Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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Edited by
Jay A. Glasel Murray P. Deutscher Department of Biochemistry University of ConnecticutHealth Center Farmington,Connecticut
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Cover photo: The 13 subunit of the E. coli replicase, DNA polymerase III holoenzyme, encircles DNA acting as a sliding clamp to tether the rest of the replicase machinery to the chromosome. The two subunits of the holoenzyme are shown in red and yellow. The commercial molecular modeling program "Quanta" (Molecular Simulations, Inc., Burlington, MA) operating on a Silicon Graphics, Inc., Indigo computer was used to produce the Postscript output. For other views of the same structure see Kong, X.P., Onrust, R., O'Donnell, M., and Kuriyan, J. (1992), Cell 69 425-437. Courtesy ofDrs. X. P. Kong and J. Kuriyan, Laboratory of Molecular Biophysics, The Rockefeller University, New York, N.Y., and Drs. R. Onrust and M. O'Donnell, Microbiology Department, Cornell University Medical College, New York, N.Y.
This book is printed on acid-free paper. Copyright 9 1995 by ACADEMIC PRESS, INC. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Academic Press, Inc. A Division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 92101-4495
United Kingdom Edition published by Academic Press Limited 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data Introduction to biophysical methods for protein and nucleic acid research / edited by Jay A. Glasel, Murray P. Deutscher. p. cm. Includes bibliographical references and index. ISBN 0-12-286230-9 1. Proteins--Research--Methodology. 2. Nucleic acids--Research-Methodology. 3. Amino acid sequence. 4. Nucleotide sequence. I. Glasel, Jay A. II. Deutscher, Murray P. QP551.I63 1995 574.19'245--dc20 95-8162 CIP PRINTED IN THE UNITED STATES OF AMERICA 95 96 97 98 99 00 QW 9 8 7 6 5
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Contents
Contributors Preface xi
ix
Chapter I Basic Physical Properties of Proteins and Nucleic Acids Jay A. Glasel
Glossary 1 I. Introduction 10 II. A History of the Concept That Molecules Can Be Very Large III. Basic Properties of Macromolecules 12 IV. Fourier Transforms 48 V. Summary 51 References 51
Chapter 2 Electrophoretic Methods David E. Garfin
Glossary 53 Symbols 55 I. Introduction 56 II. Gel Electrophoresis 57 III. Isoelectric Focusing 86 IV. Immunoelectrophoresis 92 V. Blotting 94 VI. Pulsed-Field Gel Electrophoresis VII. Capillary Electrophoresis 100 References 103
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Contents Chapter 3 Hydrodynamic Methods Walter F. Stafford and Todd M. Schuster
Glossary 111 Symbols 115 I. Introduction 118 II. Analytical Ultracentrifugation 119 III. Sucrose Density Gradient Sedimentation 132 IV. Diffusion 133 134 V. Sedimentation-Diffusion Equilibrium VI. ViscosityMeasurements 140 VII. Resources 143 References 143
Chapter 4 Mass Spectrometry Richard M. Caprioli and Marc J.-F. Suter
Glossary 147 I. Introduction 152 II. Instrumentation 153 172 III. Combined Techniques IV. Applications 174 V. Conclusions 201 References 201
Chapter 5 Electron Microscopy Arthur R. Hand
Glossary 205 I. Introduction 208 II. Principles of Electron Optics 209 III. Design and Operation of Electron Microscopes IV. Methods of Sample Preparation 222 V. Applications of Electron Microscopy in Cell and Molecular Biology 244 References 258
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vii Chapter 6 Optical and Vibrational Spectroscopic Methods Takashi Miura and George J. Thomas, Jr.
Glossary 261 Symbols 266 I. Introduction 267 II. Electronic Spectroscopy 269 III. Vibrational Spectroscopy 286 Appendix 310 References 313
Chapter 7 Nuclear Magnetic Resonance B. W. Bangerter
Glossary 317 I. Introduction 328 II. Basic Principles of Nuclear Magnetic Resonance Spectroscopy III. Experimental Methods for Structure Determination 348 IV. Nuclear Magnetic Resonance of Proteins 359 V. Nuclear Magnetic Resonance of Nucleic Acids 369 VI. Conclusion 376 References 377
Chapter 8 Diffraction Methods Norma M. Allewell and Jaishree Trikha
Glossary 381 Symbols 388 I. Introduction 388 II. Crystals 391 III. Collecting Diffraction Data 400 IV. Calculating Electron Density and Patterson Maps V. Obtaining Phases 415 VI. Building Models 422 VII. Refinement 423 VIII. Evaluating the Model 425 IX. Analyzing the Model 426
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Contents X. Neutron Diffraction 426 XI. Fiber Diffraction 428 XII. Databases 430 XIII. New Directions 430 References 431
Chapter 9 Computational Techniques in Macromolecular Structural Analysis Michael B. Bolger
Glossary 433 Acronyms 438 I. Introduction 439 II. Sequence Homology 439 III. Secondary Structure Predictions of Proteins 451 IV. Computers and Graphical Representations 461 V. Calculation of Structural, Thermodynamic, and Catalytic Properties 471 References 487
Index 491 Computer Program Supplement 507 Instructions for Using the Disk Supplements
508
Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.
Norma M. Allewell (381) Department of Biochemistry, College of Biological Sciences, University of Minnesota, St. Paul, Minnesota 55108 B. W. Bangerter (317) Department of Chemistry, Yale University, New Haven, Connecticut 06520 Michael B. Bolger (433) University of Southern California School of Pharmacy, Los Angeles, California 90033 Richard M. Caprioli (147) The Analytical Chemistry Center and Department of Biochemistry and Molecular Biology, The University of Texas Medical School, Houston, Texas 77030 David E. Garfin (53) Life Science Group, Bio-Rad Laboratories, Inc., Hercules, California 94547
Jay A. Glasel (1) Department of Biochemistry, University of Connecticut Health Center, Farmington, Connecticut 06032 Arthur R. Hand (205) Department of Pediatric Dentistry, School of Dental Medicine, and Central Electron Microscope Facility, University of Connecticut Health Center, Farmington, Connecticut 06030 Takashi Miura (261) Pharmaceutical Institute, Tohoku University, Aoboyama, Sendai 980, Japan Todd M. Schuster (111) Department of Molecular and Cell Biology, University of Connecticut, Storrs, Connecticut 06268
Walter F. Stafford (111) Boston Biomedical Research Institute, Boston, Massachusetts 02114 Marc J.-F. Suter (147) Chemistry Department, Swiss Federal Institute for Environmental Science and Technology (EAWAG), 8600 Duebendorf, Switzerland
George J. Thomas, Jr. (261) School of Biological Sciences, University of MissourimKansas City, Kansas City, Missouri 64110 Jaishree Trikha (381) Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, Massachusetts 02115
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Preface
Driven by developments in precision instrumentation, in electronics miniaturization, and in computer hardware and software, and by the growing interest in understanding structures of biomolecules, biophysical methods have entered the working lives of molecular biologists and biochemists in a forceful way. To do state-of-the-art research in many areas of biological science, a student or senior scientist must be aware of what instruments are available, what information can be obtained, what alternatives exist, etc. As an example of just how important such methods can be, most of us routinely use gel filtration chromatography to obtain molecular masses of proteins and nucleic acids with accuracies approaching + 10% (neglecting effects of shape). However, mass spectrometric methods have now been developed that can yield molecular masses of macromolecules to + 0.001%, and in less time. Yet, many graduate students and researchers in the biological sciences lack the mathematical and physical backgrounds necessary to use biophysical procedures fruitfully, and, often, they are even unaware of biophysical tools that they might effectively employ in their research. While many advanced monographs and textbooks that deal with biophysical methods are available, they generally do not serve the needs of those requiring an introduction to the field. This book is meant to occupy niches both as a textbook and as an initial reference source. Not only will it serve the needs of advanced undergraduates and graduate students learning biophysical techniques for the first time, but it also has been designed to provide experienced investigators with enough information about biophysical procedures to enable them to carry out a method on their own or to collaborate with an expert in the field. In neither case do we assume a working knowledge of the mathematics of physical chemistry. The subject areas have been chosen to cover a wide range of the methods most frequently needed to answer current biological problems. Each chapter presents a description of the physical basis of the method, the type of information that may be obtained with the method, how data should be analyzed and interpreted, and, where appropriate, practical tips about equipment and procedures. Mathematics is included at a level to make the methods understandable and useful without being necessarily complete and rigorous. Thus, we hope to provide the basic understanding that will enable a nonphysically oriented rexi
xii
Preface
searcher to begin to speak in a common language with an experienced practitioner. It is our goal to open the field of biophysical methodology to those who might otherwise not appreciate the importance and usefulness of this area for their own biological training or research problems. Biophysical methods are now so numerous that this book makes no pretense of being all-inclusive. We have attempted to include those methods that are in wide use and whose understanding is fundamental to learning about new developments. Other methods are not discussed although they are widely used and were once at the forefront of experimental biophysics. For example, molecular biology could not have advanced to its present stage without the widespread use of radioactive tracers. However, molecular biologists rarely consider the detailed physics behind their use. Furthermore, we are entering an era in which the use of newer nonradioactive methods is rapidly replacing beta and gamma counters. Thus, we have not included a chapter on biophysical applications of radioactivity. On the other hand, some techniques as old as the modern era of physical chemistry are currently undergoing revivals because of advances in instrumentation, and for such methods we have included discussion. In contrast to most biophysical methods, there is one that does not even involve direct measurements on molecules. That tool is computer molecular modeling and graphics. It was not long ago that in some universities computergenerated images of objects were under the administration of art departments. While that era may not be distant in terms of years, in technical terms it is as far away as the middle ages. Tremendous desktop computing power is now available in thousands of laboratories, and computer molecular modeling has emerged as a valuable tool for both research and teaching. The sophistication of modern software coupled with advances in every aspect of computer hardware has brought this about. In addition, many laboratories have physical links between their desktop and remote computers that can serve and receive data and programs. That is, most of us are connected to "the network." Because of the importance and increasing use of the methodologies, a chapter describing computer applications has been included. Inasmuch as a scientific language barrier often exists that prevents many students and working scientists from appreciating what biophysical specialists are talking about, each chapter includes a glossary of terms and concepts. The glossaries contain definitions and sometimes extensive discussion. They are meant for readers who are unfamiliar with the concepts of physical biochemistry. Depending on the subject, more advanced readers may want to read through a chapter with little, or only occasional, reference to the Glossary for that chapter. Glossary items are indicated in boldface type the first time they appear in each chapter. The first, introductory, chapter summarizes the basic properties of macromolecules. It discusses the mass, shape, electrical, and magnetic properties of proteins, nucleic acids, and their components. In particular, this chapter provides the reader with the scientific vocabulary used throughout the book. In addition, it indicates to the reader what aspects of macroscopic behavior are complex and what aspects are simple. The next two chapters concentrate on descriptions of modern versions of venerable techniques used to determine molecular masses, shapes, and interac-
Preface
xiii
tions. Thus, the second chapter, "Electrophoretic Methods," presents a discussion of the modern manifestation of electrophoresis. While almost all biochemists now do some type of electrophoretic measurement in their laboratories, they may not be aware of the breadth of electrophoretic methods and available detection methods. In this chapter, the poorly understood theory of electrophoresis is overshadowed by the empirical methods developed to do electrophoretic experiments. Consequently, this chapter is much more of a "how-to" discussion than any other in the book. The third chapter deals with analytical ultracentrifugation and viscosimetry. Other than in mass spectrometry, nowhere are the new technical developments more evident than in ultracentrifugation. Those of us familiar with the Beckman "Model E" ultracentrifuge, and its bulk and instrumental complexity, marvel at developments that have shrunk the size of the ultracentrifuge to that of a 3' • 3' • 3' preparative ultracentrifuge. Moreover, the new instrument is vastly more "user-friendly," and so is the associated computer analysis of the data. On the other hand, the basic explanations of the behavior of macromolecules in an analytical ultracentrifuge have not changed over the years. In Chapter 3, the description of ultracentrifugation is brought out in a simple way, and is followed by current applications of the method. Viscosimetry is also included because it is an often-neglected, simple technique that can give quick results on certain overall macromolecular properties (e.g., deviations from spherical shape). Chapter 4 describes the theory and instrumentation underlying the exciting developments that have taken place in mass spectrometry within the past ten years. While the theory of mass spectrometry is quite simple, the basis for the production of ionized macromolecules in a vapor phase is certainly neither simple nor completely understood. Consequently, ionization techniques and their respective applications to biophysical measurements are described rather than theoretically analyzed. This chapter presents an extensive discussion of applications of modern mass spectrometry that are of interest to biochemists and molecular biologists. These include protein molecular mass measurements, determination of posttranslational modifications, and the rapidly developing strategies for peptide sequencing. Chapter 5 describes the application of electron microscopic methods to the determination of macromolecular shapes. Electron microscopy has historically been of great use in visualizing overall macromolecular shapes, particularly those of nucleic acids. More recently, electron micrographic images of protein assemblies have been used, via Fourier transform techniques, to obtain macromolecular structures. The fact that this mathematical technique is brought up in two other chapters (Chapters 7 and 8) underscores the necessity for beginners to learn something about fundamental, important, theoretical concepts that can be applied to a variety of measurements. Chapter 6 is the first of two chapters devoted to spectroscopic methods. The basic aspects underlying all spectroscopy are dealt with in Chapter 1. However, Chapter 6 focuses on the application of the theory to electronic and vibrational spectroscopy. The section on electronic spectroscopy deals with measurements that are done regularly in many laboratories, for example, concentration determination of proteins and nucleic acids. However, it also deals with the resurgence in a technique m circular dichroismmthat fell from favor so completely
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Preface
that many younger workers may not know about it, but which now can be very important for assessing protein secondary structure. The discussion also includes applications of fluorescence spectroscopy to biophysical problems. The chapter then goes on to discuss vibrational spectroscopic techniques (Raman scattering, infrared absorption) that can provide information on intramolecular structural details in proteins and nucleic acids as well as information on kinetics of isotopic exchange. This section includes a discussion of the newly emerging field of ultraviolet resonance Raman spectroscopy and its application to proteins and nucleic acids. Chapter 7, the second of the spectroscopic chapters, discusses applications of nuclear magnetic resonance (NMR) techniques to biochemistry and molecular biology. This chapter forms a bridge between low and medium resolution techniques for determining molecular structure (as discussed in previous chapters) and high resolution ones such as X-ray and neutron diffraction measurements (discussed in Chapter 8). Thus, low resolution techniques such as electron microscopic methods can yield some structural information at resolutions of several angstroms. A medium resolution technique such as NMR can be used at present to determine families of structures of macromolecules in solution with molecular masses less than ~ 25,000 daltons. However, X-ray and neutron diffraction can give atomic positions for carbon and higher atomic number atoms to a few tenths of an angstrom in very large, crystallized macromolecules. NMR theory is presented at a beginning level in Chapter 7 with the object of providing the reader with both scientific concepts and vocabulary. The basic NMR experiment can be understood without a detailed knowledge of quantum mechanics. Thus, this chapter places emphasis on giving the reader a basic outline of what different parameters are derived from NMR data and how they are interpreted in terms of molecular structure. In the current era, multidimensional NMR measurements occupy a central role in macromolecular structure determination. The author of this chapter has tried to present a description of multidimensional NMR in a way that a beginner can get a physical picture of what the experiment involves. He then presents typical examples of successful applications of the technique, with particular attention to the magnitude of a project of structural determination. Chapter 8 presents the theory of X-ray and neutron diffraction with as little dependence on mathematics as we thought possible for the chapter to be useful. Furthermore, at least two mathematical concepts, the Fourier transform and phase differences in electromagnetic waves, are discussed in other contexts elsewhere in the book. Therefore, the reader should already be comfortable with the concept. The appearance of this mathematical operation in several chapters of the book emphasizes our basic pedagogical philosophy that physical methods should be approached from a unified fundamental background. For example, all forms of spectroscopy have much in common, and X-ray and neutron diffraction phenomena have much in common with their analogous optical effects. As the database of successfully solved macromolecular structures becomes larger, comparative methods of getting starting structures for new X-ray data are becoming more important, and one such method is emphasized in Chapter 8. The chapter also concentrates on explaining aspects of diffraction theory and experiments that most puzzle beginners in the field. For example, the authors have worked hard at explaining the concepts of the reciprocal lattice and the meaning of resolution in a structural determination.
Preface
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The final chapter of the book concentrates on two separate aspects of using computers, particularly desktop computers, in protein and nucleic acid research. One aspect is obtaining and interpreting structural information. The other is the current state of predicting macromolecular structure. The former is of great interest because of hardware and software advances that have made it possible to access large structural and sequence databases. With such access, it is possible for workers to compare their own structural information with that of previous structures. The author of this chapter has concentrated on how the database information is obtained over the network and how the data so obtained are analyzed. Theory and practice in prediction of aspects of macromolecular structure are also discussed at a beginning level in this chapter. Many of these methods are being used in ways that may seem insidious to a beginner. For example, as discussed in Chapter 8, after a structure has been "solved" using all available X-ray data, it has become customary to subject the structure to energy minimization on a computer to "anneal" the structure into a more physically realistic one. In some cases, this may move many atomic centers by angstrom distances. The same methods are being used to determine model conformations of, for example, antigen-antibody interactions. In this case both components are annealed using a theoretical treatment and then molecular modeling is used to fit the two structures together. A special feature of the book is the inclusion of supplementary Macintosh and MS-DOS/Windows disks. These disks contain the molecular modeling programs MAGE and RasMol along with sample data files used to obtain some of the figures in Chapter 9. These programs can be used to build and display new structures or display structural data obtained from databases such as the Protein Data Bank. Therefore, the programs pertain to data obtained by X-ray diffraction, neutron diffraction, and NMR spectroscopy. In addition, several journals now store structural information from published articles in their own databases. These may be obtained via the Internet and displayed using MAGE and RasMol. We have found that contemporary students adapt rapidly to the use of these programs and gain valuable structural insights from the calculations, such as intermolecular distances and angles, available within the programs. It is hoped that this volume will prove useful to both students and established investigators, and that it will foster greater interaction between the biochemical/molecular biological and the biophysical communities. We thank the class of 1994, "Biophysical Methods 366, University of Connecticut Health Center," Yingqun Huang, Steve Wiltshire, and Debbie Sardinha for their critiques and suggestions for selected chapters.
Jay A. Glasel Murray P. Deutscher
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GLOSSARY Absolute temperature
Absolute zero is the temperature at which atomic and molecular translational motion ceases. Temperatures above this are given in degrees Kelvin (K). The absolute zero is 273.15 K below the freezing point of pure water at 1 arm pressure, i.e., 0~ is 273.15 K.
Activity coefficient
Activity coefficients are parameters that relate the thermodynamic activities of dissolved molecules to their physical concentrations. When molecules or ions in solution are far enough apart so that no mutual forces are exerted on one another, they follow the thermodynamic laws of ideal solutions. In a solution, the chemical potential of species i,/~i, is given by [d,i =
(3G/3ni),
where ni is the n u m b e r of moles of molecular species i and G is the total free energy of the solution. That is,/~i is the partial molal free energy. In an ideal Introduction to Biophysical Methods for Protein and Nucleic Acid Research
1
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
Jay A. Glasel solution jU, i =
jU, i, 0 -4-
R T In
x i,
where xi is the mole fraction of the species i, R is the universal gas constant (see
physical constants), and T is the absolute temperature. The term/zi, 0 is the chemical potential of the species under a defined standard condition. In a nonideal solution (e.g., a concentrated electrolytic solution), a function, the activity, must be introduced in place of xi to account for deviations from ideality. The activity, ai, is defined by a i = fixi~
where fi is the activity coefficient. Then, jU, i =
/d,i, 0 -}-
R T In x i
-4-
R T In fi = [d,i,o q- R T In a i.
The activity coefficient is, in general, a function of the composition of the solution. Theoretical treatments of nonideal solutions, such as the Debye-Hiickel theory, attempt to predict experimentally determined activity coefficients.
Boltzmann's distribution law This distribution law stems from statistical mechanics (i.e., the theory of the behavior of large numbers of mass-particles in gas, liquid, or solid phases). It describes the population distribution of allowed energy states for the mass-particles. As derived by Ludwig Boltzmann in 1886, the law states that if No is the number of molecules in any given state, the number N in a state whose potential energy is AE above that of the given state is N = No e x p ( - A E / k T ) , where k is Boltzmann's constant (k = R / N , where N is Avogadro's number). Although derived without regard to quantum mechanics (which had not been discovered in 1886; see Quantum mechanics: electrons and photons), the law applies to populations of molecules with quantized energy states.
Brownian motion This term refers to random motion of small particles suspended in a fluid. The motions are caused by statistical fluctuations in the net m o m e n t u m exchange between the molecules of the fluid and the suspended particles when they collide with each other. Another term used to describe a r a n d o m process such as Brownian motion is "stochastic." Chirality If a molecule cannot be superimposed on its mirror image it is said to be chiral, a word that is derived from the Greek word for hand. Hands are chiral objects because right and left hands have a nonsuperimposable mirror image relationship. Molecules that have the same molecular bonding skeleton, but differ in the absolute arrangement of atoms in space, are called stereoisomers. Stereoisomers that are related as object and nonsuperimposable mirror image are termed enantiomers. The fact that an enantiomeric stereoisomer can exist in a variety of conformations (three-dimensional geometries) does not destroy the enantiomeric relationship. That is, it is not possible to interconvert distinct enantiomeric isomers by free rotations about single bonds. A fundamental principle of organic chemistry is that a tetrahedral carbon atom with four chemically distinct substituents (an "asymmetric" carbon atom) within a molecule will result in enantiomeric forms. Each such carbon atom
Chapter I Basic Physical Properties of Proteins and Nucleic Acids forms a separate chiral center within the whole molecule. A section of a macromolecule, or a whole macromolecule, can have chirality in the same sense that right-handed and left-handed screw threads have overall chirality. The basis of the contribution of optical rotation and circular dichroism phenomena to biophysical measurements lies in the chirality of macromolecules in different conformations. Debye-Hiickel theory This widely accepted theory predicts the thermodynamic properties (i.e., parameters such as activity coefficients) of d i l u t e electrolytic solutions. The theory begins with recognition that Coulomb's law gives the electrostatic force acting between individual pairs of electrically charged particles suspended in a medium as F = ele2/if.Y2 t where el and e2 are their respective electric charges, E is the dielectric constant of the medium, and r is the distance between the charges. This force is called a long-range force because it decreases only as 1/r 2 (a very short-range force would decrease, for example, as 1//.6 t o 1//'12). In an electrolytic solution containing highly dissociated salts, even though the ions are well separated, the total effect of all the other ions present on the potential energy of a given individual ion is large because of the long range of coulombic forces. The influence may be calculated for very dilute solutions of simple electrolytes by an approximation developed by P. Debye and E. Hfckel in 1923. The central result of the approximation is that the electrostatic energy is a simple addition to the free energy of the collection of ions. If we consider various kinds of positive and negative ions of charge z i e (where z i = q- 1, + 2, etc., depending on the charge on the ion) at concentrations ni and e is the electrical charge of the electron in coulombs (C), the approximation predicts that the electrostatic energy per mole of ions is
1
E = --~ z 2 e2KN/E,
where N is Avogadro's number and K is given by 1
K =
8r
~ l'liz2
]1/2
.
In this expression for K, the term 89 ~ Ciz2 is known as the ionic strength and is usually given the symbol L and ci is expressed in molarity of ions of a given species. Using this additional electrostatic energy formulation, various thermodynamic relations can be derived. For example, an important thermodynamic parameter is the activity coefficient fi for an electrolytic solution. The natural logarithm of the activity coefficient of an ion in a d i l u t e s o l u t i o n , on the basis of Debye-H6ckel, is given by In fi = - z a e 2 K N / 2 E R T .
Jay A. Glasel
Thus, In fi is proportional to the square root of the ionic strength. It is customary to define an activity coefficient of a salt in terms of the separate activity coefficients of its constituent ions. According to this convention, for a uni-univalent electrolyte (where both positive and negative charges are univalent) the activity coefficient takes the form f+ = (f+ f_)1/2. For a uni-univalent electrolyte, the logarithm of the mean activity coefficient is, numerically, - In f§ = 0.51(I) 1/2,
and for the more general case, - In f_+ = 0.51z+z_(I) 1/2. These results are collectively called the Debye-H6ckel limiting law for the activity coefficients in dilute solutions. Deviations from the limiting law are small below ionic strengths of approximately 0.01 M. Dielectric constant Basically, this constant is used to derive the change in coulombic force between two charged bodies when they are separated by substances instead of by a vacuum. In electrical theory, the dielectric constant is defined as the ratio of the capacitance of an electrical capacitor (e.g., two parallel conducting plates separated by a small space), when the space between its plates is filled with a substance, to the capacitance when the space is a vacuum. The capacitance is the number of charges per unit area the plates can store. When the electrostatic force between the plates is high, the capacitance is high. The dielectric constant of a substance is related, at the microscopic level, to the polarizability (how easily the electronic charge cloud surrounding the nuclei can be distorted by an electric field) and the molecular dipole moments (see Moments: Electrical and magnetic) of its molecular constituents. Dielectric constants are large for liquids made up of polar molecules and, conversely, are small for nonpolar ones. Dielectric constants are relatively easy to determine experimentally. Isoelectric point The isoelectric point for a macromolecule is the pH at which its formal net charge is zero. At its isoelectric pH a macromolecule will undergo no net motion toward either pole when subjected to an electric field (as in an electrophoresis experiment). If the isoelectric point of the macromolecule lies between pH 4 and pH 10, and the macromolecule combines only with hydrogen and hydroxyl ions, its isoionic point and its isoelectric point may be very close. The isoelectric point may be found experimentally from a titration experiment, which consists of measuring the number of hydrogen ions (H +) dissociated per macromolecule as a function of pH. Isoionic point The isoionic point for a macromolecule is the pH of a macromolecular solution when the solution contains only the macromolecule and ions arising from the dissociation of the solvent. For example, a solution of a macromolecule in deionized water can be made isoionic by exhaustive dialysis against deionized water. The isoionic pH may be found experimentally by per-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
5
forming the dialysis and measuring the pH of the resulting solution.
Magnetization Starting at the subatomic level, magnetization is the production of macroscopic magnetism by bringing about alignment of a large number of nuclear a n d / o r electron magnetic dipole moments. Sometimes this is spontaneous. For example, electrons in certain types of iron crystals will spontaneously align with their electron magnetic dipole moments parallel to each other. The total macroscopic magnetic moment is the vector sum of the individual electron magnetic dipole moments. This is ferromagnetism, and its macroscopic manifestation is a magnet. In other cases the submicroscopic permanent magnetic dipoles require external magnetic fields to bring about their parallel alignment of the dipoles. The alignment is called paramagnetism and the vector sum is called the induced macroscopic paramagnetic moment; the alignment is lost when the external field is removed. Later in this chapter a second type of external field-induced macroscopic magnetism is discussed. This is called induced macroscopic diamagnetism. Diamagnetism is a property of all atoms or groups of atoms. It results in antiparallel alignment of the induced moment with the external field and is lost when the external magnetic field is removed. Because nuclear and electron magnetic dipole moments are associated with properties of the particles called intrinsic spin, they behave dynamically like magnetic tops (i.e., like bar magnets spinning around their long axes). Moment of inertia Moments of inertia are dynamical parameters that relate to the forces necessary to accelerate a three-dimensional body in radial directions. Moments of inertia are therefore involved in the analysis of rotational motions of molecules. The moments of inertia are defined for a rigid body made up of point masses mi at coordinates xi, yi, zi (in a cartesian coordinate system) that are rigidly joined together. For example, the quantity, Ix, where Ix = E mi(y 2 + Z2)
(the symbol ~ denotes a summation over all the particles of the system), is called the moment of inertia of the body about the axis 0x. For a spherical body there are three moments of inertia (one about each axis) and they are equal. In a general x, y, z coordinate system undergoing rotation and translation with the body, the moment of inertia for an irregularly shaped, rigid body is expressed by a mathematical function with nine parameters, as opposed to the three for a spherical body. Fortunately, however, a rotation of the coordinate system can always be found (called the principal axis transformation) in which only three moments of inertia are required to describe rotational motion about the center of mass (taken as the origin of the coordinate system) for even an irregular shape. The description of rotational motion about these axes is important for understanding rotational Brownian motion (also called rotational diffusion), which is at the heart of interpretation of nuclear magnetic resonance relaxation times and the Overhauser effect described in Chapter 7.
Moments: Electrical and magnetic Electrical moments are defined by spatial arrangements of positive and negative electrical charges. Contrary to magnetic moments (see below), isolated positive or negative electrical charges can exist. The electrostatic fields surrounding isolated electrical charges are spherically symmetrical, and are given mathematically by Coulomb's law.
Jay A. Glasel
Technically, an isolated charge is called an "electrical monopole." An electrical
dipole exists whenever there are two equal charges of opposite sign separated by
a distance d. The electrostatic field surrounding an electrical dipole is highly directional in space but can be expressed in simple mathematical form at distances that are large compared to d. A molecular dipole moment, P, can be defined for this case as P = 2qd, and the electrostatic field around the dipole is described using P as a parameter. Molecular electric dipole moments arise, for instance, when two atoms of different electronegativity are covalently bound. For symmetric but nonspherical monopolar charge distributions (as might result, for example, from a football-shaped distribution of positive charge), the resulting symmetric electrostatic field, at distances that are large compared to the size of the charge distribution, is mathematically described as a monopole contribution (Coulomb's law), to which are added a series of other contributions that give the corrections from sphericity. Each succeeding term is of lesser importance. The electrostatic field correction of the first of these terms gives a nonspherical electrostatic field using a parameter called the quadrupole moment. The importance of this parameter in biophysical chemistry is that the positive charges of several atomic nuclei of biophysical interest behave as oblate or prolate ellipsoid-shaped positive electrical charge distributions that coexist with nuclear magnetic dipole moments. That is, the surrounding electrostatic field has an electrical quadrupole moment contribution. These nuclei (for example, 14N and 170) have special properties in nuclear magnetic resonance (NMR) experiments. Magnetic moments are formed by spatial arrangements of magnets, each with two poles, commonly designated "north" and "south" poles. One of the fundamental properties of all electromagnetic theory, embodied in the classical equations of Maxwell, is that although monopoles exist for electrical charge (so there can be isolated positive or negative charges), there are no magnetic monopoles in our universe. Consequently, there are no isolated north and south poles. However, unpaired electrons, certain atomic nuclei, and certain other fundamental particles can act like intrinsic magnetic dipoles. That is, they behave in an external magnetic field as if they were subatomic bar magnets. The magnitude of nuclear and electron magnetic moments is expressed in units of magnetons. Phase of a periodic wave The phase of a wave defines when any designated portion of the wave arrives at a selected point along its path. For a sinusoidally varying wave, F = F0 sin(cot + ~b),where F0 is the maximum value achieved by the wave F during a cycle, co is the angular frequency of the wave in radians/ second (the period of the wave is 1/co), t is time, and ~bis called the phase angle. Two waves are in phase when q~ = n(2cr) = 2nlr, where n is an integer (including 0). Two waves are completely out of phase when q~ = (2n + 1)~r. Physical constants Physical constants are numerical values characterizing certain physical processes (such as how rapidly light is propagated, i.e., the speed of light). Modern science postulates that these constants are fixed by the nature of the universe. They are believed to be time-invariant and the same throughout the universe. As measurement methods have become better and better over the years, the accepted values of the constants have tended to converge toward narrower and narrower limits of uncertainty. The following tab-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids ulation lists the physical constants of most use to biophysical chemists. They are given in both the International System (SI) of units and the c e n t i m e t e r / g r a m / second (CGS) system of units.
Quantity
Symbol
Avogadro's number Electron charge Light speed in v a c u o Planck's constant Bohr magneton Electron rest mass Gas constant Electron magnetic dipole moment Proton magnetic dipole moment
N e c
h jU,B
me R /d,e /d,p
Value 6.0221367 1.60217733 299792458 6.6260755 9.2740154 0.91093897 1.9858866 9.2847701 1.41060761
SI
CGS
10 23 m o 1 - 1
10 23 mo1-1
10 -19 C
10-20 emu 102 cm sec-1 10- 27erg Hz- 1 10-21 erg G -~ 10-27 g cal mol- 1 K - 1 10-21 erg G10-23 erg G -1
m sec-1 10- 34j Hz- 1 10 -24 J T -1 10 -30 kg
cal mol- ~K- ~ 10-24 j T-1 10 -26 J T -1
Polyelectrolytes Polyelectrolytes generally are long-chain molecules carrying a large n u m b e r of ionizable sites. These long-chain molecules m a y exist in solution in either linear open conformation, as do m a n y small nucleic acid fragments, or they m a y be folded into regular three-dimensional structures, as are most native proteins. RNA and long-chain D N A (for example, in chromosomes) have three-dimensional structural characteristics, but, compared to proteins, less is k n o w n of the rigidity and distribution of these structures. In all cases, solutions of the polyelectrolytes are electrically neutral: for every charged group fixed to the macromolecule there must exist, s o m e w h e r e in the vicinity, a counterion of opposite charge. Physical biochemists have studied the cases wherein the counterions are small, mobile ones, such as alkali metal and halide ions. Much less is k n o w n theoretically about biologically important counterions, such as the polyamines, that interact with RNA and DNA. Physical biochemistry is often concerned with the ways the electrical charges influence the physicochemical behavior of polyelectrolyte solutions. Although the total charge on a polyelectrolyte m a y be a constant u n d e r fixed conditions, it is actually an average total charge because of the dynamic equilibrium taking place at each ionizable group between charged and uncharged forms. At a p H near where the formal charge is zero (the isoelectric point), the effects of these flickering charges become important in determining polyelectrolyte-polyelectrolyte interactions. The formal charge is the s u m m a tion of all the positive and negative charges on the polyelectrolyte u n d e r given conditions. The s u m m a t i o n does not take into account the dynamic equilibrium going on as, for example, conjugate acids and bases associate and dissociate. Quantum mechanics: Electrons and photons D e p e n d i n g on the experiment, electrons m a y behave as mass-particles or as packets of electromagnetic radiation. This is the w a v e - p a r t i c l e duality that is incorporated into the basic theorems of q u a n t u m mechanics. If a beam of electrons is projected onto a crystal surface at a suitable angle of incidence, the distribution of intensities of the reflected electrons is not at all w h a t w o u l d be expected for particles reb o u n d i n g from a surface. Instead, the intensities are represented by a pattern with maxima and minima just like interference patterns that occur w h e n light is
Jay A. Glasel diffracted. Hence, the experiment with electrons is called electron diffraction. Experiments with electron beams accelerated by known voltages established the relation A = h/meV,
where A is the wavelength of the electron wave, h is Planck's constant, me is the mass of the electron (defined as its mass when its velocity is very small compared to the speed of light, and called its rest m a s s ) , and V is its particle velocity. This equation is one of the results that forms the basis of quantum mechanics. In some experiments described in this volume, e.g., electron microscopy (Chapter 5), the wave character of electrons is all-important. A particle moving with the velocity of light, c, is called a photon. If the above equation is applied to a photon, = h/mc.
However, for any wave, ~ , equals the velocity of the wave. In this case Av = c. Combining these two expressions, mc 2 = h v
Because the mass is moving at the speed of light it has energy, according to Einstein's famous equation, E = m c 2 = h v,
which is a fundamental equation of quantum mechanics that gives the energy of a photon of electromagnetic radiation. A photon has an equivalent rest mass of h v/c a and a momentum of h ~,/c.
Radius of gyration At the macromolecular level, the radius of gyration is the effective equivalent radius that a distribution of atoms making up the macromolecule would have if it were behaving as a sphere. The term originally referred to the classical mechanics of rigid bodies. In classical mechanics, the radius of gyration, R0, of a solid spherical body is defined by the equation I = M R 2, where I is the moment of inertia and M is the mass. Note that the requirement is for a rigid body, not necessarily a spherical one. The concept enters into macromolecular chemistry when interpreting physical measurements related to the rotational properties of a macromolecule. For example, the intrinsic viscosity of a solution containing macromolecules is related to the radii of gyration of the molecules. Random coil In polymer chemistry a random coil refers to an array of configurations differing by alternative rotational conformations about the covalent bonds making up the polymer. Differences in the energies of alternative conformations about a given bond are on the order of R T (where R is the universal gas constant and T is the absolute temperature). In a true random coil, configuration of the macromolecule in a dilute solution is devoid of discernible geometric form, and will not bear an obvious resemblance to the ordered conformation. The array of configurations may be treated statistically; in particular, we can find the average physical properties of the array of configurations. These average properties then describe the behavior of the whole system of random coils under consideration.
ChapterI BasicPhysical Propertiesof Proteins and Nucleic Acids Strictly speaking, molecular shape is the three-dimenShape, molecular sional distributions of atoms making up a molecule. However, as ordinarily used, description of molecular shapes depends on context. For example, a protein may be described as globular if its behavior in a particular experiment is approximately that of a spherical solid body. That is, if the three-dimensional distribution of atoms was tightly w r a p p e d in plastic film and the result was roughly a sphere, it would be described as globular. In another description, the same protein, in the same conformation, might be described as consisting of a relatively open series of helices, sheets, and bends. In Chapter 9 different molecular shapes are illustrated. Included with this volume, the computer programs RasMol and Kinemage allow different representations of any macromolecule.
Supercoiling: Linking number, writhing number, and twist Linking number, L, writhing number, W, and twist, T, are related parameters that are used to describe supercoiled, circular, double-stranded DNA. Consider first the most common form of double-stranded, helical, linear DNA. The two antiparallel strands form a helix with 10.4 base pairs per turn. An integral number, the linking number, L, is defined for helical double-stranded DNA as the number of times one strand of DNA twists around the other in the right-handed direction. The quantity T is the number of hydrogen-bonded (Watson-Crick) base pairs in the helix divided by 10.4. Therefore, in the linear molecule just defined, L = T. This must be true for linear DNA, but it is not necessarily true for circularized DNA. Thus, if this same molecule is circularized (like strands being attached to like), the result is a circular, unstrained, helical structure that is called "relaxed." In solution, hydrogen bonds between opposite-strand bases are continuously breaking and reforming due to thermal agitation. Even so, the relaxed structure is the stable one. However, we now consider another possible molecule of linear double-stranded, helical DNA with exactly the same composition and number of bases. If turns are physically u n w o u n d (breaking the hydrogen bonds holding them in place), both L and T decrease by the number of turns that have been unwound. However, if this molecule is then circularized before the helix winds up again, there is built-in topological strain in the resulting molecule. The circularization prevents the molecule from reforming the relaxed conformation without distorting the molecule. The strain can be partly relieved by an energetically favorable conformational change in the whole circularized molecule that reforms b a s e - b a s e hydrogen bonds so that the whole molecule tends to maximize the number of helical turns (i.e., T becomes greater than L). The only way to do this is to form a tertiary structure that is supercoiled. That is, the double helix winds around itself to relieve the strain. The mathematical relation between L, the degree of supercoiling W (defined as the number of turns that the double helical axis makes about the superhelical axis), and T, the final structure is W=L-T.
Here L is a constant for a particular structure and, as just mentioned, is an integer. Neither W nor T need be an integer. In fact, in solution neither W nor T need be a constant. For a particular nonrelaxed circular structure characterized by a certain L, structures with different combinations of W and T will be in dynamic thermal equilibrium with each other, subject to the condition that each structure satisfies the equation given above. As noted later in this chapter, the
10
Jay A. Glasel importance of supercoiling in biophysical chemistry is that supercoiled DNA is more compact than a relaxed molecule of the same length. We are all familiar with an analogous phenomenon: the behavior of the helical cord found on most telephones. We tend to introduce strains in the cord by repeatedly picking up the receiver and putting it back in different directions on the body of the instrument. Supercoils form to relieve the strain and appear as the cord twisting around itself. If we want to relieve the built-up strain we can hold the instrument up with the receiver dangling down. The receiver will then spin around the cord powered by the strain energy until it dissipates. The cord is then in its relaxed form, with no supercoils, when the receiver is placed back on the instrument.
System of units Over the years many systems of units of measurement have been used. Currently, the International System (SI, or Syst6me International d'Unit6s) is considered the world standard. It is based on the meter, kilogram, second, ampere, Kelvin, and mole (for length, mass, time, electrical current, absolute temperature, and amount, respectively). The CGS system, which may be more familiar to some readers, is based on the centimeter, gram, second, abampere, Kelvin, and mole for the corresponding SI measurements. Converting measurements using one system to units of another system is often troublesome and leads to numerical errors. However, the "Merck Index," which is readily available, contains useful conversion tables.
I. Introduction This introductory chapter deals with the basic definitions and concepts involved in the study of macromolecular chemistry. It concentrates on the physical foundations of experiments that are described in this volume. The intention is to present a largely nonmathematical picture of the physical chemistry of macromolecules as a preparation for higher level treatments in the other chapters. Readers with a good understanding of undergraduate physical chemistry may wish to go directly to the later chapters.
II. A History of the Concept That Molecules Can Be Very Large Our present concept of the existence of macromolecules began with Raoult's discovery of the ideal solution law in 1887. An ideal solution is described in thermodynamic terms, and has the following properties: (1) there is no change in volume on mixing the pure components of the solution, (2) there is no heat evolved on mixing the pure components of the solution, and (3) the change in entropy caused by mixing the pure components is governed strictly by a simple probability expression. Almost immediately after Raoult discovered the ideal solution law that now bears his name, it was found that most solutions are not ideal. However, a large majority of solutions have properties that thermodynamicists call "regular," and for this class of solutions, deviations from ideality are very small. Prior to Raoult there was no way of determining molecular masses of compounds in solution. As a result of his discovery, it was realized that molecular masses of solutes could be measured by the cryoscopic method (the freezing point de-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
11
pression that, for example, takes place when salts are dissolved in water). According to Raoult's law, low molecular masses for solutes correspond to large freezing point depressions. This method was applied to various materials dissolved in a wide variety of different solvents. Generally, organic molecules dissolved in organic solvents, and salts dissolved in water, all resulted in large freezing point depressions. However, in other cases, for example, rubber or starch dissolved in organic solvents and water, respectively, freezing point depressions were found to be small. Thus, using Raoult's laws, the molecular masses derived for rubber and starch, 18,000 and i2,000 Da, respectively, were much larger than those being observed by chemists of the time for other pure compounds. In fact, the established way of looking at things at that time, based on Graham's work in 1861, was to regard some matter as having a colloidal (gluelike) state. The word colloid comes from the Greek word for glue. This name was used because gelatin showed the typical behavior of this class of substances. The Brownian motion of colloidal particles had been discovered in 1827; the colloidal concept was developed for 60 years up to Raoult's time. According to this idea most matter in solution existed as colloidal particles. It was common not to distinguish between a colloidal particle composed of many molecules of ordinary size, held together by secondary forces, and a large molecule held together by covalent bonds. There was no reason to do so; the energies of bonds were unknown. For those familiar with the dynamics of scientific opinion, the result was predictable. Raoult's law was new and had experienced failures (almost all small) for electrolytic solutions. To reconcile the experiments on rubber and starch with what was already known, it was simply assumed that Raoult's law was inapplicable to colloidal solutions. Therefore, most interested scientists believed that the solution behaviors of compounds such as rubber and starch were manifestations of molecular association. The word macromolecule was coined by Staudinger in the 1920s to emphasize the molecular, rather than the associational nature, of what we now call polymers. Tremendous polemical battles ensued that centered around the truth or falsity of this concept. Indeed, it was not until the 1930s, largely as a result of direct chemical synthesis of polymers such as nylon, that the existence of high molecular mass substances was widely accepted. The acceptance of the macromolecular concept was also helped by the development of instruments for performing light-scattering, electrophoretic, and centrifugal sedimentation experiments during this period. The development of nonthermodynamic instrumental techniques provided the means to prove the correctness of Staudinger's viewpoint. In particular, a cornerstone of the colloidal idea was the observation from the newly developed technique of X-ray diffraction that indicated that the unit cells (the concept of unit cell is discussed in Chapter 8) for crystalline rubber and cellulose were similar in size to those of simple molecules. In 1926 it was shown that the X-ray diffraction by cellulose fibers is consistent with a chain length composed of an indefinitely large number of units (Flory, 1953). This interpretation made unnecessary the assumption that a molecule could not be larger than the unit cell. Because the first proteins were being crystallized at roughly the same time, the interpretation opened the way for acceptance of proteins as macromolecules. Developments in instrumental and theoretical techniques applied to biochemistry took place at an accelerating rate during the era from 1930 to 1950.
12
Jay A. Glasel Consequently, when the classic paper by Avery, MacLeod, and McCarty (1944) establishing the informational properties of deoxyribonucleic acid appeared, the paper contained ultracentrifugal information on the molecular mass of the DNA. The macromolecular nature of DNA was accepted much more easily because the controversy over proteins had been settled by this time. It is possible that the acceptance of both was eased by the fact that all of the methods available erred on the side of low molecular masses. Thus, the Avery group found a molecular mass of 500,000 Da (a value we know now is much too low for pneumococcal DNA) for their DNA, and early polymer chemists, using faulty theoretical analysis of physical experiments, consistently found molecular masses of macromolecules to be too low by an order of magnitude.
III. Basic Properties of Macromolecules The intrinsic properties of macromolecules that are important for the purposes of this volume include (1) mass, (2) shape and structure, (3) electrical charge, (4) electrical and magnetic moments, (5)kinetic properties (rotational and translational motions, internal motions), and (6) color (interactions with electromagnetic radiation), including (a) molecular electrical dipole, and multipole, moment interactions with radiation, (b) molecular magnetic dipole moment interactions with radiation, (c) interactions of nuclei of atoms with electromagnetic radiation, and (d ) interactions of unpaired electrons in molecules with electromagnetic radiation. Physical methods are presently available that involve using all of these properties. Sometimes many different methods employ similar properties in different ways. These redundant methods may, however, differ greatly in ease of performance and interpretation, accuracy, and expense. For example, optical rotatory dispersion (ORD) and circular dichroism (CD) have their basis in similar molecular properties, but differ very much in ease of interpretation of data. In the succeeding chapters of this volume many of the available methods are discussed. The purpose of this chapter is to discuss the fundamentals of the properties being measured. In particular, we want to highlight differences in the properties of small molecules and macromolecules. A. M a s s With the advent of highly accurate methods for measuring macromolecular masses (see Chapter 4), an accurate usage of the term mass has become necessary in biophysical chemistry. Unfortunately, some biochemistry textbooks either ignore the problem or confuse weight with mass. The weight of an object is defined as the force of the object against the earth. Thus, weight is measured in newtons (N) or dynes (kg m/sec 2 in SI units, gm cm/sec 2 in the CGS system; i.e., 1 N = 10s dynes; see System of units). Weight is not expressed in grams. The mass unit as originally defined in the metric system is that amount of mass contained in 1 c m 3 of water at a specified temperature and pressure. This amount of mass is called the gram. It was Newton who found that in any
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
13
geographical locality the masses, or amounts of inertia, of bodies are proportional to their weights. Thus, in that locality the masses of two bodies are compared by putting them on a balance and comparing their weights. A mass spectrometer is an instrument that measures inertial properties of atoms and molecules (specifically mass/charge; see Chapter 4). Because charges are integral numbers, the mass spectrometer can give the masses of individual isotopes of elements. Notwithstanding the physical difference between mass and weight, many still refer to "atomic weight" or "molecular weight" when they mean "atomic mass" or "molecular mass." Before 1960 there was a difference between chemical and physical atomic mass units for historical reasons. The chemical definition of 1 atomic weight unit was 1/16 of the average isotopic mass of atomic oxygen derived from oxygen gas as it exists in nature. This base was used for many years as the chemical atomic weight. The physical definition of I atomic mass unit was 1 / 16 of the mass of the neutral atom of the isotope 160. This base was used for decades for determining nuclidic masses. Consequently, the chemical atomic weight unit was 1.000274 times the physical atomic mass unit. The distinction between chemical and physical scales becomes important for macromolecules because they contain many atoms, and therefore the existence of even lowabundance stable isotopes can contribute measurably to their molecular mass. This confusing situation of having two different scales was resolved by international agreement whereby both scales are based on the nuclidic mass of 12C. The accepted unit of mass for nuclides, atoms, and molecules was the dalton, originally symbolized by the lowercase letter d. The dalton is defined as exactly 1 / 12 of the mass of the neutral atom 12C; the dalton is thus approximately 1.6605655 • 10-27 kg (to 6 parts per million). The symbol for the dalton (but not the definition) was changed in the 1980s to Da, which will be used in this volume when referring to molecular and atomic masses. The archaic and inaccurate terms, atomic weight and molecular weight, will not be used.
B. S h a p e and Structure The premise behind much of modern biophysical work is that the threedimensional structure of proteins determines their function. That is, the information content stored in DNA appears ultimately in functional form as threedimensional distributions of mass and charge, namely, proteins. The proteins have specific functions determined by these distributions. Much of this volume is therefore concerned with methods for determining structures of proteins. One of the important functions of some proteins is their specific interactions with nucleic acids. Consequently, there is increasing interest in the origin of the forces between these two types of molecules. We will discuss the problem in a later section of this chapter. Bloomfield, Crothers, and Tinoco (1974) have written a one-volume monograph on the detailed physical biochemistry of nucleic acids. Monographs on proteins tend to specialize in one or another aspect, such as structure or interactions. Two starting points for further reading might be a more recent monograph on structural methods (Branden and Tooze, 1991) and a classic monograph stressing thermodynamic and electrolytic analysis of mac-
14
Jay A. Glasel Table I The Genetic Dictionary a
Amino acid
Tripletb
Aminoacid
Triplet
Glutamicacid Asparticacid Glutamine Asparagine
GAPy GAPu AAPy CAPu
Lysine
AAPu
Phenylalanine Tyrosine
GGX GCX GUX CUX UUPu AUPy AUA UUPy UAPy
Histidine Arginine
Tryptophan
UGG
Serine
Cysteine Proline
UGPy CCX
Threonine Methionine
CAPy CGX AGPu AGPy UCX ACX AUG
Glycine Alanine Valine Leucine Isoleucine
a From Bloomfield et al. (1974). Exceptions to the correspondences in this dictionary exist in certain organisms and organelles. bAbbreviations: X, any base; Pu, purine; Py, pyrimidine.
romolecular properties (Tanford, 1961). Table I summarizes the informational properties of nucleic acids by showing the relation between the genetic code and the encoded amino acid residues. At present, it is not understood w h y macromolecules have different sizes; we just know that they do. In certain cases we can rationalize their size. For example, for a transmembrane protein, such as a receptor, to function, it clearly must be larger than the thickness of the plasma membrane. However, it is certainly not clear w h y two enzymes with approximately the same size can differ in catalytic efficiency by orders of magnitude. Figure I shows a variety of proteins displayed on the same scale. In an inset the sizes of a cross-section of a membrane bilayer, of transfer RNA, and of a DNA double helix are shown on the same scale as the proteins. Clearly, future theoreticians have their work cut out for them, if we are ever to understand structure-function relations in a logical and quantitative way. Although powerful methods such as X-ray diffraction and NMR have been applied to characterize macromolecular structures, the number of hours required to gather the data and solve a given structure makes these techniques prohibitive in most cases. Additionally, X-ray diffraction requires good macromolecular crystals and NMR requires large amounts of very pure material. In most cases a protein chemist would like to know some minimal information about a newly obtained protein. This information would probably include the mass of the protein, whether it is a homo- or heteromultimer, its amino acid composition, and its overall shape. With the exception of methods for determining amino acid composition, modern methods for obtaining experimental values for all of these parameters are discussed in this book. In Chapter 9 there is further discussion of analyzing the intramolecular structure of proteins and
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
15
nucleic acids by computer methods. The purpose of this section of the introductory chapter is to introduce some fundamental concepts known to underlie all macromolecular structures. As we will see below, the quantitative descriptions of the three-dimensional structures of proteins are based on recognizing various different structural motifs whose particular arrangements define each particular protein. For nucleic acids, the overall three-dimensional structural motifs are fewer in number, but within each polydeoxyribonucleotide or polyribonucleotide structure there are subtle structural variants that may have biological importance. An understanding of macromolecular structure is therefore based on understanding the descriptions of the structural motifs. These motifs, we shall see, are groups of residues in individual conformations that confer a distinct overall shape to the group. The individual conformation of a residue is described by a set of torsional angles, that is, the angle of rotation about each covalent bond in the molecule (except bonds between heavier atoms and hydrogen atoms). Proteins and nucleic acids have allowed, but sterically constrained, rotations about certain covalent bonds. The definitions of the angles have been fixed by international convention (Nomenclature, 1970, 1983). However, this has been done relatively recently. Literature previous to (and sometimes after) these agreements sometimes contains definitions of angles that are different from those currently in use. We will discuss the current definitions for proteins, because almost all available structural information uses these definitions. However, in some cases there is not complete agreement with a single convention for nucleic acids. Where appropriate, alternate conventions are pointed out for nucleic acids.
1. Description of Primary Structures of Peptides and Proteins Bonds between atoms are denoted A i ~ B j , with the bond lengths written b(A~, Bj). The symbol for the bond angle included between three atoms, Ai, Bj, Ck is written ~-(Ai, Bj, Ck). The symbols used to describe the various torsion angles important in polypeptides are q~, 6, o~,/~, and X. Torsion angles refer to a system of four atoms. A
\
B~C
/
D
If this system is projected onto a plane normal to bond B m C , the angle between the projection of A r a B and the projection of C ~ D is described as the torsion angle (also sometimes called the dihedral angle and internal rotation angle) of A and D about the bond BmC. The torsion angle is written fully as 4 (ai, Bj, Ck, DI). In the eclipsed conformation, in which the projections of A - - B and C ~ D coincide, the torsion angle is given the value 0 ~ A torsion angle is considered positive (+) or negative ( - ) as follows: when the system is viewed along the central bond in the direction B ---* C (or C ~ B), the bond to the front atom A (or D) requires rotation to the right or to the left, respectively, in order that it may eclipse the bond to the rear atom D (or A). Torsion angles are measured in the range - 1 8 0 ~ angle-< + 180 ~ It does not matter whether the system is
16
Jay A. Glasel
Fig. 1 Comparison of the sizes and shapes of some soluble proteins drawn to the same scale. The inset shows the sizes of tRNA, of a segment of double-stranded DNA, and of bilayer membranes at the same scale. From Goodsell and Olson (1993). v i e w e d from one end or the other. These relationships are s h o w n in Fig. 2, w h e r e a generic torsion angle, 0, is shown. The three torsion angles, ~b, 6, and oJ, that define the c o n f o r m a t i o n of an a m i n o acid residue in the m a i n chain of a p o l y p e p t i d e are s h o w n in Fig. 3. Table II gives the main-chain torsion angles for various conformations of peptides of L a m i n o acids. Based only on steric factors, certain torsion angles in peptides
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
17
Fig. 1 (Continued)
and proteins are more probable than others. These lead to so-called regular structures that form the basis of the motifs discussed below. Table III gives approximate torsion angles for some of these regular structures. It should be noted that a general feature of these regular structures, and indeed a major factor in protein three-dimensional structure, is the fact that ~ois almost always found to be within a few degrees of either 0 ~ or 180 ~ The physical origin of this
18
Jay A. Glasel e
D
A o.~
A
D
o
B) J
"~
e_.positlve
D-O
A
(m
oo0o r
0 negativ__.s
Fig. 2 Newman and perspective projections illustrating definitions of positive and negative torsion angles in a general system of four atoms, A, B, C, and D, joined by covalent bonds. Note that a right-handed turn of the bond to the front atom about the central bond gives a positive value of 0 from whichever end of the system is viewed. From Nomenclature (1970).
is that the peptide bond has a significant electron delocalization that forces the four a t o m s (HmNamide--Ccarbonyl--O) into a plane. When a~ is + 180 ~ the conformation of the amide hydrogen and the carbonyl oxygen is termed trans. When a~ is 0 ~ the conformation is cis. In most natural polypeptides, the trans conformation is highly favored energetically. The definition of a conformation of an amino acid residue is completed by specifying the orientation of the side-chain groups to each other. The specifica-
ACi.I \\x 0i ~
W
G! i i
+I "
Hi +
~ \\x
~r C~-
Hi ~' "" "~ ~ ~ "~ .~.
~
~'i-1
Fig. 3 Perspective drawing of a section of a polypeptide chain consisting of two residues. The limits of a residue are indicated by dashed lines and notations for atoms and the different mainchain torsional angles are indicated. The chain is shown in a fully extended conformation with ~bi = ~/i = O9i = 180~ The residues are in the L configuration. From Nomenclature (1970).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
19
Table II Main-Chain Torsion Angles for Various Conformations in Peptides of L-Amino Acids a 4) (deg)
Rotation about N - C a b
6 (deg)
Rotation about C4-C
0
C~-C trans (all referred to N - H ) C 4- H cis C~-R trans C4-C cis C 4- H trans C 4- R cis
0
C~-N trans (all referred to C - O ) C ~- R cis C 4 - H trans C 4 - N cis C 4- R trans C 4- H cis
+ + + -
60 120 180 120 60
+ + + -
60 120 180 120 60
a From Nomenclature (1970). b Note: trans to Ni-H; is the same as cis to Ni-Ci_l; trans to C;-O; is the same as Ci-Ni+ 1 . For a description of D amino acids, interchange C 4 - H and C4-R in the table.
t i o n s t a r t s a t t h e a l p h a (or) c a r b o n a t o m . F i r s t , t h e s i d e - c h a i n a t o m s a r e l e t t e r e d , or lettered and numbered,
from the Ca atom working
chain. The torsion angles are given the common two (or three) superscripts.
outward
from the main
symbol X and are specified by
I n t h e s i t u a t i o n g i v e n b e l o w , w h e r e A is t h e a l p h a
carbonation,
A~B
D / m C--E \ F
the first (or second) superscript would
indicate the bond B--C
a n g l e is m e a s u r e d ,
indicate whether
and the last would
about which the
t h e a n g l e is m e a s u r e d
Table III Approximate Torsion Angles for Some Regular Structures in Peptides of L-Amino Acids a Structure b
4) (deg)
6 (deg)
to (deg)
Right-handed ce helix [a-poly(L-alanine)] Left-handed c~ helix Parallel-chain pleated sheet Antiparallel-chain pleated sheet [fl-poly(L-alanine)] Polyglycine II Collagen Poly(L-proline) I Poly(L-proline) II
- 57 + 57 - 119
- 47 + 47 + 113
+ 180 + 180 + 180
- 139 - 80 -51, -76, -45 -83 -78
From Nomenclature (1970). b Note: For a fully extended chain ~b = 4t = to = + 180 ~
a
+ + + 153, + + +
135 150 127, + 148 158 149
- 178 + 180 + 180 0 + 180
20
Jay A. Glasel
relative to D, E, or F. For example, in leucine, ,u Xi3,1,2, Xi3,1,3 refer to the torsion angles specifying the three hydrogen atoms attached to C ~1. In valine, Xi 2'1 and Xi 2"2 refer to the torsion angles specifying atoms Ci ~/1 as Ci ~/2. One of the problems afflicting even experts in protein structure is building molecular models (including computer models) with amino acid residues in their correct r configurations about their alpha, asymmetric carbon atoms. Normally, of course, this means all the residues should be in their L configurations. Checking for this configuration step by step in building or examining a portion of a peptide is always wise and fortunately very easy. The CORN mnemonic is useful for this purpose. Looking at the Ca atom from its H atom, the other substituents should read CO-R-N. in the clockwise direction. CO, R, and N represent the carbonyl group, side-chain group, and main-chain nitrogen atoms, respectively.
2. Description
of the
Primary Structures
of Nucleic
Acids
Compared to polypeptides, relatively little is taught about the configurations of polynucleotides. However, as more interest centers on protein-nucleic acid interactions, it becomes more important to understand the structures of nucleic acids. In this section we will discuss the configurations and nomenclature of nucleosides and nucleotides (a description of planar nucleic acid bases can usually be found in most biochemistry textbooks). The rules for configuration nomenclature have been set out by international agreement as in the case of polypeptides (Nomenclature, 1983). Exactly specifying the structures for the nucleosides can become very complicated because the ring atoms of the sugar are not planar and the out-of-plane atoms depend on the compound. There are also five torsion angles not in the sugar ring, about which rotation can take place: C l ' ~ b a s e , C 2 ' ~ O 2 ' , C 3 ' ~ O 3 ' , C 4 ' ~ C 5 ' , and C 5 ' ~ O 5 ' . Figure 4 shows the general structure of ribonucleosides and deoxyribonucleosides. From studies on a large number of nucleosides, four of the sugar ring atoms form a plane to within a small fraction of an angstrom, but the fifth atom in the ring is significantly displaced. The four nearly planar atoms are C1 ', C4', O1 ', and either C2' or C3'. If the out-of-plane ring atom is on the same side of the plane as the 5' carbon, the conformation is designated endo. The conformation is exo if the out-of-plane ring atom is on the side opposite the 5' carbon. C2' endo and C3' endo are the most commonly found configurations. Their corresponding exo configurations are rare. The general conclusion is that either C2' or C3' will be out of the plane determined by C1', C4', and O1 '. The ribose pucker is important to the function of nucleic acids. For example, unless the sugars are either C2' or C3' endo, a double helix conformation for DNA is very strained. The orientation of the base relative to the sugar in a nucleoside is labeled with the symbol X. Eventually, this nomenclature will be a problem when more structures of nucleic acid-protein complexes are known in detail, because the same symbol is used for protein side-chain torsion angles (see above). Relative to the sugar, the base can have two main orientations about the C I ' ~ N link. These are called syn and anti and are shown in Fig. 5. Unfortunately, other definitions for X have been used in the past. Table IV gives conversions from other definitions to the present one. In nucleic acids, rotation about the C 4 ' ~ C 5 ' bond allows 0 5 ' to assume different positions relative to the sugar ring. Three main configurations with
Chapter I Basic Physical Properties of Proteins and Nucleic Acids H5'
21
H5"
~
/
1'
base
~O
C1' 1' IC2' 02'
03'
\.
\H
ribonucleoside
(ribose derivative)
C5'
base
OH
OH
ribose
C5'
OH
OH
arabinose
base
I~
C5'
base
C5'
OH OH
base
1
OH xylose
lyxose
Fig. 4 The configuration of the ribonucleosides found in RNA. The deoxyribonucleosides found in DNA are identical except that they lack 02'. The configuration of other possible pentoses is also shown. From Bloomfield et al., (1974).
all substituents in staggered positions are possible, as shown in Fig. 6. Normally, the three configurations are described by the two torsion angles q ~ o o ( O 5 ' m C 5 ' m C 4 ' m O 4 ') and q ~ o c ( O 5 ' m C 5 ' ~ C 4 ' m C 3 ' ) or by use of the angular ranges, (+) or ( - ) gauche or trans. However, according to the I U P A C IUB convention, it is necessary only to state the torsion angle 7 (= q~oc) in order to define the orientation about the C4' ~ C 5 ' bond. Table V gives the different definitions for %
3. Shapes of Disordered Proteins and Nucleic Acids A disordered macromolecule is one wherein distances between units on the covalent chain forming the polymer are not time invariant. That is, for an array of macromolecules we can only specify statistical distributions giving probabilities that the units will be found at given distances from one another at any given instant. Very few biological macromolecules carry out their in vivo functions in a disordered state. Indeed, most of them lose biological function when they are disordered (disordered is a term that biophysicists have come to prefer to denatured). However, order-disorder transitions caused by treatment of functional proteins with heat, solvent changes, pH changes, etc. can tell us something about what forces hold proteins in their ordered state, and in certain cases reveal what amino acid residues reside in the interior of a protein. Therefore, we need a description of the disordered state of macromolecules. A great deal of information and theoretical analyses are available for disordered proteins and nucleic acids because of the industrial uses of polymers. In biophysi-
22
Jay A. Glasel
Fig. 5 (Top) Diagram illustrating how the overall geometry of a nucleoside changes if bases are in syn or in anti orientation. Adenosine and uridine are shown in their anti orientations. 8-Bromoguanosine and 6-methyluridine are in syn orientations due to steric hindrance caused by their substituents ortho to the glycosyl link. In 8-bromoguanosine an intramolecular hydrogen bond (broken line) stabilizes the syn conformation. Note sugar puckerings, with C3'-endo preferred for anti orientation but C2'-endo preferred for syn orientation. (Bottom) Definition of anti and syn
orientation ranges (Nomenclature, 1983) shown for a pyrimidine nucleoside. X is defined as the torsion angle O4'-C1'-N1-C2. The pyrimidine base is coming out of the paper. From Saenger (1984).
cal chemistry, one often refers to d i s o r d e r e d b i o p o l y m e r s as being in a r a n d o m coil. Technically speaking, the s t u d y of the d i s o r d e r e d states of p o l y m e r s in solution is referred to as the statistical mechanics of chain molecules (Flory, 1969). A freely jointed chain, or " b e a d s on a string" model, is the starting point for analysis of d i s o r d e r e d structures. A p p l i e d to proteins a n d nucleic acids, the b e a d s c o r r e s p o n d to units, such as a m i n o acid residues or nucleotides, w h i c h are joined by m a i n - c h a i n covalent b o n d s about w h i c h free rotation is possible.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
23
Table IV Conversion of Different Definitions for Torsion Angle about the Glycosol CI'-N Linkage a Difference between Nucleic acid
Present X b
Other definition
Purine
--
O4'-C1
Pyrimidine
p
O 4 ' - C1 ' - N 1 - C 6
'-N9-C8
present and other + 180 ~
Purine
O4'-C1'-N9-C4
O2'-C1'-N9-C8
Pyrimidine
O4'-C1'-N1-C2
O2'-C1'-N1-C6
- 62.5 ~ + 116.5 ~
Purine
p
O2'-C1
'-N9-C4
Pyrimidine
--
02' -C1 '- N 1 -C2
- 62.5 ~
+ 116.5 ~
a F r o m S a e n g e r (1984). b Xp. . . . . t = Xother q- d i f f e r e n c e .
Thus, the simplest model does not consider side-chain torsional angles. If we superimposed images of all the possible configurations for a chain of this type, we would see a picture that looked like a fuzzy sphere. Theoretical analysis bears this out and shows that the mean-square radius of gyration for an unperturbed, freely jointed chain with a large number of beads is ~$2~0 =
nl 2/6,
where n is the number of beads and l is the distance between the beads (assumed here to be equal). The subscript on ~s2~0 indicates that this is the base mean-square radius of gyration for comparison with further analysis. For example, if we had 600 beads separated from each other by bonds totaling 20 nm, the root-mean-square (rms) radius of gyration would be 200 nm. This is a very large structure with a density of only 0.000018 beads / nm 3. What happens when restrictions are applied to this freely jointed model to make it more realistic? For example, suppose that the bond angles between contiguous bonds are restricted to tetrahedral angles (i.e., the chain is composed of beads joined by carbon-carbon single bonds? In this case, theory shows that for this perturbed chain, ~$2~ ' = 2~$2~0, where the prime superscript o n ~$2~' serves to indicate that this mean-square radius of gyration includes the first restriction. With double the rms radius of gyration the volume increases by a factor of 8, and the density of beads falls by the same factor. Suppose we then introduce the additional restriction that rotation about each bond is restricted to a normal distribution about a certain average angle? If this average angle is 45 ~ ~$2~ ' ' = 11.7{s2~0 for this doubly perturbed chain. Introducing these restrictions has a very large effect in the direction of increasing the dimensions of the random coil. In Chapter 3 we will see how experimental measurements on macromolecules can be related to the radii of gyration and can be used to characterize deviations from an idealized random coil. The point is that the proportionality of ~s2} to n is preserved even on introduction of various restrictions on complete flexibility. We have just seen that the general form of ~$2~ is onl 2, where ~r is a factor that reflects restrictions on free rotations about bonds. This form suggests that an actual chain can be replaced by a statistically equivalent one that contains
24
Jay A. Glasel H5'2
,04 ,
H5,1~'~05'/ C 3'
+SO
(gauche, gauche)
C2'
0 5,
SE I
C3'
(•
~
C2'
/
| BASE
C3'
ap
( gauche,trans )
-SC
( trans, gauche )
C2'
Fig. 6 Definition of torsion angle ranges about the C 4 ' - C 5 ' bond, looking in the direction C5' ~ C4'. From Saenger (1984).
fewer segments than n, each with a longer effective bond length. Then, ($2) '' = ne 12/6,
where n e and le are the effective units and effective bond lengths, respectively, subject to the condition that nl = nel e. The double prime in {s2}'' indicates that this includes both restrictions discussed above. This concept will be used shortly in describing DNA molecules in solution. Many cases are known of cyclical macromolecules (e.g., plasmid DNA). For the case of a cyclic random coil, statistical theory gives the following simple relation, <S2>0, cyclic = ($2>0, linear/2"
Table V Different Definitions for Torsion Angle ~/ about the Exocyclic C4'-C5' Bond ~ Present 7
Other definitions for orientation about the C 4 ' - C 5 ' bond
+ sc -sc ap
gauche, gauche; (+)gauche; gg; ( +)g trans, gauche; trans; tg; t gauche, trans; (-)gauche; gt; (-)g
" From Saenger (1984).
,,
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
25
Applied to a real polypeptide chain, we can see that the values of bond angles are determined by covalent forces. For example, we know that a peptide bond is planar due to delocalization of the carbonyl bond electrons, whereas the Namide~C~mCcarbonyl angle is nearly tetrahedral. On the other hand, the restrictions on rotations about bonds are determined largely by intramolecular and solvent-macromolecular forces. It is this fact that theoreticians attempt to deal with in trying to predict how a given sequence of primary structure may fold up into its "ordered" or "preferred" conformation. In the early 1950s, Pauling and Cory started working with models of polypeptides and realized that a combination of torsional angles q~ and qJ could be chosen so that all the C = O and N - - H groups could form linear intramolecular hydrogen bonds with optimal acceptor-donor distances. Thus began the study of secondary structures of polypeptides and proteins: the beads of the restricted flexible chain are allowed to interact not only with their nearest neighbors, but also with nonadjacent beads. Not too long after, Watson and Crick, using analogous reasoning applied to DNA, realized that intermolecular hydrogen bonds could stabilize two chains of DNA in certain preferred conformations.
4. Descriptions of the Secondary Structures of Proteins and Nucleic Acids Polypeptides and polynucleotides have one class of secondary structure in common: the helix. Definitions of the general parameters describing a helix are given in Fig. 7. The pitch of a helix is the distance traveled along the helical axis for complete 360 ~ rotation. The pitch height P relates the number n of units (amino acid residues or nucleotides) in one turn and the unit height h, defining the translation per residue along the helical axis by P = nh. The unit twist is t = 360~ and is the rotation between one unit and its nearest neighbor. Helices are described as right-handed if they follow the rule: they show clockwise rotation when viewed along their axes and moving from front to rear. That is, for a polypeptide or polynucleotide, looking from either end of the helix, the main chain spirals in a clockwise direction for a right-handed helix. We note two things about helices. First, because of its handedness, a helix has chirality (Testa, 1979). The uses of this property are expanded in Chapter 6, where the optical activities of helices are discussed. Second, L-polyamino acids can be part of either right- or left-handed helices. The only conclusion that can be drawn from the stereochemistry of the amino acids is that if an L-polyamino acid forms a right-handed helix, its D-polyamino acid counterpart must form a left-handed helix. A popular notation for polypeptide helices is to give the number of residues in a turn and the number of atoms forming one hydrogen-bonded unit in a single compound number. Thus a 3.613 helix is one with 3.6 residues per turn, and 13 atoms per hydrogen-bonded structure. The most frequently encountered polypeptide helices are 3.613 (an cr helix), 310 , 4.416 (a "rr helix), and the 27 ribbon (a ribbon is just a special case of a helix). Table VI shows parameters for some common polypeptide helices. For polypeptides, certain sterically favorable combinations of the torsion angles 4~ and q~exist. A two-dimensional plot of 4~ vs 6 with energy contours
26
Jay A. Glasel
b& .p. O
Fig. 7 Definitionof helical parameters. Pitch P, axial rise per residue h, and unit twist t, shown for a right-hand helix with n = 5 residues per turn. From Saenger (1984).
indicating these favorable combinations is called a q~-6 m a p or, alternately, a R a m a c h a n d r a n plot. Figure 8 s h o w s a R a m a c h a n d r a n plot, indicating regions of greatest stability a n d o b s e r v e d points for proteins (Richardson, 1981). In describing helical s y m m e t r i e s of nucleic acids the s y m b o l N m is used, w i t h no differentiation b e t w e e n p u r i n e s a n d pyrimidines. That is, there are just nucleotides. In this notation, the s y m b o l 111 w o u l d indicate 11 nucleotides in one t u r n of the helix (this is the A form of DNA). S o m e t i m e s n o n i n t e g r a l helices such as 9.331 are n o r m a l i z e d to exact repeats. That is, 3 • 9.33 = 28 a n d so this structure m a y be conveniently d e s i g n a t e d 283 . Some helical p a r a m e t e r s for each s t r a n d of D N A d o u b l e helices are given in Table VI. Nucleic acid helices h a v e chirality, just as do p o l y p e p t i d e helices. It h a p p e n s that the n a t u r a l D N A helices are m a i n l y r i g h t - h a n d e d . H o w e v e r , synthetic sequences such as p o l y ( d G - d C ) a n d regions of natural D N A form a left-handed d o u b l e helix
Table VI Structure Types and Helical Parameters for Polypeptides a Structure type helix 310 helix 27 ribbon
Polyproline helix Antiparallel fl-pleated sheet
Pitch (A)
Designation b
Axial rise (A)
Turn angle per residue (deg)
5.41 6.00 5.60 9.36 6.95
3.613
1.50 2.00 2.80 3.12 3.47
99.7 120 180 - 120c 180
310 27
Polyproline helix Antiparallel ~pleated sheet
a From Dickerson and Geis (1969). b The numbered designation format is (residues/turn)atoms per H-bondring" c The polyproline helix is left-handed.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
27
Fig. 8
(a) Ramachandran plot showing allowed combinations of the 4~ and X angles in a polypeptide. Shaded areas show sterically allowed regions; the labels a,/3, and L correspond approximately to conformational angles found for the usual right-hand a helices,/3 strands, and left-hand a helices, respectively. (b) Observed values for all residue types except glycine. Each point represents ~b-X combinations for an amino acid residue in a high-resolution X-ray structure. From Branden and Tooze (1991); adapted from Richardson (1981).
called Z-DNA, which apparently has biological significance (Saenger and Heinemann, 1989). Table VII gives helical parameters for some DNA structures.
5. Tertiary Structures of Proteins and Nucleic Acids Ramachandran plots are useful summaries of secondary structural data for a given protein. They tell at a glance the relative abundances of helical, sheet, and irregular structures for the protein. However, they cannot give an idea of the three-dimensional runs of secondary structures that determine the overall shape of a protein. Consequently, it is currently more popular to present structural data in the form of topological diagrams (Branden and Tooze, 1991). The basis for this is that simple combinations of a few secondary structure elements with specific geometric arrangements have been found to occur frequently in protein structures. These are called structural motifs. Examples of the common motifs are shown in Fig. 9. Several motifs usually combine to form domains. The domain is the fundamental unit of tertiary structure of a protein and is defined as a polypeptide chain, or part of a chain, that can independently fold into a stable tertiary structure. For example, the extremely efficient enzyme triosephosphate isomerase has a tertiary structure that is a combination of just four motifs, as shown in Fig. 10. Chapter 9 discusses the graphical presentation of tertiary structures of proteins as well as the present status of attempts to predict theoretically the arrangement of motifs from their primary structures. Nucleic acids can form strands of very high molecular masses, extending to
28
Jay A. Glasel Table VII Structure Types and Helical Parameters Derived from X-Ray Diffraction Measurements for Natural D N A s a
Structure type
Pitch(/k)
A B C Z
28.2 33.8 31.0 45.6
Helical Symmetry 111 101 9.331(283) 121
Axialrise (/~)
Turn angle per residue (deg)
2.56 3.38 3.32 3.80
32.7 36.0 38.6 - 30
a Adapted from Leslie et al. (1980). a range > 1012 Da. Beyond the formation of d o u b l e helices, w e can ask a b o u t the shapes a s s u m e d by very high molecular mass nucleic acids. In C h a p t e r 3, hyd r o d y n a m i c m e t h o d s for s t u d y i n g the p r o b l e m experimentally are discussed. F r o m the h y d r o g e n - b o n d e d structure of d o u b l e - s t r a n d e d DNA, it is easy to see that unless considerable energy is e x p e n d e d in breaking h y d r o g e n - b o n d s , it is v e r y difficult to m a k e an acute b e n d in the double helix, a l t h o u g h regions with gentle b e n d s are k n o w n . Macromolecules that can b e n d only g r a d u a l l y a n d s m o o t h l y in solution are given by p o l y m e r chemists the descriptive n a m e " w o r m l i k e chains." The shape of this type of m a c r o m o l e c u l e requires a treatm e n t slightly different from that required by r a n d o m coils. In order to characterize the stiffness of a nucleic acid chain, w e a s s u m e the chain starts at an origin and w e follow it along the positive z-axis. We then w a n t to k n o w the average projection (z) at the end of the chain (after n units that are s e p a r a t e d from each other by distances l). If the chain w e r e a completely stiff rod, (z) w o u l d have its m a x i m u m value at a distance nl. The q u a n t i t y nl is called the contour length of the chain. The theoretical t r e a t m e n t of a w o r m l i k e chain further assumes that the b e n d i n g takes place g r a d u a l l y t h r o u g h small angles, 0. That is, w e replace the freely jointed chain discussed above by a semirigid string w i t h a c o n t i n u o u s curvature. We w a n t to k n o w w h a t average quantities, such as radii of gyration, will be in this case. The result is, for angles very close to zero, a = 2l/02.
The q u a n t i t y a is called a p p r o p r i a t e l y the "persistence length." It is the average
Fig. 9 (A) An example of the helix-loop-helix motif. Two a helices connected by a short loop region constitute this motif. (B) An example of the hairpin motif. The hairpin is built up from two adjacent/3 strands that are joined by a loop region. (C) The "Greek key" motif. Four adjacent antiparallel/3 strands arranged in a pattern similar to the repeating unit of one of the ornamental patterns used in ancient Greece. An example of the structure in Staphylococcus nuclease is shown. (D) The/3- cr-/3 motif. Two adjacent parallel/3 strands connected by an a helix from the C terminus of strand 1 to the N terminus of strand 2 constitute this motif. From Branden and Tooze (1991). Fig. 10 A combination of a - / 3 - a motifs make up the three-dimensional structure of the highly efficient enzyme triose phosphate isomerase. From Branden and Tooze (1991); adapted from Richardson (1981).
Chapter 1 Basic Physical Properties of Proteins and Nucleic Acids
29
extension along the z-axis of a very long chain. If 0 is very small, as we have assumed, a can become much larger than l. If a is very large, the polymer has very long projections along the z-axis--it does not bend very much and is a rigid chain. A further result of a rigorous analysis of a wormlike chain gives a little more physical insight into the meaning of persistence length. In the discussion of random coils we introduced the concept of the effective length of bonds l e . This effective bond length was larger than the real bond length. In a wormlike chain we find that le = 2a. Thus, the effective bond length separating two units in a wormlike chain is twice its persistence length. Because a can be very much larger than l, so can the effective bond length. The result of a more complete treatment is that for wormlike chains, (z) = a(1 - exp{-nl/a}). Suppose the chain is very short so that nl << a. Approximating the exponential using exp{- x} ~ 1 - x, and substituting, we find, (z) = nl.
That is, wormlike chains of contour length much less than their persistence length behave like rigid rods. Without further proof, it can be shown that the mean square radius of gyration for a wormlike chain is given by the equation (Bloomfield et al., 1974) ~S2~worm ---
2alen e [1/6 - a / 2 l e n e + a2/(lene) 2 - a3/(lene)3(1
According to this, with nl >> a,
le =
- exp{-lene})].
2a, for wormlike chains of large contour length, so (S2)worm, nl>>a ~- 1 / 6 n e 12.
This coincides with the expression for the mean square radius of gyration previously given for a random coil. In contrast, for wormlike chains with nl << a, the expression reduces to the square of the radius of gyration of a rigid rod, S2orm,
nl < < a - -
1/12(nele) 2 - -
S r2i g i d r o d "
Thus, we expect long-chain nucleic acids to behave as random coils but with very much larger effective bond lengths than flexible chains. On the other hand, short-chain nucleic acids are expected to behave as rigid rods with effective bond lengths about the same as the real ones. There is a property of natural double-stranded DNA that is not found for polypeptide chains. The property is that some natural double-stranded DNAs exist as cyclized macromolecules with no free 5' and 3' ends. Typically, these DNAs are present in plasmids, bacteria, and certain viral genomic DNA. A phenomenon called supercoiling, somewhat analogous to tertiary structure in proteins, occurs with these molecules. Supercoiled DNA has the appearance of a helical telephone cord when the cord is in its unstretched state. The impor-
30
Jay A. Glasel tance to biophysical measurements is that the degree of coiling is affected by various small molecules, in particular those that intercalate between the bases. This can affect the shape of the molecule profoundly. For example, the sedimentation velocity (Chapter 2) of circular double-stranded DNA drops to a minimum and rises to its first value as the concentration of ethidium bromide is increased in a solution. Supercoiled DNA is characterized by the equation W = L - T, where W, L, and T are, respectively, the writhing, linking, and twisting numbers discussed in the Glossary (see Supercoiling). Forms with the same L values can be interconverted between structures with different combinations of W and T. Forms of DNA with different L values are called topoisomers. Topoisomers can be distinguished by sedimentation and electrophoresis experiments.
6. Quaternary Structures of Proteins and Nucleic Acids Many proteins are present in their biologically active forms as multiple-subunit homo- or heteropolymers (the subunits are either the same polypeptide chains, or different ones). The forces holding the subunits together are not well understood, although they are usually not strong enough to withstand high salt concentrations, changed solvents, increased temperatures, etc. This type of quaternary structure can be studied by biophysical methods. Native (i.e., nondisordering) gel electrophoresis and sedimentation equilibrium are popular methods for studying quaternary structure in proteins. Other instances of what is technically quaternary structure in proteins occur. This is the formation of very large multimers of individual protein units. The phenomenon is usually given the description "aggregation." Often, the biological function of the aggregation is unknown, or while natural, may be deleterious. One of the most common examples is in sickle cell anemia. In this disease hemoglobin molecules with one mutated amino acid residue per polypeptide ]3-chain polymerize to such a high degree that the resulting aggregates distort the shape of the erythrocytes to a characteristic sickled shape. Again, sedimentation equilibrium is a popular method for studying the formation of this type of quaternary structure. Quaternary structure of nucleic acids has not really been considered as a subject in biophysical chemistry. However, there is no physical reason to regard protein-nucleic acid complexes as anything else but heteromolecular quaternary structures. The formation of these complexes is rapidly becoming an important part of biological research. Most of the applications of biophysical techniques to this problem have come from X-ray diffraction and, more recently, NMR structural work.
C. Electrical Properties Biological macromolecules almost always have groups on them that can independently ionize to produce positive or negative charges. The degree of ionization of each of these groups depends on many factors. Among them are the pH of the solution, the temperature, the composition and concentration of smaller ionizable molecules (collectively called salts) in the solution, the positions of individual ionizable groups within the macromolecular structure, the concentration of the macromolecule, and the presence of other macromolecules in the
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
31
same solution. Because experimental methods exist (in particular, isoelectric focusing and mass spectrometry; see Chapters 2 and 4, respectively) that can determine a difference of one charge between two ionization states of the same protein in solution, it is important to understand the origins and effects of electrical charge on macromolecules. Strong electrostatic forces act between the various salt ions and between these ions and the charged macromolecules. These interactions modify nearly all the properties of macromolecules. In fact, the existence of an electrostatic charge on a macromolecule allows the use of a transport process, namely, electrophoresis (Chapter 2), for separating macromolecules with different charges. In a certain sense, theoretical study of polyelectrolytes is an extension of studies of simple electrolytes. For a polyelectrolyte of well-defined shape (e.g., a globular protein) the main distinction from simple ions stems from the polyelectrolyte's sometimes high charge and the high value of the resulting electrostatic potential. With solutions of flexible molecules, the fixed charges may be separated from each other to some extent as the chain expands when the solution is made more dilute. However, for any polyelectrolyte (in contrast to small ions such as salts), a limit is set on the possible separation of fixed charges due to the attainable conformations of the chain. Hence, as opposed to the case of simple electrolytes, for polyelectrolytes, effects produced by the interaction of ionic charges will not vanish in the limit of infinite dilution, as happens in simple electrolytes. The D e b y e - H i i c k e l treatment was the first theory to explain successfully the thermodynamic properties of very dilute simple electrolytic solutions. The Debye-H6ckel theory can be applied to solutions of charged macromolecules and their counterions, provided some assumptions are made about the shapes of the macromolecules. In fact, K. V. LinderstromLang's basic theory of polyelectrolytic solutions, which is still used, was developed only a year after Debye and H6ckel developed their theory in 1923. To illustrate a simple case that has a general message, we assume a spherical macromolecule with a single positive charge smeared over its whole surface and univalent counterions of opposite charge that are free to move about in the solution. The Linderstrom-Lang/Debye-H6ckel theory is able to predict the electrostatic potentials at distances r from the center of the macromolecule as a function of the ionic strength of the solution. Figure 11 shows a typical result. A point of importance may be derived from contemplating Fig. 11. In the presence of high salt concentrations, the electrostatic potential falls almost to zero at short distances from the surface of the charged macromolecule. At large distances at high ionic strengths, where the potential is almost zero, the macromolecule appears to be uncharged. The mechanism for this is clearly that the counterions surround the macromolecule, and, outside, this ionic atmosphere screens the charge on the macromolecule in such a way that the ensemble behaves as if it were uncharged! This model is a reasonable approximation to a globular protein at pH values far from the isoelectric point (see below) and to random coiled (i.e., disordered) proteins contained in ionic detergent micelles (see Chapter 2 on the behavior of these in electrophoretic experiments). The combination of ionic charges composed of the centrally charged macromolecule and the counterion layer is sometimes called the "electrical double layer." For charged macromolecular geometries other than spherical, and with the same low numbers of charges per unit length as for proteins, the same general picture
32
Jay A. Glasel 8 '7
"
&
'
6~ ' 45-
~~,
O
g
e 3 2 1 0
. I
!
1
I
2
3
~
4
I
5
r(nm)
I
6
7
8
9
I
10
Fig. 11 Plots of the electrostatic potential in the vicinity of a spherical polyelectrolyte, of radius 25 A and carrying a single positive charge uniformly distributed over its surface, plotted against the radial distance from its center, r, for various ionic strengths (I). The ionic strengths are in units of molarity and the potentials are given in millivolts. From Richards (1980). Reprinted with the permission of Cambridge University Press.
holds: the charged object is invariably shielded by its ion atmosphere. Thus, a highly dilute solution of a polyelectrolyte must be viewed as consisting of small regions in which polyions with a high density of "fixed" charges create high local electrostatic potentials. These potentials attract counterions strongly, with the intervening spaces having very low ionic concentrations (Fig. 12). The model of a globular macromolecule with charge varying with p H clearly is not a very realistic one for polynucleotides. For nucleic acids, the phosphate group is negatively charged at all biologically relevant p H values. The repulsive electrostatic potential between these fixed phosphate charges will tend to extend a nucleic acid molecule. Furthermore, the molecular masses of nucleic acids are usually very much larger than for proteins. Finally, if double-
|
| | A
~
X
4>_; -
\~_
@j/
| |
|
|
|
Fig. 12 Model of a wormlike negatively charged polyelectrolyte in solution. From Morawetz (1975).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
33
stranded DNA is considered, the helical conformation will make the macromolecule even more resistant to bending. The shapes of nucleic acids were discussed above in terms of the wormlike character of these macromolecules. Several theories applicable to polynucleotides have been developed. A useful short summary of more advanced aspects of polyelectrolyte solutions than discussed here is given in a monograph by Eisenberg (1976). All the theories developed so far predict the same type of behavior. However, our discussion is based on a review by Manning (1972). Theoreticians have treated the polyelectrolytic properties of nucleic acids on the basis of a worm standing at attention: i.e., nucleic acids are modeled as long rigid rods with charge densities determined by the regularly spaced phosphate groups. Nucleic acids are associated with a counterion phenomenon that is different than that associated with proteins. This is because of the high charge density existing in a nucleic acid chain at neutral pH. For DNA, the charge spacing is about 1.7 A. For globular proteins with much lower charge densities, the Linderstrom-Lang/Debye-Hfickel theory predicts a potential distribution around the macromolecule that varies continuously as a function of counterion concentration (Fig. 11). For rodlike nucleic acids with high charge densities, theoretical studies show an important difference in the behavior of counterions and the behavior of the electrical double layer around globular proteins. The difference is that, for nucleic acids, as the ionic strength is increased from zero by addition of salts, a critical concentration is reached above which counterions are suddenly attracted to the surface of the rod. The effect is called "counterion condensation." In slightly more quantitative terms, it is found theoretically that a critical charge density, ~crit, exists on the surface of a rodlike molecule; at this critical charge density counterions associate with the surface of the rod so that the net charge density in dilute solutions is maintained at the critical value. Several features of the phenomenon of counterion condensation must be noted. For water solutions, ~crit corresponds to a charge spacing of 7.14 A. Therefore, for DNA (and other single- and double-stranded nucleic acids) counterion condensation always occurs. That is, counterions condense so as to reduce the effective charge density to the critical value. Because of the properties of water, this charge density is independent of temperature, ionic strength, or the nature of the nucleic acid. The condensation takes place to the same extent no matter how much the solution is diluted. That is, the tendency of the condensed counterions to escape into the surrounding solution (and increase their entropy) is always overcome by the strong electrostatic attraction that the nucleic acid has for them. The theory of counterion condensation has been worked out approximately for solutions with salts of different valencies. The important qualitative conclusion from these studies is that ions of higher valency condense preferentially. This is probably the reason small concentrations of divalent cations have such pronounced effects on the properties of nucleic acids, and not that the ions are bound in some more specific way. The polyelectrolytic character of proteins and DNA affects their behavior in a variety of laboratory procedures. Some of these processes are discussed in other chapters of this volume, including electrophoresis (Chapter 2), viscosity (Chapter 3), and sedimentation (Chapter 3). To complete our introduction to polyelectrolytes, we now discuss their
34
Jay A. Glasel conformational changes due to intra- and intermolecular charge interactions. In a highly charged macromolecule, various charged groups will repel one another if they have charges of the same sign. If the conformation of the macromolecule can change in a way that increases the distance between the charged groups, the electrostatic energy of the molecule will decrease. From what has been previously discussed here, the magnitude of this decrease will be reduced if high concentrations of salt are present. In this case the charged groups will be shielded by the electrical double layer effect. It is for this reason that globular proteins tend to become disordered when they are highly charged at pH values far from their isoelectric point, and that double helical structures such as that of DNA tend to revert to random coils in low ionic strength solutions. Conversely, both effects can be counteracted to some extent by additional salt, increasing the ionic strength. The charge effects in helix-coil transitions of polynucleotides are dominated by the counterion condensation effect. A crucial point here is that the linear charge density on a single-stranded polynucleotide is different than that for a double helix. The values of the parameter ~crit are different for the helical and coiled forms. If ~rit,h and ~crit,c are the helical and coil values of this parameter, respectively, theory predicts 0= 1
-
(1/~crit, c -- 1/~crit, h) =
1 - 77,
where 0 is the number of counterions condensed onto each one of the fixed charges. It turns out that for DNA, rl = 0.32. It can be seen that the number of condensed counterions per charge group decreases by rl when the helix reverts to a random coil form. Most important effects accompanying this change (release of ~/counterions into the solution) are an increase in the entropy of the solution and a change in the energy of interaction of the charged groups with their ionic atmospheres. In fact, theory predicts that the change in energy of interaction, AE, when the helix reverts to a coil, is AE
oc
-
rlkT
ln(c) 1/2,
where c is the concentration of added salt. Because ~/is positive, an increase in salt concentration stabilizes the helix form. We must be concerned with another phenomenon related to disordered proteins and nucleic acids: how the dimensions of a polyion depend on the mutual repulsion of fixed charges, and how this will affect the properties of the solution. The basic phenomenon is called polyelectrolyte expansion. Clearly, any physical measurement that is dependent on the radius of gyration of a macromolecule will be sensitive to conditions that change the magnitude of polyelectrolyte expansion. The polyelectrolyte properties of polynucleotide chains are particularly pronounced and closely related to the properties of synthetic coiling polyelectrolytes, such as polyacrylic and polymethacrylic acids. The characterization of DNA as a wormlike macromolecule in solution (see the discussion of DNA shapes, Section III,B,5) has led to the use of DNA as a model for testing polyelectrolyte solutions. On the other hand, the interest in proteins is in their native structures and in the effects of their polyelectrolytic properties on maintaining those structures, in the functions of the structures, and in the purification techniques to isolate proteins.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
35
Polyelectrolyte expansion is caused by charge repulsion of like fixed charges on a disordered macromolecule. The tendency is opposed by electrical double layers and counterion condensation around charged groups in proteins and nucleic acids, respectively. As an extension of the discussion presented above, it is clear that adding exogenous salt to solutions of disordered proteins or nucleic acids will tend to oppose their expansion by shielding charges from one another. The only exception to this might be a thermally disordered protein in a pH range wherein the protein contains regions of positive and negative charges that attract one another. In this case the formation of electrical double layers around the charges at high ionic strengths could cause expansion of the chain. However, the main effects on chain expansion are with nucleic acids. Counterion condensation reduces coulombic repulsion among the backbone charges, and therefore reduces the expansion. The effects of changing ionic strength on measurements involving the radius of gyration of nucleic acid chains are very large. Consequently, ionic strengths must be precisely specified for these experiments. The physical and chemical properties of water play important roles in determining the properties of polyelectrolytes, such as proteins, in solution. In particular, two properties of liquid water are mentioned now and will be discussed in more detail later in the chapter. The first is that liquid water at any temperature has lower entropy than one might predict by analogy to other chemically similar liquids (such as its electronic congeners H2S or H2Se). Physical chemists have attempted for years to produce a theoretical description of the dynamic structuring of water that leads to this property. The picture that is widely accepted at present is based on liquid water being described as a mixture of nonbonded individual molecules and transient defective ice structures. In ice, each water molecule is hydrogen-bonded to four other water molecules. For any water molecule in ice, two hydrogen bonds result from partial donations of protons to two adjacent oxygen lone electron pairs and the remaining two bonds result from partial acceptance of protons from adjacent molecules onto the two oxygen lone pairs. The result is a very open but rigid structure for crystalline ice. The picture of liquid water is that of partial continuation of some of this structure when ice melts. It is supposed that small regular icelike structures form and break apart constantly throughout the liquid. The interval between bond formation and breakage is thought to average around 10 - 1 1 10 -12 s e c (Eisenberg and Kauzmann, 1969). A second property of water is also very important to its characteristics as a solvent. This is its high dielectric constant. As in the Debye-H~ickel theory we can generalize the electrostatic (coulombic) force between two charges i and j separated by distance rij in a vacuum as F ~ 1 / Er2j, where E is the dielectric constant of the medium between the charges. The dielectric constant is a dimensionless number. It is always greater than unity, with values of about 1.001 for gases, 2 to 10 for solid insulators such as glass, and from about 87 (0~ to 55 (100~ for liquid water. Thus, the force between two charges is much less in liquid water than when the charges are the same distance apart in a vacuum. This is the reason solid NaC1 dissolves easily in w a t e r m t h e coulombic forces between the sodium and chloride ion pairs are
36
Jay A. Glasel decreased by a factor of up to 87 when liquid water comes between them. However, the dependence of electrostatic forces on the reciprocal square of the distance means that the forces are effective over relatively long distances. Thus, all the ions in a salt solution continue to influence each other even when the solution is very dilute. Physical chemists refer to these as long-range forces. In contrast, many other forces discussed in this chapter depend on intermolecular distances, with powers as high as 1 / r 12. Finally, the dielectric constant of the solvent is of great importance for theoretical studies of protein and nucleic acid conformations in solution. The problem is that Coulomb's law as stated previously is accurate only for a continuous medium. In a polyelectrolyte such as a protein, the charges may only be separated by a few nanometers. Consequently, the m e d i u m between them is not bulk water. There may be room for only a few solvent molecules. What, then, is the dielectric constant of this medium? In many cases theoretical predictions of structure are done on the basis of a fixed dielectric constant with a value between unity and that of bulk water. If the dielectric constant used is unity, the calculation is called a "vacuum" one (Chapter 9). The equilibrium binding of hydrogen ions, metal ions, and other species to proteins and nucleic acids has a marked effect on their macromolecular structures. We first consider hydrogen ion binding by noting that the dissociation of a molecule into its anion and a proton, MH ~.-~-A- + H +, is characterized by a temperature-dependent, ionic strength-dependent, equilibrium constant K. The negative base-10 logarithm of the equilibrium constant is called the pK. The pK value is used to express the acid-base properties of individual ionizable groups on proteins and nucleic acids. For proteins, the important ionizable groups are the N- and C-terminal amino and carboxyl groups, respectively (if they are not "blocked" by chemical substitutions that prevent their ionization), and ionizable side chains of their constituent amino acids. The ranges of pK values for the groups most commonly found in proteins are given in Table VIII. Different proteins contain different mixtures of side-chain residues. They are classified according to whether the ratio, (Arginate + Lysinate) / ~ (Glutamate + Aspartate), is greater or less than one. The sum is taken over all the Arg, Lys, Glu, and Asp residues in the protein. If the ratio is less than one, the protein is called acidic. If the ratio is greater than one, it is a basic protein. Acidic and basic proteins will migrate in opposite directions in an electrophoretic experiment. In a polyacrylamide gel electrophoretic experiment to determine protein molecular mass (Chapter 2), the protein is disordered so that it assumes a flexible form whose radius of gyration is proportional to its macromolecular length and therefore to its molecular mass. It is then usual to cause the disordering with an amphoteric detergent such as sodium lauryl sulfate (also called sodium dodecyl sulfate, SDS) that has a negative charge over a wide pH range and a hydrophobic group
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
37
Table VIII pK Values for Common Acidic and Basic Groups in Proteins Group or residue
Approximate pK range in proteins
Unblocked amino-terminal residue Unblocked carboxy-terminal residue Arginine Lysine Cysteine Histidine Aspartic and glutamic acids Tyrosine
7.6-10.6 3.0-5.5 11.5-12.5 9.8-10.4 8.0-9.0 6.0- 7.0 4.0-4.8 9.5-10.5
that binds strongly to all disordered proteins. This coats the protein molecules with large numbers of negative charges so that regardless of whether their native forms are acidic or basic, the disordered, SDS-treated proteins always migrate as a polyanions. At some pH, whether they are initially acidic or basic, native proteins will assume a formal net charge of zero. That is, the total average charge is zero at this pH, even though they may have large (but equal) numbers of positive and negative charges. This point on the pH scale is called the isoelectric point (the pH at that point is usually designated the P/e)- Given the amino acid composition of a protein, an approximate pie can be calculated theoretically. The calculations are easily done on a computer and several computer programs exist to do this, and to plot out the resulting predicted titration curve. For example, the popular GCG molecular biology program has such a subprogram. These theoretical isoelectric points are approximate because the effects of the array of fixed charges in a polyelectrolyte on each pK value cannot be taken into account accurately for reasons given above. However, it is true that isoelectric points for a protein can be measured accurately (Chapter 2), and can be used to help characterize a protein. The measurement is sensitive enough to detect a change of one formal charge difference between two proteins. This means that mutations or substitutions involving an ionizable residue can be detected this way. Preparative isoelectric focusing is also possible as a method of purifying proteins. At the isoelectric point, while the net average charge on the protein, (Zp), is zero, molecules in solution will carry different electric charges at any given instant. Thus molecules with charges of 0, + 1, + 2, . . . , - 1, - 2, . . . will be present. For example, Fig. 13 shows the fractions of different charge forms for hemoglobin at its isoelectric point. Figure 13 shows that there are significant numbers of molecules with net charges between + 4 and - 4 at any instant. Because of this, the mean square charge (Zp) is not zero. This phenomenon has important consequences for the electrostatic properties of proteins because it results in a large effect on the activity coefficient of the protein. In particular, theoretical treatment (Timasheff, 1970) shows that the charge fluctuations re-
38
Jay A. Glasel 0.25
I
i
I
i
I
I
i
2
4
6
0.20 L'XI
N
(D
"~ 0.15 O3 C C
o
0.10
_
0 t-,
LL 0.05
.
I
-6
-4
-2
0
Z2 Fig. 13 Distribution of forms with net charge (Z) for isoelectric hemoglobin. Reprinted from Timasheff (1970), p. 9, by courtesy of Marcel Dekker, Inc.
sult in a significant attractive force between protein molecules at their isoionic point if the ionic strength of the solution is low. In the limit of low concentration, the net attraction is proportional to the square root of the protein concentration. As a practical matter, the effect is of interest because protein molecules held at their isoelectric points tend to precipitate due to the attraction between them. Another effect the charges on proteins have at pH values different from their isoelectric values is important in crystallizing the proteins. Both the anions and cations in a salt solution are highly hydrated. That is, the ions are quite tightly bound to water molecules, which surround them in at least one layer. At very high salt concentrations, possible with salts such as ammonium sulfate (which is saturated at 4.1 M at 25~ so little water may be available to solvate the protein that the protein molecules are driven to polymerize. The polymerized proteins may then come out of solution in some disordered polymeric form. This is called salting out a protein. The effect can be used as a crude form of purification because different proteins will salt out at different salt concentrations. However, of equal or greater importance, if the salt concentration is increased slowly under controlled temperature conditions, many pure proteins crystallize out of solution. This is the basis of many efforts to crystallize proteins for use in X-ray and neutron diffraction studies (Chapter 8).
D. Magnetic Properties One can build an intuitive picture of certain atomic properties by using a picture of an atom that disregards the wave-mechanical picture of electron proba-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
39
bility clouds around nuclei and pictures instead electrons in orbits circling atomic nuclei. When a steady external magnetic field is applied to such an atom, the motions of the atom's electrons are altered. The alteration produces an induced electrical current within each atom. Electrical currents always have magnetic fields associated with them, and for the orbital electrons just mentioned, the directions of the induced magnetic fields are always opposed to the direction of the steady applied field. These induced magnetic fields have effects within each atom, most importantly on their own nuclei, and on other atoms and nuclei that may happen to be in the same molecule. The production of these induced fields is just an extension of Lenz's law, a law discovered in the nineteenth century. According to Lenz's law, the current induced in a circular loop of wire by an applied magnetic field corresponds to a magnetization in the direction opposing the field. Because all molecules have electrons, they all respond to externally applied magnetic fields by tending to oppose them. This behavior is called diamagnetism. Note that an electrical field always induces an electrical dipole moment (electrical polarization) in the direction of the field. There is no electric analog of diamagnetism. The amount of diamagnetism a molecule exhibits, the diamagnetic susceptibility, can be measured. The diamagnetic susceptibility of even a macromolecule may be calculated to a good approximation by adding up the tabulated susceptibilities of groups of atoms within the whole molecule. In certain cases, the diamagnetic susceptibility of a group of atoms depends importantly on the spatial direction of the external field with respect to the group of atoms. The case of most importance to biophysical chemistry is that of aromatic rings. In aromatic rings the ~r electrons are, of course, delocalized. But they are delocalized in a highly directional way. For instance, when the plane of a benzene ring is perpendicular to the external field, maximum diamagnetic susceptibility is exhibited by the benzene molecule because the delocalized electrons can travel easily around the track formed by the ring. When the ring plane is parallel to the applied field, the diamagnetic susceptibility is minimized because the direction of the driving force is across the plane of the ring and therefore not part of the normal track of the electrons. Why is this effect of importance for macromolecules? The answer is that for certain macromolecules, particularly proteins and nucleic acids, aromatic rings are in fixed orientation with respect to other nonaromatic groups. Magnetic fields are characterized by "lines of force." For a steady applied homogeneous magnetic field, the external field's lines of force are parallel and evenly spaced. At the molecular level, the presence of intramolecular centers of high diamagnetism, such as caused by an aromatic ring, distort the lines of force away from homogeneity. This distortion can extend to the total (applied plus induced) field seen by neighboring atoms or groups of atoms. Certain techniques, particularly NMR (see Chapter 7), can detect the effect on these atoms in a way that is useful for identification of atoms near aromatic groups. Furthermore, the basic diamagnetic effect just outlined is the physical basis for the NMR phenomenon called the chemical shift. Thus, the position of the spectral features of aromatic amino acids in an NMR experiment is determined by their rings' extremely large diamagnetic susceptibility. In 1845, while investigating the effect of a magnetic field on the optical properties of substances, Michael Faraday discovered that magnetic properties
40
Jay A. Glasel are not confined to a few substances, but that all substances are magnetic (i.e., they interact with an external magnetic field). He discovered that all substances can be divided into two classes, diamagnetic substances and paramagnetic substances; those in the first class, we have already discussed m they are repelled from an applied magnetic field. Those in the second class are attracted into a magnetic field even though they also have a repelling component (their essential diamagnetism). Many biologically important macromolecules have paramagnetic moments associated with them. Usually, this comes about when there is an ionic or covalent bond between the macromolecule and a molecule or ion that has an unpaired electron associated with it. An example of the former is molecular oxygen, and examples of the latter are transition metal ions. The origin of molecular paramagnetism is the interaction of unpaired electron magnetic dipole moments with an externally applied magnetic field. Molecular paramagnetism is the magnetic analog of dielectric polarization. On the other hand, in Chapter 7 the interaction of certain nuclei with magnetic fields is described in terms of nuclear paramagnetism, which is the basis of NMR experiments. Electron paramagnetism arises because electrons have the physical properties of not only mass and negative charge, but also have the property that they are intrinsic magnetic dipoles. According to the Pauli principle, in most cases electrons in molecules are paired in such a way that their magnetic dipoles cancel out. The presence of an unpaired electron within the framework of a macromolecule confers to the macromolecule a measurable p r o p e r t y m overall paramagnetism. Overall paramagnetism is usually much larger, and in the opposite direction from the ubiquitous diamagnetic moment. Its magnitude is also temperature dependent, in contrast to diamagnetism. Additionally, the paramagnetic ions or molecules are often located at the site in proteins associated with the biological function of the macromolecule. For example, the oxygen molecule in oxyhemoglobin is closely associated with the iron atom of the heme group. Also, transition metal ions are often located at the active sites of enzymes, where they are required for activity. Thus, the paramagnetic moment of the macromolecule may be affected by reactions that change the valence state of their paramagnetic moieties. In this book we have not included a discussion of this type of measurement, termed electron spin resonance (ESR). However, there is another effect of paramagnetic molecules and ions. Because the unpaired electron magnetic moment is almost 2000 times larger than the nuclear magnetic moment, the presence of materials with unpaired electrons anywhere in a macromolecule (or even in a solution containing the macromolecule, such as dissolved oxygen) has an enormous effect on nuclear magnetic resonance measurements of all kinds. These effects are mentioned in Chapter 7.
E. Kinetic Properties In solution, molecules undergo translational diffusion (with components in the x, y, z directions in a Cartesian coordinate system) and rotational diffusion (specified by angles 0 and q~ in a spherical coordinate system). It is normally assumed that these processes are independent of one another and that both take place due to random collisions of molecules. Strictly speaking, translational
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
41
diffusion is characterized by three translational diffusion coefficients. However, translational diffusion is almost always assumed to be isotropic (meaning movement in any direction is equally probable) as opposed to anisotropic (where there are favored directions) and therefore can be characterized by one diffusion coefficient. As an intuitive approximation we can picture translational diffusion as taking place by discontinuous jumps of a molecule from one position to another. In a liquid the number of collisions that a given molecule undergoes per second is very large, abut 1015/sec. If the mean value of the square of the displacement is ~$2~ (this quantity is normally called the net mean-squared displacement) in any direction after time t, the translational diffusion coefficient is Dtran s =
~/~5~2/t.
D usually has units of cm2/sec. A more rigorous classical treatment for translational diffusion of a sphere was given by Stokes: Dtran s =
kT/6yr,/a,
where ~/is the viscosity of the liquid and a is the radius of the sphere, k is Boltzmann's constant, and T is the absolute temperature. Physical chemists are often interested in diffusion in pure liquids. For this case the diffusion coefficient is referred to as the self-diffusion coefficient. Here, we are interested in diffusion coefficients for macromolecules in aqueous solutions. Thus, for equally hydrated spherical molecules of molecular mass M, classical theory predicts that the diffusion coefficients should vary as 1 / M 1/3. This is approximately true. For example, ribonuclease (M = 13,683 Da) and urease (M = 480,000 Da) have translational diffusion coefficients of 11.9 x 10 -7 and 3.46 • 10 -7 cm 2 sec -1, respectively, at 20~ In contrast, water molecules have a selfdiffusion coefficient of about 10 -5 cm 2 sec -1 at the same temperature. Translational diffusion coefficients are of importance in understanding biomolecular interactions, especially the type of reaction involving a small molecule binding to an active site on a macromolecule (e.g., enzyme-substrate, receptor-drug, antibody-hapten binding). However, experimentally, translational diffusion coefficients are difficult to measure directly. The most convenient methods are probably intrinsic viscosity and sedimentation equilibrium experiments (Chapter 3). Rotational diffusion is a more complex subject to discuss theoretically, compared to translational diffusion. The reason is that most molecules, especially macromolecules, do not have overall spherical shapes. That is, they would be expected to undergo anisotropic rotational motions. Classical theory shows that the random rotational path of an irregular body dissolved in a liquid is described by a mathematical function (called a "tensor") with nine components. When interpreting data that depend on rotational diffusion (e.g., nuclear magnetic resonance relaxation times; Chapter 7), it is almost always assumed that anisotropic rotational diffusion can be described by, at most, three components. This assumption is based on the intuitive idea that rotational diffusion takes place around the same principal axes of the moment of inertia of the
42
Jay A. Glasel molecule. Strangely enough, although various sophisticated theories have been developed to describe rotational diffusion for molecules in solution, it is described very well in most cases by a simple equation developed by Einstein early in his career. This equation gives the rotational diffusion coefficient for a sphere: Dro t =
kT/8,rr,oa 3,
where a is the radius of the sphere and the other symbols have their previous meanings. Note that the units for Dro t (radians sec -1) are different from the units for translational diffusion. Rotational diffusion describes the path a point on the sphere takes as a function of time due to random rotational reorientations. Figure 14 shows what the path might look like. Consequently, if (/~-~2) is the net mean-squared angular rotation of the sphere in radians in time t, Drot ~_~ ~/~-~2) /
t,
in analogy to the similar expression for translational diffusion. The predicted rotational diffusion coefficient for a macromolecule of mass 50,000 Da in water is about 4 • 10 6 sec -1, whereas that for a water molecule is about 5 • 101~s e c -1. These values are very close experimentally to measured ones. The molecular mass dependence of Dro t f r o m this picture is much larger than for Dtran s. The rotational diffusion coefficient depends on 1 / M . Provided rotational diffusion is assumed to be isotropic, parameters derived from several different measurements can give experimental values for Dro t . In particular, NMR relaxation measurements are used (Chapter 7). Conversely, isotropic rotational diffusion has to be assumed to interpret data in terms of macromolecular structures derived from NMR measurements. In NMR relaxation experiments, the quantity being sought is the "correlation time." The correlation time can be explained as follows. At an initial time, t = 0, we assume each atom in a rigid
zl Aj
I I
Fig. 14 An example of a rotational random walk from point A to point B on a sphere. From Carrington and McLachlan (1967).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
43
molecule has some starting x, y, z coordinates with respect to axes fixed in space (these axes are often referred to as "the laboratory frame of reference"). At succeeding times, as the molecule undergoes random angular jumps, its alignment (that is, its atomic coordinates in the fixed axis system) begins to lose any deterministic relation to its alignment at t = 0. There is only a probability that it was aligned in the initial direction. This is expressed by a function called a correlation function that expresses the loss of statistical correlation between initial atomic coordinates and those at any later time. The rate at which this correlation is lost is exponential and is characterized for each spherical molecule, by a time called the correlation time, rc, that is related to the rotational diffusion coefficient by the simple equation, rc = 1 /
6Dro t .
For the macromolecule mentioned above with mass 50,000 Da, the correlation time is about 4 • 10 -8 sec. In one correlation time (0.04 ~sec) the net angle tuned will be about 33 ~ (31/2 radians) from any initial alignment. For anisotropic rotational diffusion the situation is more complex, but can be solved analytically provided it is assumed that rotational diffusion can be described by three rotational correlation times and that rotational motions take place around the moments of inertia principal axes, as described above. A more difficult situation is when there is intramolecular rotational diffusion. Simple examples are methyl group rotation and aromatic ring flips in proteins and nucleic acids. These motions are superposed onto the overall macromolecular motions. In general, there are different correlation times associated with each of the different motions. An analytical solution for the case of a methyl group freely rotating in a macromolecule has been found. However, this is the only such solution for this type of problem. F. Color In this section we are concerned with the basic concepts of spectroscopymthat is, how electromagnetic waves of different wavelengths interact with matter. At the heart of this discussion are the basic principles of quantum mechanics. If we generalize our common knowledge of color to include the results of interaction of electromagnetic radiation, irrespective of wavelength, with matter, then we can unify all the forms of interaction into one general physical picture. That is, the elements of spectroscopy that are discussed below are basic to all particle, atomic, and molecular systems. For our purposes, matter has the following properties that interact with electromagnetic radiation: 1. Permanent or induced molecular electrical dipole, and multipole, moments 2. Permanent atomic magnetic dipole moments 3. Electron and nuclear magnetic dipole moments One of the greatest examples of the unification of ideas in the short history of science took place in the 1860s and 1870s when Maxwell was able to combine the physical description of electromagnetic radiation with that of electricity and magnetism. Thus, he considered an electrical dipole moment held apart by some means, and asked, in effect, what the physical result is of two charges
44
Jay A. Glasel oscillating in simple harmonic motion with respect to one another. The equations he developed permitted a solution to this problem. The result can be described by saying that the oscillating dipole emits (loses) energy into its surroundings in the form of an electromagnetic wave. Electromagnetic radiation is made up of electric and magnetic field vectors whose magnitudes oscillate with time at a frequency v = ro/2~r radians sec-1 [09 is in units of hertz (Hz)] and propagate with the speed of light c (see physical constants). Figure 15 shows the space variations of the electric and magnetic field vectors (with magnitudes E0 and H0, respectively) in a plane-polarized wave propagating along the x axis in a Cartesian coordinate system. For this wave, Ey = E0 sin ro(t + x / c ) , G = H0 sin ro(t + x / c ) . The wavelength of the wave is ,~ = c l ~,.
In the past, the phase of a wave was defined as rot + ro x / c
and therefore the phase changed with time. At present, the time-invariant constant, rox/c, is sometimes called the phase, and sometimes the phase angle or phase shift. We will call q~ the phase angle of a wave. The point is, different q~ values correspond to motions in different phases of each wave. in the wave drawn in Fig. 15, consider a fixed plane at x = constant, transverse to the direction of propagation. At all points of this plane, the electric field intensity Ey oscillates in simple harmonic motion with angular frequency ro and amplitude E0. We describe all these motions as being in phase with each other. Thus, at any fixed point in space the electric vector performs simple harmonic motion along a fixed direction (the y axis), and the magnetic vector performs a similar vibration in a direction normal to this (the z axis). This wave is called a linearly polarized wave because the electric field vector at any point is directed along a
Y
,~'" J
Fig. 15 The space variations of the magnitudes of the electric (E0)and magnetic (H0)field vectors in a traveling sinusoidal plane wave that is linearly polarized.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
45
fixed line at all instants of time. A more general case, for a given frequency, is that there are both x and z components for both electric and magnetic fields. The resultant vectors, at a fixed point in space, will sweep out ellipses in the y - z plane. Such a wave is called elliptically polarized. A circularly polarized wave is the special case of the ellipse; that is, the two simple harmonic motions are of equal amplitude and have a 90 ~ phase difference. Finally, in an electromagnetic wave the electric and magnetic field vectors are not independent. In fact, the magnetic vector oscillates in phase with the electric vector. If the radiation were due to many dipoles vibrating in random directions with no phase relation to each other, then there would be (1) no plane of polarization and (2) no phase coherency for the emitted radiation. Radiation without phase coherency is called incoherent. It will turn out that all natural radiation (e.g., radiation from the sun) and some man-made radiation (e.g., a light bulb) are incoherent. On the other hand, some man-made radiation is coherent (e.g., laser light). Natural radiation and sources such as light bulbs produce radiation with no preferred plane of polarization. However, using filters that specifically absorb light from all planes of polarization except one, these sources can be made to yield planepolarized, incoherent radiation. The way that this light interacts with macromolecules forms the basis of the optical rotatory dispersion and circular dichroism experiments described in Chapter 6. The brief picture outlined above is the classical description of the production of electromagnetic radiation and of its interaction with electrical and magnetic dipoles. The meaning of the word classical, as used in the physical sciences, is that the phenomenon being described is nonatomic, and nonrelativistic. That is, classical physics involves descriptions and interactions of large bodies moving slowly compared with the speed of light. The classical description suffices to explain some phenomena in everyday lifemfor example, how radio waves are produced and received. However, when applied directly to atomic phenomena the classical picture fails. For example, it predicts that within a chamber made up of material consisting of large numbers of our atomic oscillators there would be an infinite electromagnetic radiation density. The reason is that classically, some of the oscillators can be oscillating at infinitely high frequency. This would produce light of ultrashort wavelength. This prediction of classical physics was called the "ultraviolet catastrophe" when its implications were understood at the beginning of the twentieth century. Reportedly, Lord Kelvin, one of the best classical physicists of the time, said words to the effect that all of physics was known except for two clouds hanging over its head. One cloud was the ultraviolet catastrophe, the other was the failure of the Michelson-Morley experiment (the failure to detect the ether that was thought to be the medium through which electromagnetic radiation traveled). The resolution of the first cloud led to the discovery of quantum mechanics and the resolution of the second led to the discovery of special relativity. This was cloud-choosing at a high level. In an intellectual event of enormous practical importance, Max Planck was able to unify the classical and atomic pictures before atomic structure was known. He did so by assuming that the classical picture of radiation emanating from oscillating dipoles was fundamentally correct. However, in a complete break from classical thinking, he assumed two things:
46
Jay A. Glasel 1. The atomic oscillators vibrate at discrete frequencies characterized by energy levels En =
nhv,
where n is an integer, h is what Planck defined as a new fundamental constant of nature (now called Planck's constant; see Glossary, physical constants), and v is the frequency of the oscillators. 2. The probability W(n) of an oscillator existing in an energy state E n is given by the Boltzmann distribution law, W(n) ~ e x p ( - E n / k T ) = e x p ( - n h v / k T ) ,
where k is the Boltzmann constant and T is the absolute temperature. From these two assumptions and the results of Maxwellian classical theory, Planck derived the equation describing the distribution of radiation frequencies within the chamber described above, held at a certain temperature, and from which radiation cannot escape. Such chamber is called a black box. Planck's equation described the distribution of frequencies found experimentally in black boxes. This was the origin of quantum mechanics. The basic concepts of quantum mechanics, discrete energy levels for the oscillators and the level populations, are all we really need to know to develop a physical understanding of all forms of interaction of electromagnetic radiation with matter. Einstein used the Planck discovery to derive some of what we need to understand. His reasoning was as follows. Assume that a dipole does have discrete energy levels, and consider two of them: the mth and the nth. Einstein assumed that when light of the right frequency falls on such a dipole, the dipole can absorb that photon of light and make a transition from state n to state m. The probability that this occurs each second depends on which starting level we are considering, but for all levels Einstein assumed that the probability is also proportional to the intensity of the light. He called this absorption probability, Bnm. He also assumed that light is emitted by the oscillating dipole and that emission can take place in two ways. One way is spontaneous emission with probability a m n . In this process the dipole in excited state m loses radiation independent of any light falling on it. Another emission process he assumed is again under the influence of the light falling on the excited oscillating dipole-stimulated emission. The rate for this he again assumed is proportional to the intensity of light and has a probability Bran. With these assumptions, Planck's black box law, and the laws of thermodynamics, Einstein deduced the following: Bnm = Bmn ,
Amn = KB,nn,
where K is a constant made up of other fundamental physical constants (such as the speed of light). Stated in plain language, Einstein's results are that the probability of absorption is equal to the probability of stimulated emission, and if we know the probability of absorption (or induced emission) we can calculate the probability of spontaneous emission. Note that no assumption as to the nature of the dipoles has been made. They can be atomic dipoles due to the separation of nuclei from their surround-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
47
ing electrons, they can be nuclear magnetic dipoles, they can be permanent molecular electric dipoles due to a molecule being made up of atoms of different electronegativity, etc. They are all subject to the same phenomena of induced absorption and emission and spontaneous absorption and the mathematical relation between these. Once we understand the implications of Einstein's and Planck's results, the way is open to exploiting them to understand all forms of spectroscopy applied to biomolecular systems. It is also useful to have an idea of the magnitudes of the probabilities just mentioned and how they affect spectral results. For a strong electric dipole transition in molecules, iron is on the order of 108 sec-1, and for magnetic dipole transitions, Am,, is on the order of 10 -3 sec -1. The quantum mechanical uncertainty principle relates the spectral width, &v, of an absorption band to the lifetime of the excited state by the simple equation A ~ = Am n
where v is in units of radians per second. Thus, a strong electric dipole transition (e.g., ultraviolet absorption) can be expected to have a spectral line width of 108/2~r Hz, whereas a magnetic dipole transition (e.g., an NMR absorption band) can be expected to have a spectral width of 10-3/2"rr H z - - t h a t is, 1011 times narrower. We also note that if the probability of spontaneous emission is low, as it is for magnetic dipole transitions, then the only path for loss of excitation energy is induced emission and that requires radiation of the same frequency as for excitation. In fact, if the radiation continuously falls on a transition with low probability of spontaneous emission, the upper and lower states rapidly become equal in population. The result is no net absorption of energy from the incident radiation. The low probabilities for spontaneous emission and consequent possibility of equalizing populations of upper and lower energy states are associated with nuclear magnetic resonance and form the basis for understanding the "relaxation" and "saturation" phenomena that are discussed in Chapter 7. Continuing our applications of Einstein's results we can easily understand the principle behind lasers. The acronym "laser" is very descriptive: light amplification by stimulated emission of radiation. In the simplest example of a laser, we have brought about an atomic or molecular system consisting of three energy levels. Conditions are arranged so.that the highest energy level has a very high probability of spontaneous emission to a middle state characterized by a low probability of spontaneous emission. Therefore, when light whose energy corresponds to the transition from the ground (lowest energy) level to the highest level falls on the system, we will pump atoms or molecules from the ground state to the highest energy state. However, as we are pumping them, they are continuously dropping to the middle state and giving off radiation with energy corresponding to the difference between upper and middle levels. This energy is lost to us but, if we pump enough, we will have succeeded in producing a middle energy level that is very highly populated. Now, if just a little light of energy, corresponding to the difference between the highly populated middle level and the ground level, falls on the system, Einstein's result says that it will stimulate emission of radiation of that energy. This will stimulate more emission, etc., until the populations of upper and lower energy levels regain their Boltzmann distributions. Thus, this is a way to stimulate large
48
Jay A. Glasel Molecular energy
Frequency
Region
Wavelength
1019 _ u Electronic
(inner
shells)
I0 m i0 rt _ 1016
Electronic (valence
shells)
Vibrational
_
iOts _ i014 _ i013 _ i012 _
Rotational
i 0 II _
i0 jo _ I09
t 108 X-ray
_ _ 10-8
1--I07
_ _ 10-7
I 106 Vacuum U V i- lOS Ultraviolet (U V) J 104 Visible
_ _ 10-6
1_103 Infrared (IR) 1 i02
~
For IR
110 Millimeter
crn-~
Microwave
IO-S _ _10 -4 -
-10-3
_ _ 10-2
10-1
m
--1 --I0
-
-
-10
2
I0 e - Nuclear orientation
(high
fields)
107--
Rodiofrequency
_ _ 10 4
106 - _
_ _ i0 5
IOs - _ 104-103 - _ Nuclear orientation (zero
field)
102 - _
_ _ 10 3
_ _ 10 6
Audiofrequency
_ _ i0 ? _ _
cm
108
I0-cycles/seconds
Fig. 16 Nomenclature of various frequency and wavelength regions and the types of spectroscopy with which they are associated. From Whiffen (1966).
amplifications of light. What has just been described is the principle underlying a pulsed laser. When the pumping is continuous, stimulated emission is continuous and we have a continuous laser. In summary, the vibrating dipole picture as modified by quantum mechanics may be used to visualize phenomena in all of spectroscopy. It does not matter whether we are talking about a nuclear magnetic dipole or a molecular electric dipole. The principles are the same. For electronic spectroscopy the vibrating dipoles correspond to electronic motions with respect to the nuclei of atoms and molecules. For vibrational spectroscopy the dipoles correspond to permanent or induced molecular electric dipole moments. For magnetic resonance spectroscopy the dipoles correspond to the motions of the nuclear (or electron) magnetic moments. Figure 16 shows the energies, frequencies, and descriptions of various parts of the electromagnetic spectrum used for different spectroscopy experiments on molecules.
IV. Fourier Transforms The readers of this volume will find the process called the Fourier transform used in several chapters (in different guises). This is a case in which a funda-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
49
mental physical principle assumes different manifestations. The Fourier transform is, in fact, a pervasive and useful tool in the physical sciences. Fortunately, Fourier transforms are familiar to almost all of us, not as abstract mathematical operations, but as definite physical operations. We will first describe the fundamental principle for periodic time-varying quantities, i.e., waves. However, as we will later point out, the same principle holds for any periodically varying quantity. Imagine two sine waves (as a physical example, violin strings vibrating at the same time but at different frequencies) added together. Figure 17 shows the individual frequencies and the resultant total waveform that results from the linear superposition of the two frequencies. Even with two sine waves, Fig. 17 shows a fairly complicated curve. Clearly, this could be extended to a large number of different waves, giving a very complex total waveform. It is also true that almost any curve can be obtained by adding together infinite numbers of sine waves of different frequencies. If we know each of their amplitudes, we can produce the total curve. This method of analyzing a periodic function is called the method of Fourier transforms or, occasionally, Fourier analysis. How is it done? The answer is that it can be done both mechanically and mathematically. Indeed, each of us does Fourier transformation almost continuously. If our sense of hearing could not sort out the different waveforms we could never pick out speech or musical tones amid superimposed noisemsomething we are normally very good at. In fact, our ears take in sounds (mixtures of time-varying amplitudes of acoustical waves) and convert them to spectra (time-varying amplitudes of different frequencies). Our ears do this by having groups of specialized detectors in the inner ear. Each group responds with high sensitivity to only a narrow range of the many frequencies that we just saw can be contained in the incoming waveform. The ear therefore reacts to sound by breaking down the incoming waveform into different frequency components. Each group of frequency-specific cells has an output signal that is proportional to the amplitude (intensity) of the sine wave component at that frequency. In short, the output of the assembly of groups is a Fourier transform of the incoming total wave. By mechanisms we are still discovering, the brain decides to interpret frequency components whose amplitudes vary regularly, such
Fig. 17 A complex waveform resulting from linear superposition of two sine wave functions F a and F b .
50
Jay A. Glasel as speech and music, and rejects as noise those whose amplitudes are randomly varying. To do this, the brain must obviously use the information that the amplitudes at the different frequencies vary in time. In an almost exact analogy, when we want to convert an electromagnetic waveform into its components, we can pass the wave through an electronic device that has groups of elements that each respond only to a narrow frequency range. This device is called a spectrum analyzer. When attached to an oscilloscope, it enables us visually to see the amplitudes of the different frequency components making up the wave and how the amplitudes vary in time. That is, we can continuously view the Fourier transform of the incoming wave. An optical mechanism for doing the same thing is a prism or optical diffraction grating. The incoming waveform of light is broken up into its component frequencies by the action of the dispersive element (i.e., the prism or grating). We call the result a spectrum. Thus, a waveform, whether optical, electrical, or acoustical, and its spectrum are physically equivalent representations of the same thing. Mathematically, we call the two representations "Fourier transform pairs." From the above information, we know that physical (or physiological) devices can analyze complex curves into sums of sine waves of different amplitudes. Can this be put into a mathematical form so that, given the equation for the curve to be analyzed, we can get the amplitudes of the waves making up the curve? The answer is, of course, yes. The mathematical forms for a continuous Fourier transform pair are
1 L F(co)ei~ dco,
f(t) = ~ F(co) =
f
--
oo
f(t) exp -i~t dt, oo
where F(co) and f(t) are the Fourier transform pair in the frequency and time domains, respectively, and i is the complex number symbol. The function F(co) is commonly called a spectrum. For those readers not used to seeing complex numbers in integrals, more understandable forms of these general equations are produced when the relation, e +-i~~
=
c o s ( c o t ) -4-
/sin(cot),
is substituted into the above equations. Thus, F(co) becomes
F(co)=Lf(t)cos(cot)dt+iLf(t)sin(cot)dt. In many cases in physics, a mathematical equation is known for f(t) and therefore the integrals can be solved exactly. However, for our present purposes a detailed mathematical discussion is not very useful, because in the experiments described in this volume, the curves are complicated and no simple equation describes them. In some experiments, what is done with these complicated curves is to mathematically approximate their Fourier transform. For example, if the curve is a time-varying waveform, such as described above, we can make the following change. Instead of the spectrum analyzer device, we substitute a computer that samples the waveform's total amplitude as a function of time. The computer puts each sample into a different memory location along with a digital representation of its amplitude at the time the sample was made. Thus,
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
51
amplitude vs time has been stored in the computer's memory. In contrast to the case in which time is continuous, the time elements here are discrete. Consequently, the approximate Fourier transform is called a discrete Fourier transformation. In even the most perfect experiment with the largest computer, we can study f(t) for only a finite amount of time; we cannot ask the computer to do the integration required in the continuous form of the Fourier transform. Instead we ask the computer to approximate the integration by a summation over the time elements for which it has amplitude information. This is called a discrete Fourier transform (DFT). The development in the 1960s of the fast Fourier transform (FFT) computer algorithms to evaluate DFTs provided means of rapidly calculating spectra of time-varying signals. We can easily see that this is much better than a physical device such as a spectrum analyzer. In an electronic analyzer only a relatively few filter elements can be present, because they are bulky. However, a modern computer's memory can contain a staggering number of memory elements. Obviously, the more samples that are taken, and smaller the sampling time, the better the approximation to the spectrum the DFT is going to be. We have described what Fourier transforms are and how they apply to time-varying waveforms. In this volume this is applied to modern NMR spectroscopy (Chapter 8). However, at the start of our discussion we mentioned that Fourier transform techniques also apply to any periodic functions. Another way a function can be periodic is to have a spatially periodic value. An example of this is atoms arranged periodically in space. In the chapter on X-ray and neutron diffraction (Chapter 7) we will see Fourier analysis applied to analysis of the diffraction pattern resulting from X-rays or neutrons falling on a crystal. A good monograph on Fourier transforms and analysis exists (Bracewell, 1986).
V. Summary The biophysical principles discussed in this chapter are the basis for methods discussed in succeeding chapters in this book. In the effort to obtain biophysical knowledge of proteins and nucleic acids, students and investigators must keep in mind the basic purpose of the knowledge. That basic purpose is to relate biophysical properties to biological function. Thus, for example, it is wonderful to be able to sequence a gene, predict the sequence of the protein it encodes, isolate the protein, and then perhaps determine its three-dimensional structure. However, even at this advanced stage of knowledge of a particular system, we still have a long way to go toward relating it to the functioning of a living system. This presents a challenge, because the basis for all our work is the hypothesis that life--that is, the integrated functions of small molecules, proteins, and nucleic acids m i s based on known rules of physical chemistry. Meeting this challenge will be a major task for twenty-first century biological science.
References Avery, O. T., MacLoed, C. M., and McCarty, M. (1944). Studies on the chemical nature of the substance inducing transformation of pneumococcal types. I. Induction of transformation by a desoxynucleic acid fraction isolated from pneumococcus type III. J. Exp. Med., 79, 137-158.
52
Jay A. Glasel Bloomfield, V. A., Crothers, D. M., and Tinoco, I., Jr. (1974). "Physical Chemistry of Nucleic Acids." Harper & Row, New York. Bracewell, R. (1986). "The Fourier Transform and Its Applications" 2nd ed. McGraw-Hill, New York. Branden, C., and Tooze, J. (1991). "Introduction to Protein Structure" Garland Publishing, New York and London. Carrington, A., and McLachlan, A. D. (1967). "Introduction to Magnetic Resonance." Harper & Row, New York. Dickerson, R. E., and Geis, I. (1969). "The Structure and Action of Proteins." Harper & Row, New York. Eisenberg, D., and Kauzmann, W. (1969). "The Structure and Properties of Water." Oxford University Press, New York. Eisenberg, H. (1976). "Biological Macromolecules and Polyelectrolytes in Solution." Oxford University Press (Clarendon), Oxford. Flory, P. J. (1953). "Principles of Polymer Chemistry." Cornell University Press, Ithaca, NY. Flory, P. J. (1969). "Statistical Mechanics of Chain Molecules." Wiley (Interscience), New York. Goodsell, D. S., and Olson, A. J. (1993). Soluble proteins: Size, shape and function. Trends Biochem. Sci. 18(3), 65-68. Leslie, A. G. W., Arnott, S., Chadrasekaran, R., and Ratliff, R. L. (1980). Polymorphism of DNA double helices. J. Mol. Biol. 143, 49-72. Manning, G. S. (1972). Polyelectrolytes. Annu. Rev. Phys. Chem., 23, 117-140. Morawetz, H. (1975). "Macromolecules in Solution," 2nd ed. Wiley, New York. Nomenclature (1970). Commission on Biochemical Nomenclature. Abbreviations and symbols for the description of the conformation of polypeptide chains. J. Biol. Chem. 245, 6489-6497. Nomenclature (1983). Commission on Biochemical Nomenclature. Abbreviations and symbols for the description of conformations of polynucleotide chains. Eur. J. Biochem. 131, 9-15. Richards, E. G. (1980). "An Introduction to the Physical Properties of Large Molecules in Solution." Cambridge University Press, Cambridge, UK. Richardson, J. S. (1981). The anatomy and taxonomy of protein structure. Adv. Protein Chem. 34, 167-339. Saenger, W. (1984). "Principles of Nucleic Acid Structure." Springer-Verlag, New York. Saenger, W., and Heinemann, U., eds. (1989). "Protein-Nucleic Acid Interaction." CRC Press, Boca Raton, FL. Tanford, C. (1961). "Physical Chemistry of Macromolecules." Wiley, New York. Testa, B. (1979). "Principles of Organic Stereochemistry." Dekker, New York. Timasheff, S. N. (1970). Polyelectrolyte properties of globular proteins. In "Biological Polyelectrolytes" (A. Veis, ed.), pp. 1-64. Dekker, New York. Whiffen, D. H. (1966). "Spectroscopy." Wiley, New York.
GLOSSARY Ampholytes Amphoteric electrolytes. Small multicharged organic buffers used to establish pH gradients in isoelectric focusing. Amphoterir Referring to molecules, such as proteins, capable of positive, negative, or zero net charges. Anolyte
The electrolyte at the anode of an electrophoresis cell.
Blotting Any of several methods in which sample molecules are probed while on the surfaces of synthetic membranes. Capillary electrophoresis ( C E ) Electrophoresis carried out in capillary tubes, with migration of the sample down the axis of the tube. Capillary gel electrophoresis (CGE) in gel-filled capillaries.
Capillary electrophoresis carried out
Capillary zone electrophoresis (CZE) The simplest form of capillary electrophoresis in which a homogeneous buffer is used throughout the system. Introduction to Biophysical Methods for Protein and Nucleic Acid Research
53
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
54
David E. Garfin The electrolyte at the cathode of an electrophoresis cell. Catholyte Clamped homogeneous electric field (CHEF) pulsed gel electrophoresis An electrode arrangement for generating homogeneous alternating electric fields oriented 120 ~ from one another.
Continuous buffer system buffer is used throughout.
Electrophoresis system in which the same
Discontinuous buffer system Electrophoresis system in which different buffer ions are present in the different parts of the system. Also sometimes called multiphasic systems. Electroosmotic flow (EOF) Fluid flow in an electrophoresis system resulting from charged groups on the chamber walls of the apparatus. Electrophoresis The motion of charged particles in an electric field. The motion is brought about by the coulombic forces acting between the particles and the field. Field-inversion gel electrophoresis (FIGE) A form of pulsed-field gel electrophoresis with alternating electric fields oriented 180 ~ from one another.
Immunoelectrophoresis (IEP) Any of several methods in which antigens are detected with antibodies following gel electrophoresis. Isoelectric focusing (IEF) An electrophoretic method for separating amphoteric molecules in pH gradients. Isoelectric point (pI)
The pH at which an amphoteric molecule carries no
net charge.
Joule heating
The heating of an electrical conductor when an electrical current flows through it. Joule heating is sometimes referred to as ohmic heating.
Micellar electrokinetic chromatography (MEKC)
A form of capillary electrophoresis in which uncharged analytes become separable on becoming trapped in micelles of an ionic detergent. Mixed-bed ion-exchange resin A special form of ion exchange chromatographic resin that is used to eliminate both anions and cations from solutions. The resin contains equivalent amounts of groups in the H + and O H - forms. Mobility The electrophoretic steady-state velocity of a charged particle per unit of electric field./~ = v/E = q/f, in cm2/V-sec, where q is the charge and f is the frictional coefficient. Poisson distribution A probability density function that is an approximation to the binomial distribution. It has the characteristic that its mean is equal to its variance. Stars in space, bacteria plated in a petri dish, radioactive disintegrations per unit time, and sizes of pores in gels are all distributed in accordance with the Poisson distribution. Poisson equation The differential equation that relates the electrostatic potential at any point in space to an electric charge distribution. The fundamental problem in electrostatics is to determine solutions to the Poisson equation appropriate to a given charge distribution in order to find out the resulting electrostatic potential.
55
Chapter2 Electr0phoreticMethods Polyacrylamide gel electrophoresis (PAGE)
An electrophoretic method in which molecules migrate through a molecular lattice (the gel) created by polymerized, cross-linked polyacrylamide.
Programmable autonomously controlled electrode (PACE) pulsed-field gel electrophoresis A computer-controlled electrode arrangement for generating alternating fields of variable magnitude and orientation.
Pulsed-field gel electrophoresis (PFGE) Methods for separating very large DNA molecules using electric fields whose directions alternate. Resolution In chromatography resolution is defined as (distance between two band centers)/(sum of the bandwidths). See Separation; see also the text for a discussion of the distinction between resolution and separation. Resolving gel
A gel in which the lattice pores are small enough to have a molecular sieving action, which serves to separate sample molecules.
Separation In chromatography, the distance between band centers is referred to as their separation. Stack The region in discontinuous electrophoresis in which sample ions are electrochemically concentrated between the leading and trailing buffer ion fronts. "Stack" is also used as a verb. Stacking gel A gel in which the lattice pores are very large and serve mainly as an anticonvective medium in the initial phase of discontinuous electrophoresis during the process of stack formation.
SYMBOLS bp
Number of nucleic acid base pairs.
%C
Proportion of cross-linker in a polyacrylamide gel, expressed as a weight percentage. %C = (grams cross-linker)/(grams acrylamide + grams cross-linker).
kb
Number of nucleic acid base pairs expressed in units of 1000 base pairs.
kDa
Units of molecular mass in increments of 1000 Daltons.
M
Relative molecular mass.
Rf
Relative mobility.
SDS
Sodium dodecyl sulfate (sodium lauryl sulfate).
%T
Percentage of total monomer in a polyacrylamide gel, expressed as a w e i g h t / v o l u m e percentage. %T = (grams acrylamide + grams crosslinker) / 100 ml.
TAE
Tris-acetate-EDTA electrophoresis buffer solution: 40 mM Trisacetate, 1 mM EDTA, pH 8.
TBE
Tris-borate-EDTA electrophoresis buffer solution: 89 mM Tris, 89 mM boric acid, 2 mM EDTA, pH 8.3.
Tris
Tris(hydroxymethyl)aminomethane; a buffer component (molecular mass 121.1 Da, pK a 8.3).
56
David E. Garfin
I. Introduction Biochemists and biophysicists devote much effort to the separation of proteins and nucleic acids for identification and characterization (Bollag and Edelstein, 1991; Deutscher, 1990; Janson and Ryden, 1989; Sambrook et al., 1989). There are many different techniques for separating proteins and nucleic acids based on their chemical and physical properties. In particular, the intrinsic charges of proteins and nucleic acids are much exploited in biochemistry. Electrophoresis, isoelectric focusing, ion-exchange chromatography, and mass spectrometry, in one way or another, use the characteristic charges of molecules to separate them. The motion of charged particles in externally applied electric fields is called electrophoresis. Several highly popular electrophoretic methods for manipulating protein or nucleic acid mixtures have been developed. This chapter consists of capsule descriptions of the types of methods most likely to be encountered. It emphasizes gel electrophoresis, because this is by far the most used electrophoretic technique. Electrophoresis is the highest resolution method available for the separation of proteins and nucleic acids and most biochemical laboratories have some capabilities for the electrophoretic analyses of their samples. In addition, the available preparative electrophoresis methods achieve levels of purity that are unattainable by other means. Electrophoresis evolved from Tiselius' fundamentally simple movingboundary technique in free solution to one- and two-dimensional gel systems capable of exquisite resolution of highly complex mixtures (Vesterberg, 1989, 1993). Sophisticated capillary instruments with on-line detection bring automation to the analytical processes. Most kinds of electrophoresis are relatively inexpensive and easy to perform, and results are easy to interpret. Despite its popularity as an analytical technique, the detailed theoretical understanding of electrophoresis is incomplete. Although it is not possible to obtain quantitative structural data from electrophoresis, valuable qualitative information about the relative charges and sizes of macromolecules can be acquired from it. The most common use of electrophoresis is the qualitative analysis of mixtures of proteins or nucleic acids.
A. Basic Concepts The fundamental concepts of electrophoresis are relatively straightforward. In fact, electrophoresis gives the impression of being very simple. It is a transport process in which externally applied electric fields drive charged molecules through various media. A molecule of charge q in an electric field E experiences a force F = qE.
Frictional, viscous drag opposes the electrical force. In free solution, the frictional force is linearly proportional to the velocity, v, of the molecule. The magnitude of viscous drag is fv, in which f, the frictional coefficient, reflects the size and shape of the macromolecule. Under the two opposing forces, mole-
57
Chapter 2 ElectrophoreticMethods
cules rapidly reach steady-state, terminal velocities, with the two forces equal
qE =fv. The electrophoretic mobility of the molecule, tt, defined as the steady-state velocity per unit field, or/z = v/E = q/f, is a characteristic property describing the response of the molecule to electric fields. The units of mobility are cm 2/ V-sec. This highly simplified calculation illustrates the basic idea, common to all theories of electrophoresis, that the electrophoretic mobility of a macromolecule is proportional to the ratio of its net charge to its frictional coefficient (Compton and O'Grady, 1991). However, a number of complicating factors are hidden in the apparent simplicity of the definition of mobility. Both the charges and frictional coefficients of proteins and nucleic acids are established by their compositions and by the nature of the solvent. Charge and shape are influenced by factors such as pH, by the types and amounts of ions in the solution, and by denaturants such as detergents, reducing agents, and urea. It is not possible to account for solvent effects on the properties of macromolecules without making major approximations. For example, the counterions surrounding a molecule shield it from the external field. The only mathematical treatment possible for this important aspect of electrophoresis is for the unrealistic case in which the macromolecule is considered to be a uniformly charged sphere, and even then simplifying assumptions must be made in order to solve the relevant Poisson equation (Mosher et al., 1992; Overbeek and Bijsterbosch, 1979; Tanford, 1961). Regardless of the mathematical difficulties in interpreting electrophoretic mobilities, they can be reproducibly determined. For any given set of electrophoresis conditions, the mobilities of individual molecules are invariant. Proper conditions for a particular separation are easily chosen with a bit of experimentation, and once identified will continue to provide reliable information about the molecules being studied. It is common and accepted practice to infer the charges and shapes of molecules by comparing their mobilities to those of similar molecules with known characteristics. A general goal of electrophoresis is to maximize differences in mobilities and thus maximize the separations of molecules in the region of interest. The most common means for altering electrophoretic mobilities is to force sample molecules to migrate through gels in order to take advantage of molecular sieving. The interactions between migrating molecules and gel structures are poorly understood, and this adds yet another element of uncertainty to theories of gel electrophoresis. Nevertheless, there is much practical knowledge about the electrophoresis of proteins and nucleic acids in different gel systems, so that one can draw on collective experience to select the appropriate procedure for any particular application.
II. Gel Electrophoresis Gel electrophoresis is by far the most popular type of electrophoresis. Equipment and reagents for gel electrophoresis are readily available and familiar to laboratory workers. The technique is easy to perform and reliable results can be expected with a minimum of practice. Although gel electrophoresis is a rela-
58
David E. Garfin
tively simple technique, it is not a trivial procedure. On the contrary, gel electrophoresis may be the most useful analytical method available in biochemical work. A. G e l s
Gels are an interesting state of matter. Structurally, they are intermediate between solids and liquids (Tanaka, 1981). Details of the structures of gels or of the interactions between macromolecules and gels are poorly understood. Models of gel structure are inadequate for full theoretical treatments of gel electrophoresis. In addition, it is difficult to cast gels of precisely controlled structure and shape. Gel electrophoresis, thus, remains a semiempirical method. Conclusions drawn about a molecule must be based on comparison of its electrophoretic mobility with those of known standards run in the same gel. Of the various support matrices that have been used for electrophoresis, only agarose and polyacrylamide gels are of any real importance (Righetti, 1989). From a practical point of view, the structural features of the two types of gels are very similar. Three-dimensional networks of the constituent polymers form when gelation takes place. As gels form, individual agarose or polyacrylamide polymers combine into fibers that then aggregate into larger bundles joined in random meshworks. Agarose gels are held together by hydrogen bond formation between components whereas covalent cross links join the fibers and bundles of polyacrylamide gels. Both types of gels exist as random distributions of solid material and open spaces, or "pores," apportioned in Poisson distributions of sizes (Rodbard and Chrambach, 1970). The concept of gel pores is imprecise. The term pore refers to no particular geometric structure. Operationally, the pores of a gel are defined by the resistance the gel imparts to the motion of charged particles. This resistance varies with the sizes and shapes of macromolecules. Gels can be thought of as three-dimensional sieves that limit the motion of migrating molecules. During electrophoresis, molecules move between the buffer-filled pores of the gel. The dense regions of the gel act as barriers to translation. The ability of proteins or nucleic acids to squeeze through the small-pore regions of the gel depends on the structures of the molecules. The greatest numbers of configurations, and thus the greatest entropy, are available to the macromolecules in the large-pore regions of the gel. To move between open regions, molecules must force their way through small-pore regions of the gel, where entropy is lower (Smisek and Hoagland, 1990). From a macroscopic point of view, migrating molecules segregate into discrete zones corresponding to their mobilities. When the electric field is turned off, migrating molecular zones cease moving. The gel matrix limits diffusion, constraining individual types of molecules in distinct bands at their final positions. In order to analyze the band pattern of a gel, separated molecules are treated to fix their positions in the gel and then are stained to make the bands visible (Fig. 1).
1. Agarose Gels The pores of agarose gels are larger than those of polyacrylamide gels. Proteins larger than about 500 kDa in size and DNA larger than about 2000 base pairs
59
Chapter 2 Electrophoretic Methods
Fig. 1 A typical sodium dodecyl sulfate-polyacrylamide gel electrophoresis band pattern. Soluble proteins extracted directly from fish meat with denaturing sample buffer were compared by electrophoresis in a commercial precast 15%T, 2.7%C resolving gel run under standard (Laemmli) conditions. The overall dimensions of the gel were 7 • 9 • 0.1 cm (h • w • t). Each of 10 sample wells was 1.25 cm high by 0.5 cm wide. There was 1 cm of 4%T, 2.7%C stacking gel between the bottoms of the sample wells and the beginning of the 15%T resolving gel (4.75 cm in height). Electrophoresis at 200 V was continued for 35 min until the bromophenol blue tracking dye reached the bottom of the gel. Starting current was 52 mA and final current was 26 mA. The gel was stained with Coomassie Brilliant Blue R-250. Only 6 of the 10 wells were used. The outer two calibrator lanes contain standard proteins with molecular masses of 6.5,14.4, 21.5, 31, 45, 66.2, 97.4,116.25, and 200 kDa, respectively, from bottom to top. The central four lanes contain muscle extracts from (left to right) salmon, catfish, shark, and sea bass. The polypeptides obtained from the different fish species are clearly distinguishable from one another.
can be separated in agarose gels. Polyacrylamide should be used for smaller molecules. Agarose is a natural polysaccharide isolated from certain agar-bearing seaweeds (FMC BioProducts, 1988; Sambrook et al., 1989). Suppliers provide several different types of agarose, qualified for particular electrophoretic purposes. Agarose varieties differ in their physical and chemical properties, such as gelling temperature, gel strength, porosity, and electroosmosis. It is important to select the appropriate agarose for each particular purpose. Agarose is usually supplied as a dry powder. For casting gels, agarose is first dispersed in water or buffer, then boiled or heated in a microwave oven until completely melted. After a short period of cooling (to about 50~ the molten agarose is poured into an electrophoresis cassette or mold, in which gelation takes place.
2. Polyacrylamide Gels Polyacrylamide gels (CH 2~ C H - - C O - - N H
are formed by copolymerization of acrylamide 2) and a cross-linking comonomer, usually N,N'-meth-
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David E. Garfin
ylenebisacrylamide (bisacrylamide) ( C H 2 - - C H - - C O m N H - - C H 2 m N H m C O m C H - - C H 2 ) . Cross-linkers are bifunctional acrylic agents that covalently link adjacent linear polyacrylamide chains (Righetti, 1989). Cross-linkers other than bisacrylamide are available for specialized purposes. For example, piperazinediacrylamide (PDA) allows low-background silver staining, important for critical two-dimensional gel electrophoresis (Hochstrasser et al., 1988a). The gel-forming reaction is a vinyl addition polymerization initiated by a free radical-generating system (Flory, 1953). For most gels in common use, polymerization is initiated by the addition of ammonium persulfate (the initiator) and an accelerator, tetramethylethylenediamine (TEMED) (Bio-Rad Laboratories, 1993a; Crambach and Rodbard, 1971). In this system, TEMED accelerates decomposition of persulfate molecules into (two each) sulfate free radicals and these in turn initiate polymerization. The free base of TEMED is required for this reaction. Polymerization efficiency falls rapidly at pH values below about pH 6 (Caglio and Righetti, 1993). Photopolymerization, with riboflavin as the accelerator, is used for low-pH gels (see Section III,A). A three-dimensional network is formed when the bifunctional bisacrylamide molecules cross link adjacent polyacrylamide chains. The rate of polymerization is dependent on (1) the net concentration of monomers and free radicals, (2) the temperature, and (3) the purity of the reagents. All of these parameters need to be controlled for reproducible gels. Because the reaction is dependent on free radicals, any compound that can act as a free radical trap will act as a polymerization inhibitor. Because oxygen is the most abundant radical trap, proper degassing to remove dissolved oxygen from acrylamide solutions is critical for absolute reproducibility (Chrambach, 1985). Nevertheless, completely acceptable gels can be obtained without degassing. By convention, polyacrylamide gels are characterized by a pair of values, %T and %C, where %T is the weight percentage of total monomer, including cross-linker (in g/100 ml), and %C is the proportion of cross-linker as a percentage of total monomer. The effective pore size of a polyacrylamide gel is an inverse function of the total monomer concentration (%T). For any given total monomer concentration, the effective pore size also varies with the proportion of cross-linker in the reaction mixture (%C). When %T is increased at a fixed, low-cross-linker concentration, the number of chains increases and pore size decreases. On the other hand, pore size is a biphasic function of %C. As %C is varied at constant %T, pore size decreases to a minimum at about 5%C. It then increases with further increases in %C, presumably because of the formation of shorter and thicker bundles of linear chains of polymer (Chrambach, 1985; Richards and Lecanidou, 1971, 1974). The use of high-quality reagents is a prerequisite for reproducible, highresolution gels. This is particularly true for acrylamide, which constitutes the most abundant component in the gel monomer mixture. Residual acrylic acid, linear polyacrylamide, and ionic impurities are the major contaminants of lowgrade acrylamide preparations. 1. Acrylic acid will copolymerize with acrylamide and bisacrylamide, thereby conferring ion-exchange properties to the resultant gel. 2. Linear polyacrylamide, by providing a nucleus for uncontrolled polymerization, can lead to irreproducibilities in gels.
Chapter2 ElectrophoreticMethods
61
3. Ionic contaminants can include both inhibitors and accelerators of polymerization. In particular, metals such as copper can inhibit gel polymerization. Buffer components should be of reagent grade and only thoroughly deionized water should be used for all phases of gel electrophoresis. High-quality electrophoresis chemicals are available from many sources. a. Polymerization Reactions Monomer solutions are commonly made as concentrated stock solutions. For protein gels, 30%T, 2.7%C monomer stock is preferred; it is made by dissolving 29.2 g of acrylamide and 0.8 g of bisacrylamide in 72.5 ml of completely deionized water (final volume 100 ml; specific gravity 1.025). The monomer solution should be filtered--disposable vacuum filtration units are convenient m and stored in the refrigerator, preferably in amber glass bottles. For nucleic acid gels, 30%T, 3.3%C stock is used, prepared as above from 29 g acrylamide and 1 g bisacrylamide. [Note: Acrylamide monomer is toxic. Direct exposure to it should be avoided.] Initiator concentrations are determined empirically to give visible polymerization in 15-20 min after addition. Under these conditions, gelation is essentially complete in 90 min. Final ammonium persulfate and TEMED concentrations of 0.05%, each, are usually sufficient for polymerization of resolving gels (see Section II,B,l,a). When stacking gels are used (see below), all that is required of them is that they have large pore structures. Because of this, stacking gels can be set to polymerize rapidly, in 8-10 min, with final concentrations of 0.05% ammonium persulfate and 0.1% TEMED. Monomer stock and buffer are combined at the desired concentrations and deaerated under moderate vacuum for about 15 min. Initiators are then added and the gel is poured into the casting apparatus. When a stacking gel is to be used (see below), the resolving gel mixture is poured first. It is overlaid with water-saturated isobutanol to exclude air from the top of the gel and aid in forming a sharp intergel boundary. After approximately 1 hr, the alcohol layer is thoroughly rinsed from the top of the gel and the stacking gel mixture is poured directly on top of the resolving gel. A sample well-forming "comb" is introduced at this time to form spaces in the gel for sample application. The gel is ready to run when the stacking gel has polymerized. Polyacrylamide gels are inherently unstable outside the pH 4 - 6 range. After storage at 4~ for about 4 months in the usual electrophoresis buffers, deterioration of the sharpness of the band patterns will sometimes be noticeable. Thus, for very high-resolution work, only fresh gels should be used. The breakdown of polyacrylamide is a slow hydrolysis of the pendant carboxamide groups (-- CO - - NH2) of the acrylamide monomers that occurs in basic buffers (Boschetti, 1989). Hydrolysis leaves behind ionized carboxyl groups (--COO-). Old gels swell, their pore structures change, and they take on ion-exchange characteristics because of this hydrolysis. The aging of polyacrylamide has commercial significance because it places limitations on the shelf-life of precast polyacrylamide gels.
B. Buffer Systems Although knowledge regarding the properties of gels is sparse, much is known about the behavior of buffer ions in electric fields. Many interesting and useful
62
David E. Garfin buffer systems have been devised, so that there is a great deal of flexibility in the choice of buffer system (Chrambach, 1985; Chrambach and Jovin, 1983; Hames, 1990; Laas, 1989a; Mosher et al., 1992). The electrolyte buffer obviously has a profound effect on the electrophoretic run. The buffer determines power conditions and affects separation and resolution. Proteins differ widely in their sensitivity to ionic strength, ionic species, pH, and cofactor requirements. The buffer chosen for the electrophoresis of native (nondenatured) proteins often depends more on the proteins under study than on the demands of electrophoresis. With nucleic acids and proteins at concentrations of about 1 m g / m l or greater, a continuous buffer system can be used. The same buffer, at constant pH, is used in the gel and electrode reservoirs of a continuous system. Also, the sample is loaded directly on the gel in which separation will occur. As molecules migrate through the pores of the gel, they are fractionated according to mobility. Bandwidths are determined mainly by the height of the applied sample volume, and this limits the resolution attainable with continuous systems. Dilute samples require large volumes to supply detectable amounts of material, and relatively wide bands are obtained. With gels of constant pore size, continuous systems are restricted to high-concentration samples for best results. Discontinuous (or multiphasic) buffer systems use different buffer ions in the gel and in the electrode solutions. These systems are designed to sharpen sample zones for high-resolution separations. In multiphasic, discontinuous zone electrophoresis, samples are applied to a large-pore stacking gel that serves as an anticonvective medium. All ionic species, including the sample molecules, form moving fronts. Buffer ions in the gel form an ion front that moves ahead of the sample molecules. Electrode buffer ions form a front that trails behind the sample. The sample ions between the buffer fronts concentrate into extremely narrow zones arranged in order of decreasing mobilities. The sample molecules rapidly "stack" into a very narrow region, no more than a few hundred micrometers thick, containing on the order of 100 m g / m l of protein (Chen et al., 1978a). Stacked samples move through the large-pore stacking gel as very narrow individual zones, regardless of the initial sample volume, and enter a resolving (or separating) gel of restrictive pore size as a series of very thin, closely spaced bands. Once in the resolving gel, sieving becomes predominant and the sample molecules "unstack" and separate on the basis of size and charge. Early studies with RNA questioned the need for stacking gels for the electrophoresis of nucleic acids (Richards and Lecanidou, 1971). As a consequence, nearly all electrophoresis of nucleic acids is done with continuous systems.
1. Discontinuous Buffer Systems Ornstein (1964) and Davis (1964) developed the first high-resolution polyacrylamide gel electrophoresis (PAGE) system for native proteins. Their popular system is still in widespread use. It was designed for the analysis of serum proteins, but works well for a broad range of protein types. The OrnsteinDavis buffer system is the first technique to try when working with a new, native protein sample. Ornstein recognized that high resolution is achieved when the starting zone of the sample proteins is as narrow as possible. He devised an electropho-
Chapter 2 Electrophoretic Methods
63
retic method that sharpens protein zones well beyond the limits attainable by mechanical means. His formulation is based on the equations describing current flow in ionic solutions and the properties of buffers. A mathematical discussion of electromigration processes is beyond the scope of this chapter. An easy-to-follow derivation of the essential equations is given by Foret and Bocek (1989) and Kleparnik and Bocek (1991). Ornstein's idea was to sandwich sample proteins between two closely spaced moving fronts of electrolyte ions. Under the influence of the electric field, sample proteins become compressed between the leading and trailing ion fronts and segregate into contiguous zones in the order of their relative mobilities. This process takes place in the region provided by the large-pore stacking gel. Sample proteins arrive at the resolving gel in a very thin starting band. Once proteins are in the resolving gel, sieving predominates to effect the separation. The Ornstein-Davis system uses chloride as the leading ion, glycinate as the trailing ion, and Tris as the common ion. Of the possible components available at the time the system was developed, the properties of these buffers were best suited to the requirements of the electrophoresis. Similar electrochemical analyses have yielded a very great many electrophoresis buffer systems. Jovin (1973a), in fact, proposed some 4269 theoretically possible buffer systems covering the pH range from 2.5 to 11 in 0.5 pH units. Very few of these buffer systems have actually been tried, probably as a consequence of the unwieldy and confusing nomenclature and the lack of clear directions on how to choose the correct system for a given application (Chrambach and Rodbard, 1981). Chrambach and Jovin (1983) simplified the nomenclature and reduced the number of buffer systems to a manageable 19. The treatment of discontinuous electrophoresis by Jovin (1973b,c,d) and those of Everaerts et al. (1976) and Schafer-Nielsen and Svendsen (1981) are more comprehensive and correct than that of Ornstein. Allen (1974) devised alternative discontinuous buffer systems that make use of conductivity differences to achieve zone sharpening at constant pH (Allen et al., 1984; Allen and Budowle, 1994). By far the most popular gel system is that of sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) as devised by Laemmli (1970). In Laemmli's system, SDS is incorporated into the original Ornstein-Davis buffers. a. O r n s t e i n - D a v i s Gels: Discontinuous and Nondenaturing It is instructive to consider the ionic events that take place during discontinuous electrophoresis. The Ornstein-Davis system is convenient for this purpose, especially considering its popularity. Other discontinuous systems function by analogous mechanisms. The Ornstein-Davis system uses two different buffers containing different anions and a common cation to separate proteins. Chloride, present in the gel when it is cast, becomes the leading-front ion and glycinate ion in the electrode buffer forms the trailing front. Tris, the common ion, maintains electroneutrality. Most serum proteins carry net negative charges in this system and migrate toward the anode. The Ornstein-Davis system consists of four interrelated parts: (1) a stacking gel, (2) a resolving gel, (3) an electrode buffer, and (4) the sample (Fig. 2). The successive stages in a separation are as follows.
64
David E. Garfin
Fig. 2 Stages in the separation of a protein mixture with the Ornstein-Davis discontinuous buffer system (see the text for details). (A) The gel is formed in two sections. A large-pore stacking gel is cast on top of a restrictive resolving gel. Each gel section contains Tris-C1 buffer, but the concentrations and pHs of the buffers in the two sections are different. The stacking-gel buffer is indicated by light shading and the resolving-gel buffer is shown with dark shading. Sample proteins, dissolved in diluted stacking-gel buffer, are placed in wells formed in the stacking gel (dark horizontal lines). Tris-glycine electrode buffer (clear) is in contact with the top of the gel, the top of the sample, and the bottom of the gel. The anode is below the gel and the cathode is above it (not shown). Serum proteins have net negative charges in this system and move downward toward the anode. Tris ions are distributed throughout the system and serve to maintain electroneutrality. The electric field intensity, E, shortly after application of voltage, is represented in the graph at the right of the gel picture. The E field in the gel is relatively low as a consequence of the relatively high conductivity imparted by the mobile chloride ions. (B) When voltage is applied, the anionic constituents of the system become aligned in the order of their electrophoretic mobilities. The magnitude of the mobility of the chloride ion (C1) in the gel buffer is greater than the mobility of the glycinate ion (Gly) in the electrode buffer. Sample proteins, with intermediate mobilities, are sandwiched (in order of mobility) between the chloride and glycinate ion fronts. The proteins in the sample become "stacked" in the very narrow region between the two moving fronts of buffer ions and form a spatially thin starting zone. Electric field intensity is influenced by the local distribution of charge carriers, which are proteins in the sample zone. The E field in the differing ion-containing zones becomes adjusted so that all ionic boundaries migrate at the same speed. (C) Shortly after stacking is completed, sample proteins enter the small-pore resolving gel, where they are slowed by sieving. In the resolving gel, the glycinate ions overtake the sample proteins and run just behind the chloride ions. During the resolving stage, proteins respond to a relatively high electric field determined by the concentration of glycinate ions in the gel. Electrophoresis continues with the sample proteins in Tris-glycine buffer until power is switched off.
i. Gel composition T h e gel is f o r m e d in t w o sections (Fig. 2A). A l a r g e - p o r e s t a c k i n g gel (4%T) is cast o n t o p of a restrictive r e s o l v i n g gel ( 5 - 3 0 % T ) (Bollag a n d Edelstein, 1991). T h e s t a c k i n g gel c o n t a i n s 0.125 M Tris-C1, p H 6.8, a n d the r e s o l v i n g gel c o n t a i n s 0.375 M Tris-C1, p H 8.8. T h e p H d i s c o n t i n u i t y b e t w e e n t h e t w o sections of the gel w a s d e s i g n e d to r e g u l a t e the effective m o b i l i t y of the g l y c i n a t e ions f r o m the c a t h o d e c h a m b e r . T h e c o n c e n t r a t i o n s of Tris-C1 in the t w o gels w e r e d e r i v e d f r o m e l e c t r o c h e m i c a l c o n s i d e r a t i o n s . T h e p o r o s i t y of the s t a c k i n g gel is large e n o u g h to n o t i m p e d e m o v e m e n t of p r o t e i n s a n d f u n c t i o n s m a i n l y as a n a n t i c o n v e c t i v e s u p p o r t m e d i u m d u r i n g f o r m a t i o n of t h i n s t a r t i n g z o n e s . P r o t e i n s e p a r a t i o n takes place in the l o w e r , r e s o l v i n g gel. T h e p o r o s i t y of this s e c o n d gel is e m p i r i c a l l y d e t e r m i n e d to m a t c h the mobilities of the p r o t e i n s in t h e s a m p l e . T h e r e is n o reliable w a y to p r e d i c t the correct gel c o n c e n t r a t i o n for a n u n t e s t e d p r o t e i n m i x t u r e w i t h o u t a n a l y z i n g it in gels. T h e choice is m a d e s u c h t h a t the p r o t e i n s of i n t e r e s t in the s a m p l e m i x t u r e are r e s o l v e d in the gel. It
Chapter 2 Electrophoretic Methods
65
is common to begin with a 7.5%T gel for the initial electrophoresis of a sample of unknown mobilities (Hames, 1990). ii. Sample composition The sample buffer is 0.0625 M Tris-C1, pH 6.8. The sample is loaded into the system by placing it between the (0.125 M) Tris-C1 in the stacker gel and the Tris-glycine in the electrode buffer (0.025 M Tris, 0.192 M glycine, pH 8.3). The ionic strength of the sample solution is lower than those of the buffers above and below it. As a consequence, when power is applied, a voltage drop develops across the sample to help drive it into the gel. iii. Stack formation When voltage is applied, and current begins to flow, chloride ions in the gel sections, anionic proteins in the sample, and glycinate ions in the electrode buffer begin to move toward the anode (Fig. 2B). Tris (a base) and any cationic proteins in the sample migrate toward the cathode. As chloride ions move out of the sample, a localized, low-conductivity, high-field region is created behind them. The increased field behind the chloride ion front accelerates the proteins in the sample and the glycinate ions from the electrode buffer to the same velocity as the chloride (E/z = constant). The degree of ionization of glycine at the pH of the electrode buffer (pH 8.3) is such that the effective mobility of glycinate ions is less than those of chloride and the proteins in the sample. (The effective mobility of a weak electrolyte is the average mobility of the ionized form;/d, e f f = /d,X,where x is the fraction of molecules ionized at a particular pH and/z is their mobility. Each molecule can be thought of as being ionized x% of the time and uncharged the rest of the time. The pK a of glycine is pH 9.8. At pH 8.3, glycine molecules are 1/30 dissociated to glycinate ions.) A moving-boundary region is rapidly formed, with the chloride ions in the front, the glycinate ions in the rear, and the sample proteins compressed between them. The proteins form into individual thin zones, stacked like coins, in order of decreasing mobility between the leading chloride and trailing glycinate ions. The pH of the stacking gel becomes pH 8.3 as the glycinate ions move through it. In the stack, a low electric field moves in front of each protein zone and a high electric field moves behind each of them. Any protein molecule moving ahead of its zone is met with a lowered electric field and is slowed down until its zone overtakes it. Conversely, a protein molecule that gets behind its zone is speeded up by the increased electric field there. In the steady state, each protein is concentrated into a thin, high-density zone determined solely by the mobility of the protein under the electrophoretic conditions. iv. Separation When the moving boundary region reaches the interface of the stacking and resolving gels, the proteins experience a sharp increase in retardation due to the restrictive pore size of the resolving gel. At the same time, the pH is sharply increased to pH 8.8 and rapidly increases to pH 9.5 as the Tris-C1 is replaced by Tris-glycinate. The effective mobility of glycinate ions at pH 9.5 is high enough that they overtake the slowed proteins in the sample and move past them to run just behind the chloride front (x = 1/3). The protein zones become unstacked, and begin to separate into macroscopic bands by molecular sieving (Fig. 2C). In the resolving gel, proteins move at pH 9.5 for the remainder of the run. The operating pH of the separating gel, pH 9.5, was included in the design specifications of the Ornstein-Davis system to arrange for an effective mobility of glycinate greater than that of the fastest serum
66
David E. Garfin
protein (prealbumin) in 7.5%T gels (Jovin, 1973d; Ornstein, 1964). As the run progresses, the initially very thin protein bands spread to thicknesses of the order of millimeters as a consequence of diffusion and dilution. b. Laemmli Gels: Discontinuous and Denaturing Laemmli modified the Ornstein-Davis system to allow molecular weight determinations to be made. The Laemmli (1970) system incorporates 0.1% SDS (an anionic detergent) in the Ornstein-Davis buffers and employs a denaturing step in sample treatment (Bollag and Edelstein, 1991; Garfin, 1990a; Hames, 1990). The treatment is designed to denature completely sample proteins to their constituent polypeptide chains prior to electrophoresis. When a mixture of proteins is heated in buffer containing SDS (2%) and a thiol reducing agent such as 2-mercaptoethanol (5%), the proteins are completely denatured and the resultant polypeptides take on a uniform charge-tomass ratio imparted by the SDS. The reducing agent breaks the disulfide bonds between segments of the native proteins, while the SDS, a well-known denaturant, coats most polypeptides with a uniform 1.4 g of SDS per gram of polypeptide (Reynolds and Tanford, 1970). The properties of the detergent overwhelm those of the polypeptides. All SDS-coated polypeptides take on similar extended, rodlike shapes with dimensions proportional to their molecular weights. In addition, the charge density of SDS-polypeptides is independent of pH in the range from 7 to 10. Fractionation in the gel is governed strictly by molecular sieving, so that separation of polypeptides in this system can be used to estimate their molecular weights. The characteristic features of a SDS-PAGE gel during an electrophoretic separation are shown in Fig. 3. Several types of proteins do not behave as expected during SDS-PAGE (Andrews, 1986; Hames, 1990; See and Jackowski, 1989). Incompletely reduced proteins, with some intra- or intermolecular disulfide bonds intact, are not saturated with SDS, because some of their SDS-binding domains are unavailable to the detergent. Glycoproteins and lipoproteins are also not saturated with SDS, because their nonproteinaceous components do not interact with the detergent. Proteins with unusual amino acid sequences, especially those with high lysine or proline content, very basic proteins, and very acidic proteins behave anomalously in SDS-PAGE, presumably because the charge-to-mass ratios of the SDS-polypeptide complexes are different than those that would be expected from size alone. Similarly, very large SDS-proteins, with molecular masses in the hundreds of kilodaltons, may have abnormal conformations. Polypeptides smaller than about 12,000 Da are not resolved well in most SDSPAGE systems. Small SDS-polypeptide complexes either have the same, roughly spherical, conformations or they do not separate from the band of SDS micelles that forms behind the leading ion front. Because the properties of SDS dominate the system, Laemmli buffers, as usually described, are somewhat more elaborate than strictly necessary. In particular, it is not necessary to cast stacking gels and resolving gels at a different pH (Wyckoff et al., 1977). Whether the stacking gel is cast at pH 6.8 or pH 8.8, SDS-polypeptides stack as a unit behind the leading chloride ion front. (This is strikingly demonstrated with prestained protein standards, which are mixtures of proteins derivatized with reactive dyes.) Stacking gels are still needed for best results, but they need not be at separate pH or ionic strengths. They can be
Chapter 2 Electrophoretic Methods
67
Fig. 3 Characteristics of SDS-PAGE. The naturally colored subunits of chromatographically pure phycocyanin are seen as they separate in a preparative SDS-PAGE resolving gel (14%T, 2.7%C). Chromophores covalently bound to two of the subunits of phycocyanin make them visible throughout the electrophoresis run. The two dark annular bands in the middle of the gel are, respectively, an 18.5-kDa subunit (lower) and a 21-kDa subunit (upper). An uncolored 23-kDa subunit migrates behind the two colored bands. Because the protein was colored, tracking dye was not needed in the sample buffer. This made the features of the gel visible. The top of the stacking gel (4%T) is visible below the raft of bubbles on top of the buffer surrounding the glass gel tube. Below the top of the stacking gel is the junction between the stacking gel and the resolving gel. The resolving gel extends to the bottom of the tube. Small air pockets between the resolving gel and the glass tube can be seen at the left. These air pockets are magnified by the curvature of the glass and did not affect the separation of the bands. The chloride- glycine moving-ion front and a zone of SDS micelles can be seen below the 18.5-kDa band. They are visible because their refractive indexes differ from their surroundings. The ion front appears as the sharp boundary beneath the broad micelle band. A cooling core is in the center of the cylindrical gel.
cast in t h e s a m e b u f f e r as t h e r e s o l v i n g gel. Also, gels d o n o t n e e d to be cast w i t h SDS in t h e m . T h e SDS in t h e s a m p l e b u f f e r is sufficient to s a t u r a t e the p r o t e i n s w i t h t h e d e t e r g e n t a n d 0.1% SDS in t h e c a t h o d e b u f f e r is sufficient for m a i n taining protein saturation during electrophoresis. T h e L a e m m l i a n d O r n s t e i n - D a v i s gel s y s t e m s can b e u s e d w i t h nucleic acids as w e l l as w i t h p r o t e i n s (Tas, 1990). T h e L a e m m l i s y s t e m is p r e f e r r e d , b e c a u s e the SDS d e n a t u r e s c o n t a m i n a n t n u c l e a s e s .
2. Continuous Buffer Systems W i t h r e g a r d to c o n t i n u o u s b u f f e r s y s t e m s , a l m o s t a n y b u f f e r b e t w e e n p H 3 a n d 10 m a y be u s e d for e l e c t r o p h o r e s i s . M c L e l l a n (1982) c o m p i l e d a p a r t i c u l a r l y
68
David E. Garfin
useful list of buffers for continuous electrophoresis. Solutions of relatively low ionic strength are best suited for electrophoresis, because these keep heat production to a minimum. On the other hand, protein aggregation may occur if the ionic strength is too low. The choice will depend on the proteins under study, but in general the concentration limits for electrophoresis buffer ions are from 0.01 to 0.1 M. Typical continuous buffer systems that have been used are Trisglycine (pH range 8.3-9.5) (Chen et al., 1978b), Tris-borate (pH range 8.3-9.3) (Margolis and Kenrick, 1968), and Tris-acetate (pH range 7.2-8.5) (Fairbanks et al., 1971). Borate ions can form complexes with some sugars and can therefore influence resolution of some glycoproteins. Very basic proteins, such as histones, are separated in acetic acid-urea gels (Spiker, 1980). Weber and Osborn's (1969) continuous SDS-PAGE system uses sodium phosphate buffer (pH 7). Omission of a stacking gel limits this popular system to high-concentration samples for best resolution.
3. O t h e r Buffer S y s t e m s As already noted, a multitude of discontinuous systems has been described (at least theoretically) (Jovin, 1973a). For basic proteins, the low-pH alanineacetate system of Reisfeld et al. (1962) is often chosen (Hames, 1990). Allen (1974; Allen et al., 1984, 1989, 1993) advocates Tris-sulfate/Tris-borate, Trisformate/Tris-borate, and Tris- citrate/Tris-borate for electrophoresis of both proteins and nucleic acids (stacking also improves the resolution of nucleic acid gels). Neville (1971) developed a useful procedure for SDS-PAGE using a Tris-sulfate/Tris-borate buffer system. (This system was actually one of those calculated by Jovin's theoretical treatment. The chloride ion included in the lower gel buffer and the operational pH shift do not play roles in the electrochemistry of this SDS-PAGE technique and are unnecessary.) The Neville system was developed to stack and fractionate SDS-saturated proteins in the 2 to 300-kDa range. It has not gained much popularity. Another system for SDSPAGE is similar to that of Laemmli but with Tris replaced by its analog ammediol (2-amino-2-methyl-l,3-propanediol) (Wyckoff et al., 1977). This system reportedly gives better resolution than either the Laemmli or Neville systems, especially in the I to 10-kDa range (Bury, 1981). Replacement of glycine with Tricine in the Laemmli electrode buffer provides excellent separation of small polypeptides (Schagger and van Jagow, 1987). At the pH values used, Tricine migrates faster than glycine in the stacking gel. This has the benefit that small SDS-polypeptide complexes separate from the broad band of SDS micelles that forms behind the leading-ion front. In particular, 16.5%T, 3%C separating gels are useful for separations in the range from 1 to 70 kDa. Stacking gels in this system are 4%T, 3%C. Resolution is sometimes enhanced by inclusion of a 10%T, 3%C spacer gel between the resolving and stacking gels. Tricine-SDS resolving gels contain 1 M Tris-C1, pH 8.45, and 13% (w/v) glycerol. Stacking and spacer gels contain the same buffer without glycerol. It is not necessary to include SDS in the gel buffer. Electrode buffer is 0.1 M Tris, 0.1 M Tricine, 0.1% SDS, pH 8.25. Sample buffer is 0.1 M Tris-C1, pH 6.8, 2% (v/v) 2-mercaptoethanol, 20% (w/v) glycerol, 0.025% bromophenol blue. Sample buffer should contain no more than 1%SDS for best resolution of the small proteins (1-5 kDa). Proteins of very low molec-
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ular mass are not completely fixed and may diffuse from the gels during staining. This system is becoming very popular for polypeptide analyses.
C. Choice of System 1. Native Proteins The choice of electrophoresis system for proteins depends on the particular proteins of interest. There is no universal buffer system ideal for the electrophoresis of all native proteins. Both protein stability and resolution are important considerations in buffer selection. The Ornstein-Davis buffers are a recommended first choice (Ornstein, 1964; Davis, 1964). The 19 discontinuous buffers selected by Chrambach and Jovin (1983) and the list of continuous buffers provided by McLellan (1982) are also recommended. Some native proteins may aggregate and precipitate at the very high protein concentrations reached during stacking in discontinuous electrophoresis. Consequently, either they might not enter the resolving gel or they might cause streaking as accumulated protein slowly dissolves during electrophoresis. If the proteins of interest behave in this manner, it is probably best to use some form of continuous-buffer electrophoresis. The pH chosen must be in the range over which the proteins of interest are stable. The pH should also be far enough from the isoelectric points (see the discussion of isoelectric focusing in Section III) of the proteins of interest that they carry enough net charge to migrate through the gel in a reasonable time. On the other hand, separation of two proteins at a given gel concentration is best near one of their isoelectric points, because the isoelectric protein will barely move in that pH range. The choice of pH is usually a compromise between considerations of resolution and stability. For best results with continuous systems, the concentrations of the proteins of interest should be at least 1 m g / m l to keep sample volume at a minimum. The sample should be loaded in a buffer with an ionic strength about 1/2 to 1/5 that of the gel and electrode buffers (dialysis may be required) so that a voltage drop can develop across the applied sample to drive the proteins into the gel. The choice of proper gel concentration is, of course, critical to the success of the separation. The separation of proteins is heavily influenced by the concentration (%T) of the gel. Too high %T can lead to exclusion of proteins from the gel and too low %T can decrease sieving. One approach, useful with the McLellan continuous buffers, is to use relatively large-pore gels (5%T to 7%T) and to alter mobilities with pH. An approach for discontinuous systems is to start with a 7.5%T gel, then, if that is not satisfactory, to try a number of gel concentrations between 5%T and 15%T. Pore-gradient gels can also be tried (Hames, 1990).
2. Denatured Proteins and Nucleic Acids It is easier to choose suitable concentrations for SDS-PAGE and DNA gels than for native protein gels because separations of SDS-polypeptides and polynucleotides are dependent mainly on chain length. Laemmli gels with 7.5%T resolve proteins in the 40- to 200-kDa range, those with 10%T resolve 20- to 200-kDa proteins, 12%T gels separate proteins in the 15- to 100-kDa range, and 15%T gels separate 6- to 90-kDa proteins.
70
David E. Garfin Electrophoresis of nucleic acids is done almost exclusively with continuous-buffer systems. TBE and TAE are used for DNA and RNA in both polyacrylamide and agarose gels. Allen's discontinuous buffers may improve resolution (Allen et al., 1989, 1993). Agarose gels (1%, w / v ) separate linear DNA molecules in the 500- to 7000-bp size range and 0.5% agarose gels separate DNAs in the 2000 to 20,000-bp range. With polyacrylamide, 5%T and 10%T gels are used for separation of linear DNA molecules of 200-2000 and 50-1500 bp, respectively.
D. Detergents and Denaturants Detergents are employed in electrophoresis when it is necessary to disrupt protein-lipid and protein-protein interactions. A variety of detergents has been used for this purpose. SDS is the most common detergent used in PAGE analyses. The basic concepts of protein-detergent interactions have been reviewed and discussed, both in general terms (Helenius and Simons, 1975; Neugebauer, 1990) and as related to electrophoresis (Hjelmeland and Chrambach, 1981). Most proteins are readily soluble in SDS, making SDS-PAGE a generally applicable method. In SDS-PAGE, the quality of the SDS is of prime importance (Brown, 1988; Margulies and Tiffany, 1984). The effects of impurities in SDS are unpredictable. Of the contaminants, the worst offenders are probably the alkyl sulfates other than dodecyl sulfate (C,2); especially decyl sulfate (C 10), tetradecyl sulfate (C14), and hexadecyl sulfate (C16). These bind to proteins with different affinities, thereby affecting mobilities. Lipophilic contaminants in SDS preparations, including dodecanol, can be trapped in SDS-protein complexes and SDS micelles, leading to loss of resolution. Only purified SDS should be used for electrophoresis, but even with pure SDS, various glycoproteins, lipoproteins, and nucleoproteins tend to bind the detergent irregularly. The resultant SDS-polypeptides then migrate "anomalously" with respect to their molecular masses. Lithium dodecyl sulfate (LDS) has been substituted for SDS in PAGE analyses (Kubo and Takagi, 1986) as has cetyltrimethylammonium bromide (CTAB) (Akins et al., 1992). LDS is more soluble than SDS at low temperatures, which allows gels to be run at 4~ CTAB is a milder denaturant than SDS and preserves certain biological activities that are destroyed by SDS. Urea is used very often as a dissociating agent in gel electrophoresis (Grierson, 1990; Sealey and Southern, 1990). Urea, which disrupts hydrogen bonds, is used in situations wherein hydrogen bonding can cause unwanted aggregation or formation of secondary structures that affect mobilities. It is well suited as a denaturant for nucleic acids. Urea is an essential component of gels in which it is necessary to maintain DNA or RNA in single-stranded configurations, such as when accurate molecular mass determinations are desired. Dissociation of hydrogen bonds requires high urea concentrations (7-8 M). Maintenance of nucleic acids as single strands requires that electrophoresis be run at elevated temperatures (60~ Complete denaturation of proteins requires also that samples be treated with a thiol-reducing agent to break disulfide bridges (Hames, 1990). High concentrations of urea increase the sieving properties of polyacrylamide gels, either because of viscosity effects or by reducing the effective size of
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water channels (pores). Urea disrupts the hydrogen bonds holding agarose gels together as well as those in the samples, so that urea cannot be used in agarose gels. Urea must be present during electrophoresis, but, unlike SDS, urea does not affect the intrinsic charge of the sample polypeptides. In urea gels, separation of proteins is on the basis of both net charge and size, so that accurate molecular mass determinations are difficult. Urea solutions should be deionized by treatment with a mixed-bed ion-exchange resin before use. (Mixed-bed ion-exchange resins, such as Bio-Rex 501-X8, contain strong anionic and cationic functional groups on inert matrices, such as styrene divinylbenzene. They are used for removing positively and negatively charged contaminants from nonionic solutions. Deionization is most easily achieved by percolating urea solutions though a resin bed in a chromatography column or Buchner funnel.) Formamide (---98%) is sometimes used as a denaturant for RNA and DNA gels (Grierson, 1990; Sealey and Southern, 1990). Like urea, it disrupts hydrogen bonding. Formamide should also be deionized with a mixed-bed resin before use.
E. Sample Preparation Samples for SDS-PAGE by the Laemmli procedure are prepared in 0.0625 M Tris, pH 6.8, 2% SDS, 5% 2-mercaptoethanol, 10% glycerol, and about 0.025% (w/v) bromophenol blue tracking dye (Bollag and Edelstein, 1991; Garfin, 1990a; Haines, 1990). It is best to prepare a stock sample buffer containing everything but 2-mercaptoethanol and to add this reagent right before use. The glycerol provides density for underlaying the sample on the stacking gel below the electrode buffer. The tracking dye allows both sample application and the electrophoretic run to be monitored (it migrates with the ion front). There is sufficient SDS present in the sample buffer to ensure saturation of most protein mixtures. Except in the rare instances when the sample is in a very high-ionicstrength solution (>0.2 M), it can be dissolved 1:1 (v/v) in stock sample buffer. It is much better, though, to dilute the sample at least 1:4 (v/v) with the stock sample buffer. The amount of sample protein to load on a gel depends on the detection method to be used. Enough of the protein of interest must be loaded on the gel for it to be subsequently located (see Section II, H). Detection in gels requires on the order of 1 ~g of protein for easy visibility of bands stained with anionic dyes such as Coomassie Brilliant Blue R-250 or 0.1 ~g of protein with silver staining (Bio-Rad Laboratories, 1993b). Complete dissociation of most proteins is achieved by heating diluted samples to 95-100~ for 2 - 5 min. For native, discontinuous gels, upper gel buffer diluted twofold to fivefold for sample application is commonly used. Tracking dye and glycerol (or sucrose) are added to these samples also, and protein concentrations should fall within the same limits as for SDS-PAGE. With discontinuous systems, the volume of sample is not very important as long as the height of the stacking gel is at least twice the height of the sample volume loaded on the gel (Chrambach, 1985; Jovin, 1973d). Continuous systems require minimal sample volumes for best resolution. Careful sample handling is important when sensitive detection methods are employed. Silver-stained SDS-PAGE gels sometimes show artifact bands
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David E. Garfin
in the 50- to 70-kDa molecular mass region and irregular but distinctive vertical streaking parallel to the direction of migration. The appearance of these artifacts has been attributed to the reduction of contaminant skin keratin inadvertently introduced into the samples (Ochs, 1983). The best remedy for these artifacts is to avoid introducing keratin into the sample in the first place. Monomer solution, stock sample buffer, gel buffers, and upper electrode buffer should all be filtered through nitrocellulose and stored in well-cleaned containers. It also helps to clean the gel apparatus thoroughly with detergent and to wear gloves while assembling the equipment. Nucleic acid samples should be freed of proteins by protease treatment and (or) phenol extraction (Sambrook et al., 1989) before electrophoresis, because residual protein can cause aggregation of the sample in the well. Nuclease treatments can be used to remove either DNA from RNA samples or vice versa. Desalting is also recommended, but this is usually accomplished by ethanol precipitation after deproteinization. Samples can be dissolved in 1:2 or 1:10 (v/v) dilutions of electrophoresis buffer for loading on gels. Denaturation is accomplished by dissolving samples in loading buffer containing 7 M urea or 50% formamide and heating them at 75~ for a few minutes. Glycerol (10%) or 10% sucrose in the sample buffer provides density for underlaying samples below electrophoresis buffer. With nucleic acids, tracking dye consists of a combination of 0.025% each of bromophenol blue and xylene cyanol FF. The bromophenol blue migrates about twice as fast as xylene cyanol FF. Bands are identified by their positions relative to the two tracking dyes (Sambrook et al., 1989). Prepared samples are placed in sample wells of gels, either in the vertical or horizontal configuration, by underlaying from a microliter syringe or micropipette. Both types of device provide good control of sample volume. Syringes must be thoroughly rinsed between applications to avoid cross contamination of different samples. Standard pipette tips are too wide to fit into narrow sample wells, but several thin tips, specifically designed for sample application, are available. The choice of sample-loading device is one of personal preference. F. A p p a r a t u s
Apparatuses for gel electrophoresis are relatively simple. Electrophoresis cells are essentially plastic boxes with anode and cathode buffer compartments, electrodes (usually platinum wire), and jacks for making electrical contact with the electrodes. Some sort of device seals the gel chamber during gel formation. Gels are held either vertically or horizontally between the electrode chambers during the run. High-voltage direct current supplies provide electrical power for electrophoresis. Gel-forming reagents and buffers able to sustain electrical currents form the basis of the systems. Micropipettes, test tubes, and heating blocks are sample-handling necessities. Many suitable devices are available from a number of suppliers. Most polyacrylamide gel electrophoresis is done in vertical chambers, but some is done in horizontal, flat-bed electrophoresis devices. Gels are cast as rectangular slabs. The slab format provides uniformity, so that different samples can be compared in the same gel. In a small number of applications, gels
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are cast in cylindrical glass tubes. For comparative purposes, slab gels are far superior to tube gels. The vertical cells currently used are variants of Studier's design in which the gel slab is formed between two glass plates (Andrews, 1986; Bollag and Edelstein, 1991; Grierson, 1990; Hames, 1990; Sealey and Southern, 1990). Polyacrylamide gels adhere to glass sufficiently to be held vertically during electrophoresis. Conventional gels are of the order of 16 or 20 cm long and can accommodate up to about 25 samples. Longer gels give better separation in SDSPAGE and are used for complex samples. A typical run takes 4 - 5 hr. Plastic spacers establish gel thicknesses and sample wells are formed in the tops of the gels using plastic comb-shaped inserts during polymerization. Deep wells accommodate larger sample volumes than can be loaded on horizontal gels. Gel thicknesses of 0.75 or 1 m m give adequate loads for good sensitivity, while at the same time allowing relatively high voltages to be applied to the cell without excessive heating. Gel cassettes are positioned between separate anode and cathode compartments. (Both electrode compartments usually contain the same buffer solution.) Samples are underlaid beneath buffer in the wells. The better cells provide means for heat dissipation, because uneven heat distribution on the gel slab can cause band distortions. The so-called minicells allow rapid analysis and are often adequate for relatively uncomplicated samples. The design of these cells allows analyses to be completed two to three times faster than is possible with conventional cells. Minigels are about 7 cm long by 8 cm wide and are very easy to handle. Each gel can hold up to 15 samples and a typical two-gel run (up to 30 samples) can be completed in less than 1 hr (not counting setup and polymerization time). Agarose gels are generally run submerged under buffer in horizontal chambers, often called "subcells" (Grierson, 1990; Sealey and Southern, 1990). Molten agarose is poured into trays for gel formation. Gel thicknesses are determined by the volumes of agarose poured into the trays. Sample wells are formed in the bodies of the gels by suspending combs in the molten agarose. Gel trays are placed on the beds of the horizontal cells. The gels are covered with buffer and samples are underlaid in the wells. Vertical configurations are also possible. Frosted glass must be used when agarose gels are run in vertical chambers to keep the gels from sliding out of the cassettes.
G. Power C o n d i t i o n s Regulated direct current (dc) power supplies, designed for electrophoresis, allow control of every electrophoretic mode. Constant voltage, constant current, or constant power conditions can be selected. If desired, free-running, unregulated electrophoresis can be carried out. Many power supplies have timers and some have integrators, allowing runs to be automatically terminated after a set number of accumulated volt-hours (Allen et al., 1984). All modes of operation can produce satisfactory results, but for best results and good reproducibility, some form of electrical control is important. The choice of which electrical parameter to control is almost a matter of preference. The major limitation is the ability of the chamber to dissipate the heat generated by the electrical current (Woolley, 1987). During an electrophoretic run, electrical energy is
74
David E. Garfin converted into heat. This Joule heating can have many deleterious consequences, such as band distortion, increased diffusion, enzyme inactivation, and protein denaturation. All good electrophoresis chambers have provision for transferring heat from the gels to the outside environment. In general, electrophoresis should be carried out at voltage and current settings at which the run proceeds as rapidly as the ability of the chamber to draw off heat allows. That is, the run should be as fast as possible without exceeding desired resolution and distortion limits--and these can only be determined empirically for any given system. Each experiment will impose its own criteria on cooling efficiency. Sometimes it is sufficient to carry out electrophoresis on the lab bench. Other situations might require that the apparatus be moved into the cold room. Occasionally, it will be necessary to employ recirculated coolant. Electrical quantities are interrelated by fundamental laws. Each gel has an intrinsic (sometimes time-varying) resistance, R, determined by the ionic strength of its buffer. When a voltage V is impressed across the gel, a current I flows through the gel and the external circuitry. These three quantities are related by Ohm's law: V = IR, where V is expressed in volts, I in amperes, and R in ohms. In addition, power P, in watts, is given by P = IV. Joule heating, H, is related to power by the mechanical equivalent of heat, 4.18 J/cal, or H = P/4.18 cal/sec. With the Ornstein-Davis and Laemmli buffers, R increases during the course of electrophoresis. Thus, for runs at constant current in these gels, the voltage, power (I2R), and consequently the heat of the gel chamber increase during the run. Under constant voltage conditions, current, power (V2/R), and heat decrease during electrophoresis as R increases. Vertical cells are run at electric field strengths of 10-20 V / c m or currents in the range of 15-25 m A / m m of gel thickness. Horizontal cells are run at lower voltages, with fields in the range of 1 - 10 V / cm. Constant current conditions, as a rule, result in shorter but hotter runs than do constant voltage runs. The increased run times of constant voltage conditions give increased time for the proteins to diffuse, but this appears to be offset by the temperature-dependent increase in diffusion rate of the constant current mode. Probably the best way to regulate Joule heating while maintaining optimum resolution is to carry out electrophoresis in the constant power mode. In this mode, voltage and current are automatically adjusted to maintain their product constant at the dissipation limit of the chamber. With continuous buffers, it is sometimes possible to shorten run times by diluting the buffer to decrease its ionic strength. Because P = V 2 / R , every twofold lowering of ionic strength allows voltage to be increased by a factor of 1.4 without an increase in heating. Not all buffer systems can tolerate dilution, however.
H. Detection Detection of proteins in gels is accomplished by staining them with dyes or metals (Bio-Rad Laboratories, 1993b; Bollag and Edelstein, 1991; Garfin, 1990a). Coomassie Brilliant Blue R-250 is the most common protein stain and is recommended for routine work. Coomassie Brilliant Blue G-250 should be used for staining gels containing low molecular mass polypeptides (Schagger and van Jagow, 1987). Silver staining (Rabilloud, 1990) is the most sensitive method for
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staining proteins and nucleic acids in gels and should be employed when electrophoresis is used to assess the purity of a preparation, e.g., an antigen preparation. Copper staining allows rapid and sensitive detection of protein bands in SDS-PAGE gels without fixing proteins irrecoverably in gels. Discussions of various detection methods, including radiolabeling, and means for quantitating proteins in gels can be found in Allen et al. (1984), Allen and Budowle (1994), Andrews (1986), Hames (1990), Merril (1990), and Syrovy and Hodny (1991). All of the steps in gel staining are done at room temperature with gentle agitation (e.g., on an orbital shaker platform) in any convenient container, such as a glass casserole or a photography tray. Always wear gloves when staining gels, because fingerprints will stain. Permanent records of stained gels can be obtained by photographing them or by drying them on filter paper or between sheets of cellophane using commercially available drying apparatus.
1. Proteins a. Dye Staining Coomassie Brilliant Blue R-250 is the standard stain for protein detection in polyacrylamide gels (Wilson, 1983). Easy visibility requires on the order of 0.1-1/xg of protein per band. The staining solution consists of 0.1% Coomassie Brilliant Blue R-250 (w/v) in 40% methanol (v/v), 10% acetic acid (v/v), which also fixes most proteins in gels. Gels are first removed from the electrophoresis cell, then soaked in an excess of staining solution for 3060 min. Background stain is removed (destaining) by soaking the gel in a large excess of 40 methanol, 10% acetic acid, with several changes. Gels containing low molecular mass polypeptides are fixed in 50% methanol, 10% acetic acid for a maximum of 1 hr. They are stained with 0.025% Coomassie Brilliant Blue G-250 (w/v) in 10% acetic acid for 1-2 hr and are destained with 10% acetic acid. b. Silver Staining The method developed by Merril and co-workers can be as much as 100 times more sensitive than dye staining (Merril, 1990). Bands containing 10-100 ng of protein or nucleic acid can be easily seen. The reagents are available in kit form for use with polyacrylamide gels. Fixation of proteins in gels is with 40% methanol, 10% acetic acid (v/v). Methanol is removed by washing gels in 10% ethanol, 5% acetic acid (v/v). Proteins are then oxidized in a solution of potassium dichromate in dilute nitric acid. Excess oxidizer is washed out of the gels with water and the gels are treated with silver nitrate solution. Silver ions bind to the oxidized proteins and are subsequently reduced to metallic silver by treatment with alkaline formaldehyde. Color development is stopped with 5% acetic acid. Another method that requires only one simultaneous staining and development step is that of Gottlieb and Chavko (1987). It can be used to silver stain proteins and nucleic acids in polyacrylamide or agarose gels and is available in kit form. Following fixation in 50% methanol, 10% acetic acid, and 5% glycerol and washing with water, gels are soaked with a solution containing a silverammine complex bound to tungstosilicic acid. Silver ions transfer from the tungstosilicic acid to the proteins or nucleic acids in the gel by an ion-exchange or an electrophilic process. Formaldehyde in the alkaline solution reduces the silver ions to metallic silver to produce the images of the bands of macromole-
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David E. Garfin
cules. Because silver ions do not accumulate in the bodies of gels, background staining is very light.
c. Copper Staining Rapid, single-step staining of SDS-PAGE gels is achieved by incubating gels in 0.3 M copper chloride for 5 min, then washing them with water (Lee et al., 1987). Proteins are not permanently fixed by this method and can be quantitatively eluted after chelating the copper. Blue-green precipitates of copper hydroxide form in the bodies of the gels except where there are high concentrations of SDS, such as that bound to the proteins. Clear protein bands can be easily seen against the blue-green backgrounds and photographed with the gels on black surfaces. The resultant, negatively stained images of the electrophoresis patterns are intermediate in sensitivity between Coomassie blue and silver staining. The electrophoretic pattern is lost when copper-stained gels are dried, so they must be photographed, restained with Coomassie blue, or stored in water. 2. N u c l e i c A c i d s Nucleic acids in either polyacrylamide or agarose gels are most easily stained with ethidium bromide (Grierson, 1990; Sambrook et al., 1989; Sealey and Southern, 1990). This fluorescent dye intercalates between stacked bases of DNA and RNA. The resultant nucleic acid-dye complex has an increased fluorescence yield compared to the dye free in solution. After electrophoresis, gels are immersed for 30-60 min in buffer or water containing 0.5 ~ g / m l of ethidium bromide (5 /~g/ml for RNA), then washed with water. When viewed under short-wavelength ultraviolet illumination (302 nm), nucleic acid bands in gels appear bright orange against clear or pale orange backgrounds. Permanent records of gels stained with ethidium bromide can only be obtained by photographing the gels. Transilluminators and camera stands are commercially available for this purpose. [Note: ethidium bromide is a mutagen. Direct exposure to it should be avoided.] Methylene blue stains RNA and DNA in polyacrylamide gels (Peacock and Dingman, 1967). Following electrophoresis, gels are immersed in 1 M acetic acid for about 30 min to drop the pH of the gel for staining. Then, the nucleic acids in the gels are stained with 0.2% methylene blue in 0.2 M acetate buffer, pH 4.7. Destaining is accomplished by many successive water washes. The gels can be dried on filter paper or between cellophane sheets or photographed for permanent records. DNA and RNA can also be stained with one of the two silver stains discussed above. I. M o l e c u l a r M a s s E s t i m a t i o n
Sample treatment during SDS-PAGE by the Laemmli procedure breaks proteins down to their constituent subunits and leaves the subunits coated with the anionic detergent. The electrophoretic mobilities of the resultant SDSpolypeptide complexes all assume the same functional relationship to their molecular mass. To a first approximation, migration rates of SDS derivatives are inversely proportional to the logarithms of their molecular masses. SDSpolypeptides, thus, move through gels in a predictable manner, with low mo-
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lecular mass complexes migrating faster than larger ones. This means that the molecular mass of a protein can be estimated from the relative mobilities of its subunits in a calibrated SDS-PAGE gel. Molecular mass estimations are among the most often used applications of gel electrophoresis and account in part for the popularity of the Laemmli SDS-PAGE method. Molecular masses are determined in SDS-PAGE by comparing the mobilities of test proteins to the mobilities of known protein markers. The relevant parameter is the relative mobility, Rf, defined as the mobility of a protein divided by the mobility of the ion front. This parameter normalizes mobilities to a significant and characteristic measurable quantity. Rather than determine mobilities, it is sufficient to calculate Rf as the quotient of the distance traveled by a protein from the top of the resolving gel divided by the distance migrated by the ion front. Because the ion front is difficult to locate, in practice, mobilities are normalized to the tracking dye that migrates only slightly behind the ion front: Rf = (distance to band)/(distance to dye). The dye front can be marked by a notch in the edge of the gel or by inserting a needle soaked in india ink into the gel before the gel is stained (the dye front is not visible after staining). It is also acceptable to normalize mobilities to that of one of the protein bands in the gel. Plots of the logarithm of protein molecular mass (log M) versus the relative mobility, Rf, fit reasonably straight lines. In each gel, a lane of standard proteins of known molecular masses is run in parallel with the test proteins. Plots of log M vs. Rf constructed from the distances migrated by the standards calibrate the gel. The Rf values of the test proteins are compared with those of the standards. Interpolation of the Rf values of test proteins into the standard curve gives their approximate molecular masses. Standard curves are actually sigmoid in shape (Hames, 1990; See and Jackowski, 1989). The apparent linearity of a standard curve may not cover the full range of molecular masses for a given protein mixture in a particular gel. However, log M is sufficiently slow, in a mathematical sense, to allow fairly accurate molecular mass estimates to be made by interpolation, and even extrapolation, over relatively wide ranges. The approximate useful ranges of single-percentage SDS-PAGE gels for molecular mass estimations is as follows: 40,000 to 200,000 Da, 7.5%T; 30,000 to 100,000, 10%T; 15,000 to 90,000 Da, 12%T; 10,000 to 70,000 Da, 15%T. Mixtures of standard proteins with known molecular masses are available commercially for calibrating electrophoresis gels. It is important to bear in mind that the molecular masses obtained using Laemmli SDS-PAGE are those of the polypeptide subunits and not those of native, oligometric proteins. Moreover, proteins that are incompletely saturated with SDS, very small polypeptides, very large proteins, and proteins conjugated with sugars or lipids behave anomalously in SDS-PAGE, as mentioned in Section II,B,l,b. Nevertheless, SDS-PAGE provides reasonable molecular mass estimates for most proteins. Similar standard curves can be constructed for nucleic acids. For reliable size estimates, DNA and RNA molecules must be in configurations in which their mobilities depend only on chain length. DNA molecules must be either linear and double stranded, without any partially single-stranded regions, or completely denatured to single strands. RNA samples must be free of aggregates and hydrogen-bonded structures. Urea is usually included in gels intended for molecular mass determinations of single-stranded nucleic acids
78
David E. Garfin (Grierson, 1990; Sealey and Southern, 1990). Nucleic acid size standards are available from a number of suppliers.
J. Special-Purpose Gels This section presents four of the many variations of gel electrophoresis that have been developed to provide more information about macromolecules than furnished by the basic methods. Procedures are described for separating extended size ranges of molecules, for studying the conformations of proteins and nucleic acids, for resolving very large numbers of proteins, and for sequencing nucleic acids. Details of the procedures can be found in the references cited.
1. Pore-Size Gradient Gels Gradient gels, that is, gels with continuously changing pore sizes in the direction of migration, are popular for analyses of complex mixtures spanning wide molecular mass ranges (Allen et al., 1984; Allen and Budowle, 1994; Andrews, 1986; Hames, 1990; See and Jackowski, 1989). They consist of gradients of polyacrylamide concentration (%T). In a gel in which the pores become continuously smaller in the direction of motion, there is an apparent band sharpening as molecules migrate to the limits of porosity and essentially stop moving (Margolis and Kenrick, 1968; Rodbard et al., 1971). This can be advantageous in a number of cases. For example, anomalous behavior of glycoproteins in SDSPAGE, thought to be due to variable SDS binding, can be overcome in gradient gels in which molecular sieving predominates over charge effects. The main advantage of pore gradient gels is that both large and small molecules can be run in the same gel. Gradient gels, however, cannot match the resolution of two molecules obtainable with a properly chosen single concentration of acrylamide. A good approach is to use gradient gels for estimates of the complexities of mixtures. This may be sufficient for some purposes. However, best resolution requires the appropriate uniform concentration gel. Various devices are commercially available for producing polyacrylamide gradients of almost any desired shape. These devices range in complexity from programmable pumps to simple cylinder pairs that form gradients hydrostatically. Precast gradient gels are also available commercially. Discontinuous buffer systems give best resolution in gradient gels: 4-15% gradient minigels, based on the Laemmli buffers, resolve SDS-polypeptides in the 40 to 200-kDa size range, 4-20%T gels separate 10 to 100-kDa SDSproteins, and 10-20%T gradients are useful in the 10 to 100-kDa range. 2. Transverse Gradient Gel E l e c t r o p h o r e s i s The unfolding of proteins and the melting of DNAs can be studied by examining their electrophoretic mobilities in continuously varying concentrations of denaturant (DeWachter et al., 1990; Goldenberg, 1989; Goldenberg and Creighton, 1984; Myers et al., 1987). In a similar way, titration curves for proteins can be determined electrophoretically in gels containing pH gradients (Rosengren et al., 1977; Righetti, 1983). Protein or DNA molecules at any point along the sample application band migrate through the gel at constant denaturant concentration or constant pH. The effect of local conditions of denaturation or pH on any particular molecule in the gel is reflected in its mobility. Unfold-
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ing of proteins and melting of DNA result in decreases in the mobilities of the affected molecules. The direction moved by a protein during electrophoresis (whether toward the cathode or anode) depends on whether its pH is above or below its isoelectric point. By applying samples as long bands extending across gels containing horizontal gradients of denaturant or pH, denaturing curves or titration curves can be directly obtained. The relevant gradients are incorporated into gels so that they are situated perpendicularly to the direction of electrophoretic migration. The shapes of the resultant bands give information on the stabilities of proteins and DNAs or on the pI values of proteins. The usual configuration of denaturing gradient gels is the vertical polyacrylamide slab. Urea is the denaturant most commonly employed. The effect of urea on DNA molecules is to denature them with the strands separating (melting). Melting is a function of urea concentration and begins at domains rich in A + T base pairs. Urea also causes proteins to unfold as hydrogen bonding is disrupted. The extent of unfolding is dependent on the concentration of urea. Separate domains of proteins can undergo distinct unfolding transitions. Modifications to the gel casting procedure are needed to incorporate urea gradients into gels. The cassettes used for this technique are rigged so that after gels containing urea gradients are cast, they can be rotated 90 ~ for electrophoresis. The two sides of the gel end up with either 0 or 8 M urea. Any point between the two sides contains urea at some linearly proportioned concentration between the two extremes. Continuous buffer systems are used. The choice of buffer for protein denaturation curves depends on the particular protein being studied. Gels for studies of protein unfolding are run at room temperature. DNA melting curves are generally run in TBE buffer at an elevated temperature of about 60~ Samples are loaded across the tops of the gels. Following electrophoresis, the gels are stained and the bands obtained are analyzed. Horizontal slab gels are used for generating pH titration curves. In these gels, pH gradients are generated by means of the same ampholytes as used in isoelectric focusing (Section III). For the initial analysis of a new protein sample, the pH range spanned should be pH 3-10. Thereafter, if warranted, other pH gradients can be used. Polyacrylamide gels are cast with narrow troughs extending across their middles. Electrofocusing is carried out with the fields parallel to the troughs for a time sufficient for the ampholytes to form stable pH gradients. The gels are then rotated 90 ~ so that the pH gradients are perpendicular to the second direction of motion. Samples are loaded into the troughs and the fields are applied. In any particular gel, each sample protein in the trough is in a fixed pH environment. Those proteins at pH below their pI move toward the cathode. Those at pH above their pI move toward the anode. Proteins at their pI do not move. Those proteins far away from their pI move with higher mobility than those close to their pI. The pI of a protein is the point in the pH gradient where the S-shaped band crosses the trough.
3. Two-Dimensional Gel Electrophoresis The resolution of gel electrophoresis can be increased by combining two different techniques to produce a two-dimensional separation of the components in a sample. One approach is to incorporate a sample treatment step, such as denaturation or enzymatic modification, between first and second electrophoresis steps run at right angles to one another. Molecules altered by the treatment
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migrate to definitive positions in the second gel. Unaltered molecules migrate along the diagonal of the second dimension. With RNA molecules, it is sometimes sufficient simply to use two different gel concentrations in two gels run at right angles to one another (DeWachter et al., 1990). The best approach is to use two different physical principles for the two different gel directions. The most common two-dimensional technique is O'Farrell's method for proteins (Dunbar, 1987; Dunbar et al., 1990; Dunn, 1987; Harrington et al., 1991). Protein samples are first subjected to isoelectric focusing (IEF; see Section III) then to SDS-PAGE in a perpendicular direction. It is this procedure that is usually referred to in discussions of high-resolution two-dimensional gel electrophoresis (2DGE). The first dimension of 2DGE, IEF, separates proteins according to their isoelectric points. The second fractionation, by SDS-PAGE, further separates the same proteins by molecular mass. Very high-resolution two-dimensional methods have been developed, allowing thousands of polypeptides to be resolved in a single slab gel. The technique works best with soluble proteins, such as those from serum or cytoplasm. It is relatively labor intensive for an electrophoresis technique, requiring a relatively high skill level for best results. Hochstrasser's modification of the original method gives very high resolution 2DGE of serum proteins (Hochstrasser et al., 1988b). In this method, the IEF gel is 5%T, 2.6%C, containing 2% (w/v) ampholytes, 9 M urea, 30% CHAPS (detergent), and 10% Nonidet P-40 (NP-40) (detergent). Gels are cast in 1.5 to 2.5-mm (i.d.) glass capillary tubes. (Some practice may be required before bubble-free gels can be repeatedly cast.) First-dimension runs are done in tanks using 6 mM phosphoric acid as the anolyte and 20 mM sodium hydroxide as the catholyte. First-dimension IEF capillary gels are extruded from their glass tubes and placed on the tops of SDS-PAGE gels, which are run with Laemmli buffers. For serum proteins, 13.3%T, 2.6%C gels, cast without SDS, are recommended. Irreproducibility in 2DGE arises from the variability in pH gradients inherent in the use of carrier ampholytes in the IEF dimension and from the difficulty in positioning the IEF capillary on the SDS-PAGE gels. Immobilized pH gradients and mechanical positioning devices may change this and allow for reproducible two-dimensional gels suitable even for clinical work. 4. N u c l e i c A c i d Sequencing Gels Gel electrophoresis is at the heart of nucleic acid sequencing methodology. Molecular biologists routinely read nucleic acid sequences from electrophoresis patterns obtained with thin, denaturing polyacrylamide gels (Andrews, 1986). When coupled with chemical or enzymatic techniques for generating defined fragments of DNA or RNA, gel electrophoresis provides records of nucleotide sequences that are easily deciphered (D'Alessio, 1982; Davies, 1982; Deininger, 1983; Maxam and Gilbert, 1980; Smith, 1980). In nucleic acid sequence analysis, a purified piece of DNA or RNA containing the sequence of interest is isolated (e.g., a DNA fragment produced by digestion with restriction endonucleases). It is used to generate arrays of partial sequences differing in length by one nucleotide and spanning the entire sequence to be determined. Specific treatments produce separate arrays of partial sequences terminating in one of the four nucleotides (Ausubel et al., 1987). For a
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given molecule, chemical or enzymatic sequencing reactions yield mixtures of progressively larger polynucleotides that are of random length, start at a common, labeled origin, and terminate with specific, known nucleotides. Four separate chemical or enzymatic reactions are used to generate radioactively labeled oligonucleotides covering the sequence of interest. Radiolabeling allows detection of submicrogram quantities of oligonucleotides. Sequence information is obtained, one nucleotide at a time, by identifying the next longest chain among the four arrays. Chemical sequencing methods are degradative. Starting material is a fragment of DNA or RNA that is labeled at one end. The end-labeled fragment is subjected to four separate chemical treatments, each of which preferentially breaks the polynucleotide backbone adjacent to one particular base. Reaction conditions are adjusted to ensure only partial chain cleavages. The enzymatic method for sequencing RNA is also degradative. Partial sequences are generated by limited digestions with base-specific ribonucleases. In contrast, the enzymatic sequencing methods for DNA are synthetic. They depend on the primed synthesis of complementary copies of a single-strand DNA template by DNA polymerase. Because DNA polymerase cannot initiate DNA chains, the enzyme is used to elongate a primer chain annealed to a specific site on the template DNA. The nucleotide added to the growing end of the elongating primer chain is selected by base-pair matching to the template DNA. Chains are terminated by incorporating 2',3'-dideoxynucleotides into the newly synthesized DNA. The dideoxynucleotides lack the 3'-hydroxyl group necessary for the incorporation of the next nucleotide into the chain. Whenever a dideoxynucleotide is incorporated at the 3' end of the growing primer chain, elongation is selectively stopped. Reaction conditions are set to produce the requisite arrays of partial sequences. Enzymatic sequencing has become more popular than chemical methods, possibly because of the availability of several commercial kits for the purpose. Gel electrophoresis is used to order the partial nucleotide sequences according to size, keeping the products of each nucleotide-specific treatment in a separate lane. Each successive partial sequence in the ladder of gel bands contains one nucleotide more than its predecessor, and the identity of this nucleotide is known from the ordering of the gel lanes. The complete sequence is read from an autoradiograph of the gel by noting the terminal nucleotide of each successively longer partial sequence. Standard sequencing gels are thinner than most other kinds of gels (0.4 m m or thinner). They are run in TBE buffer containing 7 M urea. It is important that the polynucleotide fragments be single stranded for accurate chain length separations. Thus, relatively dilute solutions are loaded on the gels to minimize reannealing of separated strands, and gels are run at elevated temperatures. Power conditions are chosen for each particular sequencing cell so that electrophoresis takes place at temperatures of 50-70~ Sequencing gels can distinguish polynucleotides containing n nucleotides from those containing (n - 1) nucleotides, where n can range up to hundreds of nucleotides. A 5%T, 5%C sequencing gel 50 cm long, run for about 2.5 hr, can be used to determine sequences about 300 nucleotides long. After electrophoresis, gels are covered with plastic wrap and exposed to X-ray film to produce the autoradiographs from which sequences are read.
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David E. Garfin The reading of sequencing gels is the most time consuming part of a sequencing project. After a bit of experience, it is possible to quickly and reliably read sequences from the radioautographs and to identify and correct for artifacts in the gels. When many gels must be analyzed, though, the process becomes tedious and error-prone. Several types of computer-based instruments simplify the task of sequence reading and computer programs automate data manipulation and comparisons of different sequences. Fully or partially automated film readers are available that enter sequence information directly into computers for storage and manipulation (Eby, 1990). In addition, instruments can be purchased that incorporate storage phosphor screens to capture the energy from radioactive emissions for later electronic data acquisition (Johnston et al., 1990). These instruments allow imaging and quantifying sequencing-gel band patterns without the need for X-ray film. Fully automated sequence analyzers make use of laser-induced fluorescence to collect sequence data (Smith et al., 1986). Sequences are analyzed directly as chains of fluorescently labeled oligonucleotides migrate past a detector. Some of the instruments for sequence analysis are relatively expensive, but they are becoming increasingly popular because of the advantages of automated data collection (Barrell, 1991).
K. Preparative Gel Electrophoresis Proteins and nucleic acids can be purified for further study by gel electrophoresis in one of two ways. In the band-elution method, proteins or nucleic acids are first separated in a slab gel, then extracted from bands excised from the gel (Grierson, 1990; Hames, 1990; Sealey and Southern, 1990). With continuouselution electrophoresis, bands of separated macromolecules are run off the bottom of the gel and swept away to a fraction collector, as is done in column chromatography. Both methods retain the high resolution of gel electrophoresis. Elution from gel slices can be done by either passive diffusion or electrophoresis. The purity of the recovered molecules depends on how well the bands of interest can be identified and how cleanly the bands can be cut out of the gel slab. With a continuous elution device, the final purity of the recovered proteins or nucleic acids depends mainly on the correct choice of gel and buffer.
1. Extraction from Gel Slices Gels intended for protein or nucleic acid extraction are cast thicker than analytical gels (1.5-3 ram). Sample wells spanning the widths of the gels accommodate as much sample as possible. The maximum amount of sample that can be loaded on a gel depends on how well the molecules of interest are separated from their neighbors in the sample mixture. Because bands become wider as the amount of material increases, as sample loads are raised, the corresponding loss of resolution will eventually become unacceptable. Loads are easily tolerated that are 10- to 50-fold greater per unit of gel cross-section than are usually run in analytical gels. Thus, with some large slab gels, proteins can be recovered in tens-of-milligram amounts. Copper staining is advisable for visualization of protein bands in preparative SDS-PAGE, because this stain does not employ fixative solvents. Desired bands are located and cut from the stained gel. Excess copper is removed by
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incubating gel slices in three changes (for 10 min each) of 0.25 M EDTA, 0.25 M Tris-C1, pH 9 (Lee et al., 1987), or in Tris-glycine electrophoresis buffer. Gel slices are then incubated in the appropriate elution buffer. With native gels, a separate marker lane for each gel is cut off the gel and stained with Coomassie blue. After destaining, the marker lane, shrunk by methanol, is swollen back to its original size by soaking it in water. The marker lane can be aligned with the preparative section of its parent gel to locate the protein bands of interest. Nucleic acid bands are located for excision by staining with ethidium bromide.
a. Passive Diffusion Proteins and nucleic acids are often extracted from macerated gel slices by simple diffusion (Sambrook et al., 1989). Pieces of gel containing the molecules of interest are crushed with a mortar and pestle and are left covered with buffer until the molecules diffuse into the supernatant fluid. Nucleic acids are recoverable from gels cast with low-melting-temperature agarose. This agarose melts at about 65~ and gels at approximately 30~ The melting temperature of this agarose is low enough that the double-strand structure of DNA is retained when it is melted. Excised gel slices are covered with buffer and warmed to 65~ until the agarose melts. Phenol extraction and ethanol precipitation are then used to recover the DNA or RNA. An alternative procedure for recovering DNA from low-melting-temperature agarose makes use of an enzyme, called agarase, that digests the molten agarose (Burmeister and Lehrach, 1989). Agarase treatment is recommended for recovery of large DNA fragments. For liquefying polyacrylamide gels, alternative cross-linkers, other than bisacrylamide, have been developed. Appropriate treatment of gels made from these alternative comonomers causes labile bonds in the crosslinkers to break so that the gels liquefy. The alternative cross-linkers are not completely satisfactory, partly because the molecules of interest must be separated from residual polyacrylamide strands. b. Electroelution Electrophoretic elution is an efficient method for recovering proteins and nucleic acids from gel slices. In the simplest versions of this method, proteins and nucleic acids are electrophoretically driven out of gel pieces into dialysis sacks in the type of apparatus used for running cylindrical gel rods (Sambrook et al., 1989). More sophisticated commercial devices are available for the rapid recovery of proteins and nucleic acids in small volumes, with expected yields of greater than 70% (Harrington, 1990). Elution takes about 3 hr and is done in any suitable buffer. In the absence of SDS, nucleic acids often become bound to the membranes used in some of these devices, limiting the yields obtainable. Andrews (1986) describes several variations of electrophoretic elution. 2. C o n t i n u o u s E l u t i o n E l e c t r o p h o r e s i s In continuous elution electrophoresis, separated bands migrate off the bottom of a gel and into an elution chamber. A flow of buffer washes material out of the elution chamber and sweeps it away to a fraction collector. Purified molecules are recovered in test tubes ready for analysis (Andrews, 1986; Chrambach, 1985; Chrambach and Nguyen, 1979; Hediger, 1984; Koziarz et al., 1978). The gels in the preparative gel electrophoresis device shown in Fig. 3 (Chen, 1989) are formed between a cylindrical outer tube and a cylindrical core.
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They can be thought of as either hollow cylinders or slab gels folded around so that their two lateral edges join. The device can hold gels that are 9 or 13 m m thick and up to 12 cm long. The elution chamber consists of a thin polyethylene frit. A dialysis membrane, directly beneath the elution frit, prevents macromolecules from being drawn out of the chamber by the electric field. Elution buffer enters the chamber around the perimeter of a specially designed gasket and is drawn out of the apparatus by a peristaltic pump. The p u m p forces eluate through a UV monitor and onto a fraction collector. Special precautions are taken during polymerization of polyacrylamide to ensure a uniform pore structure in the gel. To assure that separated molecules migrate in compact, parallel bands, temperature gradients across the gel must be minimized. The temperatures of the internal and external surfaces of the gel are equalized by continuously pumping lower electrophoresis buffer through the central cooling core. The most important parameter in preparative SDS-PAGE is the pore size of the gel. The monomer concentration that best resolves two molecules varies with their molecular weights. Changing the gel composition from the optimal concentration by increasing or decreasing the monomer concentration ultimately decreases resolution. It is important to note that the appropriate monomer concentration for preparative electrophoresis is not necessarily the same as that used for analytical work. For reasons that are not entirely clear, optimum separation of two molecules occurs when the relative mobility of the protein of interest is around 0.55. Thus, the monomer concentration that provides sharp, well-resolved bands in the middle of an analytical gel will generally be the correct monomer concentration to use in a preparative gel. Molecules running with the ion front of an analytical gel will be best separated preparatively by a gel monomer concentration greater than that used in the analytical gel. Similarly, for preparative fractionation, molecules remaining near the top of an analytical gel will require a lower %T than that of the analytical gel. A series of analytical gels should always be run to ascertain the correct preparative gel concentration for SDS-PAGE. The purification illustrated in Fig. 4 was obtained by SDS-PAGE from a properly optimized preparative gel. Elution profiles such as shown in Fig. 4A are not always attainable. Not all UV monitors can discriminate closely spaced peaks. The three components of phycocyanin shown in the figure were well resolved in this run. They were thus recovered at high purity. As shown in Fig. 4B, there was little mixing of the component polypeptides in the recovered fractions. An important technical distinction in preparative electrophoresis is that between "separation" and "resolution" (Giddings, 1969; Lunney et al., 1971; Marker et al., 1977). Separation of bands refers to the distance between band centers, whereas resolution refers to separation relative to bandwidths. Optimal purity in preparative work requires minimized bandwidths as well as wide separation of bands. Note that the bands of phycocyanin in Fig. 4B overlap very little. They are, thus, both well separated and well resolved. For analytical gels, the distinction between separation and resolution is usually not made and the two terms are used interchangeably. Preparative native-PAGE is a technique for high-yield purification of biologically active proteins. In contrast to SDS-PAGE where detergentpolypeptide complexes migrate according to size only, the mobilities of pro-
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Fig. 4 Elution profile and SDS-PAGE analysis of electrophoretically purified phycocyanin subunits. The electrophoresis run shown in Fig. 3 was continued until the bands had migrated off the bottom of the gel. A flow of buffer sweeping across the bottom of the gel drew eluted material out of the gel chamber. (A) The eluate was pumped through a UV monitor to a fraction collector. The UV absorbance of the eluate is shown. The ion front and micelleband are labeled as ionic contaminants. The three subunits were well resolved in fractions 9-32. (B) Individual fractions were analyzed by (silver-stained) SDS-PAGE using 14%T resolving minigels. Starting material for the preparative run is shown in the extreme left and right lanes. The 18.5-kDa subunit eluted in fractions 9-17, the 21-kDa subunit in fractions 18-29, and the 23-kDa subunit eluted in fractions 29-32. The single bands seen in the lanes are criteria of purity.
teins in native-PAGE systems d e p e n d on both their charges and their sizes. There is no single electrophoresis buffer system that will optimally purify all native proteins. W h e n selecting conditions for the purification of a native protein, the pI of the protein u n d e r investigation and the p H of the electrophoresis system m u s t both be considered. In preparative native-PAGE of proteins, the most i m p o r t a n t consideration is the p H of the electrophoresis buffer. The p H of the electrophoresis buffer system m u s t be within the p H range over which the protein u n d e r s t u d y is stable and retains its biological activity. In addition, the p H of the chosen buffer system m u s t leave the protein with sufficient charge for it to m o v e through the gel at a reasonable rate. Changes in p H alter the charges (and shapes) of proteins. The net charge on a protein is d e t e r m i n e d by the difference between the p H of the solvent and the isoelectric point of the protein. A buffer with an alkaline p H value relative to the pI of a particular protein imparts net negative charge to the protein. In such a buffer system, the protein migrates t o w a r d the anode. Electrophoresis buffers with acidic p H values relative to the pI of a protein impart net positive charge to it so that it migrates t o w a r d the cathode. A buffer with a p H value identical to the pI of a protein results in zero net charge and the protein will not m o v e at all in an electric field.
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In native-PAGE, protein mobilities are best modified by the pH of the buffer. Electrophoresis buffers with pH values close to the pI of the protein of interest will theoretically provide the best resolution. However, the resultant migration rate may be too slow for elution from the preparative gel column. Conversely, buffers with pH values far away from the pI of the protein of interest result in fast migration rates, but, with a loss of resolution. The choice of pH becomes a compromise between separation and speed (in the pH range of protein stability). The discontinuous buffer system of Ornstein (1964) and Davis (1964) should be the first nondenaturing gel system tried. The resolving gel of the Ornstein-Davis system becomes pH 9.5 once the glycinate ions displace the chloride in the gel. This pH may be outside the range of stability for some proteins. Alternative discontinuous buffer systems devised for preparative work, spanning the pH range from 3 to 10, can be found in the article by Chrambach and Jovin (1983). Protocols for using the Jovin discontinuous buffers are analogous to those for the Ornstein-Davis buffer system. An advantage of discontinuous systems for dilute protein solutions is the use of stacking gels to concentrate the sample. However, the stacking phenomenon can cause aggregation or coacervation of some proteins and this can severely interfere with resolution. If discontinuous systems cannot be used because of stacking-induced aggregation, a continuous buffer system will be required. McLellan's (1982) continuous buffers, from pH 3.8 to 10.2, are particularly well suited to preparative work. Conditions for purification of native proteins should first be optimized on a small scale using minislab gels. The sample should be partially purified before gel electrophoresis. A method for identifying the protein of interest, such as by immunoblotting or enzyme activity, is essential. It is difficult to predict the migration rate of proteins in native buffer systems without preliminary analysis. It is helpful to know the pI of the protein of interest. With discontinuous systems, the mobilities of native proteins can be modified by changing the pore size of the gel. This is accomplished by changing the amount of acrylamide monomer in the gel. However, the mobilities of proteins in continuous systems are best altered by pH. DNA molecules, such as restriction fragments, can also be separated by continuous-elution electrophoresis. TAE or TBE buffers are recommended. The uniform charge distribution of nucleic acid molecules makes them similar to SDS-protein complexes as far as electrophoresis is concerned. Optimization for nucleic acid purifications should follow the same procedures as for SDSPAGE. Test gels and gels used to analyze fractions from preparative electrophoresis should always be silver stained to allow detection of trace contaminants that might not be visible after dye staining.
III. Isoelectric Focusing Isoelectric focusing (IEF) (Allen et al., 1984; Allen and Budowle, 1994; Andrews, 1986; Chrambach, 1985; Righetti, 1983; Righetti et al., 1990) is an electrophoretic method for separating amphoteric molecules in pH gradients. The net charge
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on an a m p h o t e r i c molecule is determined by the p H of its local environment. Proteins, the best-known examples of amphoteric molecules, carry positive, negative, or zero net formal electrical charge, d e p e n d i n g on the p H of their surroundings. W h e n proteins move through a m e d i u m with varying pH, their net charges change in response to the p H they encounter. Under the influence of an electric field, a protein in a p H gradient will migrate until it focuses at the position in the gradient where its net charge is zero. The net charge of any particular protein is the sum of all of its positive and negative charges. These are determined by the ionizable basic and acidic side chains of the constituent amino acids and prosthetic groups of the protein. For every protein there is a specific p H at which the net charge it carries is zero. This isoelectric p H value, termed pL is a characteristic physicochemical property of every protein. If the n u m b e r of acidic groups in a protein exceeds the n u m b e r of basic groups, the pI of that protein will be at a low p H value. Conversely, if the basic groups o u t n u m b e r the acidic groups, the pI will be high. Proteins show considerable variation in isoelectric points, but pI values usually fall in the range of p H 3-10. Proteins are positively charged in solutions at p H values below their pI and negatively charged above their isoelectric points. Thus, at p H values below the pI of a particular protein, it will migrate toward the cathode during electrophoresis. At p H values above its pL a protein will move toward the anode. A protein at its isoelectric point will not move in an electric field. W h e n a protein is placed in a m e d i u m with varying p H and subjected to an electric field, it will initially move toward the electrode with the opposite charge (Fig. 5). During migration through the p H gradient, the protein will either pick up or lose protons. As it does, its net charge and mobility will decrease and the protein will slow down. Eventually, the protein will arrive at the point in the p H gradient equaling its pI. There, being uncharged, it will stop migrating. If a protein at its pI should h a p p e n to diffuse to a region of lower pH,
Fig. 5 Isoelectricfocusing. A protein is depicted in a pH gradient in an electric field. A pH gradient formed by ampholyte molecules under the influence of an electric field is indicated. The gradient increases from acidic (pH 3) at the anode to basic (pH 10) at the cathode. The hypothetical protein in the drawing bears a net charge of + 2, 0, or - 2, at the three positions in the pH gradient shown. The electric field drives the protein toward the cathode when it is positively charged and toward the anode when it is negatively charged, as shown by the arrows. At the pI, the net charge on the protein is zero, so that it does not move in the field. The protein loses protons as it moves toward the cathode and becomes progressively less positively charged. Conversely, the protein gains protons as it moves toward the anode and also becomes less negatively charged. When the protein becomes uncharged (pI) it ceases to move in the field and becomes focused.
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it will become protonated and be forced toward the cathode by the electric field. If, on the other hand, it diffuses into a pH higher than its pL the protein will become negatively charged and will be driven toward the anode. In this way, proteins condense, or focus, into sharp bands in the pH gradient at their individual, characteristic pI values. Focusing is a steady-state mechanism with regard to pH. Proteins approach their respective pI values at differing rates but remain relatively fixed at those pH values for extended periods. This type of motion is in contrast to conventional electrophoresis in which proteins continue to move through the medium until the electric field is removed. Moreover, in IEF, proteins migrate to their steady-state positions from anywhere in the system. Thus, the sample application point is arbitrary. In fact, the sample can be initially distributed throughout the entire separation system. Stable, linear pH gradients are the keys to successful IEF. Establishment of such gradients is accomplished with synthetic carrier ampholytes (Just, 1983). Ampholytes (amphoteric electrolytes) are mixtures of polyamino-polycarboxylate compounds. They are small (about 300-1000 Da in size), multicharged, organic buffer molecules with closely spaced pI values and high conductivity. Ampholytes are included with the monomer solution used to cast analytical gels and with the sample in preparative IEF chambers. When a voltage is applied across a solution of ampholytes, they partition into a smooth pH gradient, increasing monotonically from the anode to the cathode (Laas, 1989b; Mosher et al., 1992). The slope of the pH gradient is determined by the pH interval covered by the carrier ampholyte mixture and the distance between the electrodes. The proper choice of ampholyte range is very important to the success of a fractionation. Ideally, the pH range covered by the focused carrier ampholytes should be centered on the pI of the proteins of interest. This ensures that the proteins of interest focus in the linear part of the gradient, with many extraneous proteins excluded from the separation zone. Carrier ampholyte concentrations of about 2% (w/v) are best. Concentrations of ampholytes below 1% (w/v) often result in unstable pH gradients. Ampholytes at concentrations above 3% (w/v) are difficult to remove from gels and can interfere with protein staining. IEF is a high-resolution technique that can resolve proteins differing in pI by less than 0.05 pH unit. The technique is rapid and nondenaturing and can be run preparatively as well as analytically. Typical analytical gels take 90 min to run and preparative runs are over in 4 hr. Antibodies, antigens, and enzymes usually retain their activities during IEF. However, IEF does require careful sample preparation and the use of relatively expensive ampholytes. Ampholytes sometimes form complexes with proteins, which may necessitate steps for their removal. In addition, some proteins precipitate near their pI values. For best results, low-ionic-strength sample buffers are necessary and nonionic detergents or urea are often included in IEF runs to minimize protein precipitation. Some proteins, especially membrane proteins, require detergent solubilization during isolation. Ionic detergents, such as SDS, are not compatible with IEF, although nonionic detergents, such as octylglucoside, and zwitterionic detergents, such as 3-[(3-cholamidopropyl)dimethylammonio]-l-propane sulfonate and its hydroxyl analog (CHAPS and CHAPSO), can be used (Hjelmeland
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and Chrambach, 1981). Triton X-100 and NP-40 may be less satisfactory due to the slight charge content of some commercial preparations.
A. Analytical Isoelectric Focusing As an analytical tool, IEF is carried out in large-pore polyacrylamide (5%T, 3%C) or agarose gels (1%), which serve mainly as anticonvective matrices (Garfin, 1990b). Polyacrylamide IEF gels are polymerized with an initiator system, including riboflavin for photopolymerization. Photochemical initiation of polymerization with all three compounds, riboflavin, ammonium persulfate, and TEMED, results in more complete polymerization of IEF gels than does chemical polymerization alone in gels containing low-pH ampholytes. Suitable initiator concentrations are 0.015% ammonium persulfate, 0.05% TEMED, and 5/~g/ml riboflavin. Photochemical polymerization is allowed to continue for 2 hr, with the second hour under direct lighting from a nearby fluorescent lamp. The most common configuration for analytical IEF is the horizontal polyacrylamide slab gel. Gels are cast on glass plates or specially treated plastic sheets with one exposed face. They are placed on cooling platforms and run with the exposed face upward. Electrolyte strips, saturated with 0.1-1 M phosphoric acid at the anode and 0.1-1 M sodium hydroxide at the cathode, are placed directly on the exposed surface of the IEF gel. Contact between the electrical power supply and the electrolyte strips is maintained by electrodes of platinum wire. In another possible configuration, the gel and its backing plate are inverted and suspended between two carbon rod electrodes without the use of electrolyte strips (Awdeh et al., 1968). Ultrathin gels ( < 0.4 mm) allow the highest field strengths and, therefore, the highest resolution of the analytical methods. Electrofocusing can also be done in tubes, and this configuration constitutes the first dimension of two-dimensional gel electrophoresis (Dunbar, 1987; Dunbar et al., 1990). The pH gradient and the applied electric field determine the resolution of an IEF run. According to both theory (Giddings and Dahlgren, 1971) and experiment, the difference in pI between two resolved adjacent protein IEF bands (&pI) is directly proportional to the square root of the pH gradient and inversely proportional to the square root of the voltage gradient (field strength) at the position of the bands): ApI ~ [(pH gradient)/(voltage gradient)] 1/2. Thus, narrow pH ranges and high applied voltages give high resolution (small &pI) in IEF. In addition to the effect on resolution, high electric fields also result in shortened run times. However, high voltages in electrophoresis are accompanied by large amounts of generated heat (Joule heating). Thus, there are limitations on the magnitudes of the electric fields that can be applied. This is partly because resolution decreases with increasing temperature (because diffusion coefficients increase with temperature) and partly because gels can actually get hot enough to burn. Because of their higher surface-to-volume ratio, thin gels are better able to dissipate heat then thick ones and are therefore capable of higher resolution. Electric fields used in IEF are generally of the order of 100 V/cm. Urea is a common solubilizing agent, especially for those proteins that
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David E. Garfin precipitate at their isoelectric points. For maintaining protein solubility, 3 M urea is often satisfactory, but concentrations up to 8 M urea have been used. Only fresh solutions of urea, treated with a mixed-bed ion-exchange resin, should be used. Many protein samples require the use of detergents for their solubilization. For IEF work, the zwitterionic detergents CHAPS and CHAPSO, or the nonionic detergent octylglucoside, at concentrations of 1-2% in the gel, are recommended. Even in the presence of detergents, some samples may have stringent salt requirements. Salt should be present in a sample only if it is an absolute requirement. Carrier ampholytes contribute to the ionic strength of the solution and can help to counteract a lack of salts in a sample. Small samples (1 to 10 ~1) in typical biochemical buffers are usua.lly tolerated, but better results can be obtained with solutions in deionized water, 2% ampholytes, or 1% glycine. Suitable samples can be prepared by dialysis or gel filtration. Good visualization of focused lanes generally requires a minimum of 0.5/~g of protein with dye staining or 50 ng of protein per band with silver staining. One of the simplest methods for applying samples to thin polyacrylamide gels is to place filter paper strips impregnated with sample directly on the gel surface. Up to 25 ~1 of sample solution can be conveniently applied after absorption into 1-cm squares of filter paper. A convenient size for applicator papers is 0.2 • 1 cm, holding 5/~1 of sample solution. Alternatively, 1- to 2-~1 samples can be placed directly on the surface of the gel. There are no fixed rules regarding the positioning of the sample on the gel. In general, samples should not be applied to areas where they are expected to focus. To protect the proteins from exposure to extreme pH, the samples should not be applied closer than 1 cm from either electrode. Preforming the pH gradient before sample application will also limit the exposure of proteins to pH extremes.
1. Detection of Proteins Staining solution for proteins in IEF gels consists of 0.04% Coomassie Brilliant Blue R-250, 0.05% Crocein Scarlet in 27% ethanol, 10% acetic acid. Gels are soaked in staining solution for at least 1 hr. Destaining is done with several changes of a large excess of 40% ethanol, 10% acetic acid until a clear background is obtained. IEF gels can also be silver stained for increased detection sensitivity.
B. Preparative Isoelectric Focusing Laboratory-scale preparative electrofocusing (Garfin, 1990b) is accomplished in devices such as the Rotofor cell (Bier, 1986; Egen et al., 1984; A.-C. Hochstrasser et al., 1991). Preparative fractionations on the scale of from hundreds of milligrams to grams of protein, with recoveries of greater than 90%, are possible. Purifications of 10- to 100-fold place IEF procedures intermediate between ionexchange and ligand-binding chromatographies as preparative methods. IEF is well suited for use at any stage of a preparative scheme, and is particularly effective in the early stages of purification. In many cases, simple sequential fractionation and refractionation on the same device provide the desired purity.
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It is not necessary to attain steady-state focusing in preparative IEF, because adequate separations m a y be achieved before then. The Rotofor cell separates proteins by IEF in free solution (Fig. 6). Zone stabilization in the cell is achieved by rotating the sample chamber about a horizontal axis. The separation column is divided into compartments by means of screens of w o v e n polyester. The screens offer resistance to fluid convection, but do not hinder the flow of current or the transport of proteins. Proteins, which are initially dispersed uniformly t h r o u g h o u t the chamber, migrate to the one or more compartments that are at p H values nearest to their isoelectric points. The combined effect of compartmentalization and rotation is superior to either m e t h o d alone in maintaining the stability of focused zones. The segmentation of the column also facilitates fraction collection. The focusing chamber, capable of holding up to 55 ml of sample, is divided into 20 compartments by a core m a d e up of 19 disks of polyester screen (6-~m pores). A ceramic cooling finger runs t h r o u g h the center of the focusing chamber to dissipate the heat generated during the run. Two electrode assemblies hold the anolyte (0.1 M H3PO 4) and catholyte (0.1 M N a O H ) solutions.
Fig. 6 Preparative isoelectric focusing. A mixture of naturally colored proteins consisting of phycocyanin (pI 4.6), myoglobin (pI 7.0), hemoglobin A (pI 7.1), hemoglobin C (pI 7.5), and cytochrome c (pI 9.6) were combined in water containing 1% ampholytes (pH 3-10). The mixture was loaded directly into a Rotofor cell and was focused for I hr at 12 W constant power, as described in the text. Bands of focused proteins can be seen in the segmented focusing chamber. The anode (pH 3) is at the left and the cathode (pH 10) is at the right of the chamber (cf. Fig. 5).
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Appropriate ion-exchange membranes and gaskets isolate the electrolytes from the sample in the focusing chamber while allowing electrical contact with the material in the chamber. Vent caps provide pressure relief from the gases that build up in the electrode chambers by electrolysis during the run. Rotation inhibits convection, maintains even cooling and efficient electrical contact, and prevents the screens from becoming clogged by precipitated protein. Runs are done at 4~ at constant power (12 W) for 4 hr or less. Samples are collected by aspiration through tubing lines connecting the 20 individual compartments with corresponding test tubes in a vacuum chamber. The individual test tube fractions are easily sampled for assay or measured for pH with standard electrodes. Samples for the Rotofor need not be completely desalted before fractionation. Ions in the sample solution will be electrophoresed into the two end compartments in the early stages of the run. Carrier ampholyte (2%, w/v) in the initial sample solution supplies enough ampholyte for refractionation of pooled material. After the tubes containing the protein of interest have been identified, they can be pooled for a second run. The pH range covered on refractionation is centered on the pI of the protein of interest and generally covers a total pH range of less than 1 pH unit. Thousandfold purification by refractionation has been achieved. The ideal sample run on the Rotofor cell would contain only the protein mixture, water, and ampholytes. However, pI precipitation may require that 3 M urea be included for solubility. When higher urea concentrations are needed, the Rotofor cell is run at 12~ Detergents (1-2%, w/v) may also be added to samples. Zwitterionic detergents, such as CHAPS, CHAPSO, and nonionic octylglucoside, are satisfactory.
1. Removal of Ampholytes from Proteins There are a number of ways to separate ampholytes from proteins. Electrophoresis, ammonium sulfate precipitation, gel filtration, ion-exchange, and hydroxylapatite chromatographies have all been used. Dialysis is a simple and effective method for removing ampholytes from solutions of proteins. Pooled fractions are first adjusted t(~ 1 M NaC1 to disrupt weak electrostatic complexes between ampholytes and proteins, then are dialyzed against appropriate buffers. Extensive dialysis is required for thorough removal of ampholytes. There is no good way to demonstrate complete absence of ampholytes in a protein solution, but for many applications they need not be entirely removed.
IV. Immun0electr0ph0resis Immunoelectrophoresis (IEP) is a technique for studying antigens and antibodies (Axelsen, 1983; Garvey et al., 1977; Lizana, 1989; Marchalonis and Warr, 1982). Antigen samples are first separated into their component parts by electrophoresis in agarose gels. They are then probed with antibodies while still in the gels. Because the technique is based on the diffusion of large molecules, the open pore structure of agarose gels is required for the electrophoresis step. This limits the electrophoretic resolution that can be obtained. Nevertheless, the
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high specificity of antibodies allows many antigens in a given sample to be identified. In the simplest version of the method, antigen samples are placed in small (2-4 mm), circular wells punched in thin (1-2 mm), 1% agarose gels. Gels are cast on glass plates or treated plastic sheets and placed between electrode chambers in horizontal electrophoresis cells. Electrophoresis cells for IEP tend to be simple plastic boxes with separated electrode chambers. Contact between electrophoresis buffers and IEP gels is usually made with buffer-saturated filter paper wicks. A suitable IEP buffer is 0.08 M Tris, 0.02 M Tricine, 0.3 mM calcium lactate, pH 8.6. Electric fields for IEP are of the order of 5 V/cm. When electrophoresis is completed, antisera are placed into longitudinal troughs cut into the gels parallel to the migration path. Troughs, 1-2 mm wide, are placed about 0.5 cm from the sample wells. One trough is cut on each side of the sample lane. Different antisera can be placed in the two troughs. The gels are incubated overnight and the antigens and antibodies diffuse toward each other in the gel. Sweeping arcs of precipitated proteins (precipitin) form in the gels where antigens and antibodies meet at appropriate concentrations (equivalence). Major precipitin arcs are visible directly in the gels and minor ones can be visualized by staining. The presence of a precipitin arc is evidence for both antigen in the electrophoresis sample and antibody in the antiserum. The complexity of the pattern of precipitin arcs depends on both the number and types of antigens in the sample and the number and types of antibodies in the antiserum. Two major variations of immunoelectrophoresis are the so-called one- and two-dimensional rocket immunoelectrophoresis techniques. The name "rocket" is derived from the rocket-shaped precipitin peaks that form following the antigen-antibody reaction. The heights of precipitation peaks in rocket immunoelectrophoresis are roughly proportional to the concentrations of antigens in the samples, so that these two methods are semiquantitative. In rocket immunoelectrophoresis, antigens are subjected to electrophoresis in agarose gels in which antibodies are embedded. The pH of the electrophoresis buffer is near the pI of the antibody molecules, so that the antibodies do not migrate in the gel during electrophoresis. For one-dimensional rocket IEP, antigen samples are placed in wells punched out of the antibody-containing gels prior to electrophoresis. Rockets form during electrophoresis where the antigen and antibody meet at equivalence. By comparing rocket heights of test samples with those formed by known standards, concentrations of specific antigens can be determined. Identification and measurement of multiple antigens are possible with two-dimensional (or cross) rocket immunoelectrophoresis. The first step in this method is a regular agarose gel electrophoresis to separate the antigens in the sample. Next the electrophoresis lane is cut from its gel and fused to an agarose gel containing embedded antibodies. A second electrophoresis at right angles to the first direction is run. During the second electrophoresis step, antigens migrate through the antibodies in the second gel. Precipitin arcs form along the equivalence regions of the antigen-antibody pairs in the reactants. The multiplicity of precipitin arcs depends on the complexities of the antigen sample and the antiserum in the second gel.
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David E. Garfin Immunoelectrophoresis methods have been largely replaced by immunoblotting (see below) as research tools. IEP is more commonly used in clinical applications. At one time IEP methods formed the basis of serological analyses. A skilled technician can make a detailed serological diagnosis, including fairly accurate estimates of antigen concentrations, from a set of immunoelectrophoresis patterns.
V. Blotting Several types of synthetic membranes bind proteins and nucleic acids tightly enough that they can be used as supports for solid-phase immunoassays. Membrane-bound molecules are readily accessible to antibody or nucleic acid probes. This has led to the development of a variety of highly specific and sensitive procedures collectively known as blotting (Baldo and Tovey, 1989; Bers and Garfin, 1985; Bjerrum and Heegaard, 1988; Gershoni, 1987). The most informative blots are those in which proteins or nucleic acids are transferred from an electrophoresis gel to a support membrane and then probed. The most common support membrane is nitrocellulose. Proteins bind to it under conditions of low ionic strength and can be transferred from gels to membranes by electrophoresis. In contrast, high ionic strength is needed for nucleic acids to bind to nitrocellulose. Because high ionic strength is incompatible with electrophoresis, absorptive methods (from which the term "blots" is derived) were developed for transfers of nucleic acids from gels to membranes. Because this chapter is devoted to electrophoresis, only electrophoretic protein transfer is discussed. Probing of membrane-bound proteins is generally done immunologically with antibodies. For historical reasons, immunoblotting is also called Western blotting. It combines the selectivity of gel electrophoresis with the specificity of immunoassays, allowing individual proteins in complex mixtures to be detected and analyzed. Immunoblotting was developed because of the desire to probe for proteins that otherwise are inaccessible to antibodies while in highresolution polyacrylamide gels. The selectivity and specificity of immunoblotting are being utilized in clinical diagnostics. Prepared membrane strips are becoming available to clinics for testing sera for the presence of antibodies to various infectious organisms.
A. Principles of lmmunoblotting A typical immunoblotting experiment consists of six interrelated steps (Bio-Rad Laboratories, 1991; Garfin, 1992; Garfin and Bers, 1989; Timmons and Dunbar, 1990). (1) Proteins are first fractionated by electrophoresis in a polyacrylamide gel. (2) The proteins are then transferred from the gel to a membrane where they become immobilized as a replica of the band pattern of the gel. (3) Next, unoccupied protein-binding sites on the membrane are saturated to prevent nonspecific binding of antibodies. (4) The blot is then probed for the proteins of interest with specific, primary antibodies. (5) Secondary antibodies, specific for the primary antibody type and conjugated to detectable reporter groups, such
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as enzymes or radioactive isotopes, are then used to label the primary antibodies. (6) Finally, the labeled protein bands are made visible by the bound reporter groups, which in the case of enzymes convert appropriate substrates into insoluble, colored products. As might be expected, many variations in methodology have been devised.
1. Electrotransfer Nitrocellulose membrane is the best known blotting membrane. Protein binding to nitrocellulose, which is thought to be due to hydrophobic forces, is instantaneous, nearly irreversible, and quantitative over a wide range of protein concentrations (up to about 80-100 /~g/cm2). Polyvinylidene difluoride (PVDF) membranes also bind proteins tightly (170-200 ~ g / c m 2) and are stable in the chemicals used for protein sequence determination. Individual bands cut from PVDF blots can be inserted directly into solid-phase sequenators (Matsudaira, 1990). Electrophoresis is used to transfer proteins from gels to membranes. Electroblotting produces a faithful replica on the membrane, retaining the full resolution of the gel. There are currently two main types of electroblotting apparatus: tanks of buffer with appropriately placed electrodes, and flat-plate electrode arrangements for so-called semidry transfers. Blotting apparatuses are available to accommodate gels of all sizes. Transfer tanks are made of plastic with electrodes mounted at or near the walls of the tanks. Nonconductive cassettes hold the membranes in close contact with the gels. The cassette assemblies are placed in the tanks transverse to the electric fields and submerged under conducting buffer. Large volumes of buffer in the tanks dissipate the heat generated during transfer. In semidry blotting, the gel and membrane are sandwiched horizontally between two stacks of buffer-wetted filter papers in direct contact with two closely spaced, solid-plate electrodes. The term "semidry" refers to the limited amount of buffer that is confined to the stacks of filter paper. Of the two blotting systems, tanks are recommended for most routine work. With tanks, temperatures can be regulated during blotting and transfers are somewhat more efficient than with semidry systems. Under semidry blotting conditions, some small proteins are driven through the membranes, and because low buffer capacity limits run times, some large proteins are poorly transferred. Nevertheless, because semidry transfers require considerably less buffer and are easier to set up than the tank method, they are often favored by laboratories performing large numbers of blots. The buffer usually used to transfer proteins from one- or two-dimensional SDS-PAGE gels to nitrocellulose membranes is electrophoresis electrode buffer without SDS, but containing methanol. For most purposes, 25 mM Tris, 192 mM glycine, 20% (v/v) methanol, pH 8.3, will give good transfers. With semidry blotters, transfer of SDS-PAGE proteins can be accomplished with 48 mM Tris, 39 mM glycine, 20% methanol, pH 9. Methanol in blotting buffers removes SDS from protein-detergent complexes and increases the affinity between proteins and nitrocellulose. However, methanol causes a general reduction in gel pore size, restricting transfer of some proteins. It may also cause some proteins to precipitate and transfer inefficiently. Lengthy equilibration of
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the gel in the buffer should be avoided; simple washing of the gel in transfer buffer gives best results. Methanol is not required in the transfer buffer when proteins are electroblotted from gels not containing SDS.
2. Processing of Blots Regardless of the transfer method, the processing of blots involves essentially the same set of steps. The recommended buffer for all processing steps of immunoblotting is 0.02 M Tris-C1, 0.5 M NaC1, pH 7.5. Following transfers, unoccupied binding sites on the membranes must be saturated to prevent the nonspecific binding of antibody probes. Failure to block membranes adequately results in unacceptably high backgrounds. Effective blocking of nitrocellulose blots is achieved with 3% nonfat dry milk for 30-60 min, followed by washes with 0.05% Tween 20 (a nonionic detergent). Prior to probing, dried, blocked blots can be stored for months at room temperature or longer in the refrigerator or freezer. High-avidity, high-purity antibodies make the best primary and secondary probes. Tween 20 (0.05%) and a ballast of heterologous protein (e.g., 1% nonfat dry milk) should be included in the dilution buffers to minimize adsorption of probes to membranes. The ultimate sensitivity of a blot is determined by the enzyme that labels the probe. Chromogenic enzyme substrates for blotting applications allow protein bands to be directly visualized. They are converted into insoluble, colored products that precipitate and bind to membranes at the sites of the enzymes. Depending on the enzyme and substrate, sensitivities range from the low tens of picograms to the low hundreds of picograms of detected protein. Alkaline phosphatase (from calf intestines) and horseradish peroxidase (HRP) are the most commonly used labels. Alkaline phosphatase (AP) is the label of choice for sensitive chromogenic detection of immunoblots. The preferred substrate for AP blots is a mixture of 5-bromo-4-chloro-3-indolyl phosphate (BCIP) aKd nitro blue tetrazolium (NBT). The substrate BCIP is dephosphorylated by the AP, then oxidized in a reaction coupled to reduction of NBT. The resultant highly visible, purple-colored product is deposited only on the labeled bands. Sensitivities in the range 10-100 pg of detected protein can be expected. Chemiluminescent substrates are at least 10-fold more sensitive than BCIP-NBT. The disadvantage in their use is that detection requires the use of photographic (or X-ray) film. Exposures must be optimized by trial and error and the films must be developed. Storage-phosphor imaging-screen instruments can also be used for detection of chemiluminescence (Nguyen et al., 1993). In comparison, color development of BCIP-NBT can be directly observed on the blot as substrate is converted to product by the enzyme. Chemiluminescent substrates appear to be favored in laboratories doing autoradiography, because film development equipment is readily available. Luminol is an appropriate chemiluminescent substrate for HRP (Durrant, 1990) and certain dioxetane compounds are suitable for use with AP (Bronstein et al., 1992). The luminol signal fades with time, so that exposures must be set up shortly after addition of substrate to the blot, whereas the dioxetanes produce a more longlived signal. In order to identify particular protein bands, they must be compared to all of the proteins in the sample and to known standards. This requires the indis-
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criminate staining of all the proteins on the blot. It is possible to stain a duplicate gel for comparison purposes, but because the fixing and staining of gels causes them to shrink and distort, correlation of gel and blot patterns is difficult. It is more desirable to stain a lane, a section, or a duplicate blot for the total protein pattern. Amido black is the most commonly used dye for total protein staining of blots. Other dyes have been used as well, but the best current total protein stain is probably colloidal gold. Colloidal gold total protein stain, which is available as a stabilized sol, is quite sensitive. Detection limits are in the low hundreds of picrogram range of target protein and can be enhanced by an order of magnitude by subsequent treatment with silver (using kits designed for this purpose).
VI. Pulsed-Field Gel Electrophoresis Conventional agarose gel electrophoresis cannot resolve DNA molecules larger than about 20 kilobase (kb) pairs. Under special conditions (very low agarose concentration and low ionic strength), DNAs up to about 50 kb in length can be resolved, but under ordinary conditions, these large molecules do not separate from one another in the agarose matrix (Fangman, 1978). The explanation for this limitation obviously has to do with the mechanisms by which DNA molecules move through gels. The theoretical understanding of the process is being spurred on by intense interest in the structures of genomes. The dynamics of DNA molecules, with their uniform, linear charge distributions (one negative charge per nucleotide under electrophoretic conditions), are amenable to mathematical analysis. This has attracted many physical scientists to study the electrophoretic behavior of DNA. The intense activity in this field has generated fascinating insights into electrophoretic processes. A DNA molecule free in solution is in a relaxed configuration. When the molecule is placed in the midst of an agarose gel, its shape becomes constrained by entanglements with the elements of the gel matrix (Noolandi, 1992; Burlatsky and Deutch, 1993). If a static electric field is impressed across the gel, the DNA molecule will be pulled toward the anode with a uniform force per unit of its length. The material of the gel will resist the forward motion of the DNA by imposing random obstacles along its length. (Recall that the gel matrix is not uniform, but rather a statistical meshwork of solid fiber bundles and open spaces.) Eventually a segment of the molecule will be pulled into a strategically located gel pore and will move ahead of the rest of the molecule. The field will pull this leading section ahead and force the rest of the molecule to follow it through the gel. The trailing segments of the DNA will disentangle from the gel matrix and follow the path taken by the leading segment. This type of motion is called reptation (Lerman and Frisch, 1982; Lumpkin et al., 1985), and has been compared to the motion of a snake moving through bamboo. Motion continues until entanglements with the matrix so severely impede the DNA molecule that it bunches up and must start the reptation process over again (Deutsch, 1988). Once the field is removed, the DNA molecule ceases moving and relaxes. The dynamics of reptation in agarose gels are such that, on the macroscopic level, it is not possible to distinguish the distances migrated by different DNA molecules longer than 20 kb.
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David E. Garfin Separation of large DNA molecules by gel electrophoresis becomes possible when the reptation process is disrupted. The technique of pulsed-field gel electrophoresis (PFGE) allows resolution of DNA molecules millions of base pairs long (Burmeister and Ulanovsky, 1992; Gemmill, 1991; Lai and Birren, 1990; Lai et al., 1989). In PFGE, the applied electric field is pulsed so that it alternately points in one of two different directions. Each size of DNA molecule in a sample takes a characteristic time to reorient to the differing field directions. Schwartz (1985) was the first to exploit the length-dependent reorientation time of DNA in electrophoresis. The advantages of PFGE for resolving large DNA molecules were quickly recognized. Variants of Schwartz and Cantor's (1984) original method were soon developed and several sophisticated PFGE apparatuses are commercially available (Anand and Southern, 1990; Birren and Lai, 1993). Reptating DNA molecules orient along the direction of the applied electric field. If the field is turned off, and a new field, whose vector points in another direction, is applied, DNA molecules must first relax, then reorient along the new field. Return of the original field direction forces the DNAs to again relax and reorient along the field that now points in the original direction. Switching of the fields back and forth produces an alternation of the motion of the DNA molecules. The net motion of the DNA is along the resultant of the field vectors. The time required for any particular DNA molecule to reorient along a newly applied field is a sensitive function of the length of the molecule; short molecules reorient faster than large ones. The length of time that either of the alternative fields is on is called the switching time. Different populations of molecules can follow fields alternating with different switching times. For any given switching time, molecules below a certain critical size will completely align along the field and migrate appreciable distances in the gel. Somewhat larger molecules will spend a greater proportion of the switching time reorienting than the smaller ones and have less time in which to move in the direction of the field. The largest molecules spend all of their time trying to reorient to the alternating fields and hardly move at all. PFGE exploits the size dependence of reorientation times to resolve DNA molecules in the megabase pair size range. The entire genomes of some small organisms, such as yeast, have been resolved by PFGE. The simplest configuration for PFGE is that of field-inversion gel electrophoresis (FIGE) (Carle et al., 1986). A standard subcell can be used for FIGE. An electronic controller switches the applied voltage back and forth between the two electrodes to give fields pointing alternately in the forward and backward directions (180~ reorientation angle). The magnitude of the field in the forward direction and the time that this field is applied are greater than for the reverse direction, giving net forward motion to the molecules (Lalande et al., 1987). Lanes are straight, but run times are long with FIGE, because the molecules spend part of their time moving backward. The range for best resolution is up to about 100 kb. A more sophisticated configuration for PFGE is the so-called d a m p e d homogeneous electric field (CHEF) apparatus (Chu et al., 1986). In the CHEF apparatus, a gel is centered within a hexagonal electrode array (Fig. 7A and B). Each leg of the hexagon consists of four individual electrodes. An electronic controller divides the applied voltage among opposing pairs of electrodes in
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Fig. 7 Electrode configurations for CHEF (A and B) and PACE ( A - D ) pulsed-field gel electrophoresis. These two types of PFGE both make use of the same basic layout of parts. The methods differ in the number of available electric field patterns. Both techniques employ fields in the horizontal plane to separate large DNA molecules. With PACE, the electric field can point in any direction, whereas CHEF is limited to only two field orientations. Gels (stippled) are centered within hexagonal arrays of electrodes. Standard gels are 14 cm wide and 13 cm long. Other gel sizes available are 21 cm wide by 14 cm long and 14 cm wide by 21 cm long. Sample wells are formed at the tops of the gels during casting. Electrolyte buffer (usually 0.5 x TBE) covers the gels and electrodes. The hexagonal electrode arrays are 33 cm across and consist of 24 individual platinum wire segments (4 segments per leg of the hexagon). The voltage of each electrode segment is controlled electronically. For every field orientation, the electronics adjust the individual electrode voltages so as to generate a homogeneous field approximating that between infinitely long parallel wire conductors. In the CHEF method, illustrated in the upper two configurations (A and B), the sense of the net field in the gel points alternately southeast-to-northwest and southwest-to-northeast. The directions of the forces on DNA molecules are shown by arrows [(A) + 60 ~ and (B) - 60 ~ where the angles are referred to a vertical axis]. [The direction of an electric field is defined as the direction of the force on a positively charged particle. The force on a DNA molecule is opposite to the field direction.] In CHEF, the magnitudes of the two fields are the same, but can be varied. The switching time between the two directions can be also varied, but the reorientation angle is fixed at 120 ~ as shown. The net motion of DNA is in the forward direction (0~ along the resultant of the two force vectors. The PACE method allows variation of field direction, magnitude, and time. Two different applications of a PACE apparatus are illustrated. The upper two configurations (A and B) represent a PACE system operating in the CHEF mode. The lower configurations [(C) 0 ~ and (D) 180 ~ show a PACE system operating in the field-inversion (FIGE) mode. In both these applications, the force on DNA molecules alternates between two possible directions (A ~ B or C *-~ D). The net motion of DNA in both cases is in the forward direction (0~ With PACE, it is possible to program a variety of different field orientations in any predetermined sequence. This can be useful in certain situations. For example, in one particular application, combinations of the three force orientations, A, B, and D, were used to enhance resolution in a size range that was poorly resolved in a standard two-field run (Clark et al., 1988).
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David E. Garfin such a way as to produce a homogeneous field in the gel. Two electric fields of equal magnitude are used in CHEF. The field direction alternates between northwesterly and northeasterly. In each cycle, the electrical forces on DNA molecules drive them first along the + 60 ~ direction then toward - 6 0 ~ with respect to the vertical axis. Switching the fields back and forth between the two directions repeatedly reorients DNA molecules through an angle of 120 ~ Net migration of DNA molecules is along the resultant of the two field forces, along the axial (0 ~ direction. Optimal field magnitude and switching time vary depending on the size range of molecules to be fractionated. Chu et al. (1986) found the 120 ~ reorientation angle to give very good separation of DNAs in the 200- to 2000-kb size range. With CHEF, lanes are straight and many samples can be run simultaneously. Separations have been extended to 7000 kb. The programmable autonomously controlled electrode (PACE) system of Clark et al. (1988) is a very versatile modification of CHEF. The physical layout of the gel box is similar to that in CHEF (Fig. 7). Twenty-four electrode segments are arranged in a hexagonal contour, with four segments in each leg of the hexagon. Each electrode is independently controlled to allow a wide variety of fields to be produced in the gel. The PACE system can be programmed to perform all of the types of PFGE that have been described. Various pulsing schemes and combinations of field strengths (including unbalanced, asymmetric fields) are possible with PACE, thus allowing much flexibility in cases of difficult separations. Of nearly equal importance to PFGE technology as the electronics is the development of methods for keeping large DNA molecules intact once they have been released from the protective cellular matrix. As pointed out by Schwartz (1985; Schwartz and Cantor, 1984), the shear forces acting on DNA of genome size, while free in solution, are sufficient to fragment the molecules. The resultant electrophoresis pattern of such fragmented DNA will be a smear representing the multitude of fragment sizes. This problem is circumvented by never releasing genomic DNA into free solution. Instead, organisms or cells from which DNA is to be extracted are embedded in plugs of specially prepared, low-melting-temperature agarose. Cell lysis and deproteinization of DNA are accomplished by allowing detergents and enzymes to diffuse into the gel plugs. Liberated DNA is protected from shear forces by the surrounding gel matrix. DNA can be treated in various ways, such as being cleaved with restriction enzymes, while in the sample plug. The entire plug is inserted into slots formed in the electrophoresis gel and the electric field drives the DNA out of the sample-preparation plug into the electrophoresis gel.
VII. Capillary Electrophoresis Capillary electrophoresis (CE) is an instrumental technique for automating electrophoretic analyses (Foret and Bocek, 1989; Grossman and Colburn, 1992; Landers, 1993; Weinberger, 1993). CE separations are carried out in fused silica capillaries with internal diameters of 25-100/~m. The capillaries are coated with an external layer of polyimide for mechanical strength. The small internal diameter allows for efficient heat dissipation from the capillary, enabling sepa-
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rations to be carried out at high field strengths (up to 1000 V/cm). Separations are rapid, typically taking just a few minutes. The use of fused silica as the capillary material permits direct detection of separated components in the tubes. A section of the polyimide coating is removed at one end of the capillary and this "window" is positioned in the light path of an optical detector. Band peaks are recorded as they migrate past the detector window. Most CE applications use absorbance detection in the ultraviolet range. A major disadvantage of on-tube optical detectors is the short light paths of the capillaries, which reduce detection signals 100- to 400-fold compared to the more familiar 1-cm path length flow cells. Strategies used to enhance detection sensitivity in CE include short-wavelength UV detection (185200 nm) and the use of capillaries of extended path length (Albin et al., 1993). Laser-induced fluorescence detection is also employed in CE (Gassman et al., 1985). This technique can provide very high sensitivity when the molecules of interest have sufficient natural fluorescence or can be tagged with a fluorophore prior to the separation. Samples are introduced at the inlet ends of capillaries by electrophoretic injection or hydraulic injection. Electrophoretic injection is accomplished simply by dipping the capillary inlet into the sample solution and applying high voltage for a short time (typically several seconds). In electrophoretic injection, only ionic species are loaded into the capillary, and analytes are injected in proportion to their electrophoretic mobilities. Hydraulic injection is accomplished by dipping the capillary inlet into the sample solution and briefly applying pressure at the inlet or vacuum at the capillary outlet. An alternative approach is to raise the sample vial relative to the capillary outlet for a short time. Samples loaded by hydraulic injection contain analytes in the same concentrations as the sample solutions. Injection volumes are in the nanoliter range. To increase detection sensitivity, sample starting zones can be concentrated by buffer-regulated stacking, as is done with gel electrophoresis (Chien and Burgi, 1992). An important consideration in CE, in contrast to gel electrophoresis, is the magnitude of electroosmotic flow (EOF). EOF refers to a flow of liquid in a separation chamber resulting from interactions at charged groups on the chamber walls. At electrolyte values above about pH 3, the silanol groups on the inner wall of a capillary become ionized (negatively charged). Positively charged cations in the buffer, together with their waters of hydration, are attracted to the capillary wall. On application of high voltage, the cations move toward the negative electrode, dragging their hydration shells with them. The net effect is that of a liquid flow toward the cathode. The magnitude of EOF increases with increasing pH and field strength and with decreasing ionic strength. EOF causes variations in peak migration times and peak size. Control of the EOF level is therefore necessary for achieving quantitative precision in CE. Considerable effort has been spent in the development of stable, noninteractive coatings to control or eliminate EOF and to reduce adsorption (Chien and Burgi, 1992). Several coated capillaries are available commercially. CE is a very versatile separation technique. A variety of separation modes can be used with the same CE instrument. The most widely used mode is capillary zone electrophoresis (CZE), in which the capillary and electrolyte
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reservoirs are filled with a homogeneous buffer. Sample molecules are resolved into discreet zones by differences in their electrophoretic mobilities. CZE has been most successfully used for separation of peptides. For example, peptide digests and mixtures of synthetic peptides are rapidly analyzed (Frenz et al., 1989). Gels can be cast in capillaries employing a modification of the acrylamide polymerization chemistry used for conventional slab gels. A bifunctional silane, such as ~/-methacryloxypropyltrimethoxysilane, is first attached to the capillary wall. The acrylic functional group is then extended by polymerization with acrylamide and bisacrylamide. Gel-filled capillaries provide extremely high resolution for nucleic acids, and capillary gel electrophoresis (CGE) is used for analysis of synthetic oligonucleotides and polymerase chain reaction products (Turner, 1991). Capillary gel electrophoresis is not suitable for separation of proteins due to the strong UV absorption of polyacrylamide at the wavelengths required for high-sensitivity polypeptide detection. Separation of proteins and other biopolymers by size can be accomplished using solutions of hydrophilic polymers inside capillary tubes (Ganzler et al., 1992; Zhu et al., 1989). This technique is variously referred to as dynamic sieving, nongel sieving, or entangled polymer CE. The polymer solutions mimic the effects of cross-linked gels in that the migration of macromolecules is retarded in proportion to their molecular sizes. Dynamic sieving has been used for separation of oligonucleotides and polymerase chain reaction products. Resolution is not as high as that obtained with capillary gel electrophoresis, but the technique avoids the problems of short gel lifetimes and difficulty of use that is experienced with CGE. Because the polymers used for dynamic sieving are transparent in the low UV, this technique can be used for separation of SDSprotein complexes with detection in the 214- to 220-nm range. Dynamic sieving compares favorably with SDS-PAGE for many applications. Capillary isoelectric focusing is analogous to conventional IEF. Ampholytes are used to establish stable pH gradients within the capillaries, and proteins migrate to form focused zones at their isoelectric points. The capillary approach differs from conventional IEF in that focused zones must be transported past the monitoring point to detect the separated proteins. This has been achieved by hydraulic mobilization of zones (using gravity, pressure, or vacuum) (Chen and Wiktorowicz, 1992) or by using EOF as a pump for mobilization (Thormann et al., 1992). An alternative method, termed chemical or electrophoretic mobilization, induces a pH shift in the gradient by changing the composition of the catholyte and anolyte, which causes proteins to migrate past the detection point in sequence (Zhu et al., 1991). Capillary IEF has been used successfully for the characterization of related proteins with subtle differences in structureme.g., hemoglobin genetic variants (Zhu et al., 1992) and glycoforms of recombinant biopharmaceutical proteins (Yim, 1991). CE instruments can also be used for the separation of uncharged molecules by micellar electrokinetic chromatography (MEKC) (Terabe et al., 1984). In this technique, the electrolyte is supplemented with an ionic detergent such as SDS. The detergent is added at concentrations well above its critical micelle concentration, and analyte molecules become partitioned into the micelles by hydrophobic interactions. The bulk electrolyte is carried toward the cathode by a high EOF, while micelles move electrophoretically toward the anode, in a
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direction c o u n t e r to that of EOF. M E K C is u s e d for analysis of l o w m o l e c u l a r m a s s p h a r m a c e u t i c a l s . S e p a r a t i o n of e n a n t i o m e r i c d r u g s can be effected b y the a d d i t i o n of chiral selectors of the electrolyte, a n d chiral s e p a r a t i o n s can be easily d e v e l o p e d (Nishi et al., 1991). C a p i l l a r y e l e c t r o p h o r e s i s offers m a n y a d v a n t a g e s as an i n s t r u m e n t a l techn i q u e in t e r m s of q u a n t i t a t i v e analysis a n d h i g h - t h r o u g h p u t a u t o m a t i o n . It is often u s e d as a c o m p a n i o n analytical t e c h n i q u e w i t h h i g h - p e r f o r m a n c e liquid c h r o m a t o g r a p h y to c o n f i r m p e a k purity. A limitation of CE is the r e q u i r e m e n t that m u l t i p l e s a m p l e s be a n a l y z e d serially, as c o m p a r e d to the m a n y s a m p l e s that can be a n a l y z e d in parallel b y P A G E on slab gels. N e v e r t h e l e s s , the capability of CE for u n a t t e n d e d a u t o m a t i o n , w i t h r e p r o d u c i b l e l o a d i n g a n d r u n n i n g m e c h a n i s m s , short r u n times, a n d direct quantification, is m a k i n g CE p o p u l a r for r o u t i n e analyses.
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David E. Garfin Overbeek, J. T. G., and Bijsterbosch, B. H. (1979). The electrical double layer and the theory of electrophoresis. In "Electrokinetic Separation Methods" (P. G. Righetti, C. J. van Oss, and J. W. Vanderhoff, eds.), pp. 1-32. Elsevier/North-Holland, Amsterdam. Peacock, A. C., and Dingman, C. W. (1967). Resolution of multiple ribonucleic acid species by polyacrylamide gel electrophoresis. Biochemistry 6, 1818-1827. Rabilloud, T. (1990). Mechanisms of protein silver staining in polyacrylamide gels: A 10-year synthesis. Electrophoresis 11, 785-794. Reisfeld, R. A., Lewis, U. J., and Williams, D. E. (1962). Disk electrophoresis of basic proteins and peptides on polyacrylamide gels. Nature (London) 195, 281-1283. Reynolds, J. A., and Tanford, C. (1970). Binding of dodecyl sulfate to proteins at high binding ratios. Possible implications for the state of proteins in biological membranes. Proc. Natl. Acad. Sci. U.S.A. 66, 1002-1007. Richards, E. G., and Lecanidou, R. (1971). Quantitative aspects of the electrophoresis of RNA in polyacrylamide gels. Anal. Biochem. 40, 43-71. Richards, E. G., and Lecanidou, R. (1974). Polymerization kinetics and properties of polyacrylamide gels. In "Electrophoresis and Isoelectric Focusing in Polyacrylamide Gel" (R. C. Allen and H. R. Maurer, eds.), pp. 16-22. de Gruyter, Berlin. Righetti, P. G. (1983). "Isoelectric Focusing: Theory, Methodology and Applications." Elsevier, Amsterdam. Righetti, P. G. (1989). Of matrices and men. J. Biochem. Biophys. Methods 19, 1-20. Righetti, P. G., Gianazza, E., Gelfi, C., and Chiari, M. (1990). Isoelectric focusing. In "Gel Electrophoresis of Proteins: A Practical Approach"(D. Rickwood and B. D. Hames, eds.), 2nd ed., pp. 149-216. IRL Press, Oxford. Rodbard, D., and Chrambach, A. (1970). Unified theory for gel electrophoresis and gel filtration. Proc. Natl. Acad. Sci. U.S.A. 65, 970-977. Rodbard, D., Kapadia, G., and Chrambach, A. (1971). Pore gradient electrophoresis. Anal. Biochem. 40, 135-157. Rosengren, A., Bjellqvist, B., and Gasparic, V. (1977). A simple method of choosing optimum pHconditions for electrophoresis. In "Electrophoresis and Isotachophoresis" (B. J. Radola and D. Graesslin, eds.), pp. 165-171. de Gruyter, Berlin. Sambrook, J., Fritsch, E. F., and Maniatis, T. (1989). "Molecular Cloning: A Laboratory Manual," 2nd ed. Cold Spring Harbor Lab., Cold Spring Harbor, NY. Schafer-Nielsen, C., and Svendsen, P. J. (1981). A unifying model for the ionic composition of steady-state electrophoresis systems. Anal. Biochem. 114, 244-262. Schagger, H., and van Jagow, G. (1987). Tricine sodium dodecyl sulfate-polyacrylamide gel electrophoresis for the separation of proteins in the range from 1 to 100 kDa. Anal. Biochem. 166, 368-379. Schwartz, D. C. (1985). Giga-Dalton sized DNA molecules. Ph.D. Thesis, Columbia University, New York. Schwartz, D. C., and Cantor, C. R. (1984). Separation of yeast chromosome-size DNAs by pulsed field gradient gel electrophoresis. Cell (Cambridge, Mass.) 37, 67-75. Sealy, P. G., and Southern, E. M. (1990). Gel electrophoresis of DNA. In "Gel Electrophoresis of Nucleic Acids: A Practical Approach" (D. Rickwood and B. D. Hames, eds.), 2nd ed., pp. 51-99. IRL Press, Oxford. See, Y. P., and Jackowski, G. (1989). Estimating molecular weights of polypeptides by SDS gel electrophoresis. In "Protein Structure" (T. E. Creighton, ed.), pp. 1-21. IRL Press, Oxford. Smisek, D. L., and Hoagland, D. A. (1990). Electrophoresis of flexible macromolecules: Evidence for a new mode of transport in gels. Science 248, 1221-1223. Smith, A. J. H. (1980). DNA sequence analysis by primed synthesis. In "Methods in Enzymology" (L. Grossman and K. Moldave, eds.), Vol. 65, pp. 560-580. Academic Press, New York. Smith, L. M., Sanders, J. Z., Kaiser, R. J., Hughes, P., Dodd, C., Connell, C. R., Heiner, C., Kent, S. B. H., and Hood, L. E. (1986). Fluorescence detection in automated DNA sequence analysis. Nature (London) 321, 674-679. Spiker, S. (1980). A modification of the acetic acid-urea system for use in microslab polyacrylamide gel electrophoresis. Anal. Biochem. 108, 263-265. Syrovy, I., and Hodny, Z. (1991). Staining and quantification for proteins separated by polyacrylamide gel electrophoresis. J. Chromatogr. 569, 175-196. Tanaka, T. (1981). Gels. Sci. Am. 244, 124-138. Tanford, C. (1961). "Physical Chemistry of Macromolecules." Wiley, New York.
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Tas, S. (1990). Separation of the DNA molecules beyond conventional size limits by gel electrophoresis with sodium dodecyl sulfate. Anal. Biochem. 188, 33-37. Terabe, S., Otsuka, K., Ichikawa, K., Tsuchiya, A., and Ando, T. (1984). Electrokinetic separations with micellar solutions and open-tubular capillaries. Anal. Chem. 56, 111-113. Thormann, W., Caslavska, J., Molteni, S., and Chmelik, J. J. (1992). Capillary isoelectric focusing with electroosmotic zone displacement and on-column multichannel detection. J. Chromatogr. 589, 321-327. Timmons, T. M., and Dunbar, B. S. (1990). Protein blotting and immunodetection. In "Methods in Enzymology" (M. P. Deutscher, ed.), Vol. 182, pp. 679-688. Academic Press, San Diego, CA. Turner, K. A. (1991). New dimensions in capillary electrophoresis columns. LC-GC 9, 350-356. Vesterberg, O. (1989). History of electrophoretic methods. J. Chromatogr. 480, 3-19. Vesterberg, O. (1993). A short history of electrophoretic methods. Electrophoresis 14, 1243-1249. Weber, K., and Osborn, M. (1969). The reliability of molecular weight determinations by dodecyl sulfate-polyacrylamide gel electrophoresis. J. Biol. Chem. 244, 4406-4412. Weinberger, R. (1993). "Practical Capillary Electrophoresis." Academic Press, San Diego, CA. Wilson, C. M. (1983). Staining of proteins on gels: Comparisons of dyes and procedures. In "Methods in Enzymology" (C. Hirs and S. Timasheff, eds.), Vol. 91, pp. 236-247. Academic Press, New York. Woolley, P. (1987). Thermal instability of electrophoresis gels. Electrophoresis 8, 339-345. Wyckoff, M., Rodbard, D., and Chrambach, A. (1977). Polyacrylamide gel electrophoresis in sodium dodecyl sulfate-containing buffers using multiphasic buffer systems: Properties of the stack, valid Rf-measurement, and optimized procedure. Anal. Biochem. 78, 459-482. Yim, K. W. (1991). Fractionation of the human recombinant tissue plasminogen activator (rtPA) glycoforms by high-performance capillary zone electrophoresis and capillary isoelectric focusing. J. Chromatogr. 559, 401-410. Zhu, M., Hansen, D. L., Burd, S., and Gannon, F. (1989). Factors affecting free zone electrophoresis and isoelectric focusing in capillary electrophoresis. J. Chromatogr. 480, 311-319. Zhu, M., Rodriguez, R., and Wehr, T. (1991). Optimizing separation parameters in capillary isoelectric focusing. J. Chromatogr. 559, 479-488. Zhu, M., Rodriguez, R., Wehr, T., and Siebert, C. (1992). Capillary electrophoresis of hemoglobins and globin chains. J. Chromatogr. 608, 225-237.
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GLOSSARY Absorption optical system As used in this chapter, one of the principal methods used to detect concentrations of a molecule in an ultracentrifuge experiment. For proteins and nucleic acids the optical absorbance, A, in the ultraviolet is used to measure concentrations of the solutes using the standard equation A = Ecd (see Chapter 6), where E is the molar extinction coefficient at the wavelength selected, c is the concentration, and d is the path length through the centrifuge cell in the direction of the incident light. When the incident beam is Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
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Walter F. Stafford and Todd M. Schuster
scanned along the direction of the centrifugal force, direct plots of c vs x are possible at wavelengths selected to be optimal for different species. Activity coefficient Activity coefficients are parameters that connect the thermodynamic activities of dissolved molecules to their physical concentrations. They are discussed in detail in Chapter 1. Brownian motion Classically, Brownian motion is the irregular movement that small particles of microscopic size carry out when suspended in a liquid. This phenomenon was first described in 1828 by the botanist Robert Brown, who was observing pollen of different plants dispersed in water. Due in great measure to the theoretical work of Albert Einstein beginning in 1906, the physical principles underlying Brownian motion have been quantitatively applied to the random motions of molecules in liquids and gases. We now speak of Brownian motion to mean random motions of atoms or molecules in a gas or liquid. Chemical Potential In a solution, the chemical potential of species i,/d,i, is the partial molal free energy given by the expression 1.1,i = ( 3 G / 3 n i ) ,
where n i is the number of moles of molecular species i and G is the total free energy of the solution. The chemical potential refers to the increase in total free energy when I mol of component i is added to an infinite amount of solution at fixed temperature and pressure and the numbers of moles of all other components kept fixed. Diffusion coefficient In this chapter "diffusion coefficient" refers only to that for translational motion. The basic relation defining the diffusion coefficient, D, may be stated in the form Jdiff
=
--
D(3c/Ox)t,
where Jdiff is the flux of material passing through a surface of unit area per unit time and where O c / O x is the gradient of concentration. D has the dimensions c m 2 s e c -1. The equation above is called Fick's first law. The second law (see text) can be easily derived from the first law by differentiation. Donnan equilibrium The Donnan equilibrium (sometimes called the Donnan effect) results from the unequal concentration of salts on each side of a semipermeable membrane when a charged macromolecule, such as a protein, is only on one side. The Donnan equilibrium becomes negligible when the protein solution is dialyzed in the presence of low molecular mass salts in sufficiently high concentrations. Entrained water In aqueous solutions the solvent within the macromolecule is called entrained water. In order to interpret hydrodynamic measurements discussed in this chapter in terms of molecular shape, it is necessary to use a parameter called the hydrodynamic volume whose radius is the hydrodynamic radius. In this chapter relations are used for the hydrodynamic properties of dissolved macromolecules. These relations are expressed in terms of the volume of the macromolecules. This volume therefore involves the volume of the molecules, including the volume of solvent incorporated within them.
Chapter 3 HydrodynamicMethods
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Flux In most hydrodynamic experiments, one must assume that the molecular mass of the solute is unknown. This means that the number of solute molecules in a sample is also unknown. In this situation, it is convenient to describe solute transport in response to diffusion or centrifugal force as mass transport. The flux of a solute, J, is defined as the rate of mass transport across a surface of unit area. The units of flux are then g s e c -1 c m -2. In this chapter the concept is used in Fick's laws and the Lamm equation describing sedimentation and diffusion transport.
Frictional coefficient
Refers to both translational and rotational frictional coefficients. These parameters contain information on the viscous drag on a body moving either by translation or rotation in a fluid.
Hydrodynamically equivalent sphere
See Hydrodynamic radius.
Hydrodynamic radius It is often useful to suppose that the shape of a macromolecule approximates that of an ellipsoid of revolution and to interpret hydrodynamic measurements in terms of the volume and axial ratio of the hydrodynamically equivalent ellipsoid of r e v o l u t i o n - - t h a t is to say, the volume and axial ratio of the ellipsoid that has the hydrodynamic properties identical to those of the real macromolecule. If the ellipsoid has an axial ratio of one, then the resulting sphere can be characterized by a hydrodynamic radius. See also Stokes radius. Johnston-Ogston effect
In ultracentrifugation, the J o h n s t o n - O g s t o n effect is a phenomenon complicating quantitative analysis of mixtures due to the decreases in sedimentation coefficients with increases in concentration.
Molecular mass averages The simplest average molecular mass is the number average; this is defined by the relation, Mn = E m i M i / E mi, where Ni is the mole fraction of species i whose molecular mass is Mi. IL instead, the molecular mass average is weighted according to the mass fraction fi of the species, the mass average molecular mass is defined by
Mw - E f i M i / E fi The z-average molecular mass is defined by
Mz - ~ fiM 2/ ~ fi M i" For a monodisperse macromolecular solution, all these different averages are equal; for a polydisperse solution, on the other hand, the higher members of this series of averages are greater than the lower members because they give more statistical weight to the higher molecular mass species. Thus, Mn ~ Mw <- Mz.
There are experimental methods that are capable of yielding each one of these averages. In addition, it should be noted that there are experimental methods that yield molecular masses that do not belong to this series. An example is the mass average obtained from viscometry, as discussed in this chapter. For this
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Walter F. Stafford and Todd M. Schuster case,
M~ =
E NiM'd+l / E
NiMi
,
where ~/is a constant that depends on the nature of the macromolecule (e.g., for a random coil ~/= 0.5).
Partition coefficient In molecular sieve chromatography, the column containing the resin packing has a total volume made up of three components. These are the volume of exterior solvent, the solid volume of the resin, and the internal volume of the pores of the resin that are accessible to the solvent. If solute is added to such a column, it will partition between the external and internal solvent regions. This partitioning can be described by a partition coefficient, cr = mi/Vic, where mi is the mass of solute found in internal regions of total internal volume Vi, and c is the concentration of solute in the external regions. The significance of ~r is that it enters into the description of the flux of solute eluting from a column. Pycnometry The measurement of density using a pycnometer. In its simplest form it consists of a bulb of precisely known volume that is filled with the solution under study and then weighed to determine the density. Rayleigh optical system This refers to a detection system used in ultracentrifugation based on interferometry. With Rayleigh optics, the difference in refractive index between the solution and a reference column of solvent is measured by the displacement of interference fringes. Light from a point source is rendered parallel by means of a collimating lens and then passed through two slits in front of the sample cell and the solvent cell. A further optical system focuses the light from the two cells with the production of an interference pattern. The number displacement of fringes between sample and solvent is directly related to the concentration of the solute via the index of refraction difference between sample and solvent. Thus, detection with a Rayleigh optical system gives a direct plot of concentration versus distance along the direction of centrifugal force. Schlieren optical system The word Schlieren is German for streaks, such as one sees when viewing objects through air rising from a hot road or desert. When viewing an object through rising hot air, the streaks are caused by heatinduced index of refraction changes in the air. Schlieren optical systems allow concentration gradients in an ultracentrifuge cell to be viewed by revealing changes that they cause in the index of refraction that they produce. This optical system produces a derivative plot of dc/dx vs x, where c is the concentration and x is the distance along the direction of centrifugal force. The fact that this system records concentration gradients makes it specially useful for locating boundaries in sedimentation velocity experiments. Sedimentation coefficient In a centrifugal field the velocity of a molecule is proportional to the magnitude of the centrifugal field (i.e., w2r, where 02 is the angular frequency of rotation and r is the radial distance of the molecule from the axis of rotation). The sedimentation coefficient is the velocity per unit field, or s = v~ odRr. Stokes radius
In the case where the shape of a macromolecule in solution is
Chapter 3 HydrodynamicMethods
115
approximated as a hydrated ellipsoid of revolution, its hydrodynamic properties can be described by an equivalent sphere of hydrated radius r h multiplied by a shape factor. The radius of the equivalent sphere is called the Stokes radius. See also hydrodynamic radius. A method for the anaylsis of sedimentation velocTime derivative method ity data that employs the time derivative of the concentration profile. By taking the time derivative of the data, one completely removes the time independent optical background contributions from the concentration profile effecting a significant improvement in the signal-to-noise ratio of sedimentation velocity data.
Traube's rule
The volume contributions from the individual atoms or group of atoms in a molecule may be added to compute the total volume of the molecule.
Vibrating tuning-fork method This method for determining the density of a solution uses a commercially available mechanical oscillator that can be filled with the solution. A V-shaped hollow tube forms a tuning fork. The tube is filled with the sample whose density is to be measured, and the natural frequency of the fork changes. From the measured frequency, the weight of the added solution is calculated. Because the volume of the V-shaped tube is accurately known, the density can be determined. Virial coefficient These are the coefficients in a power series expansion often used to represent the variation of the activity coefficient with concentration. ln(y2) = 2BM2c2
+ ~....L 3r•/I2r2 v12L. 2
_}_
.
.
.
w h e r e Y2 is the activity coefficient, M 2 is the molar mass of the solute, and c2 is the mass concentration of the solute. The coefficients, B, C, etc. are the second, third, etc. virial coefficients, respectively. Thus, an alternative method to using activity coefficients to express deviations from ideality is to express the chemical potentials of solutions as a power series in the concentration of solute. For the solute in a dilute solution containing a single solute, t z i - tz ~ = R T V ~
+ Bc2 q- Cc 2 + "" ")
is the virial equation, where/d,i is the chemical potential of the solute,/z ~ is the chemical potential of the solute in the standard state, V ~ is the molar volume of solvent, R is the gas constant, and T is the absolute temperature.
Yphantis-type centerpiece
A six-compartment centerpiece that allows the examination of three solution-solvent pairs in a sedimentation-equilibrium experiment on an ultracentrifuge.
SYMBOLS ((~P/ (~C2)T,P,lz a
Partial derivative of the density with respect to concentration Diameter of the capillary tube, optical level arm, or major semiaxis of an ellipsoid Of revolution
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Walter F. Stafford and Todd M. Schuster
a2
Activity of the macromolecular component
B
Second virial coefficient
b
Optical path length, or minor semiaxis of an ellipsoid of revolution
C
Third virial coefficient
Ci
Mass concentration of species i
Cm Cp
Meniscus concentration (gram liter -1) Plateau concentration on the mass scale (grams liter -I )
Ct
Total macromolecular concentration on the mass scale (grams liter -1 )
D
Diffusion coefficient in units of
dc/dr dn/dr 61 F Fc Ff
cm 2
sec -1 or Ficks
Concentration gradient Refractive index gradient Hydration (grams H 2 0 / g r a m macromolecule) Ficks in units of 10 -7 cm 2 sec -1 Centrifugal force (dynes mole -1) Force of frictional resistance (dynes mole -I ) Volume fraction
f
fifo f/fmin
f, f2 [771
Frictional coefficient Frictional ratio due to shape alone Frictional ratio due to shape and hydration Weight fraction of monomer Weight fraction of dimer Intrinsic viscosity
rt0
Viscosity of the solvent
7/'
Viscosity of the solution
T~rel
Relative viscosity
~sp
Specific viscosity
Jdiff
Flux due to diffusion in units of mass concentration/cma/sec ond
Led
Flux due to sedimentation in units of mass concentration/ cma/second
Kl,n
Monomer n-mer equilibrium constant on the molar concentration scale
klr?l
Monomer n-mer equilibrium constant on the mass concentration scale
M2
Molecular mass of the macromolecular component
Mn
Number average molecular mass
Chapter3 HydrodynamicMethods Mv
Viscosity average molecular mass
Mw
Mass average molecular mass
Mz
Z-average molecular mass
117
m3
Molal concentration of salt (moles of salt/kilogram of solvent)
/z0 N
Standard chemical potential at I atmosphere Avogadro's number (6.023 • 10 23 mole -1)
n
Refractive index
/,9
Simha's viscosity shape factor
P
Pressure (dynes-cm 2)
R
Gas constant (1.99 cal mole-1 K - 1 )
R0
Stokes radius of the solvated sphere
Rs
Stokes radius of the hydrodynamically equivalent sphere
P
Density in units of grams c m -3, axial ratio of ellipsoid of revolution Radius (cm)
rm
Radius of the meniscus position
r
Radius of the equivalent boundary position
S
Svedbergs (= 10-13 sec)
S
Sedimentation coefficient (in units of seconds or Svedbergs)
S*
Apparent sedimentation coefficient as radial coordinate in units of Svedbergs
SO
Sedimentation coefficient of the equivalent hydrated sphere
Si
Sedimentation coefficient of i-mer or of species i
Sn
Sedimentation coefficient of n-mer or of species n
so
s~
Sw(Ct)
Sedimentation coefficient of i-mer or of species i at infinite dilution Mass average sedimentation coefficient at infinite dilutions Mass average sedimentation coefficient as a function of total concentration
~r
Standard deviation
o-i
Reduced molecular mass of species i
T
Absolute temperature (Kelvin)
t
Time (seconds)
U u(r)
Volume rate of flow in a capillary tube Radial velocity profile in a capillary tube
Vh
Hydrodynamic volume
vo
Specific volume of pure water
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Walter F. Stafford and Todd M. Schuster V2
Partial specific volume of the macromolecular component Angular velocity in radians/second as a function of time
Y Z
Activity coefficient on the mass concentration scale Charge on the macroion
I. Introduction In this chapter we will cover frequently used methods that allow macromolecular size, shape, and interactions to be investigated by macroscopic, classical measurements. These methods depend basically on the analysis of the movement (transport) of macromolecules through fluids. In particular, we will discuss the transport of macromolecules through fluids under the influence of a centrifugal force, the diffusion of macromolecules in solution, and the properties of macromolecules with regard to their effects on viscosities of macromolecular solutions. Collectively, methods that depend on the translational motions of macromolecules in solution are called hydrodynamic methods. Hydrodynamic methods provide information about the homogeneity, structure, and aggregation properties of biopolymers in solution under both nondenaturing and denaturing conditions. For example, since the late 1960s, electrophoresis under denaturing conditions [e.g., sodium dodecyl sulfate (SDS) or urea gel electrophoresis] has been used widely to obtain a considerable amount of information concerning the degree of homogeneity of protein and nucleic acid preparations. Electrophoresis in the presence of SDS has been nearly universally used to obtain relative molecular masses for single-chain polypeptides; however, it gives almost no information about the subunit structure or aggregation states of multisubunit components that exist under native conditions. Hydrodynamic methods can provide that information. Hydrodynamic methods can be divided into three main categories. The first category includes various types of viscosity measurements in which the effects of biopolymers on the flow properties of the bulk solution are measured. The most familiar type of measurement is capillary viscometry, in which the flow time of a given volume of solution is measured and compared to the flow time for the same volume of solvent. The second category includes various types of chromatographic methods that involve movement of a biopolymer in solution through a matrix. The most frequently used chromatographic technique for the investigation of homogeneity and macromolecular interactions is size exclusion chromatography (Winzor, 1969). Also included in the second category is electrophoresis on various types of support media. The third category includes free-boundary electrophoresis, diffusion, sedimentation velocity, and sedimentation equilibrium. In the case of viscometry, one measures primarily the intrinsic viscosity, [~/], which is strongly dependent on shape and flexibility of a macromolecule. In the case of size exclusion chromatography, one measures the partition coefficient, which can be related to the frictional coefficient, and hence the size and shape of the molecule under consideration. Gel filtration, with appropriate calibration, yields only an estimate of the hydrodynamic radius {Stokes radius) of a macromolecule, and, therefore, cannot be used for the determination of mo-
Chapter 3 Hydrodynamic Methods
119
lecular mass unless the partition coefficient data are combined with measurements from another technique, such as sedimentation velocity. The third class of hydrodynamic techniques allows the direct measurement of transport of the molecules free in solution without the complicating factors of possible interaction with a support medium. Diffusion measurements can be made by observing the rate of spreading of an artificial boundary set up between the solvent and a solution of the biopolymer. The diffusion coefficient is inversely proportional to the frictional coefficient and, therefore, gives direct information about the size of the molecules. In the case of moving-boundary electrophoresis, one measures the electrophoretic mobility of the macromolecule. From the very earliest days of the modern biochemical era, the analytical ultracentrifuge played an important role in the development of our understanding of biopolymer structure. In the 1920s, when the ultracentrifuge was first developed for the study of protein solutions by The Svedberg, it was generally believed that proteins were colloidal aggregates of smaller building blocks. Like most other colloidal structures, it was thought that proteins had no discrete, well-defined structure that could be represented by a single chemical formula. It was primarily the work of Svedberg and his colleagues in the 1920s, 1930s, and 1940s (Svedberg and Pederson, 1940) that demonstrated that proteins were in fact individual molecules having a definite chemical structure.
II. Analytical Ultracentrifugation The analytical ultracentrifuge is a high-speed centrifuge with an optical system that allows observation of the position of sedimenting boundaries as a function of time. It can be run in either of two modes, depending on the type of information desired. At relatively high speeds, the sedimentation velocity of a macromolecule is measured to obtain hydrodynamic information. In a sedimentation velocity experiment, one measures the sedimentation coefficient from which one may calculate the frictional coefficient. The measured frictional coefficient can be compared with theoretically expected values for various ideal hydrodynamic models to get an idea about the shape of a macromolecule. At relatively low speeds, the centrifuge is run from several hours to several days, depending on the size of macromolecule, until equilibrium between sedimentation and diffusion is reached. When the system is at equilibrium, one may obtain thermodynamic information about the macromolecule and its interactions from the resulting concentration distribution. For a system composed of a single macromolecular component, the primary information one obtains is the molecular mass of the component and its purity. In the case of polydisperse systems, either self-associating, heteroassociating, dissociating, or noninteracting, one obtains molecular mass averages as a function of concentration and position in the centrifuge cell. Either by analyzing the concentration distribution directly by curve fitting to various molecular models or by analyzing the dependence of the molecular mass averages on concentration, one may obtain the molecular masses of the species comprising the system. For an interacting system, one may obtain the stoichiometries and equilibrium constants of the interactions. Moreover, if the equilibrium constants are determined at various
120
Walter F. Stafford and Todd M. Schuster temperatures, one may obtain the standard enthalpies and standard entropies for the system, which in turn can provide information about the thermodynamics of molecular interactions that are predominant in stabilizing the system. This kind of information is necessary for a complete understanding of the stability of multisubunit macromolecular assemblies.
A. S e d i m e n t a t i o n Velocity Consider a particle or macromolecule suspended in water before application of the centrifugal field. Ignoring Brownian motion, the sum of the forces acting on the particle is zero and the particle will be at rest. When the centrifugal field is applied, the particle will accelerate in the direction of the applied field. As it accelerates, it will experience frictional resistance from the solvent. When the particle has accelerated to the point at which the frictional force is equal to the centrifugal force, the sum of the forces again will be zero. The particle will stop accelerating and continue moving with uniform motion. The acceleration phase lasts only a few picoseconds under the usual conditions. It is the velocity of the particle achieved at the end of this phase that is of interest. Consider Diagram 1 representing the forces acting on a particle.
Q
frictional force A
centrifugal force
Diagram I The centrifuge force, Fc, is the product of the mass of the particle, corrected for its buoyancy in water or other solvent, and of the centrifugal acceleration, ~ r , where o~ is the angular velocity (radians/second) and r is the distance between the particle and the center of rotation for the centrifuge. Fc is given by Fc = M2(1 - v2p)to2r,
(1)
where Fc has units of dynes mole -I, M 2 is the molar mass of the particle in units of grams mole -1, v2 is the partial specific volume of the particle in units of cmS-gram, p is the density of the solution in grams cm 3. The frictional force, Ff, is proportional to the velocity and is given by
Ff = Nf dr/dt,
(2)
where Ff has units of dynes mole-l, f is the frictional coefficient of the sedimenting molecule in units of dynes-sec c m -1, and N is Avogadro's number. During steady-state transport, when Fc = Ff, we can write that
Nf dr/dt = M2(1 - ~2p)~r.
(3)
If we define the sedimentation coefficient, s, in the usual way, as the velocity per unit centrifugal field, we have s
-
dr/dt ~r
-
M2(1 - v2p) Nf "
(4)
121
Chapter3 HydrodynamicMethods
For a large number of particles in a solution, a boundary will form between the solution of particles as they sediment and the buffer left in the supernatant. Figure 1A shows the progressive change in position and shape of a typical boundary as it sediments to the bottom of the centrifuge cell. Several features are worth pointing out; as the boundary progresses it spreads from diffusion, and at the same time, the concentration of the region centrifugal to the boundary (usually referred to as the plateau region) decreases with time. The rate of movement of the boundary is very nearly proportional to the first power of time. (This also applies to the rate of separation of two separate boundaries.) On the other hand, the rate of spreading of the boundary from diffusion is very nearly proportional to the square root of time. Therefore, resolution will increase with time despite the spreading from diffusion. The decrease in concentration in the plateau region is caused by dilution that occurs as the macromolecule sediments into a larger and larger volume in the sector-shaped cells used in the analytical ultracentrifuge. Figure 1B and C shows the concentration gradient and time derivatives of the concentration profile, respectively. In the older analytical ultracentrifuges, the movement of the boundary was observed with a schlieren optical system that displayed the refractive index gradient as a function of position. This optical system has been largely supplanted by the absorption and Rayleigh optical systems in the newer ultracentrifuges.
B. Particle Shape 1. General Considerations For a spherical particle moving under conditions in which flow is dominated by viscous forces (such as a protein molecule in water), we have from Stokes' law that f0 = 6 r
0,
(5)
where f0 is the viscous drag on the sphere, 77ois the viscosity of water in poise, and R0 is the radius of the solvated sphere in centimeters. If we introduce the concept of the radius of the hydrodynamically equivalent sphere, referred to as the Stokes radius, Rs, for a nonspherical particle we have f = 6 cnl0Rs .
(6)
If we combine Eqs. (6) and (4), we have a relationship that relates the Stokes radius and the molecular mass to the sedimentation coefficient [Eq. (7)], s =
M2(1 - v2p) N6 r s '
(7)
where 77ois the viscosity of the solvent and Rs is the Stokes radius of the hydrodynamically equivalent sphere. Equation (7) is the basis for much of the hydrodynamic analysis of particle shape. Particle shape is often discussed in terms of the frictional ratio fifo and is related to the ratio of Stokes radii or the ratio of sedimentation coefficients by
122
Walter F. Stafford and Todd M. Schuster A
1.0
-
|
-
.
i
i
9 i
9 i
9 |
9 ,
9 i
!
i
9 ,
9 !
-
i
.
|
9 ,
9
0.8 0 t~ =._ Q
o Ir 0 o
0.6
0.4
0.2 0.0 5.90
B
25.0
-
;
i
.
_
6.10
6 30
6.10
6.30
.
i
.
7.10
radius
,
20.0
15.0
"~
10.0 5.0 0.0 5.90
6.50
6.70
6.90
7.10
6.70
6.90
7.
radius
C0.0035
0.0030
0.0025
=., "0 0
0.0020
0.0015
O.O010
0.0005
0.0000 5.90
6.10
6.30
6.50
radius
Fig. 1 Simulated sedimentation patterns. (A) Concentration vs radius; (B) concentration gradient, dc/dr, vs radius; (C) time derivative, dc/dt, vs radius for increasing times of sedimentation from left to right.
Eq. (8), fifo = Rs / Ro = So / s,
(8)
where So and R0 are the sedimentation coefficient and the Stokes radius, respectively, of the equivalent solvated sphere. R0 is given by R0 = [3M2(v2 + 81v~
1/3,
(9)
Chapter 3 H y d r o d y n a m i c M e t h o d s
123
where ~1 is the hydration in grams of water bound per gram of protein and v ~ is the specific volume of pure water. Both v2 and (~1 can be calculated reasonably well in most cases from a knowledge of the chemical composition of the macromolecule. Sometimes the frictional ratio is given in terms of the radius of the anhydrous equivalent sphere and is designed f/fmin and is related to f/fo (Tanford, 1961) by
f/fo =
(f/fmin)[V2 /(V2 +
~lV0)]1/3.
(10)
The quantity f/fmi~ includes contributions from both shape and hydration. The partial specific volume of the protein can be computed by adding up the contributions from the individual atoms according to Traube's rule (Traube, 1899). The partial specific volumes of individual amino acids, nucleotides, and sugars have been tabulated (Cohn and Edsall, 1943; Durchschlag, 1986; Perkins, 1986) and can be used to compute the partial specific volume of a protein or nucleic acid from the mass average contribution from each of the residues. V2 = s
viMini/s
Mini,
(11)
where v-/is the partial specific volume of amino acid i, M~ is the molecular mass of residue i minus the molecular mass of water, and I"/i is proportional to the number of moles of residue i per mole of protein (Cohn and Edsall, 1943; Perkins, 1986). A typical average of v2 for proteins is 0.725 cm 3 g-1. Nucleic acids, being more dense, have average values for v2 of about 0.50 cm 3 g-1 for the sodium salts. Values for 31 of 0.3 to 0.4 g water g-1 protein and 0.59 g water g-1 nucleic acid are typical for globular proteins and DNA, respectively. Software for the computation of partial specific volume and hydration from either amino acid composition or sequence data by several methods can be obtained from the authors by e-mail request to
[email protected] or
[email protected].
2. Axial Ratios of Ellipsoidal Models: Perrin's Equations The shape of a macromolecule may often be crudely modeled as a prolate or an ellipsoid (Fig. 2). Perrin's equations are used to relate measured values of fifo to axial ratios of equivalent molecular ellipsoidal models (Perrin, 1936). For ellipsoids of revolution, we have (where a is a major semiaxis and b is a minor semiaxis) a prolate ellipsoid (p = b/a and a is the axis of revolution), f
-- =
fo
(1
and an oblate ellipsoid (p =
f
-- =
do
-- p2)1/2
p2/3 In{[1 + (1 - p2)1/2]/p}
(12)
a/b and b is the axis of revolution), (p2__ 1)1/2
p2/3 tan-1
[(p2 _ 1)1/2]"
(13)
Note that p is defined so that the axis of revolution is in the denominator and, therefore, has a different definition for prolate and oblate ellipsoids of revolution.
124
Walter F. Stafford and Todd M. Schuster
~
~I" b
prolate
a
oblate
Fig. 2
Ellipsoids of revolution.
3. Modeling General Shapes A treatment of arbitrary macromolecular shapes more sophisticated than modeling them as ellipsoids is based on approximating the shape as an assemblage of spheres. The rationale is that an arbitrary shape can be modeled using spherical beads of varying size, either filling the space of the molecule or covering its surface. For example, the frictional coefficient of any arbitrary arrangement of spheres can be calculated by the method of Garcia de la Torre and Bloomfield (1981). These methods, based on the theory of Kirkwood (1949), involve computing an equivalent Stokes radius from the model. A computer program, called HYDRO, has been developed for computing hydrodynamic parameters for arbitrary assemblages of spherical elements (Garcia de la Torre et al., 1994). Figure 3 shows several possible spherical models for the distribution of mass in a protein with molecular mass of 100,000 Da, assuming the partial specific volume, v-2 = 0.725 c m 3 g - 1 and the hydration 61 = 0.40 c m 3 g - 1 . In addition to sedimentation coefficients, HYDRO yields the following physical properties of interest to the readers of this volume: intrinsic viscosity, translational diffusion coefficients, radius of gyration, and total volume of the model. It also yields other, more advanced parameters beyond the scope of this chapter and can be adapted to include molecular flexibilities. The program HYDRO and an instruction manual may be obtained from Dr. Garcia de la Torre by e-mail at the address
[email protected].
C. S v e d b e r g Equation Introducing the Stokes-Einstein relation for the frictional coefficient in terms of the diffusion coefficient, f = RT/ND,
(14)
125
Chapter3 HydrodynamicMethods
6.72S
6.42S
Fig. 3
6.20S
CCC
An example of the use of the computer p r o g r a m HYDRO to compute frictional ratios for various models. Shown are the calculated values of the sedimentation coefficient for several different mass distributions for a molecule with a molecular mass of 100,000 Da, assuming the partial specific volume, v2, = 0.74 cm 3 g-1 and the hydration, 61, = 5.40S 0.40 cm 3 g-1. These models have frictional ratios, fifo, of 1.00, 1.05, 1.08, and 1.24, respectively, from top to bottom.
and substituting Eq. (14) into Eq. (4), we arrive at the Svedberg equation:
s/D = M2(1 - ~2p)/RT,
(15)
where D is the diffusion coefficient in units of c m 2 s e c -1 (the other symbols were defined above). Therefore, by determining both s and D by separate measurements, one may obtain an estimate of the molecular mass.
D. Determination of Protein Partial Specific Volume and Solution Density Both p and v2 may be determined by pycnometry. However, classical pycnometry usually requires relatively large volumes of concentrated solutions, obviating the use of this method for many protein samples. If only limited quantities are available, and high precision is required, the vibrating tuning-fork method is usually used for density determinations (Kratky et al., 1973). A precision of 2 to 3 parts in 106 can be obtained with care. If the equipment is available, this is the method of choice because it can be carried out on small volumes (1-2 ml), although fairly high concentrations (5-20 mg m1-1) are required for greatest accuracy. An extensive tabulation of partial volumes has been compiled by Durchschlag (1986). The buoyancy term (1 - v 2 p ) is equal to the density increment (Op/OC2)T,p,iz and is measured by determining the density of the solution as a function of protein concentration; the density increment subscript (T,P,/z) refers to measurements carried out at constant chemical potential of all dialyzable components at constant temperature and pressure. The procedure is to determine the density increment as the slope of a plot of density vs concentration. Each value of density is determined by pycnometry. The molecular mass obtained by using Op/OC2)T,p,~ is the molecular mass of that component whose concentration is
126
Walter F. Stafford and Todd M. Schuster
represented by c2. For example, if the concentration is expressed in terms of grams of isoionic protein, then M 2 will be the molecular mass of the isoionic protein. The condition of constant chemical potential can be achieved by either gel filtration or dialysis.
E. C o n c e n t r a t i o n D e p e n d e n c e
of Hydrodynamic
Parameters
Concentration dependence of the sedimentation coefficient is often observed and is usually treated by one or both of the following empirical forms, s = s o (1 1
- = s
(1 +
kcc)
kcc)
sO
,
(16) (17)
where s o refers to the value of s at infinite dilution and kc is a proportionality constant describing the dependence of s on c. Concentration dependence of the sedimentation coefficient can arise from back-flow of solvent and charge effects. At relatively low concentrations, the back-flow is proportional to the concentration and the hydrodynamic volume of the particle. Back-flow of solvent arises because the centrifuge cell has a fixed volume, causing the solvent displaced by the sedimenting molecules to flow in the direction opposite to that of the molecules. The result is an apparent reduction in the sedimentation velocity with respect to the cell reference frame. At higher concentrations the back-flow is impeded by the diminishing space between the particles, and either a term in c 2 must be introduced or the inverse form [Eq. (17)] used. Equation (17) is usually valid over a wider concentration range than Eq. (16). For random coil polymers kc is proportional to the intrinsic viscosity. Charge effects can arise for two different reasons (Svedberg and Pederson, 1940). The first, referred to as the primary charge effect, arises from the requirement of electroneutrality and is caused by the difference in sedimentation coefficient of a charged macromolecule and its counterions; it becomes significant at low ionic strength. The primary charge effect is related directly to the protein concentration and inversely to the supporting electrolyte concentration. The second type of charge effect, referred to as the secondary charge effect, arises from the electric field formed by the differential sedimentation of positive and negative salt ions. It is serious only at very high salt concentrations and can be eliminated for practical purposes by choosing a salt whose ions have similar sedimentation coefficients, such as KC1 and NaC1.
F. J o h n s t o n - O g s t o n
Effect
In a mixture of two or more components, the variation of the concentration of one component can effect the sedimentation velocity of the others. Concentration dependence of components in a mixture will have the following general
Chapter 3 Hydrodynamic Methods
127
form.
1
sO (1 + kl,lC1 -+- kl,2C2 q- kl,3C3 if- ... if- kl,nCn) ,
1
1
s2
sO
k2,nCn) ,
(18b)
s2~ (1 § kn,lc I -ff kn,2C 2 -}- kn,3C 3 q-- . . . q- kn,nCn) ,
(18c)
(1
+
k 2 , 1 c I if- k 2 , 2 c 2 -}- k 2 , 3 c 3 q - . . .
1
Sn
(18a)
if-
where the k values account for the dependence of each molecule on its own concentration and also on concentrations of the other molecules present. The consequence of this effect is that a more slowly moving component will move more rapidly in the region centripetal to the b o u n d a r y of the more rapidly m o v i n g component than it does in the centrifugal region (see Fig. 4). The result will be that the concentration of the slower component will be lower in the centrifugal region than in the centripetal region of the faster m o v i n g boundary, resulting in accumulation of material centripetal to the boundary. Consequently, the concentration of the more slowly sedimenting material will be higher in the regions of lower total concentration than in regions of higher total concentration, causing an oversestimation of the a m o u n t of the more slowly m o v i n g material in the mixture. See Fig. 4 for an example of the effect that concentration dependence can have on a two-component mixture. The J o h n s t o n - O g s t o n effect can be minimized by working at low concentration or by measuring the sedimentation coefficients as a function of total concentration and extrapolating the values to infinite dilution.
1.0
"''w'''l'''l'''l"''w'''l'''l'''W''','''w''"
A 0.8
0.6 B
0.4 C 0.2
0.0
-.-~---
...l...i..,,
5.9
6.0
6.1
6.2
6.3
6.4
6.6
6.7
6.8
6.9
7.0
7.1
radluslcm
Fig. 4 Johnston-Ogston effect for the system S1 = 5.0S, D1 = 8.0F; $2 = 8.0S, D2 = 6.5F. The
meniscus is at 5.9 cm; speed, 60,000 rpm; time, 4800 sec. The form of the concentration dependence is given by Eqs. (18a) and (18b), with kl, 1 -- kl, 2 -- k2,1 = k2,2 -- 0.2. ( A ) Total concentration; (B) concentration of the 5.0S component; (C) concentration of the 8.0S component.
128
Walter F. Stafford and Todd M. Schuster
Interacting systems also exhibit concentration dependence, but of a different type. The concentration dependence of reversibly interacting systems is discussed below.
G. M e a s u r i n g S e d i m e n t a t i o n Coefficient
1. Hardware Required In the usual double sector centrifuge cell, the sample volume required is about 0.45 ml. The concentrations that can be observed range from a few micrograms per milliliter up to several hundred milligrams per milliliter. The lower limit is determined by the lowest concentration detectable by a paticular optical system. The upper limit, however, is determined by the maximum concentration gradient that can be observed without having the light beam deflected out of the optical pathway by the gradient. For solutions of very high concentration, one must use very short path length cells, sometimes only a fraction of a millimeter in length. The factor that determines whether the light beam will be deflected out of the optics is the product ab(dn/dr), where a is the optical lever arm, i.e., the distance from the cell to the observing plane, b is the optical path length of the solution, and dn/dr is the refractive index gradient.
2. Determination of Sedimentation Coefficient The sedimentation coefficient is properly determined by measuring the rate of transport in the so-called plateau region (see Fig. 5), centrifugal to the boundary. Because the concentration gradient is zero in the plateau region, this region is featureless. Therefore, the rate of transport in the plateau is measured by following the position of the equivalent boundary position. The equivalent boundary position is the position that the boundary would have had in the absence of diffusion and polydispersity. As we will see, the equivalent boundary position moves with a velocity determined by the mass average sedimentation coefficient of the sample at the plateau concentration. The mass average sedimentation coefficient is given by Sw = ~
CiSi/~
Ci,
(19)
where ci and si are the concentration and sedimentation coefficient, respectively of species i in a mixture. The summations are carried out over all sedimenting species. The equivalent boundary position is given by ~2
1 ;rp r 2 dc,
= m Cp
(20a)
m
where
fF YP
Cp--
d c nt-
Cm;
(20b)
in
here r is the equivalent boundary position, rp is a point in the plateau where the
129
Chapter3 HydrodynamicMethods 0.35 0.30 C 0 ,,,,, r --9 tO
0.25 0.20
O
0.15
0 o
0.10
0.05
0.00 5.80
6.00
6.20
6.40
radius
6.60
(cm)
6.80
7.00
7.20
Fig. 5 Diagram showing the relationship of the equivalent boundary position to the observed boundary profile. The equivalent boundary position, r, is indicated by the vertical line.
concentration gradient is zero, r m is the meniscus position, Cp is the plateau concentration, and Cm is the meniscus concentration. Sedimentation is usually allowed to proceed to the point at which the boundary has cleared the meniscus, so that Cm = 0 before the integrations are carried out. The rate of movement of the equivalent boundary is equal to the velocity of the sedimenting particles in the plateau region at the concentration Cp, no matter what the shape of the boundary, and so we have from the definition of the sedimentation coefficient [Eq. (4)] that, m
Sw
1 d ln(r) 092
dt
/
(21)
where ~o is the angular velocity of the rotor in units of radians per second. Therefore, one obtains the sedimentation coefficient from a plot of the logarithm of the equivalent position versus time (Fig. 6). For a symmetrical boundary, the midpoint of the boundary is very close to the equivalent boundary position and is often used as an estimate for it. However, for a polydisperse system, the midpoint and the equivalent boundary position may be quite different. In this case, the rate of movement of the equivalent boundary position gives the mass average sedimentation coefficient for the material sedimenting in the plateau region at the concentration of the plateau region. This is true for both interacting and noninteracting systems.
H. Analysis of Interacting Systems
1. Self-Associating Systems The computation of Sw is required for the analysis of interacting systems as a function of concentration. The composition, and therefore Sw, of a self-associating system at any given temperature are determined by the total macromolecular concentration according to the law of mass action.
130
Walter F. Stafford and Todd M. Schuster 1.9200
1.9000
.
.
.
.
.
.
~
.
.
.
.
~
.
.
.
.
~
.
.
.
.
~
.
.
.
.
~
s = 5.0S speed = 60,000 rpm slope ra, "a
.
.
.
.
w
.
.
.
I
. . . .
.
_ ~
1.8800
1.8600 1.8400
1.8200 1.8000
. . . .
i
. . . .
1 000
I
. . . .
I
2000
. . . .
3000 time
1
. . . .
i
4000
. . . .
5000
6000
7000
(seconds)
Fig. 6 The slope of a plot of the logarithm of the equivalent boundary position versus time of sedimentation gives the sedimentation coefficient.
For example, consider the following self-associating system: A1 q" A1
-- a2,
A2 + A1 = As,
A n _ 1 q- a I -
c2 =
k2c2;
(22a)
c3 =
k3c3;
(22b)
c n - knc~;
A n,
(22c)
for which we have Ct = ~
kick,
i=1
where c t is the total concentration and kl -= 1. Thus, for any given thermodynamically ideal, self-associating system, we can express the mass average sedimentation coefficient, Sw, in terms of the equilibrium concentration of monomer in the following way: 1
Sw = m
Cp
(SlC 1 -i-
s2k2 c2 -4- $3k3 c3 "Jr- "~
nt- snknc~).
(23)
Because the monomer concentration is a unique function of the total protein concentration, Sw is uniquely determined by the plateau concentration (Fig. 7). In principle, determination of stoichiometries and estimates of equilibrium constants can be made by curve fitting to the experimentally determined values of Sw as a function of the plateau concentration. There are several drawbacks of using sedimentation velocity measurements to study interacting systems. One drawback is that a sedimentation velocity measurement is not a thermodynamic measurement, and if the system is kinetically limited so that essentially instant reequilibration cannot occur during sedimentation, erroneous results
131
Chapter 3 Hydrodynamic Methods
Fig. 7 Simulatedmonomer-dimer system. Plot of the mass average sedimentation coefficient as a function of the reduced concentration variable k2c , where c is the plateau concentration. Each point represents the result of a single sedimentation run.
will be obtained. This drawback applies to any transport method, e.g., size exclusion chromatography. Another drawback is that determination of Sw at each concentration requires a separate run, or at least a separate cell in a multicell run. Thermodynamic parameters are best determined by sedimentation equilibrium measurements (see below) because of the much higher signal-tonoise ratio of data obtained by that method and because of the relative ease with which the data can be collected. Moreover, sedimentation equilibrium analysis is firmly based on thermodynamic theory, and as long as the system under investigation is reversible on the time scale of the experiment, it is the preferred method. Sedimentation velocity analysis could be used to confirm stoichiometries or when only very small amounts of material are available. The time derivative method (Stafford 1992 a,b; 1994 a,b), using the apparent sedimentation coefficient distribution function, can extend the sensitivity of sedimentation velocity analysis at least one order of magnitude lower in concentration than that of sedimentation equilibrium using the same optical system. Therefore, sedimentation velocity may be the method of choice to detect and analyze a particular dissociation equilibrium reaction that may not be accessible by sedimentation equilibrium. The mass fraction of monomer, fl, as a function of the total macromolecular concentration, ct, can be shown to be fl = s2 - Sw(Ct),
(24)
S 2 -}- S 1
and Cl is simply
ctfl.
2. Analysis of Boundary Shape Details of boundary shape are characteristic of the stoichiometry, the rapidity of the reaction, and interactions with small ions and molecules. One of the important predictions from the theory of transport of interacting systems developed
132
Walter F. Stafford and Todd M. Schuster
in the 1950s by Gilbert and co-workers (Gilbert, 1955, 1959; Gilbert and Jenkins, 1959) was that a boundary for a rapidly reversible m o n o m e r - d i m e r system would never resolve into two boundaries no matter how far it sedimented, and would always exhibit a unimodal shape. On the other hand, boundaries for systems with higher stoichiometries (e.g., monomer-trimer or m o n o m e r tetramer) would become bimodal with time but would never resolve into two separate boundaries with a zero concentration gradient between them. Because the law of mass action must be obeyed at all points in a boundary, there will be no point where there could exist pure monomer not in equilibrium with polymer; therefore, boundaries for self-associating systems are called "reaction boundaries," because no single feature of the boundary can be attributed solely to either monomer or polymer. The exact shape of the boundary is characteristic of the stoichiometry (see Cann, 1970).
III. Sucrose Density Gradient Sedimentation In the period of time between about 1970 and 1990, when the analytical ultracentrifuge fell into relative disuse, the use of preparative ultracentrifuges to measure molecular mass by a combination of sucrose density gradient centrifugation (Martin and Ames, 1961) and gel permeation chromatography (Siegel and Monty, 1966) became popular. This technique, along with its many serious drawbacks, will be replaced again by analytical ultracentrifugation as the new Beckman Instruments XL-A analytical ultracentrifuges repopulate research laboratories. In the sucrose density gradient technique, a gradient of sucrose is chosen to just compensate for the increase in centrifugal field, with radius so that molecules sediment with a constant velocity. Once the gradient is calibrated with proteins of known sedimentation coefficients, it can be used to estimate the sedimentation coefficient of other unknown proteins. According to the Svedberg equation [Eq. (15)], the sedimentation coefficient is proportional to the molecular mass divided by the frictional coefficient. Therefore, in order to obtain an estimate of the molecular mass, one must also measure the frictional coefficient. One can measure the Stokes radius, and, thereby, the frictional coefficient of the molecule by gel filtration on a suitably calibrated column. Generally, one calibrates the column with a series of proteins of known frictional coefficient. Frictional coefficients are usually obtained from diffusion data in the literature using the Stokes-Einstein equation [Eq. (14)]. Using Eq. (4), one can compute a value of the molecular mass by combining the value of the sedimentation coefficient obtained by sucrose density gradient sedimentation with the value of the frictional coefficient obtained by gel filtration, M 2 -
6'rr~oRsNS/(1
-
v2p).
(25)
This technique became popular because it required no specialized equipment. The sucrose density sedimentation could be carried out in a swinging bucket rotor in a preparative ultracentrifuge, and the gel permeation chromatography could be carried out with inexpensive columns. However, both types of measurement have potentially very serious problems that can leave the validity of the results in considerable doubt. Sucrose at the concentrations usually
Chapter 3 HydrodynamicMethods
133
used in the gradients can cause changes in the frictional coefficient and also influence self-association. For example, if a protein has a slight tendency to dimerize, 5-10% sucrose can cause an otherwise mainly monomeric protein to dimerize nearly completely in the gradient (Cann et al., 1994). If one then performs the gel filtration measurement on the same protein in the absence of sucrose, one will obtain the frictional coefficient for the monomeric protein. Clearly, the result of combining these two results will yield an incorrect estimate of the molecular mass. In addition to the problems associated with sedimentation in the present sucrose, the error in the measurement can be compounded if the protein has any tendency to interact with gel permeation column bed material (Winzor, 1969). The amount of time required to measure molecular mass directly in a sedimentation equilibrium experiment can be just a small fraction of the time required to perform all the control experiments necessary to verify that none of these potential problems exist. It should be pointed out that sedimentation equilibrium is an absolute method for mass determination and does not require calibration with a series of "known" proteins. Under normal solvent conditions, the uncertainty in the mass determination is affected only by the uncertainty in estimating the partial specific volume. This uncertainty is small compared to the compounded uncertainty associated with combining the results of two uncertain methods, sucrose gradient sedimentation and gel permeation chromatography.
IV. Diffusion Diffusion coefficients can be estimated in the ultracentrifuge by following the spreading of a boundary created with a special boundary-forming centerpiece. The change in concentration as a function of time in a rectangular coordinate system is given by Fick's second law, (26)
(Oc/ Ot) r -- -- D(O2c/ Or2)t .
The solution to Eq. (26) (Tanford, 1961) is c=2
col 2J2Dt'112_y2 ] , 1-
~
e
dy
(27)
where x is given in units of standard deviation and is measured from the midpoint of the boundary. The concentration gradient is given by (Oc/ Or) t = - c O/ 2('tgDt)l/ae-x2/4Dt.
(28)
The diffusion coefficient is determined essentially by measuring the standard deviation of the boundary, which is equal to (2Dt) 1/2. In practice, if one has measured the concentration gradient curves as a function of time, D can be measured by computing the square of the ratio of the peak area (A) to the peak height (H) and plotting it against time. The peak height is equal to the preexponential factor in Eq. (28) and the peak area is equal to Co. The square of the ratio is ( A / H ) 2 = 4rrDt,
and the slope of the plot of 1958).
(A/H)
2 vs
(29)
t is 4rrD (Schachman, 1959; Williams et al.,
134
Walter F. Stafford and Todd M. Schuster
V. Sedimentati0n-Diffusion Equilibrium A. T h e o r y Sedimentation equilibrium can be used to measure molecular masses over a very wide range, from the size of small molecules such as sucrose (360 g mol -~ ) to the size of large viruses such as tobacco mosaic virus (40 • 106 g mol -~). As mentioned above, determination of molecular mass by sedimentation equilibrium analysis is an absolute m e t h o d that does not d e p e n d on calibration or comparison to standards. It is a nondestructive method and, therefore, can be used to determine the behavior of macromolecules u n d e r normal solution conditions. It is the m e t h o d of choice to study interactions between macromolecules or between macromolecules and other smaller molecules at thermodynamic equilibrium. The theoretical description of the m e t h o d is firmly based on t h e r m o d y n a m i c principles. In the derivation that follows, we assume a thermodynamically ideal and incompressible solution. Equations describing the effects of nonideality will be introduced briefly at the end. At equilibrium, net transport from sedimentation and diffusion is zero and there are no further changes of concentration with time (Fig. 8). The condition for equilibrium in the centrifuge can be derived directly from t h e r m o d y n a m i c principles (Williams et al., 1958) or from the kinetic equations describing flow due to sedimentation and diffusion, with the condition that at equilibrium there is no net transport of material. The following derivation is from the kinetic equations. The L a m m equation [Eq. (30)], also referred to as the continuity equation (Lamm, 1929), describes the time dependence of concentration during sedimentation in a cylindrical reference frame. At equilibrium, w h e n there are no further changes in concentration with time, we have 3c
-
3t
1 3 r Or
[Y(Jsed q- Jdiff)] - O,
(30)
where Led and Jdiff are the fluxes due to sedimentation and diffusion, respec-
1.5
. . . .
|
. . . .
v
. . . .
|
. . . .
u
. . . .
|
. . . .
1.0
u e-
O o
,
0.5
0.0 6.40
6.50
6.60
6.70
radius
Fig. 8 Concentration distribution at sedimentation-diffusion equilibrium. When the centrifugal force, Fs, arising from the gradient in the centrifugal potential is balanced by the diffusional force, FD, arising from the gradient in the chemical potential, net transport is zero and equilibrium is attained. The molecular mass of the macromolecule is directly related to the concentration gradient at equilibrium according to Eq. (32).
Chapter 3 HydrodynamicMethods
135
tively, and are given by Led
=
092ySC,
Jdiff
--
--
D(0c / 0r),
where Oc/Or is the concentration gradient and D is the diffusion coefficient in units of c m 2 s e c -1, and because at equilibrium the flux due to sedimentation transport is equal to that due to diffusional transport, we have D(Oc/Or) - ~ r s c = 0,
(31)
and, on rearranging, and substituting from the Svedberg equation [Eq. (15)], we have d ln(c) d(r2/2)
m
~oasm M2(1 - Vap)w2 D
RT
(32)
In the simplest type of analysis, ln[c(r)] vs r2/2 is plotted, where c(r) is the equilibrium concentration distribution (Fig. 9). Any quantity proportional to the concentration can also be used. The slope of this plot gives the molecular mass, M 2 . For a polydisperse system, the plot of In(c) v s r 2 / 2 will be curved upward and the slope of the tangent to the curve gives the mass average molecular mass (see Glossary, molecular mass averages) at each point in the cell, usually designated as Mw. By appropriate manipulation of the concentration data, one may also compute number and z-average molecular masses as a function of concentration and position (Roark and Yphantis, 1969; Teller, 1973).
B. Heterogeneity versus Reversible Self-Association Analytical ultracentrifugation is the method of choice for identifying and discriminating between simple heterogeneity and reversible interactions. Reversible interactions can be between like molecules (self-association) to form dis-
Fig. 9
Sedimentation and diffusion equilibrium. Plot of the logarithm of the equilibrium concentration versus the radius squared. The slope of this plot for a monodisperse macromolecular system is proportional to the molecular mass of the macromolecule.
136
Walter F. Stafford and Todd M. Schuster crete p o l y m e r s (dimers, trimer, tetramers, etc.) or b e t w e e n different molecules (heteroassociation) to form a complex. Both of these types of s y s t e m s can be d i s t i n g u i s h e d from a noninteracting, p o l y d i s p e r s e s y s t e m c o m p o s e d of a distribution of p o l y m e r s of the s a m e kind, but different masses. A heterogeneous, p o l y d i s p e r s e s y s t e m (i.e., one c o m p o s e d of several therm o d y n a m i c a l l y ideal, noninteracting species) will be distributed in a centrifugal field strictly as a function of radius, such that the composition a n d hence the m a s s average molecular mass at each point will vary according to its radial position only, i n d e p e n d e n t of the concentration at each point. On the other hand, a polydisperse, self-associating s y s t e m (i.e., one comp o s e d of several oligomers of a single m o n o m e r that are in rapid reversible equilibrium, and for w h i c h there is no v o l u m e change on association) will be distributed in a centrifugal field strictly as a function of the concentration according to the law of mass action, i n d e p e n d e n t of the radial position (Fig. 10). The m a i n feature of these plots for h e t e r o g e n e o u s (i.e., polydisperse, noninteracting) systems, w h i c h is counterintuitive at first glance, is that w h e n the molecular mass averages are plotted as a function of the local cell concentration, the data obtained at the lowest loading concentration and, therefore, also at the highest radii will yield mass averages higher than those obtained at higher cell loading concentrations, w h e r e the data for the s a m e local concentration are collected at lower radii (see Fig. 11). The ability to distinguish b e t w e e n these two types of systems is one of the features of equilibrium analytical ultracentrifugation that m a k e s it such a p o w -
A
2.0
i
i
6.4
6.5
i
.
.
.
.
1.6
1.2
0.8
0.4
0.0
6.4
6.6 radius
6,6
6.6
6.7
(cm)
Fig. 10 A schematic diagram showing the two different requirements for the equilibrium distributions of a heterogeneous and a self-associating system. The distribution curves are for three different loading concentrations in the ratio 9:3:1, respectively, from left to right. For a polydisperse, noninteracting system, the composition, and therefore the mass average molecular mass, are a function of radial position only, so that, for example, along the line marked A, the measured mass average molecular mass must be the same for all three loading concentrations, independent of the local cell concentration. In contrast, for a reversible, self-associating system, the composition, and therefore the mass average molecular mass, are uniquely determined by the local cell concentration according to the law of mass action. For example, along the line marked B, at the same local cell concentration, the mass average molecular mass must be the same, independent of the radius at any cell loading concentration.
Chapter 3 HydrodynamicMethods
137
Fig. 11 Comparison of a reversibly self-associating monomer-dimer system (A) and a simple heterogeneous monomer-dimer system (B) composed of the same species. (A) In the reversible system, the plots of mass average molecular mass vs local cell concentration obtained from different cell loading concentrations will overlap, whereas (B) for a heterogeneous (i.e., noninteracting) system composed of the same species the curves obtained from different cell loading concentrations will not overlap when plotted as a function of local cell radius.
erful tool for analysis of macromolecular systems in solution. The difference between these two types of systems can be revealed by curve fitting techniques as well as from plots of molecular mass averages (vide infra), m a k i n g sedimentation equilibrium analysis a very powerful technique for the detection of heterogeneity in otherwise reversibly interacting systems. There are two general approaches to the analysis of sedimentation equilibr i u m concentration distributions. One, just m e n t i o n e d above, is to compute point-by-point molecular mass averages across the cell and then to analyze these molecular mass distributions by various m e t h o d s to determine the n u m ber of species and their molecular mass. One m a y also determine equilibrium constants and stoichiometries. The computation of molecular mass averages is generally model independent. The other c o m m o n m e t h o d is to fit the equilibr i u m concentration distribution directly by nonlinear least-squares m e t h o d s to various models. This method, which is b e y o n d the scope of this volume, has
138
Walter F. Stafford and Todd M. Schuster been described in detail by Johnson (1994) and Bevington and Robinson (1992). Modern computer programs exist to perform this type of fit. The form of the equation describing the equilibrium distribution of a reversibly associating system is the same as that for a noninteracting system composed of the same macromolecular species. However, the preexponential factors have different meanings for the two types of systems. For a reversibly self-associating system, the preexponential factors are related to the equilibrium constants describing the system, whereas for the corresponding noninteracting system, the preexponential factors are determined by the mass fractions of each component in the original mixture, assuming no material has pelleted during the experiment. For an interacting system, the equilibrium constants calculated from the preexponential factors will be independent of cell loading concentration, as they should be for a thermodynamically reversible system. On the other hand, for a noninteracting system, the apparent equilibrium constants calculated at each loading concentration will vary inversely with the cell loading concentration.
C. T h e r m o d y n a m i c N o n i d e a l i t y Thermodynamic nonideality can become important under certain experimental circumstances and must be taken into account. Nonideality can arise from several sources involving either solute-solute or solute-solvent interactions. One solute-solute interaction that has already been mentioned is self-association, but because it can be taken into account explicitly, it is treated separately. The two important types of nonideality, one arising from charge effects because of the requirement of charge neutrality, and the other arising from excluded volume effects, will be treated. When nonideality is significant, the concentration in Eq. (32) must be replaced by the activity, a. Goldberg (1953) showed that for a system at equilibrium in a centrifugal field, d l ~ / d ( r 2 / 2 ) = M2(1 - v2p)~o2,
(33)
where/~ is the chemical potential and is given by t~ = ~o + R T ln(a2) =/~0 + R T ln(y2c2);
(34)
here/~0 is the chemical potential of the standard state at 1 atm, and a2 is the activity of the macromolecule and can be replaced by Y2r where Y2 is the activity coefficient. In general, the activity coefficient varies with concentration and is equal to 1 at infinite dilution. The variation of the activity coefficient with concentration is usually expressed as a power series in the concentration, 0 l n ( y ) / O c = 1 + 2Bc + 3Cc 2 + . . . .
,
(35)
where B, C, etc. are called the second, third, etc. virial coefficients and can be related to the solute-solute and solute-solvent interactions. For example, the dependence of second virial coefficient on the excluded volume of a spherical macromolecule is given by B = 4 N V / M 2,
(36)
139
Chapter3 HydrodynamicMethods and for a long rod-shaped macromolecule, by B = vrNrL 2/ 2M 2,
(37)
where r and L are the radius and length of the rod. Another source of nonideality is from the Donnan equilibrium, which arises from the unequal distribution of diffusible ions between the region of the macromolecular domain and the bulk of the solution that is required to maintain electroneutrality. The second virial coefficient for this case is given by B = Z2/4m3,
(38)
where Z is the charge on the macromolecule and m3 is the concentration of the salt component.
D. Measuring Sedimentation Equilibrium In a typical sedimentation equilibrium experiment, using solution column heights of 3 mm, about 0.13 ml of solution is required. For meniscus depletion conditions, the value of the highest loading concentration should be in the range of 1 - 2 mg m1-1 and two dilutions of 1/3 and 1/9 should be chosen, requiring between 200 and 400 ~zg of material for the Rayleigh optical system. For the absorbance optical system the loading absorbance should not exceed about 1.0 a.u. at the highest load. In the Beckman Instruments XL-A analytical ultracentrifuge, wavelengths available range from 190 to about 700 nm. Three different concentrations can be run simultaneously in three double-sector cells. Alternatively, if one has a six-channel Yphantis-type centerpiece available from Beckman, all three dilutions can be run simultaneously in one cell. Moreover, one can run three such cells simultaneously, allowing nine samples to be analyzed in one run.
E. Density Gradient Sedimentation Equilibrium Density gradient sedimentation equilibrium is usually used for the study of properties of high molecular mass DNA samples. In the typical experiment, both CsC1 and DNA are introduced into the centrifuge cell and the rotor is spun at a speed that will set up a gradient in CsC1 such that the buoyant density of DNA in the gradient is positive near the top and negative near the bottom. The result is that the DNA will sediment from the meniscus, but float from the bottom, so that the DNA eventually forms a band at the position in the gradient corresponding to neutral buoyant density. This technique was first described by Meselson et al., (1957). It was used subsequently (Meselson and Stahl, 1958) to demonstrate that the replication of DNA in Escherichia coli is semiconservative. The buoyant density of DNA depends also on base composition and consequently can be used to distinguish DNA samples from different sources. At equilibrium, under ideal conditions (i.e., at infinite dilution), it can be
140
Walter F. Stafford and Todd M. Schuster shown that the concentration distribution for a homogeneous DNA sample is given by c = Co e x p [ - (r
-
(39)
~.)2/2o2],
where Cois the concentration at the center of the band, c is the concentration at a distance r - r from the band center, and cris the standard deviation of the band. The gradient is calibrated with DNA samples of known buoyant density. The buoyant density of DNA can be measured to within a few parts in 104. With suitable calibration one can also determine the molecular mass of the banded material from the standard deviation and position of the band. The reader is referred to the article by Hearst and Schmid (1973), and references therein.
VI. Viscosity Measurements A. T h e o r y Viscosity is a measure of the amount of energy, dissipated as heat, that is required to maintain a constant rate of flow of a liquid in a capillary tube. Poiseuille's law of capillary flow (see below) applies to laminar flow in which the liquid at the edges of the capillary is stationary and the flow at the center is maximum. This leads to a parabolic profile of flow velocities between the wall and the center of the capillary. The velocity gradient results from attractive forces between adjacent volume elements, which must be overcome by an applied force that causes the liquid to flow. The flow velocity profile is given by u(r) = (P/4l~q)(a 2 -
(40)
/,2),
where u(r) is the velocity at radius r, P is the pressure difference between the inlet and outlet of the capillary, a is the radius if the capillary, r is the radial position measured from the center of the capillary, l is the length of the capillary, and ~/is the viscosity of the solution. Poiseuille's law is expressed in terms of the volume flow rate and is arrived at by integrating over the cross-sectional area of the capillary: 1rP
U = -~
~ra
=o
(a2 - r2)r dr -
vrPa 4
817/
(41)
The outflow time for a given volume of solution is proportional to the viscosity, ~/, of the liquid. A particle or macromolecule suspended in the viscous m e d i u m will disturb the velocity gradient, resulting in a decrease in the overall flow rate of solution through the capillary. Einstein (1906) showed that for spheres the flow rate decreases in proportion to the volume fraction occupied by the spheres. Einstein's equation for spheres is ~/'= ~/0(1 + 2.5~b),
(42)
141
Chapter 3 Hydrodynamic Methods
where ~/' is the viscosity of the solution, ~/0 is the viscosity of the solvent, and q~ is the volume fraction of the solution occupied by the macromolecule. Note that ~/' is independent of the size of the sphere and, therefore, deviations from the value expected for a sphere indicate molecular asymmetry. For nonspherical particles we have the more general Einstein-Simha equation, ~/'= ~/o(1 + vq~),
(43)
where v is 2.5 for spheres. Simha (1940) showed that for a prolate ellipsoid of revolution at small flow velocities, v is given by v
-
j2
j2
15[ln(2J)- 3/2] + 5[ln(2J) - 1/2]
14
+ ~
(44)
15'
where J = a/b and a and b are the major and minor semiaxes, respectively, as defined in Fig. 2; for an oblate ellipsoid, v is given by v-
16 J 15 tan -1 J '
(45)
where now, J = b/a; these equations are valid only for J >> 1. Note that J in Eqs. (44) and (45) is equal to the inverse of p used in Eqs. (12) and (13) for Perrin's equations. Again, for the prolate ellipsoid, a is the axis of rotation, and for the oblate ellipsoid, b is the axis of revolution. The axis of revolution is in the numerator of the definition of J for each type of ellipsoid. The volume fraction occupied by the particles, q~, in terms of the concentration of the particles, is given by ~
ch = NCVh/M,
(46)
where c is the concentration in units of g cm -3 and v h is the effective hydrodynamic volume of the particle in units of c m -3 g-1 [see Eq. (47)] and is determined by the shape and hydration of the macromolecule. For a sphere, VHis given by Vh =
4"rrNR~ / 3 M +
(~lVO,
(47)
where Rs is the Stokes radius and (~1 is the number of grams of water bound per gram of protein. In the case of viscosity, (~1 includes e n t r a i n e d water as well as water that is tightly bound on the surface of the molecule.
B. E f f e c t o f S h e a r R a t e
At high flow velocities large asymmetric molecules will become oriented by the velocity gradient. Simha's equations are valid only in the limit of zero shear rate because they apply only under conditions wherein orientation is completely randomized by Brownian motion. Therefore, when one is studying very large asymmetric particles (such as DNA), measurements should be carried out at
142
Walter F. Stafford and Todd M. Schuster different flow rates; if the results are significantly different, they should be extrapolated to zero flow velocity.
C. Measurement of Viscosity Viscosity is most simply measured by determining the outflow time from a capillary viscometer as a function of solute concentration. The relative viscosity, ~/rel, is the ratio of the viscosity of the solution to that of the buffer at the same temperature and is defined by '/~rel = 77/770 =
t/t0,
(48)
where t is the outflow time for the solution and to is the outflow time for the buffer solution in which the solute is dissolved. The specific viscosity is defined as '/~sp = T l r e l -
1,
(49)
and the intrinsic viscosity is defined as the following limit: [r/] - lim (~/~p/C). c---*0
(50)
The outflow times are plotted as a function of concentration and the intercept taken as the outflow time, t 0, of the buffer. t = to + ac +
bc 2,
(51)
where a and b are empirical. Now, rearranging, we have t/to-
1 = 7qsp = a c / t o
+ bc2/to .
(52)
Thus, a plot of t / t 0 - 1 vs c gives the specific viscosity as a function of concentration. Compare this to the Huggins equation [Eq. (53)] below.
D. Variation of Viscosity with Concentration The most commonly used equation describing the concentration dependence of the viscosity is the Huggins equation (Huggins, 1942):
9qsp/C--~
[71] -}- k ' [ r / ] 2 c .
(53)
For a polydisperse system, the viscosity contribution from each species can be described with a corresponding Huggins equation so that we will have N
'~sp/C = ~ (['lJi]Ci q- k;['rli]2c2)/~ ci,
(54)
i=1
where the summation is carried out over all the macromolecular species. The reader is referred to J. T. Yang (1961) and Eisenberg (1976) for more detailed discussions of viscosity theory and measurement.
E. Molecular Mass Averages from Intrinsic Viscosity Measurements With the appropriate calibration, viscosity measurements can be used to determine various averages of molecular mass of unknown samples. For any series
Chapter3 HydrodynamicMethods
143
of like polymers of different size, an empirical relationship of the following form may be used: [771 = K ' ( M v ) a = K I ( M n ) a = K2(Mw)a.
(55)
For an ideal solution, the exponent a may be related to theory. However, in practice the value of the exponent depends on the solvent conditions and must be determined empirically in each case for the most reliable results. Equation (55) could be used to determine the molecular mass and polydispersity of a protein solution in a denaturing solvent, for example, concentrated guanidinium chloride or urea.
F. Types of Viscometers Viscosity measurements are usually carried out using capillary viscometers in a thermostatted water bath. Either a Cannon-Fenske or Ubbelohde type capillary viscometer is employed. Another type of viscometer, the Couette rotating viscometer consisting of two concentric cylinders, one stationary and the other rotating, can also be used. One of the problems often encountered with viscosity measurements is adsorption of material to the capillary walls, resulting in a decrease in the effective diameter of the capillary. This problem can be identified and dealt with by making measurements on the solvent both before and after the measurements of the protein solution. If Eq. (51) is used to plot the outflow times, the intercept can be used to determine the correct value of to in the presence of adsorption, assuming the degree of adsorption is not concentration dependent. Another potential problem is the presence of dust or very large aggregates in the solution. Solutions should be passed through an appropriately sized filter or centrifuged before viscosity measurements are carried out.
VII. Resources An E-mail server has been set up to discuss Reversible Associations in Structural and Molecular Biology. The establishment of the discussion group was an outgrowth of a meeting by the same name held at the University of Melbourne, Australia, in February, 1994. The E-mail server is located at the Boston Biomedical Research Institute, Boston, Massachusetts. Contact RASMB E-mail server:
[email protected]. National Analytical Ultracentrifugation Facility, Biotechnology Center, University of Connecticut, Storrs, Connecticut 06268.
References Bevington, P. R., and Robinson, D. K. (1992). "Data Reduction and Error Analysis for the Physical Sciences" 2nd Edition. McGraw-Hill, New York. Bridgman, W. B. (1942). Some physical chemical characteristics of glycogen. J. Am. Chem. Soc. 64, 2349-2356. Cann, J. R. (1970). "Interacting Macromolecules." Academic Press, New York.
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Walter F. Stafford and Todd M. Schuster Cann, J. R., Coombs, R. O., Howlett, G. J., Jacobsen, M. P., and Winzor, D.J. (1994). Effects of molecular crowding on protein self-association: A potential source of error in sedimentation coefficients obtained by zonal ultracentrifugation in a sucrose gradient. Biochemistry 33, 10185-10190. Cohn, E. J., and Edsall, J. T. (1943). "Proteins, Amino Acids and Peptides." Hafner, New York. Durchschlag, H. (1986). Specific volumes of biological macromolecules and some other molecules of biological interest. "Thermodynamic Data for Biochemistry and Biotechnology." SpringerVerlag, New York. Einstein, A. (1906). A new determination of molecular dimensions. Ann. Phys. (Leipzig) [4] 19(4), 289-306. Eisenberg, H. (1976). "Biological Macromolecules and Polyelectrolytes in Solution." Oxford University Press (Clarendon), Oxford. Garcia de la Torre, J., and Bloomfield, V. (1981). Hydrodynamic properties of complex, rigid, biological macromolecules. Theory and applications. Q. Rev. Biophys. 14, 18-139. Garcia de la Torre, J., Navarro, S., Lopez Martinez, M. C., Diaz, F. G., and Lopez Cascales, J. J. (1994). HYDRO: A computer program for the prediction of hydrodynamic properties of macromolecules. Biophys. J. 67, 530-531. Gilbert, G. A. (1955). Discuss. Faraday Soc. 20, 68. Gilbert, G.A. (1959). Sedimentation and electrophoresis of interacting substances. I. Idealized boundary shape for a single substance aggregating reversibly. Proc. R. Soc. London, Ser. A 250, 377-388. Gilbert, G. A., and Jenkins, R. C. L. (1959). Sedimentation and electrophoresis of interacting substances. II. Asymptotic boundary shape for two substances interacting reversibly. Proc. R. Soc. London, Ser. A 253, 420-437. Goldberg, R. J. (1953). Sedimentation in the ultracentrifuge. J. Phys. Chem. 57, 194. Hearst, R. E., and Schmid, W. (1973). Density gradient sedimentation equilibrium. In "Methods in Enzymology." (C. Hirs and S. Timasheff, eds.), Vol. 27. Academic Press, New York. Huggins, M. L. (1942). Viscosity of dilute solutions of long-chain molecules. IV. Dependence on concentration. J. Am. Chem. Soc. 64, 2716- 2718. Johnson, M. L. (1994). Use of least squares techniques in biochemistry. In "Methods in Enzymology." (M. L. Johnson and L. Brand, eds.), Vol. 240, Academic Press, San Diego. Kirkwood, J. G. (1949). The statistical mechanical theory of irreversible processes in solutions of flexible macromolecules. Recl. Trav. Chim. Pays-Bas 68, 649-660. Kratky, O., Leopold, H., and Stabinger, H. (1973). The determination of partial specific volume of proteins by the mechanical oscillator technique. In "Methods in Enzymology." (C. Hirs and S. Timasheff, eds.), Vol. 27, pp. 98-110. Academic Press, New York. Lamm, O. (1929). Die Differentialgleichung der Ultrazentrifugierung. Ark. Mat., Astron. Fys. 21B(2). Martin, R. G., and Ames, B. N. (1961). A method for determining the sedimentation behavior of enzymes: Application to protein mixtures. J. Biol. Chem. 236, 1372-1379. Meselson, M., and Stahl, F. W. (1958). The replication of DNA in Escherichia coli. Proc. Natl. Acad. Sci. U.S.A. 44, 671. Meselson, M., Stahl, F. W., and Vinograd, J. (1957). Equilibrium sedimentation of macromolecules in density gradients. Proc. Natl. Acad. Sci. U.S.A. 43, 581-588. Perkins, S. J. (1986). Protein volumes and hydration effects. Eur. J. Biochem. 157, 169-180. Perrin, F. (1936). Mouvement Brownien d'un ellipsoide (II). Rotation libre et depolarization des flourescences. Translation et diffusion de mol6cules ellipsoidales. J. Phys. Radium 7(7), 1-11. Roark, D. E., and Yphantis, D. A. (1969). Studies of self-associating systems by equilibrium ultracentrifugation. Ann. N.Y. Acad. Sci. 164(1), 245-278. Schachman, H. K. (1959). "Ultracentrifugation in Biochemistry." Academic Press, New York. Siegel, L. M., and Monty, K. J. (1966). Determination of molecular weights and frictional ratios of proteins in impure systems by use of gel filtration and density gradient centrifugation. Application to crude preparations of sulfite and hydroxylamine reductases. Biochim. Biophys. Acta 112, 346. Simha, R. (1940). The influence of Brownian movement on the viscosity of solutions. J. Chem. Phys. 44, 25- 34. Stafford, W. F. (1992a). Methods for obtaining sedimentation coefficient distributions. "Analytical Ultracentrifugation in Biochemistry and Polymer Science," Chapter 20. (S. E. Harding, A. J. Rowe, and J. C. Horton, eds.), Royal Society of Chemistry, Cambridge, UK.
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Stafford, W. F. (1992b). Boundary analysis in sedimentation transport experiments: A procedure for obtaining sedimentation coefficient distributions using the time derivative of the concentration profile. Anal. Biochem. 203, 295-301. Stafford, W. F. (1994a). Sedimentation boundary analysis of interacting systems: Use of the apparent sedimentation coefficient distribution function. "Modern Analytical Ultracentrifugation: Acquisition and Interpretation of Data for Biological and Synthetic Polymer Systems." (T. M. Schuster and T. M. Hare, eds.), Birkhaeuser, Boston. Stafford, W. F. (1994b). Boundary analysis in sedimentation velocity experiments. In "Methods in Enzymology." (M. L. Johnson and L. Brand, eds.), Vol. 240, pp. 478-501. Academic Press, San Diego, CA. Svedberg, T., and Pederson, K. O. (1940). "The Ultracentrifuge." Oxford University Press, New York. Tanford, C. (1961). "Physical Chemistry of Macromolecules." Wiley, New York. Teller, D. C. (1973). Characterization of proteins by sedimentation equilibrium in the analytical ultracentrifuge. In "Methods in Enzymology." (C. Hirs and S. Timasheff, eds.), Vol. 27, pp. 346-441. Academic Press, New York. Traube, T. (1899). Samml. Chem. Chem.-Tech. Vortr. 4, 255. Williams, J. W., Van Holde, K. E., Baldwin, R. L., and Fugita, H. (1958). The theory of sedimentation analysis. Chem. Rev. 58, 715-806. Winzor, D. J. (1969). Analytical gel filtration. In "Physical Principles and Techniques of Protein Chemistry" (S. J. Leach, ed.), pp. 451-495. Academic Press, New York. Yang, J. T. (1961). The viscosity of macromolecules in relation to molecular conformation. Adv. Protein Chem. 16, 323-400.
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GLOSSARY* Atmospheric pressure ionization (API) Process by which ions are formed at atmospheric pressure from liquid samples. Average mass The mass of an ion, calculated using the isotopically averaged atomic mass of each element (e.g., C = 12.0112, H = 1.0080, O = 15.9994). Capillary electrophoresis (CE) A separation technique that fractionates based on charge and size of the analytes (electrophoretic mobility). The sample is loaded onto a capillary previously filled with a suitable electrolyte, and an electric field of several h u n d r e d volts/centimeter is applied to separate compounds. Chemical ionization (CI) Ionization of a neutral species by an ionized reagent species in the gas phase. This usually involves the transfer of a proton from a gaseous Bronsted acid to the neutral species (M) to form a positively charged (M + H) + ion. In a similar w a y negative ions can be formed through deprotonation of the neutral species. * Parts of these definitions are taken from Price (1991). Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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Copyright 9 1995by AcademicPress, Inc. All rights of reproductionin any formreserved.
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Richard M. Capri01iand MarcJ.-F. Suter Under CID conCollision-induced dissociation (or decomposition) (CID) ditions a given projectile ion dissociates after interaction (collision) with a neutral target gas. The dissociation is caused by the partial conversion of translational energy of the projectile ion to internal energy.
Continuous-flow fast atom bombardment (CF-FAB) A continuous-flow liquid introduction system for fast atom bombardment ionization. This can be used as an LC/MS technique; a matrix containing up to 5% of a viscous solvent (e.g., glycerol) is allowed to flow at a rate up to 10/~l/min to a target within the high vacuum of the mass spectrometer. The target is bombarded with ions or atoms as in standard FAB. A sample can also be injected into the flowing matrix using a common HPLC rotary valve. Coulombic explosion This term refers to the decomposition of charged droplets. A charged droplet in a heated gas will continuously lose solvent through evaporation. Eventually the surface charge will increase to the point where the electrostatic repulsion of the charges will overcome the surface tension. This leads to the explosion of the primary droplet and the formation of smaller droplets. Deconvolution A mathematical algorithm used in electrospray mass spectrometry to translate the spectrum of multiply charged ions (typically in the m/z range of 1-4000) into a spectrum of the molecular species (1-100,000 Da). Desorption
The process through which solid or liquid molecules are transferred into the gas phase. This transition is caused by the input of a large amount of energy into a solid or liquid sample. Examples are FAB, SIMS, PD, and MALD.
Direct liquid introduction (DLI) The direct coupling of LC to an ion source, through a very small orifice. The LC solvent acts as a chemical ionization reagent for the eluting analytes. Electron ionization (EI)
Ionization of a neutral species by electrons in the
gas phase: M + e---*M + +2eEleetronvolt (eV) A unit of energy equal to the kinetic energy a single electron acquires accelerating through a potential difference of I V. 1 eV = 1.6 x 10-19 J
Electron trap {trap}
Device found in EI sources; it is the target for electrons emitted from the filament. The current produced is measured and a decrease of this trap current indicates malfunctioning of the ion source, e.g., due to contamination.
Electrospray (ES) ionization The process of generating ions, usually multiply charged, from a spray of fine droplets in a high-voltage electric field at atmospheric pressure. Generally, it effectively increases the mass range of any mass spectrometer because these instruments measure m/z ratios, where m is mass and z is the number of charges on the molecule. The electrospray process is also used for the preparation of thin and homogeneous sample coatings on metal targets (e.g., for PD).
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Electrostatic analyzer (ESA) An ESA allows the separation of ions having different m/z values according to their kinetic energy. It is a directional focusing device, i.e., it brings diverging ions of equal kinetic energy to a common focus. Fast atom bombardment (FAB) The process of forming ions by bombarding a liquid sample with high-energy atoms, usually argon or xenon. The sample is mixed with a viscous solvent such as glycerol. Flow injection analysis ing liquid carrier.
The injection of a sample into a continuously flow-
Focus Ion optics are similar to light optics, and in that sense, a magnetic sector transforms a diverging ion beam into a converging ion beam. The point at which the converging ion beams intersect is called the focal point. Fourier transform mass spectrometry (FTMS) ICR mass spectrometers can use Fourier transform techniques to preselect, detect, and eject ions. Ions on stable trajectories within an ICR cell will induce an image current (in detection plates). The frequencies of motion of ions are an inverse function of mass. Fourier transform analysis will allow the extraction of these frequencies from the frequency of the image current. Different ion species can be selectively ejected by applying to the excitation plates a high-frequency pulse that is a function of the respective cyclotron frequencies of the ions. Full width at half maximum (FWHM) An expression used for measuring the resolving power of a mass spectrometer by measuring the peak width at 50% signal intensity (see Resolution). A separation technique for volatile organic Gas chromatography (GC) compounds in which fractionation is based on interaction with a stationary phase. Helium or hydrogen is often used as the mobile phase (carrier gas).
High-performance liquid chromatography (HPLC) A separation technique based on the interaction and partitioning of molecules between a liquid and a solid phase. A solvent delivery pump is used to give reproducible flow rates of the mobile phase within the HPLC column. Separation is affected by the choice of solvent and solid phase. Infrared spectroscopy (IR) A technique involving excitation of molecules to higher rotational and vibrational states. The amount of energy absorbed by a molecule to reach these higher states provides information about its functional groups and thus helps elucidate its structure. Ion cyclotron resonance (ICR) analyzer A device to determine the massto-charge ratio of an ion in a magnetic field by measuring its cyclotron frequency. Ion mirror An ion mirror reflects an ion beam. In a time-of-flight instrument, this ion mirror, also called a reflectron, compensates for initial energy spread in a packet of ions. Ionization potential The (first) ionization potential of a molecule X in the gas phase is the energy required for removal of the first electron: X ~ X + + eIsotachophoresis This method for preparative fractionation of molecular species differing only in net charge is also called steady-state stacking. It is an electrophoretic technique that can be performed in capillary tubes and gel rods,
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RichardM. Capri01iand MarcJ.-F.Suter slabs, or columns. The principles are similar to stacking of proteins in the upper gels used in certain forms of polyacrylamide gel electrophoresis (see Chapter 2 of this volume).
Joule (J) The standard unit of energy in SI units; equal to 1 newton-meter. Liquid chromatography (LC) See High-performance liquid chromatography. The force (F) experienced by an ion having a charge (z) movLorentz force ing in an electromagnetic field. F = z(E + v x B), where E represents the electric field strength and v x B is the vector product of the magnetic field strength B and the ion's velocity v.
Monodisperse aerosol generation interface for chromatography (MAGIC interface) In this LC/MS interface the LC effluent is forced through a small orifice and forms an aerosol that then is dispersed and undergoes desolvation. A m o m e n t u m separator separates lighter from heavier particles that then enter the MS, where they are ionized by EI or CI.
Magnetic sector analyzer (B) A magnetic sector analyzer allows the separation of ions having different m/z values according to their momentum. It is a directional focusing device, i.e., it brings diverging ions of equal m/z to a common focus. Mass defect
The difference between the mass of an atomic nucleus and its
mass number.
Mass spectrometer (MS) A device that assigns mass-to-charge ratios to ions based on their momentum, energy, cyclotron frequency, time of flight, or other parameters. Mass spectrometry/mass spectrometry (MS/MS) Also called tandem MS, uses two stages of mass analysis, one to preselect an ion and the second to analyze fragments generated by, e.g., collision-induced dissociation. With this technique it is possible to identify directly a single mass ion species out of a complex mixture of ions. Mass-to-charge ratio (m/z)
Mass spectrometers measure mass (m) as a function of the number of charges (z) an ion carries. Thus the signal of a singly charged ion of mass 100 will appear at the same position in the mass spectrum as a doubly charged ion of mass 200.
Matrix-assisted laser desorption (MALD) ionization An ionization technique in which sample molecules mixed in a UV or IR energy-absorbing matrix are desorbed and ionized by a short laser pulse. MALD mass spectrometry allows the detection of molecules with masses of several 100,000 Da, in combination with time-of-flight mass analyzers. Metastable ions
Ions that fragment during their flight from the ion source to the detector. They are often notated as m* and are found in mass spectra, acquired on magnetic sector instruments, as low-intensity, diffuse peaks, centered at m* = m2/ml, where ml is the initial mass that fragments to product ion m 2.
Moderator gas Used to reduce the motion of ions in an ion-trap mass spectrometer. Therefore, ions tend to accumulate in the center of the trap, where the
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electric field is best defined. This also increases the number of ions successfully ejected for detection.
Monoisotopic mass The mass of an ion, calculated using the exact mass for the most abundant isotope of each element (e.g., C = 12.0000, H = 1.0078, O = 15.9949). Nebulizing gas
A stream of inert gas used to convert a liquid solution to a distribution of droplets traveling with the gas.
Nominal mass The mass of a molecule or ion, calculated using integer numbers for the most abundant isotope of each element (e.g., C = 12, H = 1, O = 16). On-line reaction monitoring With this technique a reaction mixture is continuously infused into a mass spectrometer, using an ionization method compatible with liquid flow, e.g., CF-FAB or ES. For example, enzymatic digestions can be monitored continuously as a function of time. Particle beam (PB) An LC/MS interface based on the MAGIC interface, but using the thermospray technique for spray formation. Plasma desorption (PD) Desorption of sample molecules from a thin foil by impact from 252Cf fission fragments. q In instrument nomenclature, the designation of an rf-only quadrupole used as a collision cell in triple quadrupole and certain other mass spectrometers. A quadrupole used in rf-only mode is not mass selective.
Quadrupole analyzer (Q) A mass filter that uses a combined rf and dc field, applied to four parallel rods, to select ions of a certain m/z ratio. Radio frequency (rf)
Electromagnetic energy used to excite ions. For example, quadrupoles use a combination of rf and dc voltage to filter ions. The rf range is usually considered to span ---10 4 to --~3 • 1011 Hz. In the SI and CGS systems, 1 Hz is 1 cycle/sec.
Reflectron A reflectron is a device that acts as an ion mirror to compensate for initial energy spread of an ion packet and is found in high-performance time-of-flight instruments. Repeller
An electrically charged plate that aids in getting ions into the accelerating region of the MS.
Resolution For a single peak from singly charged ions at mass m in a mass spectrum, the resolution is expressed as m/Am, where &m is the width of the peak at some specified position on the mass peak, e.g., at 50% (FWHM). Rough pump
A mechanical vacuum p u m p that is capable of producing a (rough) vacuum of about 10-2 torr.
In SIMS, ions are generated by Secondary ion mass spectrometry (SIMS) bombarding a sample with high-energy ions, usually Cs+. The sample can be a solid or can be mixed with a viscous solvent such as glycerol.
Skimmer A skimmer is a cone with a small orifice, pointing toward a highpressure region. It allows selected sampling from a supersonic jet of liquid droplets or spray.
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Richard M. Caprioli and MarcJ.-F. Suter Soft ionization A general term referring to ionization techniques that initiate desorbtion and ionization of nonvolatile and thermally labile compounds, while causing minimal fragmentation. Examples are FAB, ESI, and MALD.
Thermospray (TSP) An ionization method also used as an LC/MS interface. The LC effluent is vaporized into a fine spray of droplets under reduced pressure by heating the liquid eluant. Complete evaporation of the solvent from the liquid droplets produces gas-phase ions from ionic compounds or from gas-phase CI. Time-of-flight analyzer (TOF) A TOF analyzer measures the flight times of ions; lighter ions traverse a given distance faster than heavier ions. The mass is proportional to the time squared. Flight times are converted to m/z values by calibration with compounds giving ions of known m/z values. Torr A unit of pressure, being that necessary to support a column of mercury one millimeter high at 0~ at standard gravity. One torr is equal to 1.33 mbars.
Trimeth3dsilyl (TMS) derivatives Used to increase the volatility of polar compounds containing groups such as alcohols and amines.
I. Introduction Technical advances in instrumentation and new methodologies have made mass spectrometry central to many problems in modern protein and nucleic acid research. These advances make it possible to determine molecular masses of large macromolecules conveniently, to accuracies approaching + 1 mass unit. This, in turn, makes it possible to observe posttranslational modifications of proteins, to confirm translational effects of mutagenesis, to sequence proteins, to assess macromolecule-macromolecule interactions, and much more ~ a l l by mass spectrometry and using small, and sometimes impure, samples. The utilization of mass spectrometry to investigate biological processes dates back to the late 1930s and early 1940s and the use of stable isotopes and isotope ratio mass spectrometers. These tools were essential in the work of Rudolph Schoenheimer and David Rittenberg, as well as others, in discovering the dynamic state of living organisms. Over the intervening decades, mass spectrometry continued to be of great utility in the elucidation of the structures of biological molecules through analysis of fragmentation patterns and accurate mass measurements. Complex mixtures of compounds that either were volatile or could be derivatized to enhance volatility could be analyzed by combined gas chromatography and mass spectrometry (GC/MS). In the early 1980s, there was a tremendous change in the utility of mass spectrometry for biological analyses; the reason for this renaissance was the introduction of new ionization techniques, including fast atom bombardment {FAB), plasma desorption (PD), and thermospray (TSP), that permitted the production of gas-phase ions from charged and polar compounds without prior chemical derivatization. These new ionization techniques not only saved sample preparation time and methodology development time, but made amenable to mass spectrometric analysis high-mass macromolecules that previously were not.
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Over the past decade or so, several other ionization techniques, including electrospray (ES) ionization and matrix-assisted laser desorption (MALD) ionization, have been introduced and have increased still further the use of mass spectrometry in biology. Today, substances in the 10 amol//~l range (10-17 mol//~l, i.e., about 10 -11 M) can be measured, and the molecular masses of proteins over 100,000 Da can be obtained at accuracies up to a thousand times greater than by gel electrophoresis. Of course, these capabilities are also the result of remarkable advances in analyzer technology and electronics, so that some of the modern, most powerful mass spectrometers are relatively small and easy to use. The goal of this chapter is to introduce modern mass spectrometry to readers who wish to obtain an overview and understand fundamentals. It is not intended to be a comprehensive review of the whole field or to cover all aspects of current mass spectrometry instrumentation and applications. Selected examples are used to illustrate particular areas, and are only a few of the many that could equally have been chosen. The emphasis of this volume, and therefore this chapter, is on biophysical methods involving peptides, proteins, and nucleic acids. A great deal of elegant and innovative work with carbohydrates, drugs, lipids, and many other molecules has not been included, but can be found in monographs that provide detailed descriptions of specific applications involving biological molecules and mass spectrometry (McCloskey, 1990a; Matsuo et al., 1994).
II. Instrumentation A. Basic Concepts A mass spectrometer is an instrument that produces ions and separates them in the gas phase according to their mass-to-charge ratio (re~z). Today a wide variety of mass spectrometers is available, ranging from benchtop detectors for gas chromatography to warehouse-sized instruments such as accelerator mass spectrometers. All of these share the capability to assign mass-to-charge values to ions, although the principles of operation and the types of experiments that can be done on these instruments differ greatly. Basically, a mass spectrometric analysis can be envisioned to comprise the following steps: ion detection/ Sample introduction ~ ionization ~ mass analysis ---* data analysis Samples may be introduced in gas, liquid, or solid states. In the latter two cases volatilization must be accomplished either prior to, or accompanying, ionization. Many ionization techniques are available to produce charged molecules in the gas phase, ranging from simple electron ionization (El) and chemical ionization (CI) to a variety of desorption ionization techniques, such as FAB, PD, ES, and MALD. Mass spectrometers are operated at reduced pressure in order to prevent collisions of ions with residual gas molecules in the analyzer during the flight from the ion source to the detector. The vacuum should be such that the mean free path length of an ion, i.e., the average distance an ion travels before colliding with another gas molecule, is longer than the distance from the source to the
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Richard M. Caprioli and MarcJ.-F. Suter detector. For example, at a pressure of 5 • 10-5 torr, the mean free path length of an ion is approximately 1 m, i.e., about twice the length of a quadrupole analyzer. Thus, the introduction of a sample into a mass spectrometer usually requires crossing a rather large pressure drop, and several means have been devised to accomplish this. Gas samples may be directly connected to the instrument and metered into the instrument via a needle valve. Liquid and solid samples can be introduced through a septum inlet or a vacuum-lock system. However, when connecting continuous-introduction techniques such as gas chromatography, high-performance liquid chromatography (HPLC), or capillary electrophoresis (CE), special interfacing becomes imperative to prevent excessive gas load. Once ions are formed, they can be manipulated by electrical and magnetic fields. The separation and detection of biologically relevant ions of different m/z ratios will be discussed in Section II,C.
B. Ionization
1. Electron and Chemical Ionization Volatile substances can be ionized by electron ionization in a process involving the interaction of the gaseous sample with an electron beam generated by a heated filament in the ion source (see Fig. 1). The electron energy (in electronvolts or joules) is determined by the potential difference between the filament and the source housing and is usually set to 70 eV (--- 1.12 • 10-17 J). A magnetic field keeps the electron beam focused across the ion source and onto a trap, which allows measuring the electron current through the ion source. On impact with a 70-eV electron, the gaseous molecule may lose one of its elec-
Repeller Filament
I
|
|
|
Magnet S N
S N
Vacc
Trap -"
9
9
Focus MS
Fig. 1 Schematicrepresentation of an electron ionization ion source: M represents neutral molecules; e-, electrons; M +, the molecular ion; F+, fragment ions; Vacc,accelerating voltage; and MS, the mass spectrometer analyzer.
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Chapter 4 Mass Spectrometry trons, becoming a positively charged radical ion, M + e----~ M + + 2 e - ,
where M + is termed the molecular ion. It carries an unpaired electron and can occupy various excited electronic and vibrational states. If these excited states contain enough energy, bonds will break and fragment ions and neutral particles will be formed. With an electron energy of 70 eV, enough energy is transferred to most molecules to cause extensive fragmentation. All ions are subsequently accelerated out of the ion source by an electric field produced by the potential difference applied to the ion source and a grounded electrode. A repeller, a positively charged plate, serves to push positively charged ions out of the ion source and into the accelerating field. In the case in which negatively charged ions are being analyzed, the repeller then would be negatively charged. Depending on the lifetime of the excited state, fragmentation will either take place in the ion source, giving rise to fragment ions, or on the way to the detector, producing metastable ions. If no fragmentation occurs before the ion strikes the detector, a signal for the molecular ion is generated. The mass spectrum obtained from recording all of these ions contains signals of varying m/z values and intensities, depending on the numbers of ions that reach the detector. The fragmentation pathways of the molecular ion depend on the structure of the molecule, such that similar structures give similar mass spectra. A special monograph is available for those wishing to learn more about ion fragmentation and the interpretation of mass spectra (McLafferty, 1993). Also, mass spectral databases are available today that contain over 160,000 spectra, which can be used to help identify unknowns and to search for common substructures. The sensitivity of 70-eV EI, as compared to other ionization techniques, varies widely because the signal arising from an analyte can be spread over many fragment ions. Fragmentation can be reduced by choosing an electron energy close to the ionization potential of the neutral molecule (typically 10-12 eV for simple organic molecules), but fewer ions are produced. Chemical ionization relies on the interaction of the molecule of interest with an ionized reagent species. Many such reactants are gaseous Bronsted acids. For example, some of the most widely used reactant species are generated by EI from methane. The first ion formed is CH~-, which then reacts to give the Bronsted acid CH5 § according to the following reaction: CH~- + CH 4 --~ CH5 + + CH 3. If a neutral molecule M in the source has a higher proton affinity than CH4, the protonated species MH + will be formed in an exothermic reaction, M + CHs + ~ MH + + CH 4. The instrumentation used for CI is very similar to that used for EI. The major difference in the design of the source is that it is more gastight, so that the reactant gas is retained at higher pressures in order to favor ion/molecule reactions. The pressure inside the CI ion source is typically of the order of 0.1-1 torr. A wide variety of reagents have been reported in the literature, some of which lead to fragmentation [e.g., hydrogen (H2), for which the reactant ion is H3 +]. Other reagents give rise to mass spectra that, depending on the analyte,
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Richard M. Caprioli and Marc J.-F. Suter mainly show the protonated molecule [e.g., isobutane (C4H10) , for which the reactant ion is C4H9+]. Negative ions can be generated in a similar manner by a reaction involving an electron capture process (Harrison, 1992).
2. Plasma Desorption Mass Spectroscopy A breakthrough in the analysis of biomolecules came in 1974 with the introduction of plasma desorption mass spectroscopy (PDMS) (Torgerson et al., 1974). This technique u s e s 2s2cf fission fragments to desorb large molecules from a target. The target is made of a thin aluminum foil, often covered with a layer of nitrocellulose, to which a droplet of the sample solution is applied. The adsorption of proteins to nitrocellulose is believed to be based on hydrophobic interactions and allows salts to be washed off and chemical reactions to be carried out on the target. Alternatively, the sample can be electrosprayed directly onto Ni or A1 foil, a technique that is more effective for smaller peptides. Two atomic particles, e.g., 1~ and 144Cs, are produced by the spontaneous fission of 252Cf~ both leaving the center of mass in opposite directions. One causes desorption of the analyte and the other provides the start signal for the measurement. A time-of-flight (TOF) mass analyzer, described in Section II,C,3, is generally used for ion separation. The general arrangement of the instrument is shown in Fig. 2. Similar to other desorption techniques, cluster formation and multiple charging is observed. Suppression effects, i.e., the inability to ionize some molecules due to the presence of other compounds present, are also sometimes observed. PDMS has a reasonably good sensitivity with peptides and small proteins (5000-20,000 Da), and typically about 10 pmol is needed for molecular mass determinations of such a protein. Perhaps its major virtue is that it is a simple method, both easy to use with easily interpretable spectra, and well-suited for
-fig. 2 Plasma desorption ionization with a time-of-flight mass analyzer. (Reprinted with permission from Torgerson et al., 1974.)
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the protein chemist and others not expert in mass spectrometry who wish to utilize mass specific analyses in their research programs.
3. Fast A t o m B o m b a r d m e n t Fast atom bombardment (FAB) is another soft ionization technique, i.e., one that yields minimal fragmentation and that performs well for polar a n d thermally labile compounds (Barber et al., 1981). In a typical FAB analysis, the sample is dissolved in an appropriate matrix, a viscous solvent, in order to keep the sample in the liquid state. Some of the more common liquid matrices are glycerol, 1-thioglycerol, a mixture of dithiothreitol and dithioerythritol, 3-nitrobenzyl alcohol, and triethanolamine. Because of its low freezing point, one major role of the matrix is to keep the sample in a liquid state inside the highvacuum ion source. This matrix also reduces damage to the analyte caused by the high-energy bombarding particle. In FAB ionization, the sample droplet is bombarded with energetic atoms (Ar, Xe) of 8-10 keV kinetic energy. Ions (e.g., Cs +) can be used as the bombarding particle in a similar technique termed liquid secondary-ion mass spectrometry (LSIMS). The general process leading to the formation of the molecular ion is depicted in Fig. 3 and involves several different mechanisms, including ejection of preformed ions. The phase transition, i.e., the conversion of liquid sample to gaseous ions on bombardment, is believed to result from sputtering, a redistribution of momentum from the initial high-energy particle by way of a cascade of collisions within the matrix. Initially charged analyte molecules will be desorbed as such, whereas the formation of protonated molecular ions (M + H) § or other cationized species such as (M + Na) + in the positive ion mode, and (M - H)- in the negative ion mode, can be attributed to both gas-phase reactions and solution chemistry. Doubly charged ion species and dimeric cluster ions of the analyte are occasionally observed. The major
Fig. 3 Desorptionmechanism in fast atom bombardment ionization. A- represents an anion or a negatively charged ion and C+ represents a cation or positively charged ion. (De Pauw, E., Mass Spectrom. Rev., Copyright 9 1986John Wiley & Sons, Inc. Reprinted by permission of John Wiley and Sons, Inc.
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Richard M. Caprioli and Marc J.-F. Suter advantage of FAB is that it is easy and fast to operate, the spectra are simple to interpret, and the source is easily retrofitted on most mass spectrometers. However, one of the major disadvantages of the FAB technique is that it requires a high concentration of the organic liquid matrix (typically 80-95% glycerol), overall giving only moderate sensitivity. Cluster ions derived from the matrix itself can, in some cases, dominate the mass spectrum. In addition, damage to the matrix caused by particle bombardment gives intense chemical background. It has been shown that discrimination in ionization efficiency of one analyte over another, due to differences in hydrophobicity and surface activity, causes problems when analyzing mixtures especially in quantitative applications. In some cases, the matrix also directly reacts with the analyte, forming radical anions or causing reduction of the analyte. The desorption process also produces a great many sputtered neutral molecules in addition to ions. With the development of continuous-flow fast atom bombardment (CFFAB), several of the above-mentioned problems have been eliminated. Instead of applying the matrix with the sample to the probe tip, a probe was designed that continuously delivers sample solution to the target at flow rates of up to about 10/zl/min. As a consequence, less organic matrix is necessary to keep the sample liquid, which results in an increase in the signal-to-noise ratio due to lower chemical background. A major advantage of CF-FAB is its usefulness for flow-injection analysis and on-line reaction monitoring, as well as coupling to HPLC and capillary electrophoresis (discussed later in this chapter). [Additional details of the operation and applications of CF-FAB can be found in a specialized monograph (Caprioli, 1990).] Several mixtures have been reported for mass calibration in FAB MS. For low-mass applications, one can simply use the organic matrix clusters as an internal calibrant (e.g., glycerol [Glyn + H] + or [Glyn - H]-), where n is a positive integer. Cesium iodide clusters of the form [CSn+lIn] + give very stable signals up to 10,000 Da. For better accuracy, mixtures of different salts, nonionic surfactants, or even gold clusters ( A u n ) - , a r e preferred. Today, FAB is widely used on many different types of mass spectrometers for the analysis of polar compounds having molecular weights of less than about 5000.
4. Thermospray and Particle Beam Thermospray ionization was introduced in 1983 for the coupling of HPLC to a mass spectrometer at conventional flow rates (0.5 to 1.5 ml/min) (Blakley and Vestal, 1983). The effluent from the HPLC column is vaporized under reduced pressure by heating a stainless-steel tube of 0.10 to 0.15 mm inner diameter (i.d.) to 100-200~ depending on the solvents used, as shown in Fig. 4. The resulting supersonic jet contains small droplets that vaporize further due to the hot gas in this low-pressure region of the ion source. Complete evaporation of the solvent from the liquid droplets produces gas-phase ions, either from ionic compounds in the sample solution (analytes or clusters of analyte and charged particle) or from gas-phase chemical ionization when using an auxiliary filament or low-current discharge device. Ionization requires polar or charged species and volatile buffers; the filament arrangement is used for semivolatile
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Basic c o m p o n e n t s of a t h e r m o s p r a y ion source.
samples, and the discharge device is used for highly aqueous effluents. The temperature of the vaporizer is critical and has to be adjusted for a given solvent composition to give best results. Ions are drawn into the analyzer by electric fields and enter through an orifice of about 0.5 mm diameter. Thermospray is considered a soft ionization technique and induces only limited fragmentation of the analyte. The particle beam {PB) interface, derived from the monodisperse aerosol generation interface for chromatography {MAGIC interface), has elements in common with thermospray, but gives spectra with more fragment ions (Willoughby and Browner, 1984). Again, formation of an aerosol is the initial step, followed by dispersion caused by a gas stream (usually helium), and desolvation. In the original interface, a momentum separator then separates the lighter dispersion gas and vaporized solvent from the sample particles that have higher momentum, and finally, molecules enter the mass spectrometer ion source as a beam of particles. An EI source can be used to produce mass spectra that compare well to those recorded for prevaporized samples in conventional EI sources. The PB mass spectrum, however, has a relatively intense background at low mass due to the solvent, and this limits sensitivity. PB is less sensitive than thermospray or electrospray and is not well suited for the analysis of ionic components, high-molecular mass samples, and thermally labile compounds.
5. Electrospray Electrospray ionization has had a tremendous impact over the past few years on the use of mass spectrometry in biological research. It was the first method to extend the useful mass range of instruments to well over 50,000 Da. Although introduced in its present form in 1984, the technique goes back to investigations of the electrically assisted dispersion of liquids at the beginning of this century. In fact, a major discovery took place almost unnoticed in 1968, when Malcolm Dole and co-workers were able to bring macromolecules into the gas phase at atmospheric pressure (Dole et al., 1968). This was done by spraying a sample solution from a small tube into a strong electric field in the presence of a flow of warm nitrogen, to assist desolvation, and then measuring the ions by ion mo-
160
Richard M. Caprioli and Marc J.-F. Suter bility techniques. Further innovative experiments in this field led to the introduction of the ES ionization source (Yamashita and Fenn, 1984). Since then, a wide range of biomolecules has been investigated by ES. The sample is usually dissolved in a mixture of water and organic solvent, commonly methanol, 150isopropanol, or acetonitrile. It can be directly infused, or injected into a continuous flow of solvent, or can be contained in the effluent of an HPLC column or CE capillary. The ES source design is simple, with spray formation occurring in a highvoltage field, as shown in Fig. 5. In one proposed mechanism, ion formation is believed to result from an ion evaporation process, first proposed in 1976 (Iribarn and Thomson, 1976). The spray formation is caused by electrostatic dispersion, unlike thermospray, wherein the dispersion is caused by vaporization. Assisted by the heated bath gas (usually nitrogen), the droplets undergo declustering, losing solvent molecules in the process. This leads to an increasing charge density on the droplet surface that will eventually cause a coulombic explosion and formation of smaller droplets. After going through several such explosions the ion will be able to evaporate from the highly charged droplet, carrying a high number of charges. Ions thus formed at atmospheric pressure will then enter the first vacuum stage, where they undergo free jet expansion. A skimmer then samples the ions and guides them to the mass spectrometer. Spray formation is the crucial part of the ES technique. It is usually advisable to filter all the solvents, and high concentrations of electrolytes should be avoided because they can lead to electrical breakdown and unstable operating conditions. High flow rates, compatible with full-bore and microbore HPLC, can be accommodated today by using aids such as a heated nebulizing gas to assist spray formation. Often an organic solvent, sometimes referred to as sheath liquid, is added to the HPLC effluent via a coaxial arrangement to establish a more stable spray. It has been pointed out that the electrospray chamber can be considered an electrolysis cell, in which one half-cell reaction takes place at the stainless-steel needle/liquid interface, with transport of electrons via the power supply to the counterelectrode (positive mode), and transport of positively charged droplets and ions through the gas phase to the counterelectrode. This suggests the possibility of redox reactions occurring in the source, although under normal conditions this does not appear to be a major problem. For macromolecules, ions entering the mass spectrometer usually each have a high number of charges. Because mass spectrometers measure mass-tocharge ratios rather than simply mass, it is possible for high molecular mass molecules to carry a sufficient number of charges such that they fall within the m/z range of a quadrupole mass filter, typically m/z 2500 (see below). As shown in Fig. 6A, high molecular mass ions can have a wide distribution of charge states. Figure 6 shows the mass spectrum of horse myoglobin (mass 16951.5 Da) taken at low resolution, with charge states from + 12 to + 24 readily observed. By adding the mass of the number of protons that myoglobin carries (12, as one example), then dividing the total mass (16963.5 Da) by the number of charges (12), one can calculate the m/z corresponding to the + 12 charge state to be 1413.6. Usually, the process is reversed and the distribution of ions measured in the spectrum permits the calculation of the molecular mass of the original analyte from any two neighboring ions at m/z values m 1 and m2, with n 1 and n 2
Chapter 4 Mass Spectrometry
Fig. 5
Schematic
161
representation
of an electrospray
charges, respectively. If m I M
=
t/2 =
~
m2, and/'/2
r/l(m
I -
source.
--
m A) =
(m I -- mA)/(m
nl - 1, then r/2(m 2 -
2 -
ml) ,
mA) ,
(1) (2)
where M represents the molecular mass of the uncharged molecule and m A is the mass of the charged adduct A (e.g., H +, Na +, NH4 § Thus the equations can be solved to give both n 2 and M. The measurement of the charge state distribution of large molecules is not always easy or reproducible because it can readily be influenced by relatively small changes in analysis conditions, changing pH, adding solvents or salts, partial denaturation of the protein, breaking disulfide bonds, etc. Further details are given later in specific applications. If high-resolution capabilities are available, one can in suitable cases resolve the individual carbon isotope peaks of a given charge state. Figure 6B shows the
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 6 Electrospray spectrum of horse myoglobin (16,951.5 Da); (A) multiply charged ion distribution from + 12 to + 24 shown at low resolution; (B) the + 17 charge state at a resolution of about 15,000, showing the resolved isotope peaks. (Reprinted with permission from A. R. Woolfitt, Fisons Instruments, Manchester, England.)
Chapter4 Mass Spectrometry
163
high-resolution ES ion distribution of a single charge state of horse myoglobin. Because isotope peaks are approximately whole integer m/z units apart in singly charged ions, whereas in Fig. 6B they are approximately 0.06 m/z units apart, then these ion species are in the + 17 charge state. The average molecular mass of the protein can then be easily calculated. The attainable mass accuracy for measuring molecular masses of biomolecules with ES on a magnetic sector instrument is typically about 0.001-0.005% and somewhat better when using internal calibration. Common calibration compounds are nonionic surfactants (with sodium adducts) or the different charge states of standard proteins. Electrospray has been used in conjunction with all common mass analyzers. One advantage of ES over PD and MALD is that, as a consequence of the multicharging phenomenon, the instrument can be calibrated in the low m/z range, using singly charged calibrants with known exact masses. Major disadvantages are that spray formation is adversely affected even by moderate buffer and salt concentrations, and that mixtures of high mass samples can give overlapping charge-state distributions that may be difficult to assign to individual components. Another atmospheric pressure ionization technique, termed ion spray, basically works in a manner similar to ES, but the ion spray formation is initiated by a nebulizing gas. Although both techniques give qualitatively the same results, ES and ion spray each appear to have some unique advantages in specific applications. Ion spray, for example, has been used more successfully to study noncovalent interactions, probably because of its ease of use with 100% aqueous solutions. This aspect is discussed in more detail below in Section IV.
6. Matrix-Assisted Laser Desorption The use of lasers in mass spectrometry goes back to the early 1960s. A wide range of wavelengths, from UV to IR, have been used with many different types of mass spectrometers for isotope measurements, elemental composition analysis, and pyrolysis of small organic and inorganic molecules. A major breakthrough came in 1988 with the introduction of MALD (Karas and Hillenkamp, 1988), a technique now able to detect macromolecules over 300,000 Da. The technique involves embedding the analyte in a solid matrix that absorbs energy at the wavelength of the laser. Common matrices are listed in Table I. The actual mechanism of MALD, a combination of desorption and ionization, is still being investigated. One hypothesis proposes a hydrodynamic model for the desorption of matrix and embedded biomolecules. The laser energy absorbed by the matrix, typically on the order of 106 W / c m 2, leads to intense heating and generation of a plume of ejected material that rapidly expands and undergoes cooling. Generation of ions is believed to arise through ion/molecule reactions in the gas phase. However, depending on the matrix used, enough energy can be transferred to the molecule to break weak bonds. Generally, the [M + HI + ion, or [M + Na] +, [M + K] +, etc., is preferentially formed in the positive ion mode, and the [M - H]- ion is in the negative ion mode. However, the technique also generates low intensity singly and multiply charged ion clusters, an undesirable situation in that these tend to complicate the spectrum. Mass resolution obtainable with MALD is highest when using laser power close to the threshold level required to produce ions from the solid sample, i.e., at low signal strength.
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Richard M. Caprioli and Marc J.-F. Suter
Table I MALD MS Matrices
Matrix 3-Aminoquinoline 2-Amino-4-methyl-5-nitropyridine 2-Amino-5-nitropyridine 6-Aza-2-thiothymine Caffeic acid a-Cyano-4-hydroxycinnamic acid 2,5-Dihydroxybenzoic acid 2,5-Dihydroxybenzoic acid and fucose (1 : 1) Ferulic acid Glycerol with rhodamine 6G (0.1 M) 2-(4-Hydroxyphenylazo)benzoic acid 3-Hydroxypicolinic acid Nicotinic acid 3-Nitrobenzyl alcohol 3-Nitrobenzyl alcohol with rhodamine 6G 3-Nitrobenzyl alcohol with 1,4-diphenyl-l,3-butadiene (0.1 M) 2-Pyrazinecarboxylic acid Sinapinic acid Succinic acid
Analytes
Laser wavelength (nm)
Polysaccharides, proteins Proteins, oligonucleotides Oligonucleotides Proteins, gangliosides Proteins, oligonucleotides Proteins, oligosaccharides Proteins, oligosaccharides, oligonucleotides, sulfonic acids Proteins
337, 355 355 355 266, 337, 2940 337, 10,600 337 337, 355, 2940a
Proteins, oligonucleotides Proteins Proteins, gangliosides, industrial polymers Oligonucleotides, glycoproteins, proteins Proteins, glycoproteins, oligonucleotides Proteins Proteins
337, 355, 488 532 266, 337
Proteins
337
Proteins Proteins, industrial polymers Proteins
266 337, 355 2940,a 10,600~
337
266, 308, 355, 337 266 266 532
On poly(vinylidene fluoride).
MALD produces a relatively intense matrix background, generally below
m/z 1000, that can be minimized electronically. This chemical background depends on the matrix and laser wavelength chosen. Calibration of the instrument can be accomplished either using internal standards of similar chemical behavior or by using an external calibration. A mass accuracy of + 0.01% (+ 1 Da at a molecular mass of 10,000 Da) is the best that can be achieved under favorable conditions with modern commercially available instruments. In practice, other factors contribute to error in mass measurement accuracy. For example, many of the proteins used as internal standards for calibration have not been rigorously characterized. Errors in their molecular masses can be caused by errors in sequence, chemical changes in side chains, imbedded molecules (such as phosphate and sulfate) from sample preparation, or covalently attached small molecules (such as acyl groups, metal cations, etc.), and other changes due to sample workup procedures. Nevertheless, MALD is a very fast and sensitive technique, implemented on small, relatively inexpensive instruments that do not require extensive expertise in mass spectrometry. Such instruments are ideally suited to biological scientists who need molecular mass information more quickly and more accurately than can be obtained by gel electrophoresis.
165
Chapter 4 Mass Spectrometry C. Mass Analysis 1. S e c t o r I n s t r u m e n t s
The first mass spectrometers were built in the early 1900s. J. J. Thomson (1913) used fixed magnetic and electric fields to separate ions of different mass and energy and was able to prove that the noble gas Ne was composed of two different isotopes of masses 20 and 22 Da, providing the final proof of the atomic theory of matter. To distinguish between the two Ne isotopes, Thomson made use of the different behavior of charged particles of varying momentum and energy in an electromagnetic field. An ion that is accelerated out of the ion source acquires the kinetic energy Eki n -- zWac c =
mv2/2,
(3)
where Vacc represents the potential difference that defines the acceleration region, m is the ion mass, z is the charge of the ion, and v is the ion velocity. When entering a homogeneous magnetic field on a trajectory perpendicular to the magnetic field strength B, the ion experiences the Lorentz force (F) that is perpendicular both to B and v. The resulting trajectory of the ion in the magnetic field is a circle with a radius r, because the Lorentz force just balances the centrifugal force, F = z v B = m v 2/r.
(4)
Thus, one obtains the relationship between the m / z value of an ion and the magnetic field strength, m/z
= r2B2/2Wacc .
(5)
On a magnetic sector instrument, r is a fixed value that is given by the geometry of the magnet and Vaccis usually kept constant during the acquisition of a mass spectrum by scanning the magnetic field strength B in a reproducible manner. This implies that at constant Vacc the magnetic field strength B has to be adjusted (scanned) in order to transmit ions of different m / z values successively through a magnet of radius r (see Fig. 7A). Another effect of a magnetic sector field is to focus a diverging ion beam, i.e., it acts as an ion optical lens. For that reason a magnetic sector field is called a directional focusing device. However, ions of the same mass, but having different energies, will not be focused at the same point. Thus, to improve the focusing, i.e., improve the resolution of the mass spectrometer, a device termed an energy analyzer is placed in the ion optic pathway, often before the magnet. Such an energy analyzer, also called an electrostatic analyzer (ESA), as shown in Fig. 7B, commonly consists of two concentric cylindrical electrodes. The ESA is a directional focusing device, but ions of different energy will still have different foci. However, an ESA and magnetic sector can be combined so that a diverging beam of ions with different kinetic energy can be focused, i.e., diverging ions of the same m / z but different velocities are focused at the same point. We can derive the equation for the ESA radius by equating the electrical force z E to the centrifugal force: r = mv2/zE
= 2Vacc/E.
(6)
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 7 (A) Ion trajectories in a magnetic sector field. The magentic field, B, is perpendicular to the plane of the page. (B) Trajectories of positive ions in an electrostatic analyzer, where V is the voltage applied to the sector plates, E is the focal point of ions with low energy, and dE is the energy spread of the ion beam. (C) Schematic representation of a double-focusing mass spectrometer (not drawn to scale). Lines marked A and B are lines of focus for direction and energy, respectively, and the point of double-focusing is where A and B cross. The c o m b i n a t i o n of an ESA a n d m a g n e t i c sector, then, is b o t h d i r e c t i o n (line A in Fig. 7C) a n d e n e r g y (line B in Fig. 7C) focusing, a n d is for t h a t r e a s o n called d o u b l e - f o c u s i n g at the i n t e r c e p t of lines A a n d B. S u c h a n a p p a r a t u s is c a p a b l e of a m a s s r e s o l u t i o n e x c e e d i n g 100,000. The r e s o l u t i o n R is d e f i n e d as R = m/Am,
(7)
Chapter4 Mass Spectrometry
167
where Am is the mass difference of two neighboring masses, m and m + Am, of equal intensity, with signal overlap of 10%. A resolution of 100,000 allows one to distinguish clearly an ion of mass 100.000 Da from one of mass 100.001 Da, or one of 100,000 Da from one of 100,001 Da, i.e., to 10 parts per million. Such accurate mass measurement at low mass can be used to obtain the empirical formula of an u n k n o w n ion, by determining the compatible combinations of carbon, hydrogen, nitrogen, and other atoms at the measured exact mass within the experimental uncertainty. Compared to an instrument that integrates the ion beam, i.e., records all of the ions all of the time, an instrument that scans the ion beam only records a fraction of the ions for each m/z generated. Thus, in the latter case at any given time, only one ion species is focused on the detector. As a consequence, rapid scanning will result in poor ion detection statistics, and hence poor signal intensity. Furthermore, most magnets require a short settling time after each scan to ensure return to the same starting field strength. Selected ion monitoring is one way to increase sensitivity by increasing the time spent recording ions of interest. In this method, the acceleration and ESA voltages are stepped with a fixed magnetic field to permit a few specific ions to pass in sequence, rather than scanning the magnet over the entire range. However, the ions to be monitored must be known in advance. Increased sensitivity and speed, but loss of spectral information, are the consequences. Another sensitivity-increasing technique is the use of array detectors that can simultaneously record a certain percentage of the mass range. Typically, these collect ions within 5-20% of the mass range simultaneously, but these devices are exceedingly expensive. Also, to record the entire mass range, these must be stepped in consecutive small ranges. The necessary geometry and size of high-resolution sector instruments depend on the mass range, sensitivity, and resolution that the analyst wishes to achieve. Some advantages, although not unique, are their relatively high mass range, sensitivity, and resolution, and their compatibility with a wide range of ionization techniques. The disadvantages are their size and cost compared to most other mass spectrometers.
2. Quadrupole Mass Filter and Quadrupole Ion Trap Instruments The basic principles of the quadrupole mass filter were published in the early 1950s by Paul and Steinwedel (1953). This instrument has now become one of the most widely used types of mass spectrometers because of its ease of use, small size, and relatively low cost. Mass separation in a quadrupole mass filter is based on achieving a stable trajectory for ions of specific m/z values in a rapidly changing electric field. An idealized quadrupole mass spectrometer consists of four parallel rods with hyperbolic cross-section as shown in Fig. 8 (left side). To one pair of diagonally opposite rods a potential is applied consisting of a direct current (dc) voltage and a radiofrequency (rf) voltage. To the other pair of rods, a dc voltage of opposite polarity and inversed rf voltage are applied. The potential ~b0 applied to opposite pairs of rods (see Fig. 8) is given by +~b0 = U + V c o s ~ t ,
(8)
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 8 Schematic representation of a quadrupole mass filter (left-hand side) and an ion trap (right-hand side), where q~0is the potential applied to opposite pairs of rods or end caps [see Eq. (8)].
where U is a dc voltage and V cos o~t is the time-dependent rf voltage in which V is the rf amplitude and ~o is the rf frequency. At given values of U, V, and ~o, only certain ions will have stable trajectories through the quadrupole. The range of ions of different m/z values, capable of passing through the mass filter, depends on the ratio of U to V. All other ions will have trajectories that are unstable (i.e., the ions oscillate perpendicular to the flight path with amplitudes that become greater than the dimension of the device) and hence will come in contact with the rods. The resolution of a quadrupole mass filter depends mainly on the ratio of U to V. One of the advantages of a quadrupole mass filter over a sector instrument is the low voltage applied to the ion source, i.e., the kinetic energy of the ions is on the order of 5-10 eV, compared with several kiloelectronvolts for a sector instrument. This eliminates high-voltage problems and makes interfacing to GC and LC easier. Other advantages are its good transmission efficiency, high scan speed, and wide acceptance angle to give high sensitivity. The quadrupole ion trap is based on the same principle as the quadrupole mass filter, except that the quadrupole field is generated within a threedimensional device consisting of a ring electrode and two end caps, as shown in Fig. 8. In the original design, the potential q~0was applied to the ring electrode and - q~0 was applied to the end caps (Fischer, 1959). With this arrangement, ions were detected with resonance techniques. As is the case with quadrupole mass filters, the quadrupole field is closest to the theoretical ideal in the center of the device. For this reason, a moderator gas such as helium is often introduced into the trap in addition to the sample, to dampen the oscillations of the ions and hence concentrate them in the center of the trap. As indicated by the name, the ion trap can store ions over a long period of time, making it possible to study gas-phase reactions. In particular, the ion trap has excellent MS/MS capabilities (see below). The mass range of commercial instruments is 650 Da, scanned at over 5000 Da/sec. By reducing the scan speed to 0.1 Da/sec, a resolution of 1.2 • 107 (full width at half maximum, FWHM) can be achieved. Also, under special conditions, a mass range of up to 45,000 Da and sensitivities in the attomole range have been obtained. The very high sensitivity of the ion trap is a consequence of the fact that all ions formed can in theory be detected. However, space charge effects (ion-ion Coulombic interactions) reduce the accuracy of mass assignment for an ion trap and limit the number of
169
Chapter 4 Mass Spectrometry
ions that can effectively be stored. Even though ion/molecule reactions take place within the trap, EI spectra obtained from an ion trap generally compare well to EI spectra acquired on quadrupole mass filters. The applications potential of the ion trap is very great. Size, speed, sensitivity, MS/MS capabilities, and compatibility with most ionization techniques favor further development of this mass analyzer. 3. T i m e - o f - F l i g h t
The time-of-flight mass spectrometer was first successfully used as an ion analyzer by Wiley and McLaren (1955). With the development of PDMS and later MALD MS, TOF analyzers have experienced a resurgence of use for instruments devised for the life sciences. Mass analysis in a TOF analyzer is based on the principle that ions of different m / z values have the same energy, but different velocities, after acceleration out of the ion source. Thus, the time required for each to traverse the flight tube is different: high-mass ions take longer to reach the detector than do low-mass ions. From Eq. (3), we can derive the expressions v = (2zVacc/m), 1/2
(9)
t = (m/2zVacc)l/aL,
(10)
for the velocity of an ion of mass m / z and the time, t, spent in the drift region of length L. A schematic drawing of the TOF mass spectrometer set up with MALD ionization is given in Fig. 9. With an accelerating voltage of 20,000 V and a drift tube of I m, a singly charged ion of mass 500 Da will have a velocity of approximately 9 • 104 m/sec and the time spent in the drift tube will be 1 • 10 -5 sec. From Eq. (10) a general equation relating the flight time of an ion with its m / z value can be derived: t = a ( m / z ) 1/2 4- b,
(11)
where a and b are constants for a given set of instrument conditions and are determined experimentally from flight times of ions of known masses. Several ionization techniques are suitable for TOF mass analyzers by which ions are generated or ejected from the ion source over very short periods of time. This can be achieved with a laser pulse, 252Cf fission fragments, and introduction of ions from continuous ionization sources (EI, ES, FAB, etc.) with pulsed deflection of an ion beam or pulsed extraction from an ion source. This pulse also gives the start signal for the data acquisition. From Eq. (10) it follows that m / z is proportional to t 2, which leads to the formula for resolution: r e ~ a m = (1/2)(t/At).
(12)
Modern linear TOF MS instruments are capable of attaining a resolution of 1000. A factor affecting ~instrument resolution is the time resolution of the detector and electronic circuitry, which with current technology is capable of handling a &t of a few nanoseconds. A major limitation in achieving high resolution is the consequence of the spread in time, space, and kinetic energy of the initial ion packet. The time difference in formation of two ions of the same
170
Richard M. Caprioli and Marc J.-F. Suter
Fig. 9 Schematic representation of a linear time-of-flight matrix-assisted laser desorption mass spectrometer.
mass caused, for instance, by the length of a laser pulse will remain the same during the flight to the detector. Increasing the flight time by reducing the acceleration voltage or increasing the length of the drift tube would lead to higher resolution, because &t would remain the same but t would become greater [see Eq. (12)]. Ions that are not formed at the same location, due to the thickness and dispersion of the sample on the target or width of the ion beam, will be accelerated to different kinetic energies. Also, ions can be generated with different initial kinetic energy. This spread in kinetic energy can be partially compensated by using a device called a reflectron, as shown in Fig. 10. Ions of higher energy will penetrate deeper into an electrostatic repeller field (ion mirror) and will be turned around and arrive at the detector at the same time as ions of lower initial energy that penetrate the field less. In a linear TOF (no reflectron), neutral and charged fragments generated through fragmentation of ions in the drift region cannot be distinguished from the original ion, because their velocity remains the same. Fragments of metastable ions generated prior to reflection have the same velocity as their parent ion, but a reduced energy and hence can be distinguished when spectra acquired in linear and reflectron mode are compared, due to their time difference. Reflectron TOF instruments are capable of a resolution of over 10,000. TOF analyzers have some special advantages. In contrast to sector instruments and quadrupoles, all ions accelerated out of the ion source of the TOF instrument will reach the detector, giving it a relatively high sensitivity. Of course, with pulse techniques, some dead time exists between pulses when ions are not being analyzed. Also, the mass range of TOF analyzers is virtually unlimited and any practical upper limit is dictated by the ionization process and by detector efficiency. The combinations of time-of-flight mass spectrometry with MALD, PD, and ES have produced effective tools in the laboratory of
Chapter 4 Mass Spectrometry
171
Fig. 10 Ion trajectories in a reflectron time-of-flight mass spectrometer, for two ions having an energy spread of dE.
biochemists, due to their relatively low cost, high sensitivity, and speed and ease of operation. 4. I o n C y c l o t r o n R e s o n a n c e M a s s S p e c t r o m e t r y The ion cyclotron resonance (ICR) mass spectrometer is based on technology developed in the 1950s, on Fourier transform techniques (Comisarow and Marshall, 1974), and on the development of external ion sources (McIver et al., 1985; Kofel et al., 1985). Like the ion trap, ICR MS is capable of storing ions within a cell. It consists of three pairs of parallel plates arranged as a cube, used for trapping, excitation, or detection, respectively, as shown in Fig. 11. The cell lies within a strong magnetic field that is perpendicular to the trapping plates. A trapped ion, having an initial velocity, v, will, according to Eq. (4), travel in a circular path of radius, r, r = mv/zB,
Fig. 11 Schematicrepresentation of an ion cyclotron resonance cell.
(13)
172
Richard M. Caprioli and Marc J.-F. Suter rotating with a frequency, o~, ~o = 2 v r / t = z B / m .
(14)
The frequency ~ois called the cyclotron frequency. The ion, kept within the cell by applying a dc voltage to the trapping plates, can remain trapped for hours, provided the pressure is ~ 10 -8 torr. According to Eq. (14), the cyclotron frequency is inversely proportional to the mass of an ion. Because of the initial spatial distribution of ions, an excitation pulse is applied prior to detection, so that all ions with identical cyclotron frequency absorb energy and move together coherently. This then induces a current in the detector plates (image current) that is proportional to the numbers of ions and m / z values of the excited ions. The decay of the image current is mainly caused by collisional damping and occurs more rapidly at higher pressure in the cell. An outstanding feature of ICR MS is the extremely high resolution that can be attained; for example, using electrospray ionization, a resolution of over 2 • 106 has been achieved. Another important feature of ICR MS is its MS/MS capability (see Section III,A), which makes it an important tool for fundamental research in gas-phase chemistry.
III. Combined Techniques A. T a n d e m M a s s Spectrometry Tandem mass spectrometry (Busch et al., 1988) uses two stages of mass analysis, one to preselect an ion and the second to analyze fragments induced, for instance, by collision with an inert gas such as argon or helium. The most common tandem MS instruments are the triple quadrupole (QqQ) (Fig. 12A), hybrid instruments (EBqQ) (Fig. 12B), and four-sector double-focusing instruments (EB-EB) (Fig. 12C). In this shorthand, Q represents a quadrupole mass filter; q, an rf-only quadrupole (collision chamber); E, an electric sector analyzer; and B, a magnetic sector. In the case of the low-energy triple quadrupole, an ion of interest generated in the ion source is preselected with the first mass filter Q1, collisionally activated in the collision chamber q with energies of up to 300 eV, and the fragmentation products are analyzed with the second quadrupole Q2. In this way it is possible, for example, to obtain sequence information from a peptide by selecting the ion corresponding to the intact peptide and analyzing the backbone fragments with Q2. The most common experiment is termed a "product ion" scan, but many other scans or analytical experiments can be performed. The major difference with four-sector MS/MS instruments is that preselection can be achieved at high resolution and collisions of up to 10,000 V energy are available, giving different fragmentation regimes and allowing higher masses to be analyzed. Trapping devices such as quadrupole ion traps and ICR mass spectrometers are not limited to simple MS/MS experiments, but can achieve multiple MS/MS/MS/. 9 9 measurements under optimal conditions. Using Fourier transform mass spectrometry techniques, a series of ions can be selected out of all ions present in the trap and can be activated for analysis by an appropriate radiofrequency pulse.
Chapter 4 Mass Spectrometry Q1 I-I,
173 q ,'='Z--
a)
E
Q2
B
~, ~\~,\~\
b) Q E
B
c)
E
B
Fig. 12 Tandemmass spectrometer configurations. (a) Triple-quadrupole (low energy) system,(b) hybrid system, and (c) high-performancemagnetic (high energy) system. The asterisks (*) denote the position of the collision cell. Details are given in the text.
B. Liquid C h r o m a t o g r a p h y / M a s s Spectrometry The combination of liquid chromatography and mass spectrometry (LC/MS) is perhaps the most powerful analytical tool available to the biological research laboratory involved in studying events at the molecular level. It can provide a wealth of information on individual compounds even when they are present in complex mixtures, including identification by molecular mass, structure through fragmentation, and quantitation. The combination is synergistic; better chromatographic information is obtained using an analyzer that is specific for a given m/z value, and also better mass spectrometry, because compounds in mixtures enter the spectrometer over time, maximizing the efficiency of ionization. With LC/MS, desalting and preconcentration techniques are easily employed, increasing the efficiency and sensitivity of the mass spectrometer. Most importantly, the integrated system minimizes sample handling loss and maximizes efficiency of analyses. Finally, the mass spectrometer allows stable isotopically labeled compounds to act as quantitative references in LC separations, providing the highest possible accuracy. However, all these advantages do not come without their costs. The LC/MS is a more complex instrument to operate and maintain, has limited column types because it cannot be operated with all buffers (e.g., phosphate buffers are particularly troublesome), and is relatively high in price. LC/MS has history dating back to the early 1970s, and has produced an interesting variety of "interfaces." These interfaces are required because the
174
RichardM. Caprioliand MarcJ.-F.Suter full-bore (4.6 m m i.d.) LC operates at about 1 m l / m i n flow rate, a microbore (1 m m i.d.) LC operates at about 100/~l/min, and a capillary bore (K 0.5 m m i.d.) LC operates at about I ~l/min. Even in the latter case a large amount of gas is produced on evaporation of the solvent unless an interface is placed between the LC and MS to eliminate the bulk of the solvent without eliminating the sample peak eluting off the column. Thus, interfaces such as direct liquid introduction (DLI), thermospray, particle beam, moving belt, and, more recently, continuous-flow FAB and electrospray, as well as others, were devised and have been shown to be successful to one degree or another, each often working best with particular types of compounds. It is difficult to overstate the effectiveness of LC/MS in solving problems of biological interest. The range of applications cover low to high mass, polar to nonpolar, and complex mixtures to purified compounds, all analyzed with a specificity unique to mass spectrometry. Additional details can be found in some recent reviews (Vestal, 1990; Caprioli et al., 1986; Caprioli, 1994).
C. Capillary Electrophoresis/Mass Spectrometry Capillary electrophoresis (CE) has become an important complement to HPLC because of its high separation efficiency and ability to separate molecules based on their charge in solution. The coupling of CE to a mass spectrometer (CE/MS) was first reported using an electrospray interface (Olivares et al., 1987), and several interfaces have been reported for coupling of CE to CF-FAB (Caprioli et al., 1989; Moseley et al., 1989). For the analysis of peptides in a tryptic digest, for example, one can vary the pH to effect better separations because the isoelectric points of the peptides vary widely. In one case, a 1-m (50 ~m i.d.) fused silica column nicely separated a peptide mixture using a 10 mM tricine, 45 mM morpholine, 20 mM NaC1 buffer at pH 7.9, with an applied voltage of 25 kV. However, for other digests, a simple 40 mM citrate buffer at pH 2.5 provided the required separation. The application of CE/MS to biological problems has just begun, and significant progress is expected. The technique does have some drawbacks, however. In the case of the ES interface, problems can arise from high buffer concentrations, a condition generally required for good CE performance. For CF-FAB, because ionization takes place at high vacuum, pressure-induced flow within the CE capillary can give nonoptimal performance. Also, sample size is limited to about 2% of the capillary volume if separation efficiency is not to be degraded. This can be overcome in some cases by on-column preconcentration techniques, e.g., isotachophoresis.
IV. Applications A. Determination of Molecular Mass Mass spectrometers measure mass-to-charge ratios of ions produced from molecules introduced into the ion source. For many ionization methods developed for mass spectrometry, the charge is generally (but not always) unity, so one
Chapter 4 Mass Spectrometry
175
often hears of measuring "mass" with this instrument, although this is not correct. Several newer ionization techniques routinely produce multiply charged ions, most notable among these being electrospray ionization. In the case of proteins, a wide distribution of charges usually is recorded for a single protein; for example, a 30,000-Da molecule may contain 20-30 or more charges, as described earlier in this chapter. Fortunately, these sequentially charged (m/z) states give peaks in the spectrum that can be mathematically processed (by deconvolution) to derive the original molecular mass of the molecule. The molecular mass of a compound can be expressed in several ways. The nominal mass of a molecule can be calculated using nearest whole integer atomic masses, i.e., C = 12 Da, H = 1 Da, O = 16 Da, N = 14 Da. Such a calculation is usually not useful in mass spectrometry other than to provide a "ballpark" estimation of molecular mass. Because hydrogen is the most abundant atom in most biological compounds and its exact mass is ---1.00782 Da, even relatively small molecules such as a protein of mass 10,000 Da will typically have 600-700 hydrogen atoms and thus show a mass shift 4 - 5 Da higher than one would calculate from nominal mass calculations. Thus, the monoisotopic molecular m a s s of a compound can be calculated from its molecular formula and exact atomic masses, i.e., C = 12.000 Da, H = 1.00782 Da, N = 14.0031 Da, O = 15.9949 Da, S = 31.9721 Da. Although this molecular mass calculation considers the m a s s d e f e c t s of atoms, it clearly does not take into account the presence of naturally abundant stable isotopes such as 13C, 2H, 180,15N, and 34S. Some of these isotopic abundances are high, e.g., 13C, which, on average in biological samples is about 1.11% of the abundance of the 12C atom. Thus, when these are accounted for, an isotopic pattern or distribution is produced that is centered at higher mass than that of the monoisotopic mass. Thus, the a v e r a g e m a s s of a molecule accounts for both atomic mass defect and stable isotope natural abundance. Finally, in the multiplet of isotopic masses making up the molecular ion distribution, the most abundant molecular mass ion is simply defined as the m/z peak with the highest intensity. To illustrate these concepts, consider the measurement of the molecular mass of bovine proinsulin (Cottrell and Frank, 1985), a small protein having the elemental formula C381H586N1070114S6 . The molecular mass distribution of the resolved isotope pattern is shown in Fig. 13A. Some interesting points can be made. First, the monoisotopic mass of this protein at 8676.15 Da has the lowest intensity of the isotope peaks shown in Fig. 13. At higher masses, e.g., 20,000 Da, the corresponding monoisotopic mass would be of very low abundance and typically not detectable. Second, as the molecular mass of a protein or other macromolecule increases, the mass width of the isotope distribution increases markedly; for bovine proinsulin, 11 different nominal (whole integer) mass peaks can be measured. At higher masses, say 100,000 Da, this isotope spread would extend over 40 Da. Further, each nominal mass is composed of many different isotopic species, with the more abundant ones shown in Table II for the bovine proinsulin example. Actually, the most abundant nominal mass at 8681 Da is composed of over 60 different isotopic species. In very special cases in which it is necessary to measure one or more of these individual isotopic peaks, instruments having high resolution capabilities must be used, and even so it is often not possible to resolve them all.
176
Richard M. Caprioli and Marc J.-F. Suter
100
A
90 -]
80t 70
o< 6o E 5oi
3o~ 2o~ 10 0
1! 00
8676
8678
8680
86'78
86'80
8682
8684
8686
8682
8684
8686
Mass
B
90
80 70
6O
--*-(_501 40 30 20, O
9
8676
Mass
Fig. 13
Molecular isotopic mass distribution for bovine proinsulin at resolutions of about (A) 10,000, and (B) 1000.
It s h o u l d b e c l e a r f r o m t h i s d i s c u s s i o n t h a t i n o r d e r t o m e a s u r e a u s e f u l v a l u e f o r t h e m o l e c u l a r m a s s o f a m o l e c u l e , it is n o t n e c e s s a r y t o r e s o l v e e v e n the isotopic masses that differ by one mass unit. Thus, the distribution given i n Fig. 13B a l s o s h o w s t h e m o l e c u l a r r e g i o n f o r b o v i n e p r o i n s u l i n , b u t a t m u c h l o w e r r e s o l u t i o n ( a b o u t 1000). H e r e , o n l y a s i n g l e b r o a d p e a k is p r o -
Table II Partial List of Isotopic Species for Nominal Mass 8681 from Proinsulin" %
Numbers of atoms
Mass
Abundance
12C
13C
1H
2H
14N
15N
160
170
180
32S
33S
34S
8681.16660 8681.17123 8681.17295 8681.17509 8681.17755 8681.17991 8681.18141 8681.18387 8681.18474 8681.18679
3 3 11 3 17 2 9 36 2 4
379 378 378 379 377 377 378 376 377 377
2 3 3 2 4 4 3 5 4 4
586 586 586 586 586 586 586 586 586 585
0 0 0 0 0 0 0 0 0 1
106 105 107 106 106 107 107 107 107 107
1 2 0 1 1 0 0 0 0 0
114 114 114 113 114 114 113 114 113 114
0 0 0 0 0 0 0 0 1 0
0 0 0 1 0 0 1 0 0 0
5 6 5 6 6 5 6 6 6 6
0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 0 0 0 0 0
" Data in daltons.
Chapter4 Mass Spectrometry
177
duced from an average of all the individual isotopic species. A calculation of the centroid of this peak provides an average mass of 8681.8 Da for this mass species of this protein, in this case precisely the value one obtains for the computed weighted average of the resolved isotopic peaks. Practically, however, one pays a high price to resolve the isotope pattern in terms of ion intensity. Often a high mass peak observable at low resolution disappears before the pattern is resolved as the resolution is increased, simply because ion intensity is drastically decreased as resolution is increased, sometimes to the point that too few ions are transmitted to produce a recordable signal. Mass spectrometric measurements of the molecular masses of proteins are usually performed under low-resolution conditions, i.e., where resolution is in the 200-2000 range. Today, these are most commonly performed with ES ionization on quadrupole instruments, and MALD on time-of-flight instruments. For ES MS, mass measurement accuracy is generally about + 0.005% in cases in which good signal strengths are produced, and for MALD MS, about 0.05%. Clearly, to calculate molecular masses from these measurements, isotope-averaged atomic masses of elements are used, giving average chemical masses for the molecules of interest. For low molecular mass measurements (for example, for molecules below 1000 Da), most often the nominal isotopes can be resolved and the monoisotopic mass is the most abundant. In this case, monoisotopic elemental masses should be used to calculate molecular mass.
B. Peptides Over the years, mass spectrometry has been used to analyze peptides in conjunction with ionization methods such as EI and CI after derivatization of the N- and C-terminal ends and reactive side chains in order to increase volatility. The beginning of important changes in mass spectrometry followed development of FAB ionization by Barber and co-workers (1981). This provided an easy and reliable means for direct analysis of underivatized polar and charged molecules. Today, additional ionization methods are available, notably ES and MALD, to complement FAB. These techniques are in heavy use today in biomolecular analysis, and each has some specific advantages for peptide analysis, as illustrated by examples in the following discussion.
1. Choice of Ionization Technique The major attractions of FAB for peptide analysis are that it is easy and rapid to use and the mass spectra produced are generally simple and easy to interpret, as discussed above. Although fragmentation is minor, some fragment ions can be of sufficient intensity to aid in verification of at least part of the sequence of the molecule. Figure 14 shows the positive ion FAB mass spectrum of the peptide, human luteinizing hormone releasing hormone (LHRH), whose protonated monoisotopic molecular ion appears at m/z 1182. Although the molecular species intensity is high, peptide backbone fragment ions are observed at only approximately 5-10% of [M + H] + in this spectrum, one of the better examples showing fragmentation. Generally, these fragment ions are not of sufficient intensity to enable full sequencing of a peptide of unknown structure. How-
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 14 FAB mass spectrum of the leutinizing hormone-releasing hormone (LHRH) peptide. ever with MS/MS techniques, fragmentation readily occurs and provides structural information. Sequence analysis of peptides will be considered in more detail below. The detection limit of standard FAB for molecular mass determination of most peptides is approximately 20 pmol. However, this amount varies significantly depending on the chemical and physical properties of the peptide. The upper mass limit that is considered routine is about 5000 Da, again depending on the peptide. For the calculation of molecular masses of peptides, either monoisotopic masses or average masses could be used, depending on the resolution of the instrument and the size of the peptide, as discussed earlier in this chapter. Table III lists the common amino acid residue masses, i.e., as they appear in a peptide. Molecular masses are calculated by summing these residue masses and adding the mass of the terminal groups, usually I D a (H) for the amino end and 17 Da (OH) for the carboxyl end. In positive ion FAB, the molecular species recorded is often [M + H] +, and so one additional dalton must be added for H +, or 23 Da for [M + Na] +, etc.
179
Chapter 4 Mass Spectrometry Table III Residue Masses for A m i n o Acids a
Amino acid
Single-letter abbreviation
Ala Arg Asn Asp Cys Glu Gln Gly His Ile Leu Lys Met Phe Pro Ser Thr Trp Tyr Val
A R N D C E Q G H I L K M F P S T W Y V
a
Monoisotopic Average mass mass 71.0371 156.1011 114.0429 115.0269 103.0092 129.0426 128.0586 57.0215 137.0589 113.0841 113.0841 128.0950 131.0405 147.0684 97.0523 87.0320 101.0477 186.0793 163.0633 99.0684
71.0788 156.1876 114.1039 115.0886 103.1448 129.1155 128.1308 57.0520 137.1412 113.1595 113.1595 128.1742 131.1986 147.1766 97.1167 87.0782 101.1051 186.2133 163.1760 99.1326
Data in daltons.
One of the drawbacks of FAB is the very poor sensitivity obtained with certain peptides, a consequence of their inability to be distributed adequately in the surface layers of the matrix (glycerol) droplet being b o m b a r d e d (Naylor et al., 1986). Thus, the surface layer m a y not be representative of the concentrations in the bulk sample. The problem, generically termed the ionization "suppression" effect, is a serious one in that quantitation can be quite difficult. Further, the absence of a signal does not necessarily prove that the peptide is not present in the sample. Continuous-flow FAB (CF-FAB) was developed to provide a means for introducing samples into the mass spectrometer directly in aqueous solutions, enhancing direct analysis by utilizing flow-injection techniques and providing continuous monitoring of dynamic systems (Caprioli, 1990). In using only 1 5% glycerol instead of > 90% glycerol (in the case of normal FAB), ions derived from the sample matrix, i.e., chemical background, become m u c h less abundant. In addition, the constant flow and refreshment of the surface layers of the target diminish the ion suppression effect significantly (but do not eliminate it in all cases). Figure 15 shows the molecular ion regions for a few picomoles of a peptide of molecular mass 1390.4 Da, analyzed both by standard FAB and by CF-FAB. Although this example is one of the best cases to illustrate the point, it nevertheless clearly shows one of the potential problems with conventional FAB. CF-FAB is significantly more sensitive than conventional FAB by some 20to 100-fold (Caprioli and Fan, 1986b), with detection limits in the 100 f m o l -
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 15 FAB analysis of an octapeptide of mass 1390.4 Da by (A) standard FAB, and (B) CF-FAB.
1 pmol range for most peptides. As with FAB, the upper mass limit is about 5000 Da for molecular mass determinations. Electrospray ionization has also been applied quite successfully to peptide analysis. Peptides ionized in this manner usually have only a few charges, typically 1 - 4 depending on their size, the frequency and relative position of residues with basic groups, the concentration of salts and other contaminants, etc. For a peptide of unknown molecular mass, if only one charged species is present, whether it be [M + H] + or [M + 3H] 3+, it is relatively easy to determine the number of charges by simply measuring the m/z position of the first 13C isotope peak. For example, a singly charged ion of a molecule of mass 1000.0 Da would be recorded in the spectrum at m/z 1001.0 ([M + H+]), with its 13C peak at m/z 1002.0; a doubly charged ion [M + 2H] 2+ of a molecule of mass 2000.0 Da would also appear at m/z 1001.0, but its 13C isotope peak would appear in the spectrum at m/z 1001.5; a triply charged [M + 3H] 3+ ion of a molecule of mass 3000.0 Da has a 13C isotope peak at 1001.33 Da; and so on. At higher molecular masses and greater numbers of charges, the mass increment of this isotope peak becomes too small to measure accurately with most commonly available instruments. This can be seen in the example given earlier (see Fig. 6) where myoglobin carries + 17 charges, and the isotope mass increment is 0.059 Da. In practice, it would be difficult to differentiate this experimentally from the + 18 charge state with an increment of 0.055 Da.
Chapter 4 Mass Spectrometry
181
Sensitivity of ES is quite good, with most practitioners obtaining 100 fmol detection levels for many peptides. In one case, a micro-ES ionization source has been developed to operate at low flow rates (about 0.5/~l/min) and has detection levels of 500 amol by flow injection methods and 100 amol//.d by constant infusion methods (Emmett and Caprioli, 1994). For ES the mass range is quite high, and the molecular masses of proteins over 50,000 Da can be measured. However, as with most ionization techniques, ion suppression effects exist and render direct analysis of complex mixtures inadvisable. Further, the ES ionization process can be susceptible to even low amounts of salts, which can significantly decrease sensitivity. The third technique that has been shown to be extremely useful in the analysis of peptides is MALD MS. It is extremely sensitive, being able to detect 10-100 fmol of peptide, or less. Because most MALD instruments use time-offlight analyzers, mass range is practically unlimited and the resolution is in the range of 500-2000 with most commercial systems, depending on the configuration. Of all the ionization techniques, MALD ionization is perhaps the most forgiving of the presence of salts and other contaminants in terms of interfering with the production of ions, and in some cases, mass spectra have been produced from samples containing isotonic salt solutions and 2 M urea. Because conversion of the time-of-flight of an ion to an m/z value is dependent on calibration standards, internal standards added to the sample are the best method of calibration. One potential problem in the analysis of small peptides (~ m/z 600) is the high background generated from the matrix added to the sample. Figure 16 shows this background for c~-cyano-4-hydroxycinnamic acid, one of the commonly used matrices, at both low and high laser power. Figure 16A shows the background produced at low laser power; higher laser power (Fig. 16B) is necessary for desorption of proteins from the sample. Several matrices (for example, dihydroxybenzoic acid) give a relatively low background in the low mass range and are preferable in such cases, although they are not generally the most useful matrices in terms of obtaining highest sensitivity. Another disadvantage of the matrix is that analyte-matrix adduct ions are formed and can complicate the spectrum somewhat. Mass measurement accuracies of about + 0.05%, in the typical case, can be achieved with MALD for the analysis of peptides, although not at the conditions used to obtain optimum sensitivity. Ion suppression effects also exist for this technique and, because of this, it is not advisable to attempt a complete analysis of an unknown peptide mixture by direct analysis of the bulk sample. Also, care must be taken in preparing samples because poor technique can produce poor spectra. Figure 17 shows MALD spectra for cytochrome c prepared using a sinapinic acid matrix. In Fig. 17A, the sample was air dried in a dry environment; in Fig. 17B, the sample was dried using a hot air drier. Although the latter treatment is extreme, the poor result nevertheless shows the importance of the sample preparation procedure.
2. Mixture Analysis The best approach to the analysis of mixtures of peptides includes a separation step prior to mass analysis. By far the most effective, convenient, and time-sav-
182
Richard M. Caprioli and Marc J.-F. Suter
Fig. 16
MALD MS spectrum in low m/z range of a common matrix material, a-cyano-4-hydroxycinnamic acid, at different laser power. (A) Low laser power to achieve highest resolution and lowest background, and (B) laser power required to desorb higher molecular mass peptides.
ing approach is to perform the operations on-line, using LC/MS or CE/MS technology. Ion suppression effects are virtually eliminated because compounds in the mixture are not admitted into the source at the same time and contaminants such as salts can be washed off the column prior to elution of peptides. One of the common applications of the LC/MS analysis of peptide mixtures is the identification of peptides produced from protease digests of proteins. Usually, the vast majority (> 90%) of peptides are identified even in digests containing 30-40 or more peptide fragments. For example, CF-FAB has been used for the analysis of the tryptic digest of ]3-casein, in which 24 fragments ranging in mass from m / z 284-2557 were identified by Jones et al. (1991). The
Chapter 4 Mass Spectrometry
183
Fig. 17 MALDMS of two preparations of cytochrome c. (A) Sample solution with matrix dried gently in air and (B) same sample dried rapidly with hot air.
power of mass spectrometry is nicely illustrated in this case, because not only can the individual mass spectra be used to measure the molecular mass of the peptides, but also some peptide backbone fragment ions corroborate the amino acid sequence. This is illustrated for the ]~-casein example in Fig. 18 for the peptide at m/z 742, where the Y ions are ion fragments derived from the C-terminal portion and the A and B ions are from the N-terminal portion of the molecular ion species. In a similar manner, ES can also be effectively used in LC/MS for complex mixture analysis. CE/MS is currently a rapidly growing analytical technique in terms of its application to biological molecules. Much of the published work involves analysis of peptide mixtures because of their ease of separation on capillaries and the high sensitivity of MS detection. Typically, fused silica capillaries of 2050 ~m (i.d.) are used with volatile solvents and buffer systems when possible. Typical sensitivities run in the 100-500 fmol range for total amount of peptides loaded. Since sample load volumes are very small (10-50 nl), concentrations of
184
Richard M. Caprioli and Marc J.-F. Suter
Fig. 18 The mass spectrum of a tryptic fragment of ]3-caseinobtained by LC/CF-FAB MS. The letter abbreviationsrefer to the peptide fragmentationnomenclature shown in Fig. 19. (Joneset al., 1991. Copyright 1991John Wiley & Sons Ltd. Reprinted by permission of John Wiley & Sons, Ltd.) samples are about the same as that for LC/MS, i.e., 10-50 pmol/~l. Special applications of purified peptides have demonstrated attomole sensitivities using narrow m / z range monitoring techniques, although this is not yet considered routine.
3. Sequence A n a l y s i s New ionization processes and analyzer technology have made a significant impact on the capability of mass spectrometry to sequence a few picomoles of a peptide in the molecular mass range up to about 2500 Da. Two general approaches have been, and continue to be, developed; the first involves MS/MS methodology to perform the ionization, peptide ion backbone cleavage, and final identification of products, and the second utilizes specific enzymatic or chemical reactions to form truncated peptides and subsequent use of mass spectrometry to analyze the reaction products. Each approach will be discussed briefly below. Two different types of MS/MS instruments are commonly employed to sequence peptides, the triple-quadrupole spectrometer and the tandem highperformance magnetic spectrometer. Each has special advantages and problems that are mentioned below. The reader is referred to other reviews and publications for more rigorous discussions of these techniques (Hunt et al., 1991; Biemann, 1990a). Peptide ions fragment at the peptide backbone to produce major series of fragment ions. Although this can happen to some extent as the result of internal energy acquired in the ionization process, fragmentation is made more efficient by colliding the ionized molecular species (e.g., [M + H] +) with a neutral gas molecule. The overall process is termed collision-induced dissociation (CID). The types of fragmentation that occur as a result of this process are shown in Fig. 19, using a nomenclature first reported in 1982 (Roepstorff and Fohlman,
185
Chapter 4 Mass Spectrometry I H+
C-terminal ions
.,o
I
H
C2
--C--C---NH2
I""
Xa Y3 Za X= Y= Z2 Xl Y1 Zl
'
II
/..o
I
I
I II
I
R3 0
I II
A, B, C, Aa B2 C2 A3 Bs C3
I I
N-terminal ions
H H
H
R4
]I H+
I
H H
Y2 H
N
H~N--C--C--N--C--C-=O+ HI HI HI
I II / /..O ,,c-c.--~--.~-C,o H H H
(Acylium ion)
B2
~
,,
.,o I
H
I
H
(Aldimine ion)
ff
Z2
A2
Fig. 19 Peptidecleavagenomenclature proposed by Roepstorff and Fohlman (1984).Proposal for common nomenclaturefor sequenceions in mass spectra of peptides. Copyright 1984John Wiley & Sons Ltd. Reprinted by permission of John Wiley & Sons Ltd.
1984), and since modified to account for new and less common fragmentation processes (Biemann, 1990b). The tandem magnetic high-performance mass spectrometer equipped with FAB ionization can be used quite effectively for sequencing peptides. Because high accelerating voltages are used (5-10 kV), single collisions of these highenergy [M + H] + or [M - H]- ions lead to extensive fragmentation. Another advantage is that because unit resolution is generally achieved, the 12C-containing ion (monoisotopic ion of the molecular ion cluster) can be specifically selected to pass through the first analyzer for collision-induced dissociation, simplifying the resulting product ion spectrum obtained from scanning the second analyzer. Such a spectrum is shown in Fig. 20 for a dodecapeptide obtained from the tryptic digest of a protein (Cappiello et al., 1990). Ion fragments noted on the spectrum refer to the nomenclature given in Fig. 19. The N-terminal series (A, B) and C-terminal series (X, Y, Z) provide the major sequence ions found in the spectrum of a peptide. In addition, another fragment ion series, termed the W series can be used to distinguish between isoleucine and leucine, isomeric residues having the same nominal mass, because isoleucine loses 29 Da and leucine loses 43 Da in the collision-induced dissociation process. Generally, FAB produces positive [M + H] + ions at higher intensity than negative ions, and thus the former are most often used. However, peptides that produce intense [M - H]- ions, i.e., those containing many side-chain carboxyl groups or negatively charged phosphate or sulfate groups, can also be sequenced in an analogous manner. Perhaps the major disadvantage of the tandem magnetic instrument is that it is physically large, relatively complex to operate and maintain, and is extremely expensive. Thus, such instruments tend to be housed in laboratories staffed with workers quite experienced in performing mass spectrometry. A second MS/MS instrument, the triple-quadrupole, can also be used ef-
186
Richard M. Caprioli and Marc J.-F. Suter
Fig. 20 High-energy tandem MS CF-FAB spectrum of a tryptic peptide from the cr chain of human hemoglobin. Capital letters are the one-letter amino acid designation; lower case letters are peptide cleavage nomenclature (see Fig. 19 and text). (Reprinted with permission from Cappiello et al., 1990, Fig. 9; appearing in Chromatographia 30(9,10), 477-483.)
fectively for sequencing small peptides, generally below 2500 Da. The FABgenerated ions in such instruments are of low energy (e.g., 0.3-0.5 keV) and rely on multiple collisions in the collision cell to produce CID spectra. Triplequadrupole instruments are generally run at low resolution to optimize sensitivity, and thus the entire molecular ion isotope envelope is passed through the first analyzer. The product ion spectrum is then a mixture of isotopic species. Sufficient fragmentation data are usually obtained to sequence the peptide, although in these low-energy spectra, isoleucine and leucine cannot be distinguished due to the absence of detectable levels of ions losing 29 or 43 Da from the side chain. The major advantages of the triple-quadrupole approach are that the instrumentation is smaller, less complex, and priced less than one-fourth of that of the high-energy magnetic MS/MS systems. Electrospray ionization is also beginning to be used more commonly for application to peptide sequencing. The triple-quadrupole MS/MS system is especially compatible with ES for this purpose because of its low acceleration voltage, minimizing disruptive electrical discharge. The sequencing of peptides by ES/MS/MS is nicely illustrated by work involving the sequencing of peptides obtained from the histocompatibility complex II A1 protein (Hunt et al., 1992). Figure 21 shows the CID spectrum of a triply charged 17-mer at m/z 696 (peptide mass, 2085 Da). When the triply charged [M + 3H] 3+ ions undergo collision, doubly and singly charged ions are formed, producing ions at m/z values above the m/z value of the triply charged molecular ion species. The sequence, key, shown at the top of the figure, lists possible A, B, and Y ion fragments, with singly charged ions that were found in the spectrum underlined once and doubly charged ions underlined twice. The peptide
Chapter 4 Mass Spectrometry
187
Fig. 21 The LC/ES/MS/MS spectrum of a tryptic peptide from the histocompatibility complex II A1 protein, obtained on a triple-quadrupole MS/MS system. (Reprinted with permission from Hunt et al., 1992. Copyright 1992by the AAAS.)
sequence was obtained from these ion fragments by correlating the mass differences between "common ion" series and the known amino acid residue masses. The second general approach to peptide sequencing is to use a combination of chemical a n d / o r enzymatic cleavages to form truncated peptides and then determine their mass, and thus the sequence of the original peptide, by mass spectrometry. This concept, of course, is not new, and over the years biochemists have attempted to use a variety of spectroscopic and chromatographic techniques to identify the residue released from either the N-terminal or C-terminal ends of a polypeptide or protein. These attempts have been only partially successful because of the lack of an unambiguous identification of the residue released. The introduction of direct analysis of intact peptides by FAB allowed workers to measure the residual peptides after reaction, i.e., various truncated forms of the polypeptide with terminal residues removed. Over the past several years, there have been reports describing such mass spectrometric approaches using one or more carboxypeptidases and aminopeptidases (Caprioli and Fan, 1986a). For example, the proteolytic enzymes carboxypeptidase Y and aminopeptidase M were used with FAB mass spectrometry to sequence the terminal residues of several polypeptides. The overall approach involves the identification of the molecular masses of a string of serially related molecules of decreasing mass, which differ by the mass of an amino acid residue. This approach is primarily mass dependent, rather than time dependent, i.e., the precise time of production of a truncated polypeptide
188
Richard M. Caprioli and Marc J.-F. Suter is not important, only its mass relative to its precursor. However, it should be kept in mind that the residue pairs glutamine and lysine, and leucine and isoleucine, cannot be distinguished in such an analysis because each member of these pairs has the same nominal mass. A single exopeptidase usually does not hydrolyze more than 5 - 8 residues because it often reaches a residue or sequence that is only slowly hydrolyzed. One successful approach to get around this difficulty is the use of combinations of enzymes (exopeptidases and endopeptidases) to produce a series of truncated species from several points in the polypeptide. When a 22-residue peptide was digested with a combination of subtilisin and carboxypeptidases Y, P, and B, 16 C-terminal residues were sequenced by identification of the C-terminal truncated polypeptides (Caprioli, 1989). Chemical degradation of polypeptides to form truncated fragments has also been attempted using specific reagents for removal of C-terminal residues. These reactions are not simple, and the approach has not proved to be generally successful. More recently, workers have used the normal Edman degradation chemistry, but have added a small amount of reaction-terminating reagent so that a series of molecular species were produced (Chait et al., 1993). The molecular masses of the polypeptides were then measured using MALD MS and the sequence was determined by correlating the mass differences between the truncated ion series with known amino acid residue masses.
4. Synthetic Peptides Mass spectrometry has become an essential tool for the characterization of peptides synthesized by both liquid- and solid-phase chemistry. It enables one to verify the sequence of the peptide, estimate the extent of truncated forms and side products during synthesis, and assess the extent of deprotection and release from the resin. FAB, CF-FAB, ES, and MALD are all useful because they can analyze the sample directly.
5. Sequence-Ordered Tryptic Maps When one analyzes a tryptic or other protease digest of a large polypeptide or protein, whether by mass spectrometry or other means, the individual peptides can be identified, but of course the order in which they appeared in the original polypeptide is not known. This is because the digest is usually analyzed after completion of the reaction, and positional information is lost. However, it has been shown that sufficient information exists in the time-course analysis of a single digest to, in fact, reconstruct a sequence-ordered map of the polypeptide or protein. Figure 22 shows the general strategy, which can be applied to polypeptides and proteins. As the polypeptide is digested, multiple fragments are formed over a period of time, because all bonds are not accessible to the protease at the same time nor are they hydrolyzed at the same rate. With specific mass analysis during the time-course reaction, product/precursor pairs can be determined, i.e., the sum of the molecular mass of two fragments, minus 18 Da (for one water of hydration), must equal that of its precursor. Timing of the removal of aliquots is not critical because time is not needed in the calculation, but merely allows all transient peptides to be measured. Thus, in Fig. 22,
Chapter 4 Mass Spectrometry
189
to original protein
t 4
1 6rj partial digest
7~____..f t
1
t
partial
digest
tl
4
6
f - c e .u r
3
1
Fig. 22 Scheme for the time-course analysis of the proteolytic cleavage of a protein, for use in constructing a sequence-ordered tryptic map. The terms to, tl, t2, and t24+ refer to times of digestion in hours.
limit digest
peptides 1-2 and 3 are derived from 1-2-3; peptides 6 and 7, from 6-7, etc. In the end, this gives a type of nearest-neighbor analysis and the sequence-ordered map of the fragments if the reading direction is known. For example, in the analysis of the tryptic digest of rat parathyroid hormone (4057.7 Da), 12 tryptic fragments were identified during the hydrolysis, only 4 of which were still present at the end of the digestion (Whaley and Caprioli, 1991). To obtain the correct reading direction, the peptide, which is either the N-terminal or C-terminal peptide, must be known. This is easily accomplished by hydrolysis in 1sO-labeled water, wherein all fragments except the C-terminal fragment will be labeled. Thus, the sequence order of the [M + H] + peptide fragments identified in the limit digest was
(1439.8)-(811.4)-(733.3)-(1128.6) N terminal
C terminal
C. Proteins Much of the work with proteins falls into two categories: (1) analysis of intact proteins and (2) analysis of peptides derived from chemically or enzymatically cleaved proteins. Other sections of this chapter deal with important aspects of
190
Richard M. Capri01i and Marc J.-F. Suter Table IV Comparison of Mass Spectrometric Techniques for Molecular Mass Analysis of Proteins a Parameter
ESI MS
PD MS
MALD MS
Practical upper mass limit (Da) Mass measurement accuracy (internal standard) Speed (calibration + analysis) Compatibility with salts Sensitivity
100,000 0.005-0.05% 30 min Poor 0.5 pmol
25,000 0.05-0.1% 15-120 min Good b 0.5-10 pmol
300,000 0.05-0.1% 10 min Good b 0.1 pmol
i
a Using currently available commercial instruments and assuming a protein of 20,000-30,000 Da. b Proteins can be deposited on target, and salts washed off.
measurements of molecular masses by mass spectrometry and analysis of peptides, including complex mixtures of peptides. Some additional comments follow to further characterize these approaches.
1. Molecular M a s s Three mass spectrometric ionization techniques are commonly used today to measure the molecular masses of proteins. These are ES MS, MALD MS, and PD MS, and each has specific advantages and limitations. The following discussion is based on what practitioners can reasonably achieve with commercial instruments currently available. The analytical aspects of concern for a given technique are the mass range, resolution, sensitivity, susceptibility to salts, precision, speed, and, most of all, mass measurement accuracy. These techniques are compared in Table IV, assuming the analysis of a protein in the 20,00030,000 Da range. It must be emphasized that these are typical performance comparisons that would not be applicable to all cases. Certainly, all of the techniques could be used to determine molecular mass. The biggest factor in choosing one of these is availability, because it is uncommon for all of these to be in a single laboratory. Beyond this, other factors will be important to varying degrees for different samples, and it is for the analyst to decide the best technique for that sample. However, some limitations apply to all, such as avoiding certain reagents, for example, sodium dodecyl sulfate or other surfactants, phosphate buffers, and excessive amounts of any salts or other major contaminants in the samples. Although sensitivities are high, small volumes of solutions are used to load samples, necessitating concentrations in the 0.1-1/~M range.
One additional aspect of ES MS is derived from several reports discussing the partial denaturation of proteins observed from the increase in the number of charges, i.e., the shift to lower m / z values as denaturation takes place. This presumably involves the breaking of ionic bridges within the protein and the ability of basic groups to retain a charge. An example is shown in Fig. 23 for bovine cytochrome c electrosprayed at different pH values (Chowdhury et al., 1990). This protein is known to unfold partially at lower pH, and the mass spectra are interpreted as reflecting this in that the higher charge states are a consequence of denaturation and exposure of a greater number of basic
191
Chapter 4 Mass Spectrometry 25,000
50O0
,6+
6§
pH2.6
pH 3.0
~>~
8+
Or) (--
c-
§
.............
'500
,---- ...................
1100
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0
1700
10,000
500
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m/z
1700
lo+
pH 5.2
>, Or) C
16§
0
500
12+
8+
&_x
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1700
Fig. 23 ESI mass spectrum of bovine cytochrome c obtained at different acid concentrations, at 4% acetic acid, pH 2.6; 0.2% acetic acid, pH 3.0; and no acetic acid, pH 5.2. (Reprinted with permission from Chowdhury et al., 1990. Copyright 1990 American Chemical Society.)
groups to the solvent. Other experiments have examined similar phenomena, including heat- and solvent-induced conformational changes of proteins, using ES MS, but it is not yet clear what specific factors are involved. The results are certainly interesting, but the interpretation of gas-phase structure in terms of known liquid-phase structures must be approached with caution.
2. Posttranslational Modifications A number of chemical changes to a protein can occur after synthesis on the ribosome, including partial proteolytic hydrolysis, glycosylation, acylation, phosphorylation, cross-linking through disulfide bridges, etc. What these have in common is that they change the mass of the original molecule. Table V summarizes some of the more common modifications in terms of their effect on the molecular mass of a protein or peptide (Krishna and Wold, 1993). Further, using the proper procedures, the position of these modifications within the polypeptide chain can be identified. Depending on the specific analytical task, approaches may include analysis of the intact protein before and after treatment with a chemical agent or enzyme, or hydrolysis of the protein to peptides, thus localizing the alteration to a specific small peptide, followed by identification of the specific residue modified, if necessary. One of the most common modifications of proteins that is of interest is that of glycosylation. Analysis of the oligosaccharides can be quite a difficult task
192
Richard M. Caprioli and Marc J.-F. Suter Table V C o m m o n M o d i f i c a t i o n s of Proteins and Their M a s s C h a n g e to Total Molecular Mass a
Nominal mass change (Da) -42 - 30 - 18 - 2 - 1 1 14 16 28 32 35 and 37 42 44 56 64 + isotopes 74 78 and 80 80 90 96 100 104 105 121 126 132 134 146 149 154 161 162 166 176 177 178 188 203 204 210 226 229 238 242 266 291 305 324 329 454 541 617 784
Common modifications and residues Ornithine replaces Arg Homoserine replaces Met Loss of water (cross link, dehydration, pyro-Glu replaces Glu) Disulfide formation, dehydroalanine replaces Ala Amide group replaces acid Acid group replaces amide, citrulline replaces Arg Methylene group (methylation, homolog, etc.) Oxygen atom (hydroxylation, Met sulfoxide formation, etc.) Formyl, 2-methyl groups, ethyl Addition of two oxygen atoms (dihydroxyl addition) Chlorine atom Acetyl Carboxyl addition
tert-Butyl
Selenocysteine replaces serine Glyceryl group Bromine atom Phosphoryl, sulfonyl groups Benzyl Trifluoroacetyl Butyloxycarbonyl Benzoyl Pyridylethyl Nitrophenyl Iodine atom Pentosyl Benzyloxycarbonyl Deoxyhexocyl Nitrobenzoyl Toluenesulfonyl Hexosaminosyl Hexosyl Pentafluorophenyl Glucuronosyl Glycosyloxy Trichlorophenyl Lipoyl N-Acetylhexosaminosyl Farnesyl Myristoyl Biotinyl Pyridoxyl Palmitoyl Triphenylmethyl Stearoyl phosphoryl-N-acetylglucosyl N-Acetylneuraminosyl Glutathionyl Pantetheinephosphoryl Adenosyl Coenzyme A ADP-ribosyl Heme FAD
a Adapted from Krishna and Wold (1993), with permission.
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because there are many potential sites of attachment of carbohydrates to proteins, two types of linkages (N and O linked), considerable heterogeneity in the numbers of sugars at even one specific attachment site, and, with respect to the carbohydrate group, many possible linkage arrangements. The specific strategy for the approach to such an analysis may be different, depending on the nature of the specific glycoproteins, the complexity of the carbohydrate groups, the amount of sample available, and information already known about the structure of the glycoproteins. Often, the amino acid sequence is known either from direct sequence analysis or is inferred from the DNA sequence. This is a major advantage because it helps pinpoint potential linkage sites for both N- and O-linked oligosaccharides. Although there are now many examples in the literature that illustrate the use of mass spectrometry in determining postribosomal modifications of proteins, recent work with recombinant human macrophage colony-stimulating factor (rhM-CSF) is noteworthy because it illustrates several uses of mass spectrometry (Martin et al., 1994). From standard biochemical methods, it was known that the active protein was a homodimer consisting of subunits of 223 residues each, covalently attached by disulfide bonds. From the DNA sequence, the protein sequence for the subunit contained two consensus sites for N-linked glycosylation and several potential O-linked sites. A MALD MS spectrum of the active protein contained a broad peak centered at m / z 64,900, suggesting heterogeneity in structure. Subsequent MALD analysis of the reduced, alkylated protein also showed a broad peak at m / z 33,200 (which includes the mass added from the alkylating agent). For further information on the nature of the carbohydrate groups, the strategy relied on sequential hydrolysis using enzymes that release specific carbohydrates or hydrolyze specific linkages, i.e., neuraminidase and other glycosidases and MALD analysis. From the known specificity of the enzyme and mass differences observed after enzyme treatment, conclusions could be drawn regarding the types of carbohydrate and the extent of glycosylation of the molecule. The protein was also cleaved to smaller peptide fragments by use of a specific protease, in this case, lysine-specific Achromobacter protease I. Figure 24 shows the MALD spectrum of the peptide Asn138-Lys163before and after treatment with N-glycosidase F, with both spectra obtained on about I pmol of sample. The structures of the carbohydrate groups attached to Asn-140, determined from subsequent work, are indicated in this figure. The differences of 365, 656, and 291 mass units are typical of structures Hex-HexNAc, N e u A c - H e x - H e x N A c , and NeuAc, respectively. Further, permethylation of the released carbohydrate groups at Asn-140 followed by FAB MS analysis indicated a predominantly biantennary, sialylated oligosaccharide containing fucose residues. The most abundant mass recorded corresponds to a carbohydrate composition of (Hex-NAc)4, (Hex) 5, (Fuc) 1, (NeuAc)2. Several higher molecular mass species were also recorded, showing the heterogeneity at this single site. Further detailed structure analysis of these oligosaccharides was accomplished by high-field NMR, providing anomeric configurations and linkage information. A similar approach was used with the other N-linked site and O-linked sites. In the latter case, FAB and MS/MS were used to analyze chymotryptic fragment peptides to further pinpoint sites of glycosylation on Ser-4 and Ser-9, providing some structural information on the carbohydrate group.
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 24 MALD MS spectrum of (A) the [M + H] + ion region of the glycopeptide (Asn138-Lys163) from the proteolytic digest of recombinant human macrophage colony-stimulating factor, and (B) the molecular ion region after treatment of this peptide with N-glycosidase F. (Martin, S. A., Vath, J. E., Yu, W., and Scoble, H. Co-translational and post-translational processing of proteins. In "Biological Mass Spectrometry: Present and Future" (T. Matsuo, R. M. Caprioli, M. L. Gross, and Y. Seyama, eds.). Copyright 1994 John Wiley & Sons, Ltd. Reprinted by permission of John Wiley & Sons, Ltd.)
3. Location of Disulfide Linkages The determination of the numbers and positions of disulfide links in proteins, both intra- and intermolecular, can be accomplished quite effectively by mass spectrometry (Smith and Zhou, 1990). The number of cysteinyl residues in a protein can be quickly determined by alkylation of the protein, for example, with vinylpyridine. Each pyridylethyl group adds 105 Da for each modified cysteinyl residue. The molecular mass analysis, before and after alkylation using ES or MALD MS, thus provides the total number of cysteinyl residues modified. Of course, it is possible that not all residues will be completely modified. The strategy for position assignment is straightforward in that it involves digestion of the sample protein with one or more specific proteases, and mass spectrometric analysis of the peptide fragments. A second sample of the digested protein is then treated with a reducing agent such as dithiothreitol or dithioerythritol and again analyzed by mass spectrometry. Peptides containing intramolecular disulfide bonds will shift up two m/z units if converted to sulf-
Chapter 4 Mass Spectrometry
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hydryl groups. The ion resulting from two different peptides linked by a disulfide bridge will disappear after reduction, and two new lower mass ions will appear, each containing the reduced or alkylated cysteinyl residue. If the protein sequence is known, then production of peptides containing the individual cysteinyl residues will uniquely position the disulfide bridge. If further pinpointing of the position of the disulfide is necessary because of unknown or ambiguous sequence data, or the presence of two disulfide bonds in one peptide, further hydrolysis by other endopeptidases and exopeptidases followed by mass spectrometric analysis is done. Alternatively, MS/MS sequencing of a small peptide will enable the position of the cysteinyl residue to be assigned. Although mass spectrometry offers some important advantages for the location of disulfide bonds, it does not eliminate the complex and troublesome disulfide exchange that can occur in a protein, i.e., the ability of these linkages to scramble so that the isolated sample contains disulfide links not present in the original protein. This can occur during protein isolation, sample preparation, and analysis. Also, disulfide linkages can be easily reduced to the corresponding thiols by a number of reagents, as discussed above, and although this is used to advantage to assign disulfide links, it also may occur inadvertently during handling of the sample. In addition, reduction of disulfide bonds can occur directly as a result of the sample conditions and ionization process, especially with FAB, further complicating this analysis procedure.
4. N o n c o v a l e n t Interactions Many proteins bind other molecules, such as low molecular mass ligands or other protein molecules, to form multicomponent complexes. Although a number of techniques have been used over the years to measure the stoichiometry and kinetics of these interactions, mass spectrometry has begun to be used to measure the molecular masses of these complexes. At the present time, it is not yet clear to what extent mass spectrometry will be successful because only a relatively small number of examples have been reported in the literature. Generally, measurements of nonconvalently bound multimeric complexes of proteins using MALD MS have not been successful. In part, this results from the fact that matrices used with the N 2 laser system are soluble in organic solvent/water mixtures; indeed, sample preparation employs conditions that can lead to dissociation of the complexes. However, cross-linking of noncovalently associated complexes using specific chemical reagents has proved useful. In one such approach, glutaraldehyde has been employed to bridge lysyl residues and covalently link proteins in aqueous solution (Farmer and Caprioli, 1991). If protein concentrations are kept -< 5/.~M, nonspecific associations are minimized and therefore only the subunits within the complex will be crosslinked. Figure 25 shows the MALD mass spectra of bovine hemoglobin, a n ~2/~2 complex, before and after treatment with glutaraldehyde as a cross-linker. Before reaction, the experimental conditions involved in sample preparation a n d / o r the ionization process lead to complete dissociation of the tetramer into the a and fl subunits. After cross-linking, the tetramer is clearly observed, along with monomer and aft dimer. These latter species are believed to result from some dissociation of the complex as a result of reaction conditions. The peaks are broad in the spectrum of the cross-linked protein because glutaraldehyde polymerizes and cross-links with a wide variety of cross-linking
196
Richard M. Caprioli and Marc J.-F. Suter
Fig. 25 MALDMS spectrum of bovine hemoglobin before and after treatment with glutaraldehyde.
structures. Of course, intramolecular cross links can also occur. Nevertheless, the technique clearly establishes the multimeric state of the complex. The situation with ion spray and electrospray ionization is considerably better in that a number of protein-ligand complexes have been measured. Protein-ligand complexes involving binding of drugs and cofactors have been recorded using ES MS. For many of these, the complexes are of rather low intensity and probably do not reflect the actual solution concentration. It has been pointed out by numerous investigators that use of gentle conditions during analysis, i.e., elimination of organic solvents, salts, and use of low temperature, are essential to the measurement of these complexes. Nevertheless, not all attempts have been successful, and it appears that factors other than the solution-phase association constant for the protein-ligand can be very important. For example, the noncovalently bound ras protein-GTP complex has been measured by ion spray MS (Ganguly et al., 1993). This technique allows pure aqueous solutions to be sprayed into the mass spectrometer, eliminating organic solvents. Figure 26 shows spectra obtained from a change in pH of the sample. The spectrum at pH 4 shows the complex at m / z 19,374 of high intensity, decreasing as the pH is lowered, until only the ras protein at m / z 18,853 can be observed. This is exactly what has been found in other studies of this complex involving other analytical methods. Other types of interactions reported to be measured by ES MS are globin and heme (Katta and Chait, 1991), ribonuclease A and CMP (Haskins et al., 1994), lysozyme and carbohydrate (Li and Henion, 1991b), and immunosuppressive binding protein and drugs (Li and Henion, 1991a). Some protein-protein interactions have also been measured by ES or ion
Chapter 4 Mass Spectrometry
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Fig. 26 Molecularmass analysis of ES spectrum from the ras-GTP complex in solution at (A) pH 4.0, (B) pH 3.4, and (C) pH 2.8. (Reprinted from Tetrahedron 49, Ganguly, A. K., Pramanik, B. N., Huang, E. C., Tsarbopoulos, A., Girijavallabhan, V. M., and Liberles, S., Studies of the Ras-GDP and Ras-GTP noncovalent complexes by electrospray mass spectrometry, 7985-7996; Copyright 1993, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 IGB, UK.)
spray MS, although it is not yet clear h o w effective MS will be as a general tool in such studies. For example, concanavalin A is a h o m o t e t r a m e r with a monomer molecular mass of 25,500 Da. The ES spectrum in 10 m M a m m o n i u m acetate, p H 6.7, showed both dimer and tetramer (Smith et al., 1992). It is noted that the e v e n - n u m b e r e d charge states of both dimer and tetramer overlap, i.e., the m / z values of (dimer + 20H+) 2~ and (tetramer + 40H+) 4~ are the same, but these can be distinguished by the odd charge states, i.e., the m / z of (dimer + 21H+) 21+ does not overlap with (tetramer + 41H+) 41+. Although the application of mass spectrometry to m e a s u r e m e n t s of noncovalent interactions is still relatively new, the results are intriguing and considerable progress can be expected in studying p r o t e i n - l i g a n d and p r o t e i n protein interactions.
D. N u c l e i c A c i d s The use of mass spectrometry for the analysis of nucleic acids has come in two general areas: the first involves nucleosides, nucleotides, and small oligonucleotides, and the second involves polynucleotides. By far, most w o r k has involved small molecules, due primarily to their highly charged, polar nature. Generally these c o m p o u n d s do not desorb efficiently and, compared to peptides, are considerably less sensitive with current methods and ionization processes. Only recently have ES and MALD been applied with some success to polynucleotide analysis. The results are encouraging, but are not yet at the same level of sensitivity and structural selectivity attained for protein analysis and sequencing.
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Richard M. Capri01i and Marc J.-F. Suter
1. Nucleosides, Nucleotides, and Oligonucleotides The basic approach to the measurement of nucleosides and nucleotides involves use of chemical agents or enzymes to release low mass molecules from RNA and DNA so that they are amenable to mass spectrometric techniques (e.g., LC/MS, MS/MS, and high-resolution measurements for elemental composition). Applications include structure determination of modified bases from postribosomal processing of RNA and DNA, and identification and quantitation of known bases in digests of nucleic acids (McCloskey, 1990b). The derivatization of nucleosides using trimethylsilyl (TMS) groups with analysis by EI and CI has been quite successful over the years (McCloskey, 1990c). These derivatives usually give low-intensity molecular ions, and somewhat more intense fragment 15 m/z units below that of the molecular ion. Structurally significant ions such as the B series, which contains the base moiety with various fragments of the sugar, and the S series, the sugar ring with fragments of the base, are also readily formed. Figure 27 shows the EI mass spectrum of uridine-(TMS)4, with the characteristic molecular (M), base (B), and sugar (S) ion series labeled (Pang et al., 1982). High-resolution accurate mass measurements of some of these ions establish their elemental compositions. For example, the (B + 132) ion has been shown to contain the intact base, carbon atoms 1 and 2 of the sugar, and the ring oxygen of the sugar, giving an ion of mass (B + 132.0607)Da with the composition (B + C5H1202Si). Many such identifications can be made from a single spectrum. Further details of these mass spectra can be found in a review by McCloskey (1990c). GC/MS technology, in conjunction with the use of stable isotopically labeled analogs, has been used for the high-sensitivity quantitative analysis of methylated bases in DNA. The isotope dilution method is essential because of the difficulties in performing microscale derivatization on picogram quantities of material. This procedure has also been used for the identification of other minor bases present in nucleic acids. Analyses of complex mixtures of nucleosides from RNA and DNA digests have utilized LC/MS with thermospray, CF-FAB, and electrospray ionization sources. Nucleic acids can be digested to nucleosides using a combination of nucleases and alkaline phosphatase. To illustrate the technique, the thermospray LC/MS analysis of the enzymatic digestion of a tRNA sample will be
Fig. 27 Mass spectrum of uridine-(TMS)4 with molecular (M), base (B), and sugar (S) series ions indicated. (Reprinted with permission from Pang et al., 1982. Copyright 1982 American Chemical Society.)
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described. Thermospray mass spectra of nucleosides are relatively simple in that, in the presence of an a m m o n i u m acetate buffer, a protonated molecular ion [M + H] + is formed, with fragment ions for the protonated free base [BH2] + and a sugar ion [ ( S - H ) . NH4] + resulting from the loss of a h y d r o g e n from a hydroxyl group plus addition of an NH4 + adduct (Pomerantz and McCloskey, 1990). A few other fragment ions are formed in the thermospray process, but these are of relatively low intensity. Figure 28 shows the UV chromatogram (254 nm) for the LC separation of the digest of 18/zg of tRNA from Sulfolobus solfataricus. The peak assignments were m a d e from their thermospray mass spectra and are listed in the legend for Fig. 28. These applications represent impressive uses of mass spectrometry for the analysis of quite complex mixtures having components in a wide range of concentrations. The procedure is not trivial, and considerable experience is required to perform it effectively.
2. Oligonucleotides Direct analysis of oligonucleotides and fragments of RNA and D N A can be accomplished by mass spectrometry, but have not yet been developed to the state of protein analysis. Desorption ionization techniques such as FAB and PD have been effective only with relatively small oligonucleotides (8 to 10-mers), and most of their use has been in the analyses of synthetic preparations. Oligonucleotides are highly negatively charged and therefore are generally measured in the negative ion mode. The two techniques, which currently hold promise and have given some encouraging results, are MALD and ES, and work in this area is described below. MALD MS has shown some impressive results with respect to desorbing intact large polynucleotides. In one report the (M - H ) - ion of an RNA 104-mer
lOO
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Time, minutes
Fig. 28 Chromatographic separation of nucleosides from the LC/thermospray MS analysis of the enzymatic digest of unfractionated S. sulfataricustRNA (UV profile at 254 nm). Some of the peaks are identified: 2, pseudouridine; 3, cytidine; 4, uridine; 7, 1-methyladenosine; 8, 2'-O-methylcytidine; 10, guanosine; 13, deoxyguanosine; 17, 1-methylguanosine; 18, N4-acetylcytidine; 22, N2,N 2dimethylguanosine; and 28, Na,N2-O-trimethylguanosine. (Reprinted from Pomerantz and McCloskey, with permission.)
200
Richard M. Caprioli and Marc J.-F. Suter was recorded at about m / z 33,500 using succinic acid as the matrix and an infrared laser (Nordhoff et al., 1993), as shown in Fig. 29. This is not yet routine and, at this point, analysis of 50-mers are the practical limit in size one can expect to achieve with current methods. Size is important from the view of potential sequencing strategies; the larger the fragment the less overlapping data needed to link these fragments and the faster the sequencing process. Of course, the other challenge is to produce chemical/enzymatic methods that yield all of the truncated molecular species required to sequence the polynucleotides that are also compatible with the mass spectrometric techniques used. Although it is possible that MS/MS methods can be devised to sequence polynucleotides directly, progress thus far has been slow. Several factors have limited polynucleotide analysis by mass spectrometry and are being urgently addressed by many laboratories. First, ions from polynucleotides tend to fragment easily, and not always in a coherent manner. Second, the highly charged nature of the molecules not only makes them difficult to bring into the gas phase, but leads to the association of many different cations, giving a broad, diffuse peak when observed. Also, because most of the initial effort of MALD has been on proteins, the matrices used have not been optimal for polynucleotides. In this regard, several new matrices have been reported for specific use with polynucleotides. One of these, 3-hydroxypicolinic acid (Wu et al., 1993), appears quite effective for oligonucleotides up to about 70-mers. This matrix shows a significant improvement in performance, not only in analyzing a wider mass range, but also shows greater sensitivity in the negative ion mode. A truly intense effort is underway to develop such techniques by MALD MS, and the expectation of success is high. Electrospray has also shown some interesting results for polynucleotides in the 50- to 80-mer range (Stults and Marsters, 1991). These samples were prepurified and sodium ions were replaced with ammonium ions. The deconvoluted ES mass spectrum of a 77-mer obtained from a solution of 50 p m o l / ~ l infused at a rate of 2 ~ l / m i n gave a molecular mass of 24,058 + 8 Da (theoretical: 24,039 Da). This suggests the presence of one sodium ion, with the peak at m / z 924.5, corresponding to (M - 27H + + Na) 26-, i.e., this ion contains 26 negative charges. High-purity samples, devoid of mixtures of not only other poly-
100-
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-
i
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nucleotides but also of metal cations, are critical to avoid complex overlapping charge states. As in the case of MALD, current work promises to extend the mass range and sensitivity, providing a viable technique for the rapid analysis of polynucleotides.
V. Conclusions The scope of the use of mass spectrometry in the biological sciences has grown enormously, with applications to nearly all areas of research. One of the most impressive aspects of mass spectrometry is the diversity of the technique. This allows investigation of biological systems at their extremes, because this massspecific instrument can make measurements at the molecular level. Many of the chemical reactions necessary to elucidate biological processes can take place within the mass spectrometer, e.g., collision-induced dissociations, ion/molecule reactions, and charge exchange processes. The variety of ionization methods permits the volatilization of macromolecules in the range of 300,000 Da at sensitivities below I pmol, as well as the analysis of small molecules of less than 500 Da at the attomole level. Spectral information can be obtained that produces only molecular species for molecular mass measurements, or fragmentation data of sufficient detail to allow sequencing and structure elucidation. Solid samples can now be analyzed as easily as gaseous samples, and complex multicomponent systems as effectively as highly purified compounds. From a practical viewpoint, these dramatically escalating capabilities fortunately all come at a time of significantly decreasing costs for such instrumentation. Mass spectrometry also has benefited greatly because of the enormous number and importance of the problems at the molecular level in the life sciences. Moreover, this incredibly rapid involvement in biological research has not only benefitted applications, but also has driven fundamental research in mass spectrometry.
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Richard M. Caprioli and Marc J.-F. Suter Caprioli, R. M. (1994). On-line LC/MS and CE/MS. In "Biological Mass Spectrometry: Present and Future" (T. Matsuo, R. M. Caprioli, M. L. Gross, and Y. Seyama, eds.), pp. 75-100. Wiley, New York. Caprioli, R. M., and Fan, T. (1986a). Peptide sequence analysis using exopeptidases with molecular analysis of the truncated polypeptides by mass spectrometry. Anal. Biochem. 154, 596-603. Caprioli, R. M., and Fan, T. (1986b). High sensitivity mass spectrometric determination of peptides: Direct analysis of aqueous solutions. Biochem. Biophys. Res. Commun. 141, 1058-1065. Caprioli, R. M., Fan, T., and Cottrell, J. S. (1986). Continuous-flow sample probe for fast atom bombardment mass spectrometry. Anal. Chem. 58, 2949-2954. Caprioli, R. M., Moore, W. T., Martin, M., Wilson, K. B., and Moring, S. (1989). Coupling CZE and CF-FAB MS for analysis of peptide mixtures. J. Chromatogr. 480, 247-257. Chait, B. T., Wang, R., Beavis, R. C., and Kent, S. B. H. (1993). Protein ladder sequencing. Science 262, 89-92. Chowdhury, S. K., Katta, V., and Chait, B. T. (1990). Probing conformational changes in proteins by mass spectrometry. J. Am. Chem. Soc. 112, 9012-9013. Comisarow, M. B., and Marshall, A. G. (1974). Fourier transform ion cyclotron resonance spectroscopy. Chem. Phys. Lett. 25, 282-283. Cottrell, J. S., and Frank, B. H. (1985). Fast atom bombardment mass spectrometry of bovine proinsulin. Biochem. Biophys. Res. Commun. 127(3), 1032-1038. De Pauw, E. (1986). Liquid Matrices for secondary ion mass spectrometry. Mass Spectrom. Rev. 5(2), 191-212. Dole, M., Mack, L. L., Hines, R. L., Mobley, R. C., Ferguson, L. D., and Alice, M. B. (1968). Molecular beams of macroions. J. Chem. Phys. 49, 2240-2249. Emmett, M. R., and Caprioli, R. M. (1994). Micro-electrospray MS: Ultra-high sensitivity analysis of peptides and proteins. J. Am. Soc. Mass Spectrom. 5, 605-613. Farmer, T. B., and Caprioli, R. M. (1991). Assessing the multimeric states of proteins: Studies using laser desorption mass spectrometry. Biol. Mass Spectrom. 20, 796-800. Fischer, E. (1959). Three-dimensional stabilization of charge carriers in a quadrupole field. Z. Phys. 156, 1-26. Ganguly, A. K., Pramanik, B. N., Huang, E. C., Tsarbopoulos, A., Girijavallabhan, V. M., and Liberles, S. (1993). Studies of the Ras-GDP and Ras-GTP noncovalent complexes by electrospray mass spectrometry. Tetrahedron 49, 7985-7996. Harrison, A. G. (1992). "Chemical Ionization Mass Spectrometry," 2nd ed. CRC Press, Boca Raton, FL. Haskins, N. J., Ashcroft, A. E., Phillips, A., and Harrison, M. (1994). The evaluation of several electrospray systems and their use in non-covalent bonding studies. Rapid Commun. Mass Spectrom. 8, 120-125. Hunt, D. F., Krishnamurthy, T., Shabanowitz, J., Griffin, P. R., Yates, J. R., III, Martino, P. A., McCormack, A. L., and Hauer, C. R. (1991). Peptide sequence analysis by triple quadrupole and quadrupole Fourier transform mass spectrometry. In "Mass Spectrometry of Peptides" (D. M. Desiderio, ed.), pp. 139-158. CRC Press, Boca Raton, FL. Hunt, D. F., Michel, H., Dickinson, T. A., Shabanowitz, J., Cox, A. L., Sakaguchi, K., Appella, E., Grey, H. M., and Sette, A. (1992). Peptides presented to the immune system by the murine class II major histocompatibility complex molecule 1-A d. Science 256, 1817-1820. Iribarne, J. V., and Thomson, B. A. (1976). On the evaporation of small ions from charged droplets. J. Chem. Phys. 64, 2287-2294. Jones, D. S., Heerma, W., van Wassenaar, P. D., and Haverkamp, J. (1991). Analysis of bovine fl-casein tryptic digest by continuous-flow fast-atom bombardment mass spectrometry. Rapid Commun. Mass Spectrom. 5, 192-195. Karas, M., and Hillenkamp, F. (1988). Laser desorption ionization of proteins with molecular masses exceeding 10,000 daltons. Anal. Chem. 60, 2299-2301. Katta, V., and Chait, B. T. (1991). Observation of the heme-globin complex in native myoglobin by electrospray-ionization mass spectrometry. J. Am. Chem. Soc. 113, 8534-8535. Kofel, P., Allemann, M., Kellerhals, H. P., and Wanczek, K.-P. (1985). External generation of ions in ICR spectrometry. Int. J. Mass Spectrom. Ion Processes 65, 97-103. Krishna, R. G., and Wold, F. (1993). Post-translational modifications of proteins. In "Methods in Protein Sequence Analysis" (K. Imahori and F. Sakiyama, eds.), pp. 167-171. Plenum, New York.
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Li, Y.-T., and Henion, J. D. (1991a). Detection of noncovalent receptor-ligand complexes by mass spectrometry. J. Am. Chem. Soc. 113, 6294-6296. Li, Y.-T., and Henion, J. D. (1991b). Observation of noncovalent enzyme-substrate and enzyme-product complexes by ion-spray mass spectrometry. J. Am. Chem. Soc. 113, 7818-7819. Martin, S. A., Vath, J. E., Yu, W., and Scoble, H. (1994). Co-translational and post-translational processing of proteins. In "Biological Mass Spectrometry: Present and Future" (T. Matsuo, R. M. Caprioli, M. L. Gross, and Y. Seyama, eds.), pp. 313-330. Wiley, New York. Matsuo, T., Caprioli, R., Gross, M., and Seyama, Y., eds. (1994). "Biological Mass Spectrometry: Present and Future." Wiley, New York. McCloskey, J. A., ed. (1990a). "Methods in Enzymology," Vol. 193. Academic Press, San Diego, CA. McCloskey, J. A. (1990b). Constituents of nucleic acids: Overview and strategy. In "Methods in Enzymology" (J. A. McCloskey, ed.), Vol. 193, pp. 771-781. Academic Press, San Diego, CA. McCloskey, J. A. (1990c). Electron ionization mass spectra of trimethylsilyl derivatives of nucleosides. In "Methods in Enzymology" (J. A. McCloskey, ed.), Vol. 193, pp. 825-842. Academic Press, San Diego, CA. Mclver, R. T., Hunter, R. L., and Bowers, W. D. (1985). Coupling of a quadrupole mass spectrometer and a Fourier transform mass spectrometer. Int. J. Mass Spectrom. Ion Processes 64, 67-77. McLafferty, F. W. (1993). "Interpretation of Mass Spectra," 4th ed. University Science Books, Mill Valley, CA. Moseley, M. A., Deterding, L. J., Tomer, K. B., and Jorgenson, J. W. (1989). CZE/FAB MS: Design of an on-line coaxial continuous-flow interface. Rapid Commun. Mass Spectrom. 3, 87-92. Naylor, S., Findeis, A. F., Gibson, B. W., and Williams, D. H. (1986). An approach toward the complete FAB analysis of enzymatic digests of peptides and proteins. J. Am. Chem. Soc. 108, 6359-6363. Nordhoff, E., Kara, M., Hillenkamp, F., Kirpekar, F., Kristiansen, K., and Roepstorff, P. (1993). MALDI mass spectrometry of oligonucleotides and nucleic acids. Proc 41st ASMS Conf. Mass Spectrom. Allied Top., pp. 246a-246b. Olivares, J. A., Nguyen, N. T., Yonger, C. R., and Smith, R. D. (1987). On-line mass spectrometric detection by capillary zone electrophoresis. Anal. Chem. 59, 1230-1232. Pang, H., Schram, K. H., Smith, D. L., Gupta, S. P., Townsend, L. B., and McCloskey, J. A. (1982). Mass spectrometry of nucleic acid constituents. Trimethylsily derivatives of nucleosides. J. Org. Chem. 47, 3923-3929. Paul, W., and Steinwedel, H. (1953). A new mass spectrometer without a magnetic field. Z. Naturforsch., A 8A, 448-450. Pomerantz, S. C., and McCloskey, J. A. (1990). Analysis of RNA hydrolyzates by liquid chromatography-mass spectrometry. In "Methods in Enzymology" (J. A. McCloskey, ed.), Vol. 193, pp. 796-824. Academic Press, San Diego, CA. Price, P. (1991). Standard definitions of terms relating to mass spectrometry; A report from the Committee on Measurements and Standards of the American Society for Mass Spectrometry. J. Am. Soc. Mass Spectrom. 2, 336-348. Roepstorff, P., and Fohlman, J. (1984). Proposal for common nomenclature for sequence ions in mass spectra of peptides. Biomed. Mass Spectrom. 11, 601. Smith, D. L., and Zhou, Z. (1990). Strategies for locating disulfide bonds in proteins. In "Methods in Enzymology" (J. A. McCloskey, ed.), Vol. 193, pp. 374-389. Academic Press, San Diego, CA. Smith, R. D., Light-Wahl, K. J., Winger, B. E., and Loo, J. A. (1992). Preservation of non-covalent associations in electrospray ionization mass spectrometry: Multiply charged polypeptide and protein dimers. Org. Mass Spectrom. 27, 811-821. Smith, R. D., Goodett, D. R., and Wahl, J. H. (1993). Capillary electrophoresis/mass spectrometry. In "CRC Handbook of Capillary Electrophoresis" (J. P. Landess, ed.), pp. 177-198. CRC Press, Boca Raton, FL. Stults, J. T., and Marsters, J. C. (1991). Improved electrospray ionization of synthetic oligodeoxynucleotides. Rapid Commun. Mass Spectrom. 5, 359-363. Thomson, J. J. (1913). "Rays of Positive Electricity and Their Application to Chemical Analysis." Longmans, Green, London. Torgerson, D. F., Skowronski, R. P., and Macfarlane, R. D. (1974). New approach to the mass spectroscopy of nonvolatile compounds. Biochem. Biophys. Res. Commun. 60, 616-621. Vestal, M. (1990). Liquid chromatography-mass spectrometry. In "Methods in Enzymology" (J. A. McCloskey, ed.), Vol. 193, pp. 107-130. Academic Press, San Diego, CA.
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Richard M. Caprioli and Marc J.-F. Suter Whaley, B., and Caprioli, R. M. (1991). Identification of nearest-neighbor peptides in protease digests by mass spectrometry for construction of sequence-ordered tryptic maps. Biol. Mass Spectrom. 20, 210-214. Wiley, W. C., and McLaren, I. H. (1955). Time-of-flight mass spectrometer with improved resolution. Rev. Sci. Instrum. 26, 1150-1157. Willoughby, R. C., and Browner, R. F. (1984). Monodisperse aerosol generation interface for combining liquid chromatography with mass spectrometry. Anal. Chem. 56, 2626-2631. Wu, K. J., Steding, A., and Becker, C. H. (1993). Matrix-assisted laser desorption time-of-flight mass spectrometry of oligonucleotides using 3-hydroxypicolinic acid as an ultraviolet-sensitive matrix. Rapid Commun. Mass Spectrom. 7, 142-146. Yamashita, M., and Fenn, J. B. (1984). Electrospray ion source. Another variation on the free-jet theme. J. Phys. Chem. 88, 4451-4459.
GLOSSARY Accelerating voltage
The electrical potential difference applied between the cathode and the anode of an electron gun; determines the energy of the electron beam. Airlock A small part of a vacuum system that can be isolated from the rest of the system with a valve and separately pumped or brought to atmospheric pressure; used for introducing specimens, film, etc. into the electron microscope without loss of high-vacuum conditions. Aperture A small circular hole in an opaque disk; used to limit the size of the electron beam. Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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Astigmatism The focusing of electrons traveling in different planes at different levels, due to inhomogeneities in the field of an electromagnetic lens; a major limit to resolution in an electron microscope. Backscattered electron An electron from the incident beam that is reflected from the surface of a specimen; of relatively high energy. Cathode ray tube (CRT) A vacuum tube in which an electron beam is rastered on a phosphorescent screen to produce an image; used as a video display monitor on scanning electron microscopes. Charge-coupled device (CCD) A solid-state imaging device consisting of arrays (up to 2048 • 2048) of silicon detector electron wells. Incident electrons or photons elevate valence electrons to the conduction band, where they are held until collected from each well, row by row. Chromatic aberration The focusing of electrons of different wavelengths (energies) at different distances from an electromagnetic lens. Critical-point drying A method of drying specimens by replacement of water with solvents that, when subjected to their critical temperature and pressure, undergo the transition from liquid to vapor without change in surface tension. Cryosection A section cut from a frozen specimen, using the ice as a supporting matrix during the sectioning process. Diffraction The bending of light rays or electrons by the edge of an opaque object; a significant limit to resolution in optical and electron microscopes. Diffusion pump A vacuum pump that uses heated oil vapor to force gas molecules out of a closed chamber, resulting in diffusion of the remaining gas molecules toward the pump. Digital image An image consisting of an array of picture elements (pixels) of varying brightness recorded as binary data. Electromagnetic lens A lens constructed of a soft iron core wound with an electrical conductor, producing a magnetic field used to focus a beam of electrons. Electron gun A device for producing an electron beam; consists of a cathode, anode, and Wehnelt shield. Embedding Infiltration of a specimen with a liquid medium that can be solidified or polymerized to form a solid matrix for support during subsequent procedures, such as sectioning. Evaporator A chamber equipped with electrodes and a vacuum system; used for evaporation of carbon a n d / o r metal under high vacuum as surface coatings. Field emission Electron gun of very high brightness in which electrons are extracted from a small tungsten crystal by high voltage and without heating; requires very clean high-vacuum conditions. Filament The cathode of an electron gun; often made of a thin V-shaped tungsten wire, which emits electrons when heated under vacuum.
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Fixation The stabilization and preservation of biological structure by chemical or physical methods. Freeze-drying vacuum.
Drying of a frozen specimen by sublimation of ice under
Freeze-fracture
The fracturing of frozen specimens under vacuum, followed by replication of the fractured surface by evaporation of platinum and carbon.
Freeze-substitution The replacement of frozen water in a specimen by acetone or methanol at about - 85~ Glow discharge A glowing plasma produced by low-voltage electrical discharge under low-vacuum conditions in a vacuum evaporator; used to clean carbon-coated grids and make their surface hydrophilic. Grid A specimen support used in transmission electron microscopy; usually consists of a fine metal mesh.
Immunocytochemistry The detection and localization of antigens in or on cells and tissues by using specific antibodies and labeled immunological reagents. In situ hybridization
Identification and localization of specific nucleotide sequences using labeled probes of complementary nucleotide sequences.
Lanthanum hexaboride (LaB 6) Material used to make electron microscope filaments of high brightness and long life. Morphometry The quantitative assessment of morphological features; uses principles of stereology relating three-dimensional structure to two-dimensional images. Negative A photographic image of contrast opposite to that of the original object; usually produced on film in a camera. Negative stain Used to increase contrast of macromolecules or particulate specimens by surrounding them with electron-dense material. Positive stain A stain that increases contrast of the specimen, usually by nonspecific binding of a heavy metal.
Print
A positive (same contrast as the original object) photographic image
on paper.
Resolution The ability to distinguish two objects as being separate. Rotary pump A mechanical pump with an eccentrically placed rotating piston and sliding vanes, used to produce a vacuum of approximately 10-1 torr.
Rotary shadow Metal evaporation at low angles under vacuum while the specimen is rotated; used to increase contrast of macromolecules or small particulate samples. Scanning electron microscope (SEM) An electron microscope in which a finely focused electron beam is scanned in a raster pattern over the surface of a conductive specimen; the signal generated is displayed as an image on a cathode ray tube scanning in parallel with the electron beam.
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Arthur R. Hand Scattering The interaction of a primary electron in an electron beam with an atom in the specimen; elastic scattering occurs without change in energy of the primary electron but with a large change of direction; primary electrons that are inelastically scattered lose energy but have less directional change. Secondary electron Low-energy electron ejected from an atom due to an inelastic scattering event; the main signal utilized to obtain topographic information in the SEM. Secondary electron detector Collects secondary electrons generated in a SEM and produces an electronic signal that is displayed as brightness on a cathode ray tube. Spherical aberration Focusing of electrons traversing the periphery of an electromagnetic lens at a point closer to the lens than electrons traversing the axial region of the lens. Support film A thin plastic film covering a specimen grid; used for supporting macromolecules, particulate specimens, replicas, and thin sections. Torr
A unit of pressure equal to 1 mm Hg.
Transmission electron microscope (TEM) An electron microscope in which the image is formed from electrons that are transmitted through a (relatively) thin specimen. Vacuum gauge A device for measuring gas pressure in a vacuum chamber; thermocouple, resistance, and ionization gauges are used most frequently in electron microscopes. Vacuum valve A valve used to control the pumping or ventilation of different parts of a vacuum system. Wehnelt shield An apertured shield between the filament and the anode, held at negative potential to the filament; produces an intense cloud of electrons that serves as the source of the electron beam.
I. Introduction In the 50 years that electron microscopes have been used in the biological sciences, our knowledge of cell and molecular structure and function has made tremendous strides. Although advances in many technical areas contributed to our present knowledge, it was electron microscopy that spawned the field of cell biology and provided the structural framework necessary for correlating events at the molecular level with the physiological and pathological changes exhibited by the organism. Electron microscopic examination of biological samples can provide unique information. Additionally, certain types of information can be obtained more rapidly and easier than with other methods. The 1000-fold greater resolution of the electron microscope compared to the light microscope can provide details of structure in the 1-nm range. Identification of subcellular structures in sections and in isolated preparations is greatly facilitated. Electron microscopy, in combination with the use of specific antibodies or nucleotide probes, can yield data on the distribution and localization of biologically relevant antigens and
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nucleic acid sequences. Finally, detection and analysis of the interactions of electrons with atoms of the specimen can provide information on its composition.
II. Principles of Electron Optics A. Properties of Electrons and Electron Beams 1. E l e c t r o n s
Electrons are subatomic particles of small mass, 9.1 • 10 -31 kg, which carry a negative charge of 1.6 • 10-19 C. As with light and other forms of electromagnetic radiation, electron behavior exhibits properties of both waves and particles, and can be predicted using the same principles that are applied to light optics, de Broglie showed that the wavelength of electrons is inversely related to their energy, A = h/mv,
(1)
where A is the wavelength, h is Planck's constant (6.626 • 10-23 ergs/sec), m is the mass of the electron, and v is the velocity of the electron. In an electron microscope, the energy of the electrons is determined by the accelerating voltage or potential difference between the cathode (negative electrode) and anode (positive electrode). For a potential difference of 60,000 V (60 kV), a common accelerating voltage used in transmission electron microscopes (TEMs), the wavelength can be calculated to be approximately 0.005 nm. For comparison, the wavelength of visible light ranges from 400 to 800 nm. "
2. Resolution Both electrons and light are subject to the phenomenon of diffraction, which is the bending or spreading of the waves into the region behind an obstruction that the waves have passed (Fig. 1). The diffracted waves will combine constructively or destructively with the undiffracted waves, producing a pattern of light and dark lines or rings extending from the edge of the obstruction. Thus, the edge appears fuzzy instead of sharp. Diffraction is a major limitation to resolution in light and electron microscopes. Resolution is the ability to distinguish closely spaced objects as being separate. In light optics two bright objects will just be resolved when the intensity maximum of one object coincides with the minimum intensity of the first dark diffraction ring from the edge of the second object (Fig. 1). The relationship between resolution and the wavelength of the illuminating radiation is given by Abbe's equation, d = 0.612A/n sin a,
(2)
where d is the radius of the first dark diffraction ring, n is the index of refraction, and cr is one-half of the aperture angle. The aperture angle is the angle subtended by the illumination accepted by the lens (Fig. 2). The term (n sin a) is also known as the numerical aperture, N.A. Abbe's equation clearly shows that resolution increases (d decreases) as the wavelength decreases. Thus, in a light
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Fig. 1 Diffractionand resolution. (A) Light waves or electrons are diffracted by the edge of an obstruction. (B) Airy disk showing intensity maxima and minima due to constructive and destructive interference of diffracted waves. (C) Intensity plot of Airy disk, where d is the radius of the first dark ring. An adjacent object will just be resolved when its intensity maximum coincides with the minimum of the first dark ring.
microscope with an oil immersion lens of N.A. 1.3 and A of 400 nm, resolution is approximately 0.2 ~m. In a TEM, the much smaller wavelength of electrons provides much greater theoretical resolutionmapproximately 0.003 nm. Despite the fact that lens aberrations and other phenomena limit the attainable resolution to about 0.1-0.2 nm, the 1000-fold greater resolution is the principal advantage of the electron microscope over the light microscope.
3. Interaction of Electrons with Matter When electrons encounter solid material, e.g., a thin section (50-100 nm thick), they may (1) pass through it without any interaction; (2) undergo elastic scattering, i.e., change their direction without losing any energy; or (3) undergo inelastic scattering, i.e., change direction with an attendant loss of energy. In thick or bulk samples, some electrons may lose all of their energy due to multiple inelastic scattering events and be absorbed; this results in heating of the sample. A few of the incident electrons may be elastically scattered through a large angle and emerge from the surface of the specimen with little or no loss of energy. The number of these backscattered electrons increases with the increasing atomic number of the elements in the specimen. Elastic scattering is a result of the electrostatic interaction of the incident electron with the nucleus and the surrounding electrons of an atom in the specimen. The scattering angle is relatively large (typically around 5~ and many of these electrons are removed from the beam by the objective aperture
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LENS
I
APERTURE
I
I
FOCAL PLANE
Fig. 2 Light or electrons originating from a point object and focused by a lens. The aperture restricts the illumination to those rays passing closer to the center of the lens; a is one-half of the aperture angle.
and by collision with the walls of the microscope column. Elastic scattering is the principal source of contrast in the TEM image. The transfer of energy to the atoms of the specimen during inelastic scattering results in several secondary effects. Electrons of low energy (up to 50 eV) may be ejected from the specimen; these are secondary electrons, which provide one of the main signals for image formation in the scanning electron microscope (SEM). If an inner shell orbital electron is ejected from the atom, the atom is left in an unstable state, and the empty orbital is filled by an electron from one of the outer shells. The loss of energy that accompanies this transition appears as a characteristic X-ray or as a low-energy Auger electron. The collection and measurement of the inelastically scattered electrons, X-rays, and Auger electrons form the bases for different types of microanalyses. For biological samples, energy-dispersive X-ray microanalysis and electron energy-loss spectroscopy can provide qualitative and quantitative data on specimen composition and elemental distribution. If the incident electron is decelerated through electrostatic interactions with the atom, X-rays of variable energy, up to the energy of the incident electron, are given off. This is known as Bremsstrahlung, or continuum, radiation. The energy of the continuum radiation is not characteristic of particular atoms, and it is the main source of background X-rays in the X-ray spectrum in microanalysis. Applications of microanalysis are not discussed in this chapter, and the interested reader is referred to Goldstein et al. (1992), Morgan (1985), Reimer (1984, 1985), and Egerton (1986).
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Arthur R. Hand Electron microscopes are carefully constructed in order to shield the operator from X-rays produced during interactions of the beam with the specimen and with the microscope. Nevertheless, surveys for leakage of X-rays should be conducted at least annually by the institutional radiation safety officer.
B. Electromagnetic Lenses In a TEM, electrons that pass through the specimen without interaction are focused by electromagnetic lenses, forming a magnified final image. Electric current flowing in a conductor induces a magnetic field around the conductor. A simple electromagnet consists of a soft iron core surrounded by a helically wound conductor. The magnetic field is concentrated by the iron core. The strength of the field depends on the number of turns of the conductor and the current flowing in the conductor; the latter can easily be varied. Electromagnetic lenses (Fig. 3) have a soft iron shroud surrounding the windings, and a soft iron pole piece lining the bore of the lens. The north and south poles of the pole piece are separated by a brass spacer, which serves to further concentrate the magnetic field in a very small space. An electron traveling along the axis of the lens will be unaffected by the magnetic field, and its path will be unaltered. An electron that enters the lens off-axis will be affected by the field; the force acting on the electron is at right angles to the original path of the electron and to the magnetic field. The electron will initially follow the vector that is the resultant of its velocity and the force exerted by the magnetic field. As the path of the electron changes, the resultant vector also changes; the cumulative effect on the electron causes it to follow a helical path through the lens (Fig. 4). Varying the strength of the magnetic field will change the number of turns of the helix completed by the electron, resulting in rotation of the final image. Modern TEMs are designed to minimize image rotation by using different combinations of lens currents in the projector lens system. Electromagnetic lenses have a relatively short focal length; the focal length of the objective lens of a TEM is about 2 mm. Therefore, the specimen must be placed very close to the lens, and in most microscopes actually is immersed in
Fig. 3 Electromagneticlenses consist of an electrical conductor (copper wire) wound around a soft iron core. The magnetic field is concentrated by the iron shroud surrounding the windings. A soft iron pole piece serves to further concentrate the field in the gap created by a brass spacer.
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Fig. 4 The field of an electromagnetic lens causes electrons entering the lens off of the lens axis to follow a helical path as they are brought to focus.
the magnetic field of the lens. However, electromagnetic lenses have a large depth of field, which is the axial distance over which the lens focus can be changed without a perceptible change in image focus. The depth of field is inversely related to the objective aperture angle (c~) and directly related to the lens focal length. The entire thickness of a typical thin section (50-100 nm) will appear in sharp focus in the TEM. Electromagnetic lenses also have a large depth of focus, which is the axial distance over which the image remains in focus at a given lens setting. The depth of focus is directly related to the square of the total magnification and inversely related to the objective aperture angle (a). In a TEM the depth of focus is several meters; thus the position of the viewing screen and the placement of the camera with respect to the final lens are not critical. Electromagnetic lenses are subject to several aberrations that reduce resolution. Chromatic aberration occurs when electrons with different energies enter the lens. Higher energy electrons are focused further from the lens than are lower energy electrons; slight differences (1-2 eV) in the energy of electrons from thermionic emission sources (Section III,A) will result in chromatic aberration. Electrons that are inelastically scattered by the specimen have lower energies compared to those that are transmitted without interaction. Thus, as section thickness increases, chromatic aberration also increases. Chromatic aberration can be minimized by employing highly stabilized high-voltage power supplies, by employing a field emission source (Section III,A), which produces a virtual monochromatic electron beam, and by using thinner sections.
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ArthurR. Hand Spherical aberration results in the focusing of electrons traversing the peripheral region of the lens closer to the lens than electrons traveling near the lens axis. Spherical aberration cannot be corrected and is a major limit to resolution; it can be reduced by using an objective aperture to limit the beam to the axial region of the lens. Astigmatism is the focusing of electrons traveling in different planes at different levels, and results from inhomogeneities in the magnetic field of the lens caused by defects in the iron shroud or pole piece. Astigmatism can also result from contamination of the objective aperture, which becomes electrically charged in the electron beam, or if the specimen support or the specimen is magnetized. Astigmatism can be detected by focusing on a small hole or dirt particle at 60,000-100,000 • the edge of the hole or particle will not be in focus all around, but will exhibit both under- and overfocused Fresnel fringes (Fig. 5). Alternatively, the phase contrast image of the plastic section or support film at 150,000-200,000 • can be used. With the lens set close to focus, astigmatism is evident in the phase contrast image as a linear, rather than granular, effect that changes orientation by 90 ~ when going from over- to underfocus. Astigmatism can be corrected by adjusting a set of electromagnets placed around the lens, the stigmators, to produce an external magnetic field that just counterbalances the inherent astigmatism of the lens.
III. Design and Operation of Electron Microscopes A. Illumination System The illumination system of an electron microscope (Fig. 6) consists of a source of electrons, also called an electron gun, and a series of electromagnetic lenses, the condenser lenses, that demagnify or focus the initial electron beam to a small spot on the specimen. The electron gun has three main components, the cathode, the anode and the Wehnelt (or bias) shield (Fig. 7). The cathode, more commonly called the filament, is maintained at a negative potential difference to the anode, typically 50,000-100,000 V (50-100 kV) in a TEM and 2-30 kV in a SEM. A thin tungsten wire bent into a V shape is the most common type of filament, or emitter, used. Heating the filament with a low-voltage direct current causes electrons to leave its surface, and the potential difference between the cathode ( - ) and the anode (+) accelerates the electrons toward the anode. The Wehnelt shield, positioned between the cathode and the anode, is held at 100-200 V negative to the cathode. This has the effect of creating an intense cloud of electrons in its small aperture, which then serves as the electron "source." The Wehnelt shield is connected to the high voltage and to the filament-heating voltage by resistors. The electron gun is said to be "self-biased," because changing either the high voltage or filament voltage correspondingly changes the Wehnelt voltage to control the number of electrons entering the beam. Manual adjustment of the Wehnelt voltage also will increase or decrease the number of electrons entering the beam and thus the amount of current flowing in the beam and its brightness.
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Fig. 5 Fresnel fringes produced by diffraction of electrons at the edge of a hole can be used to assess and correct objective lens astigmatism. (a) An overfocused fringe (dark) located at about 11 and 5 o'clock (arrowheads), and an underfocused fringe (bright) at about 2 and 8 o'clock, indicate the presence of astigmatism. (b) Correction of astigmatism results in a thin, even, dark overfocused fringe. Bar = 50 nm.
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Fig. 6 Diagramof a TEM. (Courtesy of JEOL USA, Inc.)
Two other types of emitters in current use are the l a n t h a n u m hexaboride (LAB6) filament and the field emission source. The LaB6 filament is a pointed rod that provides a stable current from a smaller area than is provided by a tungsten filament. Its brightness is 10 times that of a tungsten filament, and it has a lifetime of 500 hr or longer. LaB6 filaments require a vacuum of 10 -6 torr (see Section III,E) or better. A field emission source employs a single crystal of tungsten, with an emitting region of about 10 nm. Its brightness is about 1000 times that of a standard tungsten filament. A field emission gun has a double anode; the first anode (+ 2000 volts) extracts electrons from the tip; the second anode then accelerates the electrons d o w n the column. The field emission gun operates at room temperature, but requires a very high vacuum, about 10 -9 to 10-10 torr. It produces a very small probe size, with negligible energy spread. In a TEM, two condenser lenses are typically employed. The first lens usu-
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Fig. 7 An electron gun consists of a cathode (filament), anode, and Wehnelt or bias shield. The filament is heated by adjusting the current from the power supply (PS). Balancing resistors (BR) and a variable resistor (VR) between the Wehnelt shield, filament, and high voltage (HT) serve to regulate the bias potential and thus the number of electrons entering the beam. The Wehnelt also acts as an electrostatic lens, focusing the beam to a small spot above the anode.
ally has a few (4-10) settings and its excitation forms an initial demagnified beam spot. The second lens is used to vary the a m o u n t of illumination reaching the screen. An aperture of about 100-200/.~m is placed between the second lens and the specimen. The aperture serves to limit the n u m b e r of electrons reaching the specimen, to decrease the angle of illumination, and to reduce spherical aberration. In a SEM, a third condenser lens is often used, to reduce further the size of the beam (or "probe"). Because this lens also is used to focus the beam on the specimen and thus focus the image, it often is called an "objective" lens, although its design and function differ from those of the objective lens in a TEM. The size of the beam spot (or probe) is a major determinant of resolution in the SEM. With a small probe, the volume of the specimen with which the beam electrons interact to give rise to secondary electrons is smaller. Thus, the signal for each individual picture element (pixel) making up the final image originates from a smaller part of the specimen. Also part of the illumination system are deflection coils, which are used to shift and tilt the beam during operation and alignment. In a SEM, additional deflection coils present in the final condenser lens are used to raster the beam over the surface of the specimen. The size of the area covered by the raster pattern is inversely proportional to the magnification of the SEM image.
B. Specimen Carrier and Stage In both TEMs and SEMs, the specimen is located after the condenser lenses, and for highest resolution as close as practical to the objective lens. The specimen stage must be mechanically stable and allow for very precise movements of the
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ArthurR. Hand specimen. The design of the stages for a TEM and a SEM is very different, however. In a TEM, two types of stages are used: top entry and side entry. The top-entry stage utilizes a cartridgelike specimen holder that is inserted into the stage from above. A special mechanism, which in some microscopes may accommodate up to six specimen holders, is used to manipulate the specimen holder and to insert it into the stage. The side-entry stage utilizes a rod-shaped specimen holder with one or two places for specimens at one end, which are secured by a clamp and spring mechanism. The rod is inserted into the stage through an airlock on one side of the column. Although a top-entry stage provides slightly better resolution, most TEMs utilize a side-entry stage because it allows more versatility in positioning of the specimen, and the design of a device (goniometer) for tilting the specimen is also simpler. The specimen stage allows movement of the holder in order to position the specimen in the electron beam. In a TEM stage motion is usually limited to about + 1 mm in the X - Y direction; thus specimen size is very limited. If a goniometer is fitted to the stage, specimen tilting up to + 60 ~ can be achieved. The tip of the side-entry holder is fitted with a jeweled bearing, which rests against one of the stage drive mechanisms; the drive moves the specimen holder back and forth to position the specimen. The other drive mechanism moves the specimen carrier in a direction 90 ~ to the first drive. An anticontamination device is located in the specimen area of most TEMs in order to reduce the level of contamination of the specimen due to condensation of hydrocarbons from the vacuum pumps, as well as components vaporized from the specimen as a result of irradiation by the electron beam. The anticontamination device is cooled by an externally mounted dewar containing liquid nitrogen. Contaminants condense on the cold surfaces near the specimen, rather than on the specimen. The stage of a SEM is designed to accept a wide range of specimen sizes, up to 100 mm or more in diameter. It has a large motion, often 50 mm or more in the X and Y directions, can rotate a full 360 ~ and can tilt up to 90 ~ In addition to changing the angle of view, tilting and rotating the specimen relative to the electron detectors (see below) may help to enhance the signal. The stage can also be raised or lowered (Z adjustment) to accommodate large specimens. The working distance (focal length) of the final lens is varied in order to focus the electron beam on the surface of the specimen. Using a long working distance increases the depth of field, but decreases resolution and signal strength.
C. Imaging System The imaging system is the most critical part of the electron microscope. In a TEM it consists of the objective lens and aperture, the objective stigmators, and the projector lenses. The objective lens forms the initial image of the specimen and magnifies it about 100 x. The focal length of the objective lens is about 2 mm, so the specimen must be placed within the concentrated magnetic field of the lens. Varying the current to the objective lens permits focusing of the image. Two or three additional lenses, the projector lenses, are located below the objective lens. The final magnification of the image is varied by altering the current in the projector lenses. The objective aperture is the key to the formation of a useful image in the
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TEM. It is placed a short distance below the specimen and serves to eliminate electrons that have been elastically scattered by the specimen through an angle greater than c~. The elastically scattered electrons do not contribute to image formation but cause an overall decrease of contrast in the image. A smaller aperture will eliminate more scattered electrons from the beam, resulting in an increased contrast in the image. Generally, apertures of 3 0 - 5 0 / ~ m in diameter are used. Because resolution is inversely related to the objective aperture angle (Abbe's equation), use of apertures of too small size will limit the resolution obtained. By eliminating the electrons traversing the peripheral part of the lens, the objective aperture also serves to reduce spherical aberration. The imaging system of a SEM (Fig. 8) is very different from that of a TEM. Instead of detecting electrons that are transmitted through the specimen, the image in the SEM is based either on secondary electrons generated by inelastic scattering events near the surface of the specimen, or on p r i m a r y electrons of the beam that are reflected or backscattered from the specimen surface. Seco n d a r y electron detectors in c o m m o n use are based on the E v e r h a r t - T h o r n l e y design (Fig. 9). A positively charged collector attracts the low-energy secondary electrons, which are then accelerated toward a scintillator. The photons produced as the electrons strike the scintillator enter a photomultiplier, where they are converted into photoelectrons and their n u m b e r is increased 105- to 106-fold. The resulting signal is displayed as brightness on a cathode ray tube (CRT). Backscattered electrons have higher energies, and are directed mainly upw a r d in the direction of the final lens; thus they are inefficiently collected by the
Fig. 8 The imaging system of a SEM. The electron beam is focused by electromagnetic lenses to a small spot and is rastered over the specimen surface. Secondary electrons (S.E.) generated during interaction of the beam and the specimen are collected by the detector. The amplified signal from the detector is displayed as brightness on a cathode ray tube (CRT) scanning in parallel with the beam. The magnification of the image is determined by the ratio D:d.
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Fig. 9 A secondary (Everhart-Thornley) electron detector. Low-energy (< 50 eV) secondary electrons are attracted to the detector by the positively charged (about 200 V) collector, then are accelerated toward the scintillator by a potential of 10-12 kV. Photons generated by electrons striking the scintillator are conducted by a light guide to a photomultiplier, where they are converted into photoelectrons and multiplied about 106-fold.
secondary detector. Annular backscattered electron detectors of a solid-state type or a scintillator/photomultiplier (Robinson) type are placed just below the final lens.
D. Image Observation and Recording In a TEM, the image produced by the objective and projector lenses is projected onto a screen coated by a light-emitting phosphor. The screen can be viewed directly, or for increased magnification and critical focusing it can be observed through a binocular microscope. The grain of the phosphor is much larger than that of the film used to record the image, so the resolution of the screen is considerably less than that of the recorded image. In most TEMs, the image is recorded on sheet film (or emulsion-coated glass plates in older microscopes) in a camera mechanism located beneath the screen. After the microscopic field is selected, the objective lens is carefully focused and the level of illumination is reduced by defocusing the beam with the condenser lens. In most microscopes a photometer or current meter is used as a guide for setting the screen brightness a n d / o r to adjust the exposure time automatically. An unexposed film is moved beneath the screen, and the screen is raised to expose the film. After exposure, the film is retracted and placed in a receiving box. The film is developed photographically to produce a negative, and contact prints or enlargements are made in a darkroom. Other options for image recording are available on some microscopes. When many photographs must be taken (e.g., for a quantitative morphometric or radioautographic study), a 35-mm camera can be placed just below the last projector lens. The recorded image is smaller, but substantial enlargement is possible. This 35-mm film is much less expensive than the larger 31 • 4-inch sheet film, and can be loaded as rolls containing many more exposures. A video
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camera can be placed beneath the screen to display the image on a video monitor and record it on videotape. A charge-coupled device (CCD) camera can be used to record digital images that can be stored on magnetic or optical storage media and used with computers for viewing, image processing, and analysis, and transmission over computer networks. In a SEM, the signal from the secondary or backscattered electron detectors is displayed as an image on a CRT or video monitor, which is scanned in parallel with the electron beam scanning the specimen (Fig. 8). For photography, the beam is scanned very slowly over the specimen in order to generate a strong signal, and the image is recorded on a second high-resolution CRT. Generally, Polaroid black and white positive/negative film is used, but in order to reduce costs sometimes 4 • 5-inch sheet film is used instead. Because digital imaging is now a standard feature on SEMs, enhanced-resolution video printers or laser printers that produce low-cost prints can be used, and archiving on magnetic and optical media for subsequent computer processing and analysis is possible. Additionally, TV scan rates and digital processing allow averaging of several frames, lines, or pixels to improve the signal-to-noise ratio, and permit viewing of the monitor in ordinary interior light.
E. V a c u u m System Electron microscopes must be operated under high-vacuum conditions because the scattering of electrons due to collisions with gas molecules would otherwise prevent formation of a useful beam. Good vacuum conditions also reduce contamination, prevent high-voltage discharge, and prolong filament life. Most microscopes employ a dual vacuum system (Fig. 10), consisting of a rotary pump to achieve an initial vacuum of about 10 -~ torr and an oil diffusion pump to obtain an operating vacuum of 10 .6 to 10 . 7 torr. [A torr is a unit of pressure equal to 1 m m Hg. Other units of pressure frequently used in vacuum technology are bars or millibars (mbar) and Pascals (Pa) or millipascals (mPa); 1 torr = 133 Pa = 1.33 mbar.] The rotary p u m p is also used to back the diffusion p u m p and to p r e p u m p different parts of the microscope. An anticontamination device, or cold trap, is often used with the diffusion p u m p in order to condense oil vapors backstreaming into the microscope column. Also part of the vacuum system are vacuum valves, airlocks, and vacuum gauges, which allow the vacuum to be controlled in different parts of the microscope. A specimen airlock allows introduction of the specimen from atmospheric conditions into the column in a few seconds without loss of the high vacuum. A camera airlock isolates the camera from the column so that exposed film can be removed and replaced with fresh film. A gun airlock or isolation valve protects the gun and filament from accidental vacuum loss during venting of other parts of the microscope, and permits exchange of the filament while high-vacuum conditions are maintained in the rest of the instrument. Modern electron microscopes employ automated vacuum systems, which greatly simplify operation and generally prevent catastrophic errors that might damage or contaminate the instrument. Other types of vacuum p u m p s are also used in electron microscopes. Turbomolecular p u m p s are capable of achieving a vacuum in the range of 10 -9 to 10-11 torr; they are often employed when traces of hydrocarbons, which are
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Fig. 10
The vacuum system of a TEM. The electron gun, column, and camera chamber are maintained under high vacuum by the diffusion pump. The buffer tank provides a backing vacuum for the diffusion pump, allowing the rotary p u m p to be used for prepumping of the specimen airlock or other parts of the microscope, and for drying film in the desiccator. Some microscopes may have a second rotary p u m p instead of a buffer tank for backing the diffusion pump. Sometimes a separate film desiccator pumped by a dedicated rotary p u m p is employed. The isolation valves and vacuum valves allow different parts of the microscope to be ventilated or pumped while vacuum is maintained in the remainder of the instrument. Not shown are vacuum gauges used to monitor the vacuum in different parts of the system, and valves permitting ventilation with room air or nitrogen gas.
present in rotary- and diffusion-pumped systems, cannot be tolerated. Ion-getter pumps create a vacuum by electrostatic discharge, producing charged gas molecules that are attracted to plates of opposite charge. Ion-getter pumps can achieve vacuums of 10 -11 torr; they are usually employed with LaB 6 and field emission types of electron guns.
IV. Methods of Sample Preparation The properties of electrons and electron beams demand that our samples meet specific requirements before they can be observed in the electron microscope.
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Although a number of different preparative techniques will be discussed, the types of specimens that can be examined are limited when compared to the possibilities with light microscopy. A significant difference is that only nonliving specimens can be observed in the electron microscope. This is because high-vacuum conditions (better than 10 -4 torr) must be maintained in the microscope [except for some "environmental" SEMs, in which the use of partially hydrated specimens (pressures of about 10 -2 torr in the specimen chamber) is permissible], and because of the tremendous energy of the electron beam, and consequent potential for specimen damage. Another limiting factor for TEMs is the poor penetrating power of electrons. Thus, the thickness of most specimens must be less than 100-200 nm, and most cells must be cut open to view their internal contents. Because most biological specimens consist mainly of elements of low atomic number whose mass differs by relatively small amounts, it is usually necessary to employ some type of dense material (typically a metal or metal salt) that will enhance specimen contrast either specifically or nonspecifically. Additionally, for SEMs, the specimen must be coated with a thin layer of a conducting material to prevent a build-up of negative charge from the electron beam, and generally to increase the number of secondary electrons produced. Safetu Note
As in all laboratory environments, proper attention to issues of safety are essential in an electron microscopy laboratory. Appropriate protective clothing (lab coats or aprons, gloves, eye protection) should be worn, and general safe handling practices for chemicals and glassware should be followed. A properly functioning chemical fume hood is essential. Some of the chemicals that are commonly used in an EM laboratory are encountered infrequently in other types of laboratories, and special precautions are noted in the sections where these are mentioned. Additionally, highly reactive or toxic chemicals must be properly disposed of; consultation with an institutional safety officer is recommended.
A. Plastic E m b e d d i n g and Thin Sectioning The ultrastructure of specimens such as tissues, cultured cells, microorganisms, and subcellular fractions frequently can be best evaluated in thin (50-100 nm) sections examined in the TEM. Electrons at 60-100 kV can readily penetrate biological specimens of this thickness; overlapping of cellular components is generally not troublesome, sufficient contrast between cellular constituents and the surrounding medium usually can be obtained, and the depth of field of the objective lens is large enough to include the entire thickness of the section. In order to prepare such sections, the specimen must be well preserved and will require some kind of internal support, e.g., a polymerized plastic resin; a very sharp knife is required, and it is necessary to use a specialized instrument called an ultramicrotome. 1. F i x a t i o n
Many different fixative solutions and methods of fixation are available. The choice of fixative and method depends on the nature of the sample and the
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information being sought. For optimum preservation of organelle and membrane structure, a strong protein cross-linking fixative, such as glutaraldehyde, should be employed. To retain biological activity, such as antigenicity, a weak cross-linker, such as paraformaldehyde, might be used. Clearly, in the latter case, it may be necessary to compromise structural preservation in favor of biological activity. Excision of tissue from a living (anesthetized) animal, or from an animal immediately after death, and mincing in the fixative solution with a sharp, clean razor blade will generally give acceptable results. Vascular perfusion of small animals with fixative solution yields superior results, and is necessary for certain tissues (e.g., central nervous system, formative cells of the teeth). Perfusion may not be possible, however, in experiments in which samples also are collected for a number of other uses, and in studies of human tissues. Glutaraldehyde (C5H802,100 Da) is a dialdehyde that reacts primarily with free amino groups of proteins, resulting in cross-linking of adjacent protein molecules. Polymers of glutaraldehyde that form in solution may increase the effectiveness of cross-linking by allowing reaction between amino groups separated by greater distances. Glutaraldehyde fixation is typically carried out for 30 min to 2 hr with concentrations of fixative between 1 and 3%, buffered to a pH near neutrality. Typical buffers used include phosphate, cacodylate, HEPES, and PIPES; Tris cannot be used because it reacts with glutaraldehyde. For many cells and tissues, a buffer concentration of about 0.1 M can be used; for some samples, the osmolality of the fixative solution may require more critical adjustment, but this is best determined empirically. Glutaraldehyde generally provides excellent structural preservation, but its effects on the biological activity of macromolecules are variable. In some cases, demonstration of enzymatic or antigenic activity is readily achieved after glutaraldehyde fixation; in other cases, complete inhibition of activity may occur. Formaldehyde (H2CO , 30 Da) is a highly reactive aldehyde, but it has poor cross-linking ability and the degree of structural preservation obtained is significantly less than with glutaraldehyde. Its effect on biological activity, however, is generally less than that of glutaraldehyde, thus it is frequently used in situations in which maximum retention of enzymatic or antigenic activity is required. Formaldehyde fixation is typically carried out for 1-4 hr, or even overnight, at concentrations of 2-4% in a neutral buffer. To increase structural preservation, glutaraldehyde is sometimes added in concentrations of 0.0250.1%. For most uses in electron microscopy, the purity of fixative reagents is a significant consideration, and it is recommended that they be purchased from an EM supply house. Purified glutaraldehyde (EM grade) can be obtained in sealed ampules in concentrations from 8 to 70%; biological grade glutaraldehyde should be avoided. Standard formaldehyde solutions (37%) contain about 15% methanol, which has a deleterious effect on ultrastructure. Pure formaldehyde can be purchased from an EM supply house in sealed ampules in a concentration of 16-20%, or can be prepared by depolymerizing paraformaldehyde powder. The latter is done by heating a concentrated suspension of paraformaldehyde powder in distilled water to 70~ in a fume hood, then adding I N sodium hydroxide dropwise with stirring until the solution clears.
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After fixation is complete, the samples are rinsed in buffer, usually the same buffer used in the fixative solution. Sucrose m a y be a d d e d to the buffer to increase osmolality; sucrose-containing solutions should be m a d e in small quantities and used p r o m p t l y to avoid growth of microorganisms. For most applications, samples m a y be stored in buffer overnight or for a few days at 4~ Samples to be used only for morphological studies are routinely postfixed with o s m i u m tetroxide (OsO4, 254 Da), a highly reactive metal oxide. O s m i u m tetroxide reacts p r e d o m i n a n t l y with unsaturated lipids, imparting electron density (contrast) to biological membranes. It also reacts with proteins, lipoproteins, and nucleic acids. O s m i u m tetroxide postfixation imparts to cells and organelles their familiar ultrastructural appearance (Fig. 11). O s m i u m tetroxide solutions can be used unbuffered or buffered with phosphate, cacodylate, or collidine, usually at a concentration of 1-2%. Potassium ferri- or ferrocyanide is sometimes a d d e d to the o s m i u m tetroxide to further increase m e m b r a n e contrast. Typical fixation times are 30 min to 2 hr; o s m i u m tetroxide penetrates slowly, so tissue pieces should be small (about I m m or less on a side) and the vials should be gently agitated or rotated. Tissues typically blacken as the osm i u m is reduced.
Fig. 11 Thin section of a rat hepatocyte observed in a TEM. The contrast of the organelles and membranes has been enhanced by osmium tetroxide postfixation and by section staining with uranyl acetate and lead citrate. N, Nucleus; M, mitochondria; LY, lysosome; BC, bile canaliculus.
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Fixative chemicals are highly toxic and must be handled with care. Contact with skin should be avoided; immediately wash exposed areas thoroughly with water. Avoid breathing fumes; work in a fume hood, especially when depolymerizing paraformaldehyde, or when using osmium solutions. Fixative solutions should be stored at 4~ preferably in a refrigerator other than that used for storage of samples and reagents for biochemical and other sensitive analyses. After fixation, samples may be treated with solutions of various heavy metals to further enhance the final contrast obtained in the TEM. Uranyl acetate solutions (0.5-2%, aqueous or buffered to about pH 5 with acetate or maleate) are frequently used; other "block staining" reagents include lead aspartate and bismuth subnitrate. These metal solutions generally increase contrast nonspecifically by binding to various tissue components, although with some differences in affinity. With uranyl acetate, care must be taken to rinse the samples thoroughly so that they are free of phosphate or cacodylate used in previous steps, because uranyl ions will precipitate with these anions.
2. Embedding The purpose of embedding the sample is to provide a supporting matrix so that sections can be cut thin enough for electrons to penetrate and provide sufficient resolution of subcellular structures. The most widely used embedding media are epoxy resins; they are relatively easy to work with, provide consistent results, have good sectioning and staining properties, and generally withstand fairly intense irradiation by the electron beam. Epoxy resins are usually mixtures of three or four components, whose proportions can be varied (to some degree) to modify the properties of the final polymerized resin. In addition to the epoxide (Epon or Epon substitutes), anhydrides (e.g., nadic methyl anhydride, NMA; dodecenylsuccinic anhydride, DDSA) are added to the resin to modify its hardness, and an accelerator [e.g., 2,4,6-tris(dimethylamino)methylphenol, DMP-30] is used to speed up the polymerization, which is carried out at elevated temperatures (60-70~ A number of other epoxy resins have been developed during the past 35 years. One of the most useful resins is that developed by Spurt (1969); its low viscosity improves penetration of the resin into plant or mineralized tissues. Epoxy resins are immiscible with water, thus samples must be thoroughly dehydrated before embedding. Usually an ascending series of ethanol-water mixtures is used, with several changes in 100% ethanol from a freshly opened bottle. Although most resins are miscible with ethanol, propylene oxide, which is highly miscible with epoxy resins, is commonly used as a transition solvent. Because epoxy resins generally are rather viscous, mixtures of resin and propylene oxide (1 : 1, 3:1) are used to infiltrate the sample thoroughly with resin before placing it in pure resin. Before polymerization, the samples are usually placed in a silicone rubber mold shaped for convenient orientation and trimming of the block for sectioning, or in polyethylene ("BEEM") or gelatin capsules. Other resins in common use are LR White and LR Gold (London Resin Co.,
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Ltd., Basingstoke, Hampshire, England) and the Lowicryl resins (K4M, K11M) (Chemische Werke Lowi GmbH, Waldkraiburg, Germany), which are lowviscosity acrylic resins that are used principally for postembedding immunocytochemistry. These resins are hydrophilic and provide a more favorable surface for antigen-antibody reactions. LR White is typically heat polymerized; LR Gold is polymerized at - 25~ under ultraviolet light (365 nm). Lowicryl K4M is polymerized with UV light at temperatures down to -35~ and Lowicryl K l l M can be polymerized at temperatures as low as -60~ These acrylic resins are miscible with a small amount of water; thus tissues can be dehydrated through 90% alcohol (ethanol or methanol) and then infiltrated with resin-alcohol mixtures. The use of low temperatures for infiltration and polymerization also helps to minimize protein denaturation.
Safetu Note All resins used in electron microscopy are highly irritating and may cause sensitization and severe allergic reactions. Components of some epoxy resins are suspected carcinogens. If possible, work in a fume hood and avoid contact with skin; wash exposed areas thoroughly with soap and water.
3. Sectioning The preparation of thin sections for TEM examination is technically demanding; it requires expensive instrumentation, and manual dexterity, cleanliness, attention to detail, and patience on the part of the operator. An ultramicrotome (Fig. 12) is used to prepare sections from 50 nm or less up to 1 - 2 / ~ m in thickness. Specimen advance is made mechanically, through a system of pivots and screws, or by the constant expansion of an electrically heated metal specimen arm. Sections are cut from the embedded specimen employing either glass knives, prepared from strips of high-quality glass using a special knife breaking instrument, or diamond knives made from polished diamonds mounted in a special holder. Glass knives can be prepared in the laboratory and are inexpensive; however, they dull rapidly, and hard specimens (e.g., mineralized tissue) are difficult or impossible to cut. Diamond knives are expensive to purchase, but produce excellent sections from nearly all types of specimens, may retain their sharpness for up to a year or more, and can be resharpened several times. In many electron microscope laboratories, glass knives are used for trimming and preparing 1-/_~msections for light microscopic examination, and diamond knives are used for cutting thin sections. The polymerized resin blocks are trimmed (usually with a cleaned razor blade while viewing in a dissecting microscope) to a small size and shape (rectangular or truncated pyramid) that may include all or only part of the sample. The initial sectioning can be done on blocks up to 3 - 4 mm on a side, but thin sections larger than 1 mm on a side are difficult to prepare. The sample is placed in the specimen arm of the ultramicrotome and aligned with the knife edge while viewing through a stereomicroscope. The knife is positioned close to the specimen, and the sectioning mode of the ultramicrotome is engaged. The specimen a n d / o r the knife are advanced until part of the block is cut. If necessary, additional alignment is performed, then sectioning is resumed until the complete face of the block is cut. The sections float off the edge of the knife onto
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Fig. 12 (a) An ultramicrotome used to prepare thin sections for TEM observation. The specimen is clamped in a chuck on the end of the specimen arm and the knife is mounted in a holder on the stage. The stereomicroscope is used to view the sectioning process. (b) Closer view of the specimen arm, specimen (small arrow), glass knife with trough (large arrow), and stage. (Courtesy of Leica, Inc.) water held in a trough behind the edge (Fig. 13). Section thickness is estimated by interference colors produced by illuminating the sections with a fluorescent lamp. Silver-colored sections are 60-80 nm thick; gold sections are 80-130 nm thick. The floating sections are collected onto specimen supports for subsequent staining and examination in the TEM.
4. Specimen Supports Thin sections require some sort of support in order to be able to manipulate them and to observe them in the TEM. The most common type of support is a specimen grid, 3.05 mm in diameter, made of a fine metal mesh, usually copper (Fig. 14). Grids are available with openings in the mesh varying from 450 to
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Fig. 13 Sectionsare cut from the face of the specimen block as it moves past the knife edge. The sections float onto the surface of the fluid (usually water) in the trough behind the knife edge.
a b o u t 20/zm. E p o x y resin sections can be picked u p directly on bare grids. Sections of acrylic resins usually tear w h e n irradiated with the electron b e a m and require additional support. In this case the grid is first covered w i t h a thin plastic film (as described below), and the sections are collected on the s u p p o r t ing film. S u p p o r t films are also used with single-hole or slot grids (solid metal except for a central hole or slot, e.g., 1 • 2 m m ) w h e n collecting serial sections or w h e n large areas of the specimen m u s t be visible w i t h o u t an intervening mesh. The d i s a d v a n t a g e s of using s u p p o r t films include greater difficulty in collecting u n w r i n k l e d sections, decreased contrast in the microscope, and additional susceptibility to c o n t a m i n a t i o n d u r i n g collection and staining of the sec-
Fig. 14 Floatingsections are collected on specimen support grids; the grids are available in different mesh sizes and designs, and are made of copper, nickel, gold, and other materials.
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Arthur R. Hand tions. Supporting films of various types are also used for many of the other specimen preparation procedures that will be described. Polyvinyl formal (Formvar) and nitrocellulose (Parlodion, collodion), dissolved at 0.25-1% in dichloroethane, amyl acetate, or chloroform, are the most commonly used supporting films. Films can be prepared by dipping a clean glass microscope slide (or a piece of glass strip used to make knives) into the solution, allowing it to dry in a dust-free place, releasing the edges of the dried film with a razor blade, then floating the film off the glass onto the surface of clean distilled water (Fig. 15). Cleaned specimen grids can then be gently placed on the floating film. The film is recovered by placing a piece of Parafilm over it, and with a glass slide, quickly submerging the f i l m - g r i d - P a r a f i l m sandwich and sweeping it up out of the water. After drying, the grids, with attached film, can be removed individually from the Parafilm and used to collect sections. For some specimens [ultrathin cryosections (Section IV,D), negative stain preparations (Section IV,B)] the support film is coated with a layer of carbon in a vacuum evaporator (see Section IV,C). The carbon stabilizes the film and provides a uniform surface that can be rendered hydrophilic by glow discharge to improve adherence of the specimen (and spreading of the negative stain). Glow discharge is performed in a vacuum evaporator p u m p e d (by a rotary p u m p only) to about 2 • 10-1 torr. About 50 V is applied to an aluminum coil for 1 - 2 min, resulting in a glowing plasma of ionized gas molecules that "cleans" the surface of the carbon and leaves a negative charge.
Fig. 15 Supporting films (Formvar, Parlodion) can be made by (1) dipping a glass slide in a dichloroethane solution of the plastic and allowing it to dry; (2) releasing the film from the edges of the slide with a razor blade; (3) slowly submerging the coated end of the slide into water, allowing the surface tension to lift the film off of the slide; (4) placing cleaned specimen grids onto the floating film; (5) covering the film and grids with Parafilm; and (6) recovering the Parafilm-gridfilm sandwich and allowing it to dry.
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Support films consisting only of carbon are also useful for certain specimens. They can be prepared as above, by evaporating carbon onto grids covered with a supporting membrane, then dissolving the membrane in solvent vapors, or by coating the surface of a freshly cleaved piece of mica, then floating the carbon film onto the surface of water. Grids dipped in "grid glue" (adhesive from 5 cm of transparent sticky tape dissolved in 10 ml dichloroethane) are then carefully placed on the floating film. The grids and carbon film can be retrieved by quickly touching them with plastic food wrap (e.g., Saran wrap) stretched over the open end of a small glass beaker.
5. Staining For most purposes, thin sections of biological materials, even those postfixed in osmium tetroxide and block-stained with uranyl acetate, will require additional staining with solutions of heavy metals to further increase contrast. The stains used on thin sections generally are nonspecific, i.e., they stain almost all cell components. The two most widely used section stains are uranyl acetate and lead citrate. Uranyl acetate is typically used in either 2% or saturated aqueous solutions, which are acidic (pH 3.5-4.0), or alcoholic solutions ranging in concentration from 2 to 25%. Solutions of uranyl acetate are light sensitive and should be stored in aluminum foil-wrapped containers. Uranyl acetate especially increases the contrast of nucleic acids.
Uranyl acetate is weakly radioactive and must be handled carefully. Waste uranyl acetate solutions should not be dumped down the drain, but should be disposed of by the institutional safety officer. Lead citrate staining solutions are strongly basic (pH 12); they also increase the general contrast of most cells and tissues. The contrast of glycogen and ribonucleoprotein particles is strongly enhanced. Care must be taken to prevent absorption of CO2 by the lead citrate solution, because lead carbonate is insoluble and may precipitate on the sections. Section staining can be done by floating the grids on small drops of stain solution placed on a piece of dental wax or Parafilm. Staining times of 1-10 min are typical, but may require modification for optimal contrast with different plastics and tissues. After staining, the sections should be thoroughly rinsed in distilled water and dried.
B. Negative Staining Negative staining is a useful technique employed for the observation of samples containing small particulate material, such as subcellular fractions, viruses, and some macromolecules and protein complexes. It is rapid and easy to perform, requires only a few supplies, and the sample can be observed immediately. It can be used for screening the contents of a preparation or for detailed structural analyses. In negative staining the specimen is applied to a grid covered with a support film and is surrounded by an electron-dense substance so that the particles
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Arthur R. Hand in the sample appear electron-lucent, in opposite or negative contrast to that usually seen after positive staining of thin sections (Figs. 16 and 17). The stains used most frequently are 1-2% solutions of uranyl acetate, phosphotungstic acid, ammonium molybdate, methylamine tungstate, and uranyl formate. The best stain to use for any given sample is usually determined empirically. Formvar-carbon-coated grids are made hydrophilic by glow discharge shortly before applying the sample. The sample suspension (3-5 ~1) is placed on the grid for 30-60 sec, allowing the particles to adhere. The edge of the grid is then touched with a piece of filter paper to draw off the remainder of the suspension by capillary action, and 3-5/~1 of the negative stain solution is applied for the same time. After drawing off the stain solution, the grid is dried a n d can be immediately observed in the TEM. An alternative procedure is to mix the sample with the negative stain solution before applying it to the grid. [There also are more elaborate methods of performing negative staining that may be advantageous for certain specimens; the reader is referred to Hayat and Miller (1990).] Potential difficulties in the use of negative staining for the analysis and interpretation of structural details include the collapse of delicate structures, beam damage, and overlapping of small structures with stain. Collapse of larger structures, such as synaptosomes, on drying, may be prevented or reduced by prefixation with glutaraldehyde, or in some cases, osmium tetroxide. Beam damage is best avoided by using very low illumination levels for observation and focusing. Low-dose focusing systems available on some TEMs shift the beam to permit focusing on adjacent areas, then return the beam to the selected area for photography. Another problem occasionally encountered is the formation of salt crystals on drying of samples from concentrated buffer solutions. High concentrations of sucrose (e.g., samples taken directly from a sucrose gradient) will also interfere with negative staining. It is best to use buffers of low concentration, or to dilute the sample with distilled water before application to the grid. Alternatively, the grid may be rinsed after application of the sample by briefly touching it to the surface of 3 - 4 small drops of water, then applying the negative stain solution.
C. Metal S h a d o w i n g Metal shadowing is a preparative procedure used to increase contrast in certain types of specimens by depositing a thin coat of metal onto the surface. Contrast is created by depositing the metal from an angle of 45 ~ or less to the surface; objects that project above the specimen surface accumulate metal on the side
Fig. 16 In negative staining, a solution of an electron-dense substance is used to surround and outline the shape of particulate structures adsorbed onto the surfaceof a specimen support film.
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Fig. 17 (a) Negative staining of vesicles containing acetylcholine receptors isolated from the electric organ of Torpedo nobliana. A drop of the vesicle suspension was placed on a Formvar-carboncoated grid that had been glow-discharged in a vacuum evaporator. After adsorption of the vesicles, the suspension was drawn off with filter paper and a drop of neutral 1% phosphotungstic acid was placed on the grid. After staining for one minute, the grid was dried and examined in a TEM. (b) High magnification of negatively-stained receptor complexes. Bars = 50 nm.
closest to t h e s o u r c e , a n d " s h a d o w s " are c r e a t e d w h e r e m e t a l is l a c k i n g b e h i n d t h e object (Fig. 18). T h e m e t a l s h a d o w i n g is p e r f o r m e d in a v a c u u m e v a p o r a t o r , w h i c h e s s e n tially is a c h a m b e r e n c l o s e d b y a bell jar, c o n t a i n i n g o n e or m o r e p a i r s of elect r o d e s , a n d c o n n e c t e d to a d u a l p u m p i n g s y s t e m , i.e., r o t a r y a n d oil d i f f u s i o n
.J
~VA~TRATION
SAMPLE
'-.,.............. 9 ~"~N, "-~,.~...~.~ ...
~
[,
I I
\
I
I
7
SHADOW
Fig. 18 Metal shadowing imparts contrast as the evaporated metal atoms pile up on objects projecting above the surface of the specimen; metal is absent in the "shadow" of the projection.
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p u m p s (Fig. 19). A liquid nitrogen cold trap may be used to reduce contamination and improve the v a c u u m by cryogenic trapping of residual gas and hydrocarbons. The metal to be evaporated is held between a pair of electrodes and heated by an electric current. To evaporate tungsten, a piece of tungsten wire is connected to the two electrodes and heated by resistance heating. To evaporate platinum, which melts at a lower temperature than tungsten, a piece of platin u m is placed in a basket of tungsten, or a short length of platinum wire is w r a p p e d around a tungsten wire or a carbon rod. The tungsten basket or carbon rod is heated until the platinum melts and evaporates. As the metal evaporates it coats the specimen. If carbon rods are used to heat the metal, some carbon will also be evaporated along with the metal. Alternatively, an electron beam gun may be used. The metal to be evaporated is placed at the anode of the gun and bombarded with electrons generated at a tungsten cathode surrounding the anode. The appropriate thickness of the metal coating is usually determined empirically, by observation of the shadowed specimen in the TEM. Subsequent specimens can be shadowed to the same thickness by heating the metal with the same amount of current for the same time, or by the use of a film thickness monitor placed next to the specimen in the vacuum chamber. Metal deposited on a small piece of filter paper placed near the specimen can serve as a visual record of the film thickness. Molecular sizes, shapes, and interactions frequently can be determined by the use of rotary s h a d o w i n g (Figs. 20-22). A purified sample of nucleic acid or protein is adsorbed onto an appropriate substrate, and a thin film of metal is deposited on the specimen while it is being rotated. At low angles (8-10~ the metal atoms deposit preferentially on structures projecting above the substrate; rotation of the sample ensures that metal will be deposited on molecules at all orientations with respect to the evaporation source.
Fig. 19 A vacuum evaporator includes a work chamber that is enclosed by a bell jar and evacuated by both oil diffusion and rotary pumps. A cold trap (not shown), located between the diffusion pump and the main valve and cooled by liquid nitrogen, reduces contamination from oil vapors and improves the vacuum by cryosorption of gas molecules. The specimens are placed on the stage in the chamber, and the electrodes are used to heat carbon rods or metal to be evaporated.
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Fig. 20 Rotaryshadowing of DNA spread by the Kleinschmidttechnique. A preparation of mouse spleen DNA was mixed with cytochrome c and was spread on the surface of an ammonium acetate solution. The spread DNA was collected by touching Formvar-coated grids to the surface, dehydrated in ethanol, positively stained with dilute uranyl acetate in ethanol, and rotary shadowed with tungsten. Nucleic acids or nucleic acid-protein complexes can be applied to the grid by immersion of the grid in a solution of the sample, followed by dehydration through ethanol solutions and air drying. Alternatively, double- or singlestranded nucleic acids can be spread on the surface of a buffered solution, forming a monolayer. The nucleic acids are mixed with cytochrome c (Kleinschmidt technique), or with protein-free solutions containing either benzyldimethylalkylammonium chloride, anthrabis (1,4-bis[3-benzyldimethylamino) propylamino]9,10-anthraquinone dichloride), or ethidium bromide. The spread nucleic acids are collected by touching the grid to the surface, then are dehydrated and air dried. Purified protein samples are typically applied to a carbon film on a piece of mica or a grid by spraying with a nebulizer or by directing a jet of nitrogen gas across the tip of a capillary tube containing the sample solution. The grids are placed on a rotating specimen table in the chamber of the vacuum evaporator, and the evaporator is then evacuated to at least 10 - 6 torr. A thin layer of platinum or tungsten (other metals producing fine grains, such as chromium or tantalum, may be used instead) is deposited on the rotating specimen and the grid is subsequently examined in a TEM. An elegant technique for visualizing proteins, combining rotary shadowing with some of the cryotechniques discussed in the next section, has been described by Heuser (1983). A piece of mica is cut into strips, then broken into microscopic flakes in a homogenizer. A solution of protein is mixed with a thick
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Fig. 21 Rotary-shadowedpreparations of DNA-protein complexes. Small, acid-soluble spore proteins from Bacillus subtilis were bound to plasmid pUC19 DNA, fixed with glutaraldehyde, adsorbed to carbon films on copper grids, and rotary shadowed with tungsten. (a) No added protein; (b and c) protein:DNA ratio 5:1 (/zg protein:/zg DNA); (d) protein: DNA ratio 20:1. Protein binding increases the diameter and apparent stiffness of the filament. At high protein: DNA ratios, the DNA is fully coated with protein.
suspension of the mica flakes and is allowed to adsorb to the mica for a few seconds. The suspension is rapidly frozen (e.g., using a "slam freezing" apparatus as described below), then fractured u n d e r high v a c u u m in a freeze-fracture machine. The fractured surface of the suspension is allowed to freeze-dry for a few minutes, then a replica of the surface is m a d e by rotary s h a d o w i n g with platinum and carbon. The replica is cleaned with c h r o m e - s u l f u r i c acid, and the mica is dissolved in hydrofluoric acid. Observation of the replica in the TEM provides striking, high-contrast images of protein molecules arrayed on the mica surface (Fig. 23).
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Fig. 22 Rotary-shadowed preparation of complexes of laminin with type IV collagen. The proteins (40/~g/ml each) were incubated overnight at 4~ sprayed in 50% glycerol onto mica, and rotary shadowed with platinum and carbon. The elongated type IV collagen molecules are mostly dimeric, linked via their carboxy-terminal globular domains (small arrows). Arrowheads indicate laminin molecules bound to the type IV collagen. (a) Bar = 0.15 ~m; (b-e) bar = 0.1/~m. (From Laurie et al., 1986; reproduced with permission.)
D. Cryotechniques Cryotechniques, i.e., specimen preparation procedures employing ultracold temperatures (liquid nitrogen to liquid helium temperatures, - 196 to - 271~ have been developed as an alternative to the more traditional methods of chemical fixation, dehydration, and resin embedding. The main goal of most of these procedures is to retain the native structure and properties of the specimen to a greater extent than with the usual methods of preparation.
1. Cryofixation Rapid freezing preserves biological specimens, providing instantaneous stabilization of biological structure and avoiding the use of aqueous chemical fixation, which is much slower, causes variable denaturation and loss of biological activity, and may result in displacement or loss of electrolytes and other diffusible substances. The critical aspect of cryofixation techniques is the avoidance of ice crystal formation during freezing, which can severely disrupt cellular
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Fig. 23 Rotary shadowing of laminin molecules adsorbed to mica flakes. After adsorption, the mica suspension was quick-frozen,deep-etched, and rotary shadowed with platinum and carbon in a freeze-etch machine by the method of Heuser (1983, 1989). Bar = 100 nm. Insets: Cross-shaped laminin molecules at higher magnification;globular domains are visible on the short and long arms. Bar = 50 nm. (Courtesy of G. W. Laurie and M. M. Allietta.)
membranes and other structures. Freezing rates in the sample must exceed 104~ (Celsius scale) in order to form vitreous or noncrystalline ice. Even with such rapid freezing rates, only the outer 10-15/~m of the specimen can be expected to be free of ice crystal damage. In general, simply plunging the sample into liquid nitrogen is inadequate; boiling liquid nitrogen at the surface of the warm specimen forms an insulating layer of N 2 gas and the freezing rate is insufficient to avoid ice crystal formation. Other cryogenic liquids, such as liquid propane, ethane, or Freon, have a larger difference between their freezing and boiling points and thus greater freezing rates, which may provide satisfactory structural preservation for some samples. It is important to plunge the specimen rapidly and deeply into the cryogen, so that the surface of the specimen is kept in contact with cold cryogen. Various specialized instruments have been developed to achieve even higher freezing rates for improved structural preservation. "Slam-freezing" devices employ a solenoid-driven plunger to which the sample is attached and rapidly slammed against a polished copper surface that is cooled to liquid nitrogen or liquid helium temperatures. Excellent preservation of suspensions of cells or particles can be achieved by spray-freezing. Small droplets of suspension are shot into liquid propane using an atomizer. Small specimens can also be frozen by directing jets of liquid nitrogen-cooled propane at them from either one or two sides. Another technique, high-pressure freezing, relies on the phenomenon that ice crystal formation is slowed at high pressures (in the range of 2000-3000 bar); thus the depth of well-frozen sample may exceed 100 ~m. Because cells cannot withstand such high pressure for very long, it is applied for only a few milliseconds before the sample is frozen.
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2. Freeze Substitution The cryofixed samples usually are processed further in various ways. In freeze-substitution techniques, the frozen sample is placed in acetone or methanol at - 85~ for several days, then slowly brought to room temperature. The solvent dehydrates the sample by substituting for the frozen water. If desired, fixatives such as osmium tetroxide, glutaraldehyde, or paraformaldehyde, or staining solutions such as uranyl acetate or hafnium chloride, can be added to the solvent. Once room temperature is reached, the sample can be embedded in epoxy resins by routine methods; alternatively, the sample can be embedded in low-temperature resins such as Lowicryl. In addition to the advantages of rapid freezing for preserving ultrastructure, sections of specimens substituted without fixation or with a relative weak fixative may show enhanced immunoreactivity.
3. Cryosectioning To avoid all chemical processing steps, thin sections of cryofixed samples can be prepared using a cryoultramicrotome. For cryomicrotomy, a special chamber cooled by liquid nitrogen is attached to the ultramicrotome, and the specimen and knife are placed within the chamber. Heating elements in the wall of the chamber allow precise regulation of the temperature, which is maintained at - 120 to - 165~ depending on the specimen. The frozen water in the specimen provides a matrix for support of the specimen during sectioning. Sections are cut using a dry knife, are manipulated with a fine hair, and then are collected on Formvar-carbon-coated grids. The thin sections can be examined in the frozen hydrated state in the electron microscope; they are transferred to a liquid nitrogen-cooled stage using a special transfer device that prevents thawing of the sections. Frozen hydrated sections or, alternatively, freeze-dried sections are also used for microanalysis, when it is important to avoid alterations in the distribution of diffusible substances. Cryosections also are frequently used for immunocytochemistry (see Section V,C). In this case, however, the samples are usually fixed with glutaraldehyde or paraformaldehyde first, then are cryoprotected with sucrose or sucrose-polyvinylpyrrolidone (PVP) solutions in order to reduce the risk of ice crystal formation during freezing. The cryoprotected samples are mounted on small pins and plunged into liquid nitrogen. Cryosectioning is performed at - 80 to - 120~ and the sections are transferred from the knife to a Formvarcarbon-coated grid using a small drop of sucrose in a wire loop. The grids with sections can be stored at 4~ for a day or two by placing them section-side down on 10% gelatin moistened with phosphate-buffered saline (PBS).
4. Freeze-Fracture The freeze-fracture technique can provide unique views of cellular membranes as a way of studying the distribution of integral membrane proteins, especially those associated with certain membrane specializations, such as intercellular junctions (Figs. 24 and 25). If a frozen specimen is subjected to a force that causes it to fracture, the plane of the fracture will either intersect membranes in the specimen at roughly a 90 ~ angle, or extend along the membrane (Fig. 24). In the latter case the fracture plane actually splits the lipid bilayer of the mem-
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Fig. 24 During freeze-fracture, cell and organelle membranes may be cross-fractured (A) or split along the lipid bilayer to reveal the hydrophobic interior of the membrane (B and C). Depending on the point of view of the observer, either the protoplasmic half (P-face) or the external half (E-face) of the membrane is visible. If the ice (dotted line) is allowed to sublime under vacuum before replication, the specimen is "etched" and true membrane surfaces (small arrows) and structures buried within the ice are revealed.
brahe into a protoplasmic (P) leaflet adjacent to the cytoplasm, and an external (E) leaflet adjacent to the extracellular space or internal aspect (endomembrane space) of cellular organelles. Depending on their specific properties, integral membrane proteins remain with one leaflet or the other during the fracturing process, often providing a characteristic distribution of intramembrane particles. Specimens for freeze-fracture usually are fixed in glutaraldehyde and cryoprotected with 20-30% glycerol before freezing. Cryoprotection greatly reduces the rate of ice crystal formation and permits adequate preservation of samples up to about 0.5 mm in size. The cryoprotected samples are placed in special holders and are frozen by plunging them into liquid propane or Freon cooled by liquid nitrogen. The frozen specimens are transferred to a special stage in a vacuum evaporator modified to include a fracturing device (e.g., a mounted scalpel or razor blade that can be manipulated from outside of the bell jar) and a cryogenic system for maintaining the specimen in a frozen state and for precisely adjusting the temperature. Fracturing is usually done at - 100~ and the fractured surface is immediately shadowed with platinum and carbon at an angle of 45 ~ creating a replica of the surface, then with carbon alone at an angle of 90 ~ to reinforce the replica. The specimen is thawed and the replica is recovered by digesting the specimen with bleach a n d / o r acid and collecting the replica on Formvar-coated grids. When the replicas are observed in the TEM, the fractured membranes are seen either from the "outside" looking in at the leaflet adjacent to the cytoplasm (the P-face), or from the "inside" looking out at the leaflet adjacent to the extracellular or endomembrane space (the E-face) (Fig. 25). Several variations of the freeze-fracture technique can be used to obtain additional information about the specimen. Cryofixation using a slamming device may be used instead of glutaraldehyde fixation and cryoprotection, in order to preserve structures in their native state. Rather than shadowing the surface immediately after fracturing, the frozen water in the specimen may be
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Fig. 25 Freeze-fracturereplica of the turtle urinary bladder, showing portions of the lateral and apical surfaces of a mucosal epithelial cell. An extensive zonula occludens is present. Anastomosing ridges mark the P-face of the underlying cell; corresponding grooves are seen on the E-face of the upper cell that has been fractured away. The arrow indicates the shadowing direction; L, lumen.
allowed to sublime in the vacuum and condense on a liquid nitrogen-cooled shroud held above the specimen. As the water sublimes and the specimen surface is "etched," the true membrane surfaces and other buried cytoplasmic structures are exposed, providing dramatic views of various filamentous and membranous organelles (Fig. 26). The replicas of these deep-etch preparations are made while the stage is rotated in order to coat all surfaces of the relatively large structures exposed during the etching procedure. A number of labeling procedures have been developed in order to identify specific membrane components exposed during the freeze-fracture process. Cholesterol-rich membrane regions can be identified by treating the cells with certain compounds (e.g., filipin, digitonin) that have an affinity for cholesterol and produce a membrane perturbation recognizable in the replica. Other procedures employ reagents (e.g., lectins, antibodies) adsorbed to electron-dense colloidal gold particles to label glycoproteins or specific antigens. If the fixed and frozen cells are first fractured, then thawed and labeled (fracture-label), the cells can subsequently be embedded in plastic and the distribution of the label observed in thin sections. If the cells are surface labeled first, then frozen,
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Fig.26 Freeze-fracture,deep-etch, rotary shadow preparation, showing the cytoplasmic surface of
the plasma membrane of a 3T3-L1adipocyte. Smooth-surfacedcaveolae (arrowheads) and clathrincoated pits (arrows) are clearly visible. Bar = 0.25/zm. [From Robinson et al., 1992. Micrograph produced by J. Heuser, Washington University, St. Louis. Reproduced from The Journal of Cell Biology, 1992, 117, pp. 1181-1196 by copyright permission of The Rockefeller University Press.]
fractured, and replicated (label-fracture), and the replicas washed only with water, labeled external membrane leaflets are retained with the replica and can be seen associated with the corresponding fractured surfaces. The reader is referred to the reviews by Pinto da Silva (1984, 1989) and Severs (1990) for more detailed discussions of these and other labeling techniques.
E. Critical-Point Drying and Sputter Coating for Scanning Electron Microscopy The SEM provides three-dimensional views of biological specimens, for example, cells in culture or epithelial surfaces (Fig. 27). Special preparative procedures are required, however, to preserve the details of these surfaces and to make them visible in the SEM. Because of the high-vacuum conditions in the SEM, specimer~s must be dehydrated before placing them in the instrument. Air-drying or alcohol dehydration followed by evaporation of the solvent produces surface tension forces that will distort cell shapes and disrupt delicate membranous structures such as cilia and microvilli. The effects of surface tension can be avoided by using the critical-point drying method. When a solvent in equilibrium with its vapor phase is heated to its critical temperature and subjected to its critical pressure (the critical point), the densities of the liquid and vapor phases are equal and the phase boundary disappears; the transition from one phase to the other occurs without development of surface tension. If the temperature is held above the critical temperature, the vapor can be exhausted without condensation, and the specimen is dried. Liquid carbon dioxide is commonly used for critical-point drying because its critical temperature (31~ and pressure (1080 psi or 7.447 MPa) are readily achievable without risk
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Fig. 27 SEM of cultured cells. 3T3 cells grown on glass coverslips were fixed in glutaraldehyde, postfixed in osmium tetroxide, dried in a critical-point dryer, and sputter-coated with gold. A portion of the cell shown in (a) is seen at higher magnification in (b). Secondary electron images of the cells were recorded on Polaroid film; the data at the bottom of each panel include (left to right) accelerating voltage, magnification, exposure number, scale bar, and user-selectable ID.
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of damage to delicate biological specimens. For comparison, the critical temperature and pressure of water are 374~ and 3184 psi (or 21.95 MPa). After drying, the surface of the specimen must be made conductive in order to dissipate the charge that would build up as the electron beam is scanned over the specimen. For most applications in which surface topographic information is sought, and low to moderate magnifications are required, the surface is coated with a metal such as gold. The specimen, mounted on an aluminum stub with conductive tape or paste, is placed in a sputter coater. The chamber is evacuated with a rotary pump and then argon gas is introduced to maintain a pressure of about 6 - 7 Pa. The sputter coater has a ring-shaped cathode, or target, made of the metal to be sputtered, and a ring-shaped anode between the cathode and the specimen. Application of high voltage (1-3 kV) generates a plasma of ionized argon; positively charged ions bombard the target, knocking out metal atoms, which are scattered in all directions as they collide with argon ions and electrons. All surfaces of the specimen are evenly coated by the multidirectional metal atoms. Heat damage to the specimen caused by electrons that are attracted to it can be reduced by cooling the specimen, using a magnet to deflect the electrons, and by applying the high voltage in pulses rather than continuously. Because gold coatings typically are 15-40 nm thick, and gold has a relatively large grain size, gold is generally not useful for studies of surface structure at high magnifications. Gold/palladium alloy and other metals, such as platinum and chromium, have smaller grain sizes. Tungsten and tantalum have very fine grain sizes and can be deposited in thin layers using an electron beam gun in a vacuum evaporator equipped with a rotating and tilting specimen stage. If the specimen will be used for backscattered electron imaging of goldlabeled antibodies (see Section V,C), a layer of carbon is generally used as the conductive coating. The carbon can be evaporated by resistance heating of carbon rods in a vacuum evaporator, or from carbon threads in a carbon sputtering unit.
V. Applications of Electron Microscopy in Cell and Molecular Biology A. E x a m i n a t i o n of Isolated or C u l t u r e d Cells
Isolated cells, cells grown in suspension, or cells released from culture dishes can readily be prepared for thin section TEM or for SEM. About 105.106 cells are suspended in up to 0.75 ml of media (preferably serum free) in a 1.5-ml plastic centrifuge tube and mixed with an equal volume of double-strength fixative (e.g., 5.0% glutaraldehyde in 0.1 M buffer). After 1 hr the tube is centrifuged at low speed to gently pellet the cells, the fixative is removed, and the cells are resuspended in 0.1 M buffer. The cells are rinsed again once or twice in buffer; they can then be stored for several days at 4~ if necessary. To prevent loss of cells from the pellet during the various processing steps, it is convenient to embed the cells in low-gelling agarose. A 2.5% solution of agarose is prepared by boiling in distilled water; 1-ml aliquots of the molten agarose can be placed in 1.5-ml screw cap plastic microcentrifuge tubes, autoclaved, and stored at 4~ The agarose is remelted in a boiling water bath and
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cooled to 45-50~ The cells are resuspended in about 300/~1 of buffer and added to the tube of agarose. The tube is centrifuged at sufficient speed to form a pellet, then the agar is solidified by placing the tube on ice for about 30 min. The tip of the tube is cut off with a razor blade, and, if large enough, the embedded pellet can be cut into smaller pieces. The pellet can be rinsed and stored at 4~ in 0.1 M buffer. The pellets are postfixed for 1-2 hr in 1% osmium tetroxide, rinsed thoroughly with distilled water, then stained in block with 0.5% aqueous uranyl acetate. After rinsing again with distilled water, the pellets are dehydrated in ethanol solutions (50, 70, and 95%, and three changes of 100%) and are substituted with two changes of propylene oxide. For infiltration with plastic, the pellets are placed in 1:1 and 3:1 mixtures of epoxy resin and propylene oxide for 1-2 hr each, and then in 100% plastic for several hours. Often it is convenient to perform this last infiltration step overnight. The specimen vials should be agitated gently (e.g., on a rotator) during plastic infiltration. Finally, the individual pieces of the pellet are placed in embedding molds, a small label (written with pencil on a piece of paper) is placed in each mold, and the molds are filled with fresh plastic. After curing for 48-60 hr at 60~ the hardened plastic can be sectioned. Cells growing attached to plastic tissue culture dishes can be fixed in the dish for 30-60 min with glutaraldehyde, rinsed in buffer, then postfixed with osmium tetroxide, treated with uranyl acetate, and dehydrated in ethanol as described above. To allow separation of the embedded cell layer from the dish, the epoxy resin (Epon) is made without the DDSA [mixture "B"; see Luft (1961)], and the infiltration mixtures are made with 100% ethanol instead of propylene oxide, which will dissolve the dish. The dish can be placed on a rocking platform during the infiltration with plastic. For embedding, the 100% plastic infiltration mixture is drained off the dish, a thin layer of fresh plastic is added, and the dish is placed in an oven to polymerize. To separate the dish and the embedding plastic, the dish is plunged into liquid nitrogen for about 1 min; the plastic dish can then be broken away from the embedded monolayer using a pair of pliers (and wearing safety goggles). Selected areas of the embedded cell layer can be cut out and reembedded in flat molds for sectioning perpendicular to the cell layer, or glued onto the end of a blank piece of plastic for sectioning in the plane of the cell layer. For SEM, cells grown on a small (13 mm) glass or plastic coverslip are fixed with glutaraldehyde, or a few drops of a suspension of fixed cells are placed on a coverslip coated with poly(L-lysine), allowed to stand for 10-15 min, and refixed. After rinsing in buffer, the coverslip is postfixed in osmium tetroxide for 30 min, dehydrated in ethanol, and dried in a critical-point drying apparatus (Section IV, E). The coverslips are then sputter coated with gold and examined in the SEM.
B. Examination of Subcellular Fractions Both negative staining and thin-sectioning procedures are useful for examining the contents of subcellular fractions. Negative staining is easy and rapid, requires only a few microliters of suspended material, and can conveniently be
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ArthurR. Hand used to monitor the progress of a fractionation or purification procedure. Negative staining can be performed essentially as described in Section IV,B. Some organelles, such as complex membranous structures, may be difficult to identify positively in negative stain preparations. Because of their size, fractions containing nuclei, large granules, or lysosomes may not be amenable to negative staining. These structures may be best identified in thin sections; however, larger amounts of sample and longer preparation times are required for embedding and sectioning procedures. Several methods can be used to prepare subcellular fractions for fixation, embedding, and thin sectioning. Fractions that can be pelleted at g forces attainable in a microcentrifuge (10,000-12,000 g) can easily be processed in 1.5-ml plastic microcentrifuge tubes. A volume of sample suspension (up to 0.75 ml) containing material sufficient to produce a visible pellet is mixed with an equal volume of double-strength fixative (e.g., 5% glutaraldehyde in 0.1 M buffer); the mixture is allowed to stand for a few minutes, then pelleted, and fixation is continued for another hour. The fixative solution is removed and replaced with 0.1 M buffer, taking care not to disturb the pellet. The tip of the tube is cut off with a razor blade, and the tip and pellet are cut in half or quartered. The pieces of sample can then be postfixed in osmium tetroxide and processed for plastic embedding, as described in Section V,A. If the pellets do not hold together during the processing steps, use of the agarose embedding method (Section V,A) is recommended. If high g forces are required in order to pellet the sample, fixation is best carried out by carefully removing the supernatant and gently adding a singlestrength fixative (e.g., 2.5% glutaraldehyde in 0.1 M buffer) without disturbing the pellet. After 1-2 hr, the pellet is gently scraped from the wall of the tube, carefully cut into small pieces, and postfixed and processed for plastic embedding. An alternative method of examining subcellular fractions has been described by Baudhuin (1974). Aliquots of a fixed subcellular fraction are collected by filtration under positive pressure onto a 0.22-/~m pore-size Millipore (Bedford, MA) filter. Filtration is stopped, leaving a small amount of buffer covering the layered fraction. The collected fraction is then covered with a second filter and clamped into a special holder for subsequent processing. The filters will dissolve in propylene oxide, leaving the layered fraction to be embedded by itself. Alternatively, the filters can be retained by omitting propylene oxide and using ethanol to dilute the plastic for infiltration; the embedded filters section without difficulty.
C. Localization of Antigens by Immunolabeling Determination of the precise localization and distribution of molecular components in or on cells and tissues, or in subcellular organelles, is essential to understanding their function. In many cases this can be achieved by using immunocytochemistry at the electron microscopic level. Several different procedures and reagents have been used to localize antigens at the EM level, and many factors contribute to the success or failure of these techniques. First, and most importantly, the antigenicity of the molecule of interest must be retained during the preparative procedures. Second, the antigen must be accessible to
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the immunological reagents. Other factors include the specificity of the immunological reagents, the immobilization of the antigen, preservation of the ultrastructure, and the visibility of the label used to identify the site of the antigen. Although several different methods employing a variety of reagents have been used in EM immunocytochemistry, the labeling procedures generally can be described as either p r e e m b e d d i n g or p o s t e m b e d d i n g labeling. In preembedding labeling, the immunological reagents are applied to the sample prior to plastic e m b e d d i n g and cutting of thin sections. This technique is very useful for localizing cell surface antigens (Fig. 28). Intracellular antigens also m a y be detected using p r e e m b e d d i n g procedures, but the integrity of the cell m e m b r a n e must be disrupted by detergent treatment or by freezing and thawing to permit access of the antibodies and secondary reagents. In p o s t e m b e d d i n g labeling, thin sections of plastic-embedded samples (or cryosections of frozen specimens) are prepared, and the labeling is performed on the sections (Figs. 29 and 30). This m e t h o d permits access to all compartments in the tissue or cell, but has the disadvantage that only antigens exposed on (or in the case of cryosections, very near) the surface of the section are available for labeling. A further disad-
Fig. 28 Preembedding immunogold labeling of cell surface antigens. Cultured human dermal fibroblasts were treated overnight with either (a) interleukin-1]3or (b) interferon-y, then fixed in 4% paraformaldehyde. After blocking nonspecific binding with glycine and bovine serum albumin, the cells were incubated with a monoclonal antibody to the adhesion molecule ICAM-1, then with goat antimouse IgG labeled with 10-nm colloidal gold. After labeling, the cells were refixed in glutaraldehyde, postfixed in osmium tetroxide, and embedded in epoxy resin. The resin was separated from the culture dish, thin sections were cut perpendicular to the cell layer, stained with uranyl acetate and lead citrate, and examined in a TEM.
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Fig. 29 Postembeddingimmunogold labeling. Specificantibodies recognize and bind to antigens exposed on the surface of thin sections. The bound primary antibodies are detected by specific antiimmunoglobulins or staphylococcal protein A adsorbed onto the surface of electron-dense colloidal gold particles.
vantage may be deleterious effects of dehydration and resin embedding on the reactivity of the antigens.
1. Preembedding Labeling For the localization of surface antigens, isolated cells or monolayer cultures can be fixed in 4% paraformaldehyde in 0.1 M buffer for 1 hr, then rinsed several times in phosphate-buffered saline. Treatment of the cells with glycine (0.1 M) or ammonium chloride (0.05 M) in PBS can be used to block reactive aldehyde groups, and nonspecific protein binding should be blocked with 1% bovine serum albumin (BSA) a n d / o r 5% normal serum from the same species as the secondary antibody. The cells are then incubated with the primary antibody diluted in 1% BSA a n d / o r 5% normal serum in PBS for 1 hr with agitation, rinsed with PBS, then incubated for I hr with a gold-labeled secondary reagent, such as protein A - g o l d or the appropriate antiimmunoglobulin-gold. A convenient gold particle size for surface labeling studies is 10-15 nm. A variety of gold-labeled secondary reagents are available commercially. The appropriate dilution should be determined for each separate gold reagent; a convenient starting point is about 1:20 or 1:30. After incubation with the gold-labeled reagent, the cells are rinsed, fixed in glutaraldehyde, postfixed in osmium tetroxide, and processed for routine plastic embedding. For the localization of intracellular antigens, the cell membranes must be permeabilized to permit access of the antibody and secondary reagents. After the initial paraformaldehyde fixation, the cells may be treated for 5-10 min with 0.1-0.2% saponin or Triton X-100; alternatively, one or more freeze-thaw treatments will also disrupt the cell membranes. Preliminary experiments should be done to determine which procedure provides the best ultrastructure and the best penetration of reagents. After blocking of aldehyde groups and nonspecific binding as above, the cells are incubated with the primary antibody. If tissue slices are being used, it may be necessary to prolong the incubation, e.g., overnight at 4~ If gold-labeled secondary reagents are used, their size should be 5 nm or less. Secondary reagents coupled to 1-nm gold are available commercially; however, these require a silver enhancement step in order to visualize them in thin sections. Horseradish peroxidase-labeled secondary re-
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Fig. 30 Postembedding immunogold labeling of secretory proteins. Thin section of rat parotid gland fixed in 1% glutaraldehyde and embedded in epoxy resin. The section was incubated with antibody to proline-rich proteins, then with protein A labeled with 15-nm colloidal gold. Gold particles are concentrated over the secretory granules (SG). The Golgi apparatus (GA) and immature granules are also labeled. Few particles are present over the endoplasmic reticulum, and the nucleus (N) shows little nonspecific labeling.
agents, including Fab preparations, can also be used. Penetration of these reagents is good; however, they also require a visualization step, i.e., incubation in a d i a m i n o b e n z i d i n e - H 2 0 2 solution. Disadvantages of the peroxidaselabeled reagents are that their reaction product is diffuse and the reaction cannot be quantitated, whereas gold particles are discrete and can be readily counted.
2. Postembedding Labeling P o s t e m b e d d i n g methods permit immunolabeling of all of the compartments exposed during sectioning, and the procedures are easy to perform. The samples are generally fixed only in aldehyde fixatives, e.g., 1% glutaraldehyde, 4% paraformaldehyde, or p a r a f o r m a l d e h y d e with low concentrations (0.0250.1%) of glutaraldehyde. The p e r i o d a t e - l y s i n e - p a r a f o r m a l d e h y d e (PLF) fixative of McLean and N a k a n e (1974) also is often used for electron microscopic
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immunocytochemistry. Following fixation, the samples are dehydrated and embedded in plastic or are cryoprotected with sucrose-PVP and frozen in liquid nitrogen. Thin plastic sections or cryosections are collected on nickel or gold grids, to avoid any chemical reactivity with the solutions used during the labeling procedures. Epoxy resin sections can be collected on bare grids, but sections of acrylic resins (Lowicryl, LR White) and cryosections must be collected on Formvar or Formvar-carbon-coated grids. Some antigens have been found to retain sufficient reactivity for detection by immunogold labeling even after osmium tetroxide postfixation and embedding in epoxy resin. Usually it is necessary to "etch" the sections with sodium metaperiodate or hydrogen peroxide to remove unreacted osmium and decrease the hydrophobic nature of the resin surface. Etching of sections of nonosmicated samples in some cases also may increase immunoreactivity. The incubation steps of the labeling procedure can be carried out by floating the grids, section-side down, on small drops (25-30/zl) of reagent in Parafilm-lined plastic petri dishes. Washing between incubation steps can be done on larger volumes (1 ml) of solution in wells of porcelain spot plates. Possible nonspecific binding of immunoglobulins to the embedding plastic or tissue components must be blocked before incubation with the primary antibody. BSA, ovalbumin, instant milk, fish gelatin, and normal serum have been used for this purpose. With cryosections, blocking free aldehyde groups with glycine or ammonium chloride is also recommended. Incubation with the primary antibody is usually performed at room temperature for 60 min or overnight at 4~ in an humidified chamber. The antibody is generally diluted in buffer (PBS or Tris-buffered saline) containing BSA a n d / o r normal serum (5%) of the same species as the secondary antibody. The dilution of the antibody must be determined by trial and error; if the concentration of the immunoglobulin in the antibody solution is known, a good starting point is in the range of 1-10/zg/ml. Incubation with gold-labeled reagents diluted in buffer is also done for 60 min at room temperature. Again, the optimal dilution must be determined empirically; for many commercially obtained reagents a dilution of I : 10 to I :20 is adequate. As the reagents age, occasional aggregates of a few to hundreds of particles may be observed on the sections. The number of aggregates usually can be reduced by centrifugation of the gold suspension for 5-10 min in a microcentrifuge. After labeling with the gold reagent, the sections are rinsed thoroughly in PBS and distilled water, then stained with uranyl acetate and lead citrate. Labeled cryosections are stained with uranyl acetate and supported in a thin film of polyvinyl alcohol. Labeling two antigens on the same section, using gold of two different particle sizes, can often provide valuable information about their relative locations. If the primary antibodies are raised in different species, then immunoglobulin-specific gold-labeled secondary antibodies can b e u s e d and the incubation steps combined. If the primary antibodies are raised in the same species, then care must be taken to eliminate the possibility of cross-reactions with the secondary antibodies. The two-sided method of Bendayan (1982) solves this problem, but only if both sides of the section are accessible (i.e., the sections are mounted on bare grids).
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3. Negative Stain-Immunogold Labeling Surface antigens on bacteria, viruses, or subcellular organelles, and isolated macromolecules, often can be demonstrated by combining immunogold labeling with negative staining. A particulate suspension adsorbed on a Formvarcarbon-coated grid can be labeled following the procedure described above for sections, then negatively stained and observed in the TEM (Fig. 31).
4. Immunogold Labeling for SEM The distribution of surface antigens on isolated or cultured cells can be visualized dramatically by observing immunogold-labeled cells in the SEM (Fig. 32). The labeling procedures are identical to those described for the TEM localization of surface antigens. Postfixation with osmium tetroxide is omitted and the sample is coated with a conductive layer of carbon rather than sputter coating with heavy metals. Visualization of the gold label is facilitated by using a backscattered electron detector. Depending on the magnification, beam current, and efficiency of the detector, gold particles of 10-20 nm diameter should be visible as bright spots on the surface of the cells.
5. Controls The specificity of the observed pattern of immunogold labeling must be verified by the use of appropriate controls. Nonspecific binding of immunoglobulins to the specimen can be assessed by replacing the primary antibody with either preimmune serum (or immunoglobulins) from the same animal that was subsequently immunized to produce the antibody, or serum (or immunoglobulins)
Fig. 31 Immunogold labeling of antigens on bacterial fimbriae.
Bacteroides loescheii cells were adsorbed onto a Formvar-carbon-coated grid, incubated with monoclonal antibody to the Streptococcus sanguis-specific adhesin, then with goat antimouse IgG labeled with 10-nm gold particles. The preparations were subsequently negatively stained with 1% phosphotungstic acid and observed in a TEM. (From Weiss et al., 1988; reproduced with permission.)
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Fig. 32 SEM immunogold labeling of cell surface antigens. Enterococcus faecalis cells attached to poly(L-lysine)-coated glass chips were incubated with a monoclonal antibody to a plasmid-encoded surface protein, Ascl0. The bound antibody was detected with goat antimouse IgG labeled with 12-nm gold particles. The cells were then fixed, prepared for SEM observation, and examined by backscatter electron imaging at 1.3-4 kV in a field emission SEM. Bright gold particles are seen predominantly on one-half of the cell; no label is present at the septal region. (From Olmsted et al., 1993; reproduced with permission.)
from a nonimmunized animal. For monoclonal antibodies it is often useful to employ an unrelated monoclonal antibody as a substitute for the primary antibody. Nonspecific binding of the gold-labeled reagents can be determined by omitting the primary antibody from the labeling sequence (e.g., substituting BSA for the primary antibody). The specificity of the primary antibody for its respective antigen can be evaluated by preabsorption with an excess of the antigen. Finally, using biological controls in which the expression of the antigen is altered provides additional verification of the specificity of the immunogold labeling. D. Visualization of Isolated Nucleic Acids and Proteins
Purified macromolecules and macromolecular complexes often can be visualized by TEM using procedures that enhance their contrast, such as negative
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staining or rotary shadowing. Negative staining methods generally employ uranyl acetate (1-2%) and are performed as described in Section IV, B. Ammonium molybdate, phosphotungstic acid, and other stains also may be used. Negative staining provides high-resolution images of macromolecular structure, although damage from the electron beam may rapidly degrade the structure and low-dose observation procedures may be required. Metal shadowing techniques, such as those described below, lack the resolution of negative staining but result in more stable preparations that resist damage from the electron beam.
1. Surface Spreading of Nucleic Acids Nucleic acids mixed with a basic protein will assume a relaxed two-dimensional conformation on an aqueous surface as a result of denaturation of the protein at the air-liquid interface. Cytochrome c is used most commonly, but other proteins have been used and nonprotein spreading methods (Section IV,C) have been developed. Several modifications of the original Kleinschmidt technique have been devised; those described here are adapted from Sommerville and Scheer (1987) and Spiess and Lurz (1988). The hyperphase (spreading) solution consists of purified double-stranded DNA or RNA (1-10 txg/ml in 10 mM Tris-1 mM EDTA buffer, pH 7.5) mixed with ammonium acetate-EDTA and cytochrome c to give final concentrations of 0.5-5 txg/ml nucleic acid, 0.5 M ammonium acetate, 1 mM EDTA, and 0.1 m g / m l cytochrome c, pH 7.5. One end of an acid-cleaned glass microscope slide is placed in a Teflon dish containing the hypophase solution, 0.25 M ammonium acetate, pH 7.5. The hyperphase (about 50 txl) is slowly applied to the glass slide, which is held at an angle of 25-35 ~, and is allowed to run onto the surface of the hypophase. To visualize the extent of the hyperphase as it spreads on the surface of the hypophase, talcum powder or graphite may be sprinkled on the surface of the hypophase. After about I min, a Formvar-coated specimen grid is touched to the surface of the hypophase 1- 2 cm in front of the slide, then lifted straight upward. The solution adhering to the grid is drawn off with filter paper and the nucleic acids on the grid are positively stained for 30 sec with 0.5 mM uranyl acetate, 0.5 mM HC1 in 95% ethanol. The grid is then rinsed in 95% ethanol for about 10 sec and is allowed to dry on filter paper. Rotary shadowing (see Section IV,C) is done in a vacuum evaporator using platinum, platinum-palladium, or tungsten. Grids shadowed with tungsten should be examined in a TEM as soon as possible and stored under vacuum, because tungsten will oxidize with prolonged exposure to air. A modification of the above technique, the microdiffusion method, allows the use of much smaller quantities of nucleic acids and reagents. The diffusion solution consists of 0.2 M ammonium acetate buffer, 3 txg/ml cytochrome c, and about 40 n g / m l DNA. Small droplets are placed on a sheet of Parafilm and are covered with a petri dish for about 15 min. The cytochrome c and DNA diffuse to the air-liquid interface; denaturation of the protein entraps the DNA in a monomolecular film. A Formvar-coated grid is touched to the droplet, stained with uranyl acetate, dehydrated, and rotary shadowed as described. The above procedures are useful mainly for double-stranded nucleic acids. For single-stranded nucleic acids, formamide is used in the spreading mixture (40-50%) and in the hypophase (10%) to prevent random intramolecular base
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pairing, and the ammonium acetate is replaced with either Tris or carbonate buffer.
2. Visualization of DNA-Protein Complexes The surface spreading technique employing cytochrome c is unsuitable for visualizing complexes of DNA with specific DNA-binding proteins. The thick coat of cytochrome c would mask other proteins bound to the DNA; nonprotein spreading methods must be employed. Alternatively, direct mounting of the sample onto a supporting film followed by rotary shadowing may be employed. The following method is adapted from Griffith (1973) and Griffith and Christiansen (1978). A sample of DNA (purified by appropriate means), 1/~g/ml in HEPES buffer (10 mM, pH 7.0), is heated to 55~ for 5 min to reduce aggregation and is then cooled to 37~ for 5-10 min. The protein of interest is added to a final concentration of approximately 10/~g/ml and the mixture is incubated at 37~ for 5-15 min. After cooling to room temperature, the DNA-protein complexes are stabilized by addition of glutaraldehyde to a final concentration of 0.6%. A small sample of the reaction mixture is set aside and the remainder is chromatographed on a small column (about 2 ml bed volume, made with a siliconized Pasteur pipette plugged with glass wool) of Bio-Gel A-5m (Bio-Rad, Richmond, CA) in order to separate unbound protein from the DNA-protein complexes. The complexes are eluted with 10 mM Tris-acetate buffer, pH 7.5, containing 1 mM EDTA; fractions of about 200/~1 (8 drops) are collected. Aliquots of the original reaction mixture and the column fractions (fractions 4 - 6 usually contain most of the complexes) are placed in wells of a Linbro 96-well plate. A concentrated Tris buffer containing spermidine, NaC1, and MgC12 is added to final concentrations of 10, 2.5, 150, and I mM, respectively, to enhance binding of the complexes to the substrate. Grids coated with carbon film are glow-discharged and submerged in the aliquots for approximately 45 sec. The grids are then rinsed briefly in distilled water, dehydrated in ascending concentrations of distilled ethanol, and rotary shadowed at an angle of 8-10 ~ with tungsten in a vacuum evaporator pumped to at least 5 • 10 -6 torr.
3. Visualization of Isolated Proteins Rotary shadowing, when combined with independent methods for verification of size and structure, can be particularly effective for visualizing large proteins, especially those with a rodlike shape. Additionally, rotary shadowing can be used to assess the structure of different domains (e.g., fragments produced during proteolysis) and the interaction of proteins with other molecules, and to map antigenic sites using monoclonal antibodies. Purified protein at a concentration of 0.5-2.0/~M in buffer (5 mM imidazole, 50 mM NaC1) is added to two volumes of pure glycerol and is thoroughly mixed. About 50/~1 is drawn up into a calibrated glass capillary, which is held at an angle of 45 ~ in a gentle stream of nitrogen. The protein-glycerol mixture is sprayed onto a piece of freshly cleaved mica mounted on a vertical screen of absorbant filter paper. The mica is rotary shadowed with tungsten or tantalum/tungsten, then a thin carbon film is evaporated onto the shadowed surface for support. The replica is floated off of the mica onto distilled water and collected on uncoated 400-mesh grids.
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E. In Situ H y b r i d i z a t i o n Understanding specific cell function and tissue morphogenesis at the molecular level requires knowledge of gene expression and its regulation. The distribution and localization of nucleic acids containing specific nucleotide sequences by in situ hybridization has been very effective in identifying transcriptional activity in particular cells and tissues. These studies have been carried out predominantly at the light microscopic level. The development and use of nonradioactive probes has substantially increased the possibilities for extending the resolution of in situ hybridization procedures to the electron microscopic level. Riboprobes and cDNAs prepared with biotinylated nucleotides or digoxigenin-labeled nucleotides can be detected at the EM level using antibiotin or antidigoxigenin antibodies labeled with colloidal gold, or indirectly using unlabeled antibodies followed by gold-labeled antiimmunoglobulins. Simultaneous double labeling using a biotin-labeled probe and a digoxigenin-labeled probe is possible with two different-sized gold labels. Additionally, sequential in situ hybridization and immunocytochemistry can be performed. Analogous to the approaches used for ultrastructural immunocytochemistry, in situ hybridization at the cellular level can be performed using either preembedding or postembedding procedures. In situ hybridization can also be done on isolated chromosomes; this application is well-described in several references (e.g., Sommerville and Scheer, 1987), thus the focus here is on procedures used with cells and tissues. Methods for the preparation and labeling of nucleotide probes and the composition and preparation of hybridization solutions, etc., can be found in Leitch et al. (1994) and in standard molecular biology references. Although some methodological information is provided here, each study must nevertheless be individually optimized.
1. Preembedding in Situ Hybridization Preembedding methods have been used mainly with cultured cells (Singer et al., 1989). They require disruption of the cell membrane and extraction of cytoplasmic components, but they can be expected to have greater sensitivity because access of the various reagents is not restricted by the embedding plastic. To facilitate subsequent handling, the cells may be grown directly on Formvar-carbon-coated gold grids on glass coverslips placed in culture dishes. Extraction with detergent (e.g., 0.5% Triton X-100 and/or 0.5% saponin) can be performed before or after fixation of the cells. In the former case, the extraction is done for 1- 2 min and the cells are subsequently fixed with 2-4% glutaraldehyde. Cells may be stored in 70% ethanol at 4~ then rehydrated in PBS containing 5 mM MgC12, followed by blocking of aldehyde groups with 0.1 M glycine prior to hybridization. Following hybridization and detection, the cells are dried by the critical-point method and examined as whole mounts in the TEM. If the cells are fixed prior to extraction with Triton, the fixation should be relatively weak (e.g., 2% paraformaldehyde-0.2% glutaraldehyde) and short (15 rain), and the extraction is carried out for about 15 rain. After hybridization and detection, the cells can be postfixed in osmium tetroxide and embedded for thin sectioning. The cells are prehybridized for 15 rain in 50% formamide, 2 x SSC (standard sodium citrate buffer; 20 x = 3 M NaC1, 0.3 M sodium citrate, pH 7.0), then hybridized at 37~ for at least 3 hr in Tris buffer containing 50% forma-
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Arthur R. Hand mide, 2 • SSC, and 1/~g/ml of probe. Yeast tRNA, salmon sperm DNA, and BSA are added to reduce nonspecific hybridization. After hybridization the cells are washed in formamide-SSC solutions and stored overnight in I • SSC. Detection of the probe is done by incubation with antibiotin or antidigoxigenin antibody, followed by a gold-labeled antiimmunoglobulin.
2. Postembedding in Situ Hybridization Postembedding procedures, although less sensitive, utilize relatively standard processing procedures and produce a more familiar morphologic appearance. These procedures employ weak fixatives (2-4% paraformaldehyde only or supplemented with 0.1% or less glutaraldehyde) for short periods of time, followed by embedding at low temperature in Lowicryl K4M or LR Gold resin. Acetylation or pretreatment of the sections with protease, acid, or detergents is generally not necessary. For hybridization, grids are floated on 10- to 15-/~1 drops of hybridization solution in humidified chambers at 37~ for 6 hr to overnight. Posthybridization washes are done with PBS and the labeled probes are detected using immunocytochemical labeling procedures as described in Section V,C,2.
3. Controls Effective controls are critical to the success of in situ hybridization techniques. The hybridization should be performed at different stringencies to determine the effect on the signal. Negative controls include omission of the probe, competition with an unlabeled probe, and substitution with an unrelated probe. For RNA:RNA hybridizations, the sense strand synthesized during probe preparation is an excellent control. It is also useful to include a specimen that is known not to contain the sequence of interest. Positive controls also should be performed to ensure that all procedures are working properly. For DNA: DNA hybridizations this should include the detection of highly repetitive sequences; for RNA:RNA hybridizations, the detection of ribosomal RNA demonstrates that RNA has been retained during processing and is accessible for hybridization.
F. M o r p h o m e t r y Morphometry is the quantitative assessment of morphological features. It is a branch of stereology, which is the determination of three-dimensional form from two-dimensional data. The methods used are statistical in nature, thus the structure being studied must occur in relatively large numbers in the specimen, the data must be obtained in an unbiased fashion, and the results are subject to sampling error. Nonetheless, several useful parameters may be determined using simple methodology, without the need for expensive equipment. For example, the volume ratio of a particular organelle to a whole cell, the surface area of plasma membrane or smooth endoplasmic reticulum per unit volume, or the total length of a tubular structure per unit volume may provide important information for the evaluation of biochemical data. Other parameters, such as the number of organelles in a unit volume (numerical density) or the absolute sizes or volumes of different structures, also may be determined, but require somewhat more elaborate procedures and analyses [see Gundersen et al.
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(1988) and Cruz-Orive and Weibel (1990) for reviews of newer stereological procedures that simplify many of these measurements]. The methods used in morphometric analyses mainly involve measuring and counting points and profiles in sections. They are frequently carried out by superimposing a transparent overlay with a test pattern of lines, grids (intersecting lines), or circles on a photographic print of an electron micrograph. Automated or computer-aided methods employing digitizing tablets or image analysis hardware and software are also available (see Russ, 1990), but usually are no faster nor more accurate than manual methods. Unbiased sampling is critical to morphometric analyses. The tissue blocks to be analyzed can be randomized during fixation when the tissue is cut into small pieces and by mixing the blocks during the various solution changes. If the general appearance of the tissue is essentially similar regardless of the plane of section, then routine sectioning procedures will produce random sections of the cells. Tissues that are anisotropic, i.e., their appearance is highly dependent on the plane of section, such as skeletal muscle, present a special case. Various methods have been devised in order to obtain data from these tissues in an unbiased manner. Photography of the specimen must also be carried out in a fashion that eliminates observer bias. One such method is to photograph the upper (or lower) left (or right) corner of each grid square in which a section containing any part of the specimen is present. Data collection is made by placing the test pattern over the micrograph and counting the intersections of lines or points of the grid lying over the structures of interest. When structures of a wide range of sizes are studied, it is convenient to collect data on large structures using low-magnification micrographs, and on smaller structures using higher magnification micrographs. Often a double grid pattern is useful; e.g., a coarse pattern with few points can be used to estimate cytoplasmic volume, whereas a finer pattern with many points can be used to estimate volume densities of smaller, less frequently encountered organelles. The number of micrographs required and number of points to be counted in order to obtain valid estimates of the parameters under study can be determined by statistical analyses; the reader is referred to the references by Weibel (1979, 1980) and by Elias and Hyde (1983). In general, an accurate estimate of the group mean will be obtained by counting 200 points or intersections over the structure of interest; 400 points will provide an error rate of 5%. Little is gained by counting much larger numbers of points; to achieve an error rate of 1%, 10,000 points must be counted. Volume density, Vv, and surface density, Sv, are two useful parameters that can be estimated relatively easily by morphometric methods. Volume density is proportional to the areal density, AA, of the compartment of interest; both parameters can be estimated by point counting: Wv = a A = Pp.
(3)
For example, the Vv of mitochondria (Wvmito)in a cell is equal to the number of points (intersections of an overlay grid) over the mitochondria, divided by the total number of points over the whole cell. For structures of small size or unusual shape, such as the cisternal space of the endoplasmic reticulum, the volume density is equivalent to the intercept length, i.e., the combined length of all
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Arthur R. Hand lines falling w i t h i n the space d i v i d e d by the total length of all the test lines used, V v = EL.
(4)
Surface density, i.e., the surface area per unit v o l u m e , can be estimated b y counting the n u m b e r of intersections of a pattern of straight lines of k n o w n length w i t h the surface of interest. The relationship is given b y
Sv = 2/c.
(5)
For example, a test pattern of lines of 2 0 / z m total length placed over microg r a p h s of hepatocytes intersects r o u g h e n d o p l a s m i c r e t i c u l u m m e m b r a n e s 13 times on average. The surface density, S v r e r , is equal to 2 • 13/20, or 1.3 /zm2//zm 3. Linear density, Lv, or the total length of a linear structure per unit v o l u m e , can be estimated by counting the n u m b e r of intersections of the structure per unit area of the section plane, Lv = 2PA.
(6)
For example, in 25-/zm 2 areas of pancreatic endocrine cell cytoplasm, an average of 10 microtubules intersect the section plane. Thus, the linear density of microtubules, Lv m t , is 2 • 10 / 25, or 0.8/zm / / z m 3.
References Baudhuin, P. (1974). Morphometry of subcellular fractions. In "Methods in Enzymology" (S. Fleischer and L. Packer, eds.), Vol. 32, pp. 3-20. Academic Press, New York. Bendayan, M. (1982). Double immunocytochemical labeling applying the protein A-gold technique. J. Histochem. Cytochem. 30, 81-85. Bendayan, M. (1984). Protein-A gold immunocytochemistry: Technical approach, applications and limitations. J. Electron Microsc. Tech. 1, 243-270. Binder, M., Tourmente, S., Roth, J., Renaud, M., and Gehring, W. J. (1986). In situ hybridization at the electron microscope level: Localization of transcripts on ultrathin sections of Lowicryl K4M-embedded tissue using biotinylated probes and protein A-gold complexes. J. Cell Biol. 102, 1646-1653. Bozzola, J. J., and Russell, L. D. (1992). "Electron Microscopy: Principles and Techniques for Biologists." Jones and Bartlett Publishers, Boston. Carlemalm, E., Garavito, R. M., and Villiger, W. (1982). Resin development for electron microscopy and an analysis of embedding at low temperature. J. Microsc. (Oxford) 126, 123-143. Cruz-Orive, L. M., and Weibel, E. R. (1990). Recent stereological methods for cell biology: A brief survey. Am. J. Physiol. 258, L148-L156. Egerton, R. F. (1986). "Energy Loss-Spectroscopy in the Electron Microscope." Plenum, New York. Egger, D., Troxler, M., and Bienz, K. (1994). Light and electron microscopic in situ hybridization: Non-radioactive labeling and detection, double hybridization, and combined hybridizationimmunocytochemistry. J. Histochem. Cytochem. 42, 815-822. Elias, H., and Hyde, D. M. (1983). "A Guide to Practical Stereology." Karger, Basel. Gabriel, B. L. (1982). "Biological Scanning Electron Microscopy." Van Nostrand-Reinhold, New York. Glauert, A. M., series ed. "Practical Methods in Electron Microscopy." North-Holland/Elsevier, Amsterdam. Goldstein, J. I., Newbury, D. E., Echlin, P., Joy, D. C., Romig, A. D., Lyman, C. E., Fiori, C., and
Chapter 5 Electron Microscopy
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Lifshin, E. (1992). "Scanning Electron Microscopy and X-Ray Microanalysis: A Text for Biologists, Materials Scientists, and Geologists," 2nd ed. Plenum, New York. Griffith, J. D. (1973). Electron microscopic visualization of DNA in association with cellular components. Methods Cell Biol. 7, 129-145. Griffith, J. D., and Christiansen, G. (1978). Electron microscope visualization of chromatin and other DNA-protein complexes. Annu. Rev. Biophys. Bioeng. 7, 19-35. Griffiths, G. (1993). "Fine Structure Immunocytochemistry." Springer-Verlag, Berlin, Heidelberg. Gundersen, H. J. G., Bagger, P., Bendtsen, T. F., Evans, S. M., Korbo, L., Marcussen, N., Moller, A., Nielsen, K., Nyengaard, J. R., Pakkenberg, B., Sorensen, F. B., Vesterby, A., and West, M. J. (1988). The new stereological tools: Disector, fractionator, nucleator and point sampled intercepts and their use in pathological research and diagnosis. Acta Pathol. Microbiol. Immunol. Scand. 96, 857-881. Hayat, M. A. (1989). "Principles and Techniques of Electron Microscopy: Biological Applications." CRC Press, Boca Raton, FL. Hayat, M. A., and Miller, S. E. (1990). "Negative Staining." McGraw-Hill, New York. Heuser, J. (1981). Quick-freeze, deep-etch preparation of samples for 3-D electron microscopy. Trends Biochem. Sci. 6, 64-68. Heuser, J. E. (1983). Procedure for freeze-drying molecules adsorbed to mica flakes. J. Mol. Biol. 169, 155-195. Heuser, J. E. (1989). Protocol for 3-D visualization of molecules on mica via the quick-freeze, deepetch technique. J. Electron Microsc. Tech. 13, 244-263. Kleinschmidt, A. K. (1968). Monolayer techniques in electron microscopy of nucleic acid molecules. In "Methods in Enzymology" (L. Grossman and K. Moldave, eds.), Vol. 12B, pp. 361-377. Academic Press, New York. Laurie, G. W., Bing, J. T., Kleinman, H. K., Hassell, J. R., Aumailley, M., Martin, G. R., and Feldmann, R. J. (1986). Localization of binding sites for laminin, heparan sulfate proteoglycan and fibronectin on basement membrane (Type IV) collagen. J. Mol. Biol. 189, 205-216. Leitch, A. R., Schwarzacher, T., Jackson, D., and Leitch, I. J. (1994). "'In Situ Hybridization: A Practical Guide," R. Microsc. Soc. Handb. No. 27. BIOS Scientific Publishers, Oxford. Luft, J. H. (1961). Improvements in epoxy resin embedding materials. J. Biophys. Biochem. Cytol. 9, 409 -414. McLean, I. W., and Nakane, P. K. (1974). Periodate-lysine-paraformaldehyde fixative. A new fixative for immunoelectron microscopy. J. Histochem. Cytochem. 22, 1077-1083. Morgan, A. J. (1985). "X-Ray Microanalysis in Electron Microscopy for Biologists," R. Microsc. Soc. Handb. No. 05. Oxford University Press, Oxford. Newman, G. R., and Hobot, J. A. (1987). Modern acrylics for post-embedding immunostaining techniques. J. Histochem. Cytochem. 35, 971-981. Olmsted, S. B., Erlandsen, S. L., Dunny, G. M., Wells, C. L. (1993). High-resolution visualization by field emission scanning electron microscopy of Enterococcus faecalis surface proteins encoded by the pheromone-inducible conjugative plasmid pCF10. J. Bacteriol. 175, 6229-6237. Pinto da Silva, P. (1984). Freeze-fracture cytochemistry. In "Immunolabeling for Electron Microscopy" (J. M. Polak and I. M. Varndell, eds.), pp. 179-188. Elsevier, Amsterdam. Pinto da Silva, P. (1989). Visual thinking of biological membranes: From freeze etching to label-fracture. In "Immuno-Gold Labeling in Cell Biology" (A. J. Verkleij and J. L. M. Leunissen, eds.), pp. 179-197. CRC Press, Boca Raton, FL. Polak, J. M., and Varndell, I. M., eds. (1984). "Immunolabeling for Electron Microscopy." Elsevier, Amsterdam. Reid, N., and Beesley, J. E. (1991). "Sectioning and Cryosectioning for Electron Microscopy," Pract. Methods Electron Microsc. Vol. 13. Elsevier, Amsterdam. Reimer, L. (1984). "Transmission Electron Microscopy. Physics of Image Formation and Microanalysis." Springer-Verlag, Berlin and New York. Reimer, L. (1985). "Scanning Electron Microscopy: Physics of Image Formation and Microanalysis." Springer-Verlag, Berlin and New York. Robards, A. W., and Sletyr, U. B. (1985). "Low Temperature Methods in Biological Electron Microscopy," Pract. Methods Electron Microsc., Vol. 10. Elsevier, Amsterdam. Robinson, L. J., Pang, S., Harris, D. S., Heuser, J., and James, D. E. (1992). Translocation of the glucose transporter (GLUT4) to the cell surface in permeabilized 3T3-L1 adipocytes: Effects of
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Arthur R. Hand ATP, insulin, and GTP ~/S and localization of GLUT4 to clathrin lattices. J. Cell Biol. 117, 11811196. Roos, N., and Morgan, A. J. (1990). "Cryopreparation of Thin Biological Specimens for Electron Microscopy: Methods and Applications," R. Microsc. Soc. Handb. No. 21. Oxford University Press, Oxford. Russ, J. C. (1990). "Computer-Assisted Microscopy: The Measurement and Analysis of Images." Plenum, New York. Severs, N. J. (1990). Freeze-fracture cytochemistry: A simplified guide and update on developments. J. Microsc. (Oxford) 161, 109-134. Singer, R. H., Langevin, G. L., and Lawrence, J. B. (1989). Ultrastructural visualization of cytoskeletal mRNAs and their associated proteins using double-label in situ hybridization. J. Cell Biol. 108, 2343-2353. Sommerville, J., and Scheer, U., eds. (1987). "Electron Microscopy in Molecular Biology: A Practical Approach." IRL Press, Oxford. Spiess, E., and Lurz, R. (1988). Electron microscopic analysis of nucleic acids and nucleic acid-protein complexes. Methods Microbiol. 20, 293-323. Spurr, A. R. (1969). A low viscosity epoxy resin embedding medium for electron microscopy. J. Ultrastruct. Res. 26, 31-43. Troxler, M., Pasamontes, L., Egger, D., and Bienz, K. (1990). In situ hybridization for light and electron microscopy: A comparison of methods for the localization of viral RNA using biotinylated DNA and RNA probes. J. Virol. Methods 30, 1-14. Verkleij, A. J., and Leunissen, J. L. M., eds. (1989). "Immuno-Gold Labeling in Cell Biology." CRC Press, Boca Raton, FL. Weibel, E. R. (1979). "Stereological Methods," Vol. 1. Academic Press, London. Weibel, E. R. (1980). "Stereological Methods," Vol. 2. Academic Press, London. Weiss, E. I., London, J., Kolenbrander, P. E., Hand, A. R., and Siraganian, R. (1988). Localization and enumeration of fimbria-associated adhesins of Bacteroides loescheii. J. Bacteriol. 170, 1123-1128. Wischnitzer, S. (1981). "Introduction to Electron Microscopy." Pergamon, New York.
GLOSSARY Bathochromism The shift of wavelength of a spectral band to longer wavelength, i.e., a red shift (A > A0) with respect to some reference state for which A = Ao. Birefringence A property of matter that causes the left- and right-handed circularly polarized components of plane-polarized light to propagate through it at different velocities, i.e., with different indices of refraction. This leads to a change in orientation of the plane of polarization of the light. The birefringence of a chiral molecule is defined quantitatively as the difference between indices of refraction of left- and right-handed circularly polarized light ( n c -- n R). The optical rotation of a chiral molecule, which is the basis for the optical rotatory * Author to whom correspondence should be addressed. Introduction to Biophysical Methods for Protein and Nucleic Acid Research
261
Copyright 9 1995by AcademicPress, Inc. All rights of reproduction in any form reserved.
262
Takashi Miura and George J. Thomas,Jr. dispersion (ORD) spectrum, is directly proportional to the birefringence. See
also Optical activity. Boltzmann distribution
Each particle (molecule) in an ensemble of N particles (macroscopic sample) has discrete or "quantized" energy levels. The energies may be designated as El, ~2, E3, and so forth. The Austrian physicist L. E. Boltzmann showed that the average or equilibrium number of particles Nj occupying the level j, of energy Ej, is given by the relation Nj = Ne-~;kT, where the quantity k is called the Boltzmann constant and T is the thermodynamic or Kelvin temperature. Thus, energy level populations are dependent on the temperature. The distribution of populations is referred to as the Boltzmann distribution.
Born-Oppenheimer approximation Electron motions in molecules are so fast compared to nuclear displacements that the electrons follow the motions of the nuclei adiabatically, i.e., the electronic energy is effectively unperturbed by the nuclear kinetic energy. This has the effect of simplifying the molecular wave functions and properties calculated from them by allowing the factoring of nuclear and electronic coordinates. Brownian motion Random rotational and translational movements of particles (statistical fluctuations) due to thermally induced molecular collisions. See also the Glossary for Chapter 1. Chromophore A molecule or molecular subgroup that gives rise to absorption of radiation of a specified visible wavelength and is therefore colored. The term is also used in the context of electronic transitions that result from the absorption of wavelengths in the ultraviolet region. Deconvolution
See Fourier transform.
A condition in which two or more stationary states of a system Degeneracy exhibit the same energy. See also Multiplicity. The ratio (p - I • ) of intensiDepolarization ratio of Raman scattering ties exhibited by a Raman band when the spectrum of a randomly oriented collection of molecules (liquid or gas phase) is measured with the scattered electric vector polarized perpendicular (I• and parallel (I,) to the plane of polarization of the incident laser beam. The value of p is 0.75 for vibrational modes that are not totally symmetric, i.e., modes exhibiting nuclear displacement vectors that do not preserve the full symmetry of the molecule. On the other hand, for totally symmetric vibrational modes, p < 0.75.
Ellipticity
A property of matter that causes the left- and right-handed circularly polarized components of plane-polarized light to be absorbed unequally, i.e., with different extinction coefficients (EL #= ER).Whereas the electric vector of the incident light traces out a plane, that of the transmitted light traces out an ellipse. The ellipticity of a chiral molecule, which is the basis for the circular dichroism spectrum, is directly proportional to the difference in absorbance (AL- AR) between the left- and right-handed circularly polarized light components.
Exciton coupling
Interaction between identical chromophores that leads to the splitting of their excited-state energy levels. Exciton coupling between two identical chromophores is manifested in the W / v i s i b l e absorption spectrum by splitting of the band of the uncoupled chromophores into two bands, such
Chapter 6 Optical and Vibrational Spectroscopic Methods
263
that the total absorption intensity remains conserved. [See also Chapter 7 of Cantor and Schimmel (1980).]
Fermi resonance
A perturbation coupling of two vibrational states of the same symmetry, one of which is a fundamental level and the other an overtone or combination level of the same or nearly the same energy. The coupling leads to splitting of the nearly equal energies of the unperturbed states and is manifested in a separation of their spectral bands.
Fourier transformation A mathematical operation whereby a function, say f(t), is converted into its Fourier transform, F(x), by the integration f f(t) e-2"rrixt dt, between the limits - ~ < t < + ~. The reciprocal transformation also holds, i.e., f(t) = f F(x) e2~tx dx, with - ~ < x < +~. The pair of functions f(t) and F(x) are Fourier transforms of one another. If t represents time and x represents position, the Fourier transformation of f(t) has the effect of converting it from the time (or frequency) domain to the space domain, and vice versa for F(x). Fourier transformation is useful for converting the interference pattern (interferogram) obtained in the space domain by Michelson interferometry into a spectrum in the frequency domain. Further discussion is given by Griffiths and deHaseth (1986). The related mathematical operation of Fourier deconvolution is also frequently employed in spectroscopy. It provides a means for sharpening the spectral features and can be useful for improving the resolution of broad or overlapping spectral bands. Further discussion is given by Campbell and Dwek (1984) and Thomas and Agard (1984). See also Chapter I in this volume. Franck-Condon principle
The transition between molecular electronic states is so rapid that the nuclei may be considered stationary during the transition.
Gaussian distribution The most commonly occurring probability distribution is the gaussian or normal distribution, which may be represented as a symmetrical bell-shaped error curve. The gaussian distribution function, which represents the probability that a measurement of the quantity x will fall within an infinitesimally narrow interval dx, is given by f ( x ) d x = (1/s)(2~r) -1/2 e x p [ - (x - m)2/(2s2)] dx, where m is the most probable value of x, and s2 is the variance or square of the standard deviation. Formulation of the normal distribution is attributed to the German mathematician, K. F. Gauss. Hyperchromism
A term derived from the Greek hyper (greater) and chroma (color) and referring to the increased band intensity observed in absorption spectra of certain chromophores. Hyperchromism in denatured DNA or RNA is attributed to unstacking of bases.
Hypochromism
A term derived from the Greek hypo (lower) and chroma (color) and referring to the decreased band intensity observed in absorption spectra of certain chromophores. Hypochromism in double-stranded DNA or RNA is attributed to effects of electronic interactions between stacked base pairs.
Hypsochromism The shift of wavelength of a spectral band to shorter wavelength, i.e., a blue shift (A < A0) with respect to some reference state for which A - A0. Inelastic scattering In the inelastic scattering of a photon by a molecule there occurs either a transfer of energy from the photon to the molecule (Stokes scattering) or vice versa (anti-Stokes scattering). See also Raman effect.
264
Takashi Miura and GeorgeJ. Thomas,Jr. Interferometry The process of dividing a light beam into two or more paths and then recombining the beams after a path difference (interference) has been introduced. A Michelson interferometer is a two-beam interferometric device, described by A. A. Michelson in 1891, which serves as the basis for design of present-day Fourier transform infrared spectrometers. In a simple Michelson interferometer, the interference between the two beams leads to intensity variations in the emerging recombined beam, and these are measured as a function of path difference by an appropriate detector. Further discussion of interferometry is given by Griffiths and deHaseth (1986). Isosbestic point A wavelength in the absorption spectrum of a mixture of two components for which the absorption intensity is invariant to the mole fractions of the components. Lifetime The lifetime of a molecular state, sometimes referred to as a relaxation time, is a measure of how long the molecule exists in the particular state. The lifetime is dependent on the bulk environment as well as on the nature of the state. Multiplicity
The number of different electron configurations (wave functions) that yield the same molecular energy. The multiplicity or degeneracy of such a state is equal to twice the total electron spin plus one (21SI + 1). See also Singlet and Triplet.
Mutual exclusion A rigorous selection rule in vibrational spectra of centrosymmetric molecules: vibrations that are infrared-active are Raman-inactive, and vibrations that are Raman-active are infrared-inactive. A centrosymmetric molecule is one that contains an inversion center of symmetry, i.e., for each atom located at a particular point (coordinates x , y , z ) , an identical atom is located at the corresponding inverted point (coordinates - x , - y , - z ) .
Nonradiative process The dissipation of energy from an electronically excited molecule without the simultaneous emission of radiation (photon), a process that is usually facilitated by intermolecular collisions. Examples of nonradiative processes are vibrational relaxation and intersystem crossing (see also Fig. 2). Normal mode of vibration A macromolecule of N atoms has 3N - 6 vibrational degrees of freedom or normal modes. Each Raman or infrared band corresponds to one or more vibrational normal modes. Optical activity An optically active substance is one that rotates the plane of polarization of plane-polarized light, an effect that results from the difference in refractive indices for left- and right-handed circularly polarized components of the polarized light. Optical activity is exhibited by chiral molecules, i.e., structures that are not superposable with their mirror image. Examples include helical conformations of macromolecules and molecules that contain an asymmetric carbon atom. See also Birefringence and glossary item Chirality in Chapter 1. Optical rotation See Birefringence. Polarizability A tensor quantity which relates the magnitude of a dipole moment induced in a molecule to an externally applied electric field. See also
Polarization. Polarization
In general, the phenomenon of separating positive and nega-
Chapter 6 Optical and Vibrational Spectroscopic Methods
265
tive charges within an object by applying an electric field, and thus leading to an induced dipole moment. The term may also be used to describe the property of a molecule whereby the probability of a spectroscopic transition, i.e., the intensity of a spectral band, is dependent on the orientation of the electric field vector with respect to the molecule.
Quantum yield In fluorescence, the ratio of the number of photons emitted to the number absorbed. Raman effect The Raman effect consists of molecular inelastic scattering of monochromatic radiation, whereby the quantum transferred from the incident photon excites a vibrational energy level in the target molecule. In the normal (off-resonance) Raman effect, it is required that the energy of the incident photon be much greater than the molecular vibrational quanta but much less than the difference in energy between ground and first-excited molecular electronic states. This is ordinarily achieved by use of a visible-wavelength laser to excite the Raman spectrum. The effect bears the name of its 1928 discoverer, Sir C. V. Raman. The resonance Raman effect is a variant of the off-resonance Raman effect in which the energy of the incident photon is selected in resonance with a molecular electronic transition. The cross-section for the resonance Raman effect is several orders of magnitude greater than that of the off-resonance Raman effect. However, the resonance Raman mechanism yields vibrational information restricted exclusively to the locus of the chromophoric group. Selection rule A mathematical or physical constraint that must be fulfilled in order that interaction of electromagnetic radiation with matter leads to an experimentally detectable spectroscopic transition. Singlet A molecular energy state that is described in wave mechanics by a single (unique) wave function. With regard to its molecular electronic configuration, a singlet state is one that contains only paired electrons, i.e., all electron spins cancel one another identically, and thus the total electron spin quantum number is zero. See also Multiplicity and Wave function. A quantity related to the probability of a transition Transition moment occurring between two quantum states as a result of an external perturbation. For example, in spectroscopy, the perturbation of electromagnetic radiation may generate interaction with molecular quantum states, producing a finite probability of transition between the states. In this case, the nonzero transition dipole moment represents absorption or emission of a photon. [Readers familiar with the notation and methods of quantum mechanics may wish to refer to the examples given in the Appendix. More detailed discussion is also given by Cantor and Schimmel (1980).]
Triplet A molecular energy state that can be described in wave mechanics by three different (orthogonal) wave functions, differing in their respective electron spin coordinates. The state is said to be triply degenerate, or to exhibit a spin degeneracy of three. With regard to its molecular electronic configuration, a triplet state contains two unpaired electrons, i.e., the total electron spin quantum number is one. See also multiplicity. Wave function A mathematical function that describes the wavelike properties of matter (amplitude, periodicity, phase) in accordance with the postulates of wave mechanics. See also Cantor and Schimmel (1980).
266
Takashi Miura and George J. Thomas, Jr.
SYMBOLS C
molecular concentration
c
speed of light (2.998 9108 m
E,E E
s e c -1)
energy electric field strength
EL
electric field strength of left-handed circularly polarized light
ER
electric field strength of right-handed circularly polarized light
h
Planck's constant (6.626 910 T M J sec)
I
intensity of light intensity of a spectral band at frequency v
I,
parallel component of Raman band intensity
I•
perpendicular component of Raman band intensity
i
unit vector along x axis
J
unit vector along y axis
k
Boltzmann constant (1.381
L
optical path length
mi 1l
910 -23
J K -1)
mass of atom i index of refraction
HL
index of refraction for left-handed circularly polarized light
FIR
index of refraction for right-handed circularly polarized light
N
number of molecules in a macroscopic system
N
number of atoms in a molecule
P
induced dipole moment
s
standard deviation
S
total electron spin angular momentum
So
singlet ground electronic state
$1 T1 T
singlet excited electronic state
ol
crij
triplet excited electronic state thermodynamic or absolute temperature (Kelvin scale) polarizability tensor polarizability tensor component (i, j = x, y, z) phase shift angle molar extinction coefficient at wavelength A
EL
molar extinction coefficient for left-handed circularly polarized light
ER
molar extinction coefficient for right-handed circularly polarized light
Chapter 6 Optical and Vibrational Spectroscopic Methods 0
[0] @
267
ellipticity molar ellipticity transition moment integral
K
force constant
A
wavelength of electromagnetic radiation reduced mass
/z
dipole moment operator
/d, i
dipole moment operator component (i = x,y,z)
P
frequency
7/"
pi (3.14159 . . .); pi electron
p
Raman depolarization ratio
O"
wavenumber
~p
optical rotation
[~] X
molar rotation torsion angle wave function
<1>
overlap integral expectation value integral
dx
total differential of the variable x
3x
partial differential of the variable x
I. Introduction Spectroscopy is the study of interactions of electromagnetic radiation with atoms and molecules. These interactions, which include absorption, emission, and scattering of photons, provide highly sensitive probes of atomic and molecular structures. Depending on the wavelength (A) of the absorbed or emitted radiation, the spectroscopic method is usually classified as ultraviolet, visible, infrared, microwave, or radiowave spectroscopy. For the case of inelastic scattering of radiation, the additional methods of Raman spectroscopy, as well as X-ray and neutron spectroscopy, can be considered. Some spectroscopic methods are also subclassified according to the particular mechanism of interaction of photons with matter. For example, ultraviolet spectroscopy includes the specific techniques of fluorescence emission and circular dichroism, and Raman spectroscopy is often subclassified into off-resonance and resonance Raman processes. Detailed consideration of the theory and practice of optical and vibrational spectroscopy is given in three-volume series of Herzberg (1945, 1950, 1966). The reader is also referred to the text of Campbell and Dwek (1984), which provides a survey of numerous spectroscopic methods applicable to biological molecules. In this chapter, we focus on applications of the methods of ultraviolet (UV),
268
Takashi Miura and George J. Thomas, Jr. visible, infrared (IR), and Raman spectroscopy in structural analyses of proteins and nucleic acids. This treatment includes the processes of fluorescence and circular dichroism (CD), both of which are based on interaction of molecules with UV radiation. Spectroscopy techniques in the UV and visible regions of the spectrum, including fluorescence and CD, are sometimes referred to collectively as methods of optical spectroscopy, whereas the IR and Raman techniques are properly termed methods of vibrational spectroscopy. In Chapter 7 of this volume, nuclear magnetic resonance (NMR) spectroscopy, which involves radiowave absorption, is considered. The wavelength ranges (nm) of electromagnetic radiation pertinent to optical and vibrational spectroscopy and the corresponding units of wavenumber (cm-1), frequency (sec-1 o r H z ) , and energy (kJ/mole) are depicted in Fig. 1. The fundamental relationship between wavelength (A) and frequency (v) of electromagnetic radiation is given by Eq. (1), Av = c,
(1)
where c is the speed of light. In vibrational spectroscopy, it is customary to employ the wavenumber [or, Eq. (2)], usually expressed in units of cm -1, to characterize the energy of IR absorption or Raman scattering processes: or= I/A.
(2)
In SI units of energy, the photon energy is given by Eq. (3), where h = 6.626196 • 10- 34 J. sec is Planck's constant: E = hv
= hccr.
(3)
The scales corresponding to the parameters of Eqs. (1)-(3) are compared in Fig. 1. The optical and vibrational spectroscopic methods discussed in this chapter do not yield directly the three-dimensional structures of proteins and nucleic acids. However, the local structures of functionally important groups within a macromolecule, and changes in these local structures that may relate to biologi-
NEAR - UV
i
I NEAR- IR
VISIBLE
I
UV l VISIBLE ABSORPTION & EMISSION
U63
METHODS I
WAVENUMBER FREQUENCY
WAVELENGTH ENERGY
(nm)
(k J/mole)
I
RAMAN
(crn-')5(~ (Hz)
'
1.5
IX
40C~C10
10 ~6
2CI0 ~30
' 3C~ . . . . . . . . I 1.0 x 10 ~6 3C)0'" ,. 41~I0 ,
,~
] MIDIR
'
20~
'
1CICKIO
'
4~
I 1.0 x 1014 4(!30 ~
aCIO
1C~100
2&
1 ~
1130
Fig. 1 Regions of the electromagnetic spectrum pertaining to methods of optical spectroscopy [ultraviolet (UV) and visible absorption and emission processes] and vibrational spectroscopy [infrared (IR) absorption and Raman scatteringprocesses]. The corresponding ranges of wavenumber, frequency (Hz = sec-1), wavelength, and energy are shown.
Chapter 6 Optical and Vibrational Spectroscopic Methods
269
cal functions, are conveniently probed by optical and vibrational spectroscopy. Experimentally, spectroscopic methods are highly versatile, being applicable to a number of different sample morphologies and over wide ranges of sample temperature, concentration, and solvent environment. These approaches are also well suited to probing an extensive range of biodynamical processes, with time scales ranging from 10-13 s e c t o days.
II. Electronic Spectroscopy A. Theoretical Basis
1. Molecular Energy Levels, Transitions, and Lifetimes A transition between different electronic energy levels of a biomolecule is accompanied by absorption or emission of light in the UV or visible wavelength region. Although some molecules consisting of extended conjugated systems undergo electronic transitions with absorption of near-infrared light (A > 800 nm), electronic spectroscopy of biological molecules is concerned with absorption of light in the wavelength range 190 < A < 700 nm, i.e., from the nearultraviolet region to the long-wavelength limit of visible radiation. The equilibrium distribution of molecules among different energy states is governed by the energy differences between the states and the temperature, in accordance with the Boltzmann distribution law:
Xi/X j --
e[-(Ei-
Ej)/kT],
(4)
where N i and Nj are the populations (average numbers of molecules) in states with energies E i and Ej, respectively; k is Boltzmann's constant (1.3806 • 10-23 J K -1 = 6.95024 • 10 -~ cm -~ K-l), and T is the Kelvin temperature. In a thermally equilibrated system, nearly 100% of the molecules are in the ground electronic state, owing to the very large electronic energy difference, AE~ = Ee - Ey ~ 105-106 J/mol (or 104-105 cm-1), between the ground and excited electronic states. On the other hand, the energy difference between a ground and excited vibrational state (AE/'; = E~' - E~')is generally much smaller, and the populations of excited vibrational states can be significant at thermal equilibrium. For example, if AE/'; = 2.392 • 10 3 J mol -~ (=200 cm-1), only about 62% of the molecules will populate the ground vibrational state at 300 K. However, if AE;; is five times greater (1000 cm-1), m o r e than 99% of the molecules will occupy the ground vibrational state at the same temperature. The population of excited vibrational states is reflected in the appearance of "hot" bands in IR absorption spectra and in the anti-Stokes scattering in Raman spectra (Section III,A,2). The possible pathways for molecular electronic transitions are illustrated in Fig. 2. These include photon absorption and emission (fluorescence and phosphorescence) processes, as well as nonradiative transitions (intersystem crossing and vibrational relaxation). The absorption transition from the singlet ground electronic state (So) to any vibrational sublevel of the singlet excited electronic state (S1) occurs very rapidly (~ 10-15 sec). As noted above, except for vibrations of rather low energy (< 300 cm-~), only the ground vibrational sublevel (v = 0) is significantly populated at physiological temperatures. Addi-
270
Takashi Miura and George J. Thomas, Jr. 3
$1
2 v'=O
I
~
T
T
*
T1
z
LU Z
<1
UJ
3
So v--O
2
v
r
i i, ,
444
Fig. 2 Transitions of absorption and emission involving vibronic energy levels of a hypothetical molecule. Radiative and nonradiative transitions are denoted by solid and dashed lines, respectively. So, Singlet ground electronic state; $1, singlet excited electronic state; T1, triplet excited electronic state; v, vibrational quantum numbers (0, 1, 2, 3. . . . ) for sublevels of So; v', vibrational quantum numbers (0, 1, 2, 3. . . . ) for sublevels of $1.
tionally, because the absorption process is so rapid in relation to the periods of nuclear displacements, the absorption process takes place with negligible change in internuclear coordinates. Accordingly, absorption p a t h w a y s originate from the v = 0 sublevel of So (Fig. 2) and are d r a w n as strictly vertical lines in an energy level representation (Fig. 3). On the other hand, the vibrational sublevel (v') in which the absorption transition terminates m a y be other than the lowest vibrational state, as dictated by the internuclear geometries prevailing in So and $1 and by the gaussian distribution of oscillators in the v = 0 sublevel of So (see Fig. 3 and the Appendix, this chapter). The four representative absorption p a t h w a y s originating in So of Fig. 2 thus terminate in sublevels v' = 0(0 ~ 0 transition), v' = 1(0 ~ 1), v' = 2(0 ~ 2), and v' = 3(0 ~ 3) of state $1. The excited vibrational states of $1 (v' = 1, 2, 3 . . . . ) are unstable and the excess vibrational energy is released t h r o u g h nonradiative processes, such as intermolecular collisions. The molecules s u b s e q u e n t l y p o p u l a t e the v' = 0 sublevel of S1, typically within 10-10 sec following p h o t o n absorption. Because the intrinsic lifetime of the excited electronic state is considerably longer (> 10 -9 sec), the molecules are temporarily t r a p p e d in the v' = 0 state before radiative decay to So occurs. To a g o o d approximation, all radiative emission originates from the v' = 0 sublevel of S1 as depicted in Fig. 2. The p h o t o n emission that accompanies the eventual S~ ~ So transition is termed fluorescence. Again t h r o u g h nonradiative processes, the vibrational states v = 1, 2, 3, . . . become
Chapter 6 Optical and Vibrational Spectroscopic Methods
.•
1
$I -0
4 3 2 I
271
0--4 0-,-5 0-," 0 --,-2_. 0
0-*'0
So ~ ,2 =0 q
INTENSrW
INTERNAL COORDINATE----*
Fig. 3 Potential energy curves representing the ground (So) and excited (S1) electronic states of a hypothetical molecule (left), and the profile of the corresponding absorption spectrum (right). Other notation is defined in Fig. 2. (See the Appendix.)
depopulated, and the molecules return finally to the v = 0 sublevel of So. In principle, the electronic absorption spectrum can provide information about the vibrational sublevels (v') of the excited electronic state ($1), whereas the fluorescence spectrum is potentially informative of the vibrational sublevels (v) of the ground electronic state ($1). This follows from the fact that the absorption transitions differ only in the value of v', while those of fluorescence differ only in the value of v (Fig. 2). Radiative decay of electronic excitation energy may also occur by way of a triplet electronic state, depicted a s T 1 in Fig. 2. Typically, the nonradiative transition $1 ~ T1 (intersystem crossing) precedes the T 1 ~ S O radiative transition, a mechanism termed phosphorescence. Because transitions between triplet and singlet electronic states are generally forbidden on theoretical grounds (see Appendix, this chapter), the phosphorescence lifetime can be very long (10 - 4 10 sec) compared with that of fluorescence (10-9-10 -6 sec). Additionally, if the levels $1 and T 1 a r e close in energy, the S~ ~ T~ nonradiative transition may be followed by the reverse nonradiative transition ( T 1 ~ S 1) and fluorescence ($1 ~ So) before phosphorescence can occur. Technically, although the sequence of transitions, S1 ~ Zl ~ $1 ~ So, is classified as fluorescence, the lifetime is much longer than that of normal fluorescence owing to the long lifetime of the T 1 state.
272
Takashi Miura and George J. Thomas, Jr.
2. Characteristics of Electronic Spectra Electronic spectra d e p e n d on two fundamental molecular properties: the energies of transitions between electronic states and the probabilities of such transitions. (Quantitative analysis of transition probabilities requires consideration of wave mechanical principles and molecular s y m m e t r y arguments, which are treated briefly in the Appendix. A practical experimental description is given in Section II,A,3.) As noted in the preceding section, the energy of an electronic t r a n s i t i o n m or equivalently, the wavelength of its absorption b a n d m i s determined by the difference in energy between the combining electronic states. In the case of proteins, differences between electronic energy levels lead to absorption t h r o u g h o u t m u c h of the ultraviolet region. Nevertheless, transitions originating in specific types of protein residues tend to fall within distinctive wavelength intervals (Wetlaufer, 1962). 1. For A > 250 nm, the observed absorption can be attributed predominantly to the aromatic amino acids: tryptophan, tyrosine, and phenylalanine (Fig. 4). 2. For 250 > A > 210 rim, substantial absorption occurs from histidine, cystine, cysteine, and methionine, in addition to aromatic contributions. 3. For A ~ 210 rim, significant absorption results from transitions in the polypeptide main chain. The wavelength of an absorption band m a x i m u m can also be strongly dep e n d e n t on the protonation state of the c h r o m o p h o r e , as is evident for
IO,O00
g
looo
i ioo
10
i
180
200
I
i
220
J
I
240
1
1
260
i
]
280
]
i
300
1
320
Wavelength Into]
Fig. 4 Ultravioletabsorption spectra in the wavelength interval 190 < )t < 320 nm of the aromatic amino acids, tryptophan (W), tyrosine (Y), and phenylalanine (F), at pH 6. The ordinate gives the molar extinction (E) of each amino acid, which is equivalent to the absorbance of a I M solution in a 1-cm path length cell. (Note that Eis presented on a logarithmic scale, and thus the molar extinction of W at 280 nm is roughly five times greater than that of Y, and many orders of magnitude greater than that of F.) Adapted from Wetlaufer (1962).
Chapter 6 Optical and Vibrational Spectroscopic Methods
273
the t y r o s i n e - t y r o s i n a t e pair (Fig. 5). Figure 6 shows additionally that the type of secondary structure influences the short-wavelength ultraviolet absorption profile of the polypeptide chain. In practical terms, the UV absorption characteristics of a protein provide a means for determining the aromatic amino acid content, and in favorable cases the pKa values for ionizations of selected side chains, especially tyrosines. Further discussion and examples of applications are given by Wetlaufer (1962) and Cantor and Schimmel (1980). In the case of D N A or RNA, each of the purine and pyrimidine bases generates an intense UV absorption signature in the region ,~ < 300 nm. All nucleotides thus contribute to the broad ultraviolet absorption b a n d ( ~ m a x = 260 nm) characteristic of a nucleic acid. However, the UV absorption spectrum observed for double-stranded D N A is dramatically (~ 40%) lower in intensity than anticipated from the sum of contributions of the constituent nucleotides. The diminished intensity, termed h y p o c h r o m i s m , can be attributed to interactions between the paired and stacked bases of double helical DNA. Most, but not all, of the h y p o c h r o m i s m is recovered w h e n the double helical structure is thermally denatured. The absorption profiles of the bases are also s o m e w h a t p H sensitive. With appropriate measurements, the UV absorption spectrum of a nucleic acid, like that of a protein, can provide a reliable basis
12,000 I 1,000 I0,000 9000 8OOO
7000 6000 5000 4000 3000 200O lO00 0
80OO <~ 40OO
~i
-4000
210
'
[
230
'
I
'
1
'
I
250 270 290 Wavelength [nm]
'
I
310
330
Fig. 5 Ultravioletabsorption spectra in the wavelength interval 210 < A < 330 nm of tyrosine (Y) at pH 6 and the tyrosinate anion at pH 13. The bottom trace shows the difference in absorption spectra. Note the very large increase in absorbance near 240 nm on deprotonation of the phenolic OH group and the near invariance of the spectrum to deprotonation in the region 265-275 nm. Adapted from Wetlaufer (1962).
274
Takashi Miura and George J. Thomas, Jr. 8.000
6,000
/ [.....
4,000
ooo 0
\~...~ B sheet
t"
",,
co,,
tx helix
"K,.
;; "/ 180
~
, . , 190 200
, -, ~ x ~ 210 220 230 Wavelength [nm]
;- . 240 250
Fig. 6 Ultraviolet absorption spectra in the w a v e l e n g t h interval 180 < A < 250 n m of poly(L-lysine) in fl-sheet (pH 10.8, 52~ r a n d o m coil (pH 6, 25~ and a-helix (pH 10.8, 25~ conformations. A d a p t e d from Wetlaufer (1962), attributed to Rosenheck and Doty (1961).
for determining the total molecular concentration and for assessing the degree of base stacking in the native macromolecule. Comprehensive tabulations of the UV absorption properties of amino acid and nucleotide residues have been compiled. [See, for example, the "CRC Practical Handbook of Biochemistry and Molecular Biology," edited by G. D. Fasman (1992).] Representative data are reproduced in Tables I and II. 3. A b s o r b a n c e
and Absorption
Coefficient
If a beam of monochromatic light of wavelength A and intensity I0 is impingent on a medium of thickness dL containing molecules that absorb the light, the transmitted light intensity,/, is less than I0. The fraction of light absorbed by the molecules, - dI/I, is proportional to the number concentration (C) of molecules in the medium. This relationship can be expressed by Eq. (5), in which E' is the constant of proportionality: - d I / I = E'CdL.
(5)
Following integration, Eq. (5) can be expressed as I/Io = e-~'cL
(6)
ln(I0/I) = E'CL,
(7)
or
where L is the optical path length. The units of E' are determined by the units of C and L, such that the product E'CL is dimensionless. In the most commonly used form of Eq. (7), C is expressed in molar concentration units (moles/liter, or M), L is expressed in centimeters, and the natural logarithm is replaced by the base 10 logarithmic equivalent, giving log(Io/I);, - A;~ = EaCL
(8)
where E = E'/ln(10) and the subscript ,~ has been inserted to indicate that Eq.
Chapter 6 Optical and Vibrational Spectroscopic Methods
275
Table I Ultraviolet Absorption Characteristics of Amino Acid Residues a
Amino acid Tryptophan Tyrosine Phenylalanine Histidine Cysteine Half-cystine Methionine Arginine Acids b Amides c Lysine Leucine Alanine Proline Serine Threonine
Absorption maxima
Absorption minima
A
A
8A
G190
G197
G205
203.3
19.40
17.60
20.50
19.60
208.0
4.88
42.80
35.50
5.60
202.5
8.96
54.50
12.30
9.36
198.4
4.22
5.57 2.82 3.25 2.69 13.1 1.61 6.38 0.89 0.67 0.57 0.54 0.61 0.75
4.35 1.94 1.76 2.11 6.61 0.46 2.06 0.20 0.19 0.15 0.15 0.16 0.18
5.17 0.73 1.05 1.86 1.36 0.23 0.40 0.11 0.10 0.07 0.07 0.08 0.10
196.7 218.0 192.5 223.2 187.7 206.0 211.3
~ 20.60 46.70 47.5 8.26 59.60 9.34 5.86
Far-UV absorption
Molar extinctions (~ • 10 -3 M -1 cm -1) and wavelengths (nm) are from Fasman (1992). Data are evaluated at pH 7. b Aspartic acid or glutamic acid. c Asparagine or glutamine.
a
(8) a p p l i e s to e a c h p a r t i c u l a r w a v e l e n g t h of light a b s o r p t i o n . In Eq. (8), w h i c h is the w e l l - k n o w n B e e r - L a m b e r t law, EA is called the m o l a r e x t i n c t i o n coefficient or a b s o r p t i v i t y at w a v e l e n g t h A. It is c u s t o m a r y to d e f i n e the l o g a r i t h m i c q u o tient o n the r i g h t of Eq. (8) as the a b s o r b a n c e at w a v e l e n g t h A, or AA = EACL.T h e p e r c e n t t r a n s m i t t a n c e , d e f i n e d as 100 • I/Io, m a y also be e m p l o y e d as a m e a s u r e of s p e c t r a l i n t e n s i t y in a b s o r p t i o n spectra. B e c a u s e the a b s o r b a n c e is d i r e c t l y p r o p o r t i o n a l to the m o l e c u l a r c o n c e n t r a tion [Eq. (8)], the a b s o r p t i o n s p e c t r u m is p r e f e r a b l y p r e s e n t e d as a p l o t of the a b s o r b a n c e (ordinate) v e r s u s w a v e l e n g t h (abscissa). V a l u e s of E~ h a v e b e e n t a b u l a t e d for m o s t biological c h r o m o p h o r e s . E x a m p l e s are g i v e n in Tables I a n d II. U s i n g the t a b u l a t e d v a l u e of EA, the c o n c e n t r a t i o n of a biological c h r o m o p h o r e in s o l u t i o n can be d e t e r m i n e d f r o m the m e a s u r e d a b s o r b a n c e .
4. Circular Dichroism and Optical Rotatory Dispersion T h e electric fields of l e f t - h a n d e d (Er) a n d r i g h t - h a n d e d (E R) circularly p o l a r i z e d light p r o p a g a t i n g in the z d i r e c t i o n are d e f i n e d as Er = 1/2{ I E I [i cos 27w(t -
z/c)
+ j sin 27w(t -
z/c)]},
(9)
ER = 1/2{ I E I [i cos 27w(t -
z/c)
- j sin 27w(t -
z/c)]},
(10)
w h e r e I E I is the a m p l i t u d e of the electric field, v is the f r e q u e n c y , t is the time,
276
Takashi Miura and George J. Thomas, Jr. Table II U l t r a v i o l e t A b s o r p t i o n Characteristics of N u c l e o t i d e R e s i d u e s ~
Nucleotide D N A residues dAMP pH 2 pH 7-12 dGMP pH 2 pH 4.3-7 dCMP p H 1-2.5 pH 6-12 dTMP pH 1- 7 p H 12 RNA residues rAMP pH 2 pH 7-12 rGMP pH 1 pH 7 rCMP p H 1-2.5 pH 6-12 rUMP pH 2-7 p H 11
Absorption maxima
Absorption minima
A
8A
~
8A
G260
8280 / G260
258 260
14.8 15.3
230 227
3.5 2.6
14.5 15.3
0.23 0.14
256 252
12.2 13.7
11.7 12.8
0.70 0.67
280 271
13.2 9.1
6.3 7.4
2.12 0.99
267 267
9.9 7.4
9.0 6.7
0.72 0.67
257 259
15.0 15.3
14.5 15.3
0.22 0.15
256 252
12.2 13.7
11.6 11.7
0.67 0.66
280 271
13.2 9.1
6.3 7.4
2.10 0.99
262 261
10.0 7.8
9.9 7.7
0.39 0.31
241 250
230 227
3.5 2.6
241 250
Other absorption
a Molar extinctions (8 • 10 -3 M -1 cm -1) and wavelengths (nm) are from Dawson et al. (1969).
c is the speed of light, and i and j are unit vectors along the x and y axes, respectively. Note that the quantities 2~wt and 27r~z/c are dimensionless; 2vr~, represents the angular frequency of the wave and 21rvz/c represents the phase (see Chapter 1). The sum and difference ofE L [Eq. (9)] and ER [Eq. (10)] yield the electric vectors of linearly polarized light in the x and y directions, respectively. For example, Ex =
EL + ER :
I E I [i c o s 21rv(t - z / c ) ] ,
Ey = EL - ER -- I EI [j sin 2r
- z/c)].
(11a) (11b)
When linearly polarized monochromatic light (wavelength A) passes through a medium that contains optically inactive molecules, the left- and right-handed circularly polarized light components propagate through the medium with equal speed, i.e., the refractive indices for the given wavelength, nL and 1"/R,are equal. If the optically inactive molecules absorb radiation of the wavelength in question, the left- and right-handed circularly polarized compo-
Chapter 6 Optical and Vibrational Spectroscopic Methods
277
nents are absorbed equally, i.e., the respective molar extinction coefficients, EL and ER, are equal. In such a case, although the intensity is reduced in accordance with the path length, molecular concentration, and molar extinction coefficient, the transmitted light remains linearly polarized in the same plane of polarization as the incident light. This situation is represented schematically in Fig. 7A. If, on the other hand, the medium contains optically active and absorbing molecules, both the intensity and direction of polarization of transmitted light are different from those of the incident light. To illustrate the effects of optical activity we consider first a hypothetical medium that is optically active but nonabsorbing. Linearly polarized light of wavelength A passing through the medium undergoes no loss of intensity ( E L = E R = 0 ) , but the difference in refractive indices (n L =~: nR) causes the leftand right-handed circularly polarized light components to propagate at different speeds, namely, c / n c and C/nR, respectively. This phenomenon, which is
A
x
Y
to
tl
to
ts
t6
t3
tz t3
tz t3
t4
t4
t5 t6
Y
B
to
tz
x tl
t3 ~~ 6 t4 t5
I;3
t4
tz t ~ 4 4 t6 ts
(3
Y tl
tz
x t___23
__
t, t5
t6
Z
t3
Ir
t4 t t6
Fig. 7 Time evolution of electric field vectors representing left-circularly polarized light (left), right-circularly polarized light (right), and their vector sum (center), through a medium containing molecules. (A) Propagation of the circularly polarized light through a medium that is optically inactive (EL = ER) but not birefringent (n L = nR). (B) Propagation through a medium that is optically inactive (EL = ER) but birefringent (n L < nR). (C) Propagation through a medium that is optically active (EL < ER) but not birefringent (n L -- nR).
278
Takashi Miura and George J. Thomas, Jr. termed birefringence, causes a phase shift (S) between the transmitted components. If the optical path is L, the magnitude of the phase shift (radians) at wavelength ,~ is S = 2vrL(nc-
nR)/,~.
(12)
This situation is depicted in Fig. 7B. The resultant of the two light components with phase shift S still represents linearly polarized light, although the direction of polarization is now shifted with respect to that of the incident light. The plane of polarization is said to be rotated by one-half of the phase shift. The angle through which the linearly polarized light is rotated by an optically active sample is called the optical rotation of the material, represented by the symbol q~. The optical rotation (degrees) is expressed in terms of the refractive indices as
q~ = 180L(nL-
F/R)//~.
(13)
Because r/c - r/R is dependent on the wavelength of light, the optical rotation also changes as a function of wavelength. A plot of the optical rotation versus wavelength is called the optical rotatory dispersion (ORD). Next, we consider a hypothetical medium through which left- and righthanded circularly polarized light components of wavelength A propagate with the same velocity (1"/c -- F/R) but with different extinction coefficients (E L 5h ER). After passing through the medium, the two light components exhibit different amplitudes and yield elliptically polarized light. This phenomenon is illustrated in Fig. 7C. The wavelength dependence of the difference in molar extinction coefficient (AE - EL- ER) represents a spectrum called the circular dichroism (CD) spectrum. In practice, the CD spectrum is usually represented as the wavelength dependence of the molar ellipticity [0], a quantity that is directly proportional to the difference in molar extinction coefficient [Eq. (14)]: [ 0 ] = 3 3 0 0 ( E c -- ER).
(14)
In order to compare results on different samples, optical activity is more conveniently expressed on a molar or residue basis. Both molar rotation ([q~]) and molar ellipticity ([ 0]) may be expressed in terms of the measured quantities, sample concentration C (moles/liter) and path length L (cm), using Eqs. (15a) and (15b): [q~] = 100 q~/CL,
(15a)
[0] = 100 O/CL.
(15b)
For biomolecules, which are both optically active and absorbing, both EL -- ER and r/c - r/R are nonzero and the axes of the ellipse represented in Fig. 7C are rotated by the angle q~. In general, if EL exceeds ER, then F/c exceeds nR, and conversely, if ERexceeds EL, then n R exceeds r/c . Because the ORD and CD spectra are not independent of one another, it is sufficient to measure either one or the other. Current convention, dictated largely by practical considerations, is to measure the CD spectrum [Eq. (14)]. Among the practical advantages of CD over ORD are intrinsically sharper spectral bands, less overlap of structurally informative bands with one another, accessibility of the short-wavelength region of the spectrum (vacuum ultravio-
Chapter6 Opticaland VibrationalSpectroscopicMethods
279
let), and superior sensitivity of modern CD instrumentation. Proteins and nucleic acids are optically active macromolecules, and their CD (or ORD) spectra provide important structural information. Further discussion is given in Section II,D,4. The significance of accessibility of the vacuum UV region for elucidation of protein secondary structure is discussed in detail by Johnson (1990).
B. Advantages and Disadvantages of Electronic Spectroscopy There are notable advantages of electronic spectroscopy for protein and nucleic acid structure analyses. First, light absorption and emission by chromophores of proteins and nucleic acids in the UV and visible wavelength regions are very intense. Typically, extinction coefficients for the nucleic acid bases in the nearUV region are of the order 104-105 M- 1 c m - 1 The aromatic amino acid residues and peptide residues of proteins are also characterized by relatively large extinction coefficients. Similarly, the prosthetic groups that are present as cofactors in many proteins tend to absorb strongly in the visible and UV regions. Accordingly, very low concentrations of biological molecules can be detected by methods of electronic spectroscopy. Second, because water is transparent to visible and UV radiation (A > 190 nm), aqueous solutions of biological molecules can be probed by methods of electronic spectroscopy without solvent interference. This holds true for both normal water (H20) and deuterium oxide (D20) solutions. One may combine low solute concentration (~0.1 m g / m l ) with a long optical path (~ 1.0 cm), or high solute concentration (~ 10 m g / m l ) with a short optical path (~ 0.01 cm) to achieve reasonable absorbance values with typical UV chromophores. Third, because the transition between two electronic states accompanying the absorption of UV or visible radiation occurs on a very short time scale (~ 10-15 sec), a wide range of biologically important processes can be time resolved by electronic spectroscopy. For example, electronic absorption spectra of the retinal chromophore in rhodopsin have been interpreted to reveal that the conversion of the 11-cis isomer to the all-trans isomer, which is the first step in the cycle of vision, is completed within 2 • 1 0 - 1 3 s e c following irradiation (Schoenlein et al., 1991). On the other hand, the following limitations of electronic spectroscopy should be noted: First, detailed structural information is usually not obtainable from the UV/visible spectrum. For example, the three-dimensional structures of macromolecules, the local conformations of individual residues, and the hydrogen bonding interactions between donor and acceptor groups within the molecule cannot ordinarily be obtained from electronic spectra. In many cases it is very difficult even to ascertain the states of ionization, protonation, or tautomerization of biologically important chromophores. Second, although fluorescence provides, in principle, a very sensitive probe of structure transitions in biological macromolecules, the intrinsic fluorescent intensity can be affected significantly by sample temperature. Thus, fluorescence spectroscopy is generally not appropriate for monitoring temperature-dependent structural transitions in proteins and nucleic acids. Accordingly, fluorescence experiments involving thermally induced conformational changes, denaturations, association/dissociation phenomena, etc. must be interpreted with extreme caution.
280
Takashi Miura and GeorgeJ. Thomas,Jr. Third, owing to the high sensitivity of W / v i s i b l e absorption spectroscopy, sample purity must be carefully controlled in quantitative applications.
C. Instrumentation and Sample Handling An absorption spectrophotometer consists of a light source, sample compartment, monochromator, and detector. In a typical UV/visible instrument, a hydrogen discharge tube is employed as the source of short-wavelength radiation (190 < A < 320 nm) and a tungsten lamp provides the longer wavelengths (320 < A < 900 nm). The light is directed by a system of lenses and mirrors from the source into the sample compartment, through the cell, which contains the sample, to the monochromator, where it is dispersed by a grating or prism, and onto a photodetector. The detected signal is amplified and recorded. The spectrum is scanned by manipulating the angle of the dispersing element (grating or prism) in the monochromator. Alternatively, a spectrophotometer may incorporate a multichannel detector, such as a photodiode array, to collect the entire spectrum relatively rapidly and without the need of a wavelength scanning mechanism. Ordinarily, the difference in intensity of light transmitted (or absorbed) by the sample and a reference material is recorded as a function of the wavelength. This is most conveniently achieved by use of a double-beam instrument, in which parallel beams of equal intensity are passed simultaneously through the sample and reference cells and their difference in transmittance is monitored electronically. Measurements of light absorption in the far-ultraviolet (vacuum UV, A < 190 nm) require more sophisticated instrumentation in order to eliminate interfering absorption by molecular components of air. Additionally, liquid water is not a transparent solvent in this wavelength region. Sample cells for UV/visible spectroscopy contain optically flat faces fabricated from a material that is transparent over a wide wavelength range (190 < A < 2500 nm), such as quartz or fused silica. The commonly employed rectangular cuvette (10 • 10 • 40 mm), with an optical path of 10 mm, holds a sample volume of about 3 ml. The optical path and sample concentration can be changed in accordance with the Beer-Lambert relation [Eq. (8)]. Microcells accommodating sample volumes as low as 10/zl are also available commercially. It should be kept in mind that W / v i s i b l e absorption spectrometers are not capable of accurately detecting very low levels of transmitted light. Although a specimen giving an absorbance of 1.0 transmits 10% of the incident light intensity, an absorbance of 2.0 represents only 1% transmittance [Eq. (8)]. In order to avoid large errors in measurements, it is advisable to design the spectral measurement so that the optical density of the sample (i.e., absorbance) is less than 2.0. Spectrophotometers for fluorescence measurements contain two monochromators. One is located between the light source and the sample compartment and is referred to as the excitation monochromator. The second, which is located between the sample and the detector, is called the emission monochromator. The fluorescence spectrum is categorized either as an excitation or emission spectrum, depending on whether the excitation or emission monochromator is scanned. In lieu of an emission monochromator, a wavelength filter is sometimes employed.
Chapter 6 Optical and Vibrational Spectroscopic Methods
281
To obtain the fluorescence spectrum, the sample (usually in a 10-mm cuvette) is irradiated by a beam of light of the selected excitation wavelength, and the emitted beam is collected at 90 ~ to the incident beam direction. If the molecular concentration of an absorbing sample is too high, the excitation beam cannot penetrate sufficiently into the solution owing to strong sample absorption. This can pose a serious problem for measurement of fluorescence excitation spectra. Accordingly, the sample concentration should be chosen to maintain a low absorbance (-0.05). The measured spectrum may contain light components in addition to the desired sample fluorescence. For example, significant fluorescence contributions may occur from impurities in the solution or from the solvent, as well as from the cell material (quartz or silica). Additionally, light scattered extraneously by the solution and stray light that has not been adequately rejected by the monochromator(s) may contribute to the measurement. Such undesirable components should be minimized to the greatest extent possible by the experimental design. Ultimately, the fluorescence spectrum must be corrected for such artifacts. The following precautions are recommended for sample handling and data collection in fluorescence spectroscopy. Great effort should be exercised in sample purification. Only fluorescencefree solvents and cells should be used. Oxygen gas (O2), a notorious quencher of fluorescence, should be eliminated by purging solutions with N 2 throughout the experiment. Stray light associated with Rayleigh scattering can be largely eliminated by placing a suitable filter before the emission monochromator. Dust or other particulate matter in the sample solution should be removed by centrifugation or filtration. For samples of relatively low fluorescence intensity, sharp bands due to Stokes Raman scattering (see Section III,A,2) of the solvent or solute molecules can be expected to overlap the broader fluorescence band(s) and cannot be eliminated by optical filters. However, Raman bands can be distinguished from fluorescence by varying the excitation wavelength: the Raman bands shift with the change of excitation wavelength, whereas the fluorescence maxima do not.
D. Information Obtainable from Electronic and Circular Dichroism Spectra
1. Chromophore Concentration and Environment UV absorption is a convenient method for quantitative analysis of proteins and nucleic acids and is frequently employed in biochemical research. For determinations of protein concentration, it is customary to measure the absorbance at 280 nm (A280). If the molar extinction of the protein at this wavelength (E280) is known, the protein concentration can be determined using Eq. (8). As seen in Fig. 4, A280 can be attributed mainly to tyrosine and tryptophan side chains in the protein. Accordingly, knowing E280is equivalent to knowing the numbers of tryptophan and tyrosine residues per subunit. Additionally, because the contribution of tyrosine to the absorbance at 280 nm is essentially independent of the protonation state of the phenolic hydroxyl group (note the isosbestic point in Fig. 5), measurement of A280 is not sensitive to the pKa value of a tyrosine phenolic group. UV absorption spectroscopy is used routinely to determine protein concentrations and to estimate the extent of protein contamination of nucleic acid
282
Takashi Miura and George J. Thomas, Jr. preparations. To determine the protein concentration of an unknown sample it is not necessary that the nucleic acid concentration be known. The procedure is as follows. Most proteins exhibit a UV absorption maximum at 280 nm (due primarily to their tyrosine and tryptophan content). Nucleic acids, often found present in protein preparations, also have a strong UV absorption maximum at 280 nm. However, nucleic acids absorb even more strongly at 260 nm than at 280 nm. For proteins, the reverse is true. Advantage is taken of this in the relationship Protein concentration (mg/ml) = 1.55A2s0 - 0.76A260, where A280 and A260 are the absorbances of the solution measured at 280 nm and 260 nm, respectively (Warburg and Christian, 1942). The method gives considerable errors with mixtures containing more than 20% nucleic acids, or with very turbid solutions. Estimates of protein impurities in nucleic acid preparations may be made using the empirical equation, Nucleic acid percentage = (11.16R - 6.32)/(2.16 - R), where R is the A26o/A280ratio (Glasel, 1995). This equation was derived assuming proteins having 1 m g / m l absorbances of 1.00 and 0.57 at 280 nm and 260 nm, respectively, and nucleic acids at the same concentrations having absorbances of 20 and 10 at the same pair of wavelengths. It should be noted that if a protein solution is known not to contain nucleic acids it may be more sensitive to measure protein concentrations at 230 nm. At this wavelength there are contributions to absorption from peptide bond transitions. An average protein will have A230 = 3 at 1 m g / m l . On the other hand, protein absorbance near 200 n m (A200), which is due mainly to amide groups of the peptide backbone, is not strongly dependent on the amino acid composition. As seen in Fig. 6, however, A200 is rather sensitive to the protein secondary structure. Thus, the protein concentration can be determined accurately from A200, only if the corresponding molar extinction coefficient (Ea00), i.e., secondary structure, is reasonably well known. Because the chromophore environment can affect the difference in energy between electronic states, as well as the probability of a transition between them, both the wavelength of maximum absorption (~max) and the corresponding intensity (Emax) are expected to be sensitive to the environment. Although such effects may be detrimental to quantitative analysis, they favor the use of electronic spectroscopy as a potential probe of chromophore environment. In general, a more hydrophobic environment induces a shift of the chromophore absorption band to a longer wavelength (a red shift, or bathochromism) and a shift of the fluorescence band to a shorter wavelength (a blue shift, or hyp-
sochromism). As was noted in Section II,A,2, interactions between chromophores are also capable of perturbing the UV/visible absorption spectrum. For example, the strong interactions between nonidentical chromophores (purine and pyrimidine bases) in double helical nucleic acids can lead to diminished band intensity (hypochromism) without appreciable shift in the band maximum. Interactions between identical chromophores, on the other hand, usually lead to band split-
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ting, a phenomenon that is well explained by the exciton coupling model (Cantor and Schimmel, 1980). A change in chromophore environment causes much more dramatic changes in fluorescence intensities than in absorption intensities. The efficiency of a fluorescence transition (quantum yield) increases significantly as the hydrophobicity of the chromophore environment increases. Enhancement factors as large as 100:1 are observed in some cases. In the case of a biological molecule, if a fluorescent chromophore (fluorophore) binds to a hydrophobic domain within the macromolecule, the fluorescence quantum yield can be expected to change dramatically. Further discussion of this subject is given by Cantor and Schimmel (1980). Fluorophores that absorb and emit visible light and that bind selectively to specific domains or functional groups in a protein or nucleic acid can be used as probes of the molecular environment. For example, 1-dimethylaminonaphthalene-5-sulfonyl chloride (dansyl chloride) binds covalently to selected functional groups of proteins and provides information on the environment in the neighborhood of the binding site. Other probes, such as ethidium bromide, bind noncovalently and can be exploited as intercalators between base pairs of double helical nucleic acids. Because probe binding at the target may affect conformation a n d / o r stability of the biomolecule, these approaches should be pursued with caution. A detailed discussion of fluorescence probes for structural study of proteins and nucleic acids has been given by Brand and Gohlke (1972).
2. Interchromophore Distance When an initially unexcited molecule is within a relatively short distance (~ 100 A) of an electronically excited molecule and the absorption spectrum of the former overlaps with the emission spectrum of the latter, the excitation energy can be transferred to the former. In such a case, the excitation donor (D) is said to excite the acceptor (A). We may regard the acceptor as a quencher of the fluorescence of the donor. The rate of energy transfer between donor and acceptor is inversely proportional ~o the sixth power of the interchromophore separation 0"AD)(F6rster, 1966). Thus, I'ADcan be calculated from the efficiency of energy transfer. For example, if two probe molecules (Section II,D,1) bind to a protein and the binding sites are identified, the distance between the two sites can be estimated on the basis of the fluorescence energy transfer between the two probe molecules. However, it should be recognized that the efficiency of excitation energy transfer also depends strongly on the orientations of the donor and acceptor. When changes of interchromophore orientation occur slowly compared with the time scale of fluorescence energy transfer, both the interchromophore distance and the orientation determine the transfer rate, and accordingly both cannot be calculated simultaneously from a single measurement. Applications of fluorescence energy transfer to proteins and nucleic acids have been given by Valeur (1989) and Clegg (1992).
3. Macromolecular Size Polarization of fluorescence can provide information on the size and flexibility of a macromolecule. Suppose that light absorption by a molecule occurs when
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Takashi Miura and George J. Thomas, Jr. the direction of the transition dipole moment (see Appendix) coincides with that of the incident electric field. As noted above, the lifetime of fluorescence is normally longer than 10 -9 sec. In the case of a small molecule, rotation due to Brownian motion may occur before radiative decay of the electronic energy. Accordingly, the direction of the electric field of the fluorescent radiation may differ from that of incident radiation. Measurement of this fluorescence polarization can, in principle, provide insight into the period of rotation of the chromophore. For a solution in which the molecules are distributed at random, the sum of random Brownian motions should result in depolarization of the fluorescence. However, because the velocity of Brownian motion increases with temperature but decreases with molecular size and medium viscosity, rotational Brownian motion of biomolecules at low temperatures is slow compared with the fluorescence lifetime. Accordingly, the fluorescence from the biomolecule will be polarized. The approximate size of a macromolecule can be obtained by measuring the polarization of fluorescence as a function of temperature and viscosity of the medium (Weber, 1952). 4. S e c o n d a r y Structure a. Proteins The ultraviolet circular dichroism (UVCD) spectra of proteins and polypeptides in the wavelength interval 160 < A < 240 nm arise mainly from electronic transitions localized in the peptide groups. Accordingly, the UVCD spectra are highly sensitive probes of main-chain secondary structure. A thorough analysis of the UVCD profiles of model polypeptides and proteins of known three-dimensional crystal structure, as well as their application to determining secondary structure content in aqueous proteins, has been given by W. C. Johnson, Jr. and co-workers (reviewed by Johnson, 1990, 1992). Importantly, the a-helix gives the most intense UVCD bands, including two distinct minima (troughs) near 208 and 222 nm and a very strong positive peak centered in the interval 190-195 nm. The crossover point (zero ellipticity) in the a-helix CD signature occurs just above 200 nm. In contrast, the antiparallel/3-sheet motif generates a trough in the interval 210-220 nm with about half the intensity of the a-helix troughs. The antiparallel ]3-sheet also generates a peak near 195-200 nm, which is roughly half as intense as the shorter wavelength a-helix peak. Zero ellipticity in the ]3-sheet CD profile occurs just below 200 nm. Conversely, the so-called random coil or irregular peptide chain conformation exhibits only weak positive ellipticity above 210 nm and negative ellipticity below 210 nm. Distinctive UVCD signatures are also proposed for certain types of/3 turns. The CD spectrum of a typical protein, the viral capsid subunit (designated P8) of bacteriophage ~c6, is shown in Fig. 8. The pronounced spectral minima near 208 and 222 nm indicate clearly that P8 contains substantial a-helical secondary structure (Bamford et al., 1993). To illustrate the use of CD spectra for estimating the percentage of a-helical secondary structure in a protein, we consider the simple and classical method developed by Greenfield and Fasman (1969). These authors recorded CD spectra of poly(L-lysine) in the a-helical form (pH 11.1 solution, 22~ ]3-sheet form (pH 11.1 solution, heated at 52~ and then cooled to 22~ and random coil form (pH 5.7 solution). For A = 208 nm, they observed that the ]3-sheet and
Chapter 6 Optical and Vibrational Spectroscopic Methods 10---
E
-
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~
~
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0
~ -lO x -15 N
7
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~
L
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~
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220
230
240
250
260
Fig. 8 UVCD spectrum (200-260 nm) of the P8 protein of the bacterial virus ~6. The characteristic double minimum observed at 208 and 222 nm in this CD profile is diagnostic of a highly a-helical secondary structure for the viral capsid subunit. Analysis of the CD profile by the method of Johnson (1990, 1992) indicates 53% a-helix, which is in good agreement with estimates obtained by Raman spectroscopy (Bamford et al., 1993; unpublished results of R. Tuma and G. J. Thomas, Jr.).
random coil forms have very low and nearly equal negative ellipticities ([01208 ~ -4000 deg cm2/dmole), whereas the a-helix has a very strong negative ellipticity ([0]208 ~ - 33,000 deg cm2/dmole). Assuming that the CD spectrum of a protein is a linear combination of contributions from the three standard spectra, the molar ellipticity at 208 nm for the protein can be expressed in terms of the fraction a-helix (f~) as follows: [0]208
--
(-- 33,000)f~ + (-- 4000)(1 -- f~).
(16)
If [0]208 is obtained experimentally, the content of a-helix is given as f~ =
-
([{9]208 -Jr-4000)/29,000.
(17)
Determination of the a-helix content of several proteins using Eq. (17) agrees well with values determined by X-ray crystallography. Many extensions of the above method have been developed to determine not only a-helix but also ]3-sheet, ]3-turn, and irregular structural content in aqueous proteins (Johnson, 1990). Although the CD spectrum is an excellent tool for estimation of protein secondary structure, it should be kept in mind that contributions of aromatic side chains to the CD spectra of proteins are not always negligible, even in the far-UV region. Such spectral interference makes precise secondary structure analysis difficult and in some cases impossible. A good example of the hazards inherent in the method has been presented recently by Arnold et al. (1992). The CD method should be applied cautiously not only for proteins with low a-helix content, but also for proteins containing significant numbers of aromatic amino acids (Manning and Woody, 1989).
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Takashi Miura and George J. Thomas, Jr.
b. Nucleic Acids UVCD spectra are also sensitive probes of nucleic acid structure. The ordered helical forms of DNA and RNA, including right-handed Watson-Crick duplexes (A and B forms), left-handed duplexes (Z forms), and higher order helical complexes (triplexes and quadruplexes), generally exhibit very strong and characteristic CD peaks in the interval 160-300 nm. Because the ellipticities of these structures are all greatly diminished on denaturation, the formation and melting of these structures can be monitored using CD spectra. The CD spectra of nucleic acids are also highly sensitive to the nucleotide sequence. Accordingly, it is not generally appropriate to transfer ellipticities measured for a particular DNA or RNA sequence to another sequence, even if the two sequences are expected to exhibit the same form of helical structure. Further discussion of UVCD spectra of nucleic acids and oligonucleotides is given by Tinoco et al. (1980).
III. Vibrational Spectroscopy A. T h e o r e t i c a l Basis
1. N o r m a l Modes of Molecular Vibration In order to define the intramolecular geometry and location of a molecule composed of N atoms, it is necessary to specify the three cartesian coordinates of each nucleus (xi,yi,zi; i = 1, 2, 3, . . . , N). Thus, a molecule of N atoms is said to have 3N degrees of freedom. The six degrees of freedom of a diatomic molecule are depicted in Fig. 9: three are translational (along the x, y, and z axes), two are rotational (about the y and z axes), and one is vibrational (stretching of the internuclear bond). The number of vibrational degrees of freedom for a molecule of N atoms is 3N - 6 if the molecule is nonlinear, or 3N - 5 if linear. It is most convenient to describe the set of 3N - 6 (or 3N - 5) vibrational modes in terms of a unique set, called the molecular normal modes of vibration. In each normal mode, all atoms move with the same phase, i.e., all atoms achieve maxim u m and minimum displacements simultaneously and all pass through the equilibrium position simultaneously. It can be shown rigorously that only the normal modes of vibration of a molecule are capable of the interaction with electromagnetic radiation that gives rise to infrared absorption and Raman scattering spectra (Herzberg, 1950). Hence, the bands appearing in infrared and Raman spectra must correspond to the molecular normal modes of vibration. [Other criteria, including molecular symmetry and mixing of vibrational wave functions, determine the numbers of spectral bands and their respective intensities in infrared and Raman spectra (see Section III,A,2). For more detailed treatments, see the texts of Herzberg (1945, 1950).] N-Methylacetamide (NMA), which models the trans peptide group in proteins, has 30 normal modes of vibration. Neglecting the six methyl hydrogens, the number of normal modes arising from the remaining six skeletal atoms (CCONHC) is 12. Two of these, namely, the amide A mode (predominantly N m H stretching) and the amide I mode (substantially carbonyl stretching), are depicted in Fig. 10. The relatively high frequency of the N m H stretching vibration (3200-3400 cm-1 interval) isolates this type of motion from all other mo-
Chapter 6 Optical and Vibrational Spectroscopic Methods i
i
A
t
i
t
x
translation
y
translation
i w
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translation
i w i
i w
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rotation
w
2
z
rotation
w
vibration
4-
-I-
4-
i
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Fig. 9 Internal degrees of freedom of a diatomic molecule for the x,y,z coordinate system shown at the bottom. The z axis is out of the page. (Note that because the atoms are considered as point masses, there is no moment of inertia about x, and consequently rotation about the x axis is undefined.)
~X
lecular v i b r a t i o n s of N M A , a n d is r e s p o n s i b l e for a m i d e A b e i n g a v i r t u a l l y p u r e N m H b o n d s t r e t c h i n g v i b r a t i o n . T h u s , a m i d e A consists of a p e r i o d i c s t r e t c h i n g a n d c o n t r a c t i o n of the N - - H b o n d w i t h n o significant d i s p l a c e m e n t s of o t h e r a t o m s . A c c o r d i n g l y , the n o r m a l m o d e is a t r u e g r o u p f r e q u e n c y , i.e., the n o r m a l v i b r a t i o n is localized w i t h i n a specific c h e m i c a l g r o u p of the m o l e cule a n d can be i d e n t i f i e d e x c l u s i v e l y w i t h o n e i n t e r n a l c o o r d i n a t e (the N u l l b o n d ) . O n the o t h e r h a n d , the a m i d e I n o r m a l m o d e i n v o l v e s significant b e n d ing of the C - - N m H v a l e n c e a n g l e a n d significant s t r e t c h i n g of the C u N
CH3 H \ / C--N // \ O CH3
N-rnethylacetamide amide A ( 3 2 0 0 - 3 4 0 0 c r n -1 )
amide I (1630 - 1690 cm-1)
Fig. 10 Representation of nuclear displacements in the N-methylacetamide molecule (an analog for the trans peptide group in proteins), during the cycles of amide A and amide I vibrations. The internal coordinates, shown for phase angles of 0~ 45~ 90~ and 135~ are based on normal mode calculations of Miyazawa et al. (1958) and Krimm and Bandekar (1986). The wavenumber ranges for the corresponding vibrational modes in proteins are also indicated.
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Takashi Miura and George J. Thomas, Jr. bond, in addition to substantial C = O stretching. This situation is more typical of a normal mode of vibration in a polyatomic molecule. Ordinarily, a normal mode involves more than one internal coordinate. For a biological macromolecule, a very large number of normal modes is possible. However, most of the 3N - 6 normal modes of the macromolecule are highly localized m meaning that, to a good approximation, each represents a normal vibration involving a small group of atoms largely isolated from the normal vibrations of other molecular groups. For example, if the N atoms of the protein are distributed among s sets of identical groups, each of n atoms, and if each such group exhibits the same or nearly the same conformation and environment in the macromolecule, then the collection of 3 n s - 6 hypothetical spectral bands is reduced to 3n - 6. Consider the case of the amide I mode of an a-helical polypeptide chain of s residues. To a first approximation (ignoring possible differences in local environment and end effects), each p e p t i d e C O N H - g r o u p that is incorporated into the a-helix should give nearly the same amide I vibrational frequency, resulting in the appearance of a single Raman or infrared amide I band, rather than s distinct amide I bands.
2. Selection Rules for Vibrational Spectra Both Raman and infrared spectroscopy provide information on the energies of molecular vibrations. However, the two methods are based on different mechanisms of molecular interaction with electromagnetic radiation, and they are governed by different selection rules. In this section, we employ classical electromagnetic theory to treat the mechanisms of Raman scattering and infrared absorption of light.
a. Raman Scattering When monochromatic light of frequency v0 impinges on a molecule, the oscillating electric field E generates a small separation between centers of negative (electronic) and positive (nuclear) charge and thereby induces a dipole moment in the molecule. The induced dipole moment, which oscillates as a result of the electric field perturbation, does not depend on the existence of a permanent (nonoscillating) dipole moment in the molecule. This phenomenon is called polarization. To a good approximation, the induced dipole moment strength P is related to the electric field strength E according to Eq. (18), P = aE,
(18)
where the quantity a relating the two vectors is called the molecular electric polarizability tensor. Each component of P (Pi, where i = x, y, z) is related to the three components of the electric field strength (Ej, where j = x, y, z) by equations of the form
Pi = ~ aijEj,
(19)
where the sum is over both i and j. The coefficients aij are the elements of the polarizability tensor, and the subscripts i and j represent, respectively, the vec-
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tor components of P and E to which it relates. Because both a and E are time dependent, P will be time dependent. [Note that a depends on the internuclear geometry, which varies with the frequency of vibration of a particular normal mode, G (v = 1, . . . , 3N - 6), while the electric field strength oscillates with frequency v0.] Accordingly, it can be shown that P has terms that depend on u0 and v0 + G, as follows:
Pi(t) = ~[(cr~.) I E I cos 2rrvot + (1/2)(a~)lqEI cos 2rr (v0 + Vv)t], (20) where a/~ is the component ij of the molecular polarizability in the equilibrium molecular configuration, cr~ is the first derivative of the polarizability component taken with respect to the vibrational normal coordinate q, and I E I is the amplitude of E. The first term on the right in Eq. (20) represents the component of Pi that oscillates with frequency v0. According to classical electromagnetic theory, this represents energy radiated or scattered with the same frequency as that of the incident light. This is called Rayleigh scattering. The second term on the right of Eq. (20) comprises two components of Pi that oscillate at the frequencies v0 - Vvand v0 + G, respectively. The former, which is one vibrational quantum lower than the incident light frequency, is termed the Stokes Raman scattering. The latter, which is one vibrational quantum greater than the incident light frequency, is termed the anti-Stokes Raman scattering. Although both Stokes and anti-Stokes Raman effects can be observed experimentally, the former is favored by the Boltzmann distribution law [Eq. (4)] and is therefore easier to detect. The simple classical description of Eq. (20) also indicates that Raman scattering will occur only if a~ :/= 0. Accordingly, at least one component of the first derivative of the polarizability tensor, taken with respect to the normal coordinate, must be nonzero. This requirement can also be stated in the form of a selection rule as follows. A normal mode of vibration will be Raman active, i.e., will yield a band in the Raman spectrum, only if there occurs a change in the molecular polarizability during the period of vibration. Conversely, if the polarizability does not change during the normal mode of vibration, then the normal mode cannot generate Raman scattering. Such a normal vibration is said to be Raman inactive. Additional factors influencing the intensities of Raman scattering are discussed by Herzberg (1945).
b. Infrared Absorption A heteronuclear diatomic molecule (or chemical bond) has associated with it a permanent dipole moment, because the different electronegativities of the bonded atoms necessarily require that centers of negative and positive charges be noncoincident. If the bond vibrates with the normal mode frequency Vv, the dipole moment must also oscillate at the frequency G- According to classical electromagnetic theory, an oscillating dipole absorbs electromagnetic radiation of the same frequency as that of the dipole oscillation. Therefore, a normal mode of vibration that gives rise to an oscillating dipole of frequency Vv will absorb radiation of the same frequency. Such a mode is said to be infrared active. Conversely, a normal mode of vibration that does not give rise to an oscillating dipole moment (e.g., the stretching of a homonuclear diatomic molecule) cannot lead to absorption of radiation, and is said to be infra-
290
Takashi Miura and George J. Thomas, Jr. red inactive. Thus, the selection rules for infrared absorption and Raman scattering are fundamentally different. Because the frequencies of molecular vibrations occur generally in the wavenumber range 200-4000 cm -1, absorption of radiation associated with molecular vibrations will occur in the infrared region of the electromagnetic energy spectrum (Fig. 1). As noted above, the selection rules for infrared and Raman spectra are fundamentally different. Therefore, it is possible for a molecular normal mode of vibration to be Raman active but infrared inactive, or vice versa, or to be both Raman and infrared active or both Raman and infrared inactive. Often, the experimental data obtained from the two types of spectra are not identical but complementary to one another. Generally, both infrared and Raman spectra are required to assign properly and analyze the vibrational modes of a molecule. Such assignment and analysis in turn requires knowledge of the molecular symmetry and an understanding of the relationships between molecular symmetry and infrared and Raman activities (Herzberg, 1945). Even for complex biological macromolecules, which may lack any overall symmetry, knowledge of the local symmetry of specific chemical groups and the role of local symmetry in determining spectral activity or band intensity can be extremely helpful. As an example we consider the carbon dioxide molecule (O--C---O), which has four normal modes of vibration. Symmetry considerations dictate that two of these are bond stretching modes, and two are valence angle bending modes. One stretching mode is symmetrical, involving the simultaneous extension and simultaneous contraction of each oxygen-carbon double bond. This symmetrical stretching mode is infrared inactive, because no molecular dipole moment change can accompany the in-phase displacements of the two oxygens with respect to the central carbon. On the other hand, the symmetrical stretching mode is Raman active, because the in-phase bond stretching motions change the size of the molecule and therefore its polarizability during the course of the vibration. The remaining stretching mode is antisymmetrical, involving the contraction of one carbon-oxygen bond while the other is extended. The two carbon-oxygen bonds are vibrating in opposite phase, which is essentially equivalent to linearly displacing the central carbon atom between two fixed oxygens. Associated with such a vibration is a large dipole moment change (infrared activity) but no polarizability change (Raman inactivity). Each bending mode of CO2 involves a periodic change in the valence angle about its equilibrium value of 180 ~ i.e., between larger and smaller values. One mode can be defined in any given plane containing the three atoms. The other mode will occur in the perpendicular plane. Thus, the two bending modes are equivalent energetically (degenerate), but are orthogonal in directionality. Therefore, each will lead to a spectral band of identical frequency. The two degenerate bending modes cannot be distinguished spectroscopically and are sometimes referred to as a single normal mode. Because the bending modes produce a change of dipole moment but not of polarizability, they are infrared active but Raman inactive. On the basis of symmetry, we expect the IR spectrum of CO2 to consist of two bands, one assigned to antisymmetric stretching (high frequency) and the other to degenerate bending (low frequency); and we c. Symmetry Considerations
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expect the Raman spectrum to consist of only one band, assignable to symmetric stretching (intermediate in frequency). To a very good approximation, the vibrational spectra are consistent with these expectations. (In fact, the Raman spectrum of CO2 is somewhat more complex due to Fermi resonance of vibrational eigenstates; see Section III, E,4.) The above example is also relevant to carboxyl groups in biological molecules, even though they are nonlinear. Thus, symmetric and antisymmetric carbon-oxygen stretching vibrations can be anticipated from the carboxyl-terminal groups of aspartate and glutamate side chains in proteins. The symmetrical mode is expected to occur at relatively low frequency (---1400 cm-1), whereas the antisymmetric mode is expected at high frequency (--~1580 cm-1). Both modes exhibit high infrared intensities, but are of relatively low intensity in Raman spectra. The CO2 molecule, by virtue of its center of symmetry, exemplifies another important principle of vibrational spectroscopy, namely, the rule of mutual exclusion. This rule states that for any molecule containing a true inversion center of symmetry, the infrared active vibrations are Raman inactive and vice versa. The mutual exclusion rule can be helpful in assigning bands in spectra of biological subgroups that approximate centrosymmetric molecules. For example, this rule would be expected to hold approximately for the phenylalanyl side chain in proteins, because the phenyl ring approximates the centrosymmetric benzene molecule. (A more refined model for the phenylalanyl side chain is the toluene molecule.) In molecules that are of lower symmetry, the depolarization properties of Raman bands may still be useful in arriving at band assignments. In the case of molecules that lack any symmetry, all vibrations are both Raman and infrared active. However, the relative intensities of specific vibrational bands may vary greatly between the two types of spectra, as well as from one vibrational band to another within the same spectrum. Further discussion of polarization and depolarization properties of vibrational bands are given by Carey (1982) and applications to nucleic acids are discussed by Thomas and Tsuboi (1993).
B. Advantages and Disadvantages of Vibrational Spectroscopy Raman and infrared spectroscopy for protein and nucleic acid structure analysis have the following notable advantages: 1. Raman and infrared spectroscopy are nondestructive techniques. Ordinarily the sample may be recovered and assayed for biological activity after spectroscopic examination. 2. Raman and infrared methods are applicable to samples of virtually any morphological form. For proteins and nucleic acids, this includes solutions (aqueous and nonaqueous), suspensions, precipitates, gels, films, fibers, single crystals, and polycrystalline and amorphous solids. Data obtained from a given sample in one morphological state are generally transferable to another morphological state of the same sample. This has important practical benefits m for example, in comparing the molecular structure of a protein in the crystal with that prevailing in solution. 3. A small sample volume is required for these methods. Approximately I
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Takashi Miura and George J. Thomas, Jr. /~1 is sufficient for conventional Raman spectroscopy and approximately 10 ~1 for Fourier transform infrared spectroscopy. This represents an advantage over many other structural methods, including X-ray crystallography and magnetic resonance spectroscopy. 4. Raman scattering and infrared absorption processes occur on a time scale that is very short (-~ 10-15 sec) in comparison to the time scales of fluorescence (> 10 -9 sec) and nuclear magnetic resonance phenomena (~ 10 -6 sec). Thus, vibrational spectroscopy is suitable for time-resolved studies of biological processes that are inaccessible by fluorescence and magnetic resonance methods. 5. There exists a large database of infrared and Raman spectra of proteins, nucleic acids, and their constituents, for which reliable band assignments, normal mode analyses, and spectra-structure correlations have been made. This facilitates interpretation of the often complex vibrational spectra obtained from proteins, nucleic acids, and their complexes. The following advantages are specific to Raman spectroscopy: 1. Both H 20 and D 20 generate very weak Raman scattering, thus producing relatively little interference with the Raman spectrum of the dissolved solute. This constitutes a significant advantage over infrared absorption spectroscopy, where both H 2 0 and D20 are highly problematic solvents. The innocuous Raman characteristics of H 20 and D 20 likewise facilitate the exploitation of Raman spectroscopy for monitoring hydrogen isotope exchange processes in proteins, nucleic acids, and their assemblies. Similarly, hydrogen isotope exchanges can be employed in the Raman effect for purposes of measuring isotope shifts to establish or confirm definitive vibrational spectroscopic assignments. 2. The fundamental selection rule for Raman spectroscopy, i.e., that relatively high Raman intensity accrues from molecular vibrations with which there is associated a large change in molecular polarizability, favors the electron-rich substituents of proteins and nucleic acids. Thus, the Raman spectrum of a typical protein is dominated by spectral bands assignable to main-chain peptide groups, aromatic side chains (Trp, Phe, Tyr), sulfur-containing side chains (Met, Cys), and side-chain carboxyls (Asp, Glu, Asn, Gln). Raman intensities associated with saturated hydrocarbon groups are intrinsically rather weak. However, the large numbers of such groups typically present in a protein result in a few relatively intense Raman bands associated with groups frequencies of the methylene and methyl substituents. In the case of nucleic acids, the Raman spectra are dominated by bands attributable to vibrations of the backbone phosphate groups and of the purine and pyrimidine rings, especially in-plane skeletal stretching and exocyclic carbonyl stretching modes of the latter. 3. Raman intensities are enhanced dramatically (by several orders of magnitude) when the energy of the incident photon is selected in resonance with a molecular electronic transition of a protein or nucleic acid chromophore. This constitutes the resonance Raman (RR) effect. Therefore, structural information about the chromophore can be obtained by use of relatively dilute protein or nucleic acid solutions through the RR mechanism. This technique is particularly
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valuable for proteins containing chromophores that absorb in the visible (metalloproteins, retinal proteins, etc.) or near-ultraviolet (nucleotide-binding proteins, nucleoprotein complexes, etc.). Ultraviolet resonance Raman (UVRR) spectroscopy has found more extended use in applications to nucleic acids and nucleoprotein assemblies. Vibrational spectroscopy for protein and nucleic acid structure analysis has the following notable disadvantages: 1. Although band resolution in vibrational spectra is superior to that achievable in electronic spectra of condensed phases, the spectral resolution of vibrational spectroscopy is still inferior to that of high-field magnetic resonance spectroscopy. Inadequate resolution is especially problematic in infrared spectra of proteins and nucleic acids and can severely limit the usefulness of the data. To overcome this limitation, the experimentalist may employ a strategy based on chemical or biological modification, such as isotope editing or sitedirected mutagenesis. 2. The Raman process of inelastic light scattering is inherently weak compared to other light absorption and emission processes. Thus, considerable effort in sample purification and care in sample handling are necessary to avoid even minute traces of fluorescent impurities or other chromophores that may interfere with detection of the Raman scattering. 3. The inherent weakness of the Raman scattering mechanism in comparison to other mechanisms of interaction of radiation with matter also imposes a requirement for sophisticated and relatively costly instrumentation. 4. Although small sample volumes are sufficient for Raman and infrared analyses, relatively high solute concentrations are required (~ 10-100 p~g//zl).
C. Instrumentation and Sample Handling
1. Raman Spectroscopy The instrumentation required for measuring a Raman spectrum consists of a monochromatic light source (laser) that excites the Raman spectrum, a diffraction grating spectrometer that analyzes the Raman scattered frequencies, and a detector that captures the Raman photons. Laser excitation wavelengths extending from the near-infrared (~ 1000 nm) to the near-ultraviolet (~ 200 nm) have been employed. The choice of excitation wavelength is determined by the absorption characteristics of the sample and the objectives of the experiment. Inert gas lasers providing excitation wavelengths in the visible are most often employed for off-resonance Raman spectroscopy of nonabsorbing proteins and for resonance Raman spectroscopy of proteins that absorb in the visible. In the latter case, the Raman spectrum is dominated by resonance-enhanced bands of the visible chromophore, usually a metalloporphyrin or retinal cofactor. Typical excitation wavelengths include the continuous wave (CW) argon ion laser emission lines at 488.0 (blue) and 514.5 nm (green) and the helium-neon laser line at 632.8 nm (red). Intracavity frequency-doubled argon lasers, which provide CW emission in the near-ultraviolet (e.g., the second harmonics of the 488.0- and 514.5-nm emissions occurring at 244 and 257 nm, respectively), have become available for ultraviolet resonance Raman (UVRR) spectroscopy of
294
Takashi Miura and George J. Thomas, Jr. proteins and nucleic acids absorbing in the near-UV. In the UVRR spectra of such molecules, the spectrum is dominated by the resonance-enhanced Raman bands of the UV chromophores, namely, the aromatic amino acid side chains of proteins, or purine and pyrimidine bases of nucleic acids. A Raman spectrometer must be capable of efficiently rejecting the very intense Rayleigh scattering that accompanies the Raman scattering [Eq. (20)]. For this purpose, one employs either a highly dispersive (double) grating configuration in the analyzing spectrometer, or a narrow cutoff filter (holographic edge filter) before the detector. The latter are available commercially for use with excitation wavelengths in the visible and near-IR regions. Detectors for Raman spectroscopy are gradually evolving from the singlechannel photomultiplier and multichannel diode-array technologies to the more efficient charge-coupled device (CCD) detector. In recent years, the liquid nitrogen-cooled CCD camera, which virtually eliminates dark current noise and permits rapid multichannel detection, has come into wide use for detection of Raman-scattered photons. Because Raman spectroscopy of biological molecules requires a laser source of relatively high power and stability, optical components with superior stray light rejection, and sophisticated photon detection capability, the instrumentation is relatively costly in comparison to that of infrared or UV/visible absorption spectroscopy. In order to acquire state-of-the-art Raman spectroscopic data, it is advisable to establish an appropriate collaboration with a specialist in the field. More detailed discussion of instrumentation requirements for Raman spectroscopy has been given by Carey (1982). In the preparation of solutions of biomolecules for Raman spectroscopy, one generally avoids the use of high concentrations of complicated buffers. To manipulate ionic strength, monatomic cationic and anionic species are preferred whenever possible, because polyatomic species generate Raman bands that may interfere with those of the protein or nucleic acid. Thus, NaC1 would be preferred over NH4C1 or NaNO3 to increase the solution ionic strength. Low concentrations of chelating agents (~ 2 mM EDTA) are also acceptable. Although a low concentration of buffer is tolerable (e.g., 5 mM Tris), use of such buffers is largely cosmetic because they would provide negligible buffering capacity in a protein solution of ~ 100 /~g//~1 (equivalent to ~ 10 mM of a 10-kDa protein and probably much greater than 10 mM with respect to the acidic and basic side chains for which the buffering capacity is intended). Sample handling procedures for Raman spectroscopy of proteins and nucleic acids have been surveyed by Carey (1982) and Thomas and Kyogoku (1977). Special procedures for viral samples have also been discussed (Thomas, 1987). The sample solution is transferred to the Raman cell, ordinarily a glass or quartz capillary, by pipette, syringe, or direct suction; the cell is then sealed. Only I ~1 of solution is required for obtaining a high-quality Raman spectrum. The sample is irradiated by the focused laser beam and the scattered light is collected at 90 ~ from the direction of the incident beam. The time required to record a Raman spectrum varies from seconds to hours, depending upon the intrinsic strength of the Raman signal (determined by sample concentration, excitation wavelength, etc.) and the spectral resolution required. The rejection of fluorescence, due to impurities or to the sample, and the mode of detection of
Chapter 6 Optical and Vibrational Spectroscopic Methods
295
the Raman-scattered photons are also factors that determine the time required to obtain the Raman spectrum.
2. Resonance Raman Spectroscopy In addition to the foregoing, the following considerations apply to visible and ultraviolet resonance Raman experiments. First, if the laser excitation wavelength is close to or within the wavelength interval of electronic absorption by the sample, then the photons may be more efficiently absorbed than Raman scattered. In such a case, increasing the sample concentration would serve only to increase photon absorption rather than photon scattering. This is in contrast to the situation applicable in off-resonance Raman spectroscopy, where the Raman intensities increase with increasing sample concentration. Second, photon absorption in resonance Raman experiments tends to be minimized if the sample illumination scheme is in the so-called "back-scattering" geometry, i.e., if the propagation directions of incident and scattered beams are at approximately 180 ~ to one another. This minimizes collection of photons that have passed through the absorbing medium. Third, because the risk of photodecomposition is high in RR experiments, a spinning cell or flow cell is preferable to a static sample. This in turn requires a much greater volume of material (albeit lower concentration) than in off-resonance experiments. Finally, RR experiments should be conducted with the incident laser power sufficiently low that the population of molecular energy levels is not altered from the equilibrium value appropriate to the experimental objectives. A high laser power can significantly affect the distribution of molecules in electronic energy levels and thereby alter the Raman band intensities (Raman saturation). In RR experiments it is advisable to demonstrate that the observed Raman intensities are not dependent on the laser power.
3. Infrared Spectroscopy A conventional scanning instrument for recording infrared spectra consists of a source of continuous radiation over the mid-infrared region, a sample chamber, a monochromator, and a detector. The infrared beam, which passes through the sample, is dispersed by a grating monochromator and then focused by a spherical mirror onto a slit, which serves both as the exit slit of the monochromator and entrance slit to the detector. The spectrum is scanned by continuously changing the angle of the grating or by moving the focusing mirror. Although the scanning instrument requires a relatively long time to obtain a complete spectrum and is little used in biological applications, it is still convenient for routine analytical applications. At present, infrared spectroscopic studies of proteins and nucleic acids are carried out by use of Fourier transform instruments. A Fourier transform infrared (FTIR) spectrometer employs an interferometric device, such as a Michelson interferometer, rather than a grating. The infrared beam emitted by the source is divided into two beams and the optical paths of the two beams (from the light source to the detector) are changed continuously by a moving mirror. Consequently, because of interference, the intensity of infrared radiation reaching the detector changes as a function of the relative path lengths between the two beams. The measured interferogram is converted into an infrared spectrum
296
Takashi Miura and George J. Thomas, Jr. through the Fourier transformation procedure. Because radiation of all infrared frequencies (typically the interval 400-4000 cm- 1) is detected simultaneously, a complete spectrum can be obtained in a very short time. Signal averaging procedures to enhance band intensities and minimize noise are therefore rapid and convenient, even for weakly absorbing samples. The FTIR method has been discussed in detail by Griffiths and deHaseth (1986). As noted previously (Section III,B), both H a O and D 2 0 are problematic solvents for infrared spectroscopy because of their very strong infrared absorption. Infrared spectra of aqueous solutions of proteins and nucleic acids can be obtained satisfactorily in limited intervals of the mid-infrared region, namely, 500-1000 cm -1 for H 2 0 solutions and 800-1100 and 1300-2000 cm -1 for D20 solutions. Also, a relatively high solute concentration is usually required. An infrared sample cell usually consists of a uniformly narrow chamber achieved by sandwiching an inert gasket between two optically flat plates (windows) fabricated from nonabsorbing material. The window material is chosen on the basis of its high infrared transmission, low refractivity, durability, insolubility, nonreactivity, and so forth. Calcium fluoride (CaF2), barium fluoride (BaF2), zinc selenide (ZnSe), and silver chloride (AgC1) windows are commonly employed for aqueous samples. Advantages and disadvantages of these and other window materials have been discussed (Griffiths and dellaseth, 1986). The optical path within the infrared cell (gasket thickness) is generally chosen to be between 20 and 100 txm, depending on the sample concentration and molar extinction coefficient of the band(s) to be measured. Infrared absorption, like UV/visible absorption, is governed by the Beer-Lambert relationship [Eq. (14)]. Cells thicker than 100 Ixm ordinarily do not transmit sufficient energy due to strong infrared absorption by the solvent. The sample volume is of course dependent on the cell path and cross-section. Typically, an infrared cell volume is 10/xl or greater. Thin and ultrathin films of the biological sample can also be layered on a suitable window material or reflectance device for infrared analysis.
D. Analysis of Data The successful application of vibrational spectroscopy in protein and nucleic acid analysis presumes definitive band assignments and requires a combination of experimental and theoretical approaches. Tactics employed toward this objective include (1) comparison of Raman frequencies and intensities with corresponding infrared data when available; (2) determination of vibrational frequency shifts accompanying stable-isotope substitutions, such as 1H 2H(D), 12C ~ 13C, 14N ~ 15N, and 160 ~ 180; (3) evaluation of the effects of pH, temperature, and other environmental factors on the spectra; (4) detailed and well-analyzed Raman and infrared spectra of smaller, more symmetrical molecules that are structurally related to the biomolecular constituents; (5) normal coordinate calculations; (6) measurements of depolarization ratios of the Raman bands in isotropic solutions of the molecules; (7) collection and analysis of polarized spectra of oriented samples when feasible; and (8) measurement of Raman excitation profiles that correlate Raman intensities with laser excitation wavelengths.
Chapter 6 Optical and Vibrational SpectroscopicMethods
297
Digitally computed difference spectra can facilitate the visualization of changes in vibrational band intensities or frequencies accompanying changes in sample temperature, molecular environment, or the like. However, because the Raman spectrum is not an absorption spectrum, its intensities are not governed by the Beer-Lambert law, and the comparison of two independently recorded Raman spectra by subtraction can be subject to considerable uncertainty. This is dealt with by comparing intensities in the two spectra only after normalization of both the minuend and subtrahend to a reliable internal intensity standard. A normalization procedure should be deemed reliable only after careful consideration of the origin of the band in question, and preferably after validation on a suitable model system. In the absence of reliable internal normalization, a process of trial and error may be the only recourse for computation of a Raman difference spectrum. Similar concerns apply to the procedure of solvent correcting a vibrational spectrum (infrared or Raman). It should be kept in mind that the protein or nucleic acid solute may influence the structure of the aqueous solvent, and therefore its vibrational spectrum, as much as the water molecules may influence the structure of the dissolved biomolecule. Accordingly, it is virtually impossible to compensate completely a solution spectrum for contributions of the aqueous solvent by simply subtracting therefrom the spectrum of the pure solvent. The computational power of microcomputers has ushered in an era of easy manipulation of all types of experimental data, including infrared and Raman spectra. A particularly popular procedure is the method of Fourier deconvolution, which is applied to enhance the resolution of overlapping bands. Also commonly employed is the method of least-squares curve fitting, which can be used to fit a complex bandshape to an arbitrary number of simpler band components. While the utility of such procedures cannot be questioned, considerable caution must be exercised in their application. The vibrational spectroscopist is well advised to avoid these computational approaches whenever the collection of additional experimental data can serve the same objective.
E. Information Obtainable from Vibrational Spectra In this section, we discuss molecular structural and environmental factors that can affect the frequencies a n d / o r intensities of bands in infrared and Raman spectra of proteins and nucleic acids. We also consider the usefulness of vibrational spectral data for gaining an improved understanding of molecular force fields and dynamical processes in biological molecules. Spectral bands that are particularly useful as markers of residue structure or environment are tabulated in Tables III-VI. The selection is representative, rather than comprehensive. More detailed discussions of these and other marker bands of proteins and nucleic acids can be found in recent review articles on the following subjects: infrared spectroscopy of nucleic acids (Taillandier and Liquier, 1992); infrared and Raman spectroscopy of proteins (Thomas and Kyogoku, 1977); Raman spectroscopy of nucleic acids, nucleoproteins, and viruses (Thomas, 1987; Thomas and Wang, 1988; Thomas and Tsuboi, 1993); Raman spectroscopy of proteins (Miura and Thomas, 1995); resonance Raman spectroscopy of nucleic acids (Tsuboi et al., 1987); and resonance Raman spectroscopy of proteins (Harada and Takeuchi, 1986; Austin et al., 1993).
298
Takashi Miura and George J. Thomas, Jr.
Table III Vibrational Modes of Trans Peptide Group a Description
Observed frequency
Calculated frequency
Amide A Amide I Amide II Amide III N C N stretch CN stretch Amide V Amide IV Amide VI C~CN bend C N C N bend Amide VII
3236 1653 1567 1299 1096 881 725 627 600 436 289 206
3254 1646 1515 1269 1070 908 721 637 655 498 274 226
Potential energy distribution b NH CO NH NH
s (100) a (83), CN s (15), C~CN d (11) ib (49), CN s (33), CO ib (12) ib (52), C~C s (18), CN s (14) N C N s (77), C~C (17) CN s (31), C~C s (17), CO s (16) CN t (75), NH ob (38) CO ib (44), C~C s (34), C N C N d (11) CO ob (85), CN t (13) C~CN d (63), CO ib (11) C N C N (71), CO ib (19), C~CN d (13) NH ob (64), CN t (15), CO ob (12)
a Based on the observed and calculated frequencies (cm -~) of N-methylacetamide, C~CONHCN, where Ca and CN refer to the acetyl and amide methyl groups, respectively, as reported by Bandekar (1992). b Relative (unnormalized) contributions to the potential energy; s, stretch; d, deformation; t, torsion; ib, in-plane bend; ob, out-of-plane bend.
Table IV Ranges of Infrared and Raman Amide Modes for Different Protein Secondary Structures a Secondary structure c~-Helix
/3-Strand
Irregular
Amide mode Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide
I II III V I II III V I II III V
Infrared (cm -1)
Raman (cm -1)
1648-1655 1540-1545 1270-1320 ~ 660 1630-1635(_1_ ), 1690-1695( II) 1520-1525( II ), 1550-1555(_t_) 1220-1235( II ) ~ 700 1655-1660 1550-1570 1240-1255 u
1648-1655 n 1270-1320 ~- 660 1660-1680 n 1225-1240 u 1655-1665 n 1240-1250 u
a Compiled from data in Carey (1982), Thomas (1987), Bandekar (1992), Arrondo et al. (1993), Miura and Thomas (1995), and references therein, n, Not observed in the off-resonance Raman effect; u, undetermined; (II), parallel component; (_t_), perpendicular component. The UVRR-determined amide II modes in model compounds are discussed by Austin et al. (1993). Additional correlations for various types of turns are also discussed by Bandekar (1992).
299
Chapter 6 Optical and Vibrational Spectroscopic Methods Table V Raman Markers of Backbone Conformation in D o u b l e Helical Nucleic Acids a Group
A DNA
O-P-O
B DNA
706 + 5 807 + 3 b
790 828 835 839 1092 1422
1099 + 1 1418 + 2
PO 2CH 2
Z DNA
+ 5 +_ 2 (GC) + 2 (GC + AT) + 2 (AT) + 1 + 2
745 + 3
1095 + 2 1425 + 2
a Frequencies (in c m - 1 ) a r e determined from Raman spectra of D N A and RNA crystals and fibers of known structure. b This vibration occurs at 813 + 2 c m -1 in A RNA structures. A very weak line also occurs at approximately 810 c m -1 in Z D N A structures.
1. M o l e c u l a r In applying
Force Fields
the simple harmonic
cal bond
between
diatomic
molecule),
atoms
A and
oscillator approximation B of masses
the classical vibrational
m A and
to an isolated chemi-
mB, r e s p e c t i v e l y
frequency
(e.g., a
is g i v e n b y
v = o c = (1/2rr)(K/la,) 1/2, where reduced
K is t h e H o o k e ' s mass
molecules,
law
of the system,
expressions
cated, can be derived
force constant defined
analogous
as 1/~
and
(21)
1/~
is t h e r e c i p r o c a l
t o E q . (21), b u t c o n s i d e r a b l y
for each of the 3N -
of the
= 1/m A + 1/mB. In polyatomic
6 normal
modes
more
compli-
( W i l s o n et al., 1 9 5 5 ) .
Table VI Raman Markers of Nucleoside Conformation in Nucleic Acids a Base G A C T
C3'-endo/anti 664 1318 644 1335 780 1252 668 745 777 1239
+ + + + + +
2b 2 4 2 2 2 -+- 2e + 2f + 2 + 2
C2'-endo/anti 682 1333 663 1339 782 1255 668 748 790 1208
+ 2 + 3c + 2a ___2 + 2 + 5 + 2 + 2 + 3 + 2
Cl'-exo/anti 670 + 2 1343 + 2
C3'-endo/syn 625 1316 624 1360 784 1265 660 745
+ + + + + + + +
3 2 3 5 2 2 5 5f
C2'-endo/syn 671 + 2 1324 + 2
677 + 2 737 + 2
Frequencies (in c m -1 ) are determined from Raman spectra of DNA and RNA crystals and fibers of known structure, reviewed in Thomas and Wang (1988), and from unpublished spectral data obtained by T. Miura and G. J. Thomas, Jr. b Observed at 668 + 1 c m -1 in structures containing rG. c A weak companion line near 1316 c m -1 is also observed in B D N A structures. Very low intensity compared to the 664 and 668 cm -1 lines of C2'-endo/anti dG and C2'-endo/anti dT, respectively. e Very low intensity compared to the 668 cm -1 line of C2'-endo conformer. f Very low intensity compared to the 748 c m -1 line of C2'-endo conformer. a
300
Takashi Miura and George J. Thomas, Jr. The frequencies of the molecular normal modes of vibration are determined rigorously by the nuclear masses and geometry~specifically, by the forces between bonded and nonbonded atoms (Herzberg, 1945). If the molecular geometry and the force field (i.e., the complete set of nonzero force constants) are reasonably well known, the 3N - 6 normal modes can, in principle, be calculated. The results of such normal coordinate calculations can then be tested against the experimental vibrational frequencies obtained from infrared and Raman spectra, and the force constants or geometry can be subsequently refined and the normal modes recalculated. Ultimately one hopes to obtain a detailed quantitative understanding of the nature of each normal mode of vibration, namely, which atoms are in motion in a given normal mode, and how the potential energy is distributed among the various internal coordinates that constitute the normal coordinate for that mode. Although such approaches have long been feasible for small molecules (Wilson et al., 1955), it is only relatively recently that complete normal coordinate analyses have been attempted for biological macromolecules (Krimm and Bandekar, 1986; Bandekar, 1992), sometimes with mixed success. This limitation is due in part to the paucity of experimental data needed to provide reliable force constants for large molecules and the resulting inadequacy of macromolecular force fields employed in the calculations. Microbiological and chemical methods have led to the incorporation of stable isotopes of hydrogen, carbon, nitrogen, and oxygen into the sugar and base residues of nucleic acids (Kellenbach et al., 1992; Nikonowicz et al., 1992). Similarly, isotope labeling of specific side chains in proteins and their assemblies (Aubrey and Thomas, 1991; Overman et al., 1994) has facilitated the refinement of key vibrational assignments in protein spectra. The new experimental data afforded by these methods make feasible the development of improved molecular force fields for accurate normal coordinate calculations of biological macromolecules. The more accurate normal mode analyses in turn provide reliable bases for both ab initio and molecular mechanics calculations. The latter are finding increased use in energy minimizations applied to problems of macromolecular folding and dynamics.
2. Macromolecular Conformations a. P r o t e i n s The vibrational modes associated with the trans peptide group of proteins (amide modes, Table III) are generally sensitive to the detailed conformation of the polypeptide backbone. Many of the amide modes in infrared spectra (reviewed by Arrondo et al., 1993) and Raman spectra (reviewed by Bandekar, 1992; Austin et al., 1993) of proteins have been correlated with specific main-chain conformations or secondary structures. Several are listed in Table IV. In principle, protein secondary structure may be estimated quantitatively from analysis of the conformation-sensitive amide I and amide III bands. In practice, however, a rigorous quantitative analysis is highly problematic and methods so far described have not been widely applied. Quantitative amide band analyses do provide, however, a complement to CD methods and may be especially useful for systems not amenable to CD spectroscopy. Surveys of infrared and Raman spectrophotometric methods employed for protein secondary structure analysis have been given by Bandekar (1992) and Arrondo et
Chapter 6 Optical and Vibrational Spectroscopic Methods
301
al. (1993). Further discussion of this subject is also given by Miura and Thomas (1995). b. Nucleic Acids The principal families of nucleic acid double helical structures (A, B, and Z conformations) are readily distinguished by their characteristic vibrational spectra. Table V lists the most prominent Raman marker bands of the different helical conformations. Table VI contains Raman marker bands identified for different conformers of the purine and pyrimidine nucleosides that are present in the helical duplexes. Detailed discussions of these nucleic acid spectra-structure correlations, established on the basis of known three-dimensional X-ray structures of oligonucleotide single crystals, are given elsewhere (Thomas and Wang, 1988; Thomas and Tsuboi, 1993). 3. S i d e - C h a i n
Conformations and L o c a l
E n v i r o n m e n t s in P r o t e i n s
A number of reliable correlations have been established to relate specific vibrational band frequencies a n d / o r intensities with the conformations and local environments of various protein side chains. A comprehensive overview of these correlations, which deal primarily with Raman and resonance Raman bands, can be obtained from the reviews by Harada and Takeuchi (1986), Austin et al. (1993), and Miura and Thomas (1995). (Owing to the difficulties associated with quantitative measurements in infrared spectra of aqueous proteins, relatively little is known about the possible conformational dependencies of corresponding infrared bands.) To illustrate this type of spectral information we consider two examples, cysteine and tryptophan. a. Cysteine The S - H stretching vibration of the cysteinyl side chain is particularly well suited to Raman analysis. The normal mode is a nearly pure group frequency; the Raman intensity associated with the vibration is intrinsically high; and the frequency occurs in a region of the Raman spectrum (25002600 cm -1) that is essentially devoid of interference from any other Raman bands of the protein or aqueous solvent. The structural value of the Raman S - H stretching band rests on two key factors: First, the band frequency is highly sensitive to hydrogen bonding of the S - H donor and S acceptor groups. Second, the band intensity is a measure of the molecular concentration of thiol groups in the protein. The first of these factors may be exploited to determine the environment and hydrogen-bonding interactions of the S - H group(s) within the protein structure; the latter may be exploited to measure the pK a of thiolate titration or the equilibrium constant governing oxidation of a cysteinyl thiol group. The S - H stretching frequency is also sensitive, though to a lesser extent, on torsions ,u (Co _C13) and X 2 (C]3-S~/) of the C ~ - C ~ - S r - H side chain (Li and Thomas, 1991; Li et al., 1992). The C - S stretching vibration of the cysteine side chain, which is also relatively easily measured in the region 640-725 cm-1 of the Raman spectrum, is much more highly sensitive to side-chain conformation. Normal coordinate and empirical analyses of the cysteine side chain lead to the structural correlations summarized in Table VII. As noted above, the vibrational frequency is a function of the nuclear masses, internuclear force constants, and molecular configuration. Accordingly, if the force constants and configuration are known for a molecule, the
302
Takashi Miura and George J. Thomas, Jr. Table VII Conformation-Sensitive Raman Bands of Cysteine Side Chain ~ Dependence of the Raman S-H Frequency and Bandwidth on Hydrogen Bonding Hydrogen bonding S-H frequency Bandwidth state of S-H group ( c m -1 ) (cm-1 ) Examples No hydrogen bond S acceptor Weak S-H donor
2581-2589 2590-2595 2575-2580
12-17 12-17 20-25
Moderate S-H donor
2560-2575
25-30
Strong S-H donor
2525-2560
35-60
S-H donor and S acceptor
2565-2575
30-40
Mode S-H stretch C-S stretch
Thiols in C C l 4 (dilute) Thiols in CHC13 Thiol neat liquids; thiols in thioethers Thiols in acetone; crystal structures c Thiols in dimethylacetamide; crystal structures c Thiols in H20
Dependence of Raman S-H and C-S frequencies on side-chain conformationb Rotamer (cm-1) Gauche X2 Trans X 2 Gauche X 1 Trans X 1
2581 2589 650 704
a From results of Li and Thomas (1991) and Li et al. (1992). b Data for 1-propanethiol and 2-methyl-l-propanethiol in dilute C C l 4 solution. c See references cited in Li and Thomas (1991) and Li et al. (1992).
n o r m a l m o d e s of vibration a n d their frequencies can be calculated (normal m o d e analysis). Figure 11 s h o w s the calculated relationship b e t w e e n the C - S stretching frequencies a n d the X1 torsions of 1-propanethiol and 2-methyl-1propanethiol, w h i c h are m o d e l c o m p o u n d s of cysteine. In this n o r m a l m o d e analysis, X1 w a s rotated b y increments of 20 ~ w i t h o u t a n y change of the force constants. Still, the calculated results are in g o o d a g r e e m e n t w i t h the experim e n t a l l y observed frequencies for C - S stretching m o d e s in molecules exhibiting g a u c h e (X1 = 60 ~ a n d trans (X1 = 180 ~ geometries. The a s s u m p t i o n that c o n f o r m a t i o n a l change has little or no effect on force constants g o v e r n i n g the f r e q u e n c y of the C - S m a r k e r b a n d w o u l d a p p e a r to be reasonable for the molecules studied. b. T r y p t o p h a n C o n f o r m a t i o n - and environment-sensitive b a n d s of the t r y p t o p h a n side chain (indole ring) are listed in Table VIII. The intense b a n d o b s e r v e d near 1550 cm-1 in R a m a n spectra of proteins is a sensitive m a r k e r of t r y p t o p h a n side-chain conformation (Miura et al., 1989). Specifically, the freq u e n c y of this m o d e , w h i c h is designated W3 a n d consists m a i n l y of stretching of the C 2 - C 3 b o n d of the indole ring (Takeuchi and H a r a d a , 1986), is correlated w i t h the absolute value of the X2,1 side-chain torsion, as s h o w n in Fig. 12. H o w ever, m o d e l c o m p o u n d analysis based on k n o w n crystal structures s h o w s clearly that the X 2'1 correlation cannot be r e p r o d u c e d by n o r m a l coordinate calculations using a fixed set of force constants. Therefore, in this case, the
303
Chapter 6 Optical and Vibrational Spectroscopic Methods
720
/ t
T
700
9 liD"
-
9 "0
tI
O'~
68O
\
x
~"i
i ~II/
660
640
i I
0
I
I
80
160
I
X
240
320
1
Fig. 11 Calculated dependence of the C - S stretching frequencies of 1-propanethiol (C)) and 2methyl-l-propanethiol (@) on the C - C - C - S torsion angle (t,1). See Li et al. (1992) for details of the normal coordinate analysis.
change of side-chain torsion angle apparently affects the frequency of the W3 mode through changes of the force constants. The molecular configuration and force constants are not always independent of one another and the influence of conformational change on force constants cannot generally be ignored in normal coordinate calculations.
4. Hydrogen Bonding Interactions Hydrogen bonding interaction between an appropriate donor hydrogen X - H (where X is O, N, or S) and an acceptor atom Y (usually O or N) is conveniently studied by methods of vibrational spectroscopy. The X - H stretching mode is particularly sensitive to hydrogen bonding. This dependency has been extensively investigated and correlated quantitatively with internuclear distances in X - H . 9.Y linkages (Pimentel and McClellan, 1960).
Table VIII Conformation-Sensitive
R a m a n B a n d s of T r y p t o p h a n S i d e C h a i n a
i
Mode
Interval
Assignment
Conformational sensitivity b
W3 W7 W17 W18
1545-1560 1360/1340 870-885 750-760
Pyrrole localized Fermi doublet Ring and N 1 - H motions Ring breathing
I X2,11 torsion Hydropathy of indole ring N 1 - H hydrogen bonding Hydropathy of indole ring
Based on normal coordinate and model compound analyses of Harada and coworkers, as indicated in Harada and Takeuchi (1986) and Miura et al. (1988, 1989). b See Miura and Thomas (1995) for detailed discussion.
a
304
Takashi Miura and George J. Thomas, Jr.
1555
T E u (J
c 1550
O"
B
L
LI,.
~Z.1 ,..-5"C~
iv)
r
1545,
~J 6~ ~
i
9'0 ~
'
'
1do" "
Ix .,I
Fig. 12 Experimentally determined relationship between the frequency of the tryptophan normal mode W3 and the side-chain torsion t ,2,1 (Miura et al., 1989). Different symbols refer to different tryptophan model compounds, as indicated in Miura et al., 1989. [Miura et al. (1989). Journal of Raman Spectroscopy, 20, 667-671. Copyright 1989 John Wiley & Sons, Ltd. Reprinted by permission of John Wiley & Sons, Ltd.]
As a recently investigated example, we consider the case of the imino N - H donor of 3-methylindole, a model compound for the indole ring in tryptophan (Miura et al., 1988). Infrared spectra in the region 3100-3600 cm -1 of 3-methylindole dissolved in mixed CS2-dioxane solutions are shown in Fig. 13A. In pure CS2, where hydrogen bond donation is disfavored, a relatively narrow band is observed at 3476 cm -1, corresponding to the imino N - H stretching vibration of nonhydrogen-bonded 3-methylindole. As the mole fraction of dioxane is increased and hydrogen bonds of the type N - H . . -O are formed between imino N - H donors and dioxane endocyclic acceptors, a characteristic infrared absorption band appears at 3346 cm -1 due to the hydrogen-bonded N - H groups. As the sharp band due to nonhydrogen-bonded groups (3476 c m -1) decreases, the broader band due to hydrogen-bonded groups (3346 cm-1) increases. The latter infrared band is distinguished from the former not only by its lower frequency and greater bandwidth, but also by its much greater intrinsic (integrated) intensity. It is generally true of stretching vibrations of hydrogen bond donor and acceptor groups that, on hydrogen bond formation, they give rise to infrared bands of lowered frequency and increased integrated intensity. Conversely, bending vibrations are elevated in frequency on hydrogen bond formation. These phenomenon can be rationalized in terms of the electronic perturbations occurring at the donor and acceptor sites (Pimentel and McClellan, 1960). In the Raman effect, however, although hydrogen bonding interactions also give rise to similar perturbations of lowered frequency and increased bandwidth for stretching vibrations, the integrated Raman band intensity is much less sensitive to hydrogen bonding than is the case in infrared spectra. [This can be appreciated, for example, by simply comparing the infrared and Raman spectra
305
Chapter 6 Optical and Vibrational Spectroscopic Methods A
B
006 f
I00:0/i1
1(0:0 0.05
--
9
~ 0.03
9 ):10
0:I00
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5:5 -
<
0.02
8:2 -
(
0.04'
90:10
-
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o.oi
3600
3500
3400
3300
3 2 0 0 3100
W a v e n u m b e r / cm -1
900
850
W a v e n u m b e r / cm "1
Fig. 13 Infrared spectra in the region 3100-3600 cm -1 (A) and Raman spectra in the region 850-910 cm -1 (B) of the tryptophan model compound 3-methylindole dissolved in pure CS2 (100:0), in pure dioxane (0:100), and in CS2-dioxane mixtures of volume compositions 98:2, 95:5, and 90:10, as indicated (Miura et al., 1988). [Reprinted with permission from Miura et al. (1988). Biochemistry, 27, 88-94. Copyright American Chemical Society.]
of liquid water (Thomas and Kyogoku, 1977).] Obviously, it is important to take into account the large increase in intrinsic band area caused by hydrogen bonding when infrared spectra are employed for quantitative analysis of molecular interactions using the Beer-Lambert relation [Eq. (20)]. A rigorous treatment of this problem has been given by R. C. Lord and co-workers (reviewed in Lord and Thomas, 1968). In the Raman spectrum of tryptophan, the indole ring mode near 880 cm-1, which is designated as W17 and which involves both ring stretching and displacement of the imino group (Takeuchi and Harada, 1986), is sensitive to hydrogen bonding. Figure 13B shows Raman spectra of 3-methylindole recorded at the same experimental conditions as the infrared spectra shown in Fig. 13A. Figure 13 demonstrates that the frequency of the Raman W17 band decreases as the mole fraction of dioxane in solution increases, consistent with the behavior observed for the infrared N - H band. Accordingly, it can be concluded that the frequency of the W17 Raman band serves as an indicator of hydrogen bonding of indole N - H groups. On the other hand, indole normal modes that involve N - H bending motion shift to higher frequency on hydrogen bond formation. An example is the tryptophan Raman band near 1430 cm- 1 (Miura et al., 1988, 1989). Despite great sensitivity to hydrogen bonding, the O - H and N - H stretching bands in infrared and Raman spectra of aqueous proteins and nucleic acids have been relatively little used to analyze hydrogen bonding interactions. This reflects the extensive overlap of the donor stretching region (3000-3600 cm-1) by extremely intense bands of the aqueous solvent. Even in the absence of solvent, the large numbers of O - H and N - H groups present in proteins and
306
Takashi Miura and George J. Thomas, Jr. nucleic acids would depreciate the potential usefulness of the data. Nevertheless, strategies have been developed to exploit the hydrogen bonding sensitivity of infrared and Raman spectra for both structural studies and quantitative determinations of thermodynamic parameters governing biologically important interactions (Kyogoku et al., 1968; Lord and Thomas, 1968; Li et al., 1993a).
5. V i b r a t i o n a l C o u p l i n g Cyclic hydrogen bonding configurations are important determinants of biological structure and recognition. Examples are the Watson-Crick base pairing schemes and the interactions formed between side chains of gene regulatory proteins and their DNA recognition sites. A simple model of cyclic hydrogen bonding is the carboxylic acid dimer shown in Fig. 14. In Raman spectra of carboxylic acids, the C = O stretching mode is observed near 1680 cm-1. However, in infrared spectra no 1680 cm -1 band is observed. Instead an intense infrared band occurs near 1750 cm -1 (Davies and Sutherland, 1938). The centrosymmetric dimer, by virtue of its inversion center of symmetry, follows the exclusion rule (Section III,A,2,c). The two vibrational bands correspond to two C = O stretching modes: the 1680 cm-1 Raman-active mode is symmetric, i.e., corresponds to in-phase motions of the two C - - O oscillators (Fig. 14, left). The 1750 cm -1 IR-active mode is an antisymmetric or out-of-phase motion (Fig. 14, right). The two modes are shifted from a common center (1715 c m -1) where uncoupled oscillators would absorb and Raman scatter. This phenomenon, called intermolecular vibrational coupling, is expected when two identical or nearly identical oscillators are in proximal contact and their association generates a symmetry or pseudosymmetry element (typically an inversion center or axis of rotation). The phenomenon of intermolecular vibrational coupling has been demonstrated for the hydrogen-bonded GC base pairs of a model RNA structure [poly(rG).poly(rC)] using isotope substitution (Howard et al., 1969). It was shown that 160---> 180 substitution in guanine alone is sufficient to produce isotope shifts in two distinct infrared bands observed in the carbonyl region, instead of the expected single band shift. Accordingly, both IR bands involve some degree of guanine C - - O stretching. It follows that both also involve some cytosine C = O stretching, i.e., the C = O oscillators of G and C are coupled through cyclic hydrogen bonding. Evidence for intermolecular vibrational coupling has also been reported for CC base pairs in the hemiprotonated poly(rC) duplex (reviewed in Thomas and Kyogoku, 1977). In the case of proteins, the relatively large splitting observed in the IR amide I modes of antiparallel 13-
O-H R--~'C~o~
.... ~O,~c_ .-H-C) 9
/ ~, R
~ 1680 cm-1 RAMAN
ACTIVE
O-H ...... O,N
R--~C~o~
9"
/ R ~(~--
H - C )
~ 1750 c m -i INFRARED
ACTIVE
Fig. 14 Representation of symmetric (left) and antisymmetric stretching modes (right) of carbonyl groups in a carboxylic acid dimer.
Chapter 6 Optical and Vibrational Spectroscopic Methods
307
sheet structures (~ 60 cm -1, Table IV) has been explained in terms of vibrational coupling (Miyazawa and Blout, 1961).
6. Fermi Resonance Radiation-induced transitions between vibrational states that differ in energy by more than one vibrational quantum occur with low probability. Therefore, infrared bands corresponding to the absorption of multiple vibrational quanta of the same normal mode (overtones of a fundamental) or of different modes (combinations of two or more fundamentals) are usually of negligible intensity. A similar selection rule holds for Raman scattering. However, if the frequency of the overtone or combination happens to be close to or coincident with that of another fundamental of the same symmetry type, the two states may "mix," thereby resulting in two new states, neither of which retains its original identity. This situation is termed Fermi resonance. In such a case, infrared and Raman transitions involving both of the Fermi levels become possible. The spectrum (infrared or Raman) will then exhibit a doublet, i.e., a pair of bands corresponding to transitions involving each of the two Fermi states. The Fermi doublet components are observed at frequencies somewhat higher and lower than the expected unperturbed positions of the fundamental and overtone. A simple perturbation theory treatment (Herzberg, 1945) shows that the center of the Fermi doublet remains the same as the center of the theoretically unperturbed frequencies. However, the magnitude of the splitting and the relative intensities of the Fermi doublet components are strongly dependent on the frequency difference between unperturbed levels. An example of a Fermi doublet is shown in Fig. 15 for the tryptophan model compound, 3-methylindole. In hydrophilic solvents (methanol, dimethylformamide, and dioxane), 3-methylindole exhibits a single sharp Raman band centered near 1347 cm-1. This band is assigned to a fundamental stretching vibration of the indole ring. However, in hydrophobic solvents (o-dichlorobenzene, benzene, toluene, CS2, and n-hexane) a closely spaced doublet is observed. The splitting can be explained in terms of Fermi resonance involving the 1347 cm-1 fundamental band and a combination band (~ 920 + 420 cm-1) (Harada et al., 1986). In benzene and toluene solutions, the sum of frequencies of the combination band (924 and 423 cm-1; data not shown) coincides exactly with the fundamental and the resulting two Fermi components exhibit nearly the same spectral intensity. Further discussion is given by Harada et al. (1986). A corresponding Fermi doublet at 1340 and 1360 c m - 1 is observed in tryptophan and is a sensitive marker of hydrophobicity of the tryptophan side chains in proteins (Table VIII).
7. Kinetics of Isotope Exchange Reactions The isotope effects predicted for vibrational frequencies [Eq. (20)] can be exploited as a means of measuring the concentrations of different isotopomers during a hydrogen isotope exchange reaction. The time-dependent concentrations measured in this way provide the exchange rate constants, which in turn can provide insight into solvent accessibility and dynamics of biological macromolecules. In the case of spectral bands due to X - H hydrogenic vibrations, such as
308
Takashi Miura and George J. Thomas, Jr. a
b
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i
1300
|
i
A |
1350 1/~00 Wavenumberl
|
i
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i
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Fig. 15 Raman spectra in the region 1300-1400 cm-1 of solutions of 3-methylindole in the following solvents: (a) methanol, (b) dimethylformamide, (c) dioxane, (d) o-dichlorobenzene, (e) benzene, (f) toluene, (g) CS2, and (h) n-hexane. [Reprinted with permission from Harada et al., 1986.]
N - H a n d O - H s t r e t c h i n g a n d b e n d i n g m o t i o n s , the e x p e c t e d f r e q u e n c y shift, i.e., the q u o t i e n t v ( X - D ) / v ( X - H ) , following deuteration should approach ( 1 / 2 ) 1/2 [Eq. (21)]. H o w e v e r , e v e n skeletal m o d e s t h a t h a v e o n l y p a r t i a l N - H or O - H b e n d i n g c h a r a c t e r can shift significantly. I n f r a r e d a n d R a m a n s p e c t r a h a v e b e e n u s e d e x t e n s i v e l y to m o n i t o r h y d r o g e n - d e u t e r i u m e x c h a n g e reactions in p r o t e i n s a n d nucleic acids, as well as in their m o n o m e r i c c o n s t i t u e n t s a n d m a c r o m o l e c u l a r a s s e m b l i e s . S u r v e y s of a p p l i c a t i o n s to p r o t e i n s ( T h o m a s a n d K y o g o k u , 1977) a n d nucleic acids a n d their c o m p l e x e s ( T h o m a s a n d Tsuboi, 1993) h a v e b e e n given. A R a m a n flow cell d e v i c e has b e e n e m p l o y e d to m e a s u r e in real t i m e the kinetics of h y d r o g e n i s o t o p e e x c h a n g e r e a c t i o n s occur-
Fig. 16 (A) Raman spectrum in the region 500-3700 cm- 1 of reduced thioredoxin at pH 4 and 6~ Protein concentration is 100/~g//~1. The Raman band of N 2 at 2331 cm- 1 serves as a frequency and intensity reference. The complex Raman band at 2569 cm-1 is due to Cys-32 and Cys-35 sulfhydryl stretching modes. Raman bands just below 3000 cm-1, which are due to aliphatic CH stretching modes of most side chains, and the very broad, complex band of H 2 0 solvent at ---3400 cm-1 are evident in the segment recorded at 1/5 amplification. The symbols V and * indicate overtone or combination bands and a laser emission line, respectively. The rich pattern of Raman bands in the region 500-1700 cm -1 is due to vibrational modes of the protein main chain (amide I and III conformation markers) and most side chains. Detailed band assignments and dependence of the spectrum on temperature, pH, and oxidation state of active-site cysteines is given by Li et al. (1993a). (B) Raman spectra in the 2500-2600 cm- 1region of reduced thioredoxin at the indicated pH values. The bottom trace, obtained at pH 12.2, for which all sulfhydryls are titrated to thiolate ion, indicates the level of background noise in this region of the spectrum. The Raman-pH titration curve (inset), obtained from these and additional data not shown indicates unusually low pKa values (K 8) for both sulfhydryls. Analysis of the complex bandshape is consistent with pKa values of 7.1 and 7.9 for Cys-32 and Cys-35, respectively.
309
Chapter 6 Optical and Vibrational Spectroscopic Methods
500
1500
1000
2000
2500
cm-1
B
2500
2550
m-1
2600
3000
3500
,
310
Takashi Miuraand GeorgeJ. Thomas,Jr. ring in the capsid subunits and packaged nucleic acids of icosahedral viruses (Li et al., 1993b).
8. Example: Raman S p e c t r u m of E s c h e r i c h i a coli T h i o r e d o x i n Figure 16, which shows the Raman spectrum of an aqueous solution of Escherichia coli thioredoxin, illustrates many of the points noted in Sections III,B and II,E regarding the application of vibrational spectroscopy to proteins. A detailed analysis of the thioredoxin Raman spectrum has been given elsewhere (Li et al., 1993a). Here we note that the rich pattern of bands in the spectral region 500-1700 cm-1 is assignable to specific amide modes of the polypeptide main chain and to characteristic marker bands of various side chains. These provide information, respectively, about the secondary structure of the protein and the environments of key amino acid residues. In particular, the pH dependence of the complex sulfhydryl stretching band in the interval 2500-2600 cm- 1 (Fig. 16B) demonstrates both the nature of active site S - H hydrogen bonding interactions and the abnormal pKa values governing thiol-thiolate equilibria in the reduced form of this oxidoreductase.
Appendix General Rules Governing Band Intensities in Electronic Spectra The probability of a transition between electronic states is proportional to the square of the transition moment integral given by Eq. (A1): | = <~' I/z I ~>,
(A1)
where ~ ' and 9 are the total wave functions, i.e., containing both electronic and nuclear coordinates for the excited and ground electronic states, respectively, and/z is the dipole moment operator. In the Born-Oppenheimer approximation, the total wave function can be factored into electronic and nuclear terms as given in Eq. (A2)" (D = (De(I) v
and
~'
--" r
,
(A2)
where (D e and ~v are the electronic and vibrational wave functions, respectively, and the prime symbols denote excited states. Nuclear motions other than vibrations are neglected. Note that (D e is a function of both electronic and nuclear coordinates, whereas ~v depends only on the nuclear coordinates. Using Eq. (A2), the transition moment integral of Eq. (A1) is given by Eq. (A3)0
= <([-)e,(I.) v, I[.s
,
= <(I) v, [ (I)v>" <(D e, I jU, I (I)e> ,
(A3)
=- (v' l v).(e' l /z l e). A transition is allowed, i.e., has nonzero probability, when both of the integrals ( v ' l v ) and ( e ' l / z l e ) of Eq. (A3) are nonzero. We consider first the integral (v' I v), which is termed an overlap integral of vibrational wave functions belonging to two different electronic states. (As such it must be distinguished from an integral containing vibrational wave functions belonging to the same electronic state, which, in the harmonic oscillator approximation, is necessarily zero by virtue of vibrational wave function orthogonality.) The
311
Chapter 6 Optical and Vibrational Spectroscopic Methods
overlap integral of Eq. (A3) can be compared to the scalar product of two unit vectors, i and j, which are directed along perpendicular axes, x and y. If i and j are (within the same plane), their scalar product i-j must be zero. However, if i and j are not in the same plane, then they are not necessarily orthogonal, and their product need not be zero. Spectroscopic transitions that depend on the degree of nonorthogonality of the combining vibrational sublevels, v' and v, of the ground and excited electronic states can be depicted using an energy level diagram, such as that of Fig. 3. Potential energy curves representing the ground (So) and excited (S1) electronic states, their first few vibrational sublevels, and the corresponding harmonic oscillator wave functions of the molecule are shown at the left of the illustration. We consider transitions originating only from the most populated vibrational sublevel of the ground electronic state, i.e., from the v = 0 level of So. Although the molec