of the adult and developing Mongolian gerbil. Hear. Res. 94, 148-156. 5. Overstreet, E. H., Ruggero, M.A., 2002. Development of wide-band middle ear transmission in the Mongolian gerbil. J. Acoust. Soc. Am. I l l , 261-270.

DEVELOPING A LIFE-SIZED PHYSICAL MODEL OF THE HUMAN COCHLEA MICHAEL J. WITTBRODT, CHARLES R. STEELE, AND SUNIL PURIA Department

of Mechanical Engineering, Stanford University, 262 Durand, 496 Lomita Mall, Stanford, CA 94305, USA E-mail: [email protected]

The passive behavior of the human cochlea is simulated with a "box model" design. A micromachined composite material of polyimide and aluminum represents the cochlear partition. Two fluid channels were macro machined from plastic and filled with saline. The physical model demonstrated several important cochlea features: traveling waves, tuning, frequency to place tonotopic organization, and roll off at the characteristic place. Calculations using the WKB asymptotic approximation confirm the measured responses and improvements are seen in the calculation using quasi-static stiffness measurement data.

1 Introduction Mammalian hearing is characterized by narrow frequency resolution, high sensitivity, and wide dynamic range. Efforts to understand the mechanics of the cochlea with physical models have been presented by other labs, [1][2]. The current work addresses frequency resolution and mapping by implementing a design which mimics the biological material properties of the basilar membrane and the interaction with a fluid, Figure 1. Reissner's Scala Scala Media membrane ^Vestibuli __^^ B ^^_ s^ ^^^g^^^^^l^— ^ ^ S^^sS I JIL

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Figure 1. Cross-section of the cochlea and the modeling approximation as a two chamber box model. Reissner's membrane is assumed to not contribute so it is ignored.

2 Methods Using dimensions based on human data, an orthotropic cochlear partition consisting of a polyimide matrix and 9000 aluminum fibers was micro-fabricated. The fluid chambers were machined with conventional tooling. A magnet coil system represents the stapes. Vibrations were measured with a laser vibrometer.

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4 Discussion The physical model demonstrated several important cochlea features: traveling waves, tuning, frequency to place tonotopic organization, and roll off. Acknowledgments Work supported in part by grants DC05454 and R29 DC03085 from the NIDCD of NIH and from HSFP. References Hemmert, W., Durig, U., Despont, M., Drechsler, U., Genolet, G., Vettiger, P., Freeman, D.M., 2002. A life-sized, hydrodynamical, micromechanical inner ear. Biophysics of the Cochlea, Titisee, Germany 27 July - 1 August. White R.D., Grosh, K., 2005 Microengineered hydromechanical cochlear model Proc. Nat. Acad. Sci. 102: pp 1296-1301. Steele, C.R. L.A. Taber, 1979. Comparison of WKB calculations and experimental results for three-dimensional cochlear models. J. Acoust. Soc. Am. 65 (4), April.

FULLY MICROMACHINED LIFESIZE COCHLEAR MODEL R. D. WHITE AND K. GROSH University of Michigan, 2350 Hayward Ave., Ann Arbor, MI 48109 E-mail: grosh@umich. edu A life-size hydrodynamical cochlear model is demonstrated. The structure is fully micromachined and suitable for batch fabrication. Laser Doppler Velocimetry (LDV) measurements show cochlear-like traveling fluid structure waves with a phase lag of approximately 3 cycles (67t radians) and displacement magnitude of 0.2-0.5 nm/Pa at the location of maximum response. The device responds in the 10-70 kHz band.

1 Introduction To date, three groups have reported the construction of life-sized physical cochlear models [1,2,3]. These systems use a polymer membrane on a micromachined support as the "basilar membrane" (BM), and use casting, milling, or small-scale electro-discharge machining (EDM) to create two fluid ducts on either side of the membrane. The device described in this paper is fully micromachined, has fluid on only one side of the BM, and is driven by airborne sound. The BM is 3 cm long, made of a stacked thin film structure (Au/Cr/SiaNVSKVSisN,,), and tapers exponentially in width from 170 ixm to 1.9 mm. The three-layer dielectric is used to partially compensate the high tensile residual stress in the Si3N4. The metals are for optical reflectance. The fluid duct is 6.25 mm wide, 0.5 mm high, and filled with 200 cSt silicone oil. The high viscosity fluid was needed to suppress the formation of standing waves. Figure 1 shows a drawing of the device and the fabrication process. PlexJtite, vartatMe wftftfi

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Figure 2. Laser Doppler Velocimetry (LDV) data showing the magnitude (left) and phase (right) of the membrane displacement along the centerline for 5 different pure tones present in the environment. Phase lag is approximately three cycles (6n radians) at the "Best Place". The magnitude of the response is 0.20.5 nm/Pa at the "Best Place".

LDV results show traveling waves with similarity to those seen in the insensitive cochlea. The device responds at high frequencies (10-70 kHz) due to the low compliance of the BM (residual stress is -500 MPa). The magnitude of the observed displacements (0.2-0.5 nm/Pa) is smaller than those observed physiologically, due to the lack of a middle ear, lower BM compliance, and lack of any OHC-like structures. A complete description of a similar device including mathematical models can be found in a recent work by the authors [4]. Acknowledgments Funding from the Office of Naval Research and the National Science Foundation. References 1. Zhou, G., et al., 1993. A life-sized physical model of the human cochlea with optical holographic readout. J Acous. Soc. Am., 93, pp. 1516-1523. 2. Lim, K-M., Fitzgerald, A.M., Steele, C.R., Puria, S., 1999. Building a physical cochlea model on a silicon chip. In: Wada, H., Takasaka, T., Ikeda, K., Ohyama, K., Koike, T. (Eds.), Recent Developments in Auditory Mechanics. World Scientific, Teaneck, NJ, pp. 223-229. 3. Hemmert, W., et al, 2002. A life-sized hydrodynamical, micromechanical inner ear. In: Gummer, A. W. (Ed.), Biophysics of the Cochlea: From Molecules to Models. World Scientific, Teaneck, NJ, pp. 409^16. 4. White, R.D., Grosh, K., 2005, Microengineered hydromechanical cochlear model. Proc. Nat. Acad. Sci., 102 (5), pp. 1296-1301.

A GENERIC NONLINEAR MODEL FOR AUDITORY PERCEPTION

E. W. LARGE Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL 33486 E-mail: [email protected] This paper proposes a novel model for central auditory processing, a network of nonlinear oscillators. The properties of such networks are common to a family of physiological models that includes active cochlear models and oscillatory neural networks. Auditory perception can be modeled based on the generic properties of such physiological mechanisms, providing a bridge between physiology and psychoacoustics.

1 Introduction Recent evidence has led to the proposal that active amplification, in the form of Andronov-Hopf type nonlinearities, is the basic mechanism of the mammalian cochlear response [1]. The cochlea may perform a sort of nonlinear (active) frequency transformation, using a network of locally coupled outer-hair cell oscillators. Nonlinear frequency transformation has also been observed at the neural level. Neurons that respond selectively to temporal and spectral features of communication sounds have been discovered in the central auditory systems of a variety of animal species [2]. Interval selective cells in the midbrain of the fish Pollimyrus, for example, have been succesfully modeled as nonlinear neural resonators based on anatomical and physiological data [3]. Moreover, nonlinear resonance is a plausible candidate as a neural mechanism for pitch perception in humans [4]. This leads to the hypothesis that the mammalian auditory system performs nonlinear frequency transformation of incoming auditory stimuli at the periphery and also in the central auditory nervous system. After an initial analysis by the cochlea, networks of neural resonators further transform the stimulus. 2 Model and Discussion A neural resonator can be modeled as a simple network of two neurons, one excitatory and one inhibitory [5]. A nonlinear frequency transform can be computed using a network of coupled neural oscillators, each tuned to a distinct eigenfrequency, and driven by an external stimulus. Normal form analysis of such a network reveals a number of generic properties of nonlinear frequency transformation. These properties include extreme sensitivity to weak stimuli, sharp frequency tuning, amplitude compression, frequency detuning, nonlinear distortions, and natural phase differences. These properties predict many significant psychoacoustic phenomena, including hearing thresholds, frequency discrimination, loudness scaling, Stevens' rule, combination tones, pitch shift and dichotic pitch.

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Some of these phenomena can be explained by cochlear nonlinearities, however others appear to require (at least) a second nonlinear transformation operating on the output of the first. For example, cochlear frequency tuning worsens as stimulus intensity increases, yet frequency discrimination improves. Figure 1 illustrates a model that can explain this perceptual phenomenon. Nsural Network

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Figure 1. (A) Andronov-Hopf cochlea driven by a high intensity sinusoid (radian frequency ). The network of neural resonators displays sharp frequency tuning. Time and frequency (relative to the stimulus) are shown on the horizontal and vertical respectively; gray level indicates response amplitude. (C) Comparison of response amplitude and tuning.

Acknowledgments This research was supported by NSF grant BCS-0094229. References Choe, Y., Magnasco, M.O., Hudspeth, A.J., 1998. A model for amplification of hair-bundle motion by cyclical binding of ca2+ to mechanoelectricaltransduction channels. Proc. Nat. Acad. Sci, 95, pp. 15321-15336. 2. Crawford, J.D., 1997. Feature detection by auditory neurons in the brain of a sound-producing fish. J. Comp. Physio. A, 180, pp. 439-450. 3. Large, E.W., Crawford, J.D., 2002. Auditory temporal computation: Interval selectivity based on post-inhibitory rebound. J. Comput. Neurosci., 13, pp. 125-142. Cartwright, J.H.E., Gonzalez, D.L., Piro, O., 1999. Nonlinear dynamics of the perceived pitch of complex sounds. Phys. Review Letters, 82(26), pp. 5389-5392. Wilson, H.R., Cowan, J.D., 1973. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55-80.

VI. Discussion Section

DISCUSSION SESSION July 27, 2005 Moderator: Jont B. Allen This text was generated based on transcript of the discussion session held on evening of July 27 during the conference. All participates were aware that the session was recorded, and the edited transcript would be published. Note added in proof. The editors believe that certain controversial topics in this meeting did not receive balanced discussion from all points of view and thus advise the readers to consult additional independent texts. Nuttall: I have asked my colleague, Jont Allen, to take your questions and organize this discussion session. I will now give Jont control of the session. Allen: Thank you very much, Fred. We have a few ground rules for tonight. Many of you have been at one of these events previously and you know sort of what to expect. We're here for several reasons. The most important thing is that there are lots of young people entering the field, and they have never witnessed all of this opinion, disagreement and argument before. We are going to cover at least four major topics, and everybody who hasn't attended a mechanics workshop discussion session before will be shocked to find out how much disagreement there is. I suspect that will be the case. I was a little shocked myself last time, three years ago. Important science can show up in discussion and many of the comments from that previous workshop were quoted in papers. So this discussion event will also be published. We are recording the session, so when you start to speak, it's essential that you identify yourself. Try to do so clearly and that's one of the important ground rules. Ok. I am going to tell you about the organization of the discussion. First I have some general quick questions; hopefully they have very short answers. Then we are going to talk about stereocilia and tip links and associated matters. Finally, we will have a knockdown drag-out about waves in the cochlea. I will probably leave at that point and let you guys battle it out.

Quick Questions Allen: Here's a quick question. Has anybody measured the viscosity of endolymph? It's been measured in a shark, and in a pigeon, I believe. As I remember it's close to water. So, no surprises there. Should modelers be required to submit their code along with their paper? As a way of documenting what they did and what they did wrong? Yes. Who would understand it? Anybody disagree with this view? Is there anybody who has written a paper doing modeling would not agree to sharing code? Make it available. It's extra

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work. A repository. I think the way to handle this is that authors should give it to you if you want it. de Boer: I have shared code 20 or 30 years ago when computers were just starting to become important. In general, the principle is that people should be able to replicate a model program; if you want to have the program, just contact me by email. I think that's a very efficient and simple way to do it. Allen: So the next question is, can sinusoidal stimuli be used to characterize hair cell dynamics? Is it necessary for cell biologists to use steps? Any comments? How about a comment from a cell biologist? Santos-Sacchi: I think you can get different information. For example, if you look at step response, you might be able to see, for example, as Jonathan Ashmore did, a little capacitive current indicative of the charge movement that we now know is due to prestin. That might have been missed if only an A.C. analysis was done. From the audience: Why not both? Santos-Sacchi: Both are fine. But don't throw away steps. Steps are just as important as sinusoids. Guinan: The classic reason for using steps you brought something to a given voltage and held the voltage fixed; in a the voltage controlled circuit, that allows you to remove one free parameter. Allen: In my opinion if you have sinusoids in steady state, the system is so highly nonlinear you won't figure out anything. It's not like a filter, but of course there's filtering in it. From the audience: A brief comment. I think that it depends on what you are measuring. If you are measuring in the complete system, then it's a different topic than if you are measuring in single cells. Because one of the things for a complete system is that if you put in clicks or other broadband signals you are getting a very different response than if you want to focus, lets say, on the channel of the cochlea, then you have to be very careful about the amplitude of the stimulus. Allen: We have one more minute on this topic. Nobili: As far as the system is linear, the responses to steps and the responses to sinusoidal frequencies will produce the same information. The difference takes places in cases where the system is nonlinear. So you should find what is the more useful signal to test.

523 Allen: Ok. I think we should go on there are lots and lots of questions. Does the group delay always give a physically meaningful delay? Why can it be less than zero? Personally, I think this is a question that should be handled off line because it's got a straight mathematical answer, so I would like to not pursue that. Here is serious question from an experimentalist. He wants to know, what do modelers want from experimentalists? He's soliciting ideas for experiments. What do you as a modeler - this is for the modelers - what do you feel that you need to have that you don't have? Nobili: Regarding this point, the problem is whether there is capability of understanding theory by experimentalists, and whether theoreticians understand what experimentalists are really doing. In physics, the state of affairs evolved to such a point between the two categories, experimentalists and theoreticians, that another category arose, the phenomenologists. We try to mediate between the two other groups. So maybe we need to also make a third category to allow passing of information from experimentalists to theoreticians. Grosh: It's not a simple question in my opinion. There's so much information that's needed, but particularly important is a description of the experimental conditions, such as boundary conditions: how did you terminate your preparation? What kind of electrical conditions did you use? Those kinds of things are key to our simulations, although we can always come and ask you later. In terms of characterizing nonlinear systems, we need a range of voltage, force, and displacement stimuli. For instance, if you are going to measure stereocilia properties then we need to know if they have cycle-by-cycle regenerative properties, and so measurements should be made about an operating point where those properties are optimal. Those kinds of complete specifications, force, charge, voltage, and displacement, are needed for a model. Mountain: I think one word the answer is collaboration. It's really key that experimentalists and the modelers talk together - there's so much extra information, like these set points, the conditions under which the experiments are done, the variability, that it's very hard for a modeler to really appreciate the data they are extracting for publication. So what we have to do is facilitate the interaction between the experimentalists and the modelers. Allen: One more, let's say - Al. Hubbard: In a sense, this is what David was saying but it's a little more general. We need parameters. We look at a paper and we see some measurements and we say, OK, how can we glean from these data a value that goes into our model? A lot of times we can't get back to a parameter that goes into the model. We need

524 numbers. The other thing is that at the other end we need validation for our models; a model that isn't validated isn't worth considering. Santos-Sacchi: I would like to make a point from the other side. The modellers need to be careful not pick up a certain piece of information and base everything they do on it. For example, when someone sees one of Mario's nice tuning curves, they try to fit it exactly. But if they are off at a single point at particular frequency, they feel they didn't fit the data very well. But if Mario published all of his tuning curves, you would see that some of those modeling efforts would fit it and some not. So don't go crazy with the parameters that experimentalists get. There's variability in it and just keep that in mind. Allen: Ok. We are going to move on now.

Stereocilia and Tip Links Allen: Do inner hair cell cilia attach to the tectorial membrane? Fridberger: I have imaged a lot of inner hair cell stereocilia and I never seen one that was inserted into the tectorial membrane. But that doesn't exclude the possibility that there could be some kind of weaker link between the two. Some link we cannot visualize in a microscope. LePage: There are lots of pictures, e.g. in David Lims publications, and so forth have produced rather beautiful images, not of inner hair cell stereocilia embedded in the tectorial membrane but able to rub against it. Additionally there are so called 'trabeculae' that may serve to keep the tectorial membrane becoming too far separated from the stereocilia. Ruggero: Charlie Liberman has very explicitly showed an attachment between the Henson's stripe and the tallest stereocilia of the inner hair cells. I am sure he would hold on to that opinion today. Allen: Is there an effect of the cilia stiffness on the basilar membrane impedance? Chadwick: I believe that Dylan Chan showed that there was. Allen: For me it's also a question of how much. Mountain: In my lab we measured the stiffness of the basilar membrane from the underside both with the organ of Corti cells present and with the cells removed. The stiffness changed by a factor of two. It was our interpretation that most of that change was due to the Dieters' cells which could be rather stiff because of their

525 microtubules. This measurement would put a bound on how much the stereocilia stiffness could contribute to the overall stiffness. Allen: The next question is, what's the evidence that there are channels located at each (or both) ends of the tip links, versus just one end? Karavitaki: Denk et al., 1995 did calcium imaging studies and showed that the calcium entered from both sides. Gummer: When you carefully read Denk et al., 2005 it seems they were very careful about stating the location of the channels. Did he actually say they were? Definitely? Karavitaki: If you didn't expect to have channels at both ends of the tip links then you wouldn't see what they show. Let's say, you only have a channel on the side that connects toward the tallest stereocilium. Then you wouldn't expect to see calcium entering the very shortest stereocilia in the bundle. On the contrary if you only had the channels on the tip link end toward the shortest stereocilia, then you wouldn't expect the very tallest stereocilia to be labeled. Their study showed both ends actually labeled. Allen: Sounds like a pretty good line of reasoning. Guinan: That doesn't rule out, that an individual stereocilia have channels at both ends. Allen: It doesn't tell you about the distribution. Guinan: In a given row of stereocilia, you could have half of them with channels at the bottom and half at the top and it would produce that result. If the bottom row had half pointing up and half pointing down, then, you would get that same kind of pattern. Allen: Then some wouldn't label. Guinan: He didn't see labeling to all stereocilia. He saw labeling in all rows. Karavitaki: In the last figure of the Denk et al., 2005 paper you can see the entire row of the tallest stereocilia and the entire row of the shortest stereocilia are labeled. Guinan: Maybe I'm wrong. My memory was that there were a lot that were missing.

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Dallos: I think maybe a better question is whether the two channels per tip link is good. It sounds like a terrible design to me. Isn't that an inefficient design? It's anti-cooperative.

Somatic Motility of Outer Hair Cells Allen: Now we will move to outer hair cell soma, and the first question is, how stiff is the outer hair cell soma in vivo? So I guess the question is, we know that it's been measured in the microchamber so I am presuming that the nature of the question is, will it be different in the cochlea? If so, how different and does anybody have any insight into that question? Well, you might just guess that the membrane potential in vivo if you believe the high impedance recording. Santos-Sacchi: You might take the in vitro data and the in vivo resting potential if you believe the high impedance results. Just simply calculated. So at minus 70 milivolts, Peter, tell them what the stiffness was in your in vitro preparation and maybe that's the answer. Dallos: Well, extrapolating from in vitro measurements to in vivo measurements is a very difficult process and a very hazardous one. You can simply do what Joe says. Then a high negative membrane potential where also the stiffness of the cell is the highest. In other words, the cell presumably in situ is quite stiff. Which is on the top range of what people measure in vitro. Allen: So, I guess the answer is it's pretty hard to know for sure but best guess is to take existing data and project on to the resting potential as we know it. Our next question is, are outer hair cells compressible? Well, it's assumed generally that the volume is constantbecause the fluid can't get in and out. But if you squeeze it gets bigger and if you squeeze it that way it has to get longer so I guess the question is a little bit vague, in terms of what compressibility is. Allen: Is there feedback between outer hair cells? I think the question is, if two outer hair cells next to each other is there some communication or feedback? They said feedback there but let's just say some kind of communication, it is obviously a mechanical communication. Santos-Sacchi: Yeah. Yes. Hong Bo Zhao and I have a paper, I believe in nature in 1999. We looked at two isolated cells but adjacent cell was situating with supporting cells around them. We stimulated one cell with voltage, which mechanically drove that cell, and then simultaneously with another patch electrode recorded gating currents induced by tension changes from the movement of the first cell. So there are mechanically coupled. They are coupled to their neighbors, yes.

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How strong that coupling is, and whether that coupling is truly significant for the functions? Allen: Is there any gap junction in the reticular lamina? Santos-Sacchi: No gap junctions between supporting and hair cells. Allen: Is there any calcium communication like we saw today in the supporting cells? Santos-Sacchi: Between supporting cells, yes. But Fabio talked about supporting cells but not between hair cells and supporting cells. Allen: The question was, you don't have to answer the question, but the question was about outer hair cells. Santos-Sacchi: No, nothing between supporting cells and hair cells. Allen: There are certainly mechanical linkages through the tectorial membrane and the basilar membrane. Santos-Sacchi: That's right. Allen: There are also the pillar cells that are going up. Also have the cells going across and making — Santos-Sacchi: So these mechanical movements of supporting cells could influence the outer hair cell. That's possible. Allen: So we always would like to learn more about that but it's a complicated question. So next question is, what happened to Pat Wilson's swelling model? Might like to mention that we now, some of us feel turgor pressure of the hair cell is quite an important variable and I guess that you could interpret that as a swelling model. Anybody want to describe pat Wilson's swelling model? That should die a quiet death. Peter says let it die a quiet death. Ruggero: I think that this is like the story that someone used to tell about the horse that could count and somebody complained that the horse made a mistake. And he used to point out it's not how well it's done, but that it is done at all. So the swelling of the hair cells, was simply a mechanism for him to be able to explain or to give a hint of how it was possible that the stimulus frequency emissions he was measured in the ear canal could happen simultaneously without any noticeable delays with microphonics which means the acoustics, that was propagating at the speed of

528 electrical signal. In other words, it was nearly instantaneously. The outer hair cells may or may not swell but the issue of propagation is very much alive as far as I am concerned. Allen: Well, it's known if you stimulate the ear at 100 dB for a long time the cells swell up quite a bit. Right? The vesicles burst and cells explode. I don't think this is what Pat Wilson was talking about. Another thing we would learn so much about inner and outer hair cell physiology in the intervening years I think somebody's early ill-informed in the sense we knew so little at the time, it's probably — let it die. Cooper: I don't care whether it lives or dies. The physical situation that Pat wanted to exist was a hair cell to act as a source of pressure, which would initiate a rapid wave backwards. I think there has been some experimental evidence, for example, where pressure source applied near field to an outer hair cell body evoked contractions with peculiar characteristic and I would like to know whether any of you isolated outer hair cell people have looked for a pressure radiating, pressure field radiating from an electrical stimulated outer hair cell, for example, it moves with the act of the pressure source. What? Does it act as a pressure source? Santos-Sacchi: So far away can you sense the fluid? Yes. It seems a sensible experimental at least. It should be simple. Well, you mean does an isolated cylinder by changing its length send out a pressure wave? It relates to the — I would imagine in the -within the organ of Corti where there are structures that are moved like that, yes, this must get transmitted. It must move beyond its local region. Fluid is going to move. Isn't how you get the 20-db gains? The question is whether it moves, far away to go out to the ear canal? Yes. There's no ear canal when we isolate the cells. Mountain: I was going to draw an analogy with a mosquito. When you have something moving, which is very small compared to the wavelength of the sound you are interested it definitely create a pressure in your ear field. That's why we ear mosquitoes when they is almost in our ears. As soon as they are any distance away there's essentially nothing in the far field and the hair cells are so small compared to the acoustic wavelengths in water that you wouldn't expect anything from a hair cell in the far field. If it was, a bunch of hair cells were moving very large structure that would be the only way you could Allen: It's especially true given it's constant volume at acoustic frequency so it's going to have to give rise. Mountain: A mosquito is a constant volume at acoustic frequencies. [Laughter] not if it draws your blood.

529 Raphael: Maybe this pressure wave is what we are seeing in the tether experiments when we oscillate the voltage. We can modulate the model. Allen: The next and the major discussion for the rest of the night is waves in the cochlea. From the audience: Before we move on to waves, I want to propose one more question for outer hair cells, which is, what is the static load on outer hair cells? We know they have turgor pressure. But there are other external forces that impose a static load like you would do if you were building a piezoelectric drive system. Allen: Anybody have any ideas about what the static load on an outer hair cell might be? I assume you mean in quiescent state. Yes. The Dieters' cells static compression? Allen: Doesn't sound like anybody has any brilliant ideas on this. Nobili: There is evidence from a movie, detected by Fabio, that the Deiter's cells are, mainly viscous. They seem to deformate as a viscous tension so the problem is whether the Dieter's cells are mainly viscous or mainly elastic - because depending on the one or the other, we have different model of the outer cell models. Chadwick: I have a related question. How do you look at a movie and determine mechanical properties? If you look at a movie and I have seen your movie. You have sent it to me and you insist the Deiter cell is viscous. How do you know they are viscous by looking at a movie? Nobili: Because their motion, this way. So I think that something that forms these waves is viscous. Allen: Shall we vote on it?

Waves in the Cochlea Allen: The next question on waves is: are there evanescent waves in the cochlea? First, let me just describe an evanescent wave. A wave that is propagating can be described as exp(jax/c). An evanescent wave is when you have exp(-ax) - where "a" is positive and real. So it's in phase everywhere and it's in the so-called state of cutoff. I believe that's a fair definition. Now, the question goes on. If there are evanescent waves, are there certain distortion products which might be driving an evanescent wave and what would be the implications of that? That's the entire question.

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van der Heijden: To the extent that an evanescent wave would give you a phase plateau, when varying the stimulus frequency. Our measurements from the auditory nerve hardly, well, almost never give us phase plateaus such as observed in the mechanics. That's also true for high frequency neurons, high frequency fibers. So in our measurements of the auditory nerve, we don't find any indications of evanescent waves. Provided they go with phase plateaus but I don't know if that connection is true. Allen: Is that phase plateau that's seen in the basilar membrane, for example, in Rhode's data, is that a result or an artifact due to the fact that the cochlea is open? van der Heijden: That is a very interesting question because there is some controversy about it. I think that, if you look at the amplitude growth, the input/output amplitude function at the phase plateau, is more linear, that is I think a strong indication of an artifact because up until that plateau the growth is increasingly compressive. But if you go above CF ... But maybe that's not true. Ruggero: We have direct data bearing on that but before I mention that I should say that at the Careens France meeting (Auditory Physiology and Perception. Eds: Cazals et al. 1992, Pergamon Press) Pat Wilson made a very clear point: on the one hand recognizing that the best basilar membrane data, including his own, showed the plateau and that on the other hand there was very little evidence, like Marcel has said, in the auditory nerve. I think that we carried out the ultimate experiment in the Narayan et al. paper in Science (1998, 282, 1882-1884), in which we recorded in two chinchilla cochleae basilar membrane responses and auditory nerve fiber responses with the same characteristic frequencies with the cochlea in identical circumstances. The plateaus that we were seeing in basilar membrane responses were definitely not seen in auditory nerve fiber responses. Like Pat Wilson said, probably this is something that is great fun for us basilar membrane mechanicians but of no practical consequence to the brain. Allen: Since we are on this topic, I would just like to point out that an evanescent wave as I understand it, has constant phase and, therefore, has an infinite group velocity or phase velocity which if you are looking for a way to get something quick from point A to point B, an evanescent wave might be a good way to do it. However, you pay the price because it exponentially dies as it propagates. From the audience: But it [the evanescent wave] transports no energy. Fahey: Evanescent waves do transport energy. If you do total internal reflection, say, at an interface, there is energy that gets into the transmission medium and that's been used by Dan Axlerod at University of Michigan to measure objects within a wavelength of the surface of a cell. You can light up a fluorophore that way. So

531 energy does, in fact, get in there. Now, it occurred to me that I think there's evidence for evanescent waves in distortion products if you look at the upper side band, 2f2 - fl. That's created around the f2 place and Glen Martin showed a couple of years ago when he tried to suppress 2f2 minus fl, that the frequency which suppressed it was around 2f2 minus f1. In other words, it was suppressed at its own place. It had to be generated at the f2 place, propagated as an evanescent wave to its characteristic place and then radiated from there. So I think in the distortion product there is evidence. Chadwick: I would also like to remind people about Peter Narin's lecture about the golden mole. It was using evanescent waves because the Rayleigh and Love waves in elasticity are evanescent waves - they die away from the surface. So obviously there's energy in them. Nobili: I think that, yes, the evanescent wave may occur in the cochlea. Why? Because if you consider the behavior of the phase of the traveling wave, you see that the phase in the basal end is mainly imaginary and on the apical side, it is mainly real and indeed the phase changes up to a certain point, and then the amplitude falls down exponentially to zero. This happens because of the exponential decrease of the stiffness. Assume that the stiffness at a certain moment goes down and then goes up. Then you obtain a traveling wave that becomes again imaginary beyond the interval in which there is the decrease of the stiffness so you can bridge the two parts through an evanescent wave. But in order to have this, the stiffness profile must depart substantially from the regular profile we know. Mammano: I just wanted to comment on the Axelrod optics analogy. I happen to teach a course on microscopy and I have built my own total internal reflection microscope so I don't want to get into evanescent waves in the cochlea and try to make this point clear that to get the evanescent wave to work in microscopy you have to frustrate total internal reflection. There must be something there, like a fluorophore, that picks up the photons. If there is nothing there, all the energy is reflected back. Allen: So — it's like a reactive field and you have to couple energy back out of it. Mammano: It is like a tunnel effect. If you cannot tunnel, all the energy goes back. Allen: So a classic example would be to take two prisms. You have light coming in at a Brewster angle and there's an evanescent wave on the backside of the prism in the air. If you pull another prism up close to it, you can couple that exponential [evanescent] wave into the second [prism] and you will have light come out of the second prism. But, you have to have that second prism there.

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Grosh: Paul's point is one natural way where an evanescent wave might be generated. The other place is near the stapes where you generate near fields, which don't all propagate through the cochlea. That's another place where evanescent waves would occur. Gummer: Just a point to Richard's (Chadwick) comment about the golden mole and evanescent waves through the sand. That's definitely not true. I mean, that is a Rayleigh wave and the diameters of those trajectories are reduced through the sand and if you look at points of constant phase you have a traveling wave through the sand. That's not an evanescent wave in the depth of the sand. That's a traveling wave. Chadwick: Any wave that dies off ... Gummer: It's not an evanescent wave. It's a traveling wave. (Grosh:) It [the Rayleigh wave] is a surface wave. Gummer: They are traveling but they are traveling also through the sand just like a traveling wave is traveling through the fluid in the cochlea. de Boer: I would like to complicate matters. Evanescent waves are very simple things. As everybody has described them and as you have introduced them. They are occurring in models. Now, do we have evidence of evanescent waves in the response measured in the cochlea above the cutoff point, above the peak point? Then, I want to give attention to those 'wiggles' that have been described by Recio and Rhode and by Mario Ruggero and that we have found also. When you are beyond the peak of the response you will observe dips and valleys. I have been trying to find out what they were but so far in vain, and I haven't seen any explanation of it. But it's certainly not a simple evanescent wave. Such a wave might be a component in it but what the full explanation is I don't know. Have I complicated the issue enough?

Fluid Flow in the Cochlea Allen: I think we will move on. We have got some really interesting things coming up immediately. Is there fluid flow in the cochlea? I think what this question is getting at, is there actual fluid moving from one place to another? An example, which I am adding, this was not part of the question: Von Bekesy saw something called acoustic streaming in the cochlea and many people believe that it was an artifact of the extremely high sound levels that he used. But that is, I would say, probably not completely resolved, but in any case it has been observed at least in models, physical fluid models of the cochlea. They're theoretically there but I think

533 the question is, has anybody ever heard or thought about fluid motion in the cochlea? Chadwick: Well, M. J. Lighthill wrote an 80-page paper about it in The Journal of Fluid Mechanics. The title is called "Acoustic Streaming in The Ear Itself. Nobili: Excuse me. Clarify, please, the question. Do you mean that the fluid passes across the helicotrema? Allen: No, just down, probably down the cochlea. Is there actually fluid motion flow, if you put a drop of ink in there, would it move down the cochlea? Not just vibrate back and forth - a DC component. LePage: I'll just talk about that exact point: In the late 1970's Brian Johnstone and I did some experiments with dye injection. Specifically to see if there's any bulk streaming flow in the subtectorial space. We put methylene blue in artificial endolymph and injected it into the scala media, in either the outer or the inner sulcus. Indeed you could see streaming across the subtectorial space under injection pressure. But if you just left it to be controlled by sound, in other words, turning the sound on and off and going through a whole variety of different frequencies and levels, we did not see any dye movement. Allen: Steve (Neely), what about your energy calculations, the curling? Neely: This is not addressing the fluid flow question. But it does pertain to Burt de Boer's earlier question about what causes the ripples after the cutoff. If you solve the two dimensional cochlear model, you see in the transition between the traveling wave and the cutoff region, where the evanescent waves are, that there are places where the pressure goes to zero in the fluid and sometimes those places come down to the basilar membrane, (de Boer:) I have never seen that. Allen: Explain your observation about the phase delay as a function of position and how there must be discontinuities in the flow. The velocity is slower close to the wall than it is down near the basilar membrane and therefore there can't be continuity in phase? Neely: I don't know what this really has to do with flow. But in Lisa Olson's measurements of the pressure in the scalae, there are more cycles of phase down near the basilar membrane than there are higher up above the basilar membrane. So there have to be places in the fluid where there's a complete cycle of phase around one point and the pressure goes to zero at those points and maybe there's circulation

534 around those points. But I'm not sure exactly, no one has studied these points in the fluid. But they have been observed. Karavitaki: I am not sure I can give an answer but I can just say, when using electrical stimulation in an excised cochlear preparation where both ends, the end leading to the apical turn and the end leading to the basal turn, were open, that we have observed motion of the medial cochlear fibers going back and forth in response to contraction and expansion of the outer hair cells. We interpret this motion of the fibers as picking up some flow that is going back and forth in the tunnel of Corti. Allen: Anybody else? de Boer: Has this been published? Karavitaki: This work has been presented three years ago in this meeting.

Traveling Waves in the Cochlea Allen: What evidence is there for energy traveling waves in the cochlea? Or are they really just standing waves? van der Heijden: We had a poster here, from a lot of phase measurements from the apex of the cat from single animals mapping out the phase in the phase locking region from 100 Hz to 5 kHz and the phase profile was clearly consistent with a traveling wave for all frequencies we could consider. So we had enough points to unwrap phase both across stimulus frequencies and cochlear locations, that is CF, to actually map out the whole phase pattern. That was completely consistent with traveling waves, no doubt about it. Allen: How many people would vote for there being, in their opinion, energy or traveling waves in the cochlea? Raise your hands. How many people ~ don't vote twice now — how many people would vote that the waves that are seen are not traveling waves? We got one, two, we got three. de Boer: Can I vote half? Allen: Well, why don't you respond to the question? de Boer: Again, the situation is more complicated. You can describe the cochlea as having and showing traveling waves. What is that traveling wave? That is a wave that is going through an infinite number of resonators. First tuned very high and then tuned to lower and lower frequencies until you reach the region where the

535 frequency of the resonator is in the neighborhood of the frequency you are stimulating with. And it is there that something special happens. You can call that a traveling wave. You can also say, well, that is the response of a set of coupled oscillators with staggered tuning. I hesitate to use the word minimum phase. Ruggero: Why should you? Go ahead! de Boer: Then we would have to start all over again by first defining that concept precisely (for the type of signals under consideration). I think it is better to see the cochlear response either as a traveling wave leading to a maximum, or what is equivalent, the response of a set of coupled oscillators with staggered tuning. Allen: I think that we need to be very careful about a traveling wave in terms of a measured property and not in terms of a specific model. If you come to the conclusion that it's one or the other, based on a model, then, that's circular reasoning in my opinion. Ruggero: In general, I agree with what Burt (de Boer) said. To the extent it puts the emphasis on that if it walks like a duck, it quacks like a duck, it has feathers like a duck, I call it a duck. However, I do think that we should talk about minimum phase. I think that the popular conception that the cochlear traveling wave is minimum phase is wrong and, furthermore, we have evidence that when the basilar membrane is not fully developed ... By the way, I am talking about passive waves, I am talking about Bekesy's cadaver waves. Those are not minimum phase. But when the basilar membrane is not fully developed, we do have a resonant-type behavior that is minimum phase. Duit'lluis: I think the important question is not whether you see the amplitude being transported as a traveling wave because you can have lots of discussions about it and it can depend on a lot of model parameters or species parameters, the relevant question is whether there is a net energy flow. I think that is where the evidence is quite clear. Dallos: I just sort of have an auxiliary question because I think about these things in every simple-minded way. Is there a demonstrable front-end delay in a particular location where you measure in the cochlea? If there is a front-end delay, it has to be a traveling wave. It has to get there. Measure the delay with respect to the motion of the stapes and then you somehow measure, like some people are able to do now, in the higher turn in the cochlea. You send in a signal, is there a real delay or not? That's the question. Ruggero: Peter, thank you. You took my shorthand and made it into a clearer proposition. What I meant by the cochlear traveling waves not being minimum

536 phase is that there is now plenty of evidence for about 40 years courtesy of Nelson Kiang in his book that there is a real delay at the apex of the cochlea. We have now an enormous amount of evidence for the chinchilla that has been published a month and half ago in the Journal of Neurophysiology; by Gummer's group, (Zinn et al. 2000, Hear. Res. 142, 159-183) in the guinea pig cochlea in the apex; Cooper and Rhode (Aud. Neurosci. 2, 289-299, 1996) in the apical region of the chinchilla cochlea; and most interesting, Bekesy, 60 years ago, measured tone responses in the human cadaver cochleas. [Of the latter], Flanagan said that those responses were minimum phase and they were. But what Flanagan forgot is that Bekesy had measured signal front delays at the 200 Hz place where Flanagan said they were minimum phase, intervening between zero and 1.5 milisecond there was a signal front delay that was a substantial portion of the period of stimulation. So the answer is, that contrary to the popular assumption by modelers of the cochlea, the cochlea is not minimum phase and probably the traveling wave means not minimum phase. Mammano: Please let me try to make a point on what should be unequivocal physical reasoning. In all wave phenomena described in physics, there is a local relationship between one variable and another one, say, the electric field or the magnetic field or kinetic energy and potential energy, and when wave equations are derived, there is locality of the variables. What we are saying is that, by the very nature of the shape of the cochlea and the internal hydrodynamic coupling between all of its elements, this does not apply to the cochlea as a system as a whole. You cannot derive its equation based on local interactions. This is all we are saying. The consequence of having delays as a result of clicks being applied at the stapes and observing a delay at the apex does not mean that there is wave propagation. It only means that this particular oscillator takes some time to develop its response after the excitation at the stapes. You can say that there is a phase traveling and you can call it a traveling wave. However, where is the energy in the meantime? Where is it? No, the energy is not traveling because the pressure field applied by the stapes is (apart from a 10 microsecond delay due to the non-zero compressibility of water) instantaneously built up by acceleration of the stapes. Where is the energy — it's all over the place, it's in the pressure field and in the elastic energy of the basilar membrane. The moment you apply a force to an incompressible fluid that force is propagated almost instantly (within a 10 microsecond) delay all over the place. This is all we are saying. Chadwick: You are absolutely clear now. I understand what you are saying and you can say the same thing about waves in the ocean. Nobody thinks that you don't have waves in the ocean. However, you don't have a wave equation for waves in the ocean, you have a process equation. It's the same thing.

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Mammano: No, I don't think so. Because the way in which waves on a surface develop is through local interaction of elastic forces and masses and — (Chadwick:) We have gravity as a restoring force like the stiffness of the basilar membrane. Duifliuis: If there is any energy dissipation within the cochlea, you're missing that part of the story in your explanation. You're only talking about the so-called fast wave and the effects of the cochlea reacting to that. But once you consider the slow wave, there is definitely energy propagation to the place where it is dissipated. Mammano: No, I don't think so. Energy is being dissipated most near the point where the basilar membrane oscillates maximally because there you have the largest displacements and the largest velocities but you don't have to propagate energy to that point. It gets consumed there but not propagated there. It's all over the place. It's inside the fluid, in the form of kinetic energy, and as potential energy from the basilar membrane's elasticity. We are saying that, if the equations can be simplified to look like those of a transmission line, we don't disagree with that. You can make all the approximations that you want and the resulting wave shape will look very much like the one that you see. However, on the transmission line the concepts are different. The underlying mechanisms are different. In a transmission line you need sequential activation of one oscillator after the other. Allen: What you are doing — which I have a problem with — is that you are basing your comments and your opinions on a model rather than on the data. If somebody gave you the data and they didn't tell you where it came from, you would have to make a decision whether there was a traveling wave. Mammano: I think based on the data you would say that there is phase traveling. We are not questioning that. Talmadge: I have a couple of quick comments. I absolutely 100% agree with Richard Chadwick in his analogy with the surface gravity waves on the ocean. It's a perfect analogy. Another example is, there's sort of a buoyancy wave in the atmosphere where you make the assumption of an incompressible fluid, and you get traveling waves. Finally, you can write down a wave equation for the surface wave on the basilar membrane in the cochlea. Just because you can write down a wave equation, that seems to be pretty definitive evidence that there is, at least within the constraints of physics, a wave.

Are Traveling Waves in the Cochlea Going in Both Directions? Allen: Many of us have sort of agreed that there are traveling waves. I think we have been talking about the forward-going waves so the question is now: is there a

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traveling wave going in the backward direction? Of course, this has become a hot topic. Talmadge: The ordinary wave equation is a second-order differential equation and it provides a solution for both forward-going and backward-going traveling waves. In addition, when you do the modeling of cochlear mechanics, correctly, of course, you also get a compression wave and there's nothing against saying that you can't have both the compression wave and the reverse traveling wave in the model. Then, it just becomes a question of which is the dominant of the two modes that gets transmitted back to the stapes. That is more an experimental question I guess at this point. de Boer: I couldn't agree with Carrick (Talmadge) more. Allen: I have a feeling we are going back to the previous question. Nobili: It is 15 years that I am insisting about what is a traveling wave. Jont (Allen), surely you know what it is but I think that you don't say what your opinion is because you don't like to be in disagreement with people that have different opinions. Now, let me offer some other piece of information, with respect to what has been said by Fabio (Mammano). We must distinguish between phase velocity and group velocity in any sort of wave oscillating in a medium. For dynamical reasons, different parts of a wave differ in phase and under certain conditions the wave transfers energy. This is for instance the case for sound waves. If you take an elastic string and you shake it at one end, a wave oscillation suddenly starts. If you stop shaking the string, there is a wave train propagating along the string and if that string is infinitely long the train propagates forever. This wave train transports energy, there is a transfer of energy between adjacent elements of the string. If you compute the force exerted by each element of the string on the adjacent elements, and the local displacements of these elements, you find that a certain amount of work is done by each moving element. Thus you have a waveform with different phases at different points and you also have an energy flow. Since the system is symmetric with respect to the length of the string, you can have two propagation directions. Indeed, if you shake the string at some intermediate point, you obtain two propagating waves, one moving towards one end and the other one towards the other end. Both trains carry energy — Allen: When you put a distortion product on the basilar membrane and you generate energy it goes both ways. Nobili: No! What happens instead in the cochlea? In the cochlea you have phase motion. The phase travels but the energy does not. Because of local deformations, the basilar membrane accumulates potential energy (elastic energy) point by point.

539 Virtually only potential energy, as its kinetic energy is negligible. The kinetic energy of the cochlea is almost totally distributed in the fluid, which is instantly coupled with all basilar-membrane portions - (Allen tries to interrupt) (Nobili, cont'd:) Thus, speaking of energy propagation is meaningless, there is only phase delay propagation. Allen: We are changing the topic. Duifhuis: I want to make one comment. One thing is that at the place where the distortion product is generated it has to be coupled back to the fluid before it can move. However, a lot of people that I have been discussing and describing it with do not take that aspect into account. Allen: Well, they probably don't have much to say on the topic because they don't know. But it certainly gets back to the fluid because you can measure it in the ear canal. How it gets back needs to be researched. When you generate a distortion product on the basilar membrane, in some region of overlap of the primary stimulus components, there's obviously a signal that goes to the characteristic place of that distortion product and clearly there's also a signal that goes back to the ear canal where we measure it. Now the question is, are the propagation velocities of the two waves, the one that's going forward and the one that's going backward, are they the same? Or are they fundamentally different? Some people are saying the wave going back is instantaneous and some people are saying it is not. However, everybody I think claims that the wave going forward is a normal wave as if it had started at the stapes. de Boer: As far as the long-wave approximation is concerned it's the second-order differential equation that Carrick (Talmadge) was referring to. It has two solutions. One wave going one direction, and another wave going in the other direction and at every location the propagation velocities are the same. Allen: Now, is there some way to get around that very obvious possibility? (de Boer:) May I add: when I have a more complicated model, I am not too sure. When I use what you call the WKB solution (which isn't really a WKB but a LiouvilleGreen solution) and I use that for waves in that more complicated model, then again wave propagation is symmetrical but that is in both cases an approximation. Allen: What it has to be ultimately? I think that this question has to be answered experimentally. This is a theoretical conference in a lot of ways but this is a question that has to be answered experimentally and when we have the answer, if it turns out that the delay is different in the two directions, then the modelers have to deal with the issue and figure out what is going on. Is it an evanescent wave

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coupling back? A sound wave coupling back? Or is it as some of the other people believe — van der Heiden: Could I ask a helpful question? To experimenters, about the distortion product measured in the ear canal: how intense can it be? Could it be measured considerably basally from its own basilar membrane place, basally from its best site? Allen: We, Paul (Fahey) and I, did an experiment, where we held the distortion product at its characteristic place constant and looked at emissions in the ear canal. We varied the primary frequencies Fl and F2 so that the distortion product 2 Fl F2 at its characteristic place was always constant-amplitude and we measured the pressure in the ear canal. We found that within 6 dB the pressure in the ear canal always stayed the same no matter where the source was, whether it was midway down the cochlea or near the base or near the apex. It was pretty close to true that the sound pressure in the ear canal was always the same. van der Heiden: But is the distortion product strong enough to measure it halfway? At the base of the basilar membrane? Could you see the BM move at the distortion product frequency? Allen: There are limitations but how hard are those limitations? Ruggero: Well, first of all, I think we should try not to talk about the distortion otoacoustic emission (DPOAE) but about stimulus-frequency otoacoustic emission (SFOAE). My earlier argument was: all kinds of vertebrates have emissions of various sorts including SOAEs. One family, amphibians, doesn't even have a basilar membrane as we heard today. So what I was pointing out three years ago, in these animals there is no backward traveling wave of the basilar membrane because they do not have a basilar membrane. OK. Since then, a lot has happened. There has been a very wonderful paper by Tianying Ren in which he improved upon the experiment that my post doc Shamla Narayan presented at ARO, in which we showed no time delay of a backward traveling wave for the DPOAE at the F2 side. Tianying Ren did something much better which was to observe an extent of basilar membrane instead of a single point. In both cases there was no time delay for a backward basilar membrane traveling wave. Then I did a review that appeared in ARLO in 2004 (ARLO 5, 143-147), in which I showed that the same could be said about gerbils and guinea pigs. At ARO this year my post doc Qin Gong showed that for the chinchilla ~ for which we now have a very complete map of group delays and signal-front delays — that was also true. The important part comes now. Chris Shera and George Zweig did us all a great favor by creating a theory that is testable (JASA 89, 1290-1305). We have heard a lot today and the days before about DPOAEs but nothing like Chris Shera's theory. This theory of coherent reflection

541 filtering produces a prediction. It says that the group delay of the stimulus frequency emission in the ear canal should be exactly or nearly twice the group delay at the characteristic frequency of that particular place in the basilar membrane. There is now a paper JASA (vol. 118, pp. 2434-2443) showing that at the base of the cochlea that prediction fails by a factor of two. Our data for the chinchilla show exactly the same delays for the SFOAEs as for the basilar membrane. This gives us a hint that indeed the reverse wave is an acoustic wave because there's a beautiful match both for the chinchilla and for the cat. Finally, for the apex the data shows something that says that probably the waves are bouncing from the SFOAE place. This cannot be right because the delays of the basilar membrane are much, much longer than the delays of the SFOAEs. Mountain: I guess my perspective is a little different. We think that we know where the emissions are coming from, but as someone who has measured different forms of emissions I am never sure where they are coming from. We know that we are dealing with a distributed generation site when we measure something in the ear canal. We are often seeing the result of quite a bit of phase cancellation so I think: where is most of the energy that I measure in the ear canal coming from? It may very well be that at the F2 place for distortion product emissions, we get lots of activity at the basilar membrane level at the frequency of 2 Fl - F2, but we know from models that most of that stuff cancels out. Quite often the signal, depending on the primary frequency ratio, is coming from a different place. So I think this assumption that it's always coming from the 'best place' (for the frequency in the stimulus frequency emission case or from the F2 place for the case of distortion product emission) isn't correct. Let me remind you of some data that we presented at this meeting six years ago where we looked at electrically evoked emissions (EEOAEs). We looked at DPOAEs, as well as at cochlear microphonics (CM) in the gerbil at several locations. We used relatively large primary frequency ratios for the DPOAE, around 1.2 or greater, so that the Fl place was far away from the F2 place, this was done to minimize phase cancellation for the electrically evoked distortion product. We concentrated on frequencies that were below the best frequency for the location of the electrode, again to minimize phase cancellation. Likewise, we recorded the cochlear microphonic from scala media because we felt that was the most localized way to measure the CM, and we again focused on frequencies below the (local) characteristic frequency to minimize the problem of phase cancellation. We found that the travel times for what we would call reverse traveling waves from the electrically evoked emission matched the forward group delay of the CM over the same frequency range. We also found for the distortion product emission that the group delay corresponded to twice either the group delay for the reverse traveling wave as measured with the electrical stimulation or the group delay of the forward travelling wave measured with the cochlear microphonic. If I tried to do the same experiment for distortion product emissions with very closely spaced primaries, specifically if I did it at moderate to high levels, I would have gotten a

542 very different answer ~ because of the phase cancellation problem. You end up with something that looks much closer to a 'wave-fixed' as opposed to a 'place-fixed' type of phase response. So I think with all these experiments, we really have to be careful to say that we think we know where the signals are coming from. Because we can measure something at the basilar membrane this doesn't mean that that a particular location on the basilar membrane is contributing most of the energy to the emission measured in the ear canal. Talmadge: I guess there are a lot of points that have been addressed here. First, de Boer raised the question: if you go beyond a one-dimensional model (a long-wave model) do you still get a wave equation? Chris (Shera) and myself were able to actually show an extension of work that Diek (Duifhuis) has done many years ago in a slightly different formulation. In a two-dimensional and a three-dimensional fluid model you can still write a formal wave equation. That's the first point and I guess that's why you shouldn't be surprised that you get WKB solutions that are symmetric in space. The second thing is, Mario (Ruggero) made the comment that he didn't think that a predictable framework or model existed for DPOAEs. I guess I would have to take exception to that. My 1998 paper (JASA 104, 1517-1543) actually has pretty detailed predictions about the characteristics and the 1999 paper (JASA 105, 275-292) which talks about the origins of the two-source model, has more information on that. The third thing, David Mountain talked about making an assumption about where the various reflections are from. Yes, you could call it making an assumption. At some point you develop a model and you test it and you can write down mathematically what the predictions of the model are. It's not that we are making an assumption that the DPOAEs has been generated at the F2 site. No, it is a consequence of the model as such that is generated there. Furthermore, you get a part that travels basally and a part that travels apically which is reflected around its best place; you start out with the integral from zero to the end of the basilar membrane and you end up with those properties as conclusions from the model — if done properly. So it's a little more than just making an assumption. Allen: I think we have one more topic. Chadwick: I have a short comment. I am trying to remember my own work with multi-compartment, box or sandwich models. If I remember correctly, if you have a dispersive system with more than one degree of freedom, then you lose symmetry in forward and backward propagation speed. The forward speed does not necessarily equal the backward speed. I think people working on otoacoustic emissions ought to consider using models with more than one degree of freedom, more than a basilar membrane. Maybe you need to include the tectorial membrane. Allen: I have a question that I inject here. I thought I heard Mario (Ruggero) say that the first peak of the impulse response of the BM isn't exactly linear. Then I

543 certainly heard comments that the first peak was linear ~ at least on the basilar membrane but not in the nerve fibers. Are there any issues here that need to be addressed? Maybe I misheard you. (Ruggero:) No. These issues were discussed thoroughly between John Guinan and myself in relation to his paper. What I said is that the data for the chinchilla are very clear-cut as far as basilar membrane is concerned. In the guinea pig and in the chinchilla, at the base, the first peak starts out quite linear and nonlinearity grows over the period of one cycle or so of the oscillation. At the apex, in the only reliable data, available from Nigel Cooper, the situation is quite different. The very first peak is compressive. Now, I don't think Nigel measured the relative compressiveness like we did for the base. But the fact is that an easy way to tell whether you do have a first peak or not is to look at what starts out being nonlinear. And that makes perfect sense because a tuning curve is encompassed by the region of compressive nonlinearity. That's my answer as far as the basilar membrane is concerned. As far as the nerve is concerned, everybody I know says that the auditory nerve fibers follow what the BM is telling them, certainly for clicks. Guinan: Nigel (Cooper) actually had some plots of his data with him and we had a look at them, Nigel (Cooper), Bill (Rhode) and myself. The data showed that the first four peaks had a slightly compressive growth in the apex. And they were all about the same. So if you take compressive growth as indicating what you might expect the efferents to inhibit, that suggests you would see approximately equal inhibition in all the first four peaks. That's not what we saw in the auditory nerve. We saw quite a different behavior. We saw strong inhibition of the first half cycle, a tiny bit of it in the second half cycle and nothing in the next cycle. So I think there is something that is different between basilar membrane and auditory nerve, these are two different species. But I also want to say that the main point about our whole discussion wasn't so much the difference between basilar membrane and auditory nerve, it was about the typical extrapolation of what I am calling classic basilar membrane motion, which is in the base, whether you can extrapolate that throughout the cochlea. Most people seem to agree that you can extrapolate to the extreme apex. I'm even questioning whether you can extrapolate to the middle of the cochlea. I think that is something that is worth talking about. What is the evidence that the pattern that we see in the base of the cochlea even goes to the middle of the cochlea in basilar membrane motion? Allen: OK. As far as I am concerned I think we should be done. [Applause.] de Boer: As the oldest person around I think I am well qualified to say: thanks to Jont Allen for a masterful direction of this discussion. We were sometimes very wild and he was very wise and that is the thing that counts most. Another applause for Jont Allen. [Applause.]

AUTHOR INDEX (Pages of Papers, Comments and Discussion) Achenbach, A. 377-383 Albert, J.T. 489-495 Allen, J.B. 185,194-201,521-543 Alsabah, B. 115-116 Andoh, M. 237-239 Andor, D. 482-488 Anvari, B. 235-236, 270-276 Aranyosi, A.J. 260, 292, 500-501 Arruda, J. 417-424 BaiJ.P. 162-168 Bell, A. 496-497 Beltramello, M. 339-345 Bergevin, B. 388-389 Bian, L. 93-100 Blinowska, K.J. 346-353 Bortolozzi, M.M. 138-145 Boutet de Monvel, J. 254-260 Brownell, W.E. 146-154,176-186, 202-209, 231-236, 270-276, 284, 383, 424, 481 Bukauskas, F. 339-345 Bustard, G.D. 510-511 Cai, H. 498-499 Chadwick, R.S. 15, 76-77, 136, 185, 208, 216, 4Y142A, 481, 498-499, 524, 529, 531-533, 536, 542 Chan, D.K. 24-25, 268,127-137, 522 Cheatham, M.A. 218-225 Chen, F. 111-112, 502-503 Cheng, H. 3-16 Cheng, L. 408-415 Chertoff, M.E. 93-100 Cheung, E.L.M. 277-285 Chien, W. 506-507

Choi, C.H. 41-48 Choudhury, N. 111-112 Clifford, S. 146-154 Cohen, H.I. 502-503 Cooper, N.P. 3-16, 86-92, 528 Corey, D.P. 277-285 Crawford, A.C. 245-253 DaUos, P. 218-225, 261-269, 433441, 525, 524, 535 Danie, S.J. 115-116 de Boer, E. 352, 393-409, 522, 534535, 538-539, 543 De La Rochefoucauld, 0.119-120 Decraemer, W.F. 119-120 Deo, N. 408-415 Dimitriadis, E.K. 417-424 Dong, W. 56-62,119-120 Duifhuis, H. 535, 537, 539 Duke, T. 482-488 Durka, P.J. 346-353 Ermilov, S. 235-236 Fahey, P.F. 100,194-200, 530 Farkas, Z. 226-227 Farrell, B. 231-232 Fettiplace, R. 240-241, 245-253 Freeman, D.M. 49-55, 388-389 Fridberger, A. 254-260, 524 Funnell, W.R.J. 115-116 Furst, M. 384-385 Gillespie, P.G. 169-175 Glassinger, E. 210-217 Gomi, T. 26-33 Gopfert, M.C. 489-495 Grosh, K. 24, 154, 408-415, 514515, 523, 532 545

546

Guinanjr., J.J. 3-16, 86-92, 260, 352, 522, 525, 532, 543 Gummer, A.W. 209, 253, 259,1725, 48, 77,101-102, 226-227, 295-296, 315-321, 432, 440, 465, 472, 525 Hackney, CM. 55, 240-241 Hallworth, R. 187-193 Halmut, Y. 384-385 Harasztosi, C. 295-296 He, W.X. 79-85 He, D.Z.Z. 261-269 Holt, J.R. 169-175 Hubbard, A.E. 458-473, 465-472, 502-503, 508-511, 523 Hudspeth, A.J. 127-137 Huynh, K.H. 218-225 Iida, K. 26-33, 228-230 Ikeda, K. 26-33 Iwasa, K.H. 155-161 Jacques, S.L. 111-112 Jedrzejczak, W.W. 346-353 Jensen-Smith, H.C. 187-193 Jia, S. 261-269 Joris, P.X. 105-106 Julicher, F. 474-488 Kakehata, S. 26-33 Kalluri, R. 386-387 Karavitaki, K.D. 284-290, 525, 534 Katori, Y. 26-33 Kemp, D.T. 308-314 Kennedy, H.J. 245-253 Ketten. D.R. 121-122, 417-424 Khanna, S.M. 34-40,119-120 Kimura, K. 26-33 Kobayashi, T. 26-33, 228-230 Konopka, W. 346-353 Koppl, C. 377-383 Kumano, S. 26-33, 228-230

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The workshop brought together experts in genetics, m o l e c u l a r and cellular biology, physiology, engineering, physics, mathematii s, audiology and medicine to present current work and to review the i ritical issues of innei eai function. A special emphasis of the workshop was o n a n a l y t i c a l m o d e l based studies. Experimentalists and theoreticians thus shared their points oi view. I lie topics ranged from consideration of ihe hearing organ as a system lo the study and modelingOl individual auditor v (ells including molei ular aspe< te ol fun< Hon. Some of the topics in the book are: motOl proteins in hair < ells; me< hani< al MI<\ e\& trk al aspects of transduc tion by motor proteins; function of proteins in sterecx ilia oi hair i ells; production oi acousti< l o n e In stereocilia, mechanic.il properties oi hair cells and the organ oi ( orti; mechanical vibration ol the organ oi i iorti; wave propagation in tissue and fluids of the innei ear; sound amplification in the < oi hlea; ( r i t U .il os< illations; ( • >< hlear nonlinearity, and mei hanisms foi theprodui tion oi otoacoustii emissions, rhis book w i l l be invaluable io resean hers and '-indents in auditory scieni e.

Auditory Mechanism: Processes and Models

6124 he ISBN 981-256-824-7

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