Linkage Thermodynamics of Macromolecular Interactions, Volume 51 (Advances in Protein Chemistry)

ADVANCES IN PROTEIN CHEMISTRY Volume 51 Linkage Thermodynamics of Macromolecular Interactions JEFFRIES WYMAN (1901-1...

Author: Enrico Di Cera | Frederic M. Richards | David S. Eisenberg | Peter S. Kim

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ADVANCES IN PROTEIN CHEMISTRY Volume 51

Linkage Thermodynamics of Macromolecular Interactions

JEFFRIES WYMAN (1901-1 995)

ADVANCES IN PROTEIN CHEMISTRY EDITED BY FREDERIC M. RICHARDS

DAVID S. EISENBERG

Department of Molecular Biophysics and Biochemistry Yale University New Haven. Connecticut

Department of Chemistry and Biochemistry University of California, Los Angeles Los Angeles, California

PETER S. KIM Department of Biology Massachusetts Institute of Technology Whitehead Institute for Biomedical Research Howard Hughes Medical Institute Research Laboratories Cambridge, Massachusetts

VOLUME 51

Linkage Thermodynamics of Macromolecular Interactions EDITED BY ENRICO DI CERA Department of Biochemist/y and Molecular Biophysics Washington University Medical School St. Louis, Missouri

ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto

Frontispiece reprinted from A History of Biochaist?y 36 (1985), pages 99-190, with kind permission of Elsevier Science - NL, Sara Burgerhartstraat 25, 1055KV Amsterdam, The Netherlands.

This book is printed on acid-free paper. @ Copyright 0 1998 by ACADEMIC PRESS 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. The appearance of the code at the bottom of the first page of a chapter in this book indicates the Publisher’s consent that copies of the chapter may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay the stated per copy fee through the Copyright Clearance Center, Inc. (222 Rosewood Drive, Danvers, Massachusetts 01923), for copying beyond that permitted by Sections 107 or 108 of the US. Copyright Law. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Copy fees for pre-1997 chapters are as shown on the title pages. If no fee code appears on the title page, the copy fee is the same as for current chapters. 0065-3233/98 $25.00

Academic Press a division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 921014495, USA http://www.academicpress.com Academic Press Limited 2428 Oval Road, London NWl 7DX, UK http://www.hbuk.co.uk/ap/ International Standard Book Number: 0-12-034251-0 PRINTED IN THE UNITED STATES OF AMERICA 98 99 00 01 02 03 MM 9 8 7 6 5 4

3 2

1

CONTENTS

INTRODUCTION

.

ix

Electrostatic Contributions to Molecular Free Energies in Solution MICHAEL SCHAEFER, HERMAN W. T. VAN VLIJMEN, AND MARTIN

I. Introduction . 11. Theory and Calculational Methods . 111. Applications . IV. Outlook . References .

~

L

U

S

1 3 20 53 54

.

Site-Specific Analysis of Mutational Effects in Proteins

ENRICODI CERA

I. Introduction . 11. The Reference Cycle

59 61 63

.

111. Structural Mapping of Energetics . IV. Site-SpecificAnalysis of Mutational Effects . in Proteins V. Site-Specific Dissection of Thrombin Specificity VI. Concluding Remarks . References .

.

73 79 113 115

Allosteric Transitions of the Acetylcholine Receptor STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

I. Introduction . 11. Mechanistic Models. . 111. Recovery from Desensitization. . IV. Kinetic Basis of Dose-Response Curves . V. Multiple Phenotypes . VI. Deductions from Singlechannel Measurements V

.

121 127 133 137 141 149

.

vi

CONTENTS

VII. Mlosteric Effectors and Coincidence Detection VIII. General Considerations . References .

.

163 166 173

Deciphering the Molecular Code of Hemoglobin Allostery GARY K. ACKERS I. Introduction . 11. Overview. 111. Binding Curves and Stoichiometric Information . Iv. Site-Specific Aspects of Oxygen Binding . V. Experimental Determination of Site-Specific Cooperativity Terms . VI. How the Molecular Code Was Deciphered . . VII. Concluding Remarks References .

.

185 190 198 206 211 221 246 248

Statistical Thermodynamic Linkage between Conformational and Binding Equilibria FREIRE ERNESTO I. Introduction . . 11. The Most Probable Distribution . 111. Coupling of Statistical Weights to Ligands Iv. Modulation of Distribution of States by Specific Ligands . V. Modulation of Distribution of States . by Denaturants . VI. Ligand-Induced Conformational Changes VII. The Distribution of Conformational States According to . Their Gibbs Energy. VIII. Is the Unfolded State the State with the Highest Gibbs Energy? . IX. The Gibbs Energy Scale of Conformational States . X. Statistical Descriptors of the . Conformational Ensemble XI. Conclusions . References .

255 257 257 259 262 263 263 267 269 271 278 278

vii

CONTENTS

Analysis of Effects of Salts and Uncharged Solutes on Protein and Nucleic Acid Equilibria and Processes: A Practical Guide to Recognizing and Interpreting Polyelectrolyte Effects, Hofmeister Effects, and Osmotic Effects of Salts

M. THOMAS RECORD, JR., WENTAO ZHANC, AND CHARLES F. ANDERSON I. Introduction . 11. Overview of Concentration-Dependent Effects of Perturbing Solutes on Processes Involving Biopolymers . 111. Preferential Interaction Coefficients as Fundamental Measures of Thermodynamic Effects due to . Solute-Biopolymer Interactions N . Preferential Interactions of Nonelectrolyte Molecules with an Uncharged Biopolymer . V. Preferential Interactions of Electrolyte Ions with a . Charged Biopolymer Use of Three-Component Preferential Interaction VI. Coefficients to Analyze Effects of Solute Concentration on Equilibrium Constants, Transition Temperatures, or Free Energy Changes of Biopolymer Processes . VII . Two-Domain Predictions of Functional Forms of Effects of Nonelectrolyte Concentration on Equilibria ( K O b ) and Transition Temperatures ( T , ) of Uncharged Biopolymers in Aqueous Solution . VIII. Polyelectrolyte and Two-Domain Predictions of Functional Forms of Effects of Salt Concentration on Equilibria (Kobs)and Transition Temperatures ( T , ) of Charged Biopolymers in Aqueous Solution . . IX. Conclusions and Future Directions. References .

282 286 295 303 31 1

319

326

330 349 350

Control of Protein Stability and Reactions by Weakly Interacting Cosolvents: The Simplicity of the Complicated SERGE N. TIMASHEFF I. Introduction . 11. Preferential Interactions . 111. Wyman Linkages in Preferential Interactions .

.

356 360 377

...

CONTENTS

vlll

IV. Linkage Control of Protein Stability V. Linkage Control of Protein Reactions

VI. Sources of Exclusion VII. Osmolytes VIII. Conclusion References AUTHOR INDEX SUBJECT INDEX

. .

. . .

.

. .

387 409 416 423 425 428 433 453

INTRODUCTION

In a paper published fifty years ago in Advances in Protein Chemistly [ (1948) Adv. Protein Chem. 4,407-5311, Jeffries Wyman laid the founda-

tions for the theory of linked functions and brought the rigor of Gibbs’ thermodynamics to biochemistry. Wyman was the first to realize and correctly formulate the reciprocity principle between effects elicited by two ligands on each others binding. Linkage is the inevitable consequence of the first two laws of thermodynamics and permeates every aspect of macromolecular function. Through the principle of linked functions, Wyman captured the essential property of proteins as macromolecular transducers of different effects: a simple property that lies at the very foundations of biological complexity. On page 198 of the third edition of “Molecular Biology of the Cell,” Alberts, Bray, Lewis, Raf€, Roberts, and Watson write, “The [linkage] relationships . . . underlie all of cell biology. They seem so obvious in retrospect that we now take them for granted.” A fundamental consequence of the principle of linked functions has become more widely known than the principle itself. In an attempt to explain the mechanism of the Bohr effect of hemoglobin, i.e., how oxygen binding is influenced by proton binding, Wyman and Allen [(1951) J. Polymer Sci. 7, 499-5181 proposed that hemoglobin would exist in different conjgurations showing different affinities for oxygen and the proton and that the linkage between these ligands would be mediated by a change in configuration involving the hemoglobin molecule as a whole. Fourteen years later, this radically new idea was articulated in the classical Monod-Wyman-Changeux model of allosteric transitions [ (1965) J. MoZ. Biol. 12, 88-1181 and provided a monumental advance to our understanding of how proteins work. Impressive applications of allostery and linkage to many biologically important systems have since appeared in the literature, and a lucid treatment of these basic concepts and their applications was given by Wyman and Gill in the landmark book “Binding and Linkage” (1990, University Science Books, Mill Valley, CA). The contributions to this volume of Advances in Protein Chemistly document the central role and impact that the theory of linked functions maintains in all disciplines concerned with a quantitative understanding of binding energetics and structure-function relations. Schaefer, van ix

X

INTRODUCTION

Vlijmen, and Karplus discuss a new method for the calculation of protein pKa’s and pH-dependent electrostatic free energies in solution based on the theory of linked functions. The method is applied to the calculation of lysozyme pKa’sand the pH dependence of the stability of lysozyme and the capsid of the foot-and-mouth disease virus. Di Cera develops a site-specific analysis of mutational effects in proteins as an extension of the theory of linked functions. The analysis leads to the formulation of a new strategy for dissecting ligand recognition, and an application is given for the case of thrombin-substrate interactions. Important new applications of the theory of linked functions and allostery are given by Edelstein and Changeux for the acetylcholine receptor and by Ackers for hemoglobin. Freire extends the original linkage concept to model the statistical ensemble of conformers accessible to native proteins and discusses the implications of this new approach to the analysis of conformational and binding equilibria. Record, Zhang, and Anderson give a lucid analysis of linked effects arising from salts and uncharged solutes on proteins and nucleic acid equilibria. Their analysis extends the theory of linked functions to encompass the biologically relevant cases in which solutes affect the properties of macromolecules beyond simple mass action effects. Timasheff refines the concept of preferential interactions to bring new light to the effects of weakly interacting cosolvents in macromolecular systems. The exciting contributions to the field of ligand binding and linkage contained in this volume remind us of the timeliness and importance of Wyman’s theory of linked functions, which provides the logical tools to link structural and computational biology to macromolecular energetics. Work done in this field, pioneered by Wyman fifty years ago, will continue to produce important new developments and a deeper understanding of structure-function relations.

ENRICO DI CERA AND JOHN T. EDSALL

ELECTROSTATIC CONTRIBUTIONS TO MOLECULAR FREE ENERGIES IN SOLUTION By MICHAEL SCHAEFER,' HERMAN W. T. VAN VLIJMENP and MARTIN KARPLUW 'Leboratoire de Chimie Biophysique, institut ie Eel, Universitd Loulr Pasteur, 67000 Strasbourg, France, and ?Departmentof Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts02138

I. Introduction ....................................................... 11. Theory and Calculational Methods .................................... A. Titration Calculation ............................................ B. Electrostatic Free Energy Difference between Conformations ......... C. The Independent Sites Model .................................... D. Standard, Intrinsic, and Effective pK. ............................. E. Electrostatic Free Energy of a Protonation State ................... F. Electrostatic Free Energy Calculation ............................. G. Monte Carlo Titration .......................................... 111. Applications ....................................................... A. Protein Dielectric Constant ...................................... B. Variation of Stability of Lysozyme with pH ........................ C. Capsid Stability of Foot-and-Mouth Disease Virus .................. N. Outlook .......................................................... References ........................................................

1 3

5 7 8 13

16 17 19 20 21 25 39 53 54

I. INTRODUCTION Protein titration provides a notable example of the specific binding of multiple ligands (protons) to a macromolecule, the subject of the linked function theory introduced by Wyman (1948) and fully elaborated in the book by Wyman and Gill (1990).It is of particular interest because it is, at present, the only case for which theoretical evaluation of the binding constants is possible. Moreover, every protein has a large number of binding sites for protons, and in certain cases the individual site binding constants, as well as the overall binding (titration) behavior, have been measured (Tanford and Roxby, 19'72;Bashford and Karplus, 1990). The protonation of titratable sites in proteins clearly falls into the category of specific binding, i.e., every successivebinding of a proton can be expressed as a chemical reaction in which the chemical activity of the protein species and the proton chemical potential are related by the law of mass action (Wyman and Gill, 1990). The theory of linked functions thus provides the theoretical basis for a quantitative treatment

* f i e s a t address: Biogen Inc., 12 Cambridge Center, Cambridge, Massachusetts 02142. 1 ADVANCES IN PROTWN CHEMISTRY, Vol. 51

Copyright 0 1998 by Academic Press. All rights of reproduction in any form reserved. 00653239/98 $25.00

2

MICHAEL SCHAEFER ET AL.

of protein titration (Wyman, 1964; Szabo and Karplus, 1972; Schellman, 1975). Further, an accurate theoretical understanding of the pK,’s of titratable sites in proteins and the pH dependence of electrostatic free energies are important because ionizable groups play an essential role in numerous processes of biological interest, e.g., enzyme catalysis (Jhowles, 1976; Warshel et al., 1989), proton transport (Warshel, 1979; Zhou et d., 1993),and the stabilityof molecules and molecular assemblies (Yang and Honig, 1993; Antosiewicz et al., 1994; Schaefer et al., 1997). In this review of protein titration, methods for the calculation of protein pK,’s and pH-dependent electrostatic free energies in solution will be developed on the basis of linked function theory, and applied to the calculation of lysozyme pK,’s, the pH dependence of the stability of native lysozyme,and the pH dependence of the stability of the capsid of foot-and-mouth disease virus. In the latter application, the contributions from individual sites will be addressed, in particular those that are responsible for the acid lability of the capsid. Furthermore, a simplified model for the pH dependence of binding free energies will be derived based on the pK,’s of the system (“independent sites” model). To formulate the problem, we consider only two protonation states for each site, unprotonated and protonated. This “two-state model” represents an implicit averaging over multiple protonated (unprotonated) states of the anionic (cationic) sites. For example, only one unprotonated state for histidine is considered where the proton charge is equally distributed among Hg,and HCz(see Table I in Section II,D). The protonation state of a protein with Nsites can then be described by a vector S with N components, where the component si is

si=

[

0,

if site i is unprotonated

1,

if site i is protonated

(1)

When the fully unprotonated state of the protein is used as the reference, the overall reaction that leads to the protonation state S is

Y((Ti) + n(Z)H++ 9 ( S )

(2)

where we have written 8(q for the protein in state S, the fully unprotonated state is denoted S = 0, and n(S) is the number of protons bound in state S. The equilibrium constant, a(;),for this reaction is defined as (Wyman and Gill, 1990)

where x is the proton chemical activity, and where the activity coeffi-

ELECTROSTATIC FREE ENERGY IN SOLUTION

3

cients of the protein species are included in the equilibrium constant so that molecular concentrations can be used. The equilibrium constants a(?)are generally referred to as Adair constants (Wyman and Gill, 1990) after the analysis of Adair (1925) on hemoglobin. The binding polynomial, E , which is a macroscopic analog of the partition function, is defined as the sum over the concentrations of all different species relative to that of the reference species (here, the unprotonated state). For the present case, it has the form (Wyman and Gill, 1990)

where the sum is over all 2Nprotonationstates. We use the term partition function for E in what follows. On the right-hand side of Eq. (4), we have written out explicitly the contributions from the fully unprotonated state [set equal to 1 , see Eq. (3)] and from the fully protonated state, S = i.In contrast to the nomenclature that is often used in the context of multiple ligand binding, we distinguish the ( f )protonation states with k protons bound, where the expression in parentheses is the binomial coefficient. This distinction is required because the titratable sites in a protein are, in general, not equivalent, such that the electrostatic free energies of different protonation states with the same number of protons bound are distinct and lead to different statistical weights, a(?), in the partition function. In principle, it would be possible to group all terms with the same number k protons in the partition function, introducing Adair constants that depend only on the total number of protons bound. However, for an analysis of the titration behavior of the individual sites and the calculation of their pK,’s it is necessary to keep the microscopic equilibrium constants a ( i )in the generating function. 11. THEORY AND CALCULATIONAL METHODS Each term in the binding polynomial, Eq. (4), can be rewritten as a Boltzmann weight factor involving the pHdependent electrostatic free energy, AG(S, pH), of the protonation state S relative to the free energy of the unprotonated reference state:

where R is the gas constant and T is the absolute temperature. The quantity AG(S,pH) is the electrostatic free energy relative to that of

4

MICHAEL SCHAEFER ET A L

the unprotonated state because the term in the binding polynomial, Eq. <4), referring to the unprotonated state is equal to 1, such that AG(0,pH) = 0 independent of the pH. From Eq. (5), it follows immediately that the electrostatic free energy of a protonation state, AG(S,pH), can be expressed as the sum of proton activitydependent and proton activity-independent terms: AG(S,pH) = -RT n(S) In x + A C ( S )

(6)

where we have written AG’(S) for the contribution that is independent of the proton activity. If one assumes ideal solution conditions, the first term in Eq. (6) can be expressed as a function of pH: AG(S,pH) = (In lO)RTn(S)pH + G’(S)

(7)

The electrostatic free energy of a protonation state, AG(S,pH), thus increases linearly with pH, where the increase is proportional to the number of protons bound, n(S). In principle, the pH-independent contribution to the electrostatic free energy, AG’(S), could be calculated directly, i.e., from a thermodynamic cycle that includes the free energy of the removal of n ( S ) protons from the bulk solvent and the free energy of their reaction with the protein sites that are protonated in the state S. However, such an a p proach would be very challenging because these two energy terms (removal from solvent; association with the sites) are very large (on the order of 100 kcal/mol) and have opposite signs, so that high accuracy is required. To reduce the error in the computation, we use a different approach here in which the electrostatic free energy of protonating the sites in the protein is compared with the corresponding free energy difference for a solvated model compound containing the titratable site, such that only pK, shifts relative to experimentally known pK,’s of the model compounds need to be calculated (Tanford and Kirkwood, 1957; Bashford and Karplus, 1990). For the calculation of electrostatic free energies in the protein and in the model compounds, we make use of the continuum model in which the solvent and the solute are described as polarizable continua and assigned dielectric constants. This greatly simplifies the computation as compared with free energy simulation methods in which the solvent is represented explicitly (Sham et al., 1997). In the continuum approximation, the electrostatic free energy is computed by solving the PoissonBoltzmann equation (Kirkwood, 1934;Davis and McCammon, 1990).For molecules of arbitrary geometry, this can be accomplished by numerical

ELECTROSTATIC FREE ENERGY IN SOLUTION

5

algorithms, e.g., the finitedifference method which is employed in this work (Warwickerand Watson, 1982; Gilson et al., 1988; Davis et al., 1991) (see Section 11,F).

A. Titration Calculation From the theory of linked functions (Wyman, 1948, 1964; Szabo and Karplus, 1972; Schellman, 1975), the thermodynamic properties of a titrating system can be derived from the partition function E(x). Using Eq. (5), we rewrite Eq. (4) as a function of pH: E(pH) =

i

exp [- /3 AG(S,pH)];

P=I/(W

(8)

where the sum is over all 2Nprotonation states of the system, and where AG(S,pH) is the pHdependent electrostatic free energy for the protonation state S, relative to the fully unprotonated state. Furthermore, it is assumed that nonelectrostatic contributions to the free energy of the system are independent of the protonation state (i.e., they contribute a constant term) and can thus be omitted in the present treatment of the electrostatic free energy. Given the generating function, the pHdependent free energy relative to the unprotonated state is AG(pH) = -RTln E(pH)

(9)

while the pHdependent average protonation (n) and the probability (si) of finding site iin the protonated state are given by the ensemble averages (Bashford and Karplus, 1990; Beroza et al., 1991; Yang et al., 1993):

In the limit of infinite pH, the only protonation state that is energetically accessible at finite temperature is the unprotonated state [see Eq.

6

MICHAEL SCHAEFER ET AL.

(7)1. Since we used S = 8 as the reference state for the free energy of a protonation state, i.e., AG(6,pH) = 0, it follows from Eqs. @)-(lo) that the relative free energy and the average protonation asymptotically approach zero in the limit of infinite pH; i.e.,

By adding the electrostatic free energy of the unprotonated state (as defined relative to some appropriate “absolute” reference, e.g., the completely discharged system), it is possible to introduce the pHdependent absolute free energy of a titrating system according to G(pH) = Gel@) + AG(pH) = Ge,(6)- RTln E(pH)

(14)

where we have written G(8) for the free energy of the unprotonated state. Whereas the relative free energy, AG(pH), approaches 0 in the limit of infinite pH irrespective of the system, it follows from Eqs. (12) and (14) that the limit pH + co of the absolute free energy is equal to the free energy of the unprotonated state:

The introduction of G(pH) in Eq. (14) has the advantage over Eq. (9) that it makes it possible to calculate and compare the electrostatic free energies of different conformers of a system (see Section 11,B). The titration curve (Q(pH)) of the system is defined as the pHdependent net charge. It differs only by a constant from the average protonation curve; i.e., the net charge Q(8) of the unprotonated state, (Q) = ( n ) + Q(6). From Eq. (13), it follows that the titration curve approaches Q(8)in the limit pH + 03. In the following, the term “titration curve” will be used for both the average protonation (n) and the average charge (Q) as functions of pH; it is implied that the latter is obtained from the former by adding Q(6).Correspondingly, the average protonation of a site, (si(pH)),is termed the site titration curve. Given the titration curve of site i, the effective pK, is defined as the pH where (sJ = 0.5. The derivative of the free energy with respect to pH is proportional to the average number of protons bound to the titrating system (Wyman, 1964; Schellman, 1975); i.e., from Eqs. (7) to (14), we have

ELECTROSTATIC FREE ENERGY IN SOLUTION

d G(pH)

--

dPH

c

(In 1 0 ) R T y n(?)exp [-PAG(S,pH)] s(pH) i = (In 10)RT(n(pH)) -

7

(16)

This relation and Eq. (15) for the infinite pH limit of the free energy make possible the calculation of the absolute, pHdependent free energy by integration of the titration curve of the system:

= G,,(O) - (In 1O)RTIm PH (n(pH')) dpH'

(17)

In the limit pH + m, the average protonation of the system as given in Eq. (10) approaches zero exponentially [see Eqs. (7) and (lo)]. Consequently, the integral in Eq. (17) converges and yields a finite free energy for finite pH. If the number of titrating sites of a system is sufficiently small (about N < 30), it is practical to derive the free energy directly from the generating function [Eq. (14)]. With the use of Eq. (17) and of an accurate method for calculating titration curves, e.g., the Monte Carlo (MC) titration program (see below), it is possible to calculate the absolute free energy of a system with several hundred titrating sites despite the intractability of the generating function approach.

B. ElectrostaticFree Energy Difference between Confornations Given two conformers A and B of a titrating system, e.g., the bound and unbound states of a protein-ligand complex or the native and denatured states of a protein, the pHdependent free energy difference is

The direct approach to pHdependent free energy differences, where the free energy of each conformer is derived from the generating function [see Eq. (14)], has been applied to calculate the pH dependence of the binding of guanosine monophosphate to ribonuclease TI (MacKerell et al., 1995). For systems with many (>30) titrating sites, where it is computationallyimpractical to calculate the electrostatic free energy from the generating function, we use Eq. (17) and obtain for the free energy difference:

8

MICHAEL SCHAEFER ET AL

where GA(0) and G:,((0) are the electrostatic free energies of the unprotonated system in conformation A and B, and where and (n)Bare the titration curves of A and B, respectively. Equation (20) in differential form was first shown to be applicable to the pH stability of lysozyme by Tanford and Roxby (1972),where it was demonstrated that the derivative of log KDwith respect to pH (KD is the equilibrium constant for the denaturation) correlates well with the difference between the titration curves of the native and the unfolded protein. According to Eq. (19), the absolute free energy difference is given by the difference between the electrostatic energies of the unprotonated states, minus (In 1O)RT times the area between the titration curves of the two conformers in the pH range (pH, m) (see Fig. 1). Consequently, a stabilization of conformation A relative to conformation B with respect to the limiting value AGY(G) results for a pH range where (n)* is larger than (n)B.The quantity AAG,(pH) is the relative free energy difference between the two conformers. The relative stability as defined in Eq. (20) approaches 0 in the limit pH + 03, irrespective of the system and conformations that are studied. The advantage of the absolute, as compared with the relative, electrostatic free energy difference is that it makes it possible to analyze electrostatic free energy charges at any given pH, e.g., due to conformational change (including binding) or due to mutations in the sequence of a protein.

C. The Independent Sites Model If one makes the simplifylngassumption that all sites of a system titrate as simple acids, i.e., according to the Henderson-Hasselbach equation (Fersht, 1985), it is possible to calculate the generating function, the free energy, and the titration curve of the system from simple analytic formulas based on knowledge of the pK,’s alone (MacKerell et al., 1995). The assumption of simple titration behavior for the sites is equivalent to the requirement that the sites titrate independently, such that the electrostatic free energy of a protonation state relative to the fully unprotonated state is the sum of individual site contributions; i.e.,

ELECTROSTATIC FREE ENERGY IN SOLUTION

conformer B

9

conformer A

I I

"reference medium" Ei - - - - - - E s , ions

"solution"

AG,B,,,(~ ref) - - - - - - - - - -

AG,A,,,(P') - - - _ -

!

AG e( PH)

FIG. 1. Thermodynamic cycle describing the contributions to the absolute, pHdependent electrostatic free energy difference AG,(pH) between two conformations, A and B, of a titrating system. The unprotonated state is used as the reference state in the upper half of the cycle, Ire'=0. For the calculation of Coulomb energies (A,!$&, = E$,,,, - Et,,,,,) and solvation free energies (A&"), the "reference medium" (on top of the horizontal dashed line) is assigned zero ionic strength and the dielectric constant of the protein interior, ei. The pHdependent second term of the electrostatic free energy difference in Eq. (19) is concerned with the lower half of the cycle, while the pHindependent first term is derived from the upper half of the cycle.

10

MICHAEL SCHAEFER ET AL.

N

AGIs(S,pH)=

c AGiS(si,pH)

1=

1

The model is thus referred to as the “independent sites” (IS) model. From the Henderson-Hasselbach equation (Fersht, 1985), it follows that the pHdependent free energy difference between the protonated and unprotonated state of a simple acid with given pK, is AGHH(pH)= (In 10)RT(pH - pK,)

(23)

If one considers only two protonation states for each site, unprotonated (si = 0) and protonated (si = l ) , Eq. (23) can be generalized to yield the free energy contribution from site i in charge state si (protonated or unprotonated) , relative to the unprotonated states: AGfS(si,pH)= (In 10)RTsi(pH- P K , ~ )

(24)

The right-hand side of Eq. (24) is multiplied by si such that AG’iS (0,pH) = 0. The fact that the electrostatic free energy of the protonation state S in Eq. (22) is a sum of Nindependent terms permits the factorization of the generating function (Wyman and Gill, 1990) as defined in Eq. (8):

n exp [ - p AGiS(si,pH)] N

= n{l i= I

+ exp [-p

AGIS(l,pH)]}

(25)

where we have made use of the fact that in the two-state model there are only two protonation states for each site with relative free energies of 0 and AG$( 1,pH), respectively. From the generating function, Eq. (25), it follows immediately that the electrostatic free energy relative to that of the unprotonated state and the titration curve of the system are the sums of the independent contributions from the sites: N

AG,,(pH) = - R T xi= 1 In (1 + exp[-P AGtS(l,pH)]} (n(pH))ls=

exp [-/3 AGIS(l,pH)l 1 exp [-p AGjS(l,pH)]

2+

(26) (27)

ELECTROSTATIC FREE ENERGY IN SOLUTION

11

where we made use of Eqs. (9) and (10) defining the pHdependent relative free energy and the titration curve. In the literature, Eqs. (25) to (27) have been used to describe a simplified model of the unfolded state of proteins, termed the “null” or “zero interaction” model (Yang and Honig, 1993; Antosiewicz et al., 1994; Schaefer et aZ., 1997), where the pK,’s of all sites are assumed to be equal to the standard pK,’s of the amino acids. The independent sites model is also of interest for a comparison between the actual site titration curves of a protein, Eq. (1 1),and the site titration curves (terms i = 1 to N) according to Eq. (27), where the effective pK,’s from the former titration calculation are used in the latter. This makes it possible to quantify the departure of the titration curves of the individual sites from the ideal titration curve of a simple acid. Finally, the independent sites model is useful for an interpretation of free energy differences between conformations on the basis of pK, shifts alone. In accordance with the definition of the absolute pHdependent electrostatic free energy, we add the free energy of the unprotonated state on both sides of Eq. (26) and obtain N

GIs(pH) =

GeI(6)- R Ti=z1 ln{l

+ exp [-PAG$(l,pH)]}

(28)

We then rewrite the absolute electrostatic free energy as a function of the proton concentration, [H+],and the acid dissociation constants of all sites, Ka,,, N

GIS(pH) = Ge1(8) - (In 1O)RTX log I=

I

(29)

The free energy difference between two conformations A and B [see respectively, Eq. (IS)] with the acid dissociation constants KL,iand is then (Szabo and Karplus, 1972; Ascenzi et al., 1990; Casale et al., 1995)

where APK,~= P K : , ~- P K , , and ~ AGy(6) = G$(6) - GE,(G). Equation (30) has been employed in a study by Ascenzi et al. (1990) on the binding

12

MICHAEL SCHAEFER ET AL.

of the bovine pancreatic trypsin inhibitor to human and bovine factor Xa, and by MacKerell et al. (1995) on the binding of guanosine monophosphate to ribonuclease, T1. For these cases the two conformations correspond to free and bound inhibitor/substrate. In the limit pH + -03, the only protonation state that is enesetically accessible is the fully protonated state, i.e., AGIs(-00) = AGy( 1) [compare Eq. (15) for the limit pH + m of the electrostatic free energy]. Furthermore, the logarithmic term in Eq. (30) vanishes in the limit of infinite proton concentration, such that the remainder of the right-hand side is equal to the electrostatic free energy difference between the fully protonated conformers. Equation (30) can thus be rewritten in the form AGE(pH) = AGy((1) - (In 1O)RTZ log K:, + [H+I i=l K , , + [H’] where S = i is the fully protonated charge state. From Eqs. (30) and (31), it follows that in the independent sites model, the difference between AGy(fi) and A G y ( i ) is proportional to the sum of the pK, shifts of all titratable sites: N

(AGy(6) - AGy(i))Is= (In 10)RTx ApK,,, i= 1

(32)

This relation between the fully protonated and the fully unprotonated states of a system with independent sites has been given in Wyman and Gill (1990) for a single conformer (i.e., without the A’s) and referred to as the free energy of converting the unligated macromolecule to the fully liganded macromolecule. The dissociation constant of a molecular complex, K,, is related to the free energy of binding according to (In 10)RT pKI(pH) = -A GAB(pH). Equation (30) can thus be rewritten in a form that yields the pH dependence of pK, as a function of the pK,’s of ionizable groups in the complex and in the dissociated molecules. The present treatment of pHdependent electrostatic binding free energies provides, therefore, a basis for the analysis of pHdependent ligand-binding studies. In particular, the IS model, although simplified, avoids the shortcomings of some models, in which it is assumed that complex formation occurs for only a single charge state of the protein and the inhibitor, thus neglecting the contributions from the multiple alternate protonation states, as pointed out by Knowles (19’76) and by Brocklehurst (1994).

ELECTROSTATIC FREE ENERGY IN SOLUTION

13

D. Standard, Intrinsic, and Effective pK, Three different pK,’s of a titrating site are distinguished: the standard, the intrinsic, and the effective pK,. The standard pK, of an amino acid side chain is the experimental pK, of the isolated amino acid with Nterminal and Cterminal blocking groups (Fersht, 1985; Nozaki and Tanford, 1967; Tanokura, 1983; Lehninger et aL, 1993). Analogously, the standard pK,’s of the N-terminal ammonium group and the Cterminal carboxyl group are the experimental pK,’s of these groups in an otherwise electrically neutral amino acid (e.g., alanine) with respectively Gterminal or N-terminal blocking group. The effective pK, is the pK, that is observed for the site as part of the entire system (i.e., the protein). The effective pK, of a titrating site may differ from the standard pK, by several pK units. In Fersht (1985), highly perturbed pK,’s in enzymes are reported with pK, shifts of up to 5 pH units; this corresponds to a free energy shift of 6.9 kcal/mol (using 300 K for the conversion). The largest measured pK shift in the proteins lysozyme (Bashford and Karplus, 1990; Kuramitsu and Hamaguchi, 1980; Bartik et al., 1994)) ribonuclease A (Rco et aL, 1991), and myoglobin (Bashford et aL, 1993) is about 2.5 pK units. Finally, the intrinsic pK, is the hypothetical pK, of a site in the system assuming that all other titrating sites are fixed in their electrically neutral state. The standard and the intrinsic pK, are denoted by pFFd and pKF, while the effective pK, is denoted by pK, in the following. For calculating the pH-dependent properties of a system, a choice of the titrating sites which are included in the analysis has to be made. In this choice, it is possible to exclude atom groups whose standard pK,’s are far from the pH range of interest; e.g., the Ser hydroxyl group with pFFd = 13.6 in considerations of protein stability around pH = 7. Each titrating site is composed of a set of atoms whose partial charges depend on the protonation state of the site, e.g., all side-chain atoms in the case of aspartate (see Table I). The atoms of the system that are not part of any site are termed the “background atoms” or “background charges” (Bashford and Karplus, 1990). By definition, the background atoms are assumed to have pH-independent partial charges, even though the theory that is presented in this work makes use of infinite pH limits; e.g., if peptide N - H groups are excluded from the set of titrating sites, it is assumed that they are not ionized in the limit pH + w . This does not cause any difficulties, and it is understood that the pHdependent properties of a system are defined relative to a chosen set of titrating sites. By definition, the pKk’ of site i in a protein differs from the PK;”’~of the site in the isolated amino acid by a pK shift that is due to the electrostatic interaction with the protein environment (protein backbone; nontitrating side chains; titrating side chains in their uncharged

Chargeb

Chargeb Site A%

pKmd

Atom

s=o

s=

12.48

CD HD 1 HD2

NH1 HHll HH12 NH2 HH21 HH22

0.20 0.09 0.09 -0.70 0.44 0.44 -0.80 0.26 0.26 -0.80 0.26 0.26

0.20 0.09 0.09 -0.70 0.44 0.64 -0.80 0.46 0.46 -0.80 0.46 0.46

CB HBl HB2 CG OD 1 OD2

-0.28 0.09 0.09 0.62 -0.76 -0.76

-0.21 0.09 0.09 0.75 -0.36 -0.36

+

NE

Ip

HE

cz

4.00

Site

1

pP?d

His (contil.)

LYS

N-Ter

10.79

7.50

Atom

s=o

s = l

HDl CD2 HD2 CE1 HE1 NE2 HE2

0.16 0.09 0.09 0.25 0.13 -0.53 0.16

0.44 0.19 0.13 0.32 0.18 -0.51 0.44

CE HE1 HE2 NZ HZ 1 HZ2 HZ3

0.18 0.05 0.05 -0.96 0.34 0.34 0.00

0.21 0.05 -0.30 0.33 0.33 0.33

N HTl HT2 HT3

-0.96 0.34 0.34 0.00

-0.30 0.33 0.33 0.33

0.05

GTer

3.80

C OT1 OT2

0.34 -0.67 -0.67

0.76 -0.38 -0.38

cys*

10.46

CB HB1 HB2 SG HGl

-0.25 0.05 0.05 -0.85 0.00

-0.11 0.09 0.09 -0.23 0.16

Glu

4.40

CG HGl HG2 CD OEl OE2

-0.28 0.09 0.09 0.62 -0.76 -0.76

-0.21 0.09 0.09 0.75 -0.36 -0.36

CB HBl HB2 CG NDl

-0.08 0.09

-0.05 0.09

0.09 0.08 -0.53

0.09

His‘

6.42

0.19

CA HA

0.19 0.09

0.21 0.10

Serd

13.60

CB HB 1 HB2 OG HGl

-0.14 0.05 0.05 -0.96 0.00

0.05 0.09 0.09 -0.66 0.43

Thr’

13.60

CB HB OG1 HGl CG2 HG21 HG22 HG23

-0.05 0.09 -0.96 0.00 -0.35 0.09 0.09 0.09

0.14 0.09 -0.66 0.43

cz

-0.04 -0.96 0.00

10.13

OH HH

-0.27 0.09 0.09 0.09 0.11 -0.54 0.43

-0.51

“Atomsand charges compatible with the all-hydrogen parameter set of CHARMM; standard pK:s taken from Nozaki and Tanford (1967), Fersht (1985), Tanokura (1983), and Lehninger et ul. (1993). Partial charges in the unprotonated ( 5 = 0) and protonated state ( 5 = 1). ‘Protonated His: average of Hsd and Hse in the CHARMM parameter set; “macroscopic” standard pK. of His as defined in Tanokura (1983). Site excluded from calculations reported in Section II1,B.

16

MICHAEL SCHAEFER ET A L

state) and the change in the interaction with the aqueous environment, i.e., the desolvation effect upon transfer of the site from the isolated amino acid to the protein (see Fig. 2). For calculating the change in the electrostatic free energy of site i on the transfer, we use the isolated residue of site i as a model of the standard peptide. In the “model compound” for site i, the pK, is assumed to be equal to pKSCd. This permits the use of empirical data for the pPPd as a reference for the free energy change that is associated with protonating the titratable sites. In the following, we write A, for the model compound for site i. According to the thermodynamic cycle in Fig. 2, the pK shift PK’?, - p KsEdof site i is given by

1 pK’,lF- pKSCd = ;(AG - AGO) 1

=C

(G,l(S,

= 1, s;&)

-

where c = -(In 10)RT. In Eq. (33), we have wri$en s; for the neutral (i.e., uncharged) state of site j, and Gel(?) and G,,’ (si) are the electrostatic free energies of the protein in protonation state s and the model compound for site i in protonation state s,, respectively. E. Electrostatic Free Energy of a Protonation State

To derive a formula for the pHdependent electrostatic free energy of a protonation state, we first consider the case where site i in the

FIG.2. Electrostatic free energy for protonating site i as part of the protein ( P ) with all other sitesj # i in their electrically neutral state s;, and as part of the model compound A,. The quantities AGI or AGO are the electrostatic free energy difference between the protein with site i protonated or unprotonated and the protonated or unprotonated model compound A,. From the cycle, it follows that c(pK’:,T - pKzd) = AGI - AGO, where c = -(In 10)RT.

17

ELECTROSTATIC FREE ENERGY IN SOLUTION

protein is allowed to titrate and all other sites are fixed in their electrically neutral state. Since site i is the only titrating site, Eq. (24) is applicable with PK,,~replaced by the intrinsic pK, of the site, pK:Y. Using Eq. (33), we can thus write the free energy difference between site iin protonation state s, (protonated or unprotonated) and the unprotonated state of the site (s, = 0) as

where all other sites are assumed to be electrically neutral, sjYi= sf. The first term on the right-hand side of Eq. (34) is multiplied by s, to ensure that AG?(si,pH) vanishes if si = 0. Equation (34) can be generalized to be applicable to the case where + n (S) H+ all sites are allowed to titrate. In the ligation process 4 +. P(?) [see Eq. (2)],all sites change their protonation state from 0 (unprotonated) to si (protonated or unprotonated) . To evaluate the corresponding electrostatic free energy difference, the second term in parentheses in Eq. (34) is substituted by Gel@) - Gel(@,whereas the first and the third term contribute for each site independently. The pHdependent free energy of the protonation state 3, relative to the fully unprotonated state of the system, is thus

(n)

In Schaefer et al. (1997), Eq. ( 3 5 ) has been shown to be consistent with other, somewhat more complicated, expressions for AG(Z,pH) in the literature (Yang et al., 1993; Antosiewicz et al., 1994).

E

Electrostatic Free Energy Calculation To calculate the electrojptic free energy as a function of the protonation state, Gel (?) and Gel[si),we make use of the continuum model in which the solute and the aqueous solvent are described as polarizable media with dielectric constants ei and E, , respectively, and where the

18

MlCHAEL SCHAEFER ET AL.

presence of salt is accounted for by a continuous ion distribution in the solvent (Davis and McCammon, 1990; Sharp and Honig, 1990). The program UHBD (Davis et aL, 1991) is employed to solve numerically the linearized Poisson-Boltzmann equation by means of the finitedifference algorithm. Since the electrostatic potential depends linearly on the solute charges, the electrostatic free energy of the solute and the model compounds can be written as the sum of contributions from the charge groups (background atoms and the titratable sites) interacting with their own reaction field, and from the interaction between charge groups. The sites i and j consist of the atoms with indices p and v whose partial charges q;1 and respectively depend on the charge state of the sites (see Table I). Given the electrostatic potential of site i in charge state s,, @?, the charge statedependent electrostatic interaction between sites i and j is

Y

where the sum is over all atoms of site j, and where x, is the position of atom v. Equation (36) is symmetric under the exchange of the indices i and j, i.e., Gi,(si,sj)= qi(sj,si). By assigning the site index 0 and the constant charge state = 0 to the background atoms in the protein and in the model compounds, and using the definition of the electrostatic interaction between charge groups in Eq. (36), we can write the electrostatic free energy as

The sum in Eq. (38) is over all pairs of the indices 0 and i. This leads to a total of four terms, because the model compound for site i is composed of only two atom groups; i.e., the site itself, and the background atoms that constitute the remainder oLthe residue. In Eqs. (37) and (38), the terms (1/2) Gii(s,si)and (1/2) GiiI(si,si)in the summations are the self-energies [described as nonbonded Coulomb plus “Born” (Bashford and Karplus, 1990), or nonbonded Coulomb plus “chargesolvent” (Luty et d., 1992) energies] of site i in charge state si in the protein and in the model compound, respectively. The factor (1/2) and

ELECTROSTATIC FREE ENERGY IN SOLUTION

19

the double notation of the charge state siin the selfenergy are required for consistency with the definition of the energy of interaction between sites [Eq. (36)]. Using a finitedifference Poisson-Boltzmann program, e.g., UHBD, it is straightforward to calculate the potential of a group of charges in the presence of the solvent with salt and an otherwise uncharged solute. Given the potential of site i, the interaction with all other sites and the self-energy of the site are available at little computational expense, according to Eq. (36). It follows that for the calculation the electrostatic free energy terms Gq(si,sj)in.Eqs. (37) and (38), it is sufficient to perform 2N electrostatic potential calculations for the sites in the protein (two charge states each), 1 for the background charges of the protein, and 3N for the model compounds (background atoms and the site in two charge states for every Ati). With each electrostatic potential calculation typically requiring 12 min of CPU time on an HP-735/9000 workstation for an average-sized protein, and 10 s for a model compound, the electrostatic free energy calculations can be done within a few hours of central processing unit (CPU) time even for systems with several hundreds of sites. Technical aspects of the finitedifference calculations,e.g., appropriate parameters for the setup of the finitedifference grid and for the definition of the solute volume, are described in detail in the literature (Yang et al,, 1993; Antosiewicz et al., 1994; Schaefer et al., 1997).

G. Monte Carlo Titration For systems with more than about 30 titratable sites, it is computationally impractical to evaluate the free energy from the generating function or the ensemble averages in Eqs. (10)-(11), because the total number of charge states ( 2 N )increases exponentially with the number of sites. To avoid the requirement of sampling all charge states at any given pH, it is possible either to restrict the calculation to those sites whose pKsd: or pK:" is within a given interval from the pH of interest or to use the Monte Carlo (MC) importance sampling method (Metropolis et al., 1953).Whereas the former approach, the "reduced site" approximation (Bashford and Karplus, 1990), is limited to cases where not more than about 30 sites fall within the pH interval for the selection (i.e., the number of sites that can be treated by the enumeration of their charge states), the Monte Carlo approach has been successfully applied to systems with several hundred sites while providing well-defined statistical error bounds for the calculated site titration curves (Beroza et al., 1991; Beroza and Fredkin, 1996).Other titration methods have been proposed

20

MICHAEL SCHAEFER ET AL.

in recent years, e.g., a cluster method where the sites are subdivided into groups such that the interactions between sites in different groups are weak as compared with the interactions in the groups (Gilson, 1993), and a combination (Sham et al., 1997) of a cluster method with the mean field approximation introduced by Tanford and Roxby (1972). However, definitive error bounds for these methods have not been reported in the literature. Because of its applicability to large systems and the availability of statistical error bounds, a Monte Carlo program by Beroza et al. (1991) is employed for the calculations that are reported below in Section 111. It requires the standard pK,’s of the sites (see Table I ) , the electrostatic self- and interaction energies of the sites, background atoms, and the model compounds for all possible combinations of their charge states [see Eqs. (37) and (38)], and the absolute temperature as input. For details regarding the Monte Carlo program and other input parameters, e.g., the number of charge states that are sampled at each pH, see Beroza et al. (1991) and Schaefer et al. (1997).For the calculation of the average protonation of 100 sites at 150 pH values, i.e., the calculation of the site titration curves, the Monte Carlo program requires approximately 30 min of CPU time on an HP-735/9000 workstation. Since the computation time for the Monte Carlo program depends quadratically on the number of sites (Schaefer et al., 1997), it can be applied to systems with several hundred sites without requiring more time than the electrostatic free energy calculation with the finitedifference Poisson-Boltzmann method for the same system (see Section 11,F). 111. APPLICATIONS In the following subsections, applications of the theory of linked functions to the calculation of lysozyme pK,’s, the pH stability of lysozyme, and the pH stability of the foot-and-mouth disease virus capsid are reported. The calculation of lysozyme pK,’s is used to determine a value for the protein dielectric constant that leads to best agreement with experimental data, given that the present methodology does not explicitly allow for conformational relaxation of the protein due to changes in the ionization state. In the application to lysozyme pH stability, the aim is to illustrate the difference between the relative and absolute electrostatic free energy of folding as a function of pH and to elucidate the origin of the conformation dependence of the absolute electrostatic free energy. In the application to foot-and-mouth disease virus, the acid lability of the virus capsid is analyzed and the contributions from specific sites is identified. It is demonstrated that interactions involving a helix

ELECTROSTATIC FREE ENERGY IN SOLUTION

21

dipole are not responsible for the acid lability. Furthermore, the study of the virus capsid stability demonstrates the applicability of the methodology to systems with many (>loo) sites. A. Protein Dielectric Constant While the dielectric constant and ionic strength of the aqueous solvent are uniquely defined by the experimental conditions (i.e., by the temperature, pressure, and the solute concentrations), there is uncertainty about the dielectric constant (or constants) to be assigned to the interior of solutes in continuum electrostatic calculations (Gilson and Honig, 1986; Warshel, 1987). In the present approach the solutes are assumed to have a fixed structure for each well-defined conformer (MacKerell et al., 1995), so that the effects from atomic polarization and from conformational flexibility must be accounted for implicitly by the dielectric constant (or constants) that is assigned to the protein interior. Although the protein interior is known to be inhomogeneous and it would be useful (and would be possible) to vary the dielectric constant used for different parts of the solute (Statesand Karplus, 1987; Demchuk and Wade, 1996), we use a single dielectric constant in the present calculations. The conformational flexibility of proteins and, as a consequence, their dielectric response and orientational polarizability are expected to be important for changes in the protonation state of the system, i.e., for the stabilization of ionized sites in the interior of proteins (Warshel et al., 1984,1986).The effect from the reorientation of protein permanent dipoles is analogous to the difference between the equilibrium (-78) and infinite frequency (-2) dielectric constant of water. In principle, polarization effects could be accounted for by using different ensembles of structures for each charge state S. Here, we use one fixed protein structure for all charge states, standard partial charges for the neutral and the ionized state of all sites from the all-hydrogen parameter set of CWM (MacKerell et aZ., 1992; MacKerell et al., 1998), so that polarization effects must be accounted for by the protein dielectric constant. In the calculation of the solvation free energy of small molecules, dielectric constants in the range from ei = 1 to 2 have been used, and good agreement with experiments and with the results from microscopic free energy perturbation methods has been obtained (Jean-Charles et al., 1991; Sitkoff et al., 1994b). In part, the success of these approaches may be attributed to the fact that the small compounds that were studied are rigid or have very limited conformational flexibility. Furthermore, the results of solvation free energy calculations for small molecules with

22

MICHAEL SCHAEFER ET AL.

the continuum model are nearly independent of the dielectric constant that is assigned to the solute interior because of the high solvent accessibility of all atoms. In studies on electrostatic solvation effects in proteins, an internal dielectric constant of ei = 2 to 4 has frequently been used, where ei = 2 is attributed to the electronic polarizability of protein atoms, while it is assumed that E~ = 4 also accounts for fluctuations of the permanent dipoles (Gilson and Honig, 1986). However, as pointed out above, conformational changes, including side-chain reorientations (You and Bashford, 1995), are expected to play a role in stabilizing ionized sites (Russell and Warshel, 1985; Warshel et al., 1986). In the absence of approaches which account for conformational change explicitly, it is thus necessary to assign an effective dielectric constant to the protein interior that exceeds the value of 2-4 reflecting the atomic polarizability and small structural fluctuations. The requirement that the protein interior be described as a polar, rather than an apolar, medium in the context of pK, calculations for a single (fixed) structure was pointed out some years ago by Warshel and co-workers (1984; Warshel and Levitt, 1976). However, in that work and other papers (Warshel, 1978, 1987; Sham et al., 1997), it was concluded without justification, it seems to us, that the continuum electrostatic model is inconsistent altogether. The main criticism was based on the original Tanford-Kirkwood model (Tanford and Kirkwood, 1957) in which the self-energy contribution to pK, shifts was theoretically addressed but not included in the treatment because all titratable sites were assumed to be at a constant distance ( 1 from the surface of the spherical protein model to obtain reasonable agreement with experiment (Tanford, 1957). Furthermore, the Tanford-Kirkwood model did not include the interaction between ionized sites and protein permanent dipoles because structural information at the atomic level was not available at the time. This is of course not true of the continuum electrostatic methods in current use (Bashford and Karplus, 1990; Yang et al., 1993; Antosiewicz et al., 1994) and employed in the present study. Other than the interaction between titratable sites, they include the contributions from the self-energy (“Born term” or “charge-solvent energy”) and the interaction between sites and the permanent charges of the protein atoms (interaction with the “background atoms”) (Bashford and Karplus, 1990; Davis et al., 1991). In recent studies employing the continuum model for calculating the self- and interaction energies of titratable sites, the use of a high dielectric constant in the range from 10 to 20 for the protein has been suggested, based on comparisons between calculated and experimental pK,’s (Antosiewicz et al., 1994; Demchuk and Wade, 1996). The assignment of a

A)

ELECTROSTATIC FREE ENERGY IN SOLUTION

23

high dielectric constant to the protein has been interpreted as a simple way of accounting implicitly for the conformational flexibility of proteins in continuum electrostatic calculations that are based on the use of a single conformer. This is no different, in principle, from using a dielectric constant of 78 for the aqueous medium to account for the orientational polarizability of the water dipoles. Because of its simplicity and success, this approach is followed in the calculations reported here. To determine the optimal value for the protein dielectric constant, a series of titration and pK, calculations has been performed for the protein hen egg-white lysozyme, where the protein dielectric constant was varied in the range from 1 to 30. In all continuum electrostatic calculationswith the UHBD program (see Section II,F), the dielectric constant of bulk water was set equal to 80 and the ionic strength of the solution was set to 0.145 M, a value close to that found under physiological conditions. The temperature was set to 300 K. The triclinic crystal structure [protein data bank entry 21zt (Ramanadham et al., 198l)l and the tetragonal crystal structure [entry lhel (Malcolm et aL, 1990)l of lysozyme were employed. To test the dependence of the results on small structural changes, three modified structures were generated for each crystal structure with 100, 200, and 300 steps of in vacuominimization using the program CHARMM (Brookset al., 1983). The minimized structures are labeled 2lzt-m1, m2, m3, and lhel-ml, m2, m3, respectively (for details, see Schaefer et al., 1997). Figure 3 shows the titration curves of all ionizable groups in lysozyme for a protein dielectric constant of ei= 20. By definition, the effective pK,’s of the sites are given by the pH where the site titration curve equals 0.5 (see Section 11,D). At each value of the protein dielectric constant, the average absolute deviation of the lysozyme pK,’s from experiment (Kuramitsu and Hamaguchi, 1980; Bartik et aL, 1994) was calculated. The result of the calculations is shown in Fig. 4 for the tetragonal and triclinic crystal structures and the minimized structures. The average error decreases significantly when the protein dielectric constant is increased from 1 to 20. For ei > 20, there is no further significant change in the average error. In the subsequent calculations, we therefore assign an effective dielectric constant of ei = 20 to the protein interior. The fact that the average absolute error in the lysozyme pK, calculations does not change significantlyfor ei > 20 could be taken as a reason to use ei = 80, a value which would greatly simplify the calculation of electrostatic free energies. If one omits the fact that ions are excluded from the solute volume, a protein dielectric constant of ei = 80 permits the use of the Debye-Hiickel equation for the interaction between

24

MICHAEL SCHAEFER ET AL.

PH FIG.3. pHdependent protonation of the 32 titratable sites in lysozyme (21zt) as calculated with the MC titration program. Protein dielectric constant E, = 20. The two protonation curves that depart markedly from curves of independently titrating sites (pH range 12-16) are for Tyr 53 and A r g 68, with effective pK.’s of 13.0 and 14.8, respectively.

charges, while the calculation of self-energies becomes obsolete since the protein and the solvent are equally polarizable. However, the test set of lysozyme pK,values used here includes predominantly sites that are located at the surface of the protein, where the degree of conformational flexibility is expected to be more significant than it is for sites that are less exposed to solvent, e.g., in the active sites of some enzymes (Sham et al., 1997). It follows that the dielectric constant of ei = 20 derived from the lysozyme pK,’s is likely to be an upper bound to the effective dielectric constant of the protein in the context of titration calculations with a single protein conformer. Thus, we use ei = 20 rather than a larger effective dielectric constant, despite the fact that ei > 20 gives similar results in the case of lysozyme. The finding that protein relaxation due to changes in the ionization state corresponds to an effective dielectric constant of ei = 20 for the protein is consistent with the observation that the Tanford-Kirkwood model of protein titration (Tanford and Kirkwood, 1957) gives best agreement with experiment when the charges are placed at the surface of the protein sphere (with ei = 2 to 4),where the solvent screening of charge-charge interactions is significant even at short distances. Recent theoretical studies on protein pK,’s, which are predominantly using finitedifference Poisson-Boltzmann methods for calculating electrostatic free energies, thus provide evidence that computationally much

ELECTROSTATIC FREE ENERGY IN SOLUTION

25

protein dielectric constant FIG.4. (a) Average e m r of calculated pK.'s relative to experimental data for tridinic hen eggwhite Ipozyme as a function of the protein dielectric constant used in the f i n i M e r e n c e Poisson-Boltzmann (FDPB) calculations. From bottom to top: crystal structure 2lzt and minimized structures 2lzt-ml, 2lzt-m2, and 2lzt-m3. The horizontal line represents the e m r of the null model, i.e., the average absolute difference between the standard pK.'s and the experimental pKo's. (b) Same as (a) for tetragonal hen eggwhite lysozyme. From bottom to top: crystal structure lhel and minimized structures lhel-ml, lhel-m2, and lhel-m3.

simpler continuum models can give results with comparable accuracy, in particular the modified Tanford-Kirkwood model of Gurd and coworkers (Matthew et al., 1985) and of Imoto (1983) and the distancedependent dielectric approach of Mehler and Eichele (1984). However, the advantage of the numerical methods for calculating continuum electrostatic free energies [i.e., the finite-difference (Warwicker and Watson, 1982) and the finiteelement (Zauhar and Morgan, 1985) methods] is that they address the interaction and the selfenergies of all charges consistently, using a description of the molecular surface at the atomic level (Fersht and Sternberg, 1989).

B. Variation of Stability of Lysozyme with pH There are many experimental studies on the pK,'s (Kuramitsu and Hamaguchi, 1980; Bartik et al., 1994), titration curve (Tanford and

26

MICHAEL SCHAEFER ET AL.

Roxby, 1972; Roxby and Tanford, 1971), and pH-dependent stability of lysozyme (Pfeil and Privalov, 1976), making this protein an excellent test case for the Poisson-Boltzmann method. In fact, lysozyme was one of the first proteins for which a complete titration curve was measured (Roxby and Tanford, 1971). Hen egg-white lysozyme has 11 arginines, 7 aspartic acids, 2 glutamic acids, 1 histidine, 6 lysines, 3 tyrosines, and N- and Gtermini, i.e., a total of 32 titrating sites with the list of sites given in Table I (see Section II,D for the reasons to exclude serine, threonine, and cysteine). To use the method described earlier (see, in particular, Section I1,B) for calculating the pH dependence of the stability of lysozyme, structures for the native and denatured state are required. An X-ray or nuclear magnetic resonance (NMR) structure is a good model for the native protein in solution, although the variation in side-chain conformers in different crystal structures introduces some uncertainty as to which, if any, is the best one to use. However, the uncertainty concerning the native state structure is much less than that in the case of the denatured state, for which insufficient experimental data exist for a structure determination. In fact, the available data suggest that the unfolded state of a protein is characterized by an ensemble of significantly different conformations (Privalov, 1992; Fersht et al., 1994; Fiebig et al., 1996). For simplicity,we use a linear structure as a model of the unfolded state in this study. The choice of the linear model corresponds to the limiting case for the unfolded protein. It is thus an important test case for an examination of the interactions between titrating sites in the unfolded state, which are assumed to be zero in the null model (see below) that has been used previously in protein stability calculations (Antosiewicz et al., 1994; Yang and Honig, 1993). Also, in contrast to random coil structures, which can be generated by various computational techniques for denaturating a protein (Caflisch and Karplus, 1994; Hunenberger et al., 1995), the extended structure is uniquely defined by a set of +/ 9 angles (assuming that all side-chain angles are set to 180") and can easily be generated and reproduced. High accessibility to the solvent is ensured for all side chains so that the maximum effect of denaturation on the stability is likely to be included. As a simple test of the dependence of the results on the choice of 4/ I)values for an extended structure, we use two different models of the unfolded state (see Fig. 5): first, the extended ideal p structure "Beta" with (4, @) = (-140", +135"); and, second, the "Ex72" model with (4, 9) = (-72", +72"). For both models, the choice of the (4,$)angles leads to a backbone conformation that is close to a local minimum of the vacuum energy (Schulz and Schirmer, 1978; Maccallum et al., 1995);

ELECTROSTATIC FREE ENERGY IN SOLUTION

a

b

n

L

27

20 A

100 A

100 A

FIG. 5. Wire graph of lysozyme (heavy atoms). (a) Stereo view of the native state (protein data bank entry 21zt). (b) Extended structure “Beta” after 100 steps of steepest descent minimization (all +/$ angles set to -140”/+135” prior to minimization; Nterminus left). (c) Extended structure “Ex72” after 100 steps of steepest descent minimization (all + / I ) angles initially set to -72“/+72”; N-terminus left).

28

MICHAEL SCHAEFER ET AL.

while the total energy of the Ex72 model is higher than that of the ideal Beta model, the Coulomb energy (dielectric constant of 1, no cutoff) of Ex72 is lower than that of Beta. To generate the extended structures, all side-chain dihedral angles were initially set to 180". The extended chains were then minimized using 100 steps of steepest descent minimization, to reduce confonnational strain and remove bad contacts in the initial conformation (for details, see Schaefer et al., 1997).The structures obtained after minimization are referred to as Beta-ml and Ex72ml, respectively. In the null model of the unfolded state, it is assumed that there are no interactions between the ionizable groups and that the sites titrate with their standard pK,'s, i.e., the null model corresponds to the trivial model introduced in Section II,C with PK,,~= PK$~.The pHdependent electrostatic free energy and the titration curve for the null model can thus be calculated using the analytical expressions in Eqs. (28) and (27). Since the electrostatic free energy of the fully unprotonated state is undefined in the null model, the free energy difference AGF(G) is set to 0 in Eq. (19), such that only the relative pH stability of proteins, Eq. (20), can be determined in this case. The null model has also been used as a reference in pK, calculations for native protein structures, where the average error of the computational approach is compared with the average difference between the experimental pK,'s and the standard pK,'s (Antosiewicz et ad,, 1994); see Fig. 4. Structures to represent the native state of hen egg-white lysozyme were taken from the protein data bank (Bernstein et aL, 1977). As for the test pK, calculations,both the triclinic crystal structure [entry 21zt (Ramanadham et al., 198l)l and the tetragonal crystal structure [entry lhel (Malcolm et al., 1990)] were used to obtain a measure of the effect of different native configurations. It has been shown (Bashford and Karplus, 1990) that the two structures give significantly different pK, values for some sites. Hydrogen positions were calculated using the HBUILD command (Briinger and Karplus, 1988) within CHARMM (Brooks et al., 1983), and van der Waals radii (RJ2 of the Lennard-Jones potential) were taken from the all-hydrogenparameter set param22 of CHARMM (MacKerell et al., 1992; MacKerell et al., 1998). As in the pK, calculations, the ionic strength was set equal to 0.145 M; the protein and solvent dielectric constants were assigned 20 and 80, respectively (see Section III,A), and the temperature was T = 300 K. The stability measurements (Pfeil and Privalov, 1976) were performed in 0.1 MNaCl at 298 K, and the titration curve measurements (Tanford and Roxby, 1972) were made at 298 Kwith a 0.1 Mconcentration of KCl for the native lysozyme and with an additional 6 Mconcentra-

ELECTROSTATIC FREE ENERGY IN SOLUTION

29

tion of guanidine hydrochloride as a denaturing agent for the unfolded state.

1. Titration Curve Because of the large number (32) of titrating groups, the free energy and pH stability of lysozyme was calculated using the titration curve integration method [Eq. (19)]. To this end, we determined the titration curves for the crystal structures 21zt and lhel, and for the unfolded protein models null, Beta, and Ex72. Figures 6 and 7 show, respectively, the experimental and calculated titration curves for the folded and unfolded protein. From Fig. 7, there are only minor differences between the titration curves of the two crystal structures: the maximum difference is lA(Q>lmax= 0.72 at pH = 2.2. The maximum differences between the titration curves of the unfolded lysozyme models are also small, IA(Q>lmax= 0.32 at pH = 3.8 between null and Beta-ml, and lA(@lmax = 0.80 at pH = 4.0 between null and Ex72-ml (see Fig. 7b). This is to be compared with the maximum difference between the calculated titration curves of the crystal structure 21zt and the null model; the maximum is lA(Q>lmax= 5.02 at pH = 3.4 (see Fig. 7a). The maximum difference between the experimental titration curves of the native and unfolded lysozyme is IA(Q)lmax = 3.45 at pH = 3.0 (see Fig. 6). Thus, the results from the two crystal structures, on the one hand, and between the three 20 16 12

8 4

PH FIG.6. Experimental titration curves of native (0,solution 0.1 M Kcl) and denatured lysozyme (+, solution 6 M guanidine hydrochloride); data taken from Tanford and Roxby (1972).

30

MICHAEL SCHAEFER ET AL.

0

2

4

6

8 PH

10

12

14

16

0

2

4

6

8

10

12

14

16

PH

FIG.7. Calculated titration curve of lysozyme. (a) Crystal structures 21zt (-) and lhel (---); for comparison, the titration curve according to the null model is also shown (--). (b) Models of the unfolded protein, null (-), Beta-ml (---), and Ex72-ml (-.-.-),

models of the unfolded lysozyme, on the other, are much more similar to each other with respect to the calculated titration curves than the titration curves of the native and unfolded protein. It is interesting to note that in Figs. 6 and 7a, the largest difference occurs in the same pH region (between pH 2.5 and 4). This region involves the carboxyl groups, which have the largest pK, shifts in the native relative to the denatured state. The calculated average pK, shift for the carboxyl groups in the unfolded lysozyme structure, -0.18 (Betam l ) and -0.29 (Ex72-ml), is in approximate agreement with recent studies by Oliveberg et al. (1995), who estimated that on the average, the pK,’s of carboxyl groups in denatured barnase are 0.4 pKunits lower than the standard pK,’s of the sites. In Fig. 8a and b, the calculated titration curves for the native and unfolded lysozyme structure are shown in comparison with the experimental titration curves taken from Tanford and Roxby (1972) (see Fig. 6). The average difference between the calculated and the experimental titration curves in the experimental pH range from 1.5 to 10.5 is 0.82 (in elementary charge units) for the crystal structure 21zt. For the titration curve of the unfolded lysozyme, we also find good agreement between theory and experiment. The average error between the calculated and experimental titration curve for the Beta-ml model is 0.52; the error for the Ex72-ml model is larger, 0.69 (titration curve not shown). For both extended models of unfolded lysozyme, the agreement with the experimental titration curve is significantly better than for the null

31

ELECTROSTATIC FREE ENERGY IN SOLUTION

:f 0

-5

-10

0

2

4

6

8

10

12

PH

14

16

0

2

4

6

8

10

12

14

16

PH

FIG.8. Titration curve of lysozyme. (a) Native state: calculated for the triclinic crystal structure 21zt (-); experimental data (0).(b) Denatured state: calculated for the exexperimental data (+). tended Beta-ml model (-);

model, for which we determined an average error of 1.13. This implies that the extended structures Beta and Ex72 are useful models of the unfolded protein in the context of titration and pH-stability calculations. The agreement between the calculated and the experimental titration curves is best for the unfolded models Beta-ml and Ex72-ml, i.e., after the first 100 steps of minimization. The average error for the titration curves of the unminimized extended models Beta and Ex72 are 0.56 and 0.73, respectively. This may be a consequence of the high conformational energy (i.e., low probability) of the unminimized Beta and Ex72 structures, which are generated by setting all side-chaindihedral angles to 180" and bond length, bond angles, and dihedrals of the protein backbone (including prolines) to ideal values. 2. Relative Electrostatic Stability From Eq. (20), the titration curves of two conformers of a system are sufficient for calculating the relative free energy difference as a function of pH. Since we found the best agreement between the calculated and the experimental pK,'s and titration curve of lysozyme when using the crystal structures 21zt and lhel, we report the results obtained with them. For the same reason, we use Beta-ml and Ex72-ml as the models of the unfolded protein. In Fig. 9a, the relative stability AAG, Eq. (20), of triclinic lysozyme (21zt) is shown relative to the null, Beta-m1, and Ex72-ml models of the unfolded protein. The experimental stability curve (Pfeil and Privalov, 1976),which has been determined in the pH range 1.5-7, is also given;

32

MICHAEL SCHAEFER ET AL.

-20 . -2

0

2

4

6

8

PH

10

12

14

16

18

-21

-2

'

'

'

'

'

'

'

'

'

'

0

2

4

6

8

10

12

14

16

1

PH

F1c.9. Relative pHdependentstability. (a) Native lysozyme (21zt) using the null (-), the Beta-ml (---), and the Ex72-ml (...) models of the unfolded protein as the reference state; experimental data (0) for the net stability (total folding free energy, including nonelectrostatic contributions) of native lysozyme in 0.1 MNaCl solution taken from Pfeil and Privalov (1976); data points ( + ) calculated with the titration curve integration method, Eq. (19), using the experimental titration curves (Tanford and Roxby, 1972) of the native and the unfolded lysozyme for the integration and setting AAG at pH = 7 equal to the experimental value from Pfeil and Privalov (1976). (b) Unfolded models Beta-ml (-) and Ex72-ml (--) of lysozyme, using the null model as the reference.

the aggregation of lysozyme has so far prevented accurate measurements at high pH (C. M. Dobson, private communications, 1996). For comparison, we also calculated a "semiexperimental" stability curve using the titration curve integration method, Eq. (19),with the experimental titration curves of the folded and unfolded lysozyme (Tanford and Roxby, 1972). We used pH = 7 with its associated experimental stability from Pfeil and Privalov (1976) as the reference pH and reference stability, since the experimental titration curves do not extend to a pH where the unprotonated state dominates [see Eq. (20) and related text]. Although there is approximate correspondence between the measured stability curve and that calculated from the titration curves, particularly for the change in stability in the pH 2-4 range where the carboxyl groups titrate, there are significant differences at higher pH. These may be due to the assumption that the nonelectrostatic contributions to protein stability are pH independent, as well as to differences in the experimental conditions in the titration curve measurements of the native and unfolded states, in particular the ionic strength of the solutions used in the measurements (Tanford and Roxby, 1972). Regardless of the structures used, the relative stability curves always approach zero at high pH. This is a consequence of the definition of AAG, which uses the unprotonatzd state of the system as thereference

ELECTROSTATIC FREE ENERGY IN SOLUTION

33

where AAG = 0 [see Eq. (20) and related text]. Other choices for the reference state of AAG are possible, and they would lead to a different offset for the relative stability curves in Fig. 9. It is coincidental, therefore, that the calculated relative stabilityin Fig. 9 and the experimental stability of lysozyme are in the same energy range. First, nonelectrostatic free energy contributions to protein stability are not accounted for in the present theory; and, second, the electrostatic free energy difference between the native and the unfolded protein in the unprotonated reference state is not accounted for in the relative stability results [see Eq. (20) and the thermodynamic cycle in Fig. 11. As is expected from the good agreement between the titration curves of Beta-m1 and Ex72-ml (see Fig. 7b), the dependence of AAG on the unfolded model structure used in the calculation is small when compared to the change in the free energy between pH = 7 and the very low and very high pH limits. In accord with experiment, the theoretical pH-stability curve predicts a plateau for AAG in the pH range 4 5 pH 5 7 and an increase of the relative free energy of the order of 10 kcal/mol when the pH is decreased from 4 to 1.5. Pfeil and Privalov (1976) report an overall Gibbs free energy difference between the folded and the denatured state of lysozyme equal to -14.5 kcal/mol under standard conditions (pH = 7, T = 25°C);at pH = 1.5, the experimental value is -5.3 kcal/mol. Thus, the change in experimental stability between pH = 1.5 and 7 is -9.2 kcal/mol. This is to be compared with the calculated stability difference between pH = 1.5 and 7 of -13.6 kcal/mol (21zt/Beta-m1) and -11.8 kcal/mol (21zt/Ex72m l ) . If the null model is used as the unfolded reference state, the predicted change in the stability is -16.5 kcal/mol. The use of the explicit Beta and Ex72 models of the unfolded protein clearly leads to a better agreement with the experimental pH dependence of the stability of lysozyme. To analyze the difference between the extended models of the unfolded protein and the null model in more detail, we calculated the stability curves of Beta-ml and Ex72-ml relative to the null model. From Fig. 9b, it follows that the relative free energy of Beta-ml (Ex72m l ) changes by 1.4 (1.3) kcal/mol upon variation of the pH from 7 to 14, and by -2.9 (-4.7) kcal/mol upon a pH change from 2 to 7. This implies that the interactions between titrating sites in the unfolded state, although small, are not negligible. The calculated changes in the stability of 3-5 kcal/mol and about 1.5 kcal/mol upon variation of the pH from 7 to 2 and from 7 to 14, respectively, are likely to be a lower bound to the error that results from the assumption of zero interaction between sites in the null model, since the extended models are designed for

34

MICHAEL SCHAEFER ET AL.

maximum solvent exposure of the titrating sites and, as a consequence, minimal interaction between sites. In a random coil structure or a molten globule state of a protein (Ptitsyn, 1992; Fiebig et al., 1996), residual secondary and tertiary structure would cause the interactions between titrating sites to be larger than for the extended models used in this study.

3. Absolute Electrostatic Stability Use of the extended model of the unfolded protein makes it possible to calculate a meaningful absolute electrostatic free energy difference between the native state and the unfolded state. According to Eq. (19), this requires the calculation of the electrostatic free energy of the fully unprotonated protein in solution for both conformations (here, the native and the extended structures). The absolute electrostatic free energy difference between the conformers A and B is given by the relative free energy difference plus the difference between the electrostatic free energies of the unprotonated reference states, AGAB(pH)= AAG,(pH) AGy(0) [see Eq. (20)]. It follows that the absolute electrostatic free energy curves in Fig. 10 are shifted by AGY((0) = G$ (0) - G:, (0) relative to the curves in Fig. 9.

+

5 -

8 -20 -2

0

2

4

6

8

10

12

14

16

18

PH FIG. 10. pHdependent absolute electrostatic contribution to the stability of lysozyme: triclinic crystal structure 21zt relative to the Beta-ml (-) model; 21zt relative to the Ex72-ml (---) model; tetragonal crystal structure lhel relative to the Beta-ml (-.-.-) model; and lhel relative to the Ex72-ml (...) model of the unfolded protein. Experimental (0)and semiexperimental (+) stability data are the same as in Fig. 9a.

35

ELECTROSTATIC FREE ENERGY IN SOLUTION

In Table 11, the Coulomb energy, the electrostatic solvation free energy, and their sum, the electrostatic free energy in solution, are given in four different charge states for the structures 21zt, lhel, Beta-ml, and Ex72-ml used for the stability calculations.The electrostatic free energy in solution is always the lowest for the standard charge state (all sites in the standard state at pH = 7); this is in accord with the fact that lysozyme is most stable in the pH range from 5 to 9. Interestingly, the Coulomb energy alone is also the lowest for the standard charge state of each structure, but the relative ranking of the four charge states with respect to Ecouland G,, is different. Whereas the two crystal structures 21zt and lhel have very similar values in each of the charge states, the unfolded structure Ex72-ml has energies in all charge states that are about 10 kcal/mol lower than for Beta-m1. Since the only electrostatic energy term that all four charge states have in common is the interaction of (nontitrating) polar groups, the more negative electrostatic free energy of Ex72-ml must arise from the polar groups; specifically, it is due to TABLE I1 Ekctrostatic Free Enm@ fw the Charges Statesb 8, yo, is*, and 1 Structure

21zt

S

0 711 p d

1 1 he1

0

3" p d

1 Beta-ml

0 3O

-Trtd 1

Ex72-ml

0 so jsd

1

Eco"l(3

GOl"(3

Gl(3

-80.4 - 128.2 -161.2 2.4

-102.5 -17.1 -77.1 - 186.4

- 182.8 - 145.3 -238.3 - 184.0

-82.6 - 129.8 -163.1 0.8

- 102.8 -16.8 -77.1 - 186.2

- 185.3 - 146.6 -240.2 - 185.4

-104.4 -104.2 - 122.9 -62.7

-79.4 -31.2 100.0 -119.0

-183.8 -135.4 -222.9 -181.7

- 120.6 -125.4 - 143.0 -75.3

-73.3 -21.4 -90.0 -116.6

- 193.9

-146.7 -233.1 -191.9

Energies in kcal/mol; protein c, = 20, solvent G = 80, monovalent ion concentration 0.145 M. 6, unprotonated state; ?, all sites neutral; SStd, standard charge state at pH = 7; 1, protonated state. ' = Ecwi + Gm.

36

MICHAEL SCHAEFER ET AL.

the hydrogen bonds of the backbone that are present in Ex72-ml but not in Beta-ml. The electrostatic free energy differences between the four pairs of native and unfolded lysozyme structures are given in Table 111. The same set of charge states as in Table I1 are compared. Since the values of G$ (S) for 21zt and lhel are very similar, A G F (S) depends on whether Beta-ml or Ex72-ml is used for the unfolded state. As explained above, the folding free energy AG? (8) of the unprotonated state is required to calculate the absolute pH stability from the relative stability. While the other charge states could, in principle, also be used as the reference states in the thermodynamic cycle in Fig. 1, their folding free energies are mainly of interest for comparison with the calculated pH-stability curves. The folding free energies in Table I11 are all in a range from about 0 to -20 kcal/mol. Even with the use of a relatively high dielectric TABLE 111 Electrostatic Free Enera DiJfmenct? for the Charge States? 0, yo, s'*, and T Structures Native 21zt

Unfolded Beta-ml

S

0 so TS"

1

21zt

Ex72-ml

0

so

s'" 1 1 he1

Beta-ml

0

so

Ttd 1

lhel

Ex72-ml

-

0 P s'" 1

(3' 1 .o -9.9 - 15.4

-2.3 11.0 1.4 -5.2 7.9 -1.5 -11.2 -17.2 -3.7 8.5 0.1 -7.1 6.5

"Energies in kcal/mol; parameters as in Table 11. Charge states as defined in Table 11. AEY = Eti - E!i.

ELECTROSTATIC FREE ENERGY IN SOLUTION

37

constant of ei = 20 for the protein interior, the solvation free energies in Table I1 are in a range from -10 to -190 kcal/mol. The error in the FDPB calculation of solvation free energies must, therefore, be less than a few percent to obtain meaningful free energy differences between conformers. In Fig. 10, the absolute stability curves for the four combinations of the native and the unfolded state 2lzt/Beta-ml, 21zt/Ex72-ml, lhel/ Beta-ml, and lhel/Ex72-m1 are shown. They have almost identical shape, which is consistent with the good agreement between the relative stability curves in Fig. 9a (21zt only, curves for lhel not shown). However, the calculated absolute free energy difference at a given pH varies by approximately 15 kcal/mol, depending on the choice of the native and unfolded structure. Use of the tetragonal crystal structure lhel instead of the triclinic crystal structure 21zt leads to a decrease by about 2 kcal/ mol of the calculated free energy of the native state, i.e., to an increase of the calculated stability (negative shift). On the other hand, use of the Ex72-ml structure instead of Beta-ml for the unfolded conformation leads to a decrease of the free energy of the unfolded state by about 10 kcal/mol, i.e., to a decrease of the calculated stability (positive shift, upper two curves in Fig. 10). A comparison between the folding free energy AGY (Sstd) of lysozyme in the standard charge state from Table I11 with the calculated pH stability AGAB(pH)at pH = 7 from Fig. 10 shows that there are only minor differences: for the native/unfolded structure pairs 2lzt/Betaml, 21zt/Ex72-ml, lhel/Beta-ml, and lhel/Ex72-ml, one has AGF(SStd)= -15.4, -5.2, -17.2, and -7.1 kcal/mol, while AG,(pH = 7) = -15.9, -6.0, -17.9, and -8.0 kcal/mol, i.e., amaximum difference of 0.9 kcal/mol. It follows that the standard charge state represents well the equilibrium distribution of charge states in the pH range between 6 to 10, in which there is little change in the calculated pH stability. In part, this is a consequence of the fact that only two groups (His, Nterminus) titrate in this pH range and that their titration behavior is similar in the folded and unfolded state. The electrostatic free energy of folding for the electrically neutral state, S = So, differs from the folding free energy of the standard charge state (corresponding to the broad minima in the stability curves in Fig. 10) by about 6-7 kcal/mol. The value is nearly independent of the pair of crystallographic and extended structures that are used to represent the native and the unfolded states. Furthermore, the folding free energy of the uncharged state (polar interactions only) exhibits changes as a function of the native/unfolded structures that are very similar to the changes observed for the minimum of the pH stability in Fig. 10 (and

38

MICHAEL SCHAEFER ET AL.

for the folding energy of the standard charge state). It follows that it is the variation in the interactions of polar atom groups in the different lysozyme structures that accounts for the variation in the calculated absolute pH stability of lysozyme and that the interaction of titrating sites is comparatively independent of the choice for the native and unfolded structure. One reason for this difference between the contributions from polar and charged atom groups is that the latter are involving mainly long-range interactions, whereas the former are due to shortrange interactions (e.g., hydrogen bonds), which are more sensitive to structural changes. 4. Conclusions

We have used the linked function treatment of protein titration to calculate the titration curves of the crystal structure and an extended structure of lysozyme as models for the native and denatured state. Good agreement with experimental results (average difference 0.50.8 elementary charge units in the experimental pH range) was obtained. If one assumes that the individual site titration curves of the 32 sites contribute a random error of 5 6 each, this corresponds to an average error of kO.09 to k0.14 (9-14%) for each site. For the extended model of the denatured state, the agreement with the experimental titration curve is better than that for the independent sites (null) model using the standard pK,’s for all titrating groups (extended model: average error 0.5-0.7 elementary charge units; null model, average error 1.1). By calculating the relative pH stability of the extended model, using the null model as the reference, we have demonstrated that there are significant interactions between titrating sites in the denatured state. The electrostatic free energy contribution from titrating sites in the extended molecule vanes from - 1.5 to 3.3 kcal/mol for the pH in the range 2-10. The experimental data on lysozyme stability include all contributions to the free energy, whereas the present theory accounts only for the electrostatic contribution. Therefore, the comparison of the absolute electrostatic pH stability with experimental results in Fig. 10 is only qualitative. We obtained good agreement between the calculated and the experimental change in the stability of lysozyme when the pH was varied from 7 to 1.5 (acid denaturation): the experimental free energy change is 9.2 kcal/mol, as compared with the calculated free energy change of 12- 13.5 kcal/mol. However, there is considerable uncertainty as to the absolute electrostatic contribution, depending on the structures used to represent the native and the unfolded state. In an improved theoretical treatment of the pH stability of proteins, it will be necessary

ELECTROSTATIC FREE ENERGY IN SOLUTION

39

therefore to include conformational equilibria or to devise a method for selecting sets of conformations representative of the native and the unfolded state. C.

Capsid Stability of Foot-and-MouthDisease Virus

Foot-and-mouthdisease virus (FMDV) is a member of the picornavirus family and consists of a protein capsid containing one molecule of positive-sense single-strandedRNA. The capsid has icosahedral symmetry and consists of 60 identical protomers (Rueckert, 1990). Every protomer has a total of approximately 735 residues and contains four noncovalently linked chains: VPl, VP2, VP3, and VP4 (molecular weights: 23,000, 25,000, 24,000, and 8000, respectively). Crystal structures are available for serotypes 0,BFS (protein data bank entry lfod), CS8C1 (lfmd), and A22 (Curry et al., 1996). Of all picornaviruses, FMDV is the most sensitive to low pH values. When intact FMDVis taken to a pH below 7, the structure dissociates into pentamers, which appear to be symmetric assemblies of five protomers (Randrup, 1954; Brown and Cartwright, 1961; Burroughs et al., 1971). In this dissociation process, the RNA is released and the smaller of the four chains, W 4 , is detached from the protomers. It has been proposed that this provides the mechanism by which FMDV delivers its RNA into the cytosol of the infected cell (Baxt, 1987; Carrillo et al., 1984, 1985; Mason et al., 1993). Other members of the picornavirus family may also use acid-induced conformational changes within the endosome to effect cell entry. Like FMDV, the cardiovirus mengovirus also dissociates to pentamers (at pH 6.2) (Mak et al., 1970). Human rhinovirus (HRV) undergoes a conformational change at pH 5 similar to that generated by its interaction with susceptible cells although it does not dissociate (Korant et al., 1972). Nevertheless, antibiotics which specifically inhibit the vacuolar proton ATPases responsible for endosomal acidification block HRV infectivity (Perez and Carrasco, 1993). Exceptionally,poliovirus infection is not affected by these agents. Thus, endosomal acidification appears not to be the universal mechanism for picornavirus cell entry. Recently, Curry et al. (1995) measured in vitro stability curves as a function of pH for three different subtypes of FMDV A10, A22, and A24. A capture enzyme-linked immunosorbent assay (ELISA) was used to monitor the dissociation of capsids to pentamers as a function of pH. The pH corresponding to the midpoint of this transition as determined by the ELISA signal ( P H ~was ~ ) determined for each sample. The A22 subtype was least acid stable of the three, with a pH50of 7.0, while the

40

MICHAEL SCHAEFER ET AL.

pHs0values for A10 and A24 were 6.5 and 6.65, respectively. In addition, stability curves were reported for FMDV empty capsids, which lack the RNA strand. The empty capsids of all three subtypes were found to be more acid-stable by about 0.5 pH units than the corresponding virion. Curry et al. (1995) and Twomey et al. (1995) identified histidines at the pentamer-pentamer interface that might determine acid lability. Curry et al. suggested H142 (VP3)and possibly H65 (VP2).The former was suggested because it is close (4 A) to the N-terminal end of an ahelix of the neighboring pentamer, and the latter was implicated based on sequence differences between A22 and A10/A24, i.e., A10 has a Phe and A24 has a Tyr at that position. Curry et al. reasoned that the positive end of the a-helix dipole would result in an electrostatic repulsion between pentamers when the H142 is protonated. Twomey et al. counted the number of positively and negatively charged residues on the neighboring pentamer around His residues at the interface: H142 and H145 (VP3)were found to have more basic than acidic residues around them, so it was presumed that they would be destabilizing at low pH when they are positively charged. Since the crystal structures of the viruses do not include the FWA, the calculations are made for empty capsids. However, the resulting pH dependence may well approximate the behavior of native viruses, since the empty and native capsid structures are very similar. FMDV is chosen for the electrostatic calculations, rather than HRV or poliovirus, since it has been shown to dissociate into pentamers (Brown and Cartwright, 1961), whereas this has not been demonstrated for HRV or poliovirus. FMDV dissociates into pentamers at a pH that is very close to the pH value at which the crystal structure was obtained. It is thus likely that the pentamers are structurally conserved in the pH range of interest (pH 6-7). We report the calculations of titration curves and stability profiles for the FMDV serotype 0,BFS. The main purpose is to identify the residues that are important for the pH stability and to determine the reason for their importance. Furthermore, we quantify the electrostatic interaction between H142 (VP3) and the adjacent a-helix, and the charged residues in its environment, to determine whether the hypotheses of Curry et al. (1995) and Twomey et al. (1995) are consistent with the calculations. For comparison, results from calculations of the absolute electrostatic free energy of binding are also given for the FMDVserotypes A106, and A22 Iraq. Studies of FMDV have shown that the capsid dissociates into pentamers of protomers as the pH is reduced. The pentamer interface is formed by the packing of two protomers that are related by twofold symmetry. In the calculations, we used a model system involving the association of

ELECTROSTATIC FREE ENERGY IN SOLUTION

41

two protomers as indicated in Fig. 11. Although the side chains at the dimer interface may change their conformation upon dissociation, the overall protomer conformation is likely to be essentially unchanged, especially since in reality it is still part of the pentamer (see Fig. 11). The model omits consideration of protein-protein interactions at the threefold icosahedral symmetry axis and focuses on the interactions at the center of the interpentamer interface, i.e., interactions close to the twofold icosahedral axis. This simplification is justified because the vast majority of atom-atom contacts between pentamers is within the interface surrounding the twofold symmetry axis, and because the residues that have been suggested to be most important for pH dependence in FMDV (Curry et aL, 1995; Twomey et aL, 1995) are located in the vicinity of the twofold symmetry axis and are distant from the threefold symmetry axis (-35

A>.

FIG. 11. Schematic illustration of the association of two protomers treated in the calculations. In the dimer, the location of the capsid proteins W1,W2, and W 3 is indicated. W 4 is located on the inside of the capsid (below the paper plane). To show that the dimer captures most of the pentamer-pentamer interface, we also included the remaining protomers of both pentamers (dashed lines). The icosahedra1 twofold and threefold symmetry axes are indicated by numbers 2 and 3, respectively.

42

MICHAEL SCHAEFER ET AL

In the dissociated state, the two protomers titrate independently, such that the titration curve is equal to the sum of the titration curves of the protomers. Furthermore, since we assume that the structure of the protomers (proto) is symmetry related and remains the same after dissociation, the titration curve of the dissociated system (diss) and its electrostatic free energy in the unprotonated state is

To calculate the electrostatic free energy of association for the two protomers, we thus use Eqs. (39) and (40) for the titration curve and electrostatic free energy of conformation B in Eqs. (20) and (21), and the titration curve and electrostatic free energy of the protomer dimer for conformation A. The solvent and protein dielectric constants were set to E, = 80 and ei = 20 (see Section II1,A) , the ionic strength to 0.145 M, and the temperature was 293 K. Since we are mainly interested in the stability of the complex in the pH interval from 6 to 8, we selected Asp, Glu, His, and the C- and N-terminal groups for the titration calculations, i.e., we excluded sites whose standard pK, is far from the pH interval of interest [see Section 11,D;for the pPFd (Table I)]. This results in 90, 88, and 90 titratable residues per protomer for types 0,A10, and A22, respectively. In the titration program of Beroza et al. (1991), 7500 Monte Carlo steps were performed to determine the average protonation of all sites at a given pH and the titration curves were calculated using 121 pH values evenly distributed in the interval from 0 to 12. The crystal structure (resolution 2.6 of type OIBFS FMDV (full name: 01BFS1860) was obtained from the protein data bank entry lfod (Bernstein et al., 1977). Crystal structures for the types A106, and A22 Iraq 24/64 (Curry et al., 1996), and the empty capsid structure of A22 (called A22E), were provided by S. Curry, E. Fry, and D. Stuart (all structures refined to 3.0 A resolution). The root mean square deviation (C, only) after superposition between A22 and A22E is 0.35 The protomers consist of 736, 736, and 737 residues, for OIBFS, A10, and A22, respectively. Several portions of the structure are missing from the crystal coordinates. For OIBFS,these are residues 21 1-213 (C-terminus) of VP1, 1-4 of W 2 , and 1-14 and 40-64 of W 4 . For A10, VP1 lacks residues 134-154 and 209-212, VP2 lacks residues 1-11, and VP4 lacks residues 1-14 and 40-64. In A22, residues 137-155 and 211-213 of VP1, 1-11 of VP2, and 1-14 and 39-64 ofW4 are missing. The missing

A)

A.

43

ELECTROSTATIC FREE ENERGY IN SOLUTION

segments were not included in the calculations. This is unlikely to influence the calculations significantly, since only one of the missing segments, the N-terminus of W 2 , is near the pentamer-pentamer interface. Furthermore, the N-terminus of VP2 is not close to the center of the interface, where the histidines of interest are located. Hydrogen atoms were added to the structures with the HBUILD command of the CHARMM program (Brooks et al., 1983). 1. Absolute Ekctrostatic Free Energy of Binding

The electrostatic contribution to the absolute binding free energy of the dimer can be obtained from Eq. (19). This requires the calculation of the total electrostatic free energy of the unprotonated state, which consists of the Coulomb energy and the electrostatic contribution to the solvation energy, for both the protomer and the dimer (see Table IV). Since only Asp, Glu, His, N-terminal, and Gterminal residues are treated as titratable sites, the “unprotonated” state of the system includes Lys and Arg residues in their protonated (ionized) states and Cys and Tyr in their protonated (neutral) states. In fact, the unprotonated state in this study corresponds to the standard charge state of the system at pH = 7, except for the N-termini, which are neutral. Table V lists the calculated absolute values of the electrostatic binding free energy at different pH values. The value of AGbind(m) corresponds to the binding free energy for the fully unprotonated state. The pH.,, of the lowest (optimum) electrostatic binding free energy was determined from the binding free energy curve according to Eq. (19). Although there are substantial differences in the free energy of solvation and in the Coulomb energy of the different dimer (protomer) structures in the unprotonated state (Table IV), their overall binding energies are relatively similar (-5 to -12 kcal/mol). Because there are many contributions to stability other than electrostatic ones (Lazaridis et aL, 1995), the absolute AGbind(pH)values cannot be compared directly TABLE IV Coulomb, Solvation, and Binding Free Energy“for tht Unpotonated State

Solvationb lfod A10 A22 A22E

-697.01 -691.67 -619.77 -619.79

(-694.94) (-687.62) (-634.34) (-634.66)

Coulomb” - 1049.99 (- 1046.34) (-893.78) -894.68 (-977.38) -1002.76 (-976.38) -1001.07

Energies in kcal/mol. Values for the dimer; values for two protomers in parentheses.

A~

~ ~ ( 5 )

-5.72 -4.95 -11.81 -9.82

44

MICHAEL SCHAEFER ET AL.

1fod A1 0 A22 A22E

-5.72 -4.95 -11.81 -9.82

-6.33 -6.23 -13.16 - 10.84

8.2 7.7 7.5

7.7

82.62 89.56 87.01 89.88

Energies in kcal/mol. Binding free energy of unprotonated state (see Table IV). pH of lowest (optimum) binding free energy. Binding free energy at pH = 0.

with experimental data. From the small difference (maximum difference 1.35 kcal/mol) between the binding energies of the unprotonated state (here: Asp, Glu, C-terminus, Arg, and Lys in their ionized states; see above) and the binding energy at the pH.,, of binding, it follows that optimal binding requires the anionic sites that are allowed to titrate in the calculations to be predominantly in their ionized states. Further, it is interesting to note that the binding energy at the pH.,, is always more favorable than the binding energy that is calculated for the unprotonated (standard, except N-termini) charge state. To evaluate the contribution to the binding energy that originates from the interaction of the ionic sites, we also calculated the binding energy of the system at pH = 0 (Table V) . The AGbilldvalues under these extreme pH conditions are positive and on the order of 100 kcal/mol. This is caused by positively charged sites whose loss in solvation energy upon complexation is normally balanced by the interaction with negatively charged residues (Asp, Glu) ,which are now neutral. Thus, although electrostatic binding energies are relatively small at the pH.,, (Table V) , they can be very large and unfavorable under extreme pH conditions. Of course, such extreme conditions are unphysical since they would presumably lead to unstable monomers. Nevertheless, they are of interest because they demonstrate the importance of charge-charge interactions under physiological conditions.

2. Relative Electrostatic Free Energy of Binding Because of the difficulty of comparing stability curves between different serotypes or mutant structures in terms of absolute AGbind,we focus on the changes in electrostatic stability as a function of pH. In the following, we use the electrostatic binding free energy relative to the minimum of AG(pH). Formally, this means that we redefine AAG(pH)

45

ELECTROSTATIC FREE ENERGY IN SOLUTION

as AGAB(pH)- AGm(pHOp,), where AG, is the absolute electrostatic binding free energy according to Eq. (19) and pH opt is the pH of optimum binding (minimum of the electrostatic binding free energy). This is equivalent to using pH,, as the reference pH in the integral expression for AAG in Eq. (20) instead of pH = m, i.e., = -(In 10)RTIP)rOp’((n(pH’))~ - (n(pH’))~)dpH’ (41) AAGbind(pH) PH

where is the titration curve of the dimer and ( T Z ) ~is the titration curve of the dissociated monomers according to Eq. (39). The calculated relative stability curve for OIBFS is shown in Fig. 12. The minimum is at pH 8.1; the capsid becomes destabilized at lower and higher pH values. When the pH is lowered to 6.5 there is a destabilization of about 2 kcal/mol. The destabilization that occurs when the pH is raised beyond 8.1 is less important. This is due in part to the fact that we did not include Arg, Cys, Lys, or Tyr residues in the calculation. For comparison, Fig. 12 also shows the stability curve after including these residues. Since there is no difference for pH < 8.5 and we are interested primarily in the stability around pH 7, we leave out the Arg, Cys, Lys, and Tyr residues in the following. This greatly reduces the time required for the computation (180 vs. 380 titratable sites in the dimer).

= 0

g

6-

5 a

42-

0 5.0

I

6.0

I

8.0

7.0

9.0

11 .o

PH FIG.12. Relative stability, Eq. (41), of the OIBFSdimer as a function of pH. The thick stability curve results from the calculation with only Asp, Glu, His, N-terminus, and G terminus as titratable sites. For comparison, the relative pH-stability with Cys, Lys, and Tyr included as titratable sites is also shown (thin line).

46

MICHAEL SCHAEFER ET AL.

The shape of the stability curve results from differences in titration behavior of the two states of the model system-the dimer and the two separate protomers [see Eq. (41)].To analyze the contribution from individual sites to the stability, we consider their protonation (titration) curves in the dimerized and dissociated protomer states. The pH dependence of the contribution from site i to the stability of the dimer can be calculated using Eq. (41),with (n)* - (n)B replaced by A(si) = (si)* - (s,)~, the change in the average protonation of the site upon formation of the complex. From Eq. (41),it follows that the lowering of the pH from pH,,, to pH1< pH.,, leads to an increase of the relative free energy (destabilization) of the complex originating from those sites for which A(s,) < 0 in the interval (pHl,pH,,,). Thus, the term “destabilizing” in this work refers to sites that are responsible for a loss of stability of the complex upon variation of the pH, specifically the change from pH.,, to acid pH conditions, the region of primary experimental interest.

3. Important Histidines Inspection of the titration curves of the individual sites shows that the residues with a titration behavior that differs between the complex and the unbound protomer in the acid region are found at or near the protomer-protomer interface (which corresponds to the interpentamer interface in the capsid). These residues are, therefore, predicted to be responsible for the acid lability of the capsid. Figure 13 shows the p& shift between the dimer and the protomer for the titrating residues as afunction of distance from the interface. Within 10 Afrom the interface, there are 10 Asp, 11 Glu, and 8 His residues per protomer. For most acidic residues (open symbols in Fig. 13), the pK,’s are lower in the dimer than in the protomer. The desolvation of the anionic sites (Asp, Glu) upon dimerization destabilizes their charged state and thus leads to a positive pK, shift. The fact that a negative pK, shift is observed for most acidic residues indicates that there are interactions with polar groups and with cationic sites (Arg and Lys were not allowed to titrate) that favor the ionized form. From an inspection of site-site distances, there is a salt bridge formed across the pentamer-pentamer interface for only two Glu residues (E213in VP2; El46 in VP3);the salt bridges involve R60 (VP2)for E213 and K63 (VP2)for E146.A number of the Asp and Glu residues had very different pK,values between the protomer and the dimer, but none of these occur in the pH interval (pH 6-7) of interest; they are all in the pH range between 0 and 4.5. Three His residues are primarily responsible for the features of the capsid stability curve around pH = 7.5.H141 and H144 (VP3)have a

47

ELECTROSTATIC FREE ENERGY IN SOLUTION

1.5

-2.5-

B

0 0

,

'

,

,

,

I

1 FIG. 13. Differences in pK,'s between sites in the dimer and the Drotomer (pKd;""- p K y ) vs. the distance of the sites to the protomer interface,where the distance is defined as the minimum distance between ionized atoms in the titratable site (e.g., Os, or Os, in Asp) to any non-hydrogen atom in the neighboring protomer. Residue His (m); N-terminus (0); and Gterminus ( A ) . A negative ApK. implies types: Asp ( 0 ) ;Glu (0); a destabilization of the dimer when the pH is lowered from pH.,, to acid pH conditions [see Eq. (41) and related text].

reduced pK, in the dimer as compared with the protomer (6.30 in the dimer vs. 7.52 in the protomer for H141, and 4.13 vs. 7.49 for H144), causing a significant destabilization at pH < 8 (Fig. 14). H87 (VP2) is also destabilizing, but only below pH = 6. In contrast, H21 (VP2) has a stabilizing effect as the pH is lowered. However, the contribution from H21 is more than compensated by the loss in stability of the complex that is associated with H141 and H144, which results in the net increase of AAGbindwhen the pH is lowered from pH,,,, = 8.1 toward acid pH (Fig, 12).The importance of HI41 is in accord with the analysis of Curry et al. (1995) and Twomey et al. (1995) (H141 is labeled H142 in these references). H144 was also suggested by Twomey et al. (1995) as being one of the two possible destabilizing residues at the surface. The p c " values (see Section I1,D) of H141 and H144 are remarkably low, 0.90 and 0.76, respectively. This is caused by strong interactions with adjacent Lys and Arg residues,which are formally counted as background charges and not as titrating residues in this work. From a detailed analysis of the energetic contributions to the pK, shift, it was found that both residues experience a relatively small desolvation effect in the dimer (-0.68 and -0.84 pH units for H141 and H144, respectively) but that the interaction with polar and cationic atom groups is large (-4.84

1 .oo

H21 (VP2)

0

2

4

6

PH

8

10

0

2

4

6

8

10

PH

FIG.14. Titration curves of the individual sites H21 (W2),H141 (W3),and H144 (W3) for the 0,BFS virus capsid structure. Sites in the dimer, solid lines; sites in the individual protomer, dashed lines.

49

ELECTROSTATIC FREE ENERGY IN SOLUTION

and -4.83 pH units, respectively). The complex nonsigmoidal titration curves of H141 and H144 (see Fig. 14) are caused by interaction with H87 (VP2), which has a surprisingly low calculated pK, of 1.93. H65 (VP2)was also suggested by Curry et al. (1995) as being possibly destabilizing. However, we did not find a significant contribution from this residue. We calculated stability curves for OIBFS with three different point mutations: H65F (VP2),H141L, and H144L (both W3). Structures of the mutated residues were created by conserving the xl and x2dihedral angles and building the remaining side-chain atoms based on the standard bond lengths and angles of the param22 set of CHARMM (MacKerell et aZ., 1998). H65 was chosen to demonstrate that a residue with no change in p K , between protomer and dimer does not affect the pHdependent relative stability. It was changed to a Phe, the residue that occurs in the same position in FMDV serotypes A10 and A12 (Palmenberg, 1989). H141 was changed to a Leu, the consensus residue for picornaviruses at that position (Palmenberg, 1989). H144 was also changed to a Leu so as to compare it to the H141L mutation. Since mutations affect the titration behavior of other residues, new titration curves were calculated for each mutatedvirus. The relative stability curves for the three mutations are shown in Fig. 15, in comparison with the relative stability of the wild-type OIBFS sequence. As expected from the previous calculations, the H144L substitution has the largest effect, resulting in a virus dimer that is not significantly destabilized until the

5.0

6.0

7.0

8.0

9.0

10.0

PH FIG.15. Relative dimer stability, Eq. (41), for 0,BFS (thick line) and for the mutants H65F (W2) (thin line), H141L (W3) (dashed line), and H144L (W3) (dotted line).

50

MICHAEL SCHAEFER ET AL

pH is below 6 (the relative AGbind of the mutant increases by 2 kcal/mol on lowering of the pH from 8 to 5, as compared with an increase by more than 6 kcal/mol for the wild type; see Fig. 15).The H141L mutation has a similar but smaller effect on stability, whereas the stability of the H65F mutant is only marginally different from that of the wild type. 4. Effectof a-Helix on His 141 The results of Section III,C,3 suggest that H141 (VP3) destabilizes the dimer at pH < 8 (see Fig. 14). Curry et a2. (1995) proposed that the ahelix formed by residues 89-98 (VP2) is a key factor in this destabilization through an unfavorable electrostatic interaction between the helix dipole and the protonated His. Significant effects of a helix on the stability of barnase have been demonstrated experimentally (Sancho et al., 1992), although the dominant contribution appears to arise from local interactions with the helix terminus rather than the so-called helix dipole (Tidor and Karplus, 1991; &pist et aL, 1991). We analyzed this hypothesis by calculating the electrostatic interaction between the helix and the protonated and unprotonated H141, respectively. In these calculations, only the H141 partial charges in one protomer and the helix partial charges in the other protomer (related by a twofold symmetry axis) are present, while the charges of all other atoms are set to zero. Titratable sidechains of the helix were assigned their standard charge state at pH = 7. We calculated the effect of the helix backbone and the helix side chains separately for the three serotypes OIBFS,A10, and A22. From Table VI,the destabilizingeffect of the helix backbone on the protonated state of H141 is on average 0.37 kcal/mol, which corresponds to a ApK, of -0.27. Sitkoff et al. (1994a) reported a calculated ApK, of -0.29 due to the interaction between the backbone of a 21-residue a-helical peptide and a titrating cationic site. The effect of the helix side chains is smaller: TABLE VI Electrostatic Effect" of Protomer 1 on the Protonation of HI41 (W3)in Protomer 2

lfod

A10

A22

helix bb

helix sc

prot 1

DEKR

Glu

R60

H144

0.39 0.36 0.37

0.01 0.17 0.19

2.58 2.65 2.61

0.58 0.50 0.79

-0.68 -0.60 -0.64

0.59 0.55 0.56

2.73

2.72 3.07

"Energies in kcal/mol. Conversion to ApK, by multiplication with -0.75. Column heads: helix bb/sc, effect of the backbone/side chains of residues 89-98 (VP2); prot 1, all atoms of protomer 1; DEKR, all Asp, Glu, Lys, and Arg of protomer 1 (DEKR refers to their 1-lettersymbol); Glu, all Glu of protomer 1; R60, only residue R60 (VP2) charged; H144, effect of protomer 1 on H144 (VP3)in protomer 2.

ELECTROSTATIC FREE ENERGY IN SOLUTION

51

0.01 kcal/mol for OIBFS and about 0.18 kcal/mol for A10 and A22. The reason for the difference between OIBFS and A10/A22 is that residue 93 (VP2) is a Ser in OIBFS whereas it is a His in A10 and A22. The effect of the H93 side chain in A10/A22 is 0.17 kcal/mol in A10 and 0.18 kcal/mol in A22. The total destabilizingeffect of H141 protonation caused by the neighboring protomer was calculated by including all atomic charges of the other protomer (in contrast to the above, where charges were assigned only to atoms in the helix), with the titrating sites in their standard (pH 7) states. Table VI shows that the interaction energy is much larger than for the a-helix alone; on average there is a destabilization of the protonated state of H141 by 2.61 kcal/mol (ApK, of -1.89). The effect of the Asp, Glu, Lys, and Arg residues is shown in the column headed DEKR. Although these ionized residues have a strong effect (0.62 kcal/mol on average), they only contribute about 24% to the total destabilization energy. We calculated the effect of the Glu residues only, which should stabilize the protonated state of H141, and obtained results in agreement with this expectation (column Glu in Table VI).A very strong destabilization of -0.57 kcal/mol was caused by R60 (VP2), whose charged nitrogen atom is separated by only 5.2 from the Nsl atom of H141. Since the combined contribution of the ahelix and the charged residues is only 0.98 kcal/mol (Table VI), the predominant destabilizing effect is caused by the interaction between H141 and polar groups on the neighboring protomer. In agreement with our previous results, the total destabilization of the complex caused by H144 is comparable to that of H141 (Table VI, last column).

A

5. Conclusions

In this work, the pH stability of the FMDV virus capsid is calculated based on the linked function theory, i.e., by integration of the titration curves of the individual protomers and the dimer. This approach includes consideration of all charge states of the titratable sites. It is thus expected to be more accurate than calculations where only specific charge states of titrating residues are included, as, e.g., in the work of Warwicker (1992). The calculations on the pH stability of the FMDV virus capsid permit us to make a detailed analysis of which residues are responsible for the instability of the capsid in the pH range 5-6. It was shown that the importance of a given residue depends strongly on its distance from the protomer-protomer interface. Not surprisingly, the calculated effects near pH 7 are dominated by the titration behavior of histidine residues. Two His that contribute most to the destabilization at low pH are H141 and H144 in the VP3 capsid protein [H142 and H145 in Curry et al.

-

52

MICHAEL SCHAEFER ET AL.

(1995) and Twomey et al. (1995)l. They are located at the pentamerpentamer interface. H87 (VP2) is also destabilizing, but only below pH 6. H141 and H144 were identified by Curry et al. (1995) and Twomey et al. (1995) as two likely candidates for destabilization. Curry et al. (1995) based their identification of H141 on the presence of an a-helix in the neighboring pentamer (and on conservation of this His, which is unique to FMDV in the picornavirus family). We find that the helix effect is not the major cause for the pK, shift of H141, since it accounts for only 20% of the effect of the entire neighboring protomer (Table VI) . Twomey et al. (1995) counted the number of charged residues on the neighboring pentamer within 10 of any His residue and concluded that H141 and H144 could be destabilizing, since in their environments the positively charged residues outnumbered the negatively charged ones. We find that the combined effect of all charged residues (Asp, Glu, Arg, Lys) accounts for only 20-25% of the effect on H141 (Table VI); i.e., polar residues also play an important role. Thus, the structure-based analysis agrees qualitatively with the computational results. However, it is more reliable to base such conclusions on titration curve calculations, which now can be obtained relatively easily for systems as large as protomer dimers. Warwicker (1989, 1992) studied the higher acid stability of poliovirus as compared with HRV. He calculated pK, shifts of H109 (VP2) and H150 (VP3)at the pentamer-pentamer interface, assuming standard protonation states of other titratable residues (Warwicker, 1992). H150 (VP3) in HRV corresponds to H144 in FMDV, one of the residues addressed in this study. From his calculations, the protonation of the histidines does not account for the destabilization of HRV below pH 5.5. The differential stabilities of HRV and poliovirus were explained by proposing that a &sheet extension adjacent to the His residues is structurally more acid stable in poliovirus than in HRV, and prevents hydrogen ions from binding to the His residues in poliovirus. By means of an equilibrium thermodynamic model of virus capsid association, Zlotnick (1994) found that small energy differences for one contact can cause significant changes in virus stability because of the large number of units involved. In his model, every pentamer-pentamer contact contributes a fixed amount of free energy to the total system. Statistical factors were also taken into account, such as the number of ways of forming and dissociating a particular assembly. He found with this model an exponential free energy dependence of the equilibrium on the assembly concentration. Since the calculations for the mutants H141L and H144L in OIBFS showed a marked stability increase at pH values below 7 (Fig. 15) for one pentamer-pentamer contact, they could

A

ELECTROSTATIC FREE ENERGY IN SOLUTION

53

have an important effect on overall virus stability. Consequently, these mutants are highly interesting candidates for stability measurements.

IV. OUTLOOK In the applications of the linked function theory to the pH stability of lysozyme and of the capsid of FMDV, good agreement between calculation and experiment has been demonstrated. In particular, there is quantitative agreement between the calculated and the experimental loss in lysozyme stability when the pH is lowered from the physiological pH 7 to acid pH conditions (- 2). In the application to FMDV, the calculations made possible the identification of specific titratable sites that are responsible for the acid lability of the capsid, which is assumed to play an important role for the infectivity of the virus. The theory of protein titration and pH stability outlined in this work takes full account of the protonation equilibria of titratable sites as well as their mutual interactions. The interactions between ionizable groups contribute to the shift of pK,’s as a consequence of conformational change, e.g., the binding of a substrate, At the same time, the interactions lead, in general, to a departure of the titration curves of individual sites from that of a single moiety (the ideal Henderson-Hasselbach titration curve; see Fig. 3). If the deviation of the site titration curves from the ideal are neglected, the free energy difference between conformations can be evaluated on the basis of the pK,’s alone, using the independent sites model developed in Section I1,C. However, to take full account of the interaction between ionizable groups, free energy changes must be derived from the generating functions for the conformations (see Section I1,A). For systems with many (>30) titrating sites, the computational intractability of the generating function approach can be circumvented by first calculating the titration curve and then integrating the titration curve, e.g., starting from pH = m as the reference where the electrostatic free energy is given by the free energy of the fully unprotonated state of the system. The underlying proportionality between the derivative of the free energy and the average degree of protonation (titration curve) follows directly from the binding polynomial as defined in the theory of linked functions. In future work, it will be necessary to include multiple conformations in pK, and pH-stability calculations, such as those reviewed here for lysozyme and the capsid of the FMDV. First, the application to lysozyme has revealed a strong conformation dependence of the contributions to the electrostatic free energy from the interaction of polar groups. To reduce this conformation dependence, it will be necessary to incorporate

-

54

MICHAEL SCHAEFER ET AL

an average over an ensemble of structures in the methodology, or to develop methods for selecting a conformation that is representative of the ensemble at thermal equilibrium. Second, the calculations on the lysozyme pK,'s with different values of the protein dielectric constant, which give best results for ei = 20, indicate that it is necessary to account for the relaxation of the protein permanent dipoles due to changes in the ionization state of the protein. Since the polar environment around ionizable groups in proteins is inhomogeneous, an explicit treatment of the polarization effects is expected to lead to a better agreement between calculated and experimental pK,'s than that obtained by the present approach, which assumes that the microscopic polarizability corresponds to a macroscopic dielectric constant of ei = 20 everywhere. Multiple conformations can be incorporated at different levels in the theory of protein titration. A simple approach would be the use of average structures, e.g., from a molecular dynamics simulation; it would correspond to the idea of selecting a single conformation to represent the ensemble at thermal equilibrium. A more rigorous treatment of multiple conformations would involve the double summation over all conformations and charge states in the generating function, Eq. (8), similar to the approaches that have been developed to treat multiple ligands or allosteric effect in the theory of linked functions (Wyman and Gill, 1990). In implementing the different methods to include conformational averages, one important criterion will be to maintain computational feasibility, even for systems with many (several hundred) titratable sites, while achieving a high degree of accuracy.

ACKNOWLEDGMENT This work was supported in part by a grant from the National Institutes of Health. M.S. is supported by a fellowship within the Biophysics Program of the European Community. The authors thank Michael Engels for many helpful discussions. The two applications were based on an article on lysozyme in the Journal OfPhysical Chemistly (Schaefer et al., 1997) and an article o n the foot-and-mouth disease virus capsid in the Journal ofMoleculur Biology (van Vlijmen et al., 1998).

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SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS IN PROTEINS By ENRICO DI CERA Department of Blochemlatry and Molecular Biophysics, Washington Univeraity School of Medicine, St. Louis, Missouri 63110

I. Introduction ...................................................... 11. The Reference Cycle ............................................... 111. Structural Mapping of Energetics .................................... . A. Site-Specific Structural Perturbations ............................. B. Linkage between Site-Specific Structural Perturbations and Energetics ................................................. C. Limits of Single-Site Ala Scans ................................... nil. Site-Specific Analysis of Mutational Effects in Proteins .................. A. Double-Mutant Cycles .......................................... B. SiteSpecific Transition Modes ................................... C. Properties of the Coupling Free Energy V. SiteSpecific Dissection of Thrombin Specificity ........................ A. Substrate Recognition by Serine Proteases ........................ B. Thrombin Structure and Function ............................... C. Site-Specific Probes ............................................. D. Perturbation at the Pl-P3 Sites E. Why Is the Fast Form More Specific? ............................. F. Allosteric Mechanism for High-Order Coupling ................... VI. Concluding Remarks .............................................. References .......................................................

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59 61 63 63 66 69 73 73

75 76 79 79

82 87 91 96

102 113 115

I. INTRODUCTION In a seminal paper published 50 years ago in this review series,Jeffries Wyman (1948) introduced the basic idea of linked functions as a general property of any macromolecular system capable of different functions. Wyman pointed out that “whenever a molecule possesses two or more different functions . . . belonging to nearby groups in the molecule, there is the likelihood of an interdependence of the functions due to interaction between the groups.” Two functions coexisting in the same protein may exert reciprocal effects on each other. Wyman proved that if binding of a ligand X influences binding of a ligand Y, binding of Y must influence binding of X and to an extent that can be predicted exactly from the effect of X on Y. Through this reciprocity principle, which is the biochemical counterpart of the analogous Maxwell’s principle involving physical quantities, Wyman brought the rigor of the Gibbs approach (Gibbs, 1875) to the analysis of protein-ligand interactions 59 ADV.WC.%S IN PROTEIN CHEMISTRY, Vol. 51

Copyright 0 1998 hy Academic Press. AU rights of reproduction in any form reserved. 00653233/98 $25.00

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and revealed how thermodynamics could be exploited to infer information on structural properties of the system (Wyman, 1948, 1964). With structural biology still in its infancy,Wyman’s approach inevitably emphasized the functional aspects of protein energetics. This has led to the unfortunate notion in some circles that Wyman’s linkage thermodynamics is a phenomenological theory not concerned with structure and therefore bearing marginal importance in structure-function studies. Since its inception, however, linkage thermodynamics sought to understand the structural origin of effects reflected in the energetic properties of a system. When the principle of linked functions was first enunciated, Wyman was seeking a molecular explanation for the effect of pH on oxygen binding to hemoglobin, the physiological Bohr effect. He hoped to identify structural determinants involved in the proton ionization reactions linked to oxygen binding from the observed linkage between oxygenation and proton release, and the criterion of proximity of the linked groups. This might have enabled a better understanding of the mechanism of heme-heme communication leading to cooperative oxygen binding. Linkage thermodynamics was therefore conceived as a conceptual and methodological tool to extract structural information from energetics. This theory has enjoyed myriad applications in nearly all areas of protein and nucleic acids physical chemistry (Edsall and Wyman, 1958;Wyman and Gill, 1990) and set the conceptual framework for the development of allosteric theory (Monod et aL, 1963, 1965; Koshland et aL, 1966). The extraordinary developments of structural biology and recombinant DNA technology have created the conditions enabling experimentalists to effectively tackle the problem of how energetics and regulatory interactions are encoded into structure. This is an appropriate time to look at Wyman’s theory of linked functions with renewed interest and show how it can contribute to our understanding of structure-function correlations when cast into the more general framework of site-specific thermodynamics (Di Cera, 1995). In this chapter we illustrate how Wyman’s theory of linked functions can be extended to the site-specific analysis of mutational effects in proteins that are at the basis of many current studies of protein folding, enzyme catalysis,and molecular recognition. The site-specific analysis exploits the ability of recombinant DNA technology to perturb macromolecular systems at the level of single amino acids to obtain information on how individual residues contribute to protein stability and ligand recognition (Di Cera, 1995). Site-specific linkage thermodynamics is concerned with local effects and how they add up to generate the global behavior of the system that constitutes the focus of Wyman’s classical approach (Wyman, 1948, 1964; Wyman

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and Gill, 1990). This general theory of cooperativity is aimed at develop ing a mechanistic and structure-based understanding of linked effects from the model-independent analysis of experimental data. It represents a modern incarnation of Wyman’s original idea of inferring structural information on the system from the properties of its linked groups. Throughout this chapter we will make an effort to illustrate the essential aspects of the approach by emphasizing the concepts and making essentially no use of the elaborate mathematical formalism detailed elsewhere (Di Cera, 1995). The goal is to make our discussion readily accessible to experimentalistswho would benefit the most from the ideas and methods illustrated here. 11. THEREFERENCE CYCLE Wyman’s principle of linked functions is best illustrated by a reference cycle (Di Cera, 1995) in which the contribution of specific sites is explicitly taken into account. Many properties of the system can be revealed by direct inspection of the cycle and especially those pertaining to events that arise locally at each site. The reference cycle can be depicted as follows:

OAC,

Moo

MOl

e

MlO

M11

‘AG,

Here M represents the macromolecule subject to reversible transformations due to two distinct processes taking place at sites i and j . It is not necessary to specify the nature of these processes, other than to point out that they induce a transition between two states, 0 and 1. A number of biologically relevant processes are amenable to this description. In ligand-binding processes a given site of the macromolecule switches from the free (0) to the bound (1) state. In helix-coil transitions and protein folding the site is a given residue in the coil (0) or helical (1) state, or in the unfolded (0) or folded (1) configuration. Analogous considerations apply to mutational effects, where each site is a residue that can exist in the wild-type (0) or mutated (1) state. The general applicability of the cycle in Eq. (1) enables the analysis of processes of widely different nature. Ligand binding or folding at a given site can be studied in terms of the effect of binding or folding at

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a second site, or as a function of mutations introduced at other sites. The AG's in Eq. (1) reflect the energetic balance of the transformations in the cycle that generate the four possible intermediates. Depending on the nature of the process under consideration, these terms may refer to binding free energies, free energies of unfolding, or perturbation free energies due to sitedirected mutations. The reference cycle is the elementary conceptual block for understanding the mutual interference of two processes. Combination of reference cycles produces more complex patterns of linkage that are however subject to the same restrictions as is the elementary cycle in Eq. (1). The cycle contains four species. Species Moorepresents the configuration of the macromolecule where the sites are both in state 0. If site i is changed to state 1, there is a free energy change OAG, associated with the reversible 0 + 1 transition that transforms Moointo Mlo. The suffix 0 indicates that the transition takes place with site j in state 0. Likewise, when site j is changed to state 1, there is a free energy change OAG, associated with the reversible 0 + 1 transition that transforms Moointo Mol. The suffix 0 indicates that the transition takes place with site i in state 0. Each of the above transformations can occur when the other site is in state 1.The free energy change for the reversible 0 + 1 transition of site i when site j is in state 1 is lAG,, and likewise 'AG, gives the analogous free energy change for site j when site i is in state 1. The essence of linked functions stems from the dependence of the free energy change for the 0 + 1 transition of a given site on the state of the other site. Linkage exists when 'AG, # OAG,. The effect is reciprocal because of the conservation of free energy in the reference cycle. In going from Moo to MI1,the free energy change is the same along the Moo+ Mlo+ Mll or the Moo+ Mo, + MI1pathways. Hence 'AG, + OAG, = 'AG, + OAG, and necessarily 'AG, # OAG, if 'AG, # OAG,. So, if site j affects site i, then site i must affect site j . Of the four transitions in the cycle, only three are independent, and the free energy difference between the vertical or horizontal transitions is exactly the same. This quantity is the coupling free energy AG, = lAG, - OAG, = lAG - OAG, (Weber, 1975; Jencks, 1981) and measures the interdependence of the effects. If site j affects site i to a certain extent AG,, then site i must affect site j to the same extent. The value of AG, indicates whether the two sites are linked (AG, # 0) or not (AG, = 0) and whether the linkage is positive (AG, < 0) or negative (AG, > 0). In the former case the two sites enhance each other in the process under consideration; in the latter they oppose each other. It should be pointed out that the coupling free energy in Eq. (1) is the same as the free energy for the dismutation reaction Mlo + Mol =

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63

Moo + MI1where the two species Mooand MI1are generated from the parent species Mlo and Mol. This is because each intermediate can be assigned a free energy G to define the A G s in the cycle as OAGi = Go - Go,OAG, = G1- G,'AG, = GI - Gol, 'AG = GI - Go,and the coupling free energy can also be written as AGc = G1 + - GoGI,which is in fact the free energy change for the dismutation Mlo Mol = Moo + Mil. Measurements of the coupling free energy require characterization of only two parallel reactions of the cycle in Eq. (1).This has the practical advantage that information on one process can be obtained indirectly from the cycle by studying another process linked to it. Hence, if the process of interest is not amenable to direct experimental analysis, a suitable linked process can be identified and studied in its place. Implementation of this principle through sitedirected mutations that can be introduced in nearly every system enables the indirect study of processes like conformational and folding transitions that may be difficult to follow directly. In general, mutational effects can be exploited in the analysis of protein energetics using the linkage principles embodied by the cycle in Eq. ( l ) ,as illustrated below.

+

111. STRUCTURAL MAPPINGOF ENERGETICS

A. Site-Specific Structural Perturbations Current studies of protein structure and function emphasize the role played by specific residues in the observed effects. Some studies focus on the domains of the protein involved in recognition of a specific ligand or substrate. Identification of a structural epitope then opens the question of how specific residues contribute energetically to the binding event in the ground or transition state. Assessment of the structural boundaries defining an epitope and the energetic contribution of each residue to binding is instrumental to the subsequent development of small molecules that can either reproduce or inhibit the effects elicited by larger physiological ligands. Such studies benefit a basic understanding of the rules for ligand recognition, as well as more prosaic aspects related to drug design. This approach involves the combination of physical chemistry methods with X-ray crystallography,nuclear magnetic resonance (NMR) spectroscopy and above all, recombinant DNA technology through which the effects of specific substitutions on stability and recognition can be studied. Residues in a protein can be replaced by any of the 20 natural amino acids using sitedirected mutagenesis (M. Smith,

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1985).More recently, this strategy has been extended to unnatural amino acids and the ability to manipulate protein structure and function has been greatly expanded (Judice et al., 1993; Cornish and Schultz, 1994). Other powerful approaches include sitedirected isotope labeling of specific residues (Sonar et al., 1994; Spudich, 1994). A typical course of action in current studies of structure-function correlations starts with the identification of important contacts from the crystal structure. In the analysis of protein stability particular attention is devoted to residues buried in the interior of the protein and arranged in hydrophobic cores (Matthews, 1993; Yu et al., 1995; Shortle, 1996). Attention is also paid to residues engaged in ionic interactions (Meeker et al., 1996), especially if they are screened from the solvent (Milla et al., 1994; Garcia-Moreno et al., 1997). In the analysis of molecular recognition of ligands and substrates obvious targets for mutagenesis are identified from residues involved in polar and hydrophobic interactions in the bound complex (Clackson and Wells, 1995; Castro and Anderson, 1996). In the absence of structural information on the bound protein, general criteria like solvent accessibility can guide the mutagenesis screen (Tsiang et ad., 1995;Dickinson et al., 1996).To a first approximation, residues that are freely accessible on the surface of the protein are optimal candidates for functional epitopes. After a set of suitable targets is identified, perturbations are introduced in the form of sitedirected mutations, usually Ala substitutions. The rationale behind Ala-scanning mutagenesis is that all interactions of a side chain except for the C, are eliminated (Lau and Fersht, 1987; Cunningham and Wells, 1989). The contribution of the deleted groups relative to the methyl moiety of Ala is assessed from the difference between the properties of the wild-type relative to the Ala mutant. Free energies of binding in the ground or transition state or free energies of unfolding are used to quantify the effect of the Ala substitution at any given site. For this strategy to be effective, it is necessary that the Ala substitution eliminates interactions without introducing new properties. In principle, this should be the case for almost all amino acids except Gly, for which the Ala substitution can introduce new apolar interactions. In addition, for Gly and Pro the Ala substitution can introduce perturbations of the protein backbone that become less flexible (Gly -+ Ala substitution) or less rigid (Pro -+ Ala substitution). Alascanning mutagenesis has found myriad applications in the identification and energetic characterization of structural epitopes recognizing specific ligands (Tsiang et al., 1995; Dickinson et al., 1996), or the structural determinants of protein stability (Green et al., 1992;Horowitz and Fersht, 1992; Fersht and Serrano, 1993; Matthews, 1993; Milla et al., 1994; Yu

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65

et al., 1995),enzyme mechanism (Carter and Wells, 1988),and specificity (Dang et al., 1997a; Vindigni et al., 1997a).

Using Ala scans, Clackson and Wells (1995) have identified a hot spot of binding energy in the human growth hormone receptor recognizing the hormone. A small core of residues contributing to binding contains mostly hydrophobic residues and is surrounded by a region of polar and charged residues that participate in recognition to a lesser extent. This finding has potentially important consequences on drug design. In fact, if the functional epitope recognizing a ligand involves only a small number of residues clustered in space, then it becomes possible to mimic the action of large molecules with smaller ones that specifically target the hot spot of binding free energy and elicit the same biological response (Wells, 1996). Such a scenario has been shown to be realistic in the case of the receptor for the cytokine erythropoietin (Wrighton et al., 1996; Livnah et al., 1996). There are cases where the organization of the functional epitope is more complex. Mutagenesis studies of the thrombin-hirudin interaction show that the binding free energy is not localized at preferred regions, or hot spots, but rather is delocalized over the entire surface of recognition and involves many hydrophobic, polar, and charged residues (Wallace et al., 1989; Betz et al., 1991). Dickinson et al. (1996) have used Ala scans of 112 residues of coagulation factor VIIa in an attempt to identify the functional epitope for binding of tissue factor. They find that the residues most important for tissue factor binding do not cluster to define a hot spot but are interspersed among residues that are not important or only marginally so for binding. These findings underscore the difficulty of mimicking hirudin with smaller molecules and make it unlikely that a small analog of the tissue factor will be developed. Another important application of Ala scans has been provided by Tsiang et al. (1995).They have used Ala scans of charged surface residues of thrombin to identify regions that preferentially recognize fibrinogen or protein C in an attempt to dissociate the procoagulant and anticoagulant activities of the enzyme. Their studies have led to the identification of a residue, E217, whose mutation significantly affects fibrinogen binding without compromising recognition of the anticoagulant protein C (Gibbs et al., 1995).Mutation of E217 generates thrombin derivativeswith potential therapeutic application as anticoagulants (Tsiang et al., 1996). The success of these experiments shows the great virtue of Ala-scanning mutagenesis and reveals the plasticity of protein-protein interfaces and the different strategies used by different systems to achieve specificity. However, one should not overlook the fact that these impressive applications of recombinant DNA technology to the study of protein structure

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and function are modern incarnations of a principle formulated in 1895 by the Austrian chemist R. Wegscheider. He was the first to realize that information on individual sites of a molecule could be extracted by studying the effect of structural perturbations on the energetics (Wegscheider, 1895). He successfullyused alkyl derivatives of polybasic acids to infer the p&'s of individual titrating groups. Elegant applications of this approach have been offered by Neuberger (1936) and Edsall (Edsalland Blanchard, 1933) and have contributed enormously to our understanding of sitespecific energetics and to subsequent theoretical (Hill, 1944, 1985; Di Cera, 1995) and computational (Bashford and Karplus, 1991; Gilson, 1993; Yang et al., 1993) analysis of the ionization properties of proteins. Strategies similar to Wegscheider's original approach have been applied to the dissection of the energetics of enzyme-substrate complexes by substituting H for functional groups in the substrate like CH3 (Holler et al., 1973), NH2 (Blanquet et al., 1975), OH (Stubbe and Abeles, 1980), and COOH (Evans and Polanyi, 1936). These strategies can be considered as the immediate predecessors of Ala-scanning mutagenesis studies through which similar perturbations are introduced in a protein.

B. Linkage between Site-Spec& Structural Perturbations and Energetics Once structural perturbations are introduced in the system, it becomes necessary to determine the energetic consequences of the substitutions made. The correct approach is based on the definition of a reference cycle analogous to Eq. ( 1 ) where the perturbation is coupled to the process of interest. In the study of protein stability the cycle is

The 0 + 1 transition at site i [see Eq. ( l ) ] is replaced by the folding of the protein, and 'AGi is the same as the free energy of folding of the wild type, A G , . The same process can be studied after a mutation has been introduced in the system at site j to measure AG,,,,,. The difference AAG = AG,,,,, - A& quantifies the effect of the mutation on the stability of the protein (Horovitz and Fersht, 1992; Matthews, 1993; Shortle, 1996). We see from the cycles in Eqs. (1) and (2) that this difference

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

67

is the same as the coupling free energy of the cycle, which measures the linkage between the stability of the protein and the mutation. When AG, = AAG is positive, the mutation reduces stability. Enhanced stability is reflected by a negative value of AG,, and no effect is seen for AG, = 0. The equivalence between AAG and AG, in the cycle in Eq. (2) puts some important restrictions on the interpretation of experimental data. One of these restrictions is that the effect of the mutation cannot be attributed entirely to the folded state of the protein, as often assumed (Matthews, 1993). In fact, AG, measures the difference in free energy between the folded mutant and wild type relative to the same difference in the unfolded state. To assign AG, entirely as ‘AG,, the difference in free energy of stability between the mutant and wild type in the folded state, one must assume that the free energy of the unfolded state is not affected by the mutation. Under this assumption, stability measurements can be used to derive information on the structure of the folded protein by utilizing the cycle in Eq. (2) and its properties. However, there is overwhelming experimental evidence that this assumption on the unfolded state may be flawed. In a series of careful studies, Shortle and colleagues have demonstrated that mutations of staphylococcal nuclease affect to a large extent the unfolded state of the protein (Shortle et al., 1990; Green et al., 1992; Meeker et al., 1996; Shortle, 1996). The sqme conclusion applies to thioredoxin (Lin and Kim, 1991). In this case, the interpretation of AG, values in structural terms becomes problematic and the straightforward connection between stability and structural perturbations, which is claimed to exist in lysozyme (Matthews, 1993), remains to be demonstrated. An even more serious caveat in studies of protein stability comes from the definition of the unfolded state. In principle, this is an idealized state fully hydrated and devoid of interactions among the protein residues. In practice, this state is approximated by the denatured state of the protein that depends on the method used for denaturation (Makhadatze and Privalov, 1995). Reversible thermal denaturation is the most rigorous way to access the properties of the denatured state and is not equivalent to methods using denaturants like urea and GndHC1. These molecules specifically associate with the denatured state (Schellman, 1990), changing its chemical potential and therefore producing an ensemble of states energetically distinct from the thermally denatured state of the protein. For example, a mutation that opposes interaction of the denatured state with urea produces a AG, < 0 conducive to a stabilization of the folded state. However, there is no aprim’expectation for the same mutation to produce an analogous effect on stability in a thermal denaturation experiment. Similar complications arise in the study of ligand recognition. In this case, a cycle analogous to that in Eq. (2) can be constructed to study

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the effect of sitedirected mutations on binding of a ligand (L) in the ground or transition state as follows:

M*

a

M*L

AGrn",

Here OA Gi measures the free energy of binding L to the wild-type macromolecule, A&. The same process in the mutant gives AG,,,, and the - At!&, = AGc is a measure of the effect of the difference AAG = site-directed mutation on the binding process (Carter et al., 1984; Wells, 1990).As for protein stability, this difference is the coupling free energy of the cycle and measures the linkage between the binding of L and the mutation. The same cycle applies to binding in the transition state, where the free energy is directly related to the specificity constant s = k J K , and AAG = RT ln(h/s,,,,,) = AG,. When AGc > 0, the mutation reduces specificity, whereas enhanced specificity is reflected by AG, < 0 and no effect is seen for AGc = 0. As for protein stability, the effect on the coupling free energy cannot be assigned unambiguously as an effect of the mutation on the bound complex ML, as is commonly done when Ala scans are used to identify structural epitopes. In fact, AG, measures the difference ' A G - OAG, and reflects the perturbation introduced by the mutation on the ML complex relative to the free macromolecule M. If a mutation has AG, > 0 and destabilizes the binding of L, the effect is not necessarily due to destabilization of the complex ML and hence entirely to 'AG. A mutation that stabilizes the free form of the macromolecule (OAG < 0) and has no effect on the bound form ('AG = 0) also gives AG, > 0 and can be confused with a mutation that directly affects recognition of the ligand. In this case, the residue mutated is mistakenly associated with the epitope recognizing the ligand L, although it plays no role in the binding event. A value of AG, > 0 only means that the effect of the mutation has reduced the stability of the complex more than that of the free form. Assignment of the perturbation to the bound complex strictly requires experimental demonstration that the free form of the macromolecule is not affected by the mutation (OAq = 0). In the absence of this information, interpretation of the results may be problematic and must rely on

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

69

other criteria like the spatial proximity of residues affecting ligand binding or the involvement of these residues in ligand recognition based on structural information. Only when the Ala substitution does not alter the properties of the unfolded state or removes contacts important for interaction with the ligand can maps of the regions involved in stability and ligand recognition be constructed from the effect of the mutation on AGc in Eqs. (2) and (3).

C. Limits of Single-Site A h Scans The approach based on Ala scans is in principle very powerful and informative. However, in addition to the complications just dealt with in Section III,B, this approach has a serious limitation that must be kept in mind in practical applications. The limitation is that single-site Ala replacements neglect a priori the contribution of possible site-site interactions to protein stability and ligand recognition. Results from the limited number of studieswhere this problem has been addressed experimentally have fostered the general notion that residues tend to participate independently in stability and recognition (Sandberg and Terwilliger, 1989; Shirley et aL, 1989; Wells, 1990) and that interactions only occur among residues close in space (Carter et al., 1984; Carter and Wells, 1988;Wells, 1990; Horovitz and Fersht, 1992; Mildvan et aL, 1992). However, a number of instances have recently been reported of interactions among residues that can be as far as 30 %, away from each other (Shortle and Meeker, 1986; Perry et al., 1989; Howell et al., 1990; LiCata et al., 1990; Scrutton et aL, 1990; Green and Shortle, 1993;Jackson and Fersht, 1993; Robinson and Sligar, 1993; LiCata and Ackers, 1995). Hence, the role of interactions in mutational effects in proteins cannot be underestimated. There is good reason to believe that interactions are present in nearly every system and provide the most important ingredient to protein stability and ligand recognition, as the following argument demonstrates. A functional epitope for binding or stability composed exclusively of independent residues can be identified solely by single-site Ala substitutions. In this case, the residues of the epitope contribute to the energetics in an additive manner. The key assumption of Ala-scanning mutagenesis is that the Ala replacement has the only effect of eliminating the interactions of the side chain beyond the C, (Lau and Fersht, 1987; Cunningham and Wells, 1989). If this assumption is correct and the Ala replacement is an unbiased probe of the energetic contribution of a given residue to binding, then the Ala mutation at any position of the epitope should convert the free energy contribution to zero. Hence, the sum of the

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free energy losses over all sites in the epitope, with changed sign, should be close to the actual free energy of binding or stability measured experimentally for the wild type. Inspection of the results in Table I for some paradigmatic examples shows that this is far from being the case. A large discrepancy exists between the calculated and experimentally determined values. In the case of human growth hormone binding to its receptor or granulocyte colony stimulating factor binding to its receptor, the binding affinity calculated from the results of the Ala scan is greatly overestimated, and so is the stability of Arc repressor and staphylococcal nuclease. In the case of BPTI binding to t r p i n , tissue factor binding to coagulation factor VIIa, or linolenate binding to intestinal fatty acid binding protein, the binding affinity is grossly underestimated. When the affinity is underestimated, it may be argued that the functional epitope might have been incompletely characterized, thereby missing important interactions. This can hardly be the case for the interaction of tissue factor with VIIa, where 112 residues were targeted by mutagenesis (Dickinson et al., 1996), or intestinal fatty acid binding protein, where 23 important residues in the binding cavity were replaced (Richieri et al., 1997). On the other hand, when the affinity is overestimated, it may be argued that the functional epitope might have included sites of marginal importance. Again, this can hardly be the case in the interaction of human growth hormone with its receptor where the functional epitope is a small hot spot (Clackson and Wells, 1995), or for Arc repressor where the calculated value of stability was taken from the sum of only 11 out of 52 mutated residues (Milla et aL, 1994), or else for staphylococcal nuclease where only the effect of Ala replacements of 14 large hydrophobic side chains was considered (Shortle et al., 1990). The results of intestinal fatty acid binding protein are particularly instructive insofar as they show that the discrepancy between calculated and experimentally determined values depends on the particular ligand examined. The difference changes from - 11.5 kcal/mol for linolenate to 1.4 kcal/mol for stearate. Given the comparable size of the fatty acids listed in Table I and their comparable binding affinity, this large difference cannot be due to intrinsic properties of the ligand. Rather, it suggests the presence of communication among the protein residues that is sensitive to the particular ligand bound. It may seem paradoxical that an epitope containing all residues replaced by Ala should bind a ligand with a A G = 0, regardless of the system studied, if the residues are truly independent. A binding free energy of zero means that the ligand experiences no net energetic change in going from the free to the bound state and that the all-Ala binding epitope is energetically neutral. Similar arguments apply for

TABLE I Comparison of Free Energy Values (in kcal/mol) fw Stability and Ligand Recognition Measured Experimentally and Calculated jiom SingMite A h Scans" System

Process

Ala replacements

A Gd

A G.,

AAG

Reference

Arc repressor Staphylococcal nuclease hGH-hGHbpd BF'TI-chymotrypsin' VIIa-TFJ I-FABPE (palmitate) I-FABPg (stearate) I-FABPC (oleate) I-FABPC (linoleate) I-FABPg (linolenate) I-FABPg (arachidonate) GCSF-GCSF receptor*

Unfolding Unfolding Binding Binding Binding Binding Binding Binding Binding Binding Binding Binding

51' 14' 30 15 112 23 23 23 23 23 23 27

58.2 39.1 -25.9 -6.4 -9.7 -6.8 -13.1 -8.5 -5.4 2.4 -3.6 -14.5

13.8 5.5 -12.3 -10.7 - 15.4 - 10.9 -11.7 -10.7 - 10.0 -9.1 -9.5 -11.3

-44.4 -33.6 13.6 -4.3 -5.7 -4.1 1.4 -2.2 -4.6 -11.5 -5.9 3.2

Milla et al. (1994) Shortle et al. (1990) Clackson and Wells (1995) Castro and Anderson (1996) Dickinson et al. (1996) Richieri et al. (1997) Richieri et al. (1997) Richieri et al. (1997) Richieri et al. (1997) Richieri et al. (1997) Richieri et al. (1997) Young et al. (1997)

a AGd was calculated as the sum of the individual free energy perturbations, with changed sign, due to Ala replacement at individual sites. AAG measures the difference between the experimentally determined free energy for the process taking place in the wild type,AGq, and AGd. * Only the Ala replacements of residues W14, N29, M 1 , S32, E36, R40,S44, K47, E48, and R50 forming hydrogen bonds and ion-pairs protected

from the solvent were included in the calculations. ' Only the Ala replacements of large hydrophobic residues were included in the calculations. Human growth hormone (hGH) binding to the extracellular domain of its first bound receptor (hGHbp). Bovine pancreatic trypsin inhibitor (BPTI). /Tissue factor (TF) binding to coagulation factor VIIa. 8 Intestinal fatty acid binding protein (I-FABP). Granulocyte colony stimulating factor (GCSF).

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protein stability. Although this scenario is hypothetical, its validity within reasonable energetic terms is key to the approach based on Ala scans. If the large discrepancy in Table I is the result of specific favorable or unfavorable contributions to stability and recognition introduced by the presence of Ala at any given site, the assignment of epitopes with Alascanning mutagenesis becomes context dependent and questionable. It is possible that Ala replacements may introduce additional properties at the site of mutation and that these properties may bias the energetic balance of the substitution. However, this bias is likely to be small. It is more reasonable to conclude that the large discrepancy documented in Table I underscores a more serious and general problem, i.e., the neglect of energetic contributions arising from possible site-site interactions that cannot be quantified by single-site Ala scans. In the case of protein stability, the presence of interactions is the obvious result of the highly cooperative nature of the folding process (Privalov, 1979; Creighton, 1990; Dill, 1990). In the case of ligand binding, the presence of cooperativity in the recognition event may be the signature of some general rules through which biological specificity is encoded into the structure of a protein. When interactions among residues are present in the system, the analysis must be cast in terms of double, triple, and higher order perturbations. The presence of interactions obviously invalidates the energetic assignments derived from singlesite Ala scans, because the contribution of a given residue to stability or ligand binding will depend on the state (wild type or mutated) of other residues. The extent to which interactions affect the assignments based on single-site Ala scans must be evaluated in each case and clearly complicates the identification of epitopes such as those reported for the proteins listed in Table I. This problem about single-site Ala-scanning mutagenesis studies of protein structure and function poses challenging tasks from an experimental standpoint, as will be discussed in Section IV,below. In a cooperative process like protein stability or ligand recognition the contribution of a given residue involves effects of multiple order. A first-order contribution comes from contacts made directly with the ligand, or with another residue in the protein. Higher order contributions may come from the coupling between the residue and other structural components. For example, the residue may contribute to recognition of the ligand by forming an ion pair with another residue of the protein. In this case, disrupting the interaction with an Ala substitution perturbs ligand binding but also the ion pair. To dissect the contribution coming from the ion pair, one should know what effect on ligand binding is caused by the Ala replacement of the other residue forming the ion

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

73

pair and compare the results with the double Ala replacement at both residues. This requires the construction of the two single mutants and the double mutant. In general, the residue recognizing the ligand may be involved in a number of interactions with other residues, like shortrange van der Waals coupling, long-range electrostatic coupling, or even large-scale conformational transitions. In the case of protein folding where the close packing of residues in the hydrophobic core may represent a crucial determinant for stability (Dill, 1990), the contribution of a residue clearly involves strong interactions with other residues and cannot be assessed solely from single-site substitutions. For second-order interactions, double mutations are necessary to assess the energetic contribution to stability and ligand recognition. In the case of higher order interactions, triple and quadruple substitutions become necessary. If an epitope contains Nresidues, a complete singlesite Ala scan requires N mutations and a double-site Ala scan requires N(N - 1)/2 mutations. The problem of correctly assessing the energetic contribution of residues in a functional epitope using sitedirected mutational perturbations is therefore a complex one and demands elucidation of site-site coupling patterns. This makes it necessary to develop a systematic theory for the analysis of mutational effects in proteins where the role of interactions is explicitly taken into account.

IV. SITESPECIFIC ANAL.YSIS OF MUTATIONAL EFFECTSIN PROTEINS A. Doubh-Mutant C’chs Consider the general case of a system composed of Nsites that can exist in two states, 0 and 1. In what follows we will assume that state 0 is the unperturbed wild-type state of the site, while state 1is the perturbed or mutated state. The system so constructed has a total of 2Npossible configurations, ofwhich 2N- 1 are independent if the wild-type configuration is taken as reference and used to scale all others energetically. It is convenient to associate each configuration with an Ndimensional vector of binary digits, 0 and 1, that depict the states of a site. The vector labels are arranged in a preassigned order, usually lexicographic. For example, the vector [OOll] labels one of the 16 possible configurations of a system containing four sites ( N = 4), where sites 1 and 2 are in the wild-type state and sites 3 and 4 are mutated. In general, a given configuration can be represented with the vector [a/3. . . 01 , where a, p, . . . , w = 0, 1. The first index refers to site 1, the second index to site 2, and so on, up to the w index for site N.

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Let AG, be defined as the free energy change associated with the 0 + 1 transition at site j when all other sites are in state 0. This term is the difference in free energy between the configuration with site j perturbed and the wild type resulting in the loss (AG, > 0) or gain (AG, < 0 ) of specificity or stability due to the first-order perturbation of that site. There are Nsuch terms to be taken into account, one for each site. Consider, then, the double perturbation at sites i and j . The free energy change for such perturbation can be written as the sum A GI A G AG,, where AG, is the interaction free energy between sites i and j when the perturbation is applied at both sites; AG, is the same as the coupling free energy in the thermodynamic cycle:

+

+

M*

a A G,

D

A G+ ~ AG,,

(4)

M*@

+ A G,,

where * and denote the two different perturbations at sites i and j . A negative value of AG, indicates positive coupling between the perturbations at sites i and j in enhancing specificity or stability, or negative coupling in reducing it, and vice versa for a positive value. A value of AG, = 0 indicates the absence of coupling between the perturbations at sites i and j; AG, is also the free energy change for the dismutation reaction M* M@= M + M*@. Since there are N sites, there are N(N - 1)/2 independent secondorder coupling free energies. Information on these terms is necessary to assess the extent of interactions between pairs of sites. Interactions that involve higher order coupling among three, four, up to Nperturbations can be analyzed in a similar manner. For example, the triple perturbation at sites i, j , and I can be written as AG, + A 5 + AG, + AGYl,where AG,, is the free energy of the dismutation M* + M@ + M' = 2M + M*@€and defines one of the N(N - 1 ) ( N - 2)/6 independent third-order coupling free energy values of the system. In general, any one of the N!/ ( N - k) !k! kth-order coupling free energies can be associated with the free energy change of the dismutation where the k singly perturbed configurations generate the configuration with k perturbed sites and k - 1 copies of the unperturbed configuration. The sum of all perturbation free energies A y s and the coupling free energies up to Nth order gives a total of 2N-1independent terms, equal to the number of independent configurations in the system of N sites. @

+

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

75

Previous discussions of double-mutant cycles have emphasized the importance of dissecting the interaction between residues in the analysis of protein stability and ligand recognition (Carter et al., 1984; Ackers and Smith, 1985; Shortle and Meeker, 1986; Horovitz and Fersht, 1990; Wells, 1990; Mildvan et al., 1992; LiCata and Ackers, 1995). Particularly important has been the analysis by Horovitz and Fersht (1990), who were the first to point out that these cycles can also be used to dissect more complex interactions involving multiple sites. Our approach differs from all previous analyses of the same problem insofar as it exploits the principles of site-specific thermodynamics- (Di Cera, 1995) and their general applicability to ligand binding, protein folding, and mutational perturbations. This approach captures the essence of the cooperative interactions among the sites through some basic properties of the free energy for the 0 + 1 transition at any site and the coupling free energy of double-mutant cycles to be discussed below. These properties provide clues on the mechanism underlying site-site coupling independent of any a prim' assumption.

B. Site-SpeciJc Transition Modes Current mutational studies of proteins use single-site Ala scans to assess the energetic contribution of individual residues to stability and ligand recognition. The scan provides information on Nsite-specific free energies of perturbation, A q s , obtained from the difference between the properties of the N single-site mutants and wild type. This is a minuscule amount of information compared to the other 2N- N - 1 coupling free energy terms that are necessary to fully describe the energetic balance of the perturbations. The coupling free energies are all zero if perturbations are additive and sites are independent. However, in the presence of nonadditivity and site-site coupling, the coupling free energies are finite and affect the response of the system to mutational perturbations at any given site. The nontrivial consequence of nonadditivity is that the energetic contribution of a residue to stability and ligand recognition depends on the state of other residues and changes as mutations are introduced at other sites. This immediately raises the question of defining the energetic cost of a mutation. An unambiguous answer to this question is only possible for the case N = 1, or in the absence of site-site coupling. For N 2 2 the state of other sites must be specified when the energetic cost of perturbing a given site is considered. The free energy cost of a perturbation reflects the free energy change associated with the 0 + 1 transition at the site. When the site is independent from the rest of the system,

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the free energy spent in its 0 + 1 transition is equal to AG, and can be obtained from a scan involving only single-site substitutions. When the site is coupled to the rest of the system, the result depends on the configuration of other sites. For a given mutation at site j there could be as many as 2"'-' different values of the free energy of perturbation, one for each independent configuration of the remaining N - 1 sites. All values bear equal importance, because they are associated with independent configurations accessible to the system. Hence, in the presence of site-site interactions one should consider a distribution of free energies of perturbation rather than thefree energy of perturbation at a given site. The values defining the distribution of free energies for the 0 + 1 transition represent the modes accessible to the site in all possible configurations of the other sites. The properties of the distribution of transition modes have been studied in great detail for Ising lattices where sites are equivalent and interact with all other sites. In this paradigmatic case, the distribution of free energy values is Gaussian, with a standard deviation that measures the average strength of interaction between pairs of sites (Keating and Di Cera, 1993). The distribution of transition modes for specific cases can be interpreted to a first approximation in terms of the properties of the Ising lattice model, with the mean and standard deviation of the distribution taken as measures of the susceptibility of the site to the perturbation and the strength of coupling with other sites. These parameters are derived from the ensemble of configurations accessible to the system and provide a more realistic assessment of the energetic contribution of a given site to stability or ligand recognition.

C. pfoperties of the Coupling Free Energy As for the site-specific perturbation free energy, the coupling between two sites may be subject to the state of other sites in the system. This problem was first approached by Horovitz and Fersht (1990) in the analysis of double-mutant cycles. They concluded that by comparing the values of the coupling free energy in a cycle in the two states, wild type and mutated, of a third residue it is possible to assess whether the third residue affects the interaction between the two sites. This approach can be extended to an arbitrary number of sites by constructing a hierarchy of perturbed cycles: first, the effect of a third site is examined on the coupling between two sites; then, the effect of a fourth site is studied on the coupling between the third site and the first two sites; and so forth. This approach is somewhat cumbersome and overlooks a basic

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

77

property of the coupling between two sites that is key to unravel the mechanism of site-site interaction. The coupling free energy between two mutations at sites i and j has been defined in the double-mutant cycle in Eq. (4) by implicitly assuming that all other sites are in state 0. Since the system contains N sites and sites i and j may be linked to each other and also to other sites, in general other sites may influence the coupling between sites i and j . By studying how the coupling between any two sites is affected by the configuration of other sites, much information can be gained on the mechanism of coupling. A cycle analogous to that in Eq. (4) can be drawn for any configuration of the other N - 2 sites. There are 2N-2 such configurations and N(N - 1)/2 distinct pairs of sites, i and j , leading to a total of N(N - 1)/2”’ possible thermodynamic cycles and coupling free energies. Not all these cycles are independent. In fact, the energetics of the system are fully described in terms of 2N - 1 independent terms, Nof which are site-specificfree energies of perturbation A q ’ s and the remainder are coupling free energy terms from second up to Nth order. Since no additional information can be generated by constructing double-mutant cycles beyond that embodied by the independent coupling terms, of the N(N - l ) Y 3possible cycles only 2N1 - Nare necessarily independent. However, for any given pair of sites i and j, the 2N-3coupling free energy values are all independent. Once coupling free energies are calculated for all possible configurations of the system, it is possible to decipher the code for site-site interactions by using the following property of a thermodynamic cycle whose proof is given elsewhere (Di Cera, 1995):

If the coupling between two sites is direct and involves on4 second-mder interactions, then the couplingj-ee energy is i n d e p e n h t of the configuration of other sites. Otherwise, the coupling is indirect and involves interactions higher than second order.

To understand the significance of this property of the coupling free energy, it is useful to consider two key examples of direct and indirect coupling. An example of direct coupling is provided by models of nearest neighbor interactions, like the Ising model (Wang and Di Cera, 1996) or the Koshland-Nemethy-Filmer model of ligand binding cooperativity (Koshland et al., 1966). In these models, interactions involve pairs of sites and are therefore second order in terms of the model-independent site-specific formalism (Di Cera, 1995). No matter how two sites are linked to each other and to any other site, the coupling between them remains energetically the same as the system changes its configuration.

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This has the nontrivial consequence that when the coupling between a pair of sites is not affected by a third site, one cannot conclude that the third site is not coupled to the pair as the Horovitz-Fersht approach would imply (Horovitzand Fersht, 1990). In fact, in any nearest neighbor model where the third site is coupled to each site in the pair, the state of the third site is inconsequential on the coupling free energy of the pair. Though somewhat counterintuitive, this conclusion can be proved in a rigorous manner (Di Cera, 1995) and provides an important reference point for the correct interpretation of coupling free energy profiles. Indirect coupling manifests itself in a more obvious manner. An example of indirect coupling is provided by the Monod-Wyman-Changeux model of concerted allosteric transitions (Monod et d., 1965) where interactions involve all sites through a linked global conformational change. As a result, sites are always positively coupled and the order of coupling changes according to the state of other sites as the protein switches from one state to another. The widely used mechanisms of cooperativity discussed above make very unrealistic predictions on the properties of the coupling free energy. In the case of nearest neighbor interactions, the prediction is that the coupling free energy between two sites will not depend on the state of other sites, while the concerted two-state model predicts coupling free energy values that change with the state of other sites but are always negative. There is obviously no a priori reason why the coupling between two sites should be independent of the state of other sites or it should always be negative. As we shall see in practical applications, coupling free energies are often positive, contrary to the prediction of the concerted allosteric model, and also change with the state of other sites, contrary to the prediction of any nearest neighbor model. This calls for more elaborate descriptions of cooperativity that merge the basic tenets of the two models. The underlying implication of the foregoing property of the coupling free energy is that basic mechanisms of coupling like direct nearest neighbor interactions or indirect, concerted allosteric transitions can be identified from the analysis of double-mutant cycles. Critical to the implementation of this approach is the availability of a highdimensional manifold of perturbations where the coupling between two sites can be studied in terms of a large number of configurations of other sites in the system.This poses challenging tasks from an experimental standpoint because the construction of triple or higher order mutants in a protein is clearly problematic. However, this approach appears to be ideally suited for the site-specific dissection of ligand recognition when most of the perturbations are introduced in small peptides that bind to the

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

79

protein. A detailed characterization of enzyme specificity can be obtained through the combination of perturbations in the ligand and the protein that generates the complexity necessary to dissect the high-order interactions in the system. A paradigmatic example of how this approach can be implemented in practice in the study of protein structure and function is offered next in Section V, dealing with the energetic origin of thrombin specificity.

V. SITE-SPECIFIC DISSECTION OF THROMBIN SPECIFICITY A. Substrate Recognition by Serine Proteases Serine proteases of the chymotrypsin family (Rawlings and Barrett, 1993, 1994) participate in key physiological functions like digestion, blood coagulation, fibrinolysis, and complement activation (Neurath, 1984; Perona and Craik, 1995). Proteases involved in digestive processes, like trypsin, have wide specificity and are also found in organisms as primitive as eubacteria. In contrast, proteases involved in the more specialized functions of blood coagulation, fibrinolysis, and complement activation have narrow specificityand are found almost exclusivelyin vertebrates (Doolittle and Feng, 1987; Patthy, 1990).Among these more evolved proteases, activity and specificity is controlled allosterically by the binding of Na+,whereas more primitive proteases and those involved in fibrinolysis are apparently devoid of such regulation (Dang and Di Cera, 1996). Serine proteases share a common fold composed of two six-stranded Pbarrels of similar structure that pack together asymmetrically to host at their interface the residues of the catalytic triad H57, D102, and S195 (Lesk and Fordham, 1996). The catalytic triad polarizes the side chain of the active site S195 for a nucleophilic attack on the C atom of the scissile bond of the substrate. The C atom is converted into a tetrahedral intermediate in the transition state, which is stabilized by hydrogen bonds between the charged carbonyl 0 atom of the peptide group of the scissile bond and the amide hydrogen atoms of G193 and S195 forming the oxyanion hole. The substrate is then acylated by the 0, atom of S195 after transfer of a proton to H57 and its Gterminal fragment is released. Deacylation is catalyzed by the nucleophilic attack of a water molecule that releases the carboxylic acid product and the N-terminal fragment of the substrate restoring the state of the catalytic triad. D102 anchors H57 in the correct orientation for proton transfer from and to S195, compensating for the developing positive charge (Warshel et az., 1989).

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Although serine proteases have a common catalytic mechanism, they differ widely in specificity. The molecular origin of this difference remains elusive. The preference of trypsin-like enzymes for Arg residues is due to the presence of D189 at the bottom of the catalytic pocket. Replacement of G216 and G226 by Ala in trypsin mimics the molecular environment of elastase, partially occludes the primary specificitypocket, and changes the specificity from Arg to Lys residues (Craik et aL, 1985). However, these substitutions fail to elicit the expected preference for amino acids with small hydrophobic side chains as found in elastase. In chymotrypsin, residue 189 is a Ser and the preference is for bulky aromatic side chains. However, the D189S replacement in trypsin does not result in a chymotrypsin-like specificity. This is instead obtained by exchange of the chymotrypsin surface loops 185-188 and 221-225 with the homologous regions in trypsin (Hedstrom et al., 1992), though none of the residues in these loops contacts the bound substrate. These observations suggest a molecular basis for protease specificity that may involve multiple critical sites. A useful framework to approach the study of protease specificity takes into account the interactions made by the enzyme with the substrate (Schechter and Berger, 1967). Residues of the substrate interacting with the enzyme are labeled with a P and a number from 1 to N, starting from the scissile bond and moving to the N-terminus. Residues of the enzyme making contacts with the substrate are called specijicity sites and are labeled with an S. The amino acid at P1 of the substrate makes contacts with the specificity site S1 of the enzyme, P2 contacts S2, and so forth. The P residues of the substrate are necessarily contiguous in sequence, whereas this restriction does not apply to the S residues of the enzyme. Residues on the Gterminal portion of the scissile bond of the substrate are numbered P l ’ , P2’, and so forth, and the corresponding specificity sites on the enzyme are Sl’, S2’, and so on. The scissile bond is positioned between P1 and PI’. The existence of multiple recognition sites effectively narrows down specificity by reducing the probability that the required sequence is found in a random sample of potential substrates. The longer the consensus sequence interacting with the enzyme, the smaller the probability that it will occur in another potential substrate. The best illustration of the effectiveness of this strategy is provided by the bloodclotting proteases (Davie et al., 1991). These enzymes have a trypsin-like primary specificity and cut substrates at Arg residues. However, they do so with extraordinary selectivity because of several other interactions made by the substrate with the enzyme. For example, the vitamin Kdependent factors Xa, thrombin and activated protein C are highly homologous in

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

81

sequence and have a similar three-dimensional structure (Bode et al., 1992; Padmanabhan et al., 1993; Mather et al., 1996). Yet, factor Xa is the only protease in the blood that can generate thrombin from prothrombin and thrombin is the only protease that can activate protein C. The subtlety of the molecular strategy to achieve specificity in these enzymes is astounding. For example, the chromogenic tripeptide substrate Asp-Arg-Arg-pnitroanilide is 67-fold more specific for thrombin than activated protein C when Asp at P3 is in the L enantiomer, whereas it is 22-fold more specific for activated protein C than thrombin when Asp at P3 is in the D enantiomer (Dang and Di Cera, 1997). Understanding the molecular origin of specificity in serine proteases is important for structure-function and evolutionary studies and also bears on rational drug design. In the case of a serine protease like thrombin, an orally available active-site inhibitor could offer a safer alternative to anticoagulants like warfarin and heparin (Stirling, 1995; Grinnell, 1997). In some cases, the optimal sequence of an inhibitor can be deduced from that of a natural substrate. For example, the first chromogenic substrates and active-site inhibitors of thrombin were synthesized after the sequence of fibrinopeptide A (Blomback et al., 1969; Svendsen et al., 1972). Highly selective substrates for activated protein C have been designed after the sequence of the natural substrate Va (Dang and Di Cera, 1997). In general, this information may not be sufficient if the natural substrate interacts with the enzyme through residues that are distant in sequence although close in spatial arrangement due to a precise tertiary structure that cannot be mimicked by a short peptide. Structure-function correlations are often used in this case and form the basis of the empirical approaches of medicinal chemistry (Claeson, 1994). This entails the synthesis and laboratory testing of substrate libraries containing hundreds of molecules. A modern but equally empirical incarnation of the same strategy is phage display (G. P. Smith, 1985; Smith and Petrenko, 1997) and its extension to the method of peptides on phage (Scott and Smith, 1990; Devlin et aL, 1990; Cwirla et al., 1990; Ding et al., 1995). A rational approach to specificity in serine proteases must address two critical questions: What is the free energy cost of a replacement made at a P or S site? And do these sites contribute to recognition independently or cooperatively? These questions are central to the analysis of mutational effects discussed earlier in Section IV.The free energy cost of a given perturbation can be estimated from the distribution of values obtained by perturbing all recognition sites. The coupling pattern between pairs of substitutions can be identified in a similar manner leading to important information on the mechanism of linkage. Construction

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of an ad hoc set of perturbations in the sites involved in the recognition event enables the identification of the energetic signatures of specificity.

B. Thrombin Structure and Function The serine protease thrombin is capable of two important and opposite roles that are at the basis of the efficiency of blood coagulation (Fenton, 1988; Mann et al., 1990; Davie et al., 1991; Gailani and Broze, 1991; Berliner, 1992; Grinnell, 1997; Di Cera et al., 1997). The procoagulant role entails the conversion of fibrinogen into the insoluble fibrin clot, the promotion of platelet aggregation, the stabilization of the ensuing clot by activation of factor XIII, and the feedback enhancement of its own generation from prothrombin by activation of factors V, VIII, and XI. The anticoagulant role involves the thrombomodulin-assisted conversion of protein C into an active component that cleaves and inactivates factor Va together with protein S, thereby limiting the conversion of prothrombin into thrombin catalyzed by the prothrombinase complex. In addition to its primary roles in coagulation, thrombin elicits a variety of important effects on a number of cell lines upon binding to its receptors (Vu et al., 1991; Grand et al., 1996; Ishihara et al., 1997). A list of natural substrates for thrombin is given in Table 11. With the exception of the newly identified second thrombin receptor, there is a consensus Arg at P1. There seems to be little conservation at other sites around the cleaved bond. A striking difference emerges from the comparison of fibrinogen and protein C insofar as this substrate carries TABLEI1

Site of Cleavage ( ) ty Thrombin on Natural Substrates Substrate

Sequence

Reference

Fibrinogen (Aa chain) Fibrinogen (BP chain) Factor XI11

FLAEGCGVRJ GPRVVERH

Rlornback (1969)

NEEGFFSAR~GHRPLDK

Blomback (1969)

TVELEGVPRJ GVNLQQ

Factor VIII Factor V Factor VII Thrombin receptor 1 Thrombin receptor 3 Protein C

LSNNAIGPRJ SFSQNSRHP RLAAALGIRJ S F R N S SLNQ RNASKPQGRJ IVGGKVCPK ATNATLDPR 4 S FLLRNPND LAKPTLP I K J T F R G A P P N S NQGDQVDPR J L I DGKMTRR

Takagi and Doolittle (1974) Eaton etal. (1986) Mann et al. (1988) Hagen et al. (1986) Vu et al. (1991) Ishihara et al. (1997) Foster and Davie (1984)

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

a3

Asp at P3 and P3', where fibrinogen has Gly or Ser (P3) or Arg (P3') residues. This suggests that the specificity site S3 of thrombin cannot be the same for fibrinogen and protein C and that a conformational transition must take place when thrombin switches from a procoagulant to an anticoagulant factor. This transition is linked to the release of Na+ from its site, leading to the fast-slow conversion of the enzyme (Wells and Di Cera, 1992). Na+ is required for the optimal conversion of fibrinogen into fibrin monomers, which is catalyzed by the fast (Na+-bound) form with high specificity. The slow (Na+-free) form of thrombin performs the same task with much lower specificity. This form, on the other hand, has higher specificity than the fast form toward protein C (Dang et aL., 1995, 1997a; Berg et al., 1996; Rezaie and Olson, 1997). Na+is the most important ligand of thrombin because of its ubiquitous presence in the physiological milieu where the enzyme functions in vivo. The fact that the Na+concentration is tightly controlled in the blood does not detract from the importance of Na+ as the key effector of thrombin function. In fact, Na+ is actively exchanged in the transition state upon binding of fibrinogen or protein C, just as the proton of the active site histidine is actively exchanged during catalysis although the pH of the solution remains constant. Since fibrinogen binds to the fast forms with higher affinity, it promotes the slow+fast conversion and Na+ binding. On the other hand, binding of protein C promotes the fast-slow conversion and Na+release. Hence, the notion that a constant concentration of Na+in the blood must result in a constant saturation of the Na+site during all steps of thrombin catalysis or ligand recognition contradicts the very basic principles of linkage thermodynamics (Wyman, 1948,1964) and is fundamentallywrong. Na+binding and dissociation are the key molecular events that control substrate recognition by thrombin. Thrombin is composed of two polypeptide chains of 36 (A chain) and 259 (B chain) residues that are covalently linked through a disulfide bond (Bode et al., 1992). The B chain carries the functional epitopes of the enzyme and has an overall architecture similar to that of pancreatic serine proteases (Fig. 1 ) . The extraordinary specificity of thrombin toward fibrinogen arises not only from contacts made in the interior of the active site (see below) but also from interactions with exosite I located about 20 away from the active site (Martin et aL, 1992; Stubbs et al., 1992). This region is homologous to the Ca2+-bindingloop of trypsin and chymotrypsin, is rich in positively charged residues, and is stabilized by the side chain of K70 that permanently substitutes the Ca2+.Exosite I serves as an extended primed recognition site. Binding of hirudin derivatives or thrombomodulin to this site also allosterically enhances Na+ binding and switches the enzyme to the fast form, thereby changing activity and specificity (Ayala and Di Cera, 1994; Guinto and Di Cera,

A

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FIG.1. Ribbon rendering of the B chain of human thrombin in the fast form derived from the thrombin-himdin complex (Rydel et al., 1991) with the inhibitor removed. The side chains of the catalytic triad are shown and occupy the interface between the two @barrel domains. The catalytic triad is located about 20 A away from the bound Nat (circle). Important regions of the enzyme are noted.

1997; Vindigni et al., 199713).Another factor that influences thrombin specificity is the W60d insertion loop, which is unique to thrombin and shapes the apolar specificity site S2. This loop narrows significantly the access to the active site by protruding into the solvent. Replacement of W60d with the less bulky Ala or Ser profoundly affects the interaction of thrombin with the natural inhibitor antithrombin I11 (Rezaie, 1996) or fibrinogen (Guinto et al., 1995; Guinto and Di Cera, 1997). A similar function has been hypothesized for the autolysis loop shaping the lower rim of the access to the active site, but proteolytic cleavage of this loop produces no significant functional changes (Hofsteenge et aZ., 1988; Brezniak et al., 1990). Deletion of the entire loop, however, results in a selective loss of fibrinogen binding (Dang et aZ., 1997b). The Na+ binding site (Fig. 2) displays octahedral coordination involving the carbonyl 0 atoms of R221a and K224 and four buried water

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

85

FIG.2. Molecular environment of the Nat binding site of thrombin (1hah.pdb) and the conspicuous network of water molecules embedding the region. The hydrogenbonding network involves the bound Na+, 17 water molecules (gray circles), and several protein atoms (dark circles). Some hydrogen bonds (continuous lines) are conserved topologically with trypsin, which does not bind Na'. Others (dashed lines) are specific to thrombin. The bound Na' is octahedrally coordinated by the carbonyl 0 atoms of K224 and R221a and four water molecules (419, 416, 445 and 447). The side chain of D189 is nearby, with water 447 mediating a contact between 0%of D189 and the bound Na'.

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molecules that are tetrahedrally coordinated by protein atoms and other water molecules (Di Cera et al., 1995; Zhang and Tulinsky, 1997) that altogether define a complex hydrogen-bonding network within the catalytic pocket (Krem and Di Cera, 1998). Some of the hydrogen bonds in the network are conserved with trypsin (Bartunik et al., 1989). Others are specific to thrombin and are associatedwith Nat and its coordination shell. The bound Na+ is located 15-20 away from the catalytic triad and lies within 5 from D189 in the specificity site S1 with a water molecule mediating a hydrogen-bonding interaction between the bound Na+ and 0, of D189. The Na+ site lies within a cylindrical cavity formed by three antiparallel P-strands of the B chain (M180-Y184a, Y225-Y228, V213-C220), diagonally crossed by E188-El92 and shaped by the loop D221-K224 connecting the last two P-strands (Fig. 3). The sequence C220-G226 involving the Na+-bindingloop and part of the last P-strand of the B chain is absolutely conserved in thrombin from 11 different species, from hagfish to human (Banfield and MacGillivray, 1992), s u p porting the importance of Na+ binding in thrombin function. A crucial residue controlling Na' specificity in thrombin and all serine proteases of the chymotrypsin family (Rawlings and Barrett, 1993, 1994) is Y225, whose mutation to Pro abolishes Na+ binding (Dang and Di Cera, 1996) and produces a thrombin stabilized in the anticoagulant slow form that has enhanced specificity toward protein C (Dang et al., 1997a). The Nat site also appears to be stabilized by three ion pairs: R221a is ion paired to El46 of the autolysis loop; K224 is ion paired to E217; D221 and D222 form a bidentate ion pair with R187 (Fig. 3). The effects of altering the bidentate ion pair are revealed by the double mutant D221A/D222K made to mimic the sequence found in factor Xa in the same region (Di Cera et al., 1995). This mutant is stabilized in a conformation that is intermediate to the slow and fast forms, with reduced activity toward fibrinogen but enhanced activity toward protein C. There is no evidence of bound Nat in the crystal structure of this mutant, and disruption of the ion pair makes the segment portions of the 184 loop completely disordered (Zhang, Tulinsky, Guinto, and Di Cera, unpublished results). The effects of disrupting the R221aA-El46 are revealed by the properties of the natural mutant thrombin Salakta (Miyata et al., 1992), E146A, that has a reduced clotting activity. The R221aA mutant displays similar properties and has reduced Na+ binding (Dang et al., 1997a). Disruption of the K224-E217 ion pair in the E217A mutant produces a drastic loss of clotting activitywith a modest reduction of protein C activation (Gibbs et al., 1995). The K224A replacement produces similar effects and reduced Na' binding (Dang et al., 1997a).

A

A

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

87

FIG.3. Contacts between the irreversible inhibitor H-mPhe-Pro-Arg-CH&I and the active site of thrombin (Bode et al., 1992). Shown are the thrombin residues D189, P60c, W60d, L99, and W215 that interact with the inhibitor. The guanidyl group of the Arg at P1 makes an ion pair with the carboxyl group of D189 at S1 at the bottom of the active site. Pro at P2 packs optimally in the S2 apolar cavity provided by the W60d loop. H-LIPhe at P3 makes favorable hydrophobic contacts in the cleft with L99 and especially a perpendicular alyl-aryl edge-on interaction with W215 at S3. The D enantiomer of Phe at P3 enables it to interact favorably with the aromatic moiety at S3 with minimum strain in the backbone of the inhibitor, fixed by Pro at P2. Also shown are the residues of the catalytic triad the backbone of the 215-224 segment comprising the Na+ (circle) binding loop. R221a is ion paired to El46 in the neighbor autolysis loop, whereas K224 is ion paired to E217.

C. Site-Specijic Probes

The molecular strategy used by thrombin to achieve specificity toward fibrinogen and protein C is deeply rooted in the mechanism through which Na+ binding affects the environment of the active site of the

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enzyme. Recent attempts to crystallize the slow form of thrombin (Zhang and Tulinsky, 1997) have documented extraordinarily small changes compared to those of the fast form. Based on these structural results, the slow and fast forms of thrombin should be functionally equivalent. Since there is overwhelming experimental evidence to the contrary (Wells and Di Cera, 1992; Ayala and Di Cera, 1994; Dang et al., 1995, 1997a; Vindigni and Di Cera, 1996; Di Cera et al., 1997; Vindigni et al., 1997a,b), a more effective approach to understanding the molecular origin of thrombin specificity should emphasize the functional energetics using the strategy already outlined in Section IV. The main question is how the Na+-induced slow-fast conversion enhances specificity toward fibrinogen and small chromogenic substrates. A related question is which allosteric form should be targeted with activesite inhibitors to guarantee optimal specificity. In both cases, much information can be gained from a dissection of the energetic contribution of the specificity sites. Current studies of enzyme specificity employ libraries generated from combinatorial chemistry or phage display to identify consensus sequences for binding. Substrates generated in this manner, however, can be used as powerful probes of the molecular environment of the specificity sites of the enzyme to elucidate how they contribute to recognition in the transition state. The theoretical developments outlined in Section IV make it possible to unravel sitespecific contributions to binding from the effects of small ad hocperturbations introduced in the system. If the perturbations are made in the sequence of a substrate to generate a library containing all species required for a site-specific analysis, much information can be derived on the energetics of the specificity sites that is difficult to obtain from mutagenesis of the enzyme. In order to understand the molecular origin of the higher specificity of the fast form toward fibrinogen, the chromogenic tripeptide substrate FPR (Table 111) was synthesized to mimic the interaction of the natural substrate with the active site of the enzyme (Stubbs et al., 1992; Martin et al., 1992). Like fibrinogen, this synthetic substrate is cleaved by the fast form with a specificity 30-fold higher than that of the slow form (Table IV). The crystal structure of thrombin inhibited with H-DPhe-ProArg-CH2Cl(Bode et al., 1992) provides information on the interactions of the Pl-P3 groups of FPR with the enzyme: Arg at P1 makes an ion pair with D189 at S1 at the bottom of the catalytic pocket; Pro at P2 interacts with the apolar moiety of S2 lined up by P60b, P60c, and W60d; Phe at P3 forms a favorable edge-to-face interaction with the aromatic ring of W215 at S3 (Fig. 3). The D enantiomer at P3 is necessary to mimic the interaction of F8 at P9 of fibrinogen (Table 11) with W215 of thrombin

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

89

TABLE 111 Substrate Library fw the Analysis of Thrombin Specijicity Abbreviation FPR FPK FGR VPR FGK VPK VGR VGK

Substrate

H-o-Phe-Pro-Arg-pnitroanilide H-o-Phe-Pro-Lys-pnitroanilide H-o-Phe-Gly-Arg-pnitroanilide H-o-Val-Pro-Arg-pnitroanilide H-wPhe-Gly-Lys-pnitroanilide H-o-Val-Pro-Lys-pnitroanilide

H-o-Val-Gly-Arg-pnitroanilide H-o-Val-Gly-Lys-pnitroanilide

Site(s) perturbed None P1 P2 P3 P1 and P2 P1 and P3 P2 and P3 PI, P2, and P3

after the /%turn made by the Aa chain following the P3-P5 Gly-Gly-Gly flexible region to reenter the catalytic pocket in a parallel configuration to the /3-strand hosting W215 (Ni et al., 1992). The chromogenic group pnitroanilide attached to the Gterminus enables quantitative spectroscopic measurements of the released pnitroaniline upon cleavage by thrombin at the P1-pnitroanilide scissile bond. Starting from FPR, seven substitutions were made to generate the library in Table I11 (Vindigni et aL, 1997a). The main idea was to introduce enough perturbation at P1, P2, and P3 while retaining sufficient specificity for accurate experimental measurements. The perturbation would then act as the source of information on the environment of the specificity sites of the enzyme S1, S2, and S3. H-DPhe was replaced with H-D-Val in VPR, VPK, VGR, and VGK to alter minimally the size of the side chain while replacing the aromatic moiety with a hydrophobic one. Pro was replaced with Gly in FGR, FGK, VGR, and VGK to avoid steric hindrance with S2 and relieve the rigidity of the P2-P3 bond. Arg was replaced with Lys in FPK, FGK, VPK, and VGK, to preserve the positive charge at P1 needed to contact D189 at S1. These substitutions generate all possible intermediates from the parent substrate FPR the three singly substituted substrates FPK, FGR, and VPR the three doubly substituted substrates FGK, VPK, and VGR and the triply substituted substrate VGK. The library therefore maps the intermediates in a three-site system where each site can exist in two states. To obtain the relevant free energy changes associated with the perturbations, the specificity constant s = k,,,/K, for substrate hydrolysis was measured in all cases (Table IV) to estimate the free energy of stability of the transition state. The value for FPR was used to scale energetically all others to obtain the relevant free energy changes in the transition state (Table V). Similar measurements were carried out with the three

TABLE N Specilicity Constants k,,/K, (in p M - ' s - ' ) for the Hydrolysis of Synthetic Substrates by Wild-Type (wt) and Mutant Thrombins in the Slow and Fast F m "

FPR

FPK

FGR

90 80 44 26

7.9 4.6 7.7 3.2

2.0 0.75 0.93 0.33

0.35 0.040 0.034 0.010

0.86 0.042 0.012 0.0025

WR

FGK

WK

VGR

VGK

Fast fm wt

R221aA K224A R221aA/K224A

100 36 24 13

0.021 0.01 1 0.027 0.011

2.1 0.96 1.4 0.70

0.34 0.14 0.17 0.049

0.0047 0.0024 0.0044 0.0017

0.0026 0.00038 0.00039 0.00021

0.11 0.0097 0.0063 0.0018

0.17 0.0086 0.0020 0.00063

0.00079 0.00013 0.00013 0.000063

slow fm wt

R221aA K224A R221aA/K224A

3.0 1.6 0.47 0.34

6.7 1.o 0.28 0.077

"Experimental conditions: 5 mM Tris, I = 200 mM, 0.1% PEG, pH 8.0 at 25°C. The slow form was studied in the presence of 200 mM choline chloride. The properties of the fast form refer to the limit "a'] + 03, at constant I = 200 mM. Errors are typically 22%.

91

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

TABLE V Free Energy Valws (in kcal/mol) dw to Perturbation ofthe PI-P3 Sites4 AGi

AGq

AGs

AGiq

AGls

AGqs

AG,,,

1.4 1.7 1.0 1.2

2.3 2.8 2.3 2.6

-0.1 0.5 0.4 0.4

1.3 0.8 1.1 0.8

0.8 0.5 0.7 0.5

1.1 0.5 0.6 0.7

2.2 1.2 1.8 1.5

1.3 2.2 1.6 2.1

0.7 2.2 2.2 2.9

-0.5 0.3 0.3 0.9

2.2 0.6 0.5 -0.6

1.2 0.6 0.7 0.1

1.4

0.7 0.8

3.3 1 .o 0.8 -0.8

Fast fm Wt

R221aA K224A R221aA/K224A slow fonn Wt

R221aA K224A R221aA/K224A

-0.1

"Values were obtained from the specificity constants s = k,,/K, in Table IV as follows (the suffixes refer to the sequence of the substrate): AG, = -RTln(sFpR/smn);AGq = -RTln(sdsmn); AGs = -RTln(swR/swn); AGiq = -RTln(SFCKSwR/~wKSFGR);AGis = -RTln(SVPKSFPR/SFPKswn); = -RTln(svcnsFPn/sFCnswn); AGLZ = -RTln(SvmShn/ sWKSFGRSWR). Errors are typically ZO.1 kcal/mol.

thrombin mutants R221aA, K 2 2 4 , and R221a/K224 to assess the role of the two ion pairs that seem to stabilize the Na+ binding environment (Fig. 3). This resulted in the complete dissection of a fivedimensional manifold of species in both the slow and fast forms of the enzyme from which detailed information can be derived on how perturbations of the substrate are coupled to each other and to perturbations in the enzyme. The five sites perturbed are P1, P2, and P3 in the substrate and R221a and K224 in the enzyme. The specificity constants relative to the 32 possible intermediates in the manifold are listed in Table IV for each thrombin form.

D. Perturbation at the PI -P3 Sites There is a large and significant nonadditivity in the effects induced by perturbations of the Pl-P3 sites that emerges from inspection of the second-order and third-order coupling free energies listed in Table V. The extent of nonadditivity changes for each pair of substitutions and is also affected by the allosteric state of the enzyme and mutations made around the Na+-binding environment. The presence of interactions among the P1-P3 sites generates complexity in the response of the enzyme to specific perturbations of the substrate sequence. This demands an analysis of the perturbations based on the principles illustrated earlier in Section IV.

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The free energy change due to replacing Arg with Lys at P1 in all possible combinations of the state of P2 and P3 is summarized in Table VI. The values are all positive in both the slow and fast forms, for wildtype and mutant thrombins, indicating that the Arg + Lys replacement at P1 always causes a loss of specificity. A similar finding was reported for trypsin (Craik et al., 1985; Perona et al., 1993; Vindigni et al., 1997a) and is due to the change in interaction with D189 in the specificity pocket S1. The side chain ofArg at P1 is long enough for the guanidinium group to form an ion pair with D189 (Fig. 3), but Lys at P1 can interact with D189 only through a water-mediated contact. The cost of this replacement is about 1 kcal/mol in both the slow and fast forms when no replacement is made at P2 and P3, which suggests that the same mechanism may cause the loss of specificity in both allosteric forms. In trypsin, perturbation of the environment of D189 with the mutations G216A and G222A alters the catalytic register of the substrate leading to a decrease in k,,, and an increase in K , (Perona and Craik, 1995). These changes in catalytic parameters echo those observed in the fast+slow conversion of thrombin for both synthetic substrates (Wells and Di Cera, 1992) and fibrinogen (Vindigni and Di Cera, 1996). This would suggest that binding of Na+ orients the side chain of D189 for optimal coordination of the guanidinium group of Arg at P1, perhaps using water 447 that bridges the bound Na+and the 0, atom of D189 (Fig. 2). However, if this were the case, the loss of specificitywith the Arg += Lys substitution at P1 would be more pronounced in the fast form, contrary to what is seen experimentally. The similarity of effects between the two forms argues against a direct influence of the allosteric switch on the position of the side chain of D189. This conclusion is supported by the fact that water 447 is also present in trypsin (Bartunik et al., 1989; Krem and Di Cera, 1997),which does not bind Na+ (Dang and Di Cera, 1996), where it bridges the 0, atom of D189 to the carbonyl 0 atom of K224. The origin of the increased specificity of the fast form must therefore reside at other specificity sites. Due to the strong interactions among the Pl-P3 sites, the cost of replacing Arg with Lys at P1 depends on the residue at P2 and P3 and reveals the importance of going beyond single-site substitutions in the analysis of ligand recognition. With Gly at P2, the cost of the Arg + Lys replacement at P1 increases significantly by 1.3 kcal/mol in the fast form and 2.1 kcal/mol in the slow form, introducing a significant difference of -0.7 kcal/mol between the two forms (Table VI). This difference measures the coupling between the replacement at P1 and the slow+fast transition. A negative value indicates that the replacement promotes the slow+-fastconversion in the transition state, or that the replaced residue

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

93

binds preferentially to the slow form. A positive value signals a stabilization of the slow form, or that the replaced residue binds preferentially to the fast form. The absence of coupling seen when no perturbation is present at P2 and P3 cannot be taken as an absolute measure of the molecular events that accompany the substitution at P1. The environment around D189 in the transition state may be different in the slow and fast form, but this difference becomes appreciable only when Gly is present at P2. Similar considerations apply when a substitution is made at P3, although the energetic penalty for the P1 substitution increases by nearly 1 kcal/mol in both thrombin forms. The extent of interaction of P2 and P3 with P1 is significant. When Gly is present at P2, the interaction with P1 actually exceeds the cost of the replacement at P1 itself in the slow form. The free energy change due to replacing Pro with Gly at P2 in all possible combinations of the state of P1 and P3 is summarized in Table VI.As for the substitution at P1, the values are significantly positive. In this case, the effects tend to be more pronounced in the fast form, underscoring an obvious change in the environment of the S2 site in the slow+fast transition. The significantdifference is conducive to stabilization of the slow form in the transition state when Pro is replaced by Gly. The apolar site S2 of thrombin is formed by residues in the W60d loop that has no counterpart in other serine proteases. Residues in the apolar site are perhaps oriented differently in the slow and fast forms, causing a better discrimination of the residue at P2 in the fast form. W60d may play a key role in this respect because replacement of the bulky side chain with Ser in W6OdS abolishes the differences between the slow and fast forms in recognizing substrates with Pro or Gly at P2 (Guinto and Di Cera, 1997). The indole ring of W60d may produce steric hindrance in the slow form but not in the fast form. The differences between FPR and FGR are not due to effects on the free substrates arising from differences in the rate of diffusion into the active site. In fact, the substitution at P2 affects not only the specificity constant, which depends on the rate of diffusion, but also k,,, (Vindigni et al., 1997a), which depends exclusively on the acylation and deacylation rates pertaining to the transition state (Wells and Di Cera, 1992). The perturbation at P2 depends strongly on the residue present at P1 and P3. The cost of the Pro + Gly replacement increases by 1.2 kcal/mol in the fast form and 2.2 kcal/mol in the slow form as a result of the substitution at P1. This effect is exactly (taking into account round-off error) the same as that seen for the perturbation at P1 when P2 is perturbed, as a consequence of the reciprocity of the linkage between the perturbations at P1 and P2. Again, an approach based on

TABLE VI Free Energy Change (in kcal/nwl) in Specificity due to Perturbation of the PI-P3 Sites" ~~

Fast form

Slow form

R221aA

K224A

R221aA/ K224A

1.4 2.7 2.3 2.5

1.7 2.5 2.1 2.4

1.o 2.1 1.7 2.2

1.2 2.0 1.7 2.0

2.3 3.5 3.4 3.6

2.8 3.6 3.3 3.5

2.3 3.3 2.9 3.4

-0.1 0.8 1.0 0.9

0.5 0.9 1.0 0.9

0.4 1.o 1.o 1.1

wt

Coupling

R221aA

K224A

R221aA/ K224A

wt

R221aA

K224A

1.3 3.4 2.4 3.2

2.2 2.8 2.7 2.5

1.6 2.0 2.2 1.6

2.1 1.5 2.2 1.4

0.2 -0.7 -0.1 -0.6

-0.5 -0.3 -0.6 -0.1

-0.5 0.1 -0.6 0.5

-0.8

2.6 3.4 3.3 3.6

0.7 2.9 2.2 2.9

2.2 2.8 2.8 2.6

2.2 2.6 2.9 2.3

2.9 2.3 2.8 2.0

0.6 0.8 0.5 1.0

0.1 0.7 0.0

-0.3

0.6 1.2 0.7

1.1

1.6

0.4 0.9 1.1 1.1

-0.5 0.7 1.0 0.7

0.3 0.8 0.9 0.6

0.3 1.o 1.1 0.7

0.9 1.o 0.8 0.7

0.4 0.1 0.1 0.2

0.2 0.1 0.1 0.3

0.1 0.0 -0.1 0.4

-0.5 -0.1 0.3 0.4

wt

R221aA/ K224A

Replacement at P1 (Arg + Lys):

Fpx

(W

FGX (10) VPX (01) VGX (11)

-

Replacement at P3 (Phe Val): XPR (00) XPK (10) XGR (01) XGK (11)

1.5

0.5 -0.5 0.6

1.1

0.5

"Listed are all possible configurations of the other two P sites (0 = unperturbed; 1 = perturbed) in the order P1, P2, P3, along with the corresponding substrate. Errors are 20.1 kcal/mol or less. Values were obtained from the data in Tables IV and V. The difference between the values for the fast and slow forms gives the coupling between the substitution and the slow-fast transition. Positive values are indicative of stabilization of the slow form in the transition state, whereas negative values signal stabilization of the fast form. Values of the coupling in excess of 2 R T (0.6 kcal/mol) are set in boldface.

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

95

single-site substitutions would underestimate the cost of the Pro + Gly replacement at P2 because it would neglect the negative coupling between P1 and P2. Similar arguments apply when the substitution is made at P3. The free energy change due to replacing Phe with Val at P3 in all possible combinations of the state of P1 and P2 is summarized in Table VI.The unexpected finding is that VPR is actually a better substrate for thrombin than FPR itself, contrary to the predictions drawn from the crystal structure (Bode et al., 1992) that emphasize the virtues of an aromatic residue at P3. Furthermore, previous data obtained on bovine thrombin have documented a higher specificity for the sequence FPR compared to VPR (Lottenberg et al., 1983). Introduction of a hydrophobic group at P3 may bring about a more favorable interaction with the hydrophobic moiety of L99 (Fig. 3), which is close to the apolar site S2. Interestingly, residue Y3 of hirudin contacts W215 of thrombin in a manner similar to that of Phe at P9 of the fibrinogen Aa chain (Rydel et ad., 1991), but replacement of Y3 with the more hydrophobic Trp brings about a fivefold enhancement in binding affinity (De Filippis et al., 1995), consistent with the enhanced specificity of VPR compared to FPR and VPR. The energetic effect linked to replacement of the residue at P3 is of the same magnitude in both forms and excludes a direct involvement of the S3 site in the slowefast equilibrium. The perturbation at P3 depends strongly on the state of P1 and P2. The cost of the Phe + Val replacement increases by 0.9 kcal/mol in the fast form and 1.2 kcal/mol in the slow form as a result of the substitution at P1 and is the reciprocal of the effect seen for the perturbation at P1 when P3 is perturbed. The data in Tables IV and V reveal the presence of coupling among perturbations at P1, P2, and P3. The coupling is the result of constraints imposed by the enzyme on the bound substrate in the transition state and is therefore revealing of the molecular environment underlying the recognition process (Vindigni et al., 1997a).The coupling free energies for the three possible pairs of P sites in the two possible states of the third site are listed in Table VII. The values are constructed from the specificity constants pertaining to the four species in the double-mutant cycle in Eq. (4),where the mutations are replaced by the substitutions at the P sites. For example, the coupling between P1 and P2 is OAGI2= -RTln(SFGKSFPR/SFpKSFGR) in the absence of perturbation at P3 and 'AGI2 = -RTln(sVCKSWR/SWKSVGR) when P3 is perturbed. The value of OAG,, is the same as AG12in Table V. The coupling free energies in the case of wild-type thrombin are mostly positive and quite significant, demonstrating that perturbations at the P1, P2, and P3 sites are negatively

96

ENRICO DI CERA

Fast form wt

1.3 0.2 0.8 -0.2 1.1 0.1

Slow form

R221aA

K224A

R221aA/ K224A

0.8 0.3 0.5 -0.1 0.5 -0.0

1.1 0.6 0.6 0.1 0.6 0.1

0.8 0.3 0.5 -0.0 0.7 0.2

wt

2.2 0.7 1.2 -0.2 1.4 0.0

R221aA

K224A

0.6 -0.3 0.6 -0.3 0.7 -0.2

0.5 -0.6 0.7 -0.4

0.7 -0.3

R221aA/ K224A -0.6 -0.9 0.1 -0.1 -0.1 -0.3

*Listed are the two possible configurations of the third P site (0 = unperturbed; 1 = perturbed) in the order P1, P2, P3. Errors are 20.1 kcal/mol or less.

coupled in enhancing specificity.When a site is perturbed, perturbation at a second site reduces specificitybeyond simple additivity.Furthermore, the coupling between any two sites is enhanced by more than 1 kcal/mol when the third site is perturbed, underlying an even stronger cooperative effect in reducing specificity that progresses with the extent of perturbation in the substrate. There are six possible coupling free energy values for the three pairs, but only four are independent. Hence, the difference between any two values for each pair is exactly the same for all pairs. From the property of the coupling free energy (Section N,C)we conclude that the sites are coupled indirectly through interactions higher than second order. A simple nearest neighbor mechanism of interaction is inadequate to describe these interactions, and so is a concerted mechanism because of the negative nature of the coupling. A more elaborate mechanism needs to be developed to account for these findings. The nature of the coupling among the P1-P3 sites is such that interactions are significantly weakened in the fast form when any site is perturbed. A similar result is seen for the slow form, with the notable exception of the Pl-P2 coupling. The presence of coupling among the Pl-P3 sites and the way interactions change upon the allosteric transition reveal the site-specific origin of thrombin specificity.

E. Why Is the Fast Form More Specific? The Arg + Lys replacement at P1 slightly promotes the slow+fast transition when Gly is present at P2. On the other hand, the Pro + Gly replacement at P2 strongly stabilizes the slow form. The replacement at P3 is inconsequential on the allosteric equilibrium. Hence, the slow+fast

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

97

transition affects mostly the environment of the S2 site, with modest effects on the S1 site and no effect on the S3 site. Constraints at the S2 site accounts for the lower specificity of the slow form compared to the fast form and become inconsequential if the substrate acquires flexibility with a Gly at P2 and can readjust in the active site to compensate for the increased steric hindrance of the S2 site in the slow form. These findings explain why the thrombin mutant W6OdS cleaves FPR with the same specificity in the slow and fast forms (Guinto and Di Cera, 1997) and suggest the bulky side chain of W60d as the likely origin of the constraints at S2. Two factors contribute to specificity: the rigidity of the P2-P3 bond and the strength of the P1-S1 interaction. When Pro is present at P2, the P2-P3 bond is rigid and the substrate finds a more favorable S2 environment in the fast form. Replacement of Pro with Gly causes specificity to drop more in the fast form and reduces the differences between the allosteric forms of thrombin. The acquired flexibility of the P2-P3 bond is almost inconsequential in the slow form because of the more constrained environment of this form around the W60d loop lining the S2 site. The substrate FGR must assume essentially the same conformation as FPR to optimize its interaction with the slow form. In the fast form, however, the increased flexibility of the P2-P3 bond may relax the optimal interaction of Arg at P1 with D189 at S1, this effect being favored by a more open environment of the active site in this form. Consistent with this effect, the second replacement of Arg at P1 with Lys results in larger energetic penalty in the slow form, because the optimal Pl-Sl interaction has already been partially disrupted in the fast form by the Pro + Gly replacement. The coupling between substitutions at P1 and P2 comes partially from an intrinsic effect on the substrate, the loss of rigidity of the P2-P3 bond, and partially from the different environment of the enzyme in the slow and fast forms. The less constrained environment of the specificity sites in the fast form also act to reduce the extent of negative coupling among the various perturbations in the substrate, causing the interactions to essentially disappear as more substitutions are made at the P sites. The two ion pairs R221a-El46 and K224-E217 stabilizing the Na+ binding environment (Fig. 3) provide other important constraints in the slow form. The R221aA mutant has a reduced Na+ affinity (Dang et al., 1997a), suggesting that the R221aA-El46 ion pair may be broken in the slow form. This conclusion, however, is not supported by the data obtained with the substrate library because disruption of the R221aAEl46 ion pair affects specificity more in the slow than the fast form (Table IV).The parameters pertaining to the fast form are practically

98

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unchanged relative to the wild type, whereas those in the slow form show enhanced sensitivityto perturbation at P1 and P2. This perturbation is also less dependent on the state of other groups, indicating a reduction in the coupling among substitutions at the P1-P3 sites. Inspection of the coupling free energy values in Tables V and VII illustrates this point directly. Disruption of the R221a-El46 ion pair has a direct influence on the specificity sites S1 and S2 of the enzyme in the slow form and affects the way these sites discriminate between Arg and Lys at P1 or Pro and Gly at P2. The molecular basis of this effect may be due to enhanced mobility of the autolysis loop on the Glu side of the ion pair upon disruption of the contact. The enhanced mobility may interfere with substrate recognition in the slow form. On the Arg side of the ion pair, the mobility of the Na+-binding loop is hindered upstream by the C22O-Cl91 disulfide bond and downstream by the bidentate ion pair involving D221 and D222 with R187 in the p-strand distal to the 184 loop that defines the Na+ environment from behind (Fig. 1). The increased mobility of the 184 loop subsequent to disruption of the D221,D222R187 bidentate ion pair leads to the loss of Nat and several water molecules in the channel (Zhang et al., 1997). In addition, the replacement of the side chain of R221a with Ala may alter the orientation of the carbonyl 0 atom and reduce the Na' affinity. This may in turn alter the architecture of the loop and cause a rearrangement of the water molecules in the channel embedding the specificity site S1 (Krem and Di Cera, 1998). The R221a-El46 ion pair contributes to the integrity of the S1 environment in the slow form, but not in the fast form because the perturbation is practically abolished by Nat binding. The ion pair is energetically stronger in the slow form and may play an important role when Nat is released from its site. Perhaps this ion pair tightens up in the fast+slow conversion, bringing the autolysis loop closer to the Na+-binding loop and triggering the release of water molecules from the water channel embedding the specificity pocket S1 and the Na' site (Zhang and Tulinsky, 1997; Krem and Di Cera, 1998). As for the R221aA mutant, mutation of K224 to Ala reduces the Na+ affinity (Dang et al., 1997a), suggesting that the K224-E217 ion pair may be broken in the slow form, but again this proposal is contradicted by the experimental data that document a larger effect in the slow form (Table IV). Disruption of the K224-E217 ion pair produces effects very similar to those seen for the R221aA mutant, with a reduction of the coupling among the Pl-P3 sites especially in the slow form. The ion pair between K224 and E217 bridges two residues on the last two p-

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

99

strands of the B chain (Fig. 3) and seems to contribute to the integrity of the S1 and S2 environments in the slow form. The region in immediate proximity to K224 and E217 plays a key role in substrate selectivity and is absolutely conserved in thrombin from different species (Banfield and MacCillivray, 1992). The state of this ion pair can therefore control the access of substrates into the bottom of the catalytic pocket where the specificity site S1 is located. Strengthening the ion pair in the slow form may trigger the release of some of the water molecules in the channel embedding the specificity site S1, leading to a reorganization of the network. There is evidence of weak synergism between the ion pairs in the slow form but not in the fast form, as demonstrated by the results on the double mutant R221aA/K224A. The perturbation induced by the double mutation is more drastic and almost abolishes Nat binding (Dang et al., 1997a).The mutation affects the response to perturbations at the Pl-P3 site, with an effect more pronounced in the slow form. The site-specific parameters are profoundly altered in the slow form and, interestingly, the painvise coupling pattern shows the disappearance of indirect coupling in both the slow and fast forms, with the onset of positive secondorder direct coupling between P1 and P2 (Table VII). This effect is peculiar to the double substitution, though it is somewhat anticipated by the single substitutions.The molecular basis for the synergism between the R221a-El46 and K224-E217 ion pairs in the slow form is in the participation of residues R221a and K224 in Nat and water coordination. In the fast form, the carbony10 atoms of R221a and K224 directly ligate the Na". Mutation of these residues reduces the Nat affinity, but high concentrations of Nat oppose the structural perturbation induced by the mutation, restoring a molecular environment for the specificity sites that is essentially that of the fast form of the wild type. When Nat is released, the carbonyl 0 atom of K224 may reorient as seen in the structure of trypsin and may hydrogen bond to water 447 in concert with the carbonyl 0 atom of R221a (Gem and Di Cera, 1997). Water 447 hydrogen bonds to the side chain of D189 in the specificity pocket S1, and through the switching mechanism any perturbation of R221a and K224 changing the orientation of the carbony10 atoms will not be compensated as in the case of the fast form and therefore may lead to more drastic structural changes. These changes may eventually affect the orientation of the side chain of D189, bringing about changes in K , and k,,,. From the foregoing analysis we conclude that the more constrained environment in the slow form of thrombin is partially due to stronger ion pairs formed by R221a and K224 in the Nat-binding loop with El46

100

ENRICO DI CERA

in the autolysis loop and E217 in the penultimate /3-strand of the B chain. The integrity of these ion pairs is essential for maintaining the correct architecture of the Sl-S3 sites through the effect on the water molecules in the channel that embeds the specificity site S1. The role of the ion pairs in the fast form appears to be less critical, and their disruption can be compensated by the binding of Na+.The origin of the reduced Na' affinity in these mutants should be seen in a perturbation of the slow form leading to an impaired ability to switch to the fast form. The coupling free energy for allosteric switching from the slow to the fast form in the transition state becomes more negative upon mutation of R221a and K224 (Fig. 4), indicating an increased preference for binding to the fast form.

FPR

FPK

FGR

VPR

FGK

VPK

VGR

VGK

FIG.4. Coupling free energy for allosteric switching from the slow to the fast form in the transition state, calculated from the specificity values s = k,,JK, (Table N )of the substrates listed in the abscissa as AGc = -RTln(spa,/s,,ow).Symbols: ( 0 ) wild-type; ( 0 ) R221aA; ( 0 ) K224A; (m) R221aA/K224A. The difference between the two forms increases upon mutation of R221a and K224 due to perturbation of the slow form.

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

101

The foregoing analysis is invaluable to structure-function studies and to practical issues revolving around the design of better activesite inhibitors. Much improvement in the potency of these molecules can be obtained by reducing the negative coupling among the specificity sites. This effect is obtained by keeping a rigid backbone around the P2-P3 position that facilitates the coordination with D189 at S1 and by breaking the ion pairs R221a-El46 and K224-E217. The analysis also facilitates the identification of optimal pathways for enhancing or reducing specificity. This is illustrated directly in Fig. 5, where the free energy loss in specificity for any given substrate relative to FPR is plotted vs. the number AG (kcal/mol)

fast

slow

form

form

[W

6.0

5.5 5.0 4.5 4.0

3.5 3.0 2.5

2.0

1.5 1.0

0.5 0 4.5 0

1

2

3

FIG.5. Free energy penalty due to substitutions in the P1-P3 sites of substrate relative to FPR, [ O O O ] , plotted vs. the number of perturbed P sites, for wild-type thrombin in the slow and fast forms. Values were computed from the free energies listed in Table IV. Vector labels refer to the P1, P2, and P3 sites in lexicographic order, with 0 = unperturbed and 1 = perturbed. Optimal pathways for enhancing specificity can be identified directly from the plot (see the text).

102

ENRICO DI CERA

of substitutions made at the P sites. Starting from FPR, the optimal pathway to reduce specificity in the fast form is by replacing Pro with Gly at P2 and then Arg with Lys at P1, followed by the Phe + Val substitution at P3. In the slow form, however, the first two steps must be inverted because the Arg + Lys replacement at P1 is more deleterious. The optimal pathway to increase specificity in the fast form starting from VGK is to replace Gly with Pro at P2, followed by the Lys + Arg substitution at P1. The first step by far dominates the gain in specificity and contributes 3.7 kcal/mol to stabilization of the transition state. In the slow form, on the other hand, the first step should be the Arg + Lys substitution at P1 resulting in 3.2 kcal/mol gain in specificity, followed by the Gly + Pro replacement at P2. The Val + Phe substitution at P3 results in a small loss of specificity in both forms. These results set three basic guidelines for the improvement of active-site inhibitors of thrombin (Vindigni et al., 1997a): the P2-P3 bond must be rigid (Pro at P2), especially when targeting the fast form; coupling with S1 must be strong (Arg at P1) , especially when targeting the slow form; and P3 must carry hydrophobic residues.

F. Allostm’c Mechanism fw High-Order Coupling The coupling pattern emerged from the analysis of the substrate library is conducive to negatively cooperative interactions higher than second order. The development of novel allosteric schemes that merge the basic tenets of nearest neighbor and concerted allosteric models becomes necessary to account for these interactions. When this is done, the number of independent parameters to be resolved experimentally increases rapidly and may exceed the information provided by the data. A possible model would require the assumption that the slow and fast forms of wildtype thrombin in the transition state exist in two states in equilibrium, A and B, each containing second-order nearest neighbor interactions among the P1-P3 sites that change in a concerted fashion upon the allosteric transition from A to B. This model has seven independent parameters, three second-order nearest neighbor interaction constants for each state plus a constant describing the equilibrium between the states. However, the number of independent coupling free energies derived experimentally is four (Table VII), thereby making the task of resolving the seven independent parameters for this hybrid model impossible. One way to overcome this problem is to include other variables to increase the dimensionality of the system and generate enough constraints from experimental data. This is done by modeling the slow and

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

103

fast forms each as a fivedimensional manifold containing the sites P1, P2, P3, R221a, and K224 in order. Each configuration in the manifold is mapped into a fivedimensional vector of binary digits, 0 (unperturbed) and 1 (perturbed), to which a given value of the specificity constant is associated from Table IV.All relevant free energies are calculated by operating on these values. The results are summarized in Tables VIII and IX. Inclusion of R221a and K224 in the set of sites increases the number of configurations to be analyzed when a perturbation is applied to a given site, say, P1. The same applies to the number of configurations of other sites when the coupling between any two sites is considered. This analysis yields complete information on the coupling between perturbations in the substrate and the enzyme, within the enzyme, and within the substrate. A graphical illustration of the site-specific transition modes in Table VIII linked to perturbations in the five-dimensional system defined by P1, P2, P3, R221a, and K224 is given in Fig. 6a-e. The plots encapsulate the essential features of the results given above in Section V,D and especially the presence of strong coupling revealed by the significant standard deviation of the distributions. The distributions also point out the serious limitation of an approach where the energetic balance of the perturbation at any site is estimated from a single value obtained in the absence of perturbations at other sites (configuration 1 in the abscissas of Fig. 6a-e). The discrepancy is particularly serious in the case of perturbations made in the substrate. In the case of P2 in the slow form, there is a difference of 1.8 kcal/mol between the value estimated from the specificity of FPR and FGR compared to the mean of the entire distribution. Broader distributions for perturbations in the slow form underscore the stronger coupling in this allosteric state. Changes in the profiles between the slow and fast forms are particularly evident for P2 and K224, and to a lesser extent for P1 and R221a, documenting the different susceptibility to perturbation of specific structural domains in the two forms. Analysis of the coupling pattern involving all possible pairs (Table IX) shows how interactions change with the state of other sites. When only differences of at least 5 R T (0.6 kcal/mol) in the coupling free energy are considered, the patterns can be analyzed to identify the nature of the interaction. In the fast form only the Pl-P3 sites are significantly coupled and in an indirect way. Perturbation of any P site influences the coupling at other sites. In the slow form all sites are strongly coupled. Each coupling can be dissected to identify the element perturbing the interaction. A direct way to illustrate the effect of a third site on the coupling between two sites is to calculate the difference in

TABLE VIII Free Energr Change (in kcal/mol) in Speajicip due to Perturbation of the PI-P3 Sites of the Substrate or Residues R221a and K224 of Thrombin" 0000

1000

0100

0010

0001

1100

1010

1001

0110

0101

0011

1110

1101

1011

0111

1111

Fast fm P1 P2 P3 R221a K224

1.4 2.3 -0.1 0.1 0.4

2.7 3.5 0.8 0.3 0.0

2.3 3.4 1.0 0.6 0.4

1.7 2.8 0.6 0.8

1.0 2.3 0.4 0.3 0.7

2.5 3.6 0.9 0.4 -0.1

2.5 3.6 0.9 0.5 0.2

2.1 3.3 1.0 0.5 0.2

2.1 3.3 1.0 0.5 0.4

1.7 2.9 1.0 0.6 0.5

1.2 2.6 0.4 0.4 0.6

2.4 3.5 0.9 0.4 0.0

2.2 3.4 1.1 0.5 0.0

2.0 3.4 0.9 0.4 0.2

1.7 3.3 1.1 0.7 0.6

2.0 3.6 1.1 0.6 0.2

slow fm P1 P2 P3 R221a K224

1.3 0.7 -0.5 0.4 1.1

3.4 2.9 0.7 1.3 1.4

2.4 2.2 1.0 1.8 2.5

2.2 2.2 0.3 1.1 1.9

1.6 2.2 0.3 0.2 0.9

3.2 2.9 0.7 1.1 1.1

2.8 2.8 0.8 1.4 1.7

2.0 2.6 1.0 0.7 0.8

2.7 2.8 0.9 1.8 2.6

2.2 2.9 1.1 0.9 1.7

2.1 2.9 0.9 0.8 1.5

2.5 2.5 0.6 1.1 1.1

1.6 2.3 0.6 0.4 0.3

1.5 2.3 1.0

2.2 2.8 0.8 0.7 1.5

1.4 2.0 0.7 0.4 0.4

0.5

0.7 1.0

"Listed are all possible configurations of the other sites (0 = unperturbed; 1 = perturbed) in the order P1, P2, P3, R221a, K224. Errors are 20.1 kcal/mol or less.

TABLEIX Coupling Free Energy Values (in kcal/mol) for Perturbation of the PI-P3 Sites of the Substrate and Residues R221a and K2.24 of Thrombin" 000 Fast f i Pl-P2 Pl-P3 Pl-R221a Pl-K224 P2-P3 P2-R221a P2-K224 P3-R22 1a P3-K224 R221a-K224 slow f

1.3 0.8

0.2 -0.4 1.1 0.5

0.0 0.2 0.4 0.2

100

010

0.2 -0.2 -0.2 -0.6 0.1 0.1 -0.2 0.1 0.2 0.2

0.8 0.5

-0.1 -0.6 0.5

-0.1 -0.4 -0.1 -0.0 0.0

00 1

110

101

01 1

1.1 0.6 0.2 -0.4 0.6 0.3 -0.2 0.0 -0.1 -0.2

0.3 -0.1 -0.1 -0.4

0.5

0.8

0.1 -0.1

0.5

-0.0

-0.1 -0.2 0.0 0.2 0.1

-0.5

0.1 0.0 -0.2 -0.1 -0.0 -0.0

111

Couplingb

0.3

0.0 -0.4 0.7 0.4 0.0 0.1 0.1 0.2

-0.2 -0.4 0.2 0.1 0.0 0.0 0.2 0.2

Indirect Indirect None None Indirect None None None None None

-0.6 0.1 -0.0

-0.9 -0.1 -0.3 -1.1 -0.3 -0.3 -0.6 0.1 0.1 -0.6

Indirect Indirect Indirect Indirect Indirect Indirect Indirect Indirect Indirect Indirect

-0.0

Mediated by

P3 P2

P3, R221a, K224 P2 P2 P2 P1, R221a, K224 P1, P3, K224 P1, P3, R221a P2 P2 P2

P1

i

Pl-P2 Pl-P3 Pl-R221a Pl-K224 P2-P3 P2-R221a P2-K224 P3-R221a P3-K224 R221a-K224

2.2 1.2 0.9 0.3 1.4 1.4 1.4

0.7 0.8 -0.2

0.7 -0.2 -0.6 -1.4 0.0 -0.1 -0.3 0.1 0.3 -0.6

0.6 0.6 0.3 -0.2 0.7 0.6 0.7 -0.0 0.1 -0.9

0.5

0.7 0.5 -0.1 0.7 0.7 0.7 0.6 0.6 -0.4

-0.3 -0.3 -0.7 -1.6 -0.2 -0.4 -0.6 -0.1 -0.0 -0.8

-0.6 -0.4

-0.6 -1.3 -0.3 -0.4 -0.5

0.0

0.2 -0.7

-0.5

-0.1 -0.1 0.0 -0.2 -0.1 -1.1

~

~~

"Listed are all possible configurations of the other sites (0 = unperturbed; 1 = perturbed) in the order P1, P2, P3, R221a, K224. Errors are 20.1 kcal/mol or less. *Indirect coupling requires values in the distribution that differ by at least ?RT (0.6 kcal/mol). Direct coupling of less than -CRT on the average is considered zero.

106

ENRICO DI CERA

a

Perturbation at P1 t

o 0

t

9 ,- 1

1

m

. . . . . . . . . . . . . . . . I 1

2

3

4

5

6

7

8

910111213141.516

configuration FIG.6 (pp. 106-108). Sitespecific perturbation of (a) P1, (b) P2, (c) P3, (d) R221a, and (e) K224, as indicated, in all possible configurations of the other sites. The 16 configurations refer sequentially to those listed in Table VII. Data are for the slow ( 0 ) and fast ( 0 ) forms. The average value of the perturbation is depicted by a continuous (fast form) or broken (slow form) line. Note how the value obtained in the absence of perturbations at other sites (configuration 1 in the abscissa) usually does not coincide with the average value derived from the ensemble of states of the other sites. This reflects the intrinsic coupling among the sites. The mean and standard deviations of each distribution are (in kcal/mol) as follows: (Pl) 2.0 2 0.5 (o), 2.2 2 0.6 ( 0 ) ; (P2)3.2 Z 0.4 (o), 2.5 Z 0.5 (0); (P3) 0.8 Z 0.3 ( o ) ,0.7 2 0.4 (0); (R221a) 0.5 2 0.2 (o), 0.9 2 0.5 (0); (K224) 0.3 -C 0.3 ( o ) , 1.4 Z 0.6 ( 0 ) .

coupling free energy of a pair due to the 0 + 1 transition of a third site, in all possible configurations of the remaining sites. These calculations are summarized in Table X, where differences of at least ? RT are highlighted. The P2 site emerges as a major node of interaction. In the slow form, the state of P2 influences all interactions (Table IX). The state of R221a and K224 influences the Pl-P2 and P2-P3 interactions but has no effect on the Pl-P3 coupling that is influenced by P2. Finally, the coupling between R221a and K224 is influenced by P2 only. As a result, the Ala replacements at these thrombin residues produce additive effects on specificity when Pro is at P2 but are positively linked when Pro is replaced by Gly.

107

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

i

Perturbation at P2

b/

0

1

2

3

4

5

6

7

8

910111213141516

configuration

-

s t

.

.

.

.

.

.

.

,

,

,

1

2

3

4

5

6

7

8

910111213141516

configuration FIG.6- Continued

.

.

.

,

.

.

108

ENRICO D1 CERA

2

d

Perturbation at R221a 9 n

r-l

d

8 9 3

1

2

3

4

5

6

7

8

910111213141516

configuration

e

Perturbation at K224

9

0

0

0

0 0 0

. o O

0

0

0

3

4

5

6

7

8

0 0 A

- 0 0 .

0 0

0

I 2

0

0

0

0

9 1011 1 2 1 3 1 4 1 5 1 6

configuration FIG.6- Continued

TABLE X Effect of Other Sites on the Coupling Free Energy Values (in kcal/mol) for Perturbation of the PI -P3 Sites of the Substrate and Residues R221a and K224 of Thrombin" 000-100 Fast form Pl-P2 Pl-P3 Pl-R221a Pl-K224 P2-P3 P2-R221a P2-K224 P3-R221a P3-K224 R221a-K224

1.1 1.o 0.4 0.2 1.o 0.4 0.2 0.1 0.2 0.0

slow fonn Pl-P2 Pl-P3 Pl-R221a Pl-K224 P2-P3 P2-R221a P2-K224 P3-RZ21a P3-K224 R221a-K224

1.5 1.4 1.5 1.7 1.4 1.5 1.7 0.6 0.5 0.4

010-110 0.5 0.6

0.0 -0.2 0.5

0.0 -0.2 -0.1 -0.2 -0.1

0.9 0.9 1.0 1.4 0.9 1.0 1.3 0.1 0.1 -0.1

001-101 0.6 0.5 0.3 0.1 0.5 0.3 0.0 0.1 -0.1 -0.2

1.1 1.1 1.1

1.4 1.0 1.1 1.4 0.6 0.4 0.3

011-111

0.5 0.5

0.2 0.0 0.5 0.3 0.0 0.1 -0.1 0.0

0.3

0.2 0.3 0.6 0.2 0.2 0.6 -0.3 -0.2 -0.5

)00-010

100-110

001-011

101-111

300-001

100-101

010-011

110-111

0.5 0.3 0.3 0.2 0.6 0.6 0.4 0.3 0.4 0.2

-0.1 -0.1 -0.1 -0.2 0.1 0.2 0.0 0.1 0.0 0.1

0.3 0.1 0.2 0.0 -0.1 -0.1 -0.2 -0.1 -0.2 -0.4

0.2 0.1 0.1 -0.1 -0.1 -0.1 -0.2 -0.1 -0.2 -0.2

0.2 0.2 0.0 0.0 0.5 0.2 0.2 0.2 0.5 0.4

-0.3 -0.3 -0.1 -0.1 0.0 0.1 0.0 0.2 0.2 0.2

0.0 0.0 -0.1 -0.2 -0.2 -0.5 -0.4 -0.2 -0.1 -0.2

-0.1 0.1 0.0 -0.2 -0.2 -0.2 0.0 0.0 -0.1

1.6 0.6 0.6 0.5 0.7

1.0 0.1 0.1 0.2 0.2 0.3 0.3 0.2 0.3 0.2

1.1 0.6 0.5 0.4 0.8 0.8 0.7 0.8 0.7 0.7

0.3 -0.3 -0.3 -0.2 0.0 -0.1 0.1 -0.1 0.1 -0.1

1.7 0.5 0.4 0.4 0.7 0.7 0.7 0.1 0.2 0.2

1.3 0.2 0.0 -0.1 0.3 0.3 0.2 0.1 0.1 0.1

0.8

0.7 0.7 0.7 0.7

1.2

0.5 0.3 0.3 0.8 0.7 0.7 0.2 0.2 0.2

0.0

0.6 -0.2 -0.4 -0.5 0.1 -0.1 0.0 -0.2 -0.1

-0.2

Listed is the difference in coupling free energy due to a change in the state of a third site, in the four possible configurations of the other two sites (0 = unperturbed; 1 = pertubed) in the order P1, P2, P3, R221a, K224. For example, the value of 1.1 kcal/mol for the Pl-P2 coupling in the fast form is the difference between the coupling free energy with P3, R221a, and K224 unperturbed (000) and that with P3 perturbed (100). Errors are 50.1 kcal/mol or less. Values exceeding +-RT (0.6 kcal/mol) are set in boldface.

110

ENRICO DI CERA

The intricacy of the coupling patterns for the 10 possible pairs of sites can be resolved by using an allosteric scheme belonging to a class of general models detailed elsewhere (Di Cera, 1995). The minimal model enabling us to describe the data in Tables VIII-X is to assume that the enzyme-substrate complex in the transition state can exist in two states, A and B, with state A being more stable in the absence of perturbations (i.e., in the [OOOOO] configuration of the P1, P2, P3, R221a, and K224 sites) and state B becoming more stable as perturbations are introduced in the system. These states may reflect alternative binding modes of the substrate and/or alternative conformations of the enzyme. They are not to be confused with the slow and fast forms. In such a model, the perturbations introduced in the system are coupled through a concerted allosteric equilibrium between two states with the sites experiencing nearest neighbor interactions in each state. It is intuitively obvious that since A and B have different coupling interactions for the possible site pairs, the apparent site-site coupling will change as more perturbations are introduced in the system and the transition from A to B takes place. A unique solution can be found by casting the coupling free energies measured experimentally in terms of the model parameters. For a system existing in two states, each of which has 10 possible site pairs, there is a total of 31 independent parameters that describe the perturbations. For each state there are 5 perturbation free energies for each site and 10 possible painvise interaction constants, leading to a total of 30 parameters. The free energy AGL defining the stability of the A state relative to B in the absence of perturbations completes the set. The independent constraints provided by experimental measurements for a fivedimensional system are 31, and a unique solution of the problem is therefore possible. Analysis of the data in terms of this allosteric picture can be simplified by noting that the site-specific perturbation free energies need not be different in the two states and can be set equal to the values determined experimentally. This reduces the number of independent parameters to 26. To evaluate all other terms, the free energy of any intermediate in the manifold must be evaluated. This is done by expressing the specificity of any intermediate relative to that of the reference species, [00000], which is FPR interacting with wild-type thrombin, and converting this ratio into kcal/mol using the expression A GaSyh= -RT In (sagyB/ sooooo),where a,0, y , 6, E = 0, 1 label the state of the five sites in the system. The values of these free energy levels are given in Fig. 7. For each case, the relevant expressions in terms of the model parameters are evaluated. The calculated free energy is given by the sum of the sitespecific perturbation free energies, which are the same in states A and

111

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFEmS

[000@31 0.0,o.o (0.0,O.O)

[loooo]

[OlOOO]

[OOlOO] [OOolO]

[ml]

1.4.1.3 (1.4,1.3)

2.3,0.7 (2.3,O.n

-0.1,4,5

0.4.1.1 (0.4,l.l)

(4.L4.5)

0.1,0.4 (0.1.0.4)

[110001

[loloo] [loolo]

[10001]

[OllOO] [OlOlO]

[Olool]

[oollO]

[OOlOl]

4.9.4.2 (4.9.4.2)

2.22.0 (2.2,2.0)

1.5,2.6 (1.5.2.6)

3.3.1.7 (3.3,l.n

2.8,Z.S (2.8.2.5)

2.7,3.3 (2.7,3.3)

0.5,0.6 (050.6)

[ o o w

0.8,1.4 (0.8,1.4)

0.7.1.3 (0.7,1.3)

[11100]

[nolo] [llool]

[10110] [10101] [looll]

[OlllO]

[OllOl]

[OlOll]

[OOlll]

5.8.4.9 (6.1,4.8)

5.3.55 (5.3,S.S)

2.7,3.6 (2.8,3.5)

3.8,3.5 (3.8,3.5)

3.7,4.3 (3.4,4.2)

3.3.4.2 (3.e4.1)

1.1,2.3 (1.22.3)

1.8,2.6 (1.8,2.6)

4.8.5.5 (4.8,5.5)

2.5,3.7 (2.4,3.6)

2.43.3 (2.43.3)

[11110] [lllOl]

[11011]

[lo1111

[Ollll]

6.25.8 (6.5.5.7)

5.4,S.S (5.4,5.4)

2.9,4.5 (3.0.4.4)

4.4,5.3 (4.25.3)

5.959 (5.8,5.7)

[11111] 6.4,6.5 (6.4,6.3)

FIG.7. Manifold of intermediates for the five-dimensional system composed of sites P1, P2, P3, R221a, and K224 in order. Listed are the free energy levels associated with each configuration relative to the [OOOOO] species for the fast (upper left value) and slow (upper right value) forms. The comparison with the values predicted by the allosteric model (Fig. 8) are given by parentheses for the fast (lower left wlue) and slow (lower right value) forms. These values were calculated from the free energy terms of the model given in Fig. 8. For example, the calculated free energy level where sites 1 and 4 are perturbed, AGlwlo(i.e., FPK interacting with the R221aA mutant), depends on the sitespecific perturbations of sites 1 and 4, AGl = A G I m and AG4 = AGmlo, and on their painvise interaction free energy in the two states, so that AGlwlo = A G l

+ AG4 - RTln

[[ (

exp -AGL

p 1 4 )

+ exp(

- 3 1 / [ -2)+ 'xp(

I]]

The best fit values of the model parameters in the fast form are (in kcal/mol) as follows: AGi. = -0.5; 'AGI = 'AG1 = 1.4; 'AG2 = BAG2 = 2.3; 'AG3 = BAG3= -0.1; 'AG4 = BAG4 = 0.1; 'AG5 = = 0.4; 'AGi2 = 3.8; BAGi2 = 0.5; 'AGis = 1.2; BAGIS = 0.4; 'AG14 = BAGi4 = 0.3; 'AG15 = BAG15 = -0.4; 'AG23 = 1.3; BAG2s = 0.8; 'A& = 0.9; BAG24 = 0.1; = 0.1; 'AGz = -0.2; 'AGX = 1.1; = 0.0; 'AG35 = 1.0; 'AG35 = 0.1; 'AG45 = 'AG45 = 0.2. The best fit values of the model parameters in the slow form are (in kcal/ mol) as follows: AGL = -2.2; 'AGI = BAGl = 1.3; 'AGp = BAG2 = 0.7; AAG~= BAG^ = -0.5; 'AG, = BAG4 = 0.4; 'AG5 = 1.1; AAG12 = 2.2; BAG12 = 1.2; 'AG13 = 1.3; = 0.0; 'AG14 = 1.0; = -0.3; 'AGI5 = 0.4; = -1.0; 'AG23 = 1.6; 'AG23 = 0.0; 'AGq4 = 1.6; *AG24 = 0.0; 'AG25 = 1.6; BAG25 = 0.0; 'AGM = 'AGH = 0.8; AAG35 = 'AG35 = 0.8; AAG45= BAG45= -0.2. All errors are t O . l kcal/mol or less.

112

ENRICO DI CERA

B, plus a term that contains the contribution of the allosteric switching and the pairwise interaction free energies involving the sites in each state. The model reproduces the experimentally determined values within 20.3 kcal/mol. A diagram depicting the relevant nearest neighbor interactions in states A and B for the slow and fast forms of thrombin is sketched in Fig. 8. The properties of the A and B states recapitulate the information gathered from the model-independent analysis already presented in Section V,D. The strength of nearest neighbor interactions decreases in state B and practically vanishes for a number of pairs. Overall, interactions are more pronounced in the slow form with strong coupling involving the P sites. Coupling is also strong between these sites and the

form

-0.5

FIG.8. Schematic representation of the nearest neighbor interactions in state A and B for the slow and fast forms of thrombin. Interacting - sites are connected and the pairwise interaction energy is given. The values of the model parameters are listed in the legend to Fig. 7.

SITE-SPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

113

thrombin perturbations at R221a and K224, whereas no significant coupling is observed between R221a and K224. Upon switching to the B state in the slow form there is a significant reduction of coupling and the main interactions involve P1 with P2 and K224, and P3 with R221a and K224. This state is considerably less populated than the A state in the absence of perturbations. In the fast form, the properties of the A state echo those seen for the slow form, except for weaker coupling between P1 and R221a and K224. However, the B state is almost as stable as the A state in this form, and the main interactions involve the P2-P3 pair. The A and B states may represent different binding modes of the substrate in the transition state or different substates available to the enzyme-substrate complex in the slow and fast forms. Since most of the interactions are routed through the P sites, it may be expected that A and B refer to distinct modes for substrate binding. One binding mode, the A state, appears to be more constrained, with stronger negative coupling involving residues at the P sites. This mode of binding also couples strongly with the state of the ion pairs involving R22la and K224. The coupling is particularly evident in the slow form. In the fast form, there is a peculiar weakening of the coupling of P1 with the thrombin residues R221a and K224, indicating that the strength of the ion pairs R221a-El46 and K224-E217 influences the environment of the S1 site. The higher flexibility of the fast form is also indicated by the lower energy barrier (0.5 kcal/mol) to switching from the A to the B state where most of the interactions disappear. The B state may well reflect a less constrained conformation of the substrate bound in the transition state, consistent with the stabilization observed upon the Pro + Gly substitution at P2.

VI. CONCLUDING REMARKS Wyman’s theory of linked functions (Wyman, 1948, 1964) provides the conceptual framework needed for a rigorous, model-independent analysis of mutational effects in proteins. Once this analysis is formulated in terms of the principles of sitespecific thermodynamics (Di Cera, 1995), a hierarchy of effects can be unraveled from experimental data. Each site subject to structural perturbation can be treated as a unit switching from two states, 0 = wild type and 1 = perturbed, and the energetics of the system can be mapped into a manifold of Nsites coupled through high-order interactions. Coupling among the sites leading to nonadditivity is the dominant feature emerging from mutational studies of protein stability and ligand recognition in a variety of systems. Basic

114

ENRICO DI CERA

properties of the coupling free energy of a double-mutant cycle enable the identification of the precise mechanism of coupling from a modelindependent analysis of the data. This in turn guides the development of ad hoc allosteric models that encapsulate the relevant features of the system. The applicability of the approach presented here is only limited by the availability of high-order perturbations in the system. When one is dealing with a protein, triple and quadruple mutations are necessary to fully exploit the virtues of this analysis, which may represent a serious drawback in many systems of interest. However, at least in the case of ligand recognition, the approach is feasible insofar as the highdimensional manifold can be constructed with perturbations in the ligand. Short peptides can be synthesized easily to construct substrate libraries carrying substitutions such as those used to dissect thrombin specificity. These libraries can then be combined with perturbations in the enzyme to enhance the dimensionality of the system. Higher dimensions in the system can be introduced by studying the effect of linked ligands on the coupling among sitedirected mutations. The energetics of the library of substrates used for wild-type thrombin has recently been characterized in the presence of thrombomodulin (Vindigni et aL, 199’7b).Each variable introduced in the system, subject to the requirements of the double-mutant cycle in Eq. (4)that the site be in two possible states, increases the dimensionality of the manifold of configurations by one. Hence, significantly complex systems can be constructed by suitable combinations of ligand binding and mutational events involving the protein and/or the ligand. The key advantage of the approach based on site-specific thermodynamics is that effects of different nature can be treated within the same conceptual framework and analytical formalism. Other possibilities to extend the dimensionality of the system is by exploring the effect of different substitutions at the same site, which can test the context dependence of the interaction patterns obtained experimentally. When ligands are used as probes of site-specific properties of the protein, much information can be obtained on the nature of interactions stabilizing the complex and determining recognition. The combination of structural perturbations and the analysis presented here provide a rational strategy for the dissection of protein stability, ligand binding, and enzyme specificity. This approach brings Wyman’s original idea of linked functions into the mainstream of current studies of structurefunction correlations.

SITESPECIFIC ANALYSIS OF MUTATIONAL EFFECTS

115

ACKNOWLEDGMENTS I am grateful to all members of my laboratory who have contributed at various levels to the experimental and theoretical aspects of this work, and especially to Quoc Dang, Enriqueta Guinto, Alessandro Vindigni, and Luyu Wang. I am also indebted to Frederic Richards andJames Wells for valuable comments and suggestions. This work was supported by NIH Research Grants HL49413 and HL58141, and was carried out under the tenure of an Established Investigator Award in Thrombosis from the American Heart Association and Genentech.

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ALLOSTERIC TRANSITIONS OF THE ACETYLCHOLINE RECEPTOR

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By STUART J EDELSTEIN13 and JEAN-PIERRE CHANGEUX’ ‘Neurobiologle Moibcuialre. institut Pasteur. 75734 Paris Cedex 15. France. and *DBpartement de Biochlmle. Unlverslt6 de Genbve. CH-1211 Genbve 4. Switzerland

I . Introduction ................................ A. The Acetylcholine Receptor: Similarities and Differences with Respect to Other Allosteric Proteins ........................... B. Consequences of Pseudosymmetric Oligomeric Structure ......... C. Role of Mutational Studies .................................... I1. Mechanistic Models .............................................. A . The Allosteric-Type Model .................................... B. Linear Free Energy Relations ................................. C. Alternative Models ........................................... 111. Recovery from Desensitization ..................................... Iv. Kinetic Basis of Dose-Response Curves ............................. A . Dependence on the Desensitization Rate ....................... B. Desensitization by Low-Concentration Prepulses ................. V. Multiple Phenotypes ............................................. A. A Generalized Allosteric Network .............................. B. The KPhenotype ............................................ C. The L Phenotype ............................................ D. T h e y Phenotype ............................................ E. Limiting Properties at Extremes of L ........................... VI. Deductions from Single-Channel Measurements ..................... A. Kinetic Consequences of Mutant Phenotypes .................... B. Single Ionic Events vs Single Ligand-Binding Events in Relation to Binding-Site Nonequivalence ............................... VII . Allosteric Effectors and Coincidence Detection ...................... VIII . General Considerations ........................................... A. Evaluation of Mechanistic Models .............................. B. Implications for Synaptic Plasticity ............................. C. Diseases and Nicotine Dependency ............................ References ......................................................

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121 121 123 126 127 127 129 132 133 137 137 139 141 141 143 144 146 147 149 149 157 163 166 166 168 171 173

I . INTRODUCTION

A.

The Acetylcholine Receptor: Similarities and Differences with Respect to Other Allosta’c Proteins

The nicotinic acetylcholine receptor (nAChR) and other members of the superfamily of ligand-gated channels are responsible for rapid chemo-electrical transduction in the nervous system.The chemical relay 121 ADVANCEY IN PROTWN CHEMISTRY Val. 5 1

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Copyright 8 1998 by Academic Press. All rights of reproduction in any form resewed . nnfiewwwt 7 5 nn

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between electric impulses at the synapses of neuromuscular junctions or between neurons occurs via the quanta1 release into the synaptic cleft of neurotransmitter molecules in “pulses” of millimolar concentration and millisecond duration (Kuffler and Yoshikami, 1975; Clements et al., 1992). The postsynaptic membrane contains a high density of these ionotropic receptors, present mainly in closed states prior to neurotransmitter release, but capable of interconverting rapidly on binding of neurotransmitter to an open state with a permeable ion channel. However, the open state is transient and closure occurs either by returning to the initial state (followinga brief pulse of neurotransmitter, as commonly occurs under physiological conditions) or by converting to desensitized states (when neurotransmitters or other modulators are present for longer times). Presynaptic effects of nAChR may also contribute to synaptic function by potentiating the response of other ligand-gated channels (Brussard et al., 1995; Gray et al., 1996; Role and Berg, 1996; Wonnacott, 1997; Lena and Changeux, 199713). Mechanistic models capable of representing these various properties include principles of the Monod-Wyman-Changeux (MWC) theory of concerted transitions between conformational states (Monod et al., 1965). This theory was initially developed to account for the kinetic properties of bacterial and mammalian regulatory enzymes on the basis of symmetry features of their quaternary structures. It had it origins in Wyman’spioneering developments of linkage relationships for hemoglobin (Wyman, 1948, 1964) and has been applied to various aspects of ligand gating (Changeux et al., 1967, 1984; Karlin, 1967; Edelstein, 1972; Colquhoun, 1973; Heidmann and Changeux, 1979; Changeux, 1990; Jackson, 1989; Galzi et al., 1996b), including an extended form that generates values for all of the relevant kinetic constants through the application of linear free energy relations (Edelstein et al., 1996). More restricted sequential-type models (Del Castillo and Katz, 1957; Colquhoun and Sakmann, 1985; Lingle et d., 1992; Edmonds et d., 1995; Wang et al., 1997) along the lines of the induced-fit mechanism (Koshland et al., 1966) have also been widely employed. The sequential models assume that the ion channel opens only on binding of two ligand molecules (or possibly with one molecule in the case of brief openings) and thus do not account for the occurrence of spontaneous openings that have been observed in a number of cases (Jackson, 1984;Jackson et al., 1990; Auerbach et al., 1996). One of the goals of this chapter is to formulate experimental approaches that can distinguish between the two types of models. The nAChR and other ionotropic receptors constitute a special class of allosteric proteins (Galziand Changeux, 1995).They possess a number

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of features in common with allosteric enzymes and hemoglobin (Monod et al., 1965; Edelstein, 1975; Perutz, 1989), including ( 1 ) an oligomeric structure; (2)topologically distinct sites responsible for homotropic and heterotropic interactions that can be related to the interaction of pharmacological agonists, antagonists, and effectors; and (3) concerted transitions between discrete conformational states as revealed by all-ornothing opening of the ion channel. In addition, the nAChR possesses distinct features (Galzi and Changeux, 1995; Galzi et al., 1996b), including (1) pseudosymmetry among the subunits related by a fivefold rotational axis perpendicular to the plane of the membrane; (2) homotropic interactions between partially equivalent sites; (3) a set of conformational states (activatable, active, and desensitized) with interaction times that operate in ranges varying from milliseconds to minutes; and (4)pleiotropic phenotypes in which point mutations result in concomitant modifications of apparent agonist affinity, channel conductance, and agonist-vs.antagonist specificity. The nAChR also possess properties permitting observation of singleion channels (Sakmann et d., 1980), a powerful experimental approach for the determination of kinetic properties and conductance levels of the channel. In this respect, conformational changes dependent on the ligand concentration are more readily measured than direct binding interactions. In contrast, for many other allosteric proteins ligand binding is more readily monitored than independent indices of conformational change (Edelstein and Changeux, 1996). Hence, for certain approaches, particularly analysis of stochasticprocesses, the nAChR appears in advance of other allosteric proteins and may lead to novel experimental approaches that could be applied to other allosteric systems. In addition, the possible monitoring of single ligand-binding events (see Section VI,B) may be possible with anticipated technical advances in fluorescence correlation spectroscopy (Eigen and Rigler, 1994; Schwille et al., 1997).

Consequences of Pseudosymmetric Oligomeric Structure Historically, concepts concerning the nAChR were developed initially from studies on receptors from fish electric organs and vertebrate muscle (Changeux, 1990). Biochemical analysis, cloning, and sequencing of these receptors’ subunits established their heteropentameric [2a:lp:1y / ~ : 1 6 structure ] and led to the identification of related neuronal forms (see Fig. l ) ,as well to more distant invertebrate forms (Le Nodre and Changeux, 1995). The neuronal subunits a2-a5 require interactions with /3 subunits in order to form functional receptors, with a putative B.

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I

1

400

600

800 1

1

1

1

1

MYA

200 1

1

1

a9

FIG.1 . Evolutionary relationships between the subunits of the nAChR based on the analysis of Le Novkre and Changeux (1995),updated for sequence information published subsequently (as kindly supplied by N. Le Novkre).

[2a,:3Pj] stoichiometry (Cooper et al., 1991; Lindstrom, 1996) or more complicated combinations in certain cases (Conroy et al., 1992; Vernallis et al., 1993; Ramirez-Latorre et al., 1996; Le Novcre et al., 1996), whereas a7-a9 subunits may form functional homopentamers (Couturier et al., 1990; Sargent, 1993; Elgoyhen et al., 1994; Palma et al., 1996). Several experimental approaches have lead to the identification of functional domains, particularly chemical labeling and sitedirected mutagenesis (Changeux, 1990). In this respect, studies on a7 using sitedirected mutagenesis have been particularly fruitful and have contributed to the current structural model (Devillers-Thiky et al., 1993; Unwin, 1993a; Galzi and Changeux, 1994; Bertrand and Changeux, 1995; Karlin and Akabas, 1995), with the agonist binding site in the N-terminal domain (Karlin and Akabas, 1995; Galzi and Changeux, 1994) and the ion channel constituted by residues of the M2 transmembrane domain (Giraudat et al., 1986; Hucho et al., 1986; Imoto et al., 1988; Devillers-ThiCry et al., 1993), as presented in Fig. 2a. However, other transmembrane regions may also contribute directly o r indirectly to channel properties (Lo et al., 1991; Li et al., 1994; Akabas and Karlin, 1995). Features of the threedimensional structure of the Torpedo nAChR have been obtained by

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a

C

d

M2

s L G IT v L*Ts L T Y F M

L Lv A

Chick a7:

I

Human GlyR a1 :

VGL GITTV LTMTT Q S SG S R

Human AChR al:

MTLS I S ~ L L S

Human AChR pl: Human AChR E: Human AChR ct4:

L T V FL L V I V MGLSIFALYTL L LT L' I YFL C T V S I N V L L A QF Y V IA FL I T L C I T V L LLS~ L L LT TI V F

FIG.2. Structural models of the nAChR. (a) Schematic representation of functional domains. (b) Longitudinal outline of a receptor molecule with respect to the cytoplasmic membrane (Unwin, 1996). Putative a-helices of the M2 domain lining the ion channel are indicated by the two angular bars. (c) Schematic cross-sectional view of the receptor showing binding sites at a-y and a-dinterfaces with subunits in the arrangement deduced for the receptor from Torpedo (Machold et al., 1995).In adult mammalian muscle r e c e p tors, the embryonic subunit y is replaced by E . (d) Sequence of the M2 channel domain for chick a7,with mutations indicated (discussed in the text) and the corresponding residues for other receptor subunits, including mutations that produce a genetic disease.

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electron microscopic studies of ordered arrays at 9 resolution (Unwin, 1993b, 1996), as represented in outline in Fig. 2b. Numerous studies indicate that the binding sites for nicotinic ligands are located at the a-y and a 4 interfaces, or at equivalent positions for nonmuscle receptors (Oswald and Changeux, 1982; Pedersen and Cohen, 1990; Chatrenet et al., 1990; Galzi et al., 1991b; Czajkowski et al., 1993; Fu and Sine, 1994; Corringer et al., 1995), with the subunits arranged as shown in Fig. 2c (Machold et al., 1995). However, alternative interpretations have been presented that place the nicotinic binding sites closer to the center of each a subunit and the fl subunit between the two a subunits (Unwin, 1996). For nicotinic agonists, it has been suggested that higher affinity binding takes place at the a-S interface and that lower affinity binding occurs at the a-y interface (Blount and Merlie, 1989;Sine and Claudio, 1991;Prince and Sine, 1996).In contrast, higher affinity has been assigned to the a-y site for the competitive antagonist d-tubocurarine (Pedersen and Cohen, 1990). Hence, the site that binds more strongly may vary for different agonists or antagonists and, for a particular ligand, the degree of nonequivalence may vary from one conformational state to another.

C. Role of Mutational Studies In this chapter, the generalized MWC-type allosteric model (Edelstein et al., 1996)will be described and contrasted with the sequential-typemodel (Del Castillo and Katz, 1957;Colquhoun and Sakmann, 1985;Lingle et al., 1992; Edmonds et al., 1995;Wang et al., 1997) that has also been used to analyze the kinetic properties of the nAChR.Attention will also be directed to the degree to which differences in the affinities of the two binding sites for ACh are responsible for characteristic properties of muscle receptors. Applications of the models to experimental data for both wild-type receptors and for several mutant forms will be evaluated for dose-response experiments and for kinetic experiments (including single-channel recordings). The analysis of both sitedirected and spontaneous mutations has been critical to the current understanding of the functional mechanism. For example, the channel mutant L247T (see Fig. 2d), first studied bysitedirected mutagenesis in a 7 (Revah et al., 1991; Bertrand et al., 1992),was subsequently incorporated into muscle nAChR (Filatovand White, 1995; Labarca et al., 1995) and recently identified in a congenital myasthenic syndrome (Gomez et al., 1996). Neighboring sites have also been implicated in receptor function, by sitedirected mutagenesis in a 7 (DevillersThikry et al., 1992;Galzi et al., 1992),or as naturally occurring myasthenic mutants (Lena and Changeux, 1997a).The phenotypes proposed for the

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a 7 channel mutants can also be related to the natural mutations identified in patients of human startle disease, as discussed in SectionV, C. The myasthenic and startle mutations in the M2 region are presented in Fig. 2d. Among the myasthenic mutants characterized to date, the data published for the myasthenic mutant ~T264P(Ohno et al., 1995) are particularly valuable for the discrimination between functional models and are described more fully in Section VI,A. Overall, various experimental approaches involving both wild-type and mutant nAChR will be considered in order to delineate the differences in the predictions of the allostericand sequential-type models. 11. MECHANISTIC MODELS A.

The Allosteric-Type Model

In order to account for in vitrofast kinetic observations on ligand binding and ion channel opening with Tmpedoreceptors,four conformational states, B, A, I, and D, were postulated (Heidmann and Changeux, 1980; Neubig and Cohen, 1980;Changeux, 1990),where B is the basal (resting) activatable state, A is the active (open) state, I is the initial desensitized state, and D is the final desensitized state. The four states are in equilib rium, with an interconversion pattern that corresponds to the vertices of a tetrahedron (Fig. 3a), and three degrees of ligation ( i = 0, 1, or 2) are possible for each state. The affinity of each state for agonist increases in the order EA-I-D. The B state was originally designated as “R,” but “B” (for “basal”) was proposed (Edelstein et al., 1996) to replace “R” in order

”i

Di

FIG.3. The interconversion of conformational states for the nAChR. (a) The full set of reactions. (b) The linear progression of states imposed by the relative magnitudes of the rate constanrs (Edelstein et al., 1996).

128

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

to avoid confusion with the high-affinity state in the original MWC formulation (Monod et al., 1965). According to the scheme in Fig. 3a, all interaction pathways are possible in principle. Hence with 6 pairs of interactions and 3 degrees of ligation, a total of 36 conformational interconversion rates would be required to characterize the system fully (in addition to the ligand on and off rates for each state). The 36 interconversion rates are clearly too numerous to be evaluated, but their number can be limited by structural or kinetic constraints of the receptor that render obligatory a certain order of passage between states. Indeed, the different time regimes observed for the various transitions (-1 ms for B + A; -100 ms for A + I; -10 s for I + D) lead to selection of a predominant kinetic pathway, as indicated in Fig. 3b, that corresponds to the passage between states over the lowest transition state barriers. Since the secondary pathways (indicated by dashed arrows) can be assumed to contribute to less than 1% (Edelstein et al., 1996), the tetrahedral arrangement reduces to the linear cascade: Bi P Ai Ii Di. The linear progression permits the full description of all ligandbinding and conformational transition rates in the two-dimensional kinetic network depicted in Fig. 4,with ligand (agonist) reactions r e p

* *

BAko & A0+2X

Akoff

I)

Alko

& 10+2X IAko

2Akon

Ikoff

III/

2'kon

)IkO" B, + X

B2 FIG 4. The complete network of rate constants for conformational interconversions and two agonist binding sites, based on the linear progression of conformational states. Each column corresponds to a series of ligand binding events at two identical sites per receptor, with the rates specified along the vertical arrows by the state-specific intrinsic "on" and "off' constants, with statistical factors included. Each row corresponds to a series of transitions between states governed by rate constants that vary with the number of ligand molecules bound ( i = 0, 1, or Z ) , with the initial and final states in the superscript and the number of ligands in the subscript (Edelstein et al., 1996).

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

129

resented vertically and conformational interconversion reactions represented horizontally. The ratios of the various ligand binding and interconversion rate constants define the equilibrium parameters with respect to the key affinity ratio, c, as summarized in Fig. 5 for the B-A pair of states. The linear progression reduces the number of independent interconversion rate constants that must be evaluated to describe the system from 36 to 18. Nevertheless, 18 interconversion rate constants remain too large a number of independent parameters to be determined, but a substantial additional reduction can be achieved through the application of linear free energy relations.

B. Linear Free Energy Relations Linear free energy relationships have been widely used to relate the kinetic features of related reactions to properties of their respective

FIG.5. The reaction cycle for the B and A pair of states as a function of binding one molecule of agonist. Linkage relations require that each step of ligand binding produces a decrease in the allosteric equilibrium constants "L,, as follows from "C = "LJ"&-,. Since for each value of i the "L, value is set by the ratio of the appropriate rate constants, BAI_3 = ABk,/"k,, the decrease in "L, with each zth ligand binding step must correspond to changes in the interconversion rates such that % = ("k,/"k,) (%-,/''%-,). According to this equation, the stabilization of the higher affinity member of each pair of states resulting from the binding of one molecule of agonist must be reflected by a decreasing interconversion rate constant toward the lower affinitystate and/or an increasing interconversion rate constant toward the higher affinity state. Thus, for the progression from BAZ+I to BAL,,since B"L,_I> BALp, the decrease upon agonist binding must correspond to ABk,/"k,-l < 1 and/or "k,-l/BAk, < 1. Hence, ligand binding drives the B, a A, equilibrium toward A by systematically increasing the B -+ A rates and/or decreasing the A + B rates. Equivalent relations apply to the A-I and I-D pairs of states (Edelstein et al., 1996).

130

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

\ \

I I

\

I

\ \ \

B j

\

2,

\ \

... I

+

... D

State FIG.6. Linear free energy relations and the scaling of transition state barriers. For each conformational state (A or B) or the transition states (TS), the energy of stabilization resulting from ligand binding is depicted by a “ladder” of equally spaced steps. The vertical positions of the ladders are set by AG = 0 for B, and by AG = - R T In for Ao.The transition states are placed according to the free energy of activation A d derived from transition state theory as expressed by the equation k = K(kBT/h)e-ACt/Rr,where K is the transmission constant (which can be assumed to equal 1.0 if there are no barrier recrossings), ha is Boltzmdnn’s constant, h is Planck’s constant, R is the gas constant, and

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

131

transition states (Leffler, 1953; Szabo, 1978;Jencks, 1985; Fersht et al., 1986).They have been particularly successful in describing the variations as a function of ligand binding for the interconversion rate constants of the two principal conformational states of hemoglobin over a wide range of rates (Sawicki and Gibson, 1976; Eaton et al., 1991; Henry et al., 1997). Similar principles have been assumed to apply to the conformational interconversions of the nAChR and have been used to characterize the transition state for the interconversion between each pair of conformations in terms of its position on a hypothetical linear reaction coordinate (Edelstein et al., 1996). The position determines the effect of ligand binding on the interconversion rates, thereby limiting the degrees of freedom in the assignment of values to the rate constants. Specifically, the application of linear free energy relations is based on the difference in affinity for agonists between the partners of each pair of states, as indicated by affinity ratio BAc= kJKB defined in Fig. 5 (or the equivalent ratios for AIcand IDc for the A-I and I-D pairs of states, respectively). The dependence of conformational interconversion rates on ligand binding is assumed to follow from the stabilization of the transition state for each interconversion by the ligand. The extent of this stabilization is assumed to be intermediate with respect to the effects of ligand binding on each on the two participating allosteric states and weighted toward the properties of the allosteric state that the transition state more closely resembles. This assumption may be expressed quantitatively in terms of the position of the transition state on a hypothetical reaction coordinate. In this case, for each pair of states a positional parameter is defined ("p, AIp,or IDp),as presented in Fig. 6 for "p, such

T is the absolute temperature (Steinfeld et al., 1989). For the interconversions between states, the rate constants for the doubly liganded forms are specified o n the basis of the experimental data, as summarized in Table I. The changes in the rates for the unliganded and singly liganded forms are determined by the transition state positional parameters, For the series of interconversion reactions, the differences in the activation energies for the successive transition states reflect the differences in the energy of stabilization of the B and A states with each successive ligand binding, weighted by the "p. Hence, the successive interconversion rate constants scale with the corresponding affinity ratio, with the positional parameter in the exponent: = "c exp("p) and "k,-,/"k, = BAc exp (1 - "p). Since the product of these two equations is equivalent to BAc = ("kJ %,) (BAkt,-I/"Bka-I) (see the legend to Fig. 5), these relations permit the positional parameter to define the dependence of the interconversion rate constants on ligand binding (Edelstein et al., 1996). For example, with "p = 0.2 (Table I), it can be seen that the vertical spacing of the transition states for the B, P A, interconversions at different degrees of ligand binding more closely resembles the spacing between the A, forms than the spacing between the B, forms. Equivalent relations apply to the A-I and I-D states.

132

STUART J. EDELSTEIN AND JFAN-PIERRECHANGEUX

that this parameter characterizes the transition state on a linear scale between 0 and 1 with respect to its proximity to the lower affinity state of the pair. On the basis of these relations the full series of rate constants for the Bi P A, interconversions can be generated from the ligand binding parameters ( B A ~ ) with three additional values: BAp,one B + A rate constant, and one A + B rate constant (see legend to Fig. 6). In this way the six rate constants for each pair of states in the linear scheme are reduced to two rate constants and one positional parameter. With homopentameric receptors, the same number of parameters provides estimates for all 12 interconversion rates for each pair of states (Edelstein and Changeux, 1996). For detailed kinetic studies on muscle nAChR, because of the distinct time ranges over which the three pairs of states interconvert, sufficient data are available to permit reasonable estimates for all values (Edelstein et al., 1996), as listed in Table I. The value of ““p = 0.2 indicates that with each ligand-binding step the increase in the B + A rate is larger than the decrease in the A + B rate.

C. Alternative Models For many of the experimental measurements on nAChR reported in the literature (Lingle et al., 1992; Edmonds et al., 1995), the data for activation have been interpreted in terms of a “sequential” model, in which channel opening for muscle-type receptors occurs only upon binding of the second molecule of agonist, as represented in Fig. 7 by the step B2 P A2. In this case, channel opening and closing are characterized by only two rate constants, fi and a,respectively. The reasons for having invoked this model include the difficulties of implementing a full MWCtype model prior to the introduction of the linear free energy relations (Edelstein et al., 1996) and the fact that under certain experimental conditions (such as relatively high agonist concentrations), the assumption that channel opening occurs only for biliganded molecules provides an adequate description of the system. In some cases, singly liganded openings have been incorporated into the sequential model to account for brief openings (Colquhoun and Sakmann, 1985; Wang et al., 1997). However, in other cases that include channel opening of unliganded receptors, the sequential-type model is not adequate; such cases are considered in Sections V and VI. Additional aspects concern desensitization (as represented in Fig. 7 by the step A, P D2) and recovery. Ever since the benchmark studies of Katz and Thesleff (1957) it has been generally noted that following desensitization, recovery occurs spontaneously upon removal of the ago-

133

ALLOSTEIUC TRANSITIONS OF THE ACh RECEPTOR

B, + X

D;

+x

2 Bkoff

FIG.7. The sequential-type model, with ligand binding to the B and D states and formation of the open state (A,) from B2 as defined by the constant k&. = [Bn]/ [A,] = a/@.In this scheme, only one desensitized state is included; it is designated “D,” but its properties would correspond to “I” in Fig. 4.

nist, but “silently,” i.e., with no channel opening during the recovery period. Since return to the resting state via A2 would imply channelopening events, it has been argued that a distinct “recovery” pathway must exist, as represented in Fig. 7 by the series D2 + D1 + Do + B,. The overall model presented in Fig. 7, with activation restricted to biliganded molecules and a distinct recovery sequence, represents the “cyclic” scheme that has been used to interpret experimental data (Franke et aL, 1993). However, an explanation of how silent recovery can also be accommodated by an allosteric-type model is presented in the following section. 111. RECOVERYFROM DESENSITIZATION When the relationships linking ligand binding, allosteric equilibria, and transition state barriers were evaluated for all three pairs of states for muscle receptors studied by single-channel measurements or rapid agonist application (Colquhoun and Sakmann, 1985;Franke et al., 1993), the values for the various parameters presented in Table I were deduced (Edelstein et al., 1996). The overall properties of the system may then be represented by the free energy profile presented in Fig. 8. The vertical

TABLE I Parameter Valws for the Four-State Allosteric Kinetic Mechanism" State parameters

Independent parameters Ligand on rates ( A T ' S - ' ) Ligand off rates (s-') Deduced parameters Equilibrium constants (M) Amnity ratios

I state

A state

B state Bk,,b.= 1.5 X loR Btr = 8000

A%.

=

1.5 X lox

'k,," = 1.5 X lo8 'k,,, = 4.0

At = 8.64

I(B = 5.3 x 10-5 % = 1.08 X

D state

I(A = 5.7 x 10-8

K, = 2.7

"k,,. = 1.5 X lo8 = 4.0

"k,,S

&

X

"c = 0.46

= 2.7 X

lo-'

mc= 1.0

Interconversion parameters B e A Independent parameters TS positional parameter Interconversion rates (s-l) Deduced parameters Interconversion rates (s-')

Allosteric constants

"p "b "b

A-I

I w D

"p = 0.99

= 0.2 = 3.0 x 104 = 7.0 X lo2

Mkq

"k, = 0.54 m& = 1.08 x 104 "kl = 1.3 X lo2 "kl = 2.74 X lo3 "L,, = 2 x 104 "15, = 21.6 "& = 2.3 X

'"p = 0.99 '"b= 5.0 X

= 20.0 = 0.81

D'b

= 1.2 x 10-3

"'k, = 5.0 X = 1.2 x 10-3

Mk, = 19.7 "k, = 3.74

01%

Mkl = 19.85

'"k, = 5.0 X

uLkl= 1.74

"'k, = 1.2 X lo-%

M L g = 0.19 "L1 = 8.7 X

=

ID&

= 2.5 X

"4 = 2.5 X

4.0 X

ID&

= 2.5 X

lo-'

~

For the 14 independent rate constants (4 on and 4 off rates for the ligand, 3 forward and 3 back allosteric transition rates for the doubly liganded forms, and 3 transition state positional parameters) necessary to define the B, A,, A, P I,, and I, D, allosteric transitions with two equivalent agonist binding sites per molecule, parameter values were deduced for the nAChR on the basis of results with rapid agonist application techniques using outside+ut patches containing embryonic-like nAChR from mouse muscle (Franke et al., 1993) and earlier singlechannel measurements (Colquhoun and Sakmann, 1985), as reported previously (Edelstein et al., 1996).

*

*

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

135

20 -

-a,

h

E"

10-

L Y

v

A

P a 0C

W

-10 -

State FIG.8. Free energy diagram for the fourstate allosteric model, including all liganded and unliganded allosteric states, as well as their respective transition states. The B, A, I, and D states are each represented by a free energy ladder, with details as described for the B and A states in Fig. 6 and values of the relevant parameters as described in Table I (Edelstein et al., 1996).

ladders for each state and the intervening transition states correspond to the change in free energy for each molecule of agonist bound. Hence the step sizes for the B, A, I, and D states increase with affinity according to the series of dissociation constants & > KA > KI > KD.The vertical alignment of the ladder for each state is set by the values assigned to the relative concentrations of Bo, &, Io, and Do. The transition state heights are determined by the positional parameters (see Fig. 6 ) . The progression of doubly liganded states B2+A2+ I2 + D2represents the allosteric cascade for the conformational changes elicited by application of a strong and prolonged pulse of agonist, with the time of passage through A2 corresponding to the average open time in singlechannel measurements. The kinetic properties of the system can be represented in simulations, as shown in Fig. 9a and b, with the time axis presented on a logarithmic scale to permit visualization over several time regimes (Edelstein et d.,1996). Since the concentration of agonist is high, this

a

1 0.8 Q, v)

C

0.6

0

a v)

0.4

Q,

U

0.2

0

b

4

-2

4

-2

log time

0

2

1 0.8

0.6 0.4 0

a 0.2

0 0

2

2

4

log time C

1

0.8 c 0 .c m S

a

0.6

0.4

0

a

0.2 0

-2

0 log time

FIG.9. Kinetic simulations presenting activation, progression through the states on agonist binding, and recovery following agonist removal. The states are labeled, with the number of ligand molecules bound indicated by the line format (0, dotted line; 1, dashed line; 2, solid line). The ligand concentration is lo-' M. Values of the parameters utilized are presented in Table I. (a) The appearance of the open state (in the form of a current change, 1 - [A states]) on a scale of log time (in seconds), with the inset presenting the same data on a linear scale (the vertical bar = 0.1 fractional amplitude change; the horizontal bar = 0.5 s). (b) The fractional population represented by each of the four states during an agonist pulse, with time on a logarithmic scale. (c) Recovery begins upon removal of free agonist at the point marked by the arrow in (b). (Edelstein et al., 1996.)

WOSTEIUC TRANSITIONS OF THE ACh RECEPTOR

137

simulation follows the path Bo + B1 + B2 + A2 + Ip + D2. At early times in Fig. 9b the progression from unliganded to liganded forms is apparent for B, followed by interconversion of biliganded B to biliganded A and I. Transient channel opening corresponds to the appearance and disappearance of A. The population of biliganded D increases only at longer times via conversion from biliganded I due to the slow rate of the I2 + D2 interconversion. Following termination of the pulse, agonist dissociation drives the system to the unliganded states and the initial distribution is reestablished relatively rapidly, particularly from I2 along the pathway I2 + I1 + I,, + A,, + Bo (Fig. 8). These features can be visualized in the kinetic simulation of recovery presented in Fig. 9c. With "ko 9 Y\ko, recovery along the pathway I. + A. + Bo occurs with so rapid a passage through the A,, state that channel opening is negligible (Edelstein et al., 1996). Following agonist removal, the I2 state loses agonist molecules and is transformed to Bo in less than 1 s. The D2 state loses agonist molecules to form Do within 10 s, but requires longer times (103-104s) to reequilibrate with Bo and to return to the initial low levels. Such long recovery times could account for certain slow physiological responses, possibly related to nicotine pharmacology (see Section VII1,C). It is clear from this simulation that the four-state model predicts virtually negligible channel opening during the recovery period, but without the necessity of imposing a separate recovery pathway from I (or D) to B that arbitrarily disallows passage through A, as required in the "cyclic" model (Franke et al., 1993).

IV. KINETICBASISOF DOSE-RESPONSE CURVES A . Dependence on the Desensitization Rate The dose-response analysis has been widely used for characterization of the cooperativity and affinity (EC,,) of ligand-gated channels, but it is important to ascertain under what conditions such an equilibriumbased analysis is appropriate for a transient phenomenon. Therefore, simulations were performed with the complete four-state model to test this issue (Edelstein et al., 1996). The relative rate of the initial phase of desensitization,A2+ 12, can result in systematic errors in the apparent values of the Hill coefficient, n, and ECS0,as described in Fig. 10. The errors are relatively minor for the value of Nk2 = 20 s-l (Table I ) , but for higher values of "K2 significant distortions in the simulated doseresponse curves were predicted. For example, the apparent values of

138

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

a

b

log (ACh) FIG.10. Dose-response simulations. (a) Kinetic simulations for increasing concentrations of agonist in the concentration range 10-6-10-3 M, with the value of Mb = 20 S K I (Table I). Simulations for each concentration (in increments of 10” = 1.58 times the previous concentration) are presented as “Response” (calculated as 1 - A,,,,) vs. log time (in seconds), and the minimum of each curve, corresponding to the maximal channel opening at that concentration, is marked by a filled circle. (b) Dose-response curves for the simulation in (a). Tke predicted response curve (presented as the continuous dotted line) is described by A.,,, the theoretical equilibrium for the normalized fraction of A in a system limited to the B and A states:

where aAis the concentration of ligand [XI normalized to the a f h i t y of the A state: aA= [X]/KA and the values of the relevant parameters are from Table I. The individual points for maximal channel opening at each concentration from (a) are transferred to give the corresponding filled circles. In addition, the filled squares correspond to simulations carried out with Mb = 200 s-’ (Edelstein et al., 1996).

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

139

the Hill coefficient and affinity at MuK2 = 20 s-’, n = 1.6 and EC50= 10 p M , differ only slightly from the values observed with a desensitization sufficiently low (“k2= 2 s-l) to avoid any distortions: n = 1.7 and ECSo= 9 pM.Hence, for both the n and EC50values, the apparent rate constants for the AChR (Table I ) are such that errors are limited to -10% (Fig. lob). However, were the “k2value 10-fold faster (NUk2 = 200 s-I), the relevant values would be n = 1.3 and EC50 = 20 p M (Edelstein et aZ., 1996), with major discrepancies between the apparent and true (desensitization-free)properties. Therefore, as long as desensitization is sufficiently slow so as not to introduce significant errors, doseresponse analysis for the nAChR can provide a useful experimental protocol and a number of investigations relying principally on such measurements have led to important observations concerning pleiotropic mutant phenotypes, as described in Section V. Nevertheless, it is important to emphasize that for a multistate system such as the ligandgated channels, kinetic effects may prevent the distribution of conformational states from attaining their equilibrium positions. B. Desensitization

Low-Concentration Prepulses

A prominent feature of ligand-gated channels is the desensitization by low “prepulse” concentrations of agonist that are insufficient to provoke significant channel opening but elicit desensitization when followed by a stronger test pulse (Katz and Thesleff, 1957; Rang and Ritter, 1970). By studying a range of prepulse concentrations and plotting the fraction of residual activity observed with the strong pulse, investigators have obtained desensitization curves with the midpoint defining an apparent inactivation constant, IC50.Typically, the prepulse is applied for a duration of -10 s (Franke et al., 1993). If equilibrium conditions prevailed, the ICs0value obtained would be related to the dissociation constant for the high affinity of the desensitized state (Heidmann and Changeux, 1978). Therefore, to test whether the equilibrium assumption is reasonable for such an analysis, simulations were performed at very low prepulse concentrations of ligand. As presented in Fig. 1la, kinetic simulations reveal that for a low concentration such as 0.4 p M , progression through the l3-A-I-D states is relatively slow and for a 10 s prepulse some I state appears, but only a small fraction of the D state that would be produced by a pulse sufficiently long (-1000 s) to reach the final equilibrium value. When a series of simulations at different concentrations are performed, the degree of desensitization after 10 s can be measured and compared to the equilibrium value of desensitization. In this way a

140

STUART J. EDELSTEIN AND JEAN-PIERRE CHANCEUX

a

1

C

0.8

0 .-

m 0.6 3 Q

0 0.4

a

0.2

L

/

_I

0

b

1

€

0.8

0.6 7

0.4 02 0

t t

-8

-7

I -6 log (ACh)

5

4

FIG. 1 1 . Simulations of prepulse desensitization with low concentrations of agonist. Simulation of the populations of states for an agonist concentration of 4 X M. (a) Data presented as a function of time in seconds for the predominant molecular species, B,,, I p , D,,and DP. (b) Inhibition-response curve to obtain apparent IC,o values. The solid line shows values pr_edicted by the allosteric theo-v for the normalized fraction of molecules in the D state (Dn0,) and presented as 1 - D.,,, where

and aDis the concentration of ligand [XI normalized to the affinity of the D state: aD= [XI/&. Using the values in Table I leads to an IC,,, values of 2.66 X M. The points in (b) are from a series of simulations as in (a) for the fraction of activatable receptors remaining after a 10 s prepulse at different concentrations of ACh. The dashed curve through the points corresponds to an apparent IC,,, value of 1.2 X 10-fiM(Edelstein et al., 1996).

hypothetical curve for the determination of IC5,]is produced for the equilibrium properties and compared to the simulated values with 10 s prepulses. These data, presented in Fig. l l b , show the systematic divergence of the two curves. The points obtained from the simulations for 10 s prepulses are considerably to the right of the equilibrium curve

WOSTERK TRANSITIONS OF THE ACh RECE€TOR

141

and imply an apparent affinity for the D state (when IC50values are used) that is significantlyweaker than the true equilibrium value (Edelstein et al., 1996).

V. MULTIPLEPHENOWES A . A Generalized Allosteric Network Point mutations within receptor subunit genes often result in “complex” and extremely pleiotropic phenotypes with, for instance, concomitant modifications of the apparent affinity for agonist, channel properties, and agonist vs. antagonist specificity (Revah et al., 1991; Bertrand et al., 1992; Devillers-ThiCry et al., 1992; Yakel et al., 1993; Langosh et al., 1994; Rajendra et al., 1994; Labarca et al., 1995). Following the discovery of these mutations, the interpretation of their complex phenotype in molecular terms became a challenging issue. For example, a single mutation in the M2 channel domain of the a7 nAChR, Leu-247 to Thr (Revah et al., 1991; Bertrand et al., 1992; Devillers-ThiCry et al., 1992),yields a receptor that is insensitive to the channel blocker QX222, has lost desensitization, and displays an apparent affinity for acetylcholine (ACh) up to 200-fold higher than for wild type. In addition, the mutant receptor exhibits two conducting states activated by high (the 40 pS state) vs. low (the 80 pS state) concentrations of ACh. Moreover, a competitive antagonist of the wild-type receptor, dihydro-O-erythroidine (DHPE), behaves on this mutant as a full agonist (with 10-fold higher apparent affinity than ACh) and exclusively activates the highconductance state. In order to interpret such complex properties it is necessary to take into account the fact that mutations at several different positions along the primary sequence of receptor subunits may produce similar, although not identical, phenotypes. For instance, shifts in the neurotransmitter dose-response curve are obtained by mutating amino acids contributing to either the ligand-binding domain (Schmieden et al., 1992; Galzi et al., 1991a;Tomaselli et al., 1991; O’Leary and White, 1992; Aylwin and White, 1994) or the ion channel domain (Revah et al., 1991; Bertrand et al., 1992; Devillers-ThiCry et al., 1992; Yakel et al., 1993; Langosh et al., 1994; Rajendra et al., 1994; Labarca et al., 1995), even though they are located 20-40 A away from each other in nicotinic receptors (J. M. Herz et al., 1989). Moreover, mutations may alter the number and distribution of the multiple conducting states, as noted for the L247T mutation of the a7 nAChR, as well as for the hyperekplexia

142

STUART J. EDELSTEIN AND JEANPIERRE CHANGEUX

mutations of the glycine receptor (Langosh et al., 1994; Rajendra et al., 1995; Lynch et al., 1997). A context for these phenomena has been provided (Galzi et al., 1996b) by noting that the four-state allosteric model can be extended to a generalized allosteric network, as summarized in Fig. 12. Receptor molecules are assumed to exist in several (at least three) discrete conformations, S,, which correspond to thermodynamically stable states with defined tertiary and quaternary structures. These conformations are qualitatively described by a structural parameter Z,, and functionally defined as closed (but activatable), active (channel open), and desensitized (closed but refractory states). Each state is characterized by its affinity for the agonist ( K , ) or other ligands, and its conductance ( y t , in pS). The interconversion between any two conformational states S, and S, occurs freely with an allosteric equilibrium constant YL = [SJ/ [S,], and ligands stabilize the conformations to which they bind with higher affinity. One receptor oligomer, with a given subunit composition, has access to a unique set of conformational states, possibly including more than one conducting (Revah et al., 1991;Bormann et al., 1993) or desensitized (Heidmann and Changeux, 1980; Sakmann et al., 1980) state. Substituting one subunit for another, or mutating amino acids in one or more subunits, may alter the pattern of the conformational network by changing the intrinsic binding properties ("K' phenotype) or the conductance ("y" phenotype) of one or more conformations, or by changing the

5 Ki Ci Yi

FIG 12. The allosteric network of receptor molecules in multiple conformational states. Each conformation S, corresponds to a unique quaternary structure (s,)with intrinsic binding properties ( K , )and conductance ( y , ) .The interconversion between any two conformational states S, and S, is described by an allosteric equilibrium constant "L = [S,]/[S,] (Galzi el al., 1996b).

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

143

equilibrium constants between conformational states (“L” phenotype). In addition, the number of conformational states may vary, i.e., certain conformations may become virtually inaccessible, or conversely, stable. For the sake of simplicity, in all cases considered both the wild-type and mutant receptors were assumed to interconvert to the same finite number of identical quaternary structures ( S ) .Also, as kinetics of recep tor activation and desensitization take place over significantly different timescales (desensitization is generally slow compared to activation, as discussed above in relation to Fig. lo), the conformational scheme used to describe receptor activation was, in a first approximation, reduced to only those interconverting states involved in the activation process (resting and active states). Taking into account the intrinsic properties of individual conformational states and their possibilities to isomerize to other conformational states (Fig. 12), three main classes of effects may be expected in such an allosteric system with increasing numbers of interconverting states (Galzi et al., 1996b): (1) the binding of “ K ’ phenotype; (2) the conformational interconversion or “L” phenotype; and (3) the conductance or ‘‘7” phenotype.

B. The K Phenotype The K phenotype is assumed to result from mutations that selectively alter the intrinsic binding affinities of individual conformational states. In this context two possibilities may be envisioned. First, the affinity of each conformation changes but the affinity ratio ( y c = K,/K,) between conformations remains constant. The apparent affinity (EC,,) for response activation would then change with neither modifications of cooperativity (Hill coefficient) nor response amplitude. In other words, the wild-type and mutant dose-response curves are parallel. Second, the mutation selectively alters the affinity of certain states only, leading to changes in the affinity ratios (”c). In this case, not only would the apparent affinity be affected, but also cooperativity and possibly response amplitude. Furthermore, as c increases, agonists may progressively become partial agonists or even competitive antagonists. Finally, for none of the K phenotypes would the spontaneous equilibrium between any states S, and S, be altered in the absence of ligand. A possible example of this phenotype may be considered on the basis of the amino acids Tyr-93, Trp-148, Tyr-190, and Tyr-198 identified by affinity and photoaffinity labeling of the ACh-binding site from the electric organ nicotinic receptor (Devillers-ThiCry et al., 1993). Substitution of their homologs to phenylalanine on the corresponding chick neuronal a7 residues Tyr-92, Trp-148 and Tyr-187 (Galzi et al., 1991a)

144

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

or on mouse muscle a 1 subunits (Tomaselli et al., 1991; Aylwin and White, 1994) yields functional receptors, with reduced sensitivity to ACh but unchanged Hill coefficients and maximal current amplitudes. These alterations may be interpreted in terms of a K phenotype, with the intrinsic affinity of the activatable and active conformations being affected to the same extent. Indeed, simulations of a7 nicotinic receptor dose-response curves with changes in solely the K values for Y92F, W148F, and Y187F mutant receptors (Galzi et al., 199613) fit the experimental data points and yield EC5, values and Hill coefficients consistent with the experimentally determined values (Galzi et al., 1991a). Mutations in other parts of the extracellular domain of ligand-gated ion channels alter the pharmacological specificity in a different way. Mutation of Asp900 in muscle a1 (O'Leary and White, 1992) or Gln198 in neuronal nicotinic a3 (Galzi et al., 1992), as well as Ile-111 and Ala-212 in a 1 glycine receptor subunits (Schmieden et al., 1992), affect the relative affinity and efficacy of distinct agonists. Mutation of Asp200 to Asn, in particular, converts the partial agonists TMA and PTMA into competitive antagonists (O'Leary and White, 1992), as expected for changes of intrinsic binding properties of only certain states within the network, i.e., altered c values in a K phenotype (Galzi et al., 1996b). Yet, uncertainties persist about this interpretation since the properties of these mutants may also be accounted for by an L phenotype. Additional experimental data are required to reach definitive conclusions.

C. The L Phenotype The L phenotype is assumed to result from mutations that selectively alter the equilibrium constant between two given interconvertible conformations. The intrinsic properties of each conformation, i.e., the microscopic binding constants and the state of channel activity, are further assumed to remain unchanged. If two states are considered, namely, an inactive (channel-closed) B state and an active (channel-open) A state, the fraction of receptor molecules spontaneously existing in the active state in the absence of ligand is described by BALo = [B,] / [A,]. Furthermore, regulation of channel opening by an agonist depends on its affinity for the active state, as compared to its affinity for the inactive state ("c = KA/KB).Agonists are characterized by a small value of %, partial agonists by a larger BAcvalue, and competitive antagonists by an even larger one. For an L phenotype, as BALo increases, agonists may progressively become partial agonists and competitive antagonists, as shown in Fig. 13.For decreasing BALo values, the reciprocal progression takes place, and, in addition, competitive antagonists may become partial agonists

145

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

a

b 6%

= 800,000

_ _ A, Y

I

-8

I

-6

-4

-8

-2

-6

Log [XI

-4

-2

Log [XI

i7cpJv rl

C

IT-

0.8' l B A B ALc == 20.1 0

0.2

,

-

.

i l v ; p - #

0 -8

-6

-4

Log [XI

-2

-8

-6

-4

-2

Log [XI

FIG. 13. The L phenotype as illustrated with curves of a n d x for four combinations of "Lo and "c (Edelstein and Changeux, 1996): (a) high "Lo and low "c; (b) high "Lo and high "c; (c) low BALoand low "c; (d) low "Lo and high "c. The values of "Lo and "c correspond to the data analyzed with a two-state model (Galzi et al., 1996b) for the nAChR a7,wild type ("Lo = 800,000) and the channel mutant V251T ("Lo = 20), with respect to the agonist ACh ("c = 0.1) and the partial agonist DHPE ("c = 0.5) on the basis of published experimental data (Devillers-ThiCryet al., 1993; Galzi et al., 1992). In addition the absolute values of the binding affinities are fixed by KA = 2.5 X Mfor ACh, and K A = 3.5 X 10-6Mfor DHPE.

(intermediate BAcvalues) or remain competitive antagonists (large BAc values). Also, in equilibrium binding experiments, apparent affinities will be displaced more for ligands with small % values than for ligands ~ Furthermore, the model predicts that for very low with large B A values. values of BALo,spontaneous stabilization in the active state may occur, yielding constitutively active mutants (spontaneous channel opening), a phenomenon that cannot be accounted for by the sequential-type model. In addition, at low BALo positive allosteric effectors of the wild type, which behave as very weak agonists, may become partial agonists of the mutant. Finally, changes in the BALo value will generally be accompanied by changes in cooperativity and maximal response amplitude.

146

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

A possible example of this phenotype arose from studies of chemical labeling of T e e d o nicotinic receptor with noncompetitive blockers, which led to the identification of amino acid rings from the M2 segment of all five subunits that contribute to the channel domain and are conserved in the family of nicotinic receptors (Devillers-ThiCryet al., 1992; Karlin, 1993). In the case of the a 7 nicotinic receptor, the available data on the alterations of receptor properties that take place on substitution of the ring of Val-251 to Thr or of Thr-244 to Gln can be interpreted in terms of L phenotypes. Indeed, ACh dose-response curves can be simulated for wild-type and mutant receptors (Galzi et al., 1996b), with the single assumption that L values are high for the wild type (BALo= 8 X lo5) and low for the mutants (BALo= 20), corresponding (within the limits of precision of the experimental data) to the simulated curves presented in Fig. 13. Such simulations also account for the higher maximal amplitudes of the ionic response observed for these mutants (Devillers-ThiCry et al., 1992; Luetje et al., 1993). Furthermore, the competitive antagonist of the wild-type receptor, DHPE, with its specific binding K and BA~values (see details in the legend to Fig. 13), behaves as a competitive antagonist when the BALo value corresponds to the wildtype receptor, and as a partial agonist when the ‘*Lovalue corresponds to the V251T or T244Q mutant receptor. An interesting comparison with the L phenotype for the nAChR is afforded by certain mutations in the channel domain of glycine receptors. Two mutations identified in M2 from the glycine receptor, R271L and R271Q (see Fig. 2d) cause the neurological disorder hyperekplexia (Shiang et al., 1993) by drastically reducing the apparent affinity of the receptor for the agonist glycine (Langosh et al., 1994; Rajendra et al., 1994, 1995). These mutations, in addition, decrease the maximal amplitude of agonist-evoked currents, reduce the number of conducting states when present in the homooligomeric a 1 receptors from 5 (wild-type) to 3 (R271L) or 1 (R271Q), and convert the partial agonists p-alanine and taurine into competitive antagonists. Accordingly, their phenotype appears as a “mirror image” of the phenotypic changes observed in the nicotinic a 7 receptor L247T or V251T: the glycine receptor mutants would then resemble nAChR wild-type (Galzi et al., 1996b).

D. They Phenotype The y phenotype is assumed to result from changes of the state of activity of the ion channel (e.g., nonconducting to conducting) in one (or possibly more) conformation, with no alterations of the intrinsic binding parameters of each state (i.e., its pharmacological specificity)

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

147

nor of the equilibria (and kinetics) of interconversions. For example, it may be assumed that one desensitized conformation, which exhibits high affinity for agonists but has a closed channel, changes to the conducting state after mutation. In such a three-state model (one activatable and two conducting states), the expected changes of the physiological response properties are fourfold, as compared to the wild type: (i) desensitization of the response to agonists is reduced, since isomerization to a desensitized conformation is no longer accompanied by a closing of the ion channel; (ii) the apparent affinity for activation is higher for agonists, since desensitized conformations exhibit higher affinity for agonists; (iii) a new conducting state, in addition to the wildtype conducting state, may be observed; and (iv) the pharmacological drug profile of the two conducting states differ. Agonists cause the opening of one conducting state at low concentration (the high-affinity, desensitized but conducting state) and of two conducting states at high concentration, whereas competitive antagonists, if stabilizingthe desensitized conformation, will activate only the new conducting state at any concentration used. Analogies exist between the phenotypes of the M2 mutants L24’7T, on the one hand, and T244Q or V251T, on the other. Yet, if the L247T mutant receptor were to correspond to an L phenotype, a single change in L value would not fully account for the experimentally determined ACh and DHPE dose-response curves (Revah et al., 1991; Bertrand et al., 1992; Devillers-ThiCryet al., 1992). Indeed, with the L value yielding an appropriate ECS0for ACh, DHPE will not behave as a full agonist, but rather as a partial agonist as on the T244Q or V251T mutants; moreover, under no circumstances will the apparent affinity for DHPE be, as observed,higher than for ACh. Rather, the occurrence, in addition, in L247T of two conducting states with distinct pharmacological profiles (Revah et al., 1991; Bertrand et al., 1992; Devillers-ThiCry et al., 1992), favors an interpretation in terms of the y phenotype scheme. In such a case, simulated dose-response curves satisfactorily fit the experimental data, as shown in Fig. 14 for both ACh (ligand 2) and DHPE (ligand 1),assuming that one of the conducting states is identical to the wild-type conducting states (not stabilized by DHPE), while the other (assumed to correspond to a desensitized conformation of the wild-type) binds DHPE with affinity higher than that for ACh (Galzi et al., 1996b).

E, Limiting Properties at Extremes of L The range of properties resulting from the L phenotype arises from differences in the binding (Q and ionic response (A)functions. As

148

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

Ligand 1 Ligand 2

--

Y

.c 0 3 -0

6-A

-I

c

$ 0.5.

I

c

.-0 .I-

0

?

LL

0

I

-8

-6

-4

-2

Log [ligand] FIG. 14. Theoretical dose-response relationships describing the y phenotype. The curves are generated with a three-state model, B P A P I, assuming that either only the A conformation or both the A and I conformations contribute to the physiological response, for the curves as indicated. The equation for the case of both A and I as open states is

*

where a = [XI/& The L values are for the B A transition, BALo= 8 X lo", and for The affinity values are, for ligand 1, K A = 2.5 X the A P I transition, "Lo = 1.2 X "Ic = 0.4; for ligand 2, K A = 3.5 X lo-', "c = 0.5, Kl = 3 X % = 0.1, KI = lo-', "c = 0.0857. Intrinsic affinities increase from state B to A to I for both ligands. Ligand 1 is a competitive antagonist when the I state corresponds to a closedchannel state and becomes an agonist when the I state has an open channel. Ligand 2, which is an agonist in both cases, stabilizes one or two conducting states depending on the biological activity of the I conformation (Galzi et al., 1996b).

pointed out some 30 years ago (Rubin and Changeux, 1966; Changeux and Rubin, 1968), where it is possible to monitor and separately, distinctive differences in the two functions may be observed, thereby constituting a diagnostic test of the two-state model. For very low values of L, a significant fraction of molecules is in the A state in the absence of ligand: the system may be qualified as hyperresponsive (Edelstein and Changeux, 1996). On addition of ligand, the curve f o r x remains above the curve for as a function of ligand binding, with the curve for approaching saturation at ligand concentrations that give incomplete binding. For very high L values, the curve for remains below the curve for with a maximal value of < 1, even when all binding sites

r

r

r,

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

149

are saturated: the system is hyporesponsive. At intermediate values of L, differences between and may also occur, but they involve more subtle distinctions in the shape of curves. The full extent of possible differences between y and as a function of the L value are presented in Fig. 15 for a protein with five sites (Edelstein and Changeux, 1996), such as the a 7 nAChR (Palma et al., 1996). For ligand binding, y always varies from 0 to 1 and occurs, for a protein with A and B states, within the affinity limits of YAand YBthat define the “ligand binding range.” In contrast, for the state function, at the extremes of L, does not vary between 0 and 1 with increasing ligand binding, but has a limited allostmi range, Q (Rubin and Changeux, 1966), as summarized in the lower portion of Fig. 16. Moreover, as noted in Fig. 15, the “ligand response range” can extend significantly beyond the limits of K Aand KB.For a protein with five sites, the apparent affinity, EC50(as reflected by [XI,,, the concentration of ligand at the midpoint of the curve) may be as much as 6.7 times lower than K A (the extreme hyperresponsive pattern) or 6.7 times higher than KB (the extreme hyporesponsive pattern). This distinction is relevant for a7 receptors, since for the wild type, according to the simulations described in Fig. 13, the EC5, value is -5 times higher than the value of K B and thus close to the theoretical limit of 6.7 for a pentamer. Differences in the cooperativity of the binding and state functions also occur, as measured for example by the Hill coefficients, n50 at = 0.5 and n.;” at A‘ = 0.5 (Fig. 16), where is the normalized form of the response (Changeux and Rubin, 1968), as defined in the legend to and at the Fig. 15. The maximum value for nLo is higher than for extremes of L the value of %, falls to the limit of 1.0 (Rubin and Changeux, 1966), but the lower limit of A‘ for a homopentamer (for BAc= 0.1) is nj, = 1.27 (Edelstein and Bardsley, 1997). This value > I arises from the contributions of higher order reactions to the formation of molecules in the A state, as summarized in Fig. 17. In this context, the cooperativityof the dose-response curves of the a 7 nAChR predicted by a two-state model, nLo = 1.27 (Fig. 13),and the value observed experimentally, n = 1.4 (Revah et al., 1991), imply that the system is near the lower theoretical limit for a pentamer.

A’

r

VI. DEDUCTIONS FROM SINGLE-CHANNEL MEASUREMENTS A. Kinetic Consequences of Mutant Phenotypes Several classes of congenital myasthenic syndromes have been described involving specific components of the neuromuscular junction

150

STUART J. EDELSTEIN AND JEANPIERRE CHANGEUX

-

Y -

FIG.15. The state and binding functions a t d theiflcooperativity for a homopentamer with B and A states. The allosteric functions A and Y are presented as a function [XI/ K A for a series of values of the allosteric parameter, BAl,o. All cumes are calculated with B A = ~ 0.1; is determined with the equation

r

v

= [a(l

+ a)"' + " L

0 BA

ca(1

+ " c a ) N - ' ] / [ ( l + a)"+ "Lo(l + " c a ) N ) I

where N is the number of ligand-binding sites and a is i h e concentration of ligand normalized to the affinity of the A state: a = [XI/&. For Y the apparent affinity, [XI,, (defined as the value of [XI at F = 0.5), occurs between the limits K Aand KB corresponding, respectively, to the pure A state ( YA) at the low "Lo extreme and the pure B state ( Y , ) at the high BAZA,,extreme. These limits constitute the "ligand-binding range." The equation for reduces at very low '"'Loto FA= 1/(1 + K , / [ X ] ) and at very high B.4Lo to FB= 1/(1 KB/[X]). The limits for binding are thus independent of N a n d reflect only the intrinsic binding constants of the B and A states. For the state function, the cumes are described by the equation

r

+

A = 1/[1

+ "Lo(l + " c ( ~ ) ~ / ( +l a ) " ]

which predicts variations between A,,,in the absence ligand and A,, at the saturating ligand, where A ,,,,,, = 1 / ( 1 + "L,) and .&, = 1/(1 + BALo["~]~v). The low ',Lo and high "Lo limits of the midpoints ofA are set, respectively, by [XI,, = KA - 1 and [XI,, = &/[( ~ - )11, constituting the "ligand-response range" that considerably exceeds the "ligand-binding range." Adapted from Edelstein and Changeux (1996).

(6)

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

151

Allosteric

0.1

1.o

10

100

[XLdK<, FIG.16. The Hill coefficients (n)and the allosteric_range_(@, in the lower panel, are presented as a function of [x],o/FAfor the curves ofA and Y presented in Fig. 15, where nSocorresponds to the value for Y = 0.5 and n& the value for A ' = 0.5. At low "Lo and low ligand concentration-A,,. LO, and at high "Lo and saturating ligand concentration A,, < 1. The difference, A,, defines the allosteric range, Q (Rubin and Changeux, 1966). Conceriing the Hill coefficients, thce values of nio for the state function are presented for A ' , the normalized value of A, as defined in the legend to Fig. 15. The peaks of the curves of n50and n& vs. log "Lo occur at " L = ("c)-"*. At this value of " L the curves for and are symmetric and _nso corresponds to the point of maximal cooperativity ( TI,,). At other values of BALo,for Y the values of nM and ,,n fall off toward 1.0 as the extremes of BALo are approached, with nN < n,, and the value of Y corresponding to n,, 4ecreasing progressively toward Y = l / N a t lowFLo and increasing progressively toward Y = ( N - l ) / N a t high "Lo. The value of nM for Y = 0.5 can be calculated directly from a sum of binding fractionyeach multiplied by its net reaction order (Edelstein and Bardsley, 1997). While TI,, for Y_ollows a bell-shaped curve as a function of "Lo (Rubin and Changeux, 1966), TI,,,, for A ' is independenlof "Lo and always equal to the value of n,&,at "Lo = ("c)-"~. However, the value of A ' corresponding to It, varies widely, approaching 0 at low "Lo and 1 at high "Lo, with the exact value given by 1/[1 + BALO(BA~)N'2]. Variations in njo also follow a bell-shaped curve as a function of log "Lo, but with limits of n > 1 at the extremes, as described in Fig. 17. Adapted from Edelstein and Changeux (1996).

(Engel, 1993),including a series of point mutations in the nAChR (LCna and Changeux, 1997a),most of which are hyperresponsive. Site-directed mutations of the a 7 neuronal nAChR had previously permitted identification of residues in the M2 transmembrane segment where substitution of the wild-type residue produces dramatic increases in the sensitivity to ACh (Revah et aL, 1991; Galzi et al., 1992; Devillers-ThiCry et al., 1992), also known as "gain of function" (Treinin and Chalfie, 1995). Pathological myasthenic syndromes have also been reported for two

152

STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

FIG.17. Receptors at various degrees of saturation during ligand binding. At vely high values of L, virtually all channel opening coincides with formation of the fully liganded species, S5. [For B A L O = 800,000 and BAc= 0.1, the fraction of S5 in the A state is given by 1/(1 ‘*L0”c5) = O.Ll, whereas the fraction of S, in the A state is only 0.01.1 At the point corresponding to A ’ = 0.5 (where the dashed horizontal and vertical lines cross), the observed reaction for the formation of receptor species with 5 ligands (S,) can be represented by the linear sum of the reactions S4 + S,, Ss + S,, S2 + S,, etc., each with increasing reaction order. As a result the overall cooperativity at 50% is given by the equation

+

where the numbers in the brackets correspond to the order of the reaction for formation of S, from S,, and where S, is the fraction of molecules with i ligands bound (Edelstein and Bardsley, 1997). In this case, the value of n;o = 1.27 arises from 2([-110.37 [-210.11 + [-3]0.016), where the values after the intergers in brackets correspond to the fractional population of the species S,, Ss, and Sp at their values along the dashed vertical line and the terms for S, and So do not contribute significantly. For the case of BAc< 0.1, the lower limit of cooperativity is n& = 1.29.

+

mutants that provoke “loss of function” (Ohno et al., 1996, 1997). The myasthenic mutant ~T264P(Ohno et al., 1995) is of particular interest, since it displays high affinity that could contribute to excess calcium uptake, with pathological consequences. When expressed in HEK (human embryonic kidney) cells, receptors with this mutation exhibit spontaneous channel opening and a trimodal distribution of open times (Ohno et al., 1995). Since no mechanistic interpretations were provided for this mutant, these data were examined to test whether the allosteric

AILOSTERIC TRANSITIONS OF THE ACh RECEPTOR

153

model could provide an explanation of these properties. Therefore, simulations based on the data reported with ~T264Pwere carried out for an ACh concentration of 3 X lo-’ M and compared to wild-type human muscle receptors expressed in HEK cells, as presented in Fig. 18. Although a complete kinetic analysis was not included in the initial description of the ~T264Preceptors, the simulation presented in Fig. 18 corresponds approximately to the properties described for an ACh concentration of 0.3 pMand is contrasted to the wild-type human muscle nAChR. An adequate fit of the mutant data was achieved by modifylng the interconversion rates between states based on lowering the wild-type value of BALo= 9 X los to a value for the ~T264Pmutant of MLo= 100, which markedly facilitates the B + A transitions (Edelstein et al., 1997a). The result is a substantial increase in the sensitivity to ligand, such that at 3 X lo-’ MACh the probability of opening increases to Popen = 0.22 = for the ~T264Pmutant, compared to the wild-type value of Popen at the same concentrations (Fig. 18). For ~T264Preceptors, the assumption of a diminished value of MLo but of normal ligand-binding constants leads to the prediction of three distinct peaks in the dwell time profiles of opening events (Fig. 19b), in contrast to a single peak for wild-type receptors (Fig. 19a). For the latter, the predictions of the allosteric model are in excellent agreement with the data points (.) obtained from the kinetic constants reported to describe an extensive data set for wild-type receptors expressed in HEK cells (Milone et al., 1997). The simulations demonstrate that for wild-type receptors the allosteric model can represent patchclamp data in as satisfactory a manner as can the sequential-type models. Whether critical experiments can be designed to distinguish between the models remains to be ascertained. The principal difference concerns channel opening in the absence of ligand. While such events are predicted only by the allosteric model, for wild-type receptors they are expected to be rare (- 1/ 15 s) and rapid (-5 ps), and may therefore escape detection. With respect to the mutant, the trimodal pattern predicted by the model for the mutant is compared to the three peaks reported for recombinant ~T264Preceptors (Ohno et al., 1995) and represented in Fig. 19b by the individual points (*) calculated by summing the three experimentally observed phases and scaling the total number of events to minimize amplitude differences with the dwell time peaks predicted by the allosteric-typemodel. This initial fitting gives a reasonably satisfactory agreement between theory and experiment, considering the difficulties in extracting the parameters from the three overlapping experimental curves and the relatively limited quantity of data reported (Ohno et aL, 1995). Because the change in BALoresults in a low value of the %:,rate

a

WILD TYPE Molecular species:

Channel openings: closed open

[

U

~T264P

0.1 s

Molecular species:

Channel openings:

FIG.18. Stochastic simulations of conformational transitions between the B and A states at various degrees of ligand binding. Passages among the possible molecular species and the corresponding channel-opening events for human wild-type receptors in (a) and for the myasthenic mutant eT264P in (b). The simulations were conducted for a ligand concentration of 3 X lO-'M (Edelstein et al., 1997a) using the following parameters: all ligand "on" rates were set at 1 X 10"M-ls-l., hgand "off' rates were for the wild type, 5k,,, = 1.65 X 10' s-' and hk,,, = 0.1 S - I , and for the mutant eT264P, Bk,ll = 7.56 X lo5 s-I and *ken = 4.4 s-l. Interconversion rates were for the wild type, B.4k,, = 2.06 X lo-' s-l, Bhkl = 3.08 s-I, "b = 4.60 X lo's-), "ko = 1.86 X lo5 s-l, = 1.68 X ,*b = 1.52 X lo5 SC', and for the mutant eT264P, nAko = 65.8 s-', Wkl = 3.94 X los s-', = 2.40 X lo5 s-', '\Bk, = 6.58 X 10%s-I, "k, = 2.29 X lo2 s-', "b = 8.0 s-'. For wildtype nAChR the parameters were based on measurements of human muscle receptors expressed in 293 HEK cells (Milone et al., 1997; Wang et al., 1997). The values for and nhbwere set by the published values of aP and p2, respectively, with the other interconversion rates calculated using linear free energy relations on the basis of the value of the transition state parameter, "p = 0.2 (Edelstein et al., 1996). Values for the A state were obtained by principles of microscopic reversibility. The ratio "Bk/'*k2 yields a value of the primary constant for the allosteric transition, nALo= 9 X 10" for the wildtype nAChR. For the eT264P mutant, "kn and "b were calculated using the T~ and T? values reported for 0.3 p M ACh (Ohno et al., 1995). For "k,, the value derived from T~ (see the legend to Fig. 19) was corrected to 229 SKI, since according to linear free energy relations it should be intermediate between "ko and "b o n a logarithmic scale (Edelstein et al., 1996). For eT264P, the value of the transition state parameter is "p = 0.45. From fitting the dwell time distributions, the value of RALo was set at 100 and the rates for '"k0, "kl, and "*k2were deduced according to linkage relations. While the change in the value of "Lo dominated the properties of the ~ T 2 6 4 Pmutant, the fit to the data was improved by additional changes in Bk,U and *kOU.

ALLOSTERlC TRANSITIONS OF THE ACh RECEPTOR

a

155

WILD TYPE

FIG.19. Openchannel dwell times for stochastic simulations of singlechannel events: (a) wild type; (b) mutant ~T264P.The dwell time probability density function, or pdf

(Sigworth and Sine, 1987; Colquhoun and Hawkes, 1995), with the square root of the number of events vs. time on a logarithmic scale, present the predicted distribution of all species (thick line) and the contributions of the individual components (thin lines) for simulations as described in Fig. 18 for an ACh concentration of 3 X lO-'M. At this concentration, Popen = for the wild-type nAChR and Pop" = 0.22 for the mutant cT264P. where Popen= 1/(1 + "Lo {([XI/&) + l}z/{([X]/KA + 1)}2).with the ligand concentration indicated by [XI and the equilibrium constants as defined in Fig. 5. For wild-type receptors in (a), the individual points are obtained from the kinetic rate constants presented in the legend to Fig. 8b of the article by Milone et al. (1997) to represent activation over a wide range of ACh concentrations. For ~ T 2 6 4 Preceptors in (b), the individual points (-) are presented for the sum of the three phases of the experimentally observed open dwell times corresponding to the published values (Ohno et uL, 1995) for 0.3 pMACh of To = 150 ps, a, = 0.67; TI = 1.8 ms, a, = 0.16; and T~ = 69.5 ms, u2 = 0.17. The contributions to the pdf for eT264P of Az channel opening involve passage to BP,as well as passage to A,, and the sum of both processes is indicated by ZA, [in (b)]. The simulations corresponding to 10 bins for each integer interval of log t, with peak heights based on the number events occurring in a total time of t of 1 s. Other details concerning the calcuation of dwell time probabilities are presented in the legend to Fig. 22. From Edelstein et al. (1997a). (0)

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STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

constant, only about twice the value of (see the legend to Fig. 18), a significant fraction of the opening events involving A2 will terminate by dissociation of a ligand to yield Al. The sum of events terminating by both A2 + B2 and A2 + A, + B 1 is indicated by the peak labeled ZA2 (Fig. 19b). On the basis of this analysis, the three peaks of the cT264P mutant receptors may be readily interpreted in terms of the allosteric model as reflecting non-, mono-, and biligand receptors. The sequential-type models, which do not include an open state for nonliganded receptors, cannot satisfactorily represent such data. The sequential scheme contrasts with the basic postulate of the allosteric model according to which the conformational equilibrium is established prior to ligand binding (Fig. 4). While certain quantitative aspects thus remain to be clarified, the simulations and comparison to experimental data illustrate the key role predicted for the value of BALo in determining the relation between binding and ionic events. On the basis of the available data, it may therefore be tentatively concluded that the altered properties of cT264P receptors represent an L phenotype (see Section V,C, above). Altered desensitized states may also contribute significantly to mutant phenotypes, as deduced for the myasthenic mutant identified in the region of the agonist binding site, aG153S (Sine et al., 1995). This position occurs in the loop B region that has been found to play a critical role in the ligand-binding properties of the desensitized states, while the loop C region participates in agonist selectivity (Corringer et al., 1997),where A, B, and C refer to the three regions identified in specific labeling experiments (Devillers-ThiCryet al., 1992). The distinctions in the fine structure of the agonist-binding sites concerning desensitization and agonist selectivitywere deduced by comparing the a 7 homooligomer and the a4P2 heterooligomer, which display striking differences in their apparent affinities for ACh and in their pharmacological specificity for ACh vs. nicotine. Sets of residues from the regions initially identified within the agonist-binding site of the a4 subunit were introduced into the homooligomeric a7-V201 -5HT3 chimera, which carries the intact a 7 agonist-binding site (Eiselk et al., 1993). Introduction of the a 4 residues 151-155 of loop B produced an approximately 100-fold increase in the apparent affinity for both ACh and nicotine in equilibrium binding measurements, whereas electrophysiologicalrecordings revealed a much smaller increase (3- to 4fold) in the apparent affinity for activation. These observations are consistent with the notion that the residues mutated alter the transition to the desensitized state. In contrast, introduction of the a 4 residues 183-191 (from loop C) into a 7 selectively increased the apparent affinities for binding and activation by ACh, resulting in a receptor that no longer displays differences in the responses

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157

to ACh and nicotine, demonstrating the importance of the C loop in agonist selectivity (Corringer et al., 1997).

B. Single Ionic Events vs. Single Ligand-Binding Events in Relation to Binding-Site Nonequivahce Single-channel measurements on muscle nAChR have made a prm found contribution to the understanding of these receptors since they provide high temporal resolution and the advantage of observations at the level of individual molecules (Neher and Sakmann, 1976; Sakmann et al., 1980; Colquhoun and Sakmann, 1985). However, to the present time, the linked events of ligand binding have only been inferred, indirectly, from single-channel recordings, since parallel observations on binding steps have not been possible. As a result, considerable ambiguity exists concerning the degree of equivalence of the two ligand-binding sites. Two equivalent sites were used in the sequential-type scheme to model single-channel measurements (for reviews, see Lingle et al., 1992; Edmonds et al., 1995), as well as in the four-state allosteric model (Edelstein et al., 1996). In contrast, in a number of other studies with muscle nAChR, marked apparent differences (up to 2 orders of magnitude) in the affinities of the two ligand-binding sites, such as may result from specific differences for binding sites at the a - y and a 4 interfaces (see Section I,B), have been used to develop alternative interpretations of experimental data (Jackson, 1988; Sine et al., 1990, 1995; Chen et al., 1995; Zhang et al., 1995; Akk et al., 1996; Ohno et aL, 1996; Milone et al., 1997). Moreover, a wide range of magnitudes for the differences in the kinetic parameters of the two sites for wild-type receptors have been assigned in these reports. Species differences and dependence on expression systems may in part explain such variability in the nonequivalence of the two binding sites (Edmonds et al., 1995), but uncertainties remain concerning the intrinsic functional properties of the two sites. Indeed, widely different rate constants can provide a satisfactory apparent description of the same data, since the properties of human muscle nAChR expressed in HEK cells have been interpreted in terms of a rather wide range of ligand-binding affinities (Sine et al., 1995; Ohno et al., 1996; Milone et al., 1997; Wang et al., 1997), varying from a 350-fold difference for the affinity of the two sites in the B state (Sine et al., 1995) to identical affinities for the two sites (Wang et al., 1997). It is clear that independent binding measurements are needed to overcome these ambiguities, and developments in the field of fluorescence correlation spectroscopy (Eigen and Rigler, 1994; Rauer et al., 1996; Edman et al., 1996; Schwille et al., 1997) now place such measurements in the realm of possibilities

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for the near future. Therefore, simulations were performed in order to study what additional insights would be available with measurements that simultaneously follow both single ionic and binding events (Edelstein et al., 1997b). In this respect, theory has preceded experiment but has provided a stimulus for the necessary technical advances. The allosteric model was modified to incorporate two nonequivalent sites as described in Fig. 20. When the model is evaluated in stochastic simulations, trains of molecular forms are generated that vary with respect to the conformational state and/or the degree of binding site occupancy (Fig. 21a). Each change in the number of ligands bound is scored as a binding event (Fig. 21b), and each transition to an A-state molecular species is scored as an ionic event (Fig. 21c). Hence, Figs. 21b and c correspond to measurements that are expected to be produced experimentally in joint single-binding and singlechannel recordings, respectively. These stochastic simulations extending over 0.5 s only partially illustrate the behavior of the system. A more complete description is provided by the probabilities of events for each time interval (bin

BL

FIG.20. Subunit structure and ligand binding sites at the a - y and a-6 interfaces within the B state. Receptors with the ligand occupying the higher affinity site for agonist (a-6)are designated by the subscript H and those with the ligand occupying the lower affinity site for agonist (a-y)by the subscript L. Equilibrium constants are defined by the ratio of the corresponding "on" rates (k) and "off" rates (k'), e.g., = Bk'/sk. In the framework of a two-site protein with ligand binding characterized by two apparent ligand-binding dissociation constants, KI and K2,if Ke(H) &(I.). then KI = KB(H) and K2 = K B ( l lWhere . differences between KB(H)and KB(Llare smaller, the exact values are KI = KB(H)KB(l)/(KB(IIl + KB(L))and K2 = KBCH) + KBl,.,.For identical sites, where KB = = K B ~the ) , values of Kl and K2 are set by K, = K B / 2 and K2 = 2KB.The equilibrium = 'k,,/'k+, and KB([.)= "/lL /%,. constants are defined by the corresponding rates: Similar definitions may be applied to the other states to incorporate nonequivalence of their binding sites. (Edelstein et al., 1997b.)

*

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

159

a Molecular species

b

Binding events

!E t

C

Ionic events

closed

I[

open

I

I

u u uu

0.05 s

FIG.21. Stochastic simulations of ligand-binding and conformational transitions for a receptor with two nonequivalent sites: (a) passages among all possible molecular species; (b) passages scored as binding events; (c) passages scored as ionic events. For the species with one molecule of agonist bound, its presence on the high- or low-affinity site is noted, respectively, by H or L in the subscript, e.g., BI(H) or BI(,, for the B state. The simulations M for nonequivalent ligandwere conducted for a ligand concentration of 2 X binding sites using the following parameters derived from the data of Jackson (1988), with corrections incorporated (Jackson, 1993), and small adjustments made to permit agreement with the model based on linear transition state theory: k, = 1 X lo8 M-ls-’ for all sites except BL, for which k,, = 0.05 X 108M-ls-1 . The “off” rates (s-l) are = 2.5; A#L = 30; for the I state identical “off” rates Bk’H = 500; ’& = 1.8 X lo’; = for both sites were set at 4.0. The interconversion rates (s-’) were “ k , = 0.028; 1.8; nAkl(L)= 44; BAh = 2800; *’k, = 5013; “4 = 1604; “k, = 670; mb = 214. For the A P I transition, since no specific data are available on site nonequivalence, the values for equivalent sites (Table I ) were utilized. (Edelstein et al., 199%)

width) sampled, leading to the “probability density function,” or pdf (Sigworth and Sine, 1987; Colquhoun and Hawkes, 1995). However, since ligand binding dwell times will be lengthened by multiple passages between two conformational states at the same degree of ligand saturation, the contributions to the total binding events of all such multiple passages (which for nAChR involve the A state) must be included, as illustrated in Fig. 22. This analysis permits the complexity of binding events to be anticipated and potentially to provide information on the

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time

FIG 22. Consequences of multiple transitions between conformational states. The individual dwell time profiles are presented for A2 binding events prolonged by passages to BP. Each pdf is presented as the square root of the number of events vs. time o n a ugo(z,),where a, is the fractional amplitude logarithmic scale and is defined by g(x) = of the$h component and go(z,) = exp[zJ - exp(z,)], with z, = x - sJ, x = In t, 1 = time in seconds, and s, = logarithm of the fi time constant (Sigworth and Sine, 1987). Since the number of events is proportional to t (the length of time examined), J (the fractional concentration of the reacting component), and 1 / ~ ,(the rate of relevant reaction), the amplitude of the jth component is given by: a, = ( A t ) / ? . The peak height for a specific class of events is given by A$ = ( J t drcr,[l - p,]e-')/q, where dx is the interval of In t used to set the width of the bins, r, is the relevant ratio of kinetic rate constants, [l - p,] gives the fraction of events remaining after a series of passages to a neighboring state, each with a probability of p,, and 6' corresponds to the maximum value of g(x), which occurs at the logarithm of 5. For the simulations presented here dx = 0.23, corresponding to 10 bins for each integer interval of log 1, with peak heights based on the number of events occurring in a total time t of 1 s. The term r, is calculated from the appropriate rate constants of alternative pathways. For example, each passage viaA2may be terminated by a transition (to I? or B4) or by a ligand dissociation; hence, the probability of a transition "#, to B2 will be given (for nonequivalent binding sites) by r, = ABk.J("& + *kL ,"&). Successive passages correspond to the series of distinct pdf curves presented here, with reduced probability and progressively longer characteristic values of the average 7,. The probability for each successive passage to A2 is diminished by a factor, p, = (BAh 'KL B#I ) ] [ A B b / ( M k l =k;C M k 2 ) The ] . sum of all such events is given by the series HS = 1 + p, + p,2 + ... = 1/[1 - p,], and the fraction of primary ligandbinding events without passage to another state is given by [ l - p,]. The contributions of all prolongations are summed, added to the primary A-state binding events, and the totals are indicated by HAPin Fig. 23. (Edelstein et al., 1997b.)

+

+

+

+

+

+

+

mechanism of signal transduction that would not be available from single-channel recordings alone. For example, it would be possible to resolve the contributions of the two potentially nonequivalent binding sites, as illustrated in Fig. 23. For simulated recordings of muscle AChR at low ligand concentrations, only minor differences are predicted for dwell time profiles of ionic

161

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

a Bindinq events

C

10-6

time

102

1

FIG.23. Dwell time probability profiles for stochastic simulations of binding events and ionic events for nAChRat low ligand concentrations: (a) ionic events and (b) binding events for simulations based on data interpreted with equivalent sites; (c) ionic events and (d) binding events for simulations based on data interpreted with nonequivalent sites. The dwell times are presented as the total events, corresponding to simulated experimental measurements (thick lines), along with the underlying contributions of the individual components (thin lines). The simulations are based on the values in Table I and the legend to Fig. 21, with a ligand concentration of [XI = 0.3 p M in (a) and (b) and [XI = 1.7 pMin (c) and (d), corresponding in both cases to a probability of channel & = 0.002, computed with the equation Pop. = 1/(1 + K,,.{(BK,BK,)/ opening, F [XI' + BK2/[X] + l}/{(*K~K,)/[X]* *&/[XI + 1)). Other details are as described in Fig. 22. (Edelstein et al., 1997b.)

+

events with parameters based on analyses with equivalent sites (Fig. 23a) vs. nonequivalent sites (Fig. 23c). At the concentrations of these simulations, ionic events are predicted to be rare, - l / s (corresponding to a probability of channel opening of Popen = 0.002), whereas binding events are predicted to be at least an order of magnitude more abundant (Fig. 23b and d). With respect to the two principal models, for both equivalent (Fig. 23a) and nonequivalent sites (Fig. 23c), more ionic events (at shorter average times) are predicted by the allosteric model (thick lines) compared to the sequential model (thin lines, correspond-

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STUART J. EDELSTEIN AND JEAN-PIERRE CHANGEUX

ing to At, the only molecular species producing ionic events in the simple form of the sequential model). The predicted profiles for normal human receptors expressed in HEK cells (Fig. 19a) are dominated to a great extent by AS, since the data analyzed yielded a higher value of BALocoupled with a higher affinity of the A state (Edelstein et aL, 1997a). With the parameters based on nonequivalent sites, the shoulder at longer times (- 10-2s) on the profile of ionic events in Fig. 23c is slightly more pronounced and at all concentrations fewer events are predicted than for equivalent sites, due to a lower estimate for the value of ABk2. However, for single-channel experimental data with the usual limits of precision, it would be difficult to distinguish between the equivalent and nonequivalent interpretations. It can thus be concluded that a compensation of parameters leads to similar properties in the two cases. This compensation may explain why experimental single-channel recordings have been interpreted with equivalent sites in some cases and with nonequivalent sites in other cases (Lingle et al., 1992; Edmonds et aL, 1995). As a result, meaningful conclusions cannot readily be drawn from single ion channel recordings alone. In contrast to the similarity of ionic events, larger differences in the simulated binding events are predicted for equivalent sites (Fig. 23b) vs. nonequivalent sites (Fig. 23d). In the latter case, binding of the first ligand to a receptor molecule is predicted to occur almost exclusively at the higher affinity site to generate BI(H).Since an off rate 16-fold lower than in the case of equivalent sites was deduced, the peak in the dwell time profile for binding events is predicted to lie at significantly longer times: 2 X s for nonequivalent sites (Fig. 23d) compared to 1.2 X s for equivalent sites (Fig. 23b). Hence, if single ligandbinding events were measured experimentally, their dwell time profiles could provide a direct test of the extent of binding site nonequivalence. At higher ligand concentrations in the range of a probability of channel opening of Popen = 0.5, the simulated ionic events arise mainly from transitions to A2 and are anticipated to be almost as abundant as the binding events. As a consequence, the predictions of the allosteric and sequential models are virtually identical for ionic events, and very similar binding events are also predicted for both equivalent and nonequivalent sites. Therefore, experiments at low ligand concentrations should be favored in order to distinguish between allosteric vs. sequential models and equivalent vs. nonequivalent sites. In comparison to these deduction for muscle-type nAChR, the situation for neuronal nAChR is more complicated because of the variety of neuronal forms and the differences for homopentameric and heteropentameric assemblies. For homopentameric neuronal nAChR composed

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163

of a?,a8,or a9, the identical subunits presumably impose an equivalence of sites at each interface, with each subunit contributing a principal component at one interface and a c o m p k t a r j component at the other interface (Corringer et aL, 1995). Other neuronal receptors with the heteropentameric composition a4P2 or a3P4 would presumably possess functionally equivalent ligand-binding sites at identical a4-/32 or a3-P4 interfaces, with the complementary component provided in these cases by the P-type subunit. More complicated combinations may be expected for receptors with subunit compositions a3a5P4 (Vernallis et aL, 1993), a4a5P2 (Conroy et aZ., 1992; Ramirez-Latorre et aL, 1996) or a6P2P3 (Le NovSre et aZ., 1996). For these receptors, it has been suggested that a5 and P3 could exert a y-like role (Le NovSre and Changeux, 1995). However, these systems have not as yet been analyzed in sufficient detail to draw conclusions concerning the degree of functional nonequivalence of the ligand-binding sites. EFFECTORS AND COINCIDENCE DETECTION VII. ALLOSTERIC Various modifications of the functional properties of AChR are produced by noncovalent interactions with pharmacological agents and other modulators (Lena and Changeux, 1993; Changeux, 1996) and covalently by phosphorylation (Huganir and Greengard, 1990; Levitan, 1994). In general, when differences in current are observed in the presence and absence of a potential allosteric effector, it has not generally been determined whether affinity changes and/or specific conductance changes are responsible for the differences. In this respect the study by Mulle et al. (1992) is of particular interest since potentiation by calcium was shown to result from an increase (-%fold) in the frequency of channel opening. A modeling of these data shown in Fig. 24 indicates that the potentiation by calcium can be represented simply in terms of a 2.3-fold reduction in the allosteric constant, with all other parameters remaining unchanged from the values in Table I. The lower value of BALois sufficient to account for the shift of the curve to the left and the augmented increased response (Fig. 24a). The effect of calcium is thus a true allosteric modulation, because the change in frequency of openings indicates an altered value of the rate constant 9 z 2 that corresponds closely to the change estimated for "Lo, since BALoBAC2 = ABk2/BAk2.Calcium modulation of the Lvalue for activation has also been observed for the nAChR-5HTSR chimera (Galzi et aL, 1996a), and more general implications of calcium as an intracellular signal may be related to the fact that neuronal nAChRs as a class have a high relative permeability to calcium (Rathouz et al., 1996; Vernino et aL, 1992).

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a 1

0.8 a,

a C

0.6

0

n

u:

0.4 0.2

..

0

01 0.1

1

10

I 100

Frequency FIG. 24. Data and theoretical curves for the potentiation of rat medial habenular neurons by external calcium. (a) Dose-response curves for the effect of ACh and currents in the presence of 4 mM calcium (B) and in the absence of added calcium ( 0 )from the report by Mulle et al. (1992). The dashed lines are obtained with the four-state allosteric model using the parameters of Table I, with the exception of the values of BALo = 5.25 X lo5for the curve that coincides with the squares (corresponding to the presence of

ALLOSTERIC TRANSITIONS OF THE ACh RECEPTOR

165

Allosteric effects of the type observed for potentiation by calcium have a number of implications for regulation of activity in the nervous system. At synapses, allosteric modulators could provide signals for coincidence detection (Heidmann and Changeux, 1982; Changeux and Heidmann, 1987). Such an effect for ACh and calcium may be visualized in Fig. 24b, assuming a constant threshold that is attained only in the presence of both ACh and calcium (on the left), but not with ACh alone (on the right). Since calcium may enter neurons via the open ligand-gated cation channel of various neuronal AChR or voltage-gated channels, regulatory effects may also be produced related to intracellular accumulation (such as phosphorylation) or extracellular depletion (such as habituation resulting from repeated stimulation by ACh). In addition to its role in regulating synaptic efficiency, diminished extracellular calcium concentrations might also participate in retrograde signaling. In general, calcium or other allosteric effectors might provide an alternative to the NMDA (&methyl-D-asparticacid) Ca'+/M$+ coincidence detection system (Wigstrom and Gustafsson, 1985), as discussed more fully in Section VII1,B. Similar effects that could play a role in coincidence detection by shifting the dose-response curve with a change in maximal response

4 mMcalcium) and RALo = 1.25 X 10' for the curve coincidingwith the circles (corresponding to no added calcium). (b) Illustration of coincidence detection. For kinetic simulations (time in seconds) with an agonist concentration of 2 X 10-4M, only the response on the = 5.25 X lo5 (corresponding to 4 mM calcium), but not the response on left with RALO the right with "Lo = 1.25 X 10' (corresponding to n o calcium), reaches a hypothetical threshold for neuronal firing (dashed line). (c) A sliding threshold model. The normalized response is presented as a function of the stimulation frequency (Hz). For the system at "Lo = 5 X 10' it is assumed that the B # A equilibrium may be displaced by phosphorylation away from A and by dephosphorylation toward A. Entry of calcium proportional to the stimulation frequency produces activation of the relevant kinase and phosphate, but with the former more sensitive and the latter more cooperative. In this case is calculated with the standard equation (see the legend to Fig. 15) for "Lo = 5 X lo5 and a ligand concentration (0.17 mM) corresponding to 50% response in the absence of stimulation. The value of "Lo is assumed to vary with frequency of stimulation and subsequent calcium influx according to the equation wLi = "Lo (1 + 4y4)/(l+ cpf"'),where I$ and cp are coupling coefficients for the activation of kinase or phosphatase by calcium and ~ I # Jand ncp give the apparent Hill coefficients for the interactions, respectively. The biphasic depression-potentiation pattern requires I$ > cp and n 4 < ncp. For the simulation presented here, since phosphorylation leads to inhibition, I$ corresponds to the kinase and cp corresponds to the phosphatase (4 = 1.2 and cp = 0.6 in arbitrary units; nI$ = 1.2 and ncp = 1.9). Simulation for the mutant kinase with increased activity is obtained by setting 4 = 3. The simulation assumes that the receptor is partially phosphorylated in the absence of stimulation. (a) and (b) from Edelstein et al. (1996).

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amplitude are observed for modulators such as steroids (Valera et al., 1992; Buisson and Bertrand, 1997). Allosteric effects may also involve modulation of desensitized states, for example, as is observed with substance P (Valenta et al., 1993) or following phosphorylation with CAMPdependent protein kinase (Huganir et al., 1986). Overall, any substance that alters the preexisting equilibria between states can exert an effect on synaptic efficiency or coincidence detection (see Changeux, 1990, 1996). More complex effects involving a sliding threshold (Bienenstock et al., 1982) may also be formulated (Fig. 24c), and the general implications for sliding thresholds are presented in Section VII1,B.

CONSIDERATIONS VIII. GENERAL

A. Evaluation of Mechanistic Models The simulations presented were used to determine conditions that could lead to experimentally testable differences in the predictions of the allosteric-type and sequential-type models. In addition, the simulations explored what additional distinctions could be furnished by measurements of single ligand-binding events, particularly for establishing the degree to which the binding sites are nonequivalent. The analysis of single binding events remains hypothetical at present compared to the single-channel measurements that have been extensivelydeveloped since the early applications of this technique (Neher and Sakmann, 1976; Sakmann et al., 1980). While a singlechannel event can be recorded because of the amplification derived from the flux of thousands of ions, no such amplification is produced by a single binding event. However, recording of single binding events are in principle feasible with fluorescence correlation spectroscopy (Elson and Magde, 1974; Magde et al., 1974; Ehrenberg and Rigler, 1974), in light of recent advances (Eigen and Rigler, 1994; Rauer et al., 1996; Edman et al., 1996; Schwille et al., 1997). As indicated by the simulations described here, such measurements could be utilized to evaluate critically the degree of nonequivalence of the ligand-binding sites. While singlechannel data have been interpreted both in terms of equivalent and nonequivalent sites (Edmonds et al., 1995),compensating effects in the values of the parameters result in similar predictions in the two cases (see Fig. 23a vs. Fig. 23c). However, larger differences are predicted for the dwell time profiles of the binding events at low agonist concentration (Fig. 23b vs. Fig. 23d)

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that should readily distinguish between the equivalent and nonequivalent schemes if the appropriate experiments could be conducted. Concerning the extent of nonequivalence of the binding sites, an allosteric-type model with substantial nonequivalence was proposed by Jackson (1988) to account for the data of wild-type muscle receptors. The extent of nonequivalence of the ligand-binding sites for the B state was evaluated entirely on the basis of kinetic measurements derived from single-channel recordings. Other measurements, particularly the degree of cooperativity in dose-response curves, can also provide relevant information, where a Hill coefficient ( nH)> 1indicates positive cooperativity. For wild-type receptors, with the parameters deduced by Jackson for nonequivalent sites, and at ligand concentrations near the ECS0virtually all of the openings accompany binding of the second ligand molecule to the low-affinity site. As a result, the predicted dose-response curve is noncooperative ( n 1.0). In contrast, for wild-type receptors with equivalent sites (described by the parameters in Table I), the predicted dose-response curve is strongly cooperative: n = 1.7 (Edelstein et al., 1996). Similarly, for the ~T264Pmutant receptors, the relevant parameters (Fig. 23) predict highly cooperative dose-response curves, with n = 1.8. Hence, there is a discrepancy between the noncooperative dose-response curve predicted for wild-type receptors with strongly nonequivalent sites and the widely observed cooperativity characterized by n > 1.5 (Changeux and Edelstein, 1994). One possible explanation for this discrepancy in the predicted and observed Hill coefficients is the presence of a channel block that modifies the response in such as way as to generate an “apparent” cooperativity (Sine et al., 1990; Forman and Miller, 1988). Adding an ACh channel block with a dissociation constant of 1.3 mM (Colquhoun and Ogden, 1988) reduces the maximal amplitude of the response to about 50%. However, if the maximum ligand concentration examined for the doseresponse curve is limited to -1 mM, the reduced amplitude could be considered as a full response and scaled to 100%. In this case, the vertical “stretching” of the dose-response curve would result in an increase in the Hill coefficient to 1.5. Since the dose-response measurement is generally evaluated between arbitrary end points assumed to correspond to 0 and loo%, the presence of channel block could explain the degree of cooperativity generally observed, even if there is strong nonequivalence of the binding sites. Rapid desensitization that also impinges on the maximal amplitude of the response could in principle exert a similar effect (see Fig. lo), but measured desensitization rates following rapid ligand application are too slow to cause a significant attenuation of the amplitude (Franke et al., 1993).

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B. Implications fw Synaptic Plasticity

The allosteric model with preexisting equilibria between a minimum of four conformation states, B, A, I, and D, satisfactorily accounts for the kinetic properties of the AChR in vivo and in uitro. Application of the model to single-channel events by conversion of kinetic constants into probabilities of microscopic events clarifies the effects of ligand binding on the patterns of interconversions between the various states. The formulation of the model in terms of single-channel events also opens the possibility for simulations at the level of a synapse, with a finite number (-lo3) of receptors. While many issues still need to be clarified in order to model a synapse more accurately, particularly with respect to quanta1 analysis (Bekkers, 1994))simulations with a full functional model of the type presented here could provide new insights, since previous efforts have not included desensitization (Bartol et al., 1991; Faber et al., 1992). With respect to artificial neural networks, an understanding of these aspects should lead to more realistic modeling. While synaptogenesis has also been considered and incorporated in some models (AdelsbergerMangan and Levy, 1994; Foldiak, 1990), detailed schemes based on experimental observation have been proposed mainly for the neuromuscular junctions (Changeux et al., 1973; Changeux and Danchin, 1976; GouzC et al., 1983). Other important features for the development of more biologically realistic modeling concern delays and oscillatory behavior (A. Herz et al., 1989; Kerszberg and Zippelius, 1990; Buonomano and Merzenich, 1995; Hopfield, 1995; Hangartner and Cull, 1996; Kerszberg and Masson, 1995), but these aspects have not as yet been brought to the molecular level with respect to ligand-gated ion channels and metabotropic receptors. In contrast, for the basic concept of synaptic plasticity (Hebb, 1949), as applied in numerous models (Bienenstock et al., 1982; Amit, 1989; Churchland and Sejnowski, 1992; Edelman et al., 1992; Montague and Sejnowski, 1994),plausible mechanisms based upon allosteric regulation of ligand-gated channels have been formulated, particularly in relation to synaptic triads (Heidmann and Changeux, 1982;Dehaene et al., 1987; Changeux and Dehaene, 1989; Dehaene and Changeux, 1989, 1991; Changeux, 1993). In this approach, signals produced by a synaptic terminal C acting on neuron B are assumed to regulate the efficacy of the postsynaptic synapse of A + B with an allosteric switch of postsynaptic receptors from neuron B. The regulatory effects could intervene to stabilize one of the allosteric conformations and as a consequence alter the corresponding rates of interconversion. Networks based on such

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triads can learn and produce temporal sequences (Dehaene et al., 1987) and have been used to formalize neural networks able to perform a number of complex temporal processes, such as delayed-response tasks (Dehaene and Changeux, 1989) or the Wisconsin card sorting test (Dehaene and Changeux, 1991). The role of these synaptic triads in recognizing and producing temporal sequences is related to their capacity to function as coincidence detectors (Dehaene et al., 1987).Where the A+ B postsynaptic receptor can undergo transitions to short-lived ( I ) and long-lived (D) desensitized states, systems composed of such triads are capable of both short-term detection and long-term storage and retrieval. We assume that the multiple conformational states of the nAChR, as well as other ligand-gated receptors, could fulfill such functions. Such coincidence detection based on changes in receptor conformation may be contrasted with the conventional view (Montague and Sejnowski, 1994) that the NMDA receptor is responsible, based on its voltagedependent M$+ channel block (Wigstrom and Gustafsson, 1985). While such a mechanism can play a physiologically important role, it can only be short term in its direct effects and limited to the specific features of the NMDA channel; any subsequent learning processes must be dependent on other cellular components capable of long-term storage (see “LTP” below). Hence, coincidence detection based on conformational transitions would have the advantage of being applicable to virtually all members of the superfamily of ligandgated channels and capable of participating, in principle, in both shortterm discrimination and long-term storage. In a specific example of possible coincidence detection, we have suggested that allosteric effectors of the neuronal nAChR operating at sites distinct from the channel can provide a suitable mechanism (see Fig. 24b). This hypothesis assumes a direct effect of calcium on receptor properties. Indirect effects could also occur, as postulated in the model assigning a role to calcium in the modulation of intracellular phosphorylation responsible for the forms of hippocampal synaptic plasticity hiown as long-term potentiation (LTP) or long-term depression (LTD). This model proposes that LTD results from activation of phosphatases at low calcium influxes,whereas LTP results from activation of kinases at higher calcium influxes (Lisman, 1989, 1994). This biphasic pattern has been interpreted in terms of the sliding threshold model (Bienenstock et al., 1982) first developed to account for aspects of visual cortical development and subsequently observed in other neurological systems (Bear, 1995). The role of CaM kinase I1 in this form of plasticity has been addressed by the production of genetically modified mice. Mice with a targeted

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disruption of the CaM kinase a subunit lack LTD (Silva et al., 1992; Stevens et al., 1997).A specific application of the sliding threshold model has been reported for mice with a site-directed mutation (T286D) in CaM kinase I1 that possesses high constitutive activity in the absence of activation by calcium (Mayford et al., 1995). Compared to wild-type mice, the threshold for the transition form LTD to LTP in the CAI region of the hippocampus appears to move to higher frequencies in the transgenic mice with the T286D mutation of CaM kinase I1 (Mayford et al., 1995). While evidence for a role of phosphorylation is accumulating, the targets of the phosphorylation effects are not yet fully established. Although receptor phosphorylation may be involved, particularly AMPA (cu-amino-3-hydroxy-5-methylisoxazole4proprionate)-type glutamate receptors (Raymond et al., 1993; Barria et al., 1997), presynaptic processes, possibly triggered by retrograde signals, have also been implicated, as demonstrated in mice with reduced synthesis of NO leading to reduced LTP in the same region of the hippocampus (Son et al., 1996). While the exact role of phosphorylation in LTD and LTP remains unclear, it is of interest to note that phosphorylationdependent changes in the equilibria between allosteric states for a ligand-gated receptor can readily lead to biphasic responses and sliding thresholds, as illustrated in Fig. 24c. If phosphorylation activates the receptor, the requirement is simply that the appropriate phosphatase is activated at low calcium concentrations but with low cooperativity with respect to calcium, whereas the relevant kinase is activated at higher concentrations but with a more cooperative response to calcium. In this case, the phosphatase will dominate at low calcium (corresponding to low stimulation frequencies) to produce LTD, but the kinase will gradually become dominant as the calcium concentration rises (corresponding to higher frequencies), producing LTD. Such biphasic behavior can also be generated if phosphorylation inhibits the receptor, but in this case the kinase must be activated at lower calcium concentrations with low cooperativity and the phosphatase activated at higher calcium concentrations with high cooperativity. In the simulation presented in Fig. 24c, the threshold is displaced to higher frequencies by increased phosphorylation. This behavior is achieved by assuming that phosphorylation shifts the equilibria between the B and A states in favor of B, or in an equivalent manner by favoring one of the desensitized states (Huganir et al., 1986). It is further assumed that in the presence of a mutated kinase phosphorylation is enhanced, resulting in increased LTD and displacement of the threshold to the right. This simulation is based on the parameters of the nAChR, but the curves resemble the data presented for wild-type and mutant CaM

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kinase I1 (Mayford et al., 1995). Thus a sliding threshold based on the allosteric transitions of a ligand-gated channel could be responsible for the biphasic behavior reported, but considerable additional data will be required to establish the detailed molecular basis for such a mechanism in hippocampal LTD-LTP (Lisman et al., 1997).

C. Diseases and Nicotine Dependenq While additional insights should be obtainable in future studies of wild-type receptors under conditions where alternative models differ in their predictions, more critical experiments may be achieved with receptors resulting from mutations that produce strong perturbations. Site-directed mutations can play an important role in this respect (see below), but spontaneous mutations responsible for myasthenic syndromes have also provided new insights into the mechanism of muscle nAChR and clarified the pathology of these clinical syndromes (Ohno et al., 1995, 1996; Sine et al., 1995; Gomez and Gammack, 1995; Gomez et al., 1996; Vincent et al., 1997; Lena and Changeux, 1997a). Opening frequencies superior to the wild-type levels appear to cause cellular damage, probably due to an excessive influx of electrolytes, particularly calcium (Engel, 1993). Among the mutations responsible for the various myasthenic syndromes, the high-affinity eT264P mutant receptors examined here illustrate the physiological consequences resulting from facilitation of the transition to the open state. The results reported for eT264P mutant receptors (Ohno et al., 1995) are particularly striking, since the profile of open channel dwell times displays three peaks, compared to the single peak for wild-type receptors. Assuming that the energy required for the B + A transition is reduced, as represented by a value of "Lo = 100 for eT264P (Fig. 18), significant channel opening is predicted for receptors with no ligands or one molecule of ligand bound (Fig. 19b).The three peaks for the mutant receptors may then be readily interpreted with the MWC-type model (L phenotype) as reflecting non-, mono-, and biligand receptors, with reasonable agreement obtained between theory and experiment (Fig. 19b). The failure of the sequential-type model to accommodate these data stems principally from the absence of non- or monoliganded open states (Fig. 7). The eT264P mutation represents a class of high-affinity mutants lying in the channel, as first discovered for the L247T mutation of neuronal a7 AChR (Revah et al., 1991) and subsequently confirmed with muscle nAChR (Labarca et al,, 1995; Filatov and White, 1995), as well as with 5-HT3receptors (Yakel et al., 1993) and GABAA receptors (Chang et al., 1996). A Leu + Met mutation at the position in the p subunit of human

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muscle AChR corresponding to L247 in a7 (see Fig. 2d) is responsible for a severe slow-channel myasthenic syndrome (Gomez et aL, 1996). The a 7 mutations such as L247T dramatically increase the sensitivity to ligand, convert the competitive antagonist DHPE to a partial agonist (Bertrand et aL, 1992), alter single-channel conductances (Revah et aL, 1991), and lead to spontaneous channel opening (Bertrand et aL, 1997). These results are most readily interpreted by a normally closed, highaffinity desensitized state that is rendered conducting by the Leu + Thr replacement in the channel, thereby constituting a y phenotype (Galzi et aL, 1996b). Related mutations such as V251T, characterized in a 7 receptors (Devillers-ThiCry et al., 1992; Galzi et aL, 1992) share some features with L247T but can be interpreted in terms of an L phenotype (Galzi et aL, 1996b). The myasthenic mutation ~T246Poccurs at the residue adjacent to the Val corresponding to the a7 site mutated in V251T (see Fig. 2d). Similarly,an Ile + Asn mutation in the deg-3 AChR gene that induces neurotoxicity in Caenmhabditis elegans occurs at the site in M2 equivalent to the Val mutated in a 7 V251T (Treinin and Chalfie, 1995). Neuronal nAChRs have also been implicated in inherited forms of epilepsy due to channel mutations in the neuronal AChR a 4 subunit (Steinlein et aL, 1995, 1997). In one case (Steinlein et al., 1995;Weiland et aL, 1996), mutation of Ser 248 to Phe at the homologous site of the chlorpromazine-labeled Ser in Torpedo receptor M2 (Giraudat et al., 1986; Hucho et al., 1986) causes a significant enhancement of desensitization and a reduction of maximal response at saturating ACh concentrations. In the other case, insertion of an additional Leu at the C-terminal end of M2 causes an increase of affinity associated with a lower calcium permeability (Steinlein et al., 1997). The sites of these mutations within the M2 domain are summarized in Fig. 2d. With respect to other neurological disorders, indirect evidence has linked a 7 to an inherited form of schizophrenia (Freedman et al., 1997). Finally, studies on the molecular properties of nAChR should clarify the molecular basis of nicotine addiction via smoking. Some insights may already be available from desensitization experiments. The utilization of the lowconcentration prepulse method to evaluate desensitization is shown to produce measurements of IC5,, that introduce systematic distortions, since the system is far from equilibrium unless prepulse duration times approach tens of minutes (Fig. 11). Because of these latter limitations for obtaining equilibrium IC5,,values, considerable additional data will be required with long prepulse times in order to define the parameters of the D state more fully. Recovery times from the D state can be extremely long (hours), since they will be limited by D'ko, which may be

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as low s-’ (Table I; see also Fig. 9c). It is interesting to note that slow structural changes have been reported (Chang and Bock, 1977). Response times in this range could contribute to upregulation, downregulation, and other pharmacological effects associated with both chronic and acute nicotine administration (Ochoa et al., 1990; Lukas and Bencherif, 1992; Peng et d.,1994; Dani and Heinemann, 1996; Lena and Changeux, 1997a). Heavy and light smoking regimes may be related to maintaining the D state by the former and permitting stimulatory effects via action on the A state by the latter (Wonnacott, 1990). Nevertheless, a great deal of additional information will be required to establish the exact sites where nicotine exerts its pharmacological effect as a drug of abuse and which forms of the neuronal nAChR participate. Although a4P2 has been suggested as a likely target (Peng et al., 1994), a prime role for a 6 has recently been proposed (Le Novere et al., 1996). Studies using transgenic mice are also providing a powerful tool for the elucidation of specific effects of neuronal nAChR subunits (Picciotto et al., 1995, 1998). Ultimately, the allosteric scheme may contribute insights into diseases related to altered transitions between conformational states and aid in the understanding of drug addiction. ACKNOWLEDGMENTS The research described here from our own laboratories was supported by the Swiss National Science Foundation, the Association Franqaise contre les Myopathies, the CollPge de France, the Centre National de la Recherche Scientifique, the Institut National de la SantC et de la Recherche Medicale, the Direction des Recherches Etudes et Techniques, Human Frontiers, EEC Biotech and Biomed, and the Council for Tobacco Research.

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By GARY K ACKERS Department of Biochemistryand Molecular Biophysics. Washington University School of Medicine. St Louis. Missouri 63110

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I . Introduction ..................................................... I1 . Overview ........................................................ A. Research Leading to the Symmetry Rule ........................ B. Structural Probes and Heterotropic Responses ................... C. Microstate Cooperativity Components of HbCO and HbOp . . . . . . . . 111. Binding Curves and Stoichiometric Information ...................... A . The Adair Binding Function . .............. B Using Dimer-Tetramer Assem Binding Cooperativity ......................................... C. The Hill Coefficient .......................................... IV. Site-Specific Aspects of Oxygen Binding ............................. A. Microstate Components of the Adair Function ................... B. Implications for Allosteric Model Analysis ....................... C. Impediments to Microstate Resolution .......................... V . Experimental Determination of Site-Specific Cooperativity Terms ...... A . Active Site Analogs of Oxygenation . . . . . ..................... B. Linkage Cycle Analysis of the Partially Ligated Intermediates . . . . . . C. Statistical Weights of the Tetramer Binding Function . . . . . . . . . . . . . D. Hybridization Techniques and Free Energy Distributions .......... VI. How the Molecular Code Was Deciphered ........................... A. Cooperative Free Energies of HbOpAnalogs ..................... B. Oxygen-Binding Tests of the Consensus Function . . . . . . . . . . . . . . . . C. Prediction of Site-Specific Binding Parameters for Native HbOp .... D . Structure-Sensitive Probes and Heterotropic Responses . . . . . . . . . . . E. Quaternary Assignments and Molecular Code .................... F. Confirmation of the Molecula e Partition Function .................. and HbCO Intermediates ... VII. Concluding Remarks .............................................. References . . . . . . . . . . . . . . . ...................

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I. INTRODUCTION Molecular biologists and biochemists have long been intrigued by the concept of molecular codes for the structure and function of biological macromolecules. i.e., a set of rules which translate the multiple combinations of simple structural elements into a more complex phenomenon of biological function . The landmark solution of the genetic code. whereby triplet combinations of DNA base pairs were found to dictate amino 185 ALIVANC.G IN PROTEIN C H M S l R Y . Vol. 51

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acid sequences of proteins (cf. Khorana, 1968;Judson, 1979), has been followed by extensive ongoing efforts to find rules that predict how primary sequences and secondary structural features of proteins may determine their transitions into compactly folded conformations (cf. Gierasch and King, 1990; Sauer et al., 1990; Kim and Berg, 1996). A third category of potential molecular codes has been for multisub unit protein assemblies that switch their functional behavior under the control of ligand binding (or covalent reaction) at multiple combinations of sites (Ackers and Smith, 1986). These “macromolecular switches,” originally exemplified by the allosteric enzymes and respiratory oxygen carriers (hemoglobins and hemocyanins), have also been found among gene regulatory proteins (Steitz, 1993; Muller-Hill, 1996), signal transduction cascades, and membrane ion channels (Jackson, 1988). Their regulatory functions frequently entail changes in quaternary interaction and tertiary conformation in response to external signals (e.g., reaction with a specific metabolite, transcription factor), while the protein assembly acts as a transducer for the free energy costs of regulation. Such transduction of active site binding energy (via protein structure changes) is also central to the extraordinary rate enhancements of enzyme catalysis (Lumry, 1959;Jencks, 1969; Weber, 1975). Regulation occurs when two or more active site processes exert mutual influences on each other by using the macromolecule as a common transducer. A most important framework for understanding the mutual influences among coupled macromolecular reactions and their driving forces has been the theory of “linked functions,” which was created and developed extensively by Jeffries Wyman (1948, 1964; Edsall and Wyman, 1958; Wyman and Gill, 1990). Wyman’s ideas had a wide-ranging influence on early attempts to understand cooperativity of hemoglobin oxygen binding as well as the ligand-mediated regulation of multisubunit enzymes. During the period 1935-1966, two mechanistic lines of thought had emerged. The earliest model, by Linus Pauling (1935), and its later extensions by Daniel Koshland and colleagues (Koshland, Nemethy, and Filmer, 1966; hereafter called the KNF model), used the concept of ligand-induced conformation changes that were coupled by nearest neighbor interactions among the subunits of multimeric protein structures. This “sequential” concept was also advanced by Jacques Monod and his associates (1963) in their original allosteric model. However, a sharply contrasting concept had also been proposed by Wyman as early as 1948. In his analyses of the hemoglobin Bohr effect (Wyman, 1948; Wyman and Allen, 1951), Wyman postulated an equilibrium between alternative conformational forms of the hemoglobin molecule, with preferential binding of ligands to one of them. This “concerted transition”

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concept was incorporated into the famous “two-state model” paper of Monod, Wyman, and Jean-Pierre Changeux (1965; hereafter called the MWC model). The early crystallographic work of Max Perutz supported Wyman’s concept by unequivocally demonstrating that two quaternary forms of the tetrameric molecule (Fig. 1) designated “T” and “ R ’ had 0,driven switching properties that validated Wyman’s early conjecture (Perutz, 1970, 1976, 1990; Wyman and Gill, 1990). Subsequent to these germinal developments much understanding has been achieved regarding the general nature of allosteric regulation and the associated structural transitions in a number of important systems. The formal models of Monod et al. (1965) and of Koshland et al. (1966) contributed monumentally by defining plausible rules by which protein conformation changes could regulate the mutual influences of binding reactions among substrates, activators, and inhibitors. Cooperative interactions among widely separated binding sites have thus been explained either as a sequence of “ligand-induced” changes in tertiary conformation that alter pairwise interactions among nearest neighbor contacts of the ligated subunit (KNF), or alternatively as a “symmetry-conserved”

FIG. 1. Subunit structure of the Hb tetramer. (a) Front view showing the a’and P2 subunits (light gray) in front of the az and P’ subunits (dark gray). At center lies the alPPcontact region, which, along with the a1a2 contact, forms half of the a’/?’ interface. The other half of the interface includes the azP’and aZdcontacts. (b) Side-view cartoon illustrating the major CUPdirner movement from the quaternary T * R structure.

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transition where the subunits switch in concert from their low- to highaffinity “states” (MWC). Wyman (1972) showed how both the MWC and KNF models could be understood to be special limiting cases of a more general model in which sequential reaction cascades were “nested” within each global T and R conformational state. Extensive research has established that both sequential and concerted processes occur in real biological systems and that hybrid combinations of the two are also evident (e.g., Wyman, 1972; Viratelle and Seydoux, 1975; Levitski, 1978; Lipscomb, 1994; Kurganov, 1982; Neet, 1983,1995;Leslie and Wonacott, 1984; Robert et al., 1987; Schachman, 1988; Louie et al., 1988; Kantrowitz and Lipscomb, 1988; Decker and Sterner, 1990; Perutz, 1990; Wyman and Gill, 1990;Acharya et al., 1991; Brzovic et al., 1994; Auzat et al., 1995; Muller-Hill, 1996; Steitz, 1993; Van Holde, 1995; Grant et al., 1996). The landmark crystallographic research of Max Perutz established major structural features which underlie cooperative O 2 binding by mammalian hemoglobins and the modulation of affinity by heterotropic effectors [2,3-diphosphoglycerate,C 0 2 , chloride] (Perutz, 1970, 1976, 1979, 1990; Perutz et al., 1960, 1987) (Figs. 1 and 2). These features include the deoxy “T” and oxy “ R ’quaternary structures (cf. Baldwin and Chothia, 1979; Fermi, 1975), which differ by a 15” rotation of one dimeric half-molecule (alp’) relative to the other (a2P2) as shown in Fig. lb. Correlation of the T + R structural transition with the cooperative (sigmoidal) shape of the O2 binding curve and with its modulation by organic phosphates (Arnone, 1972) established a key structural role of the T + R switch in mediating physiological cooperativity. Extensive research on native and mutationally altered human hemoglobins has also revealed the following mechanistic features:

1. Crystallographic and spectroscopic data have shown that partially ligated tetramers which have the quaternary T dimer-dimer orientation may nevertheless contain subunits in the “oxy” (r) and/or “deoxy” (t) tertiary conformations (Brzozowski et al., 1984; Arnone et al., 1986; Luisi et al., 1990; Ho, 1992; Mukerji and Spiro, 1994;Jayaraman et al., 1995). The presence of mixed tertiary conformations among subunits within the same quaternary structure violates the MWC model’s postulated “symmetry conservation” rule (Monod et al., 1965) but is required by rules of the KNF model (however, KNF does not postulate the Hb molecule’s global T + R transition). 2. Noncovalent bonds (i.e., salt bridges and H bonds) were identified (Perutz, 1970; Kilmartin, 1976) that break upon oxygenation of an individual subunit or upon T + R switching. Breakage of these bonds generates positive free energy and thus contributes to cooperativity by

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reducing net affinity of the accompanyingO2binding steps. Many studies on mutant human Hbs have supported these phenomena (cf. Bunn and Forget, 1985;Turner et al., 1992; LiCata et al., 1993;Abraham et al., 1997). 3. An “allosteric core” of structural elements within each subunit was identified by Karplus and colleagues (Gellin and Karplus, 1977; Gellin et al., 1983) that can mediate Orinduced tertiary conformation changes ( t + r) of the respective (Y and /3 subunits (Fig. 2). Their computational analysis showed two unstrained conformations for each of the allosteric cores, i.e., when an unligated subunit (t) is within a T quaternary structure, and alternatively when a ligated subunit (r) is within an R tetramer. Conformational strain that accompanies ligation of subunits within the T tetramer provides positive free energy (in addition to that arising from noncovalent bond breakage) and favors quaternary switching to the R interface (whereupon the Oz-induced tertiary conformational strain is relieved). Reciprocally, a deligation step within R would promote switching to T. 4. An important methodology for translating the crystallographic,and computationally derived structural features of the Hb molecule into statistical thermodynamic properties that are predicted to control its functional behavior was pioneered by Karplus and associates (Szabo and Karplus, 1972; Lee and Karplus, 1983; Lee et al., 1988). These studies have helped elucidate the roles of tertiary structure changes induced by heme site ligation of individual (Y and /3 subunits within the two quaternary forms of the tetramer. Additional relationships which connect the structural findings of Perutz and those of Karplus have been discovered by the work on partially ligated intermediates that is reviewed here. The possibility that oxygenation-induced changes of subunit tertiary conformation might generate cooperativity among the Hb subunits in the absence of quaternary T + R switching had been suggested by Perutz (1976) but remained an open question. The model of Lee and Karplus (1983; Lee et al., 1988) extended the earlier work (Szabo and Karplus, 1972) by allowingvariable Opdriven energetic contributions from salt-bridge breakage compared with those from tertiary conformational strain (Lee and Karplus, 1983). A principal result of the work discussed in the present chapter is that 0,driven tertiary strain is coupled within the symmetry-related dimeric half-molecule (a’fi’or azfi2) and this coupling is reflected in the observed binding cooperativity between the intradimeric a and /3 heme sites prior to the quaternary T + R transition. The significance of intradimeric coupling within the T tetramer (Ackers et al., 1992; Huang et al., 1996a) lies in promoting the T -+ R transition at specific reaction steps of the Hb tetramer’s oxygen binding sequence. The new findings have thus

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GARY K. ACKEFS

FIG.2. Movement of F-helix and FG corner residues (proximal side of heme) upon ligation. Deoxy-Hb (black) and COHb (gray) structures are from Kavanaugh et al., 1992, and Silva et al., 1992, respectively. a-Carbons are indicated on the deoxy F helices; bound CO is shown on the distal side of the (gray) heme. The mean planes of the hemes were superimposed mathematically. When bound CO (or 0,) is released, the iron atom moves about 0.6 A from a position within the heme plane toward the proximal side. The His residue bonded to the heme Fe (position F8) likewise moves away from the heme plane. This motion is translated to the FG corner residues, which interact with residues on the opposite dimer within the Hb tetramer, i.e., across the dimer-dimer interface. This series of motions may form the basis of the structural communication between the heme and the dimer-dimer interface.

extended the mechanistic understanding of Hb, while remaining consistent with the earlier discoveries summarized above. 11. OVERVIEW This chapter reviews developments between 1985 and 1997 of concep tual strategies and experimental databases that have led to a determina-

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tion of site-specificcontributions to O2binding cooperativity by the eight partially ligated intermediates of Hb (Fig. 3) and that have correlated the site-specific binding steps with tertiary and quaternary structural transitions of the H b tetramer and with the interactions of heterotropic effectors. This research has revealed specific rules of liganddriven T -+ R quaternary switching and of tertiary cooperativity that do not coincide with either the concerted MWC or the sequential KNF models and may be viewed as extensions to the more detailed structure-based models of Perutz and of Karplus cited above. The Hb allosteric mechanism has been found to employ elements of both the classical models (i.e., MWC and KNF); however, the elements are combined in specific ways that carry previously unrecognized structural implications. These discoveries resulted from a 12-year sequence of investigations (1985-1997) that has occurred in two stages.

A . Research Leading to the Symmetq Rule Using thermodynamic linkage cycles (Ackers and Halvorson, 1974; Smith and Ackers, 1985), our research group developed a strategy for

FIG.3. Symmetry rule: Ligand binding to either the a! or /3 subunits of microstate species 01 is communicated to the unligated subunit within the alp’ dimer in quaternary T structures. When at least one subunit is ligated on each dimeric half-molecule, the resulting tertiary changes disfavor the T interface and promote quaternary switching to R. While most of the binding cooperativity results from the quaternary transition, its distribution is controlled by the six “switchpoint” binding steps that implement the symmetry rule.

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GARY K. ACKERS

evaluating the free energy contributions to cooperativity by all eight partially ligated Hb intermediates (Fig. 4; see Smith and Ackers, 1983, 1985; Smith et al., 1987; Perrella et al., 1990a; Ackers, 1990; Speros et al., 1991) for three well-established O2analog systems, i.e., Fe'+/FeR+CN, FeS+/Mn9+, and Cozf/Fe2+CO, that were known to mimic stereochemistry of the native Fe2+/Fe2'O2system (Perutz, 1979) and to exhibit the native T + R structural transition on overall ligation (Moffat et al., 1976; Fermi et al., 1982; Smith and Simmons, 1994; Silva et al., 1992). These experimental microstate free energies (Table I, cols. 2-5) provided an unprecedented opportunity to analyze the characteristics of contributions by the eight tetrameric binding intermediates. In each analog system the microstate cooperativity terms were found to exhibit similar distributions, from which a consensus function was deduced. The common relationships among cooperative free energies of the three analog systems were then used to calculate the distribution of native H b 0 2 microstates (Table I, col. 6) from independently measured stoichiomet-

FIG. 4. CdSCdde of stepwise ligation reactions for Hb microstate tetramers in linkage with representative constituent dimers. The ligated heme sites are denoted by X; the unligated ones are empty. Linked dimer-tetramer assembly reactions (left to right) are used to measure energetic costs of tetrameric cooperativity for the various steps. Molecular species are depicted topographically, with dimers assembling to form the nip2(or dimerdimer) interface (vertically bisecting each tetramer). Stepwise ligation accompanied by tertiary constraint is denoted by reactions 1 and 2; ligation with simultaneous quaternary T-+ Rswitching is denoted by reactions 3,5,7,8,10,and 11; and ligation not accompanied by either is indicated by reactions in gray.

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Table I. Cooperative Free Energies of Partially-Ligated Human Hemoglobin

“Experimental conditions: pH 7.4; 21.5OC; 0.18 M CI-. Cols. 2-5,7,8: Microstate species [ Zjl of five ligation analogs. Col. 1: Stoichiometric cooperative free energies of the native HbOs system. Col. 6: The microstate free energies predicted from the consensus distributions of cols. 2-5, which were constrained to also conform with stoichiometric terms (col. 1) of the native system. Cols. 7,8: Additional analogs that were subsequently characterized. Col. 9: Microstate distribution for the native HbOs system, which was determined independently of data from cols. 2-5 (used in col. 6 prediction). References: col. 1, Ackers et al., 1992; Chu et al., 1984; col. 2, Smith and Ackers, 1985; Perrella et nl., 1990a; col. 3, Daugherty et al., 1991, 1994; col. 4, Ackers, 1990; col. 5 , Speros et al., 1991; Huang and Ackers, 1996; col. 6, Ackers et al., 1992; col. 7, Huang and Ackers, 1996; cols. 8, 9: Huang et al., 1996b.

’

ric HbOBconstants (Fig. 5; Table I, col. 1) (Ackers et al., 1992; Ackers and Hazzard, 1993; Holt and Ackers, 1995). Using structuresensitive probes it was found that the T R quaternary transition occurs at the six reaction steps of the binding cascade (Fig. 4) that yield ligated heme sites on both of the symmetry-related halfmolecules alp’ and aZpp(see Fig. 3). This “symmetry rule” provided a simple molecular code that translates reactions of the Hb binding cas-

194

GARY K. ACKERS

(a) 0.8 0.6

v

0.4 0.2

0.0

0.4

0.8

1.2

[o,]

(b)

- 14.3

2D

- 11.4

2DX 2(-8.3{

)

2DX, - 33.2

total

kcal

1.6

2.0

2.4

lo5 Cooperative Free Energy

b Tet - 5.4

+ 2.9

- 5.7

+ 2.6

-6.7

+Im6

- 9.1

-0.8

- 26.9

+ 6.3

kcal

J

- 8.8 kcal

Tea,

-7.2 kcalb

- 8.0 kcal

l,, J

W Tea,

COST OF STRUCTURAL REARRANGEMENT = + 6.3 kcal

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195

cade into the quaternary switchpoints that mediate cooperativity. Significant cooperativitywas also found to accompany specific binding steps within the half-tetramer (alp’ or a‘p’) prior to the global T + R structure change. These findings have supported the view that the quaternary and tertiary “switches” already known to mediate Hb cooperativity (Perutz, 1970, 1976; Gellin et ul., 1983) do so by specific rules of configurational site occupancy that were previously unanticipated. Consideration of these new insights in context with the earlier discoveries cited above has led to the following general picture: 1. Initial ligation on either of the symmetry-related half-tetramers

(a’P’ or aspncf. Fig. 1) generates a tertiary conformation change involving both subunits of the ligated dimer (Fig. 3). The associated conformutional work is resisted by the T interface, which remains intact, while the accompanying unfavorable free energy (designated “tertiary constraint”) reduces net binding affinity relative to that of the isolated subunits.

FIG. 5. (a) Binding isotherms at decreasing Hb concentrations (right to left). The rightmost curve pertains to tetramers T ( % = 3.2), and the leftmost curve to dissociated a’P’ dimers D (nH = 1.0). Intermediate curves were measured at H b concentrations between 4 X and 0.5 rnMheme (left to right): T = 21.5”C; pH 7.4; 0.1 rnMTris-HC1 buffer plus 0.1 M NaCl in the presence of 0.1 mM NazEDTA. Data were fit globally to the composite equation:

where Z? and Z, are the binding partition functions of dimers and tetramers, respectively (Ackers and Halvorson, 1974). Here Z, = 1 + KZIx+ &x2 and Z, = &x + &f + &x9 + K44# [cf. Eqs. ( 1 ) and (2) for definitions and discussion]; Z,l = &,x 2K2$ and Z,!= K4,x 2K& + 3K& 4K&. The K2,and &,are Adair binding constants of the dimer and the tetramer, respectively:

+

+

+

where the brackets denote concentrations of the respective protein species. (b). Linkage diagram showing stoichiometric free energy components of cooperativity. Binding of ligand X to tetramers is depicted on the right and that to dimers on the left. Dimertetramer assembly reactions at the five degrees of ligation are indicated by horizontal arrows. Gibbs energy values are given for X = Oz.

196

GARY K ACKERS

2. A second ligation on the same dimer is accompanied by a generally smaller tertiary constraint effect and hence occurs with increased net binding affinity. The T interface remains essentially intact so that there is tertialy cooperatiuity without quaternaly switching. This intradimeric cooperativity occurs between heme sites that are separated by -34 and disappears on dissociation of the tetramer into dimers. 3. Binding at heme sites of both dimers (in any combination) generates unfavorable free energy, i.e., “dimer-dimer anticooperativity,” which triggers the T + R transition. This quaternary switch releases dimer-dimer interactions of the T interface along with conformational strain of the assembled dimeric half-molecules. It contributes energetically through breaking the T interface bonds and forming the alternative R interface bonds at each of the six switchpoints specified by the symmetry rule (Fig. 3).

A,

The formation and release of tertiary constraint is thus a fundamental driving force of cooperative binding in Hb. Whereas the T interface can withstand one dimer having tertiary constraint, it cannot accommodate two such perturbed dimers. Since the movement of the iron into the heme plane upon O2 binding has been termed a trigger for tertiary conformation change (Perutz, 1970), the trigger for the T+R switch must be the structural event that causes dimer-dimer anticooperativity. In their extensive review of H b stereochemistry Perutz et al. (1987, p. 314) noted that “the shape of the alpl and anp2dimers is altered by changes in tertiary structure: on oxygenation the distance between the a carbons of residues FGla, and FGlP, shrinks from 45.6 to 41.3 A. These changes make an alp’ dimer that has the tertiary oxy structure a misfit in the quaternary T structure, and an alp’ dimer that has the tertiary deoxy structure a misfit in the quaternary R structure.” This observation undoubtedly provides an important clue to the structural origins of the energetic coupling that occurs between a and /3 heme sites of the same half-tetramer (a’ and p’) prior to the quaternary T + R transition (LiCata et al., 1993), and thus contributes to this ‘‘second trigger. ”

B. Structural Probes and Heterotropic Responses 1. Structure-sensitive probes have provided quaternary assignments of the intermediates that have supported the symmetry rule’s predicted switchpoints within the binding cascade (cf. Section VI,D) . 2. Modulation of the microstate energetics by heterotropic allosteric effectors and by temperature has also been found to exhibit symmetry rule behavior.

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C. Microstate Cooperativity Components of HbO and HbCO

Studies on other ligation systems of Hb have provided strong support for the symmetry rule mechanism (also designated the “molecular code”) that was proposed in 1992: 1. The application of new methods for evaluating energetic perturbations by metal substitution at the hemes (Huang and Ackers, 1996) has delineated the contributions to cooperativity for all eight partially ligated intermediates of carboxy-Hb (Fe/FeCO) . These cooperative free energies showed the characteristic distribution predicted by the molecular code (Ackers et al., 1992). 2. Extension of these methods to the native H b 0 2system (Fe/Fe02) yielded site-specific cooperativity terms (Huang et aL, 1996a) in excellent agreement with those predicted earlier from direct O2 binding results (e.g., Figs. 5-7) using the molecular code partition function (Ackers et al., 1992).Contributions to cooperativityby the O2binding intermediates that were determined independently of data from the three initial analogs, and also independent of direct O2 binding data, were found to yield the correct highly cooperative O2 binding curve of native Hb to within the accuracy of its experimental measurement (Huang et aL, 1996a). This chapter reviews the current status of work on the hemoglobin molecular code, including methodology and discoveries from the initial

Fractional Saturation FIG.6. Stoichiometric fractions h, of tetramers with i ligands bound as a function of 0, saturation. Conditions: pH 7.4; 21.5”C;NaCl concentrations of 1.40 M (solid curves) and 0.08 M (dashed curves); 0, 1, 2, 3, 4 indicate the number of oxygens bound. (Doyle et aL, 1997).

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GARY K. ACKERS

three analogs (1985-1992), subsequent findings on the partially ligated intermediates of O2and CO binding to native FeHb, and on the modulation of partially ligated intermediates by heterotropic effectors and other probes. Also discussed are arguments that have been proposed against this approach for elucidating the Hb allosteric mechanism. CURVES AND 111. BINDING

A.

STOICHIOMETRIC INFORMATION

The Adair Binding Function

A fundamental characterization of tetrameric hemoglobin’s O2 binding affinity and cooperativity has been the determination of equilibrium binding constants K , ( i = 1, 2, 3, 4) by numerical fitting of O2 binding data. Beginning with the classic researches of Roughton (Roughton et al., 1955; Roughton and Lyster, 1965; Rossi-Bernardi and Roughton, 1967),the “Adair constants” K i have been evaluated from measurements of the fractional saturation Y,i.e., the molar ratio of O2 reacted with the heme-binding sites; 7 is determined over a range of dissolved O2 concentration, x, and the data are fit to the tetramer Adair equation (Adair, 1925): -

Y=

+ 2 K 2 x 2+ 3K3x3+ 4K4x4 4(1 + Klx + K2x2+ K3x3+ K4x4) K,x

(1)

Each resolved Adair constant, defined by K , = [HbX,]/ [Hb] x’, reflects the molar free energy (AGi = -RTln K , ) of reacting the deoxy tetramer with a stoichiometric number i of O2 molecules. Thus, i = 0, 1, 2, 3, 4 ( K O = l ) , corresponding to the possible numbers of ligated hemes, irrespective of their site confgurutions within the tetrumer. Each K , contains a numerical factor, i.e. n ! / [ i ! ( n- i)!], which accounts for statistical degeneracy of the reaction product [Hblx,. Thus division of the respective equilibrium constants K , by 1, 4, 6, 4,and 1 yields the “intrinsic” constants [cf. also Antonini and Brunori, 1971; Edsall and Gutfreund, 1973; Imai, 1982; Wyman and Gill, 1990, for discussion of Eq. (1) and related functions]. “Stepwise” binding energies A G;, (corresponding to successive numbers of bound sites) are plotted in Fig. 7 at a sequence of heterotropic NaCl concentrations. The denominator of Eq. (1),excluding the factor of 4,is the fundamental grand partition function Z(x) for the four-site binding system of tetrameric Hb (cf. Hill, 1985), comprising the “statistical weights” K,x’ for successive degrees of ligation (for discussion of the statistical weight

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199

concept in biopolymers, see Zimm and Bragg, 1959; Flory, 1969; Cantor and Schimmel, 1980). The way in which Z(x) varies with the concentration of dissolved O2determines the shape and x coordinate “position” of the binding curve, since -

Y = 1/4[d In Z / d In x]

(2)

By comparison with the noncooperative curve of its dissociated dimers (Fig. 5), the Hb tetramer’s binding curve exhibits a sigmoidal shape and “right-shifted” midpoint. These features facilitate the unloading of O2from red cells in the peripheral circulation and also the efficient O2 uptake in the lungs (cf. Bunn and Forget, 1985). Such physiologically important characteristics of the O2 binding curve, which are found in mammals, fish, birds, and many invertebrate organisms, reflect the structure-based changes in Adair constant values with the successive numbers i of bound 02.An unchanging affinity over the successive degrees of binding would yield a 7 vs. x curve with hyperbolic shape like that of dissociated dimers shown in Fig. 5. The resolution of unique values for the four K iparameters from numerical analysis of the highly cooperative binding curves of human Hb has always placed severe demands on experimental accuracy because of the high statistical correlation among K , values in the data-fitting problem (Johnson et al., 1976; Imai, 1990; Gill et al., 1987; Doyle and Ackers, 1992a) combined with the low abundance of partially ligated species (e.g., Fig. 6), which is characteristic of cooperative systems (cf. Edsall and Gutfreund, 1983). Modern instrumental methods developed by Imai (1982) and by Gill and colleagues (see Dolman and Gill, 1978; Gill et al., 1987) have contributed greatly by facilitating the determination of high-quality binding curves over extended ranges of conditions and sample types. Adair constants K , and other properties of the Hb binding curves have thus been evaluated extensively by nonlinear regression analysis (cf. Imai, 1990;Johnson et aA, 1976; Poyart et al., 1978; Gill et al., 1987; Doyle and Ackers, 1992a; Doyle et aL, 1994, 1997). The prodigious work of Imai has generated extensive and systematic determinations of Hb Adair constants over wide ranges of conditions, effectors, and structure modifications, leading to numerous mechanistic correlations, as summarized in his important monograph (Imai, 1982). Oxygen binding studies from the present author’s laboratory during the period 1975-1997 have generated findings that are in general accord with those of Imai and of Gill and colleagues. Most notably, a striking difference between the enthalpy for oxygenating tetramers anP2compared with their dissociated dimers was accounted for by the heat terms for 02-

200

GARY K. ACKERS

linked Bohr proton release during the first three tetramer-binding steps (Imai, 1979; Mills and Ackers, 1979a,b; Mills et al., 1979; Imai et al., 1980; Chu et al., 1984). Figure 7 shows the four stepwise O2 binding free energies of normal human Hb at a series of NaCl concentrations (Doyle et al., 1997), obtained using the elegant technique pioneered by K Imai (1982), and corrected for the contributions of all dimeric species. Structural Implications. The Adair constants (and their ratios) have been widely recognized as reflecting the Ordriven structure changes that accompany the saturation process (Perutz, 1970; Monod et al., 1965; Imai, 1968, 1982; Weber, 1972; Szabo and Karplus, 1972; Ackers and Halvorson, 1974; Mills et al., 1976).Thus the binding of each stoichiometric number of oxygens ( i = 1, 2, 3, 4) may generate changes in the molecule’s tertiary and/or quaternary structure (plus altered interactions with heterotropic effectors, solvent, etc.) for which the “free energy costs” are balanced (by the Hb molecules) against the chemical affinity of O2 bonding onto the heme iron atoms. Because of this central role of the Adair constants in reflecting structure-energy responses of the Hb molecular mechanism and the fact that physiological uptake and delivery of O2is essentially controlled by the equilibrium thermodynamic binding curve (cf. Bunn and Forget, 1985),a “predictive” understanding of the structural, energetic, and dynamic origins of the Adair constants would arguably constitute a solution to the classic problem of the Hb mechanism. The discoveries reviewed in this chapter have shown that such understanding requires each stoichiometric Adair constant to be

-9 -10

-=.,

- w’ I

I

, I

Y

--

4,,m--w-I

I

I

I

I

I

I

I

I

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

201

dissected into its constituent “microstate constants” in order for the 02-driven tertiary and quaternary transitions to be related individually to the site-specific components of the binding cascade (Fig. 4). Strategies and techniques by which thermodynamic contributions to 7 have been elucidated for the 10 unique ligation “microstates” (Fig. 3) are described below beginning with Section IV.The methodology employed was an extension of the cooperativefree energy approach that was developed earlier in HbOpstudies at the stoichiometric level (Ackers and Halvorson, 1974; Mills et al., 1976;Johnson et al., 1976; Chu et al., 1984; Doyle et al., 1992b, 1994, 1997). This approach evaluates free energy “costs” of the binding cooperativity by simultaneously utilizing the “Wyman linkages” that connect heme site ligation and dimertetramer assembly with resolution of Adair constants for the interacting tetrameric and dimeric species. The following subsections summarize aspects of this methodology that have formed the basis for its extension to the Hb microstate level (Section II1,B) and the relationship of these stoichiometric-level parameters to the traditional Hill coeficient that has been widely employed as a descriptor of cooperativity (Section 111,C).

B.

Using Dimer-Tetramer Assembly to Evaluate the Energy Costs of Binding Cooperativity

Determinations of thermodynamic parameters for the oxygen-linked dimer-tetramer assembly reactions (e.g., Fig. 5a) have provided a sensitive probe of Hb allosteric properties (Ackersand Halvorson, 1974; Mills et al., 1976;Johnson et aL, 1976; Atha et aL, 1979; Chu et al., 1984; Doyle et al., 1991, 1992a,b, 1994, 1997). This strategy is based on the following rationale: (1) Oxygenation-induced interactions that generate cooperativity within the Hb molecule are decoupled by dissociation of the tetramers into dimers. (2) The difference between the dimer-tetramer assembly free energy of a tetramer with i bound oxygens and that of the unligated tetramer reflects the net energetic cost from the subsystem tertiary conformation changes (t + r), the pairwise interactions (salt bridges, H bonds), and quaternary transition (T + R) that accompany binding ioxygens onto the tetramer’s a and p subunits. In principle these cooperativitycomponents may be estimated equivalently as differences in successive binding free energies, or as the corresponding differences in dimer-tetramer assembly energies (Fig. 5b). Thus a cooperutivefree energy may be defined for each degree of binding:

‘AG:= - R T I n ( ’ K f )

(3)

where ‘K: = ‘K;/’K; and each equilibrium constant ( i = 0,1, 2, 3, 4) characterizes formation of the tetrameric species having i ligated

202

GARY K. ACKERS

heme sites from ap dimers bearing appropriate ligated hemes (Ackers and Halvorson, 1974;Johnson et al., 1976).Independent determinations of dimer-tetramer equilibrium constants for the end-state species (i.e., OK; and 4K;) have been carried out extensively using analytical gel chromatography (Ackers, 1970, 1975; Valdes and Ackers, 1979; Turner et al., 1992) in combination with stopped-flow kinetics and haptoglobin trapping kinetics (Ip et al., 1976; Ip and Ackers, 1977; Turner et al., 1981). These methods have been used to characterize more than 60 mutant and chemically modified human hemoglobins (Pettigrew et al., 1982; Doyle et al., 1992a,b; Turner et al., 1992). Values for the dimertetramer assembly constants at partial degrees of oxygenation ( ‘ K ; ,‘K;, and 9 K ; )were resolved from analysis of concentration-dependent binding curves determined at a sequence of Hb concentrations, also yielding Adair constants of the linked dimers and tetramers (cf. Figs. 5 and 7). The difficulties in obtaining unique values of the four Adair constants (cf. Imai, 1982, 1990; Di Cera et al., 1987; Kister et al., 1987; Doyle and Ackers, 1992a) had led Marden et al. (1989) to conclude that unique affinities for partially ligated species “may be impossible.” This conclusion was in accord with early analyses (Ackers et al., 1975) that stimulated our research group to develop the linkage strategy based on Wyman principles, which incorporates multiple dimensions for resolving the system’s thermodynamic properties, even at the stoichiometric level (cf. Chu et al., 1984). It should be noted that the tetramer-dimer dissociation rate of normal deoxy-Hb is remarkably slow (e.g., tlIP= 10 h at 21.5”C), corresponding to an Arrhenius activation energy of 33 kcal/mol (Ip and Ackers, 1977). Such slow kinetic properties of the quaternary T tetramer’s disassembly reactions are totally consistent with the more rapid processes of tertiary and quaternary transition that are driven by heme site binding onto the already assembled tetramers (Eaton and Hofrichter, 1990; Henry et al., 1997). When tetramer-dimer dissociation reactions are linked to those of heme site binding in order to evaluate the thermodynamics of cooperativity, the Wyman linkage methodology is rigorous and the resulting information on cooperativity of the bindingenergeticsis path independent. This great utility of the linked functions approach as applied to subunit assembly/hybridization techniques has been exploited extensively in the analyses of Hb microstate cooperativity that are reviewed in this chapter. Relationships to the Tetramer Adair Function. Central to the usage of thermodynamic linkage cycles for evaluating contributions to binding cooperativity at both the stoichiometric and microstate levels is the realization that when cooperative free energies are calculated from a

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203

ratio of dimer-tetramer assembly constants (Eq. 3) they also provide a measure of the free energy contributions from tertiary and quaternary structural transitions that accompany the tetrameric binding in excess of those from binding to the same sites of dissociated dimers. The distribution of iAG: terms will also reflect the OTlinked free energies of heterotropic effector binding (Bohr protons, DPG, C 0 2 , or chloride) in excess of the respective heterotropic effects on O4 binding by the dissociated dimers (Chu et al., 1984; Doyle et aZ., 1997). Reciprocally, a determined set of Adair constants Ki (i.e., uncorrected for statistical factors) can also be used in combination with binding constants evaluated - for the dissociated dimers, to yield the same cooperativity terms, 'AGL, since

where k, and k, are respective binding constants to a and p subunits of the dissociated dimers, i.e., Eqs. (4a), (5a), (6a), and (7a) (Pettigrew et aL, 1982; Doyle et al,, 1997).When the dimeric sites have equal binding affinities (Mills et aL, 1976; Chu et al., 1984; Doyle et al., 1997), k , k, = kp, yielding Eqs. (4b), (5b), (6b), and (7b). These formulas have provided a framework whereby the free energy costs of tetrameric cooperativity may be evaluated either through determinations of 'Kp and OK2 or equivalently from the tetramer binding constants K, in combination with those of the constituent dimers. Experimental implementation of this strategy, which links the dimer's heme site binding reactions to those of the same sites within the assembled tetramers, has made it possible (1) to evaluate and correct for the effects of dissociated dimers on O2binding curves, increasing the accuracy of the resolved tetrameric properties, and ( 2 ) to combine experimental information from multiple

204

GARY K. ACKERS

techniques, thus minimizing the impact of systematic bias of any single method. This methodology has also been used to analyze the Orlinked subunit assembly reactions of H b containing cobalt-substituted hemes (Doyle et al., 1991) and with mutant and chemically modified species (LiCata et al., 1990; Atha et al., 1979; Doyle et al., 1992a,b). An especially illuminating example of the interplay among these reciprocal linked functions is the study by Riggs and associates on the mutant H b Kansas where the affinity of /3 subunits k , is greatly reduced by the amino acid replacement @lo2 asnAthr) (see Atha et al., 1979). Anticipating the extension of this approach to the microstate level (Section IV),we can reformulate the tetramer Adair function, Eq. ( l ) , in terms of the cooperativity constants and affinities of the dissociated dimer sites ( k , and k,, or k d ) . When a and /3 subunits of the dimers have essentially identical intrinsic affinity k d (as with normal Hb over a wide range of conditions) the tetramer Adair function may be written -

Y=

+ ['K:]( k , , ~ ) ~ [TI( k d x ) + 3 [ F ] ( k d x ) ' + 3C-I (1 + 4[=] ( k d x ) + 6[?K,'] (&x)' + 4['KK:] ( k , , ~ ) + [TI( k d x )'}

(8)

If subunits within the dissociated dimers have differing affinities, the corresponding function may be written to incorporate formulas (4a), (5a), (6a), and (7a). This method of transforming the classical Adair binding function into a combination of dimer affinities and cooperativity terms that are derived from subunit assembly data played a crucial role in the early solution of the Hb molecular code (Ackers et al., 1992). At the stoichiometric level, Eq. (8) specifies how a knowledge of the 'K: values and dimer affinities k d will always provide a correct set of the Adair constants K , and partition function Z( x) . Extension of this concept to each of the ligation microstates (Smith and Ackers, 1985) was a major feature of the strategy (to be described in Section VI) that eventually yielded cooperative free energies for all intermediates of the HbOB system (Ackers et al., 1992). This usage of dimer-tetramer assembly energies for evaluating cooperativity constants 'K, of tetramers having i ligated heme sites is valid whenever sites of the dissociated dimers d o not interact cooperatively; validity of the method does not require the dimer sites to have identical affinities with any of the tetramer-binding steps. The cooperative free energies ;AGC- RTln('K,) listed in Table I, col. 1, will be compared with those of the corresponding microstate tetramers in subsequent sections of this chapter. Quaternaly Enhancement. The discovery that assembled Hb molecules may exhibit higher O2affinity than their dissociated subunits (i.e., "qua-

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

205

ternary enhancement”) was initially made for the association of Hb p subunits into tetramers (Valdes and Ackers, 1978; Kurz and Bauer, 1978). ) O paffinity at the fourth In the case of the normal tetramer ( a 2 p 2the binding step had been inferred earlier from model analysis (Szabo and Karplus, 1972) to be higher than that of isolated (Y or /3 subunits. Experiments with normal Hb have found the tetramer’s affinity for the fourth O2to exceed that of the dissociated dimers (or isolated monomers) over wide ranges of conditions (Mills et al., 1976; Mills and Ackers, 1979a,b; Imai and Yonetani, 1975; Di Cera et al., 1987; Chu et al., 1984; Ackers andJohnson, 1990; Doyle and Ackers, 1992b; Doyle et al., 1992b, 1994). The recent discovery that quaternary enhancement can be titrated to a negligible magnitude by increasing [NaCl] is illustrated in Fig. 7 (Doyle et al., 1997). Recent time-resolved circular dichroic studies of HbOB photolysis intermediates by Kliger and associates (GhelichKhani et al., 1996) have also supported the findings of quaternary enhancement in human Hb. Arguments against quaternary enhancement (Gibson and Edelstein, 1987) have been made on grounds that (1) measured O2rebinding rates (after flash photolysis) did not require a sufficiently high equilibrium constant for quaternary enhancement (i.e., based on expected values for the “off” rates) and that (2) quaternary enhancement was thought to violate the concerted MWC model, which was believed to have a greater preponderance of supporting evidence than did the quaternary enhancement effect. By contrast, however, it had been demonstrated earlier (Ackers and Johnson, 1981) that thermodynamic constants determined for the linkage scheme (Fig. 5b) were fully compatible with the constraint requiring tetramers to follow a two-state MWC model, while their dissociated dimers constituted a “third state” in the sense of having an O2 affinity different from either the MWC model’s T or R tetramers (Ackers and Johnson, 1981). The aforementioned independent findings that dissociated dimers may bind O2with lower affinity than the fourth tetramer step do not constrain the possible models of tetrumm’callostery.The O2 affinities of dissociated dimers per se have no mechanistic bearing on their use as “built-in” reference reactions for gauging “thermodynamic distances” between the tetrameric species with which they share linked equilibria.

C. The Hill CoefJient A traditional measure of cooperative interaction among the binding sites within a protein is the Hill coefficient nH = d ln[F/(l - F ] / d In x, which is usually determined as the slope of a logarithmically trans-

206

GARY K. ACKERS

formed binding curve (cf. Gutfreund and Edsall, 1978; Wyman and Gill, 1990). The maximum value of n H ,or its value at half-saturation, is frequently used as an index of the degree to which ligation events exert their mutual influences. Common usage of the above formula (Hill, 1910) has fostered the notion of nH as a measure of “the number of cooperating sites.” In Hill’s original derivation, a (nonintegral) number n Hof Hb sites were assumed to react in concert with ligand (cf. Fersht, 1985). However, the above nHfunction was shown independently by K. Linderstrom-Lang to be a normalized statistical variance of the species abundances over all stoichiometric degrees of binding ( i = 0, 1, 2, 3, 4 for tetrameric Hb), such that n H = [y‘ - ( y ) ‘ ] / [ y ( l - P)] (cf. Cohn and Edsall, 1943; Edsall and Gutfreund, 1983, pp. 182-201; Wyman and Gill, 1990). Thus, cooperativity, as determined by the Hill coefficient is a purely statistical characterization of the population distribution, and not a stoichiometric “number of cooperating subunits” within the tetramer. In principle, the nH vs. x function, in combination with higher statistical moments of the binding curve, can be used to estimate the four Adair K,values (cf. Wyman and Gill, 1990). However, such characterizations of the global y vs. x binding curve cannot be used to obtain the unique contributions by individual microstates, for the reasons detailed below in Section IV. The methods by which this classical limitation has been overcome are a major focus of the present chapter. Whereas neither the Adair constants nor Hill’s nHcan yield the specific intramolecular cooperativity of subunits within the Hb tetramer, the site-specificthermodynamic methods reviewed here have accomplished this fundamental goal.

IV.

SITE-SPECIFIC ASPECTS OF OXYGEN

BINDING

A. Microstate Components of the Adair Function Each tetrameric species ijof Fig. 3 may be characterized thermodynamically as the reaction product of i ligands binding onto heme sites of the “deoxy” species 01 in the particular configuration ij. The resulting site-spec@ equilibrium constant is defined by k , = [ VHbX ,] / [ “Hb] x’, where [‘’Hb] and x are thermodynamic activities (or ideal concentrations) of the unligated tetramer (species 01) and the unreacted heme site ligand, respectively, while [ ‘HbX ,] denotes the concentration of ligation microstate i j ( kol = 1 ) . The fraction of binding sites occupied at each ligand activity x (proportional to partial pressure for gaseous ligands) may be formulated by the law of mass action to yield

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

-

Y=

2 [ k l l + k 1 2 ] X + 2 [ 2 ( k 2 1+ k z ) + k23 f 4{1 + 2[kll + k l s ] + ~ [2(k21 + k 2 2 ) + k23

k241.x’

6[k3 + k3z]XS

207 4k44X4

+ k443X2 + 2[k31 + k 3 2 1 ~ ’ + k41x4} (9)

Equation (9) is a site-specific formulation of the classic Adair function [Eq. ( l ) ] and explicitly accounts for the free energy contributions (AG,,-= -RTln k l l ) of all microstate tetramers to the fractional saturation Y (Ackers et al., 1992; Doyle and Ackers, 1992a; Huang and Ackers, 1995a). Comparison between Eqs. (1) and (9) shows that each Adair constant K, is a weighted sum of contributions from the configurational isomers ij, each having i ligands bound:

[2kii

+ 2k121

K3 = [2k31

2k321

K1

=

K2 = [2k21

K4 =

+ 2k22 + k23 + k241 (10)

[k4,I

The numerical factor g, preceding each k , denotes the number of ways that species ij can be formed by reacting i ligands with the unligated species 01 (Fig. 3). Thus the 10 microstate tetramers contribute to the binding curve according to their statistical weights g g k g x ’ .Table I1 depicts the 16 formal tetramer configurations (col. d) and their relationships to the 10 unique combinations of heme site occupancy (col. c). Also shown are the correspondences between the 16 terms bearing statistical weights and the stoichiometric cooperativity constants K . Since each Adair K, is a weighted sum of the particular “microconstants” k , for forming configurational isomers having i ligands bound, it follows that all combinations of the nine k , values which sum, within the respective brackets of Eq. (lo), to the same four K , values will speca3 a n identical binding curue us. x. In principle, then, an infinite number of sets of the nine microstate constants k , can predict each experimental binding curve [Eq. (9)] since the exact form of the curve is determined solely by the numerical coefficients of successive powers of x. Thus, while numerical fitting of a measured vs. x data set (e.g., by nonlinear regression) can resolve only the four “best fit” K, parameters, such analysis cannot provide unique values of the nine constituent microconstants. This observation is a simple matter of principle that does not depend on the accuracy of experimental data nor on the statistical confidence limits of parameter estimates, etc. (what is not possible in principle cannot be improved in practice). As discussed in Section 111, this limitation must also apply to other functions that depend solely on y, including the Hill coefficient n H ,and other “statistical moments” of the P function (Wyman and Gill (1990), pp. 74-76).

r

r

TABLE I1 Relationships between Cooperativity Constants of Hemoglobin Intermediates

a. Number of sites occupied

(0)

b. Stoichiometric statistical weight

1

c. Microstate species

d. Site configuratior

ij

[Cu'/3'ayP]

01

0000

Site-specific statistical weight I I

e. Gen.

1

f. Experimental consensus

I 1

)

h. Molecular code parameters

g. Quaternary

structure

1

I

11 4('K:)s

6(Tc)s'

(3)

(4)

4(3K:)s3

(4K:)sd

1000 0010

................................................ 12

0100 0001

21

1100 001 1

22

1001 0110

................................................ 23 1010 ................................................ 24

0101

31

1101 011 1

I .........................I ''kc * s "k, * s "k,.

KS KS

s

I

KS

"kc. s

I

KS

]

4KS'

T T T T

}

4KC5

]

4K,',K,s2

]

K$

.................. L ........................... I as!! I 4s'

R

"k, * s2 j qs2 ......................... 24kc * s2 qs2

R R

"kr * s2 "kc * sz

.................1.......

R

................................................ 32

1110 1011

R

41

1 1 1 1

R

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

209

B. Implications fw Allosteric Model Ana2ysi.s Analyses of experimental binding curves (Pvs. x) in terms of allosteric models have often been conducted by reformulating the Adair constants K , as combinations of model parameters (e.g., L, c, and kR of MWC) which portray assumptions of the particular model chosen. Then, model parameter values that are consistent with each experimental binding curve may be estimated by fitting the data (Bvs. x) to the transformed Adair equation. This strategy provides an important means of estimating contributions of the molecular processes within an already-assumed model (e.g., Szabo and Karplus, 1972; Ackers and Johnson, 1981; Gill et al., 1987; Di Cera, 1990) but seldom affords a unique way of discriminating between alternative models such as MWC, KNF, or more detailed extensions thereof (seeJohnson et al., 1984; Lee et al., 1988, for discussion of these issues).Such ambiguity may also result from the aforementioned limitation that data-fitting algorithms are capable only of analyzing a given binding curve to yield coefficients of the four powers of x, i.e., the stoichiometric Adair constants K , or their equivalent. Since the four resolved K , values cannot be used to calculate a unique set of constituent microstate constants k , , neither can they provide unique tests for models whose rules impose microstate-level properties. As an example of the last point, the concerted MWC model (Monod et al., 1965) postulates two alternative quaternary structures (T and R) along with the special rule that all subunits in quaternary structure “T” have the same tertiary conformation (designated t), whereas they have a second tertiary conformation (designated r) in the alternative quaternary form “R.” The changing net affinities at successive binding steps are generated solely through a progressively increasing abundance of the high-affinity (R) species relative to those with the low (T) affinity; i.e., this (“two-state”) model assumes cooperativity properties that vary with the number of bound ligands, irrespective of site configuration. Critical tests of the simplest two-state model for tetrameric hemoglobin would thus require determination of cooperativity properties for all the configurational isomers at each stoichiometric degree of heme site ligation. By contrast, the sequential KNF model postulates that changes in affinity arise during the binding sequence from altered near-neighbor subunit interactions as a result of liganddriven tertiary conformation changes. These divergent mechanisms have long been known to represent O4 binding isotherms with equal accuracy (Koshland et al., 1966), demonstrating that a unique mechanism cannot be established from classical ligand saturation curves alone. It has been proposed (Edelstein, 1971) that a specific bell-shaped relationship between maximal nH values for a series of mutant Hbs and

210

GARY K. ACKERS

their apparent MWC L values provided a rigorous proof of the MWC model vs. the KNF model. While this claim has been challenged on the basis that a wide range of experimental data do not show the purported bell-shaped relationship (Minton, 1971; Bunn and Guidotti, 1972; Imai, 1973), it is also clear that the limited information content of the n H function noted above and in Section V,C would by itself invalidate such proposals. Only partial relief from the ambiguities of stoichiometric-levelresolution may be gained by combining databases that simultaneously reflect additional dimensions of functional behavior such as temperature, pH, [DPG], and [NaCl], or from hemoglobins bearing mutationally altered residues Uohnson et al., 1984; Lee et al., 1988). The realization that a unique evaluation of thermodynamic properties for the partially ligated Hb microstates is not possible from global binding curves has motivated the development of methods that explicitly resolve the microstate contributions (e.g., Yonetani et al., 1974; Imai et al., 1977, 1980; Perrella and Rossi-Bernardi, 1981; Miura and Ho, 1982; Simolo et al., 1985; Smith and Ackers, 1983, 1985; Shibayama et al., 1987, 1995). In principle, such methods permit the researcher to first conduct a model-independent determination of cooperativity parameters at the level of the ligation microstates and subsequently to assess the relationships between heme site ligation, tertiary and quaternary structural transitions, and the responses to heterotropic effectors, temperature, etc. Experimental correlation between the energetic responses and the structural transitions when each microstate species binds an additional ligand onto one of its vacant sites provides information at a level of molecular detail that is comparable to the postulates of traditional allosteric models (Ackers, 1990).The determined microstate contributions may therefore be tested against mechanistic assumptions with greater discrimination than is ever possible at the stoichiometric (Adair) level.

C, Impediments to Microstate Resolution Given the inherent desirability of analyzing HB cooperativity at the microstate level of resolution, why were determinations of the nine sitespecific constants k , [Eq. (lo)] not carried out during the 25 years subsequent to publication of the first Hb crystal structures (i.e., Perutz et al., 1960)? From the standpoint of experimental feasibility the answer to this question is that the following obstacles had to be overcome: ( 1 ) Abundances of the partially ligated intermediates are generally low relative to the end-state species 01 and 41, making them difficult to analyze (e.g., see Fig. 6). (2) Rapid dissociation of heme-bound O2 has

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

21 1

precluded isolating and studying the native H b 0 2 intermediates in pure form. (3) Dissociation of partially ligated H b tetramers into dimers leads to reassembly reactions that form tetramers with different combinations of occupied sites. Next, in Section V, we consider conceptual strategies and experimental methods that have circumvented these barriers and have led to the determination of cooperativity terms for the nine microstates of human hemoglobin. DETERMINATION OF SITE-SPECIFIC COOPERATMTY TERMS V. EXPERIMENTAL

A. Active Site Analogs of Oxygenation To circumvent the obstacles just noted pure samples of the “symmetric” doubly ligated species 23 and 24 have often been prepared and studied using (a) tightly bound oxygenation analogs that mimic the native heme sites (e.g., CO, CN-met, or NO); (b) metal-substituted hemes that mimic the stereochemistry of natural Fez+heme, e.g., replacement by Co2+,Zn2+,MnS+,or Cr3+;o r (c) metal-substituted hemes in combination with non-oxygen ligands (e.g., Co2+/FeCN).Usage of these analog systems has had a logic similar to that of systems which mimic enzymesubstrate complexes. While such analogs are often physiologically unacceptable due to the formation of “dead-end” complexes, inappropriate reaction rates, or deleterious side reactions, their stereochemistry has been exploited powerfully to elucidate both active-site mechanisms and allosteric regulation. The allostei-ic enzyme aspartate transcarbamylase (ATCase) has thus been characterized extensively through binding of the analog PALA (N(phosphonacety1)-L-aspartate) which mimics the native enzymesubstrate complex (cf. Schachman, 1988). For hemoglobin, the structural features of surrogate “oxy” heme sites must mimic those of the Fe2+02site within the native molecule, whereas surrogates of the “deoxy” site must have structural features of the native Fe2+Hb heme, in accord with stereochemical requirements that were delineated by Perutz (1976, 1979, 1990; see also Pemtz et al., 1987). When these requirements are met, the analogcontaining hemoglobins have been observed to assume the respective T or Rquaternary structures. The first three analog systems for which complete microstate free energy distributions were determined [Fe2+/FeS+CN; Fe2+/Mn3+;Co2+/Fe2+C0 (see Ackers, 1990)] had previously been shown to have similar tertiary and quaternary structures to normal Hb and to elicit normal quaternary structural response to heme site ligation (Fermi et al., 1982; Yonetani et al., 1974; Imai et al., 1977; Ikeda-Saito and Verzilli, 1981; Hoffman et

212

GARY K. ACKERS

al., 1975; Moffat et al., 1976). These analog systems were thus used as prototypes for initially resolving the rules of HB cooperativity, even though quantitative differences from native Fez+/Fez+02were expected (Ackers, 1990). While it is reasonable to expect that analogs which conform to normal Hb stereochemistry and execute the overall T + R quaternary response to ligation would also follow rules of the native HbOzsystem at intermediate states of ligation, such analogs generally show quantitative deviations from native behavior (as with enzyme-substrate analogs that exhibit altered K , and kc,, while mimicking the native catalytic mechanism). It has thus been central to the strategy of the present authors’ research program to analyze a range of chemically diverse analogs that were known to execute the T +Rquaternary structural transition upon overall heme site ligation. The molecular code mechanism for Hb oxygenation (Ackers et al., 1992) was thus not formulated under the premise that mechanistically valid O2 analogs would necessarily have functional responses that are quantitatively identical to those of the native system or of each other. By contrast, the following strategy was used: (1) The common characteristics for a range of analogs were determined at the microstate level. (2)A general (consensus) binding function was formulated, incorporating the characteristic functional and structural relationships exhibited by ligation intermediates of the various analog systems. (3) The native H b 0 2 parameters were evaluated by constraining the consensus relationships to conform with Adair constants from direct oxygen binding. It was emphasized in Ackers (1990, p. 380) that “in our choice of the CN-met system for tlie first complete resolution of the intermediate species, we may have serendipitously forced the molecule to reveal, in bold caricature, a state that is usually manifested with more subtlety in other ligands.” These issues, which lie at the very heart of efforts to obtain a site-specificsolution to the mechanism of Hb allostery (and of other complex macromolecular systems), are revisited for more detailed and specific consideration in subsequent sections of this chapter.

B. Linkage Cycle Analysis of the Partial4 Ligated Intermediates Contributions to cooperativity by all eight ligation intermediates have been evaluated extensively using an experimental strategy that takes advantage of the natural dissociation of Hb tetramers into their constituent ap dimers (i.e., a’@ and a2p2,cf. Fig. 1). This strategy, which uses thermodynamic reference cycles (Ackers and Halvorson, 1974; Smith and Ackers, 1985), had been applied previously to the stoichiometric level of HbOz cooperativity, as shown in Fig. 5 (Mills et al., 1976; Mills and Ackers, 1979a,b; Atha et al., 1979; Chu et al., 1984; see also Doyle

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

213

and Ackers, 1992a; Doyle et al., 1997), and was subsequently extended to the microstate level (Smith and Ackers, 1983, 1985). It was first established that the dissociated dimers bind heme site ligands noncooperatively (Mills and Ackers, 1979a; Ackers and Johnson, 1990; Doyle and Ackers, 1992a) with affinities for O2that are essentially identical to those of separated a and p subunits (Chu et al., 1984; Doyle et al., 1997). Thus ligation of the dimeric hemes provides a “built-in” reference reaction for assessing energetic contributions to cooperativity that accompany the 16 tetramer ligation steps of the binding cascade (Fig. 4).Cooperativity arising from ligation-induced tertiary and quaternary structure changes (including the breakage of noncovalent bonds) may thus be reflected in the energetic “penalties” for ligating a specific set of tetrameric sites, compared with the same sites on dissociated dimers. The thermodynamic linkage cycle of Eq. (11) has provided a means of determining the cooperutivity constant, qkc from measured dimer-tetramer assembly equilibrium constants qk2 and 0 1 k 2 , which are combined according to Eq. (12) (experimental techniques by which qk2 parameters of the microstate tetramers have been determined are discussed in Section V,D) :

“k, k,/ ( k a )p ( kp) 9 = ,kp/O1kp= ,kc

(12) In Eq. (11), ’’kcand 0 1 k 2 are the equilibrium constants for assembly of species ij and 01 from their constituent dimers; k, and kp are binding constants for a and p subunits of the dissociated dimers; and p and q are respective numbers of ligated a and /3 subunits within the dimers that serve as the reference reaction for determination of each particular qkk,(Smith and Ackers, 1985;Ackers et al., 1992; Doyle and Ackers, 1992b; Huang and Ackers, 1995b). By path independence of free energy, each ‘JAGcterm obtained by measuring ‘Jk2and O’k2 [i.e., YAG, = -RT ln(~k2/01k2)] is identical to that which would be found if one could directly measure the reaction processes on the right and left of Eq. (12). The strategy of Eq. ( l l ) , whereby measured dimer-tetramer assembly free energies are employed to determine “thermodynamic distances” between the 10 microstate

214

GARY K. ACKERS

tetramers (i.e., each distance being relative to species O l ) , is rigorously exact and is independent of the specific magnitudes of dimer-binding energies regardless of whether the site affinities of dissociated dimers (k,, k,) are equal or whether affinities are different for a and /3 subunits within the tetramers. Such differences are automatically taken into account in the calculation of y k , by Eq. (12). All other methods of calculating free energy distances between the tetrameric microstates from these Ilk2 databases (e.g., Di Cera, 1995) are entirely equivalent as a consequence of the path independence of free energy. 1 . Nondissociating Heme Site Analogs

For nondissociating ligands or analog heme sites (e.g., created by metal substitution or surrogate ligands that are covalently bonded to the heme) a value of ‘AG, determined from dimer-tetramer assembly data represents the molar free energy for replacement of the “deoxy sites” having configuration ij within the tetramer by their (surrogate) “oxy sites” minus the free energy of similar replacement reactions at corresponding sites of the dissociated dimers. The energetic contributions of such “replacement reactions” in thermodynamic cycles like Eq. (11) are conceptually rigorous for evaluation of the microstate cooperativity terms. Even when the replacement reactions per se are not practicable, the correct value of qkk,is still determined by measurements on the assembly reactions of species ij and 01. Each VAGrvalue measures the free energy for i mol of (equivalent) site replacement within tetrameric species 01, which produces the surrogate species ij, in excess of that for similar “replacement” at corresponding sites of the dissociated reference dimers. A striking example of nondissociable ligation analogs is that of ruthenium carbonylporphyrin H b (Ishimori et al., 1989),which has been a model for carbon monoxide ligation even though the “ligand” is nondissociably bonded to the heme site. Although this assembly-linkage approach to determining cooperativity constants ‘’k,for tightly bound, o r nondissociable, O2analogs is thermodynamically rigorous, the resulting values cannot be assumed identical with *jk,terms for the native H b 0 2system. It has therefore been necessary to develop strategies for “translating” the y k r distributions into those of the native H b 0 2 system, that d o not rely on any assumed identity of Yk, values. Strategies that have been successful in achieving this goal are discussed in Section VI.

2. Structural Origtns .f the Thermodynamic Ligation-Assembly Linkages The measured affinity for binding O2 (or another ligand) onto the a or p site of a dissociated dimer (a’p’)is a net resultant of the chemical

THE MOLECULAR CODE OF HEMOGLOBIN WOSTERY

215

bonding energy for O2onto the heme iron, balanced against the unfavorable energy of conformation change which the heme-plus-protein must undergo to accommodate stereochemical requirements of the O2 bonding product (Fig. 2) (cf. Perutz, 1976; Gellin and Karplus, 1977; Perutz et al., 1987). This net free energy of reacting O2at a or p heme sites of the dissociated dimer is found to be -8.3 kcal/mol at a standard set of conditions (Mills et al., 1976; Chu et aL, 1984; Doyle et al., 1997). Whereas the dissociated dimers bind O2noncooperatively with affinities nearly equal to their (monomeric) subunits (Mills and Ackers, 1979b), these affinities are modulated when the dimers are subject to additional structural constraints including the intersubunit H bonds and salt bridges that must be overcome to accommodate bonding at the heme site, as follows:

a. Free energy oftertiary constraint. In an unligated quaternary T tetramer, the alp’ dimer is tightly associated with a second dimer (a2P2) by noncovalent interactions worth -14.3 kcal in free energy (Ip and Ackers, 1977). However, the subunit tertiary structures are not under significant strain from these interface bonds in the absence of ligation (Gellin and Karplus, 1977). Strain is induced when the first heme site is ligated and energy of the protein’s conformational accommodation opposes the Fe-O,, energy. Net free energy of the tetramer’s O2 binding reaction is less favorable than for binding to the dissociated dimers because the ligation-induced conformation change required of the protein now also includes conformational work against the structural constraints imposed by the dimer-dimer interface. Net free energy from the binding reaction would be additionally reduced by positive free energy from breakage of the noncovalent bonds (Perutz, 1970). Conformational work against the interface constraints and/or from bond breakage is reflected in the 3 kcal reduction of net binding energy, i.e., yielding the -5.4 kcal that is observed for the initial O2 bound onto a tetramer vs. the -8.3 kcal/ mol for the same reaction onto a dissociated dimer (Mills et al., 1976). This 3 kcal “penalty” for initial ligation within the T tetramer has been designated by the term “tertiary constraint energy” (LiCata et al., 1993). b. Quaternary transition. When successive ligation steps lead to quaternary T + R transitions, those steps are also accompanied by “penalties” that reflect the net difference between the free energies of breaking the T interface bonds and of forming those of the R interface. c. The cooperativity effect. Increasingly favorable (net) binding free energies at successive steps results from the progressive accumulation of such ligationdriven free energy “penalties.” After a tetramer has been ligated once there may be a penalty of smaller magnitude for the next subunit

216

GARY K. ACKERS

ligated, i.e., on the basis of altered conformational strain, bond breakage, or a combination of both. If the magnitude of the penalty depends on which of the possible steps is taken, the “cooperative energies” will have a “combinatorial” character through the binding cascade (e.g., Fig. 4). The findings reviewed in this chapter have shown that cooperativity in human hemoglobin follows this combinatorial pattern. When cooperativity (positive or negative) occurs in the binding sequence along any pathway of the reaction cascade (as evidenced by altered affinities during progressive ligation), values of qA G, will reflect the ligation-linked contributions from the tertiary and quaternary structural transitions plus any coupling between them. Experimental YAG, values may also reflect energetic contributions from linked reactions of heterotropic effector binding and release, including those known to occur at protein sites remote from the hemes (i.e., for Bohr protons, DPG, NaCl, C 0 2 ,etc.). Solvation energy changes may also be implicit contributors to these processes.

C. Statistical Weights of the Tetramer Binding Function

By incorporating the experimental vkk,terms that are evaluated by Eq. (12) into the site-specificbinding function, Eq. (9), the relationships of Eq. (10) that connect microstate parameters to the Adair constants [also yielding Eq. (S)] may be written

Thus Eq. (9) may be reformulated using statistical weights that occur as respective products of the dimeric site affinities k, or k,, and the tetramericcooperativity terms Ykcto yield the general site-specific isotherm, Eq. (14):

Equation (14) and its equivalent forms (Ackers et al., 1992; Doyle and Ackers, 1992a;Huang and Ackers, 1995a) comprise the essential thermodynamic framework for connecting ligation-linked subunit assembly data

217

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

with the site-specific hemoglobin binding function, Eq. (9). From Eq. (14) it follows that a determination of Yk, terms for all H b 0 2microstates, along with O2 affinities of the dissociated dimers (k,, k,), would completely specify the k , terms. This goal was accomplished in 1992 using a strategy described in Section VI. The relevant formulas may first be simplified by noting that, when k, = k, = kd, as in the case of O2binding to normal human Hb (Mills et al., 1976; Mills and Ackers, 1979a), Eqs. (13) and (14) simplify to relations (15) and (16), respectively:

K, = 2[”k, + 12k,]kd

K2 = [2 ( 21kr+ 22k,) + ” k ,

K3 = 2 [31k, + 32k,] k!

K4 = 41k,k4d

+ “k,]

k% (15)

Equation (16) provides a site-specific breakdown of Eq. (8) into microstate statistical weights for the case of identical a and p affinities of the dimers, while Eq. (14) portrays the more general case. This formulation of the tetrameric Hb binding problem, whereby independently resolved linkage cycles [Eq. (12)] are incorporated into the site-specific binding function to yield Eqs. (14) or (16) (Smith and Ackers, 1985), was a logical extension of the analogous strategy (Ackersand Halvorson, 1974) that had been developed earlier for analysis of Hb oxygenation linkages at the stoichiometric level of resolution (Mills et al., 1976; Johnson et al., 1976; Atha et al., 1979; Chu et al., 1984; Doyle et al., 1997). Correspondence between linkage cycle formulations of the Hbbinding partition function at the stoichiometric, and site-specific levels is summarized by recognizing that the denominators of Eqs. (8) and (16) must be equal so that 4

2 (y) i=O

4

[’K:]k;x’

g,(qkl)

k)xi

= i=O

[ijl

This fundamental relationship [or its more general version, obtained by incorporating Eq. (14) on the right-hand side] could have served as a starting point for the present chapter. However, its most general

218

GARY K. ACKERS

applications, which are considered below in Section VI,have been motivated by the experimental and historical developments presented in the foregoing sections. Table I1 provides a spreadsheet of relationships between the various terms of Eq. (17) that were used to evaluate free energy components of the Hb “molecular code” partition function.

D. Hybridization Techniques and Free Energy Distributions Using stable analogs of hemoglobin’s native oxygenated and deoxygenated heme sites, experimentalists have long been able to create and study four of the Hb microstate species in pure form (i.e., species 01, 23,24, and 41). Taking advantage of their dissociation into dimeric halftetramers (cf. Fig. la) that subsequently undergo assembly into hybrid combinations (Fig. 8) researchers have successfully analyzed thermodynamic properties of the remaining six tetrameric species (Fig. 8). The

83 2m

H 01

w

23

AB

AA

z /z

83

2E

11

p!

24

12

22

41

21

32

31

01

23

24

BB

/

2

41

PARENT BB FIG.8. Hybridization scheme for H b microstates via dimer-tetramer dissociation and reassembly. By use of nonlabile ligands or ligand analogs, the “parent” species, AA or BB, are each prepared in pure form since their dissociation and reassembly does not rearrange the combinations of site occupancy. Six microstate tetramers are formed by hybridization of dissociated parent tetramers, as illustrated for the species 21 tetramer (upper right).

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219

combined usage (and further development) of four experimental techniques proved essential to these studies: (1) analytical gel permeation chromatography (Ackers, 1970, 1975); (2) stopped-flow kinetics (Nagel and Gibson, 1972; Kellett and Gutfreund, 1970; Ip et al., 1976; Ip and Ackers, 1977); (3) haptoglobin kinetics (Ip et al., 1976; Ip and Ackers, 1977;Turner et aL, 1992);and (4) low-temperatureelectrophoresis methods pioneered by Michele Perrella (see Perrella et al., 1981,1983,1990a; also LiCata et aL, 1990). In various combinations, these techniques have provided a versatile repertoire for determining dimer-tetramer assembly free energies of the asymmetric hybrid species 11, 12, 21, 31, and 32 in the presence of their respective “parent species,” with which they are equilibrated. An example of the resolution that is routinely achieved for quantitation of microstate species in hybrid equilibria by the cryogenic isoelectric focusing (cryo-IEF) method is shown in Fig. 9. Initial data on microstate tetramers of Fe‘+/FeCN (Smith and Ackers, 1985),Fe*+/Mn(III) (Smith et al., 198’7) and Co2+/FeC0 (Speros et al.,

.03

.02 .01

0

.02

.01

0

Distance FIG.9. Cryo-IEFof hybrid mixtures forming CN-met species 21 (panel a) and 22 (panel b) at pH 7.4, 21.5”C (cf. Ackers et al., 1997). Species 21 was formed by mixing deoxyHbS (species 01) with CN-met HbA (species 41) and the mixture was incubated for 119 h. Species 22 was formed by mixing CN-met HbA species 23 with CN-met species 24 (HbS), and the mixture was incubated for 46 h.

220

GARY K. ACKERS

1991) had uniformly indicated that the cooperativity mechanism was “combinatorial,” i.e., dependent on specific pathways through the reaction cascade (Fig. 4), and that species 21 made a different free energy contribution from that of species 23 or 24, as shown in Table I. While this finding was inconsistent with rules of the concerted “two-state’’ model (cf. Ackers, 1990), the discovery that CN-met species 22 had characteristics like species 23 and 24 (Perrella et aL, 1990b) helped greatly to clarify the analog databases that were systematically under study. A series of studies on the effects of pH, mutational modification, and other structure-sensitive probes on the CN-met intermediates (Daugherty et al., 1991) then provided a basis for interpreting the thermodynamic information in terms of quaternary switchpoints (Daugherty et al., 1991) that led to the “symmetry rule” (or molecular code) mechanism (Ackers et al., 1992; Doyle and Ackers, 1992b; LiCata et al., 1993). Resolved Microstate Distributions. Table I summarizes the distributions of cooperative free energies YAG, = RTln gk, for six Hb ligation systems that were characterized under comparable solution conditions. Columns 2-5 list values for the nine ligation microstates of the initial three analog systems that had yielded reliable data by 1991: an initially incorrect value of the CN-met species 22 assembly free energy that was evaluated from kinetic data (Smith and Ackers, 1985) was detected by cryogenic electrophoresis (Perrella et al., 1990a) and traced (by M. A. Shea) to misassignment of one of the kinetic phases. This corrected data set for the nine CN-met Hb species (col. 2) and corresponding data at pH 8.8 (col. 3), plus values on the other two analog systems (cols. 4 and 5 ) were used in making thermodynamic inferences of the 1992 analysis (Ackers et al., 1992). Column 1 lists cooperative free energies at the stoichiometric O2 binding levels for native Hb, ‘AG, = -RT ln[K,/ ( A d ) ‘I, as calculated from direct 0, binding data (Chu et al., 1984; Doyle and Ackers, 1992a; Doyle et al., 1997); K, are tetramer Adair constants, and kd is the O:, binding constant for sites of the dissociated (noncooperative) dimers. Thermodynamic relationships between stoichiometric cooperativity constants F,and their constituent microstate terms Ykk,are listed in Table 11. Based on Eqs. (8) and (14)-(17), these relations provided modelindependent constraints for reconciling microstate parameters with the stoichiometric ones obtained by analysis of binding curves measured at a sequence of total Hb concentrations (Fig. 5 ) , in combination with independent dimer-tetramer assembly measurements on species 01 and 41.

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221

VI. How THE MOLECULAR CODEWASDECIPHERED A.

Cooperative Free Energies of HbOpAnalogs

During 1989-1992, extensive efforts were aimed at applying the conceptual framework discussed above to the emerging microstate databases in order to determine whether a common site-specific partition function could accommodate both a consensus of OAGc distributions -from the HbOe analogs and the stoichiometric cooperativity terms iAGcof native Hb04. Based on the previously established structural and functional properties of the three analogs, it was assumed that they would each manifest essential rules of the native system. It was not assumed, however, that they would exhibit cooperativity in a quantitatively identical fashion to that of native Hb02,nor with respect to each other (see Ackers, 1990). These expectations were consistent with the earlier findings that O p binding to cobalt-substituted Hb (Co2+/Fe2+02) exhibits significantly altered affinity and cooperativity compared to native HbOz (Yonetani et al., 1974; Imai, 1990; Doyle et al., 1991), but nevertheless exhibited a T + R quaternary transition and Bohr effect on oxygenation (Imai et al., 1977; Ikeda-Saito and Yonetani, 1980; Ikeda-Saito and Verzilli, 1981). With regard to the question of whether CN-met ligation of Hb is an appropriate analog for studying mechanisms of the native allosteric response, it was noted by Unzai et al. (1996) that (1) the crystal structure of CN-met Hb closely resembles that of oxy-HbA (Deatherage et al., 1976); (2) the cyanide-bound ferric heme is low spin, like that of normal oxygenated subunits (Scheidt and Reed, 1981); (3) CN-met hybrid species 23 and 24 had shown nuclear magnetic resonance (NMR) spectra that were similar to the spectrum of fully ligated species 41; and (4) the ferrous subunits of CN-met species 23 and 24 had shown rapid ligand-binding kinetics and high affinity for oxygen. Unzai et al. (1996) pointed out, however, that certain techniques of direct oxygenation might not be applied to CN-met hybrid systems with reliability because of (a) autoxidation of the ferrous subunits, coupled with (b) unwanted reduction of met hemes that could result from efforts to control autoxidation by reducing agents or enzyme reduction systems. These cautions regarding direct O4 binding studies on partially ligated CNmet hemoglobins are in accord with the findings of Doyle and Ackers b( 1992a). However, these problems were eliminated in the Doyle and Ackers study by (a) appropriate usage of KCN, which suppresses loss of CN3- from the ligated heme sites that otherwise leads to autoxidation and electron exchange. This problem was solved by the cryogenic electro-

222

GARY K. ACKERS

phoresis techniques developed by Perrella and colleagues (Perrella and Rossi-Bernardi, 1981, 1994; Perrella et al., 1990b, 1994, 1998), which have also been used extensively and developed further in the present author’s laboratory (e.g., LiCata et al., 1990; Speros et al., 1991; Daugherty et al., 1991; Doyle and Ackers, 1992b; Huang et al., 1997). The clyogenic quenching procedure, which stabilizes partially ligated CN-met tetramers against subunit dissociation, also affords a clear-cut way to determine the extent of “valency exchange” that may have occurred during sample incubation (see Ackers et al., 1997). It was recently claimed (Shibayama et al., 1997) that in the hybridization experiments performed in the laboratories of Perrella and of Ackers to determine assembly free energy of the species 21 tetramer, cyanide release from the ligated heme sites might have allowed extensive electron exchange among heme sites and thus compromised the equilibrium free energies reported from the cryogenic determinations (i.e., Daugherty et al., 1991). However, it was recently reaffirmed and experimentally demonstrated (Ackers et al., 1997) that neither cyanide loss nor electron exchange occurs with the protocols that have been used for studies by the laboratories of Perrella (e.g., Perrella et al., 1983, 1990b) or ofAckers (LiCata et al., 1990; Daugherty et al., 1991) and that differ critically from the experiment presented by Shibayama et al. (1997) in support of their claim. These authors also suggested that the molecular code mechanism (Ackers et al., 1992) was based solely on the properties of a single analog (i.e., CN-met Hb) and that, since this analog does not perfectly mimic the cooperativity of HbOs, it was concluded that the molecular code mechanism is incorrect for the native HbOs system. By contrast, the sitespecific binding function that was deduced coequally from data on the three diverse analogs of Table I, cols. 2-5, used only their common qualitative behavior and not their magnitudes per se. Their consensus function was then used to solve the stoichiometric HbO:, values F, for their component microstate terms gk,. While no single analog should be trusted to portray all aspects of the native system, the “free energy” of -10.1 kcal that was suggested by these authors (Shibayama Pt al., 1997) would have led to the same result that was found (Table I, col. 6) for the native HbOB system by use of Eq. (19), described below in Section VI,A,2 (see Ackers et al., 199’7, for additional discussion of these issues). 1. Characteristics of the Analog Microstate Distributions Based on the conceptual framework of Eqs. (9)- (17) and the expectation that cooperative free energies VAG, would reflect the heme sitedriven tertiary and quaternary structural transitions plus any coupling

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223

between them (see Section V,B), it was assumed (Ackers et al., 1992) that oxygenation analogswhich conform to the native system’smolecular rules would exhibit qualitatively similar distributions among their nine YAG
Combinatorial Partitioning among Doubly Ligated Tetraws. The YAGC value of species 21 was always significantly smaller than those of species 22, 23, and 24, which were equal to one another. Contributions to cooperativity by the doubly ligated tetramers were thus dependent on the configuration of occupied heme sites and not solely the number of ligands bound. Moreover, the specific combinatorial splitting among these microstate free energies was robust with respect to (1)metal substitution at the unligated heme sites (Co2+for Fe2+);(2) use of different surrogates for the oxygenated sites (i.e., with hemes containing Fe2+C0, Fe3+CN,or Mn3+);and (3) a 25-fold concentration change of the heterotropic effector, H+ (i.e., Table I, col. 3 vs. col. 2). From the striking differences between VAG, terms of species 21 and 22 (each containing one ligated a subunit and one ligated /3 subunit) and the finding that species 23 and 24 behaved identically with species 22, it was inferred that contributions to cooperativity were controlled at vs. a‘p‘): whenever the level of the symmetry-relatedhalf-tetramers (alp’ two ligated subunits occupied opposing half-molecules, YA G, had one value (species 22, 23, 24), whereas placement of both ligands on the same half-tetramer (species 21) generated a distinctly different YAG, response. This combinatorial rule was evident in all three analog systems, suggesting that the distinct YAG, responses arise from separate kinds of ligationdriven structure change. Contrasting sharply with these findings, a strong prediction of the classical MWC model was that configurational isomers of the doubly ligated tetramer must have identical VAG, values (Ackers and Johnson, 1981; Ackers, 1990). This essential feature of the

224

GARY K. ACKERS

concerted model was thus inconsistent with cooperativity rules of the first three H b 0 2 analogs ever analyzed at this level of molecular detail.

Triply Ligated Microstates. The 31AG,and 'lAG, terms were equal in all three analog systems and had identical values with three of the doubly ligated isomers (i.e., species 22, 23, and 24), as shown in Table I. Singly Ligated Microstates. Two analog systems (i.e., Fe2'/FeS+CN and Fe3+/Mn3+)showed equal "AG, and '"G, terms, whereas the Co'+/ Fe2+C0species were just barely consistent with this equality (to within their larger relative error). Although equality of SAG, terms for the two singly ligated tetramers had the weakest supporting database in 1992, subsequent work has found it to be correct for Fe2+/FeC0 (Huang and Ackers, 1996) and also for the Fe2+/Fe02system (Huang et nl., 1996b), as described in Section VI,F. Quaternaly Enhancement. An ordered relationship between the third and fourth stoichiometric cooperativity terms (%, > %,) has been extensively documented for the native H b 0 2 system as described in Section II1,B. Quaternary enhancement was also clearly exhibited by microstate species of the Co2+/FeC0system (Table I, col. 5 ) but was not evident in data of the other two analogs. However, since a quaternary enhancement effect had been observed for oxygen binding to cobaltous hemoglobin C02+/Co'+O (Doyle et al., 1991) and for O2 binding onto the vacant sites of the triply ligated CN-met species 31 and 32 (Doyle and Ackers, 1992b),it was concluded that this phenomenon would have to be accommodated by consensus rules that reconciled microstate linkage data of the various systems. 2. The Consensus Partition Function Consensus relationships exhibited by microstate cooperativity terms of the three analog systems are summarized in Table 11, col. f. For singly ligated species a consensus parameter, equivalently representing Ilk, and IPk,, is denoted by K ; for triply ligated species 31krand 32kf, by q; among doubly ligated isomers the 21kfterms are each designated by 7,while the 22kc,23kc,and 24kcterms are denoted by q in recognition of their equality with 31k,and 32k,;finally, the consensus term 41kfof fully ligated tetramer was designated r. Thus the common characteristics of experimental distributions that were revealed by the microstate analog data of Table I are summarized by adding the terms of Table 11, col. f, to obtain the consensus partition function 2':

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

225

where s’ = k d ( x ’ ) , i.e., the product of heme site analog activity ( x ’ ) and the dimer reaction constant: k ; = exp[-AG;/RT], where AG; is the molar free energy of “replacing” the dimer’s “deoxy” sites (native or surrogate) with corresponding “oxy” sites (discussed in Section V,B, 1; when the qkc terms, corresponding to K, T, q, and r, are evaluated from the Eq. (12) linkage cycles, ( x ’ ) is effectively at the standard state, 1 mol/liter). Equation (18),which was written in terms of consensus tetramer cooperativity parameters K , T, q, and r, and dimeric statistical weights (s’) also implied specific constraints on the stoichiometric cooperativity terms (Table 11, col. b). For any particular ligand, or analog, the terms of the left- and right-hand sides of Eq. (17) must be equal at each stoichiometric level i so that the ( s ’ ) terms cancel, yielding 1,

-

‘K: =

K;

*K: =-&r+-$q;

-

3K: = q;

-

4K’ = r

(19)

and hence T = 3(%) - 2(%). These formulas provided a means of calculating the microstate parameters K, T, q, and of the native HbOp system from the stoichiometric O2cooperativity ‘K: ( i = 1 , 2 , 3 , 4 ) under the two premises that (a) cooperativity terms were expected to reflect the liganddriven tertiary and quaternary structural transitions by following the same molecular rules with the analogs as with native HbOz, and that (b) the magnitudes of cooperativity terms, however, were expected to be different for the native H b 0 2 microstates and the analogs. While the significance of premise (a) to this analysis is self-evident, premise (b) also played a crucial role in two ways: (1) it permitted the form of the consensus partition function [Eq. (18)] to be identified uniquely by using only the common free energy “change points” that were correlated with site-specific ligation events of the binding cascade (Fig. 4; Table I ) , and (2) it permitted the use of formulas (19) to evaluate site-specific contributions by the H b 0 2 microstate tetramers soZeZy from independently of the magnitudes of analog the H b 0 2 parameters free energies. It is important that the only information used from the three analog databases in formulating Eq. (18) was the strong consensus of configuration-specific change-points exhibited by their VAG, distributions. There was thus no usage of VAG, magnitudes from the analogs per se to estimate microstate “AG,values of the HbO, system. This strategy was essential because (1) the different analogs exhibited nonidentical

r,

226

GARY K. ACKERS

ranges for their JJAGG, values (Table I ) as well as differences in their relative energetic spacings, and (2) these data provided no objective values from any one of the analogs (nor for basis for selecting the JJAGG, averaging among the three) to obtain parameters that could be assumed correct for the (as yet unknown) H b 0 2 microstate distribution. Additional to these empirical considerations was an important issue related to Eq. (17). This equation specifies quantitative reconciliation between stoichiometric cooperativity terms and their constituent microstate components ‘Jkconly when the ligand x or ligand analog x f is the same for both the stoichiometric (left) and microstate (right) sides. In that case the dimeric statistical weights ( k d x ) ’cancel for each stoichiometry i, leading to the set of equations:

which is equivalent to the independent relations (15). However, when the left and right sides of Eq. (17) represent different ligands (e.g., if x represents O2 on the left-hand side while x f in the right-hand terms denotes an O2 analog), the equalities indicated in Eq. (20) would not be expected to hold with exactness even though the analog may follow the same “molecular rules” of liganddriven tertiary and quaternary switching as apply to native Hb02.Perturbations in free energies (relative to Hb02)would generally be expected, even among microstate analogs that conform to the statisticalweights of Eq. (18) because (1)at standardstate conditions the kdx’ terms may differ energetically by an amount that reflects the free energy of O2 replacement by the analog on the dimer sites, or (2) the ykc terms for an O2 analog [on the right-hand of Eq. (20)] are expected to differ somewhat from their Orbinding counterparts that lie within the ‘ K : terms, even when tertiary and quaternary transitions occur at the same change-points of the binding cascade. For reasons 1 and 2 the potential energetic perturbations by the three heme site analogs to the magnitudes of cooperativity (compared with the native system) could not be assumed sufficiently small for the analog qAGc values to be assumed identical with those of H b 0 2 microstates. Therefore no estimates were made for the yAGCterms of native H b 0 2 on the basis of magnitudes from analog systems. An entirely different approach that was used to avoid this problem (Ackers et al., 1992) is described in Section VI,C. First, however, we consider critical tests of Eq. (18) using microstate tetramers having mixed combinations of O2 and CN-met ligation.

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227

B. Oxygen-Binding Tests of the Consensus Function A strong prediction from premises (a) and (b), following Eq. (19) above (also see Section VI,C), which provided the basis for Eq. (18), was that O2binding onto the vacant sites of microstate tetramers bearing mixed types of ligands should exhibit the same free energy changepoints as the homogeneous ligation systems of Table I. Thus to investigate the range of applicability for the specific GAGcchange-points prescribed by Eq. (18), experiments were conducted to measure free energies of binding O2onto vacant heme sites of the eight partially ligated CN-met tetramers (Doyle and Ackers, 1992b). These determinations, which were obtained by dimer to tetramer assembly linkage measurements in combination with direct binding, showed precisely the same combinatorial distribution for the “remainder binding energies” as predicted by Eq. (18). Especially striking were the results for configurational isomers of the doubly ligated tetramers (shown in Fig. 10). Here the four configurationally distinct linkage schemes connect the respective dimer-tetramer assembly free energies (horizontal) to those of the “remainder oxygen binding’’ steps (vertical) of dimeric (left) and tetrameric (right) species. For CN-met species 21 and 22, oxygenation of the vacant a and /3 sites showed dramatically different energetic responses, i.e., high cooperativity for the remaining species 21 a and /3 sites but no cooperativity for those of species 22. The “remainder O2 steps” for CN-met species 23 and 24 also had negligible cooperativity compared with species 21. These data, and those for O2binding onto the singly and triply CN-met tetramers (Doyle and Ackers, 1992b), showed exact correspondence with the YAG? change-points prescribed by Eq. (18). The “remainder affinities” for CN-met species 11 and 12 were intermediate between the overall tetrameric and dimeric values, whereas triply ligated CN-met tetramers exhibited O2 affinities considerably higher than those of the dissociated dimer’s a and p subunits, i.e., exhibiting a quaternaq enhancement effect. Noncooperativity of sites within the dissociated dimer was inferred by the observation that the O2 binding free energy for the (Y subunit within a dimer having a CN-met /3 subunit, plus that for O2 binding to the /3 subunit of an a-CN-met dimer, summed to the free energy for O2 binding at both dimeric sites (Doyle and Ackers, 1992b). It was clear from these results that the binding of ligands elicited thermodynamic responses according to the same combinatorial rules, whether the ligand was O2or CN-met and that their common “molecular choreography” was described by Eq. (18).

228

GARY K ACKERS

8.8

N a

-8.4

-8.4

22

21

1

1-4.7

-8.1

1

1-8.4

1-8.7

-8.1

1

1

24

23

-8.2

1

-8.2

1

-8.2

5

-8.0

-8.1

1

-8.5

-8.1

i

1-7.9

5

-8.5

FIG.10. Thermodynamic linkages between dimer-tetramer assembly and 0, binding to the doubly ligated cyanomet species 21,22,23, and 24. The ligand cyanomet is denoted

by CN. Orientation of (Y and subunits within the dimer and tetramer is indicated in the deoxy species (Doyle and Ackers, 1992a).

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229

C. Prediction of Site-Specz$c Binding Parameters for Native Hb02

The discovery that, while the value of a given 9AGcterm varied substantially among the three analog systems, the terms within each system satisfied Eq. (18) (Ackers et al., 1992) had provided an objective basis for calculating the y k c values of singly, doubly,andtriply o a e n a t e d microstates of native H b 0 2 from the measured ’KO2Kc,and ’K, values, under the premise that the H b 0 2 intermediates would also satisfy relations (19). The cooperative free energies of doubly ligated microstates for native HbOp were thus predicted to distribute “combinatorially” into the two specific levels listed in Table I, col. 6 (Ackers et al., 1992). From this analysis the cooperative free energy of species 21 in the H b 0 2 system was inferred (Ackers et al., 1992) to be -2 kcal more positive than for singly ligated species 11 and 12. This difference corresponded to a 6fold higher binding constant for the second step leading to formation of species 21. In the Co2+/FeC0system this intradimer cooperativity was determined to be only 2.5-fold,whereas a 170-fold enhancement was exhibited by the Fe‘+/FeCN system and also by the Fe/Mn(III) system. Contrary to this published record (Ackers et al., 1992), it has been suggested (Edelstein, 1996; Bettati et al., 1996; Shibayama et al., 1997; Henry et al., 1997) that Ackers et al. (1992) had proposed intradimer cooperativity for native HbO, of l70-fold, rather than the lower value actually estimated. Each of the reports cited above has promoted this incorrect claim as an argument that the molecular code mechanism must be invalid because it would be incapable of accommodating the actual cooperativity of native Hb02.However, the free energies predicted for HbO:, intermediates including species 21 (Ackers et al., 1992) were never calculated from the analog magnitudes but solely from the four stoichiometric HbOpconstants by Eqs. 18-19, yielding the values of Table I, col. 6. Consequently, all cooperativity properties of the calculated H b 0 2 microstate distribution (Table I, col. 6) were constrained from the outset to be identical with those of the native Ozbinding data (i.e., Table I, col. l ) ,with Hill coefficient nH = 3.2. In addition to the strategy discussed in this section, which determines cooperativity terms of the native HbOBsystem by using the consensus relations to resolve the stoichiometric HbOz terms into their eAG, parameters, a second strategy that yielded the same partition function is discussed in Section VI,F, below. It was recently proposed (Edelstein, 1996) that the validity and results of this approach to analysis of hemoglobin allosteric behavior should be dismissed on the basis of claims that (1)cooperativity properties of the O2intermediates were allegedly deduced from only a single oxygenation

(z),

230

GARY K. ACKERS

analog (i.e., CN-met Hb), which putatively does not follow the same allosteric mechanism as the native O2system, and that (2) the proposed molecular code (Ackers et al., 1992) is incapable of accommodating the high degree of cooperativity manifested by the native oxygen binding curve. These claims were argued from calculations using a very different model having molecular species and assumed rules that were not proposed by Ackers et al. (1992) and with assumed O2affinities for the intermediates that do not correspond to the measured O2values. Eaton and associates have proposed that their transient O2kinetic data (see Henry et al., 1997) might not accommodate rate distributions compatible with free energies of the molecular code mechanism (i.e., the Table I, col. 6, #kc terms for species 21 vs. those of the other doubly oxygenated tetramers). However, these authors did not show that their estimated “85state” rate parameters corresponded in any unique way to the 16 specific chemical reactions of the H b 0 2binding cascade (Fig. 4). Moreover, their discussion suggested that a 170-fold enhanced relative abundance (appropriate to the CN-met system) was being tested, rather than the &fold difference that would be appropriate for the H b 0 2 species 21 tetramer. (The species 21 tetramer would be favored by 3 6 fold relative to species 22, 23, or 24 on a molar basis from the qAG, values of Table I, col. 6.) When the total population of all doubly ligated microstates is only a few percent (i.e., in the presence of other partially ligated tetramers), a capability to unequivocally assign amplitude or rate differences of only severalfold could be of great benefit to the elucidation of HbO, microstate properties. When kinetic studies are carried out with slowly equilibrating hybrid systems, an appropriately long preequilibration may be necessary to obtain either the relevant amplitude or rate information. Marden et al. (1996) conducted CO-rebinding experiments with mixtures of HbCO and HbCN that were incubated for short periods relative to the long times previously shown necessary for achieving hybrid equilibrium of CN-met systems (LiCata et al., 1990; Huang and Ackers, 1995b). Flash photolysis of the samples thus created only a small fraction of species 21 CN-met hybrid, so that measured rebinding was mostly to heme sites which were not part of a CN-met containing tetramer, as acknowledged by Marden and colleagues.

Cooperativity Within the Dirneric Half-Tetrama. The unequivocal splitting among YAGLlevels observed for doubly ligated species of the explicitly resolved analogs implied that successive ligation steps within the dimeric half-tetramer (a’@’) were cooperative, i.e., affinity for the second binding step is enhanced by -RT ln(k21/kll)compared with the first ligation.

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231

The second step was predicted to occur with a &fold higher affinity than the first binding step (Ackers et aL, 1992; Doyle and Ackers, 1992b). This prediction, and its independent verification (Table I, col. 9) are incompatible with the two-state concerted model, which requires cooperativity to depend solely on the number of bound O2 irrespective of site configuration (Ackers and Johnson, 1981; Ackers, 1990). Similar conclusions have been reached by Perrella (Perrella et al., 1998) from studies on the Fe2++/Fe2+C0 intermediates. An argument against such cooperativity has been proposed by Eaton and associates based on O2binding experiments on crystals of human Hb (see Rivetti et aL, 1993; Bettati et aL, 1996). The crystals employed in these studies were found incapable of executing the normal T + R transition even after complete O2saturation, had no binding cooperativity nor a Bohr effect, and bound O2 with abnormally low affinity. In spite of these severely compromised functional properties, the data were proposed as proof that quaternary T tetramers are also incapable of O2 binding cooperativity under solution conditions. On the basis of these data, Eaton has suggested that the molecular code mechanism should not be considered relevant to normal human Hb, since it has revealed that cooperativity does accompany ligation of the quaternary T tetramers in solution. The argument presumes: (1) that crystal lattice constraints, which block the normal Orinduced tertiary and quaternary structure changes, have nevertheless allowed Hb tetramers to be identical with the unligated T molecules in solution; (2) that O2binding data on such a sample would follow rules of the quaternary T tetramers in solution; and (3) that the observation of crystalline samples binding O2noncoop eratively thus proves that quaternary T tetramers in solution are also incapable of cooperativity.This argument assumes that cooperative interactions among Hb subunits would not have been suppressed by the crystal lattice and would thus have produced cooperative crystal isotherms. However, the tertiary structure changes required to mediate “tertiary cooperativity” (in the absence of a quaternary change) may well have been suppressed by the crystal lattice. The conjecture that if cooperativity without quaternary switching occurs in solution it would also be manifested under the additional crystalline constraints is thus not validated by these careful oxygenation experiments. The same difficulties of interpretation apply to recent data on O2binding by Hb tetramers that have been tightly confined within silica gels (Bettati and Mozzarelli, 199’7). D. Structure-Sensitive Probes and Heterotropic Responses

Using CN-met Hb as a representative system, experimentalists have employed a variety of probes to assess quaternary structures of the ligation

232

GARY K. ACKERS

microstates, and also to evaluate their specific ligation-linked responses to the presence of heterotropic effectors and to changes of temperature, providing the enthalpic and entropic components of their cooperative free energies. 1. Mutational Perturbations of the Dim-Dimer Intdace Free energy perturbations by single-site mutations at the dimer-dimer interface were analyzed for tetramers in three of the ligation microstates, i.e., species 01,21, and 41 (LiCata et al., 1993). Hybridization techniques illustrated by Fig. 11 were employed to determine the assembly free energies for each of the three microstate species bearing a single-residue modification per tetramer. The modification sites were located at 13 backbone positions shown in Fig. 12. Resulting perturbations to the dimer-tetramer assembly free energy SAG, (i.e., relative to wild-type HbA) are plotted in Fig. 13. Strikingly, the free energy perturbations to dimer-tetramer assembly caused by the altered residues were found to be essentially identical for ligation species 01 and 21 of each mutant hemoglobin but were substantially different for the fully ligated species 41 molecules. These findings implied that the tetramers had retained their “deoxy” dimer-dimer orientation (i.e., the T interface) after ligation of two subunits within the same alp1half-tetramer (Fig. 14).

i

I

PARENT BB FIG.11. Hybridization scheme for tetramers bearing a single-site modification with ligation states 01, 21, and 41. Each was created and studied as a hybrid betweb parent tetramers shown. Dimer-tetramer assembly free energies of parent species were determined independently on pure samples. These values were combined with data from the crydEF hybrid experiments to yield the free energy of assembly for the hybrid microstate (LiCata et al., 1993).

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233

FIG.12. The Hb dimer-dimer interface depicting noncovalent interactions in deoxy Hb (heavy lines) and COHb (dashed lines). Residue sites in gray are those studied in LiCata el al. (1993). Scheme adapted from Dickerson and Geis (1983).

Inferences of Tertialy Constraint and DimerAutonomy. In addition to identification of the T quaternary structure for the asymmetric doubly ligated species 21 tetramer, these studies also revealed that the ligation-induced tertiary constraint response (3 kcal) was maintained in all of the asymmetric doubly ligated mutant tetramers, as seen by inspection of Fig. 15. The common energetic features that have been deduced from the data of Figs. 13 and 15 are summarized by diagram (I). Processes a and c denote ligation of the dimeric half-molecule to form tetrameric species 21 in the native molecule (A) and in the structurally modified molecule (m). In processes b and d the quantities ''AGE, and 21AG:;t denote the respective free energies for introducing a

234

GARY K ACKERS

Mutant Hybrid Hemoglobin FIG.13. Perturbations to the assembly free energies for Hb tetramers bearing a singleresidue modification in each of three ligation microstates. Mutant and chemically modified Hbs are denoted on the abscissa. It is seen that the free energy perturbations for species 01 and 21 are nearly identical over the entire spatial distribution of sites within the dimer-dimer interface (LiCata et al., 1993).

deoxy

doubly ligated lnterrnedlate

fully ligated

FIG.14. Schematic diagram showing the two dimeric halves of the Hb tetramer: black dots and white circles represent interacting residues in the dimer-dimer interface. Ligation of subunits (denoted with X ) on only one dirner does not result in displacement of residues in the interface, as occurs when ligands are bound to both dimers (LiCata et al., 1993).

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235

single-residue modification into the normal species 01 tetramer or into the half-ligated species 21 molecule. Cooperative free energies for ligating species 01 to form species 21 are denoted by 21AG$ and 21AG': in the normal and structurally modified tetramers, respectively. The measured assembly free energies for the four tetrameric species of this diagram yielded common relationships among free energies of processes a through d, for each of the Hbs, which are summarized in the next two subsections. (a) Independence between ligation of one dimer and mutation of the other. The experimental findings of Figs. 13 and 14 are summarized by the following pair of equivalent relationships, which apply to each of the modified Hbs investigated:

While either of these equalities implies the other (by path independence of free energies in diagram I, above), each relationship provides a separate physical meaning. The left-hand relation of Eq. (21) specifies that the free energy penalty 21 AGc which accompanies ligation of the dimeric half-molecule is not influenced by structurally modifylng a residue site on the adjacent (unligated) dimer even when the site is directly at the interface and its alteration may destabilize the dimer-dimer complex by several kcal. The right-hand relation of Eq. (21) states that the free energy of modification for each residue (including those at the dfi2interface) is not influenced by ligation of the adjacent dimer. This finding is remark-

GARY K ACKERS

Mutant Hybrid Hemoglobin FIG.15. Cooperative free energies of fully ligated (solid bars) and half-ligated (striped bars) Hb mutant hybrids. The free energy of half-ligating the tetramer to form species 21 was found to be essentially independent of structural modifications on the opposite side of the dimer-dimer interface from the ligands. This is found to be the case even though interdimer salt bridges and H bonds have been altered by the residue modifications (from LiCata et al., 1993).

able in view of the fact that association of the dimers to form the dimerdimer interface is prerequisite for the 3 kcal “ligation penalty.” The data thus showed that in the half-ligated species 21 tetramer the processes of heme site ligation on one dimer and modijication of a single residue on the adjacent dimer are energetically independent. Ligation of the two remaining heme sites, however, significantly alters the profile of the collective thermodynamic response grid, reflecting the altered structural environment within the dimer-dimer interface that accompanies the T to R switchover (Fig. 14). (b) Structural wigins Of cooperativefree energy in quaternaly T. Since 2’AG, is the free energy of ligation-induced structure change for the tetramer (relative to its dissociated dimers), this quantity must reflect all contributions from the breaking (or making) of noncovalent bonds at the dimerdimer interface as well as from conformational change that is “internal”

THE MOLECULAR CODE OF HEMOGLOBIN W O S T E R Y

237

to the ligated subunits, i.e., not involved in breakinga’p‘ interface bonds. The observed independence between the energetics of local residue modification and ligation of heme sites on the adjacent dimer bears directly on this issue: If ligation of a dimer within the native quaternary T tetramer generates broken bonds across the dimer-dimer interface, for which the energy of breakage is ’’AG,, then the absence of those bonds which were eliminated by mutation would be reflected in the respective mutant YAG, values measured. It was concluded that dimer ligation within the T tetramer did not break a small subset of the noncovalent bonds among the 13 interface sites, although they could all have been weakened by an average of 0.3 kcal per site to account for the total 3 kcal observed per tetramer (LiCata et aL, 1993). The 3 kcal of 21AGcwas thus inferred to reflect the free energy of tertiary conformation change that accompanies subunit ligation within the T tetramer (i.e., in excess of tertiary changes that accompany ligation of the dissociated dimers). Likely origins of *lAG, may include (1) conformational strain associated with the allosteric core (Gellin and Karplus, 1977; Gellin et aL, 1983), which is induced by ligation at heme sites on the dimeric half-molecule, and (2) alteration of noncovalent bonds within the tertiary structure of the ligated dimer. These studies ensued from an especially fmitful implementation of strategies that were proposed earlier (Ackers and Smith, 1985, 1986) for using thermodynamic linkage cycles with site-specific combinations of mutational and functional perturbations to “decipher the molecular codes” of macromolecular systems. The results in Figs. 13 and 14were the first instance where Hb ligation intermediates bearing a single-residue modification per tetramer have been characterized. The remarkable “dimer autonomy” within the Hb tetramer that was revealed by these data could not have been seen from the global functional characterizations that have been carried out on hundreds of mutant human Hbs (cf. Bunn and Forget, 1985) bearing two modified residue sites per tetramer (i.e., one on the alp* half-molecule; the other on a’/?’). 2. Analysis of Ligation Intermediates b~ Vibrational Spectroscopy

Ultraviolet resonance Raman (UVRR) spectra for partially ligated CNmet Hb microstates have been obtained by Spiro and associates (see Jayaraman et aL, 1995; Jayaraman and Spiro, 1995). They found that species 11,12, and 01 all showed T/R difference UVRR bands which are associated with T quaternary contacts across the dimer-dimer interface, involving the Trp p37 and Tyr a42 residues. Triligated species showed quite different signals, arising from the interior residues Trp a14 and/ signals were attributed to E helix displacement or /?15. These Rdenxy

238

GARY K. ACKERS

toward the heme in deoxy subunits within the R tetramers, resulting in weakened Trp H bonds. Species 21 samples showed signals characteristic of the T quaternary contacts that were attenuated in strength. An equilibrium mixture of T and R molecules was ruled out by the absence of significantly strong Rdeovdifference bands. Rather, the spectral attenuation was attributed to weakening of the T contacts at the dimer-dimer interface. This interpretation was consistent with observations noted above that the mutational pattern of free energy perturbations for the asymmetric hybrid is T rather than that of a T/R equilibrium or an R molecule. Spiro et al. concluded that the asymmetric hybrid 21 represents a “third cooperativity state” having a T quaternary arrangement of the subunits but a deformed dimer-dimer interface, with weakened contacts, in accord with the conclusions of LiCata et al. (1993). 3. Reactivities of the P93 Cysteine Groups

The kinetics of reacting free sulfhydryl groups P93 Cys (Riggs, 1961; Benesch and Benesch, 1962) were evaluated for species of the CN-met system using 4,4’dithiodipyridine (Ampulski et al., 1969) for the 10 ligation species (Doyle and Ackers, 1992a).This study yielded the following correlations: (1) a 35-fold change in kinetic behavior was found between deoxy-Hb and CN-met (or equivalently fully oxygenated) Hb; (2) nearly identical patterns of sulfhydryl reaction kinetics were observed for the hybrid mixtures containing species 11, 12, and 21; by contrast (3) the kinetics of species 22, 23, 24, 31, and 32 were all rapid, with rates similar to that of species 41. These results indicated that the species 21 tetramer, like the two singly ligated ones (i.e., species 11 and 12) was predominantly in the quaternary T structure, whereas the other doubly ligated species were predominantly in quaternary R. These data were consistent with those of Makino and Sugita (1982), who studied 4PDS titration rates of Hb at intermediate O2 partial pressures.

4. Enthalpic and Entropic Components of Cooperativity Assembly reactions of the 10 CN-met microstates were studied as a function of temperature (Huang and Ackers, 1995a) to evaluate the enthalpic and entropic components of their cooperativity. It was found that the cooperative enthalpies and cooperative entropies (Table 111) followed also predictions of the symmetry rule mechanism: a. In unligated Hb (quaternary T) ,dimer-tetramer assembly is driven by a large negative enthalpy (Ip and Ackers, 1977; Huang and Ackers, 1995a), whereas in the fully ligated molecule (R)the net driving force for quaternary assembly is entropic (Mills and Ackers, 1979a). For the

THE MOLECULAR CODE OF HEMOGLOBIN WOSTERY

239

eight intermediate ligation species, the switchover from enthalpic to entropic control was found to follow precisely the symmetry rule predictions; i.e., switching from enthalpic to entropic control occurs at each of the six steps that create ligated heme sites on both symmetry-related half-tetramers. The combinatorial distribution of cooperative free energies that was found previously does not therefore arise from coincidental enthalpy-entropy compensation that masks a more fundamental distribution. b. The free energy of tertiary constraint AG,,, which pays for intradimer cooperativity prior to quaternary switching, contains large enthalpic and entropic components AHtcand AS,, as shown in Table 111. Like ACtC, these terms vanish at the second binding step within the T tetramer. It was found that AC,, arises from a net enthalpic dominance over an almost equally large T AS,,. c. The stepwise enthalpies were correlated with stepwise values of Bohr protons and Bohr free energies (Daugherty et aL, 1994) throughout the cascade of 16 stepwise reactions; the clusters of all these correlated values followed predictions of the symmetry rule. d. These results obtained with CN-met Hb were consistent with and similar in magnitude to the corresponding data on oxygenated Hb which had been resolved at each stoichiometric level of oxygenation (Chu et al., 1984; Huang and Ackers, 1995a), as shown in Table 111.

5. Microstate Contributions to the Bohr E f f t Because structural analyses of the HB molecule have indicated a number of specific ionizable amino acid side chains that may contribute to the 0-linked release of protons (Perutz, 1970, 1990; Peruu et aL, 1980; Kilmartin, 1976;Ho, 1992; Sun et aL, 1997), it was of particular interest to determine proton linkages to the formation of each microstate tetramer containing ligated heme sites. Do the partially ligated Hb intermediates exhibit nine distinct Bohr effects? How are the numbers of ligationinduced “Bohr protons” distributed among the various configurational isomers of heme site ligations? By determining pH dependence of the cooperative free energy for each CN-met microstate, the number and free energy of protons released upon formation of each microstate species was assessed (Daugherty et aL, 1994) and the corresponding proton release (relative to that of dissociated dimers) was determined for each step of the binding cascade (Fig. 4). These studies showed that (1) only two values for Bohr proton release were exhibited by the nine microstates, and (2) the distribution of these two Bohr effects among the sixteen reactions precisely followed predictions of the symmetry rule, as shown in Table 111. These data were

TABLE I11 Synchronized Clusters of Cooperatiue Response Parameters for CN-met Hemoglobin (pH 7.4)"

Stepwise parameter Free enerpy" Enthalpf Entropy' Bohr protonsd CI- effect'

AG AH, - T AS< Aa:(H+) Au<(Cl-)

Generation of tertiary constraint (1Af 3.2 ? 14 2 -11 0.7 5 0.5

* *

0.2 3 3 0.2 0.1

Null reactions ( 4,6,9,12-16)/ -0.1 ? 0.3 1 2 3 -1 ? 3 0 5 0.2 0 0.1

*

' Smith and Ackers, 1985; Perrela et al., 1990a; Huang and Ackers, 1995a. b,r Huang and Ackers, 1995a. dMoles of Bohr protons released (Daugherty et al., 1994). 'Moles of chloride released (Huang et al., 1996~). /Italic numbers relate to the stepwise reactions depicted in Fig. 6.

Switchpoin t reactions (3,5,7,8,10,I I)/

3.1 5 14 -11 2 0.8 2 0.7 2

0.3

*3

3 0.2 0.1

Overall transitions T + R CN-met 6.2 5 29 2 -23 2 1.5 2 1.3 ?

0.3 3 3 0.3 0.1

O?

6.3 2 0.2 34 2 3 -27.7 2.7 1.2 ? 0.2 1.3 0.1

* *

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

24 1

in good accord with those of Perrella et al. (1994), who measured the “remainder Bohr effect,” i.e., proton release, which accompanied oxygenation at the vacant sites on several partially ligated CN-met tetramers. The simplest interpretation of these distributions is that the overall Bohr proton release includes both tertiary and quaternary components. The “tertiary Bohr effect” arises from heme site ligation within the quaternary T tetramer: Bohr proton release which accompanied formation of species 21 from 01 (0.7 H + ) is manifested entirely when the first ligand is bound to form species 11 or 12, i.e., prior to quaternary switching. The second, “quaternary” Bohr effect was observed at all steps of the binding cascade (Fig. 4) when both dimeric half-molecules acquired at least one ligated subunit. The concept of a significant tertiary Bohr effect for Hb tetramers was not new, having been predicted from statistical thermodynamic models (Lee and Karplus, 1983; Perutz, 1990). In these models, the tertiary Bohr effect arises from the breaking of salt bridges of the T interface, whereas the experimental tertiary Bohr effect appears to result mainly from conformational events that produce tertiary constraint and intradimer cooperativitywithin the T tetramer. These various sources of tertiary Bohr protons are not necessarily incompatible, and further studies should be conducted on microstate tetramers with structurally altered residues that have been implicated in other Bohr effect studies.

4. Heterotropic Chloride Effect Assembly reactions of the 10 CN-met microstates were studied as a function of NaCl concentration while constant water activity was maintained by the addition of compensating sucrose (Huang et al., 1996b). Chloride releases of 1.6 and 0.3 mol were found for the assembly of fully ligated and deoxy-Hb, respectively; i.e., a net release of 1.3 mol chloride is coupled to the ligation of tetramers for both O2and CN-met ligation. When the detailed salt linkages accompanying all 16 stepwise CN-met ligation reactions were experimentally resolved, only two “chloride” effects were found. The first chloride effect correlates with the ligation steps which create tertiary constraint, and the second effect is coupled to the six T + R switchpoints. The distribution of these chloride effects thus conforms with predictions of the symmetry rule mechanism.

E. Quaternary Assignments and Molecular Code The structure-sensitiveprobes and heterotropic responses summarized in Section VI,D have strongly supported the quaternary assignments listed in Table 11, col. g, indicating that the observed combinatonal

242

GARY K ACKERS

thermodynamic responses (Table I) reflected quaternary transitions that followed a symmetry rule: T + R switching was thus inferred to accompany the binding steps which produce tetramers with ligated subunits on both symmetry-related half-molecules (alp’ and (r2p2).For the 16 steps of the CN-met cascade (Fig. 4), contributions of Bohr protons, chloride, enthalpy, and entropywere found to be synchronized into three clusters of cooperativity terms (Table 111). These functional response parameters (i.e., the stepwise excess of tetramer value minus dimer value) were identical at the six quaternary T + R switchpoints and also for the two initial binding reactions that generate “tertiary constraints.” Moreover the close similarity in overall magnitudes of these response parameters for CN-met Hb and for H b 0 2 has provided very strong support for the premise that a common allosteric mechanism is followed by the two ligation systems. The composite of resolved microstate thermodynamics and structuresensitive probes has thus provided a molecular code that translates the 16 site-specific ligation reactions of the binding cascade into six switchpoints of quaternary (T + R) structure change (Fig. 4). For each switchpoint binding step the increment in ‘iAGc reflects the net free energy cost of (1) breaking the T interface and forming the R interface; (2) specific binding energy accompanying the switchpoint reaction, minus that of reacting the same site on the dissociated dimer; and (3) any additional tertiary conformation changes or subunit couplings that accompany (1) and (2). 1. Tertialy Constraint

An important dividend from the quaternary assignments (e.g., Figs. 12-15) was that the increments of VAG, which accompanied binding at steps other than the T + R switchpoints were inferred to reflect tertiary contributions within a given quaternary structure. Comparison of the quaternary assignments shown in Table 11, col. g, with the microstate correlations of Table 11, col. f, suggested that a cooperativity constant K,, for the first binding step may be used to denote initial formation of a ligated tertiary structure within the quaternary T tetramer. Similarly, K?: denotes the tertiary conformational change that accompanies formation of species 21 from species 01 within the T quaternary structure; K:, reflects quaternary enhancement arising from the presence of an unligated tertiary structure within an “oxy” quaternary structure R (e.g., upon dissociation of an O2from fully ligated Hb) . Parameter K:, corresponds to the quaternary enhancement effect when K:, is less than unity. The fourth model parameter, K,, reflects the net free energy penalty that accompanies complete oxygenation of the tetramer along any complete pathway through the binding cascade (Fig. 4).

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

243

2. Molecular Code Representation of the Site-Specific Adair Constants These connections between energetic and structural responses to heme site ligation were completed (Ackerset al., 1992; Doyle and Ackers, 1992a) by substituting each of the four “molecular code parameters” K,,, K:, K;,, and K, for their equivalent qkc terms (Table 11) into the sitespecific equations (15). This provided a translation of the Adair constants into molecular code parameters from which the following binding isotherm was formulated (cf. Doyle and Ackers, 1992a): K,,kdx+ [K?:

-

+ 2K,Kk]k2dx2 + 3K,KLk3dx3+ KCk;x4

Y = 1 + 4Kt,kdx+ [2K;,‘

+ 4KCK~Jk2dx2 + 4K,K;k:x3 + K,k;x4

(22)

The formulas of Table I1 thus permit translation of all stoichiometric constants ‘K, into the four molecular code parameters.

Conjirmation of the Molecular Code Partition Function for Hb02 and HbCO Intermediates As already discussed in several contexts throughout this chapter, the use of analog heme sites as models for elucidating cooperativity properties of the native HbOp system must generally be expected to entail perturbations from normal behavior even when they follow native rules of tertiary and quaternary response. It has therefore been necessary to develop strategies that may circumvent this problem. One such strategy (described in Section VI,A) has been that of deducing a consensus partition function from the VAG, change-points exhibited in common among analog systems, and then solving for YAGc terms of native H b 0 2 under the premise that it also has the same change-points (Ackers et al., 1992). A second strategy that has proved especially enlightening and has provided an important cross-check on results obtained by the consensus strategy has been (1) to determine free energy perturbations of the native tetramer that result from metal substitution (e.g., CoZt or Zn2+ for Fez+in all 10 combinations of surrogate “deoxy heme sites” but in the absence of bound ligand, and subsequently (2) to make the same determinations on tetramers that also contain “ligated” heme sites (either as FeP+02 or as surrogates such as Fe2+C0or Fe2+CN).The measured perturbation free energies yielded correction terms that permitted reconstruction of the native system’s cooperativity distribution, by a model-independent “thermodynamic transformation” of the analog databases (Huang and Ackers, 1996;Huang et al., 1996b). The correction

F.

244

GARY K. ACKERS

terms were of two general types, reflecting (1) direct thermodynamic perturbation by the analog heme sites or (2) coupling between heme site substitution (i.e., of analog sites for the native ones) and ligation of heme sites on other subunitswithin the same tetramer. This methodology was first used to resolve cooperative free energies of intermediates in the Fe2+/Fe2+C0 system (Huang and Ackers, 1996).The HbCO coop erative free energies were thus determined by “transformation” of the assembly free energies determined earlier for species of the Co2+/ Fe2+C0system (Table IV) in which Co-substituted hemes comprised the unligated sites. Using hybridized combinations of normal and Co-substituted Hb, Huang and Ackers studied the microstate species of two analog systems (Co2+/FeX,where X = CO, CN) . Free energies of cobalt-induced perturbation were determined for all species of both the “mixed metal” Cozf/ Fez+system containing no ligands and also for the ligated Co2+/FeCN system. It was found that energetic perturbations of the Co2+/Fe2+ hybrid species (Table IV)originate from a pure cobalt substitution effect on the (I! subunits. These perturbations are transduced to the p subunit within the same ap dimeric half-tetramer, resulting in altered free energies for binding at the non-substituted (Fe) sites. The resulting coupling energies YAGcoupare listed in Table IV.By use of thermodynamic cycles to correct for the metal-substitution perturbation and the adirected coupling terms YAGcoup,assembly free energies for the Co2+/FeC0species were converted on model-independent grounds into cooperative free energies of the 10 Fe’+/FeCO species according to the relationship TABLE IV Transformation of Cooperative Free Energy between Co2’/Fe2+C0 and Fe”/Fe’+CO Ligation S y s t d ~~~

-10.6 -9.0 -8.4 -8.3 -7.4 -7.5 -7.4 -7.7 -7.6 -8.0 a

t 0.1 2 0.2 5 0.2 -C 0.2

t 0.2 2 0.2 t 0.2 2 0.2 2 0.2 ? 0.1

-10.60 -12.32 -10.78 -12.44 -12.88 -14.09 -11.55 -12.83 -14.19 -14.35

t 0.12 t 0.15

-

2 0.13 2 0.15

-1.0 t 0.2

t 0.08 ? 0.27 ? 0.16 t 0.11 2 0.18 t 0.11

-1.0 2 0.3

-

-2.3 t 0.2 -1.3 ? 0.2

~~~

0 3.3 3.4 4.2 6.5 6.6 6.5 6.5 6.6 6.3

2 0.2 2 0.3 2 0.3

t 0.3 t 0.3 ? 0.3 t 0.3 t 0.2 t 0.1

Free energies are in kcal. Experimental conditions: 0.1 M Tris, 0.1 M NaC1, 1 mM

EDTA; pH 7.4; 21.5”C.

245

THE MOLECULAR CODE OF HEMOGLOBIN WOSTERY

qAGFe/FeCO r

=

yAGCWFeCO 2

- yAGC"/Fe - qAGcoup 2

(23)

The resulting distribution obtained for VAG, terms in the Fe/FeCO system are listed in Table IV (right-hand column) and also in Table I, col. 7. These values, in combination with an independently derived value for CO binding to dissociated Hb dimers, provided the four statistical weights of Eq. (18). The resultant binding isotherm was highly consistent with accurate CO binding data of Perrella et al. (1990b) as shown in Fig. 16, and with analyses of Perrella and Denisov (1995). It can be seen that the microstate distribution obtained for the Fe/FeCO system by this independent methodology exhibited all the characteristic features of the 1992 molecular code distribution predicted for the HbO, system (Table I, col. 6), especially demonstrating the same VAGc change-points that had been deduced from the three initial analog systems, and that were the basis of the consensus partition functions [Eq. (18) 1. Symmetry rule behavior with regard to species 21 and 22 was also found by Perrella for the HbCO system (Perrella et al., 1998). In a second study using this methodology (Huang et al., 1996a), Hb tetramers with zinc-substituted hemes (Zn2+/Fe2+02) were constructed and studied to determine all microstate contributions to the cooperativity

1.o 0.8

-0.6 Y

0.4 data of Perrella et al. (1593)

0.2

- from resolved microstate values (Huang&*1=9

0.0 0.00

0.02

0.04

0.06

FIG.16. Carbon monoxide binding curve for tetrameric hemoglobin calculated from experimentally resolved microstate cooperative free energies of Table I and the independently estimated intrinsic free energy for CO binding. This curve depicts behaviorcorrected to experimental conditions of the directly measured data points (Perrella et al., 1990b).

246

GARY K. ACKERS

of O2binding at their Fe heme sites. Table V lists the determined free energies of assembly for these species (left-hand data column). Energetic consequences of perturbation by Zn substitution were thus found negligible in all combinations of unligated Zn2+/Fe2+hybrid tetramers (middle data column). The thermodynamic strategy described above which evaluates the energetic effects of substituting a second metal for Fe (Huang and Ackers, 1996).This permitted cooperative free energies of the native Fe2+/Fe02intermediates to be calculated from data on the corresponding Zn2+/Fe02molecules. These parameters, for all eight native 02binding intermediates, were identical within errors to those predicted earlier (Ackers et al., 1992) from analyzing the O2binding data of normal Hb according to the molecular code partition function [Eq. (IS)]. The values of Table V (rightmost column), in combination with the known dimer O2 binding constant kd, yielded an accurate computation of the tetramer's binding curve, as shown in Fig. 17. The finding that Zn substitution generates only negligible thermodynamic perturbations to the dimer-tetramer free energies in any of the site combinations of Table V (middle data column) is strikingly different from the case of C o substitution (Table IV). This result, however, may not be surprising in light of the finding that Zn protoporphyrin IX is isostructural with the native deoxy heme (Scheidt and Reed, 1981; Simolo et al., 1985).

VII. CONCLUDING REMARKS The new conceptual approaches and experimental findings reviewed in this article have revealed previously unknown rules of tetrameric Hb TABLE V Assembly Free Energies and Cooperative Free Energies of the Zinc/Iron Hybrid Hemoglobin System" qA G Z d F e

Species ij

-14.4 -11.6 -11.6 -9.4 -7.7 -7.6 -7.9 -7.5 -7.5 -8.1

t 0.2 2 0.3 2 0.3 t 0.8 t 0.4 2 0.1 t 0.1 2 0.3 2 0.3 ? 0.10

-14.4 -14.4 -14.5 -14.4 -14.4 -14.5 -14.4 -14.1 -14.3 -14.4

2 0.2 2 0.3 2 0.3

t 0.2 t 0.3 2 0.1

t 0.2 ? 0.2 2 0.2 2 0.2

GZn/FeOl

0 2.8 2 0.3 2.8 +- 0.3 5.0 t 0.8 6.7 2 0.4 6.8 2 0.2 6.5 ? 0.2 6.9 2 0.3 6.9 2 0.3 6.3 t- 0.2

Free energies are in kcal. Experimental conditions: 0.1 MTris, 0.1 M NaCI, 1 mMEDTA pH 7.4; 21.5%.

247

THE MOLECULAR CODE OF HEMOGLOBIN ALLOSTERY

1.0

I

Y

0

10

5

15

Po (torr) 2

FIG.17. Oxygen binding by human hemoglobin at pH 7.4, 21.5”C, 0.18 M chloride. Solid line is the tetramer binding curve obtained by direct measurement (Chu el al., 1984); (+) values calculated by Eq. (22) from microstate cooperative free energies (Table I, col. 6) of the consensus partition function (Ackers et al., 1992; Doyle and Ackers, 1992a); (0)values calculated by Eq. (16) from microstate free energies (Table I, col. 9) that were resolved independently of data from the three analogs used to obtain col. 6 of Table I.

cooperativity at a subunit-specific level. These discoveries have extended the classical frameworks of Monod and of Koshland in ways that are consistent with the structural and energetic discoveries of Perutz and of Karplus and their associates. This work has also exemplified and extended the thermodynamic linkage analyses of Hb that were pioneered byJeffries Wyman. The new findings-of symmetry rule T R switching and long-range intersubunit coupling within the half-tetramer prior to quaternary transition-have provided a foundation for the more detailed analyses that must eventually provide an ultimate understanding of the Hb mechanism. Within this new framework a detailed structural mechanism will be discovered for the Opinduced generation and release of intra-dimeric tertiary constraint that triggers the hemoglobin T + R switch. The greatest significance ofwork reviewed here is that the general strategy developed for this problem may be applicable to the “molecular codes” of other protein assemblies that also function by combinatorial mechanisms of ligand binding.

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ACKNOWLEDGMENTS I am grateful to the current and former members of my research group who have contributed to the exciting adventure of understanding hemoglobin cooperativity at a new level, including Paula Dalessio, Margaret Daugherty, Ilya Denisov, Michael Doyle, Jo Holt, Yingwen Huang, Alexandra Klinger, George Lew, Vince LiCata, David Myers, Madeline Shea, Francine Smith, and Phil Speros. This research has benefited greatly from the powerful cryogenic methodology developed by Michele Perrella and by the important research contributions from his laboratory on the intermediate ligation states of hemoglobin. The synthesis of new information reviewed here is also an outgrowth of the accurate and sensitive methodology pioneered by Kiyohiro Imai for the determination of oxygen binding isotherms that were necessary for the interpretation of microstate data on HbOs analogs. This work has been supported by NIH Grants R37 GM24486 and HL51084 and by NSF Grant MCB9723606.

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STATISTICAL THERMODYNAMIC LINKAGE BETWEEN CONFORMATIONAL AND BINDING EQUILIBRIA By ERNEST0 FREIRE Department of Biology and Biocaiorimetry Center, The Johns Hopklns University, Baltimore, Maryland 21218

I. 11. 111. N.

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Introduction .................................................... The Most Probable Distribution .. ........ Coupling of Statistical Weights to .. ........ Modulation of Distribution of States by Specific Ligands .............. A. Binding Site in the Subensemble of States and the Native State ... B. Binding Site in the Subensemble of States Only . . . . . . . . . . . . . . . . . C. Realistic Estimates of Modulation Factors ....................... Modulation of Distribution of States by Denaturants . . . . . . . . . . . . . . . . . Ligand-Induced Conformational Changes ........................... The Distribution of Conformational States According to Their Gibbs Energy ................................................. Is the Unfolded State the State with the Highest The Gibbs Energy Scale of Conformational States Statistical Descriptors of the Conformational Ens A. Ensemble Averages and Experimental Probes . . B. Stability Constants per Residue ................................ C. Coupling of Residue Stability Constants to Ligand Binding D. Function-Specific Probabilities ................................. Conclusions . . . ...... . . . . ............ References ......................................................

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I. INTRODUCTION For many years, our view of the conformational equilibrium in proteins has been distorted by the so-called two-state model, in which a protein (or protein domains in the case of large proteins) is assumed to be in equilibrium between two discrete states. Today, we know that the twostate view is misleading. Even though many physical properties of proteins can be represented in terms of two o r at most a few discrete states, other properties like the pattern of hydrogen exchange protection measured by nuclear magnetic resonance (NMR) under equilibrium conditions (Bai et al., 1995;Jacobs and Fox, 1994; Kim and Woodward, 1993; Loh et al., 1993; Morozova et al., 1995; Radford et al., 1992; Schulman et al., 1995; Swint-Kruse and Robertson, 1996) reveal the presence of a large number of conformations and cannot be rationalized in terms of the two-state model. The view that has emerged from those experiments is that, even under native conditions, proteins must be 255 ADVANCES IN

PROTUN CHEMISTRY, V d 5 1

Copyright 0 1998 by Academic Press. All rights of reproduction in any form reserved. 0065;5293/98$25.00

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considered as a dynamic ensemble of different conformational states in which each state is populated according to its Gibbs energy. Despite this realization, the analysis of experimental data is still usually performed with equations developed for simple chemical equilibria rather than statistical thermodynamic approaches. An immediate consequence of the statistical nature of the conformational equilibrium is that measured physical properties, which are ensemble averages where each conformational state contributes according to its population, cannot be directly assigned to specific states since in many instances conformational states with “average properties” do not even exist. In this situation, the tools of statistical thermodynamics provide the bridge between macroscopic and microscopic properties for the system under consideration. Under a given set of physical conditions (solvent, pH, temperature, pressure, etc.) a protein is characterized by a probability distribution of states, which at equilibrium corresponds to the most probable distribution for those conditions. It must be realized that the most probable distribution under a given set of conditions may not be the most probable distribution under another set of Conditions. Consequently, from a statistical standpoint, conformational changes or other protein processes need to be understood as changes in the most probable distribution of states. Changes in the most probable distribution can be elicited by changes in the physical or chemical environment and can be formally expressed by a set of linkage equations that relate the effective Gibbs energy of each state with changes in those conditions. Ligands, including pH and other ions, play an important role in modulating the character of the most probable distribution of states that are accessible to a protein. These states might have different functional properties or different biological activities, in which case ligands play the role of molecular switches by preferentially stabilizingcertain conformations. There are, however, certain limits to the nature of the conformational states that can be stablized by ligands. These limits are determined by both the magnitude of the Gibbs energy of stability and the magnitude of the Gibbs energy of binding. In this review, the coupling between conformational and binding equilibrium for a canonical ensemble is discussed. The basic statistical thermodynamic theory as well as some practical implications dictated by experimental constraints will be addressed. In particular, the energetic requirements for the stabilization of conformational states by ligand binding will be evaluated. The extension of the linkage concept to a statistical ensemble has been inspired by the seminal work of Jeffries Wyman (1948, 1964;see also Wyman and Gill, 1990).

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11. THEMOST PROBABLE DISTRIBUTION In our discussion, we consider a monomeric protein existing in thermodynamic equilibrium between a large number of possible conformational states. The most probable distribution of states under a given set of conditions is defined by the entire set of population probabilities {Pi}found under those conditions. This set defines the most probable distribution of states. At equilibrium, the probability of any given conformational state, 4, is given by the following equation:

p. = exp ( -A Gi/ RT)

Q

(1)

where the statistical weights or Boltzmann exponents [exp(-AGJRT)] are defined in terms of the relative Gibbs energies AGi for each state (Ris the gas constant and Tthe absolute temperature); Qis the conformational partition function defined as the sum of the statistical weights of all the states accessible to the protein: N

Q = x e x p ( -A GJ RT) i=O

As defined, the partition function not only enumerates conformations with different degrees of folding but also multiple conformations of the native state or any arbitrary conformation accessible to a protein. The relative Gibbs energy of each state (AGi) is expressed in terms of the standard thermodynamic equation, as follows:

AG, = AH, - TAS,

(3)

where AG,, AH,, and ASi are the relative Gibbs energy, enthalpy and entropy of state i at temperature T, respectively. The selection of a reference state is a matter of convenience. In the above equations, state 0 is chosen as the reference state. This state is usually identified with the native state, since the native state is usually a well-defined and structurally characterized state. For those situations in which the native state has multiple conformations, it is convenient to choose the one with the lowest enthalpy as the reference. OF STATISTICAL WEIGHTS TO LIGANDS 111. COUPLING

Ligands affect the probability distribution of conformational states by differentially modulating the magnitude of the statistical weight of

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each state. The statistical weight of any given conformational state can be written as the product of two terms, the intrinsic statistical weight, exp( -AGP/RT), and a modulation factor, Ai, that accounts for changes in concentration of the ligand under consideration: exp( -AGi/RT) = Ai exp( -AGP/RT)

(4)

If the modulation factors had the same magnitude for all states, the probability distribution will be unaffected by the presence of a ligand (i.e., it will be possible to factorize the constant A from the partition function). In the presence of a ligand X, the modulation factor Ai for each conformational state has the following form:

where K , is the association constant of X for site j in conformation z; & k is the association constant of X for site kin the reference state (native state); Ni and No are the number of binding sites in state i and the reference state, respectively; and [XI is the free concentration of X. It follows from Eq. (4)that states for which A, is greater than 1 will be stabilized with respect to the native state, while those with Ai values smaller than 1 will be destabilized. The change in the statistical weight of each state as a function of the concentration of X can be evaluated by taking the partial derivative of ln(A,) with respect to [XI:

where Y,jis the degree of saturation of site j in conformation i, and &,k is the degree of saturation of site k in the reference state. It follows from Eq. (6) that an increase in the concentration of ligand X will stabilize state i if the total amount of ligand bound to that conformation is greater than the amount of ligand bound to the native state. There are two ways in which this situation can be achieved: higher binding affinity or a larger number of binding sites. It must be noted, however, that at high

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ligand concentrations all Yx,y+ 1 and the conformation with the largest number of binding sites is the one that is ultimately stabilized at saturating ligand concentrations. Figure 1 illustrates different situations that might arise as a result of different combinations of binding affinities and number of binding sites. If the number of binding sites is equal in state i and the reference state, the modulation factor reaches a constant value at saturating ligand concentrations (line A). If, on the other hand, state i has a larger number of binding sites, it is stabilized at saturating ligand concentrations independently of the magnitude of the binding constant (line C) , Conversely, if state i has fewer binding sites, it will be destablized at saturating ligand concentrations. In this case a situation similar to that shown in Fig. 1 (line B) may arise in which state i is first stabilized because it has a higher affinity but then is destabilized because it has fewer binding sites. At low ligand concentrations, the state with the highest binding affinity is the one that is stabilized. OF DISTRIBUTION OF STATES BY SPECIFIC LIGANDS IV. MODULATION

We consider the situation in which a ligand binds to specific sites that are present in some conformational states of a protein. Two situations

-10

-8

-4

-6

-2

0

1% [XI

FIG.1. The natural logarithm of the amplitude factors as a function of the logarithm of ligand concentration for three different situations: curve A, the number of binding sites is the same in state i and the reference state (one binding site), but state i has a higher binding affinity; curve B, the number of states is larger in the reference state (two binding sites), but state i has a higher binding affinity; curve C, the number of states is higher in state i (two binding sites) and also has a higher binding affinity. For the simulations, the binding constant to the reference state was lo4 MI; for state i, lo6 MI.

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will be discussed-one in which the binding site is present both in a subset of the states accessible to the protein as well as the native state, and one in which the binding site is absent in the native state.

A. Binding Site in the Subensembb of States and the Native State Figure 2 shows the magnitude of the modulation factor A, for each of the states in the ensemble that express the binding site. In this case, the magnitude of A, only depends on the magnitude of K and &. At saturating ligand concentrations the magnitude of A, is equal to K/&. At the midpoint of the effect, the ligand concentration is given by the following equation:

This situation usually occurs when partially folded states become populated and only a fraction of those states retain the ability to bind the ligand.

B. Binding Site in the Subensemble of States Only Figure 3 shows the magnitude of the modulation factor A, for the case in which the binding site is absent in the native or reference state. In this

l2 10

s 7 1 K~ = lo9 M-I

-

8 -

*-c

6 4 2 -

0 -10

-8

-6

-4

-2

0

1% [XI

FIG.2. The natural logarithm of the amplitude factors as a function of the logarithm of ligand concentration for different values of the binding constant for state i. For the simulations the binding constant to the reference state was set to 10' M-I.

CONFORMATIONAL AND BINDING EQUILIBRIA

20 [

4-

c

15

-

10

-

-10

-8

-6

-4

-2

0

log [XI

FIG.3. The natural logarithm of the amplitude factors as a function of the logarithm of ligand concentration for different values of the binding constant for state i. In this case, the binding site is assumed to be absent in the reference state.

case the denominator in Eq. ( 5 ) is equal to 1.As shown in Fig. 3, the amplitude factors do not plateau at high ligand concentrations, as expected for all those cases in which the number of binding sites in state iis larger than in the native state. This equation also describes the case in which the native state exists in different conformations depending on the presence or absence of a specific ligand that binds to only one of the forms. C. Realistic Estimates of Modulation Factors

Ligands can shift the probability distribution of states; however, there are limits to the extent by which a ligand can alter the probability distribution and stabilize a partially folded conformation, for example. These limits are dictated by the magnitude of the intrinsic statistical weights and the binding affinities of the ligand, as well as practical or experimental constraints. For example, in most situations in biochemistry there is a correlation between the binding affinity of a ligand and their solubility. High affinity ligands (K > lo9 M-l) tend to be highly hydrophobic and cannot be used at concentrations significantly higher than 1/K. If we assume that a ligand can be used at concentrations as high as 6 orders of magnitude higher than 1/K, then it is possible to provide upper limits for the magnitude of the modulation factors. This is certainly a very reasonable upper limit since, for example, ligands with micromolar affinities cannot be usually concentrated to 1 M. If it

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also assumed that the binding site is absent in the native state, which represents the optimal situation, the maximum Aivalue for a single binding site is lo6, which corresponds to a favorable contribution of 8 kcal/mol to the Gibbs energy of state iat 25°C. At ligand concentrations 3 orders of magnitude higher than the dissociation constant, the favorable contribution is reduced to only 4 kcal/mol. The contribution is certainly smaller if the ligand also binds to the native state. It is clear from the above discussion that a single ligand cannot be expected to realistically stabilize a conformational state with a Gibbs energy 8 kcal/mol or more higher than that of the native state. Multiple binding sites will certainly improve the situation; however, high-affinity binding sites are highly specific and it is extremely rare to identify a conformation with several high-affinity sites. Protonation sites will give rise to modulation factors as high as 10APKo. For a typical situation in which a shift in ApK, amounts to no more than 2-3 pH units, the contribution to AG is at most 3-4 kcal/mol per site. OF DISTRIBUTION OF STATES BY DENATURANTS V. MODULATION Chemical denaturants (urea, GuHC1) represent a situation in which different protein conformations exhibit many low-affinity binding sites. The binding is highly nonspecific and apparently discriminates states only on the basis of the surface area exposed to the solvent (Myers et al., 1995). Since the number of denaturant binding sites is proportional to the change in solvent accessible surface area, AASA, the unfolded state which is the state with the largest AASA is the one ultimately stabilized at high denaturant concentrations (see Fig. 1). Within the context of the denaturant binding model, the denaturant binding constant is assumed to be similar for all binding sites, in which case the modulation factors [Eq. ( 5 ) ] assume the following form:

where K is the binding constant; X, the activity of the denaturant; and AN, the difference in the number of binding sites between state i and the native state. For the linear extrapolation model, the effect of a concentration C, of denaturant is proportional to the so-called m value as A, = exp( - m G / R T ) . A rigorous treatment of the stabilization of different states by chemical denaturants has been presented before and will not be repeated here (Haynie and Freire, 1993, 1994). These authors demonstrated the exis-

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tence of conditions under which the addition of GuHCl to a protein solution stabilizes intermediate conformations at moderate concentrations and the unfolded state at higher concentrations. For certain proteins like a-lactalbumin (Kuwajima,1977,1989) it has been shown experimentally that mild concentrations of denaturants do in fact stabilize the molten globule state while higher concentrations lead to the complete unfolding of the protein.

VI. LIGAND-INDUCED CONFORMATIONAL CHANGES In many cases proteins are observed to exist in different conformations in the presence or absence of a ligand. The addition of a ligand appears to induce a conformational change in the protein. Within the statistical thermodynamic framework, this situation is no different from the one described above. The conformation in which the protein is found in the presence of the ligand is one of the conformations existing in the ensemble except that in the absence of the ligand that conformation has a very low probability. According to Eq. (4),the stability of the conformation preferentially stabilized by the ligand is equal to exp(-AG,/RT)

=

A,exp(-AG:/RT) + K,[X]) exp(-AG:/RT)

= (1

(94 (9b)

where the reference state is assumed not to bind the ligand. If the intrinsic statistical weight is negligible, the above equation reduces to exp(-AG,/RT) = KJX] exp(-AG:/RT) = Kapp,,[Xl

(104 (lob)

where the apparent constant Kapp,, should be recognized as the constant for the reaction of the form

A

+ X P B*X

(11)

which corresponds to the so-called ligand-induced conformational change. It must be noted that the apparent constant is defined by two Gibbs energies: the intrinsic Gibbs energy of the conformation of the ligand-bound state and the Gibbs energy of binding to that conformation. OF CONFORMATIONAL STATES ACCORDING TO VII. THEDISTRIBUTION THEIR GIBBS ENERGY

The foregoing discussion indicates that there are certain energetic constraints to the states that can be significantly stabilized by ligand binding

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and that, from an energetic point of view, binding cannot be expected to stabilize any arbitrary conformation independently of its energy. In order to estimate the number and type of states that can be stabilized by binding, it is necessary to evaluate the distribution of states according to their free energy. What percent of all possible states have Gibbs energies within the reach of ligand stabilization?This issue will be addressed by a structurebased thermodynamic analysis of protein structure. Recently, our laboratory has developed a structural parameterization of the folding energetics that accurately predicts the stability of proteins or partially folded conformations. The most current refinement is contained in the following references: Bardi et al. (1997), D’Aquino et al. (1996),Gomez and Freire (1995),Gomez et al. (1995),Hilser et al. (1996), and Luque et al. (1996). Also, we have developed an algorithm (CORE) aimed at generating nativelike partially folded states using the crystallographic or NMR solution structure of a protein as a template (Xie and Freire, 1994a,b).This algorithm presumes that the protein is formed by an arbitrary number of folding units. Each folding unit can be either in the native or unfolded states. For a total of Ndifferent folding units a total of 2Nstatesare generatedwith the computer by folding and unfolding the folding units in all possible combinations. The number of folding units determines the resolution of the analysis. Once the ensemble of states is generated, the energetics of each state is calculated using the structural parameterization of the energetics. This approach has been shown to correctly predict the global stability of proteins, the structural determinants of molten globule states (Freire, 1995c; Xie et al., 1994; Xie and Freire, 1994a,b).The CORE algorithm was recently extended into a version able to generate over lo5states (COREX),which is capable ofcorrectly estimating the stability constants per residue as reflected in the pattern of NMRdetected hydrogen exchange protection factors (Hilser and Freire, 1996, 1997; Hilser et al., 1997). In order to estimate the distribution of conformational states in terms of their Gibbs energies, a large number of nativelike partially folded states for different proteins were generated with the computer and their Gibbs energies calculated as described. Of particular interest were proteins like a-lactalbumin (pdb file 1 alc) or staphylococcal nuclease (pdb file 1 snc), which have been shown to exhibit a high propensity to populate partially folded states and therefore were expected to have a higher proportion of states with relatively low Gibbs energies, as well as to provide an upper limit to the fraction of states with a potential to be stabilized by ligands (Kuwajima, 1989; Shortle and Abergunawardana, 1993; Shortle and Meeker, 1989; Wang and Shortle, 1995; Xie et al., 1994; Xie and Freire, 1994a,b).

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265

The results of the analysis for a-lactalbumin and staphylococcal nuclease are shown in Fig. 4a and b). As shown there, for a-lactalbumin the mean Gibbs energy is close to 35 kcal/mol above the native state, with 99.7% of the states having Gibbs energies greater than 10 kcal/ mol. The unfolded state is only 8 kcal/mol above the native state and

c

,eE

L

kcdrnol

FIG.4. The distribution of partially folded states as a function of their Gibbs energy relative to that of the native state: (a) the results for a-lactalbumin; (b) the results for staphylococcal nuclease. The fraction of states with Gibbs energies lower than 10 kcal/ rnol is 0.3% for a-lactalbumin and 0.2% for staphylococcal nuclease. All structure-based thermodynamic computations were performed with the structural parameterization of the energetics developed in our laboratory (see the text for details).

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is also included in the 0.3% of states with the lowest Gibbs energy. For staphylococcal nuclease the mean energy is close to 40 kcal/mol above the native state, with 99.8% of the states having Gibbs energies greater than 10 kcal/mol. It is clear from this analysis that only a miniscule fraction of the total number of nativelike partially folded conformations have a chance of being significantly stabilized by binding. For comparison, the results of the structure-based thermodynamic calculations for the protein hen egg-white lysozyme (pdb file llzt), which is structurally similar to a-lactalbumin but does not have a propensity to populate partially folded intermediates, are presented in Fig. 5. In this case the fraction of states with Gibbs energies lower than 10 kcal/mol was less than O . l % , consistentwith the observation that in this protein partially folded states do not become significantly populated. The differences in the distribution of states between a-lactalbumin and hen egg white lysozyme are shown in Fig. 5. It is clear that the distribution for lysozyme is shifted to higher Gibbs energy values and that consequently the number of states with low Gibbs energies is significantlysmaller. The type of distributions shown in Figs. 5 and 6 are typical of globular proteins and indicates that, in general, very few conformational states have a reasonable chance of being stabilized by solvent conditions or ligands.

kcdmol

FIG.5. The distribution of partially folded states of a-lactalbumin and hen egg-white lysozyme as a function of the Gibbs energy. Even though these proteins are structurally homologous, the distribution is shifted to higher values for hen egg-white lysozyme. Also, the fraction of states with Gibbs energies lower than 10 kcal/mol is less than 0.1% for hen egg-white lysozyme. Both results are consistent with the observation that this protein does not have as high a propensity to populate partially folded intermediates as does a-lactalbumin.

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VIII. Is THE UNFOLDED STATE THE STATE WITH THE HIGHEST GIBBS ENERGY? According to the discussion presented above, the unfolded state is not the state with the highest Gibbs energy. It usually has a Gibbs energy about three or four times lower than the mean Gibbs energy of all nativelike partially folded states. If the unfolded state were the state with the highest Gibbs energy and partially folded states had Gibbs energies intermediate between the native and unfolded states, the folding reaction would not be a cooperative but a continuous process in which states would become gradually populated according to their Gibbs energies. Furthermore, it would be impossible to populate the native state to a significant degree. The large number of partially folded states coupled to their relatively low Gibbs energies would preclude any state from achieving high population levels. The ordering of states in terms of their Gibbs energies includes the contribution of the conformational entropy relative to that of the native state. It is clear that the unfolded state and also partially folded states gain significant conformational entropy from the backbone and side chains as they become unfolded. In the unfolded state all side chains and backbone gain conformational entropy. In partially folded states the unfolded regions gain backbone and side-chain entropy, and in the folded regions the side chains that becomes exposed to the solvent from a previously buried location also gain conformation entropy (D’Aquino et al., 1996; Xie and Freire, 1994,b). More properly, the unfolded state as well as partially folded states do not represent unique conformations but subensemble of states characterized by an average Gibbs potential in which the conformational entropy reflects the degeneracy of each state. The Gibbs potential function has been introduced in our laboratory (Luque and Freire, 1997; Luque et al., 1997) as a way of identifylng conformations that minimize the Gibbs energy. This function includes all internal interactions as defined in the structural parameterization of the energetics, plus the solvent-related entropy, but it does not include the conformational entropy since the Gibbs potential function is defined for a single conformation. Figure 6 illustrates the differences between the Gibbs potential function and the Gibbs energy for hen egg-white lysozyme. The ensemble of conformations considered in the analysis included the native state, unfolded state and nativelike partially folded states. In this figure, the two functions have been plotted as a function of the degree of folding of the protein. It is clear that any of the conformations that can be classified as unfolded (no internal interactions, hydration of backbone and side chains) have the highest Gibbs potential in this

I

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ERNEST0 FREIRE

Fraction Unfolded

FIG.6. The Gibbs potential function and the Gibbs energy as a function of the degree of folding of hen egg-white lysozyme. The Gibbs potential function is maximal for the unfolded state, whereas the Gibbs energy is maximal for degrees of folding close to 50%.

ensemble. Also noticeable is that the average Gibbs potential decreases monotonically with the degree of folding of the protein. For comparison, the average Gibbs energy is maximal for conformations about 50% folded, a trend noticed previously and attributed to the observation that the largest uncompensated exposure of hydrophobic residues occurs at this point (Freire et aL, 1993). Most important, perhaps, is that for any given degree of folding the Gibbs potential (like the Gibbs energy) shows a rather large range of values. This trend reflects the fact that not all conformations with the same degree of folding have the same energy. In fact, a line that connects the points with the lowest Gibbs potentials along the folding axis defines the minimum energy folding pathway, i.e., the hypothetical folding path in which the protein is at the minimum Gibbs potential at all stages during the folding process. In the discussion concerning the stabilization of states by ligands it is implicitly assumed that a subensemble of states rather than a unique conformation is stabilized. This subensemble can be very large, such as in the case of the unfolded state, or very small, as in the case of a protein with two functionallydifferent native conformations. Within this context, the term “state” defines a subensemble of conformations in which all the members share some common features and are characterized by a mean enthalpy. The stabilization of a partially folded state implies the stabilization of a family of conformations in which a common region is

CONFORMATIONAL AND BINDING EQUILIBRIA

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folded and the remaining regions occupy any allowed unfolded conformation.

IX. THEGIBBS ENERGY SCALE OF CONFORMATIONAL STATES In principle, the number of conformations accessible to a protein is astronomically large. In practice, however, the vast majority of possible conformations are characterized by extremely unfavorable Gibbs energies and their population is essentially zero under normal conditions in aqueous solution. For most small globular proteins under conditions in which the native state is maximally stable, the Gibbs energy of stabilization is on the order of 10 kcal/mol. Usually, partially folded states have very high free energies and consequently low probabilities because they expose to the solvent a relatively large amount of hydrophobic surface, with an unfavorable energy of exposure which is not compensated by a parallel increase in conformational entropy. The unfolded state exposes all residues to the solvent; however, the unfavorable energy of exposure is compensated by the large gain in conformational entropy (Fig. 6). This gain in conformational entropy is absent in the folded regions of partially folded states, and therefore the exposure of hydrophobic residues by these regions is not compensated, resulting in a highly unfavorable Gibbs energy. This uncompensated exposure occurs primarily at the so-called complementary regions (Freire et al., 1993),i.e., those surfaces in the folded regions that are structurally complementary and are buried from the solvent by the regions that become unfolded in the partially folded state. It is not surprising that in most cases the partially folded states that become populated maintain a significant hydrophobic core. This situation is possible because polar and apolar residues are not homogeneously distributed within the protein, therefore enabling some states to expose a relatively larger fraction of polar buried residues. As shown above, the population of partially folded states with low Gibbs energies is exceedingly small (<0.1% for most proteins). Analysis of the structural characteristics of those states reveals that for a given protein the partially folded states that are characterized by low free energies possess common structural features. Usually, a unique highly stable structural core is present in all these partially folded intermediates. For a-lactalbumin, for example, most of the partially folded states with low Gibbs energy have the alpha domain or significant portions of this domain in a nativelike conformation (Freire, 1995c; Peng and Kim, 1994;Xie and Freire, 1994a,b).For staphylococcal nuclease, on the other

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hand, portions of the P-barrel appear to have a higher persistence (Hilser and Freire, 1997; Xie et al. 1994). Figure 7 illustrates in graphical form the Gibbs energy diagram for globular proteins. The unfolded state is about 10 kcal/mol higher than the native state. Some partially folded states might have Gibbs energies intermediate between that of the unfolded and native states, but the vast majority of states have higher Gibbs energies than the unfolded state. On occasion, partially folded states form dimers or higher order oligomers. These oligomers have lower Gibbs energies than the individual components because these higher order structures bury a significant portion of the exposed hydrophobic areas from the solvent. As discussed above, partially folded states expose relatively large hydrophobic surfaces to the solvent without a compensating gain in conformational entropy. Aggregation is an alternative way to lower the Gibbs energy by sequestering those surfaces from solvent exposure. This effect explains why molten

FIG. 7. Schematic view of the Gibbs energy scale of protein states. Only states with Gibbs energies lower than 10 kcal/mol can be expected to have a reasonable chance of being stabilized to significant populations by ligand binding.

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globules or other partially folded conformations have a high propensity to aggregate. Modulation factors are able to increase or decrease the population of certain states; however, from a practical standpoint, states with Gibbs energies higher than 10 kcal/mol cannot generally be stabilized to a significant population level by ligands.

DESCRIPTORS OF THE CONFORMATIONAL ENSEMBLE X. STATISTICAL A . Ensemble Averages and Experimental Probes The characteristics of the conformational ensemble of a protein cannot be described by a simple enumeration of the members of the ensemble and their properties. The large number of states that are accessible to a protein requires a statistical description. The most common descriptors are those that describe the average values of specific physical properties. Experimental observables are by definition statistical averages over the ensemble of conformations accessible to a protein. For an arbitrary observable, a, the ensemble average (a)is defined by the contributions of all states accessible to the protein weighted according to their probabilities:

c aipi N

(a)=

i= 0

where a, represents the value of the physical property for state i, and where P,denotes the probability of that state. Equation (12) provides the foundation for the experimental analysis of conformational equilibrium. Except for differential scanning calorimetry, however, Eq. (12) cannot be solved exactly for more than two states (Freire, 1995a,b; Freire and Biltonen, 1978). Differential scanning calorimetry represents a special case because the excess enthalpy (the integral of the excess heat capacity function) is simultaneously a physical observable and a component of the Gibbs energy. For other physical observables the correlation between the quantity measured and the Gibbs energy is nonexistent. In what follows,we consider a situation which has become experimentally feasible with the emergence of new technologies that permit observation of the conformational equilibrium using individual residues in the protein. These residue specific probes include NMR and other spectroscopic techniques in which a measurable signal that can be assigned to a specific residue is sensitive to its conformational state. If the number

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of signals is large enough to include a significant number of residues in the protein, then a detailed map of the equilibrium ensemble can be constructed. The simplest situation occurs when the physical observable assumes one value when the residue under consideration is in the native or folded state, aJJ,and a different value when it is unfolded, a,,,].In this case, the observed value of that observable, (aj),is

folded)

i

In the derivation of Eq. (13), the states accessible to the protein have been divided into two groups, those in which residue j is folded and those in which residue j is unfolded. Since aJjand are experimentally accessible as the values of the observable when residue j is folded or unfolded, respectively, rearrangement of Eq. (13) yields

The right-hand side of Eq. (14) is similar to the equation conventionally used in the analysis of conformational equilibrium. In the conventional analysis, however, Eq. (14) is assumed to represent the fraction or probability of molecules in the native state. In the statistical thermodynamic analysis, Eq. (14) represents the sum of the probabilities of all the states in which residue j is folded. The dependence of Eq. (14) on temperature or the concentration of ligands provides access to im ortant properties of the ensemble. The temperature derivative of In i ) E , j = f o l d e d is equal to

and yields the difference in the average enthalpy for the subensemble of states in which residue jis folded, (AH)j=folded, and the average enthalpy for the entire system, (AH). Here ( A H ) is the average excess enthalpy

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function that can be obtained by differential scanning calorimetry (Freire, 1995a,b;Freire and Biltonen, 1978). So, if the data are accurate enough, (hH)j=folded can be obtained by subtracting the calorimetrically obtained (AH). If the native state is the only state in which residue j is = 0. If, on the contrary, residue j is folded folded, then (AH)j=folded in other states besides the native state, then (All)j=foldedwill provide information regarding the characteristics of the subensemble. A small value for (AH)j=folded is an indication that most states in which residue j is folded are close to the native state, whereas a larger value will be indicative of a more unfolded ensemble. Since the probability distribution is linked to the presence of a ligand by the equations presented above, it is apparent that (AH)j=folded Will show a dependence on the concentration of ligands. From a theoretical point of view, (hll)j=folded can be deconvoluted using procedures developed for the excess enthalpy function (Freire and Biltonen, 19’78). From a practical point of view, however, the implementation of this approach will require precisely matched spectroscopic and calorimetric data.

B. Stability Constants per Residue The summed probabilities 2 P,J=folded permit the definition of an a p parent stability constant per residue. The apparent stability constant per residue, K ~ , , has been introduced recently by Hilser and Freire (1997; see also Hilser et al., 1996, 1997). This constant is defined as the ratio of the summed probabilities of all states in which residue j is folded P$,]=folded) to the summed probabilities of the states in which residue j is not folded:

(x

The corresponding apparent free energy is simply AGjj = -RTln KL,. The apparent stability constant per residue, K,-~, is the quantity that one would measure if it were possible to experimentally determine the stability of the protein by monitoring each individual residue. The importance of this quantity is that it can be directly related to hydrogen exchange protection factors measured by NMR. It has been shown that a significant number of the hydrogen exchange protection factors measured for a protein accurately measure K ~ implying ~ , that NMR provides a direct observation window into the conformational ensemble of a protein

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ERNEST0 FREIRE

(Hilser and Freire, 1997; Hilser et al., 1996,1997).The protection factors, PF,, are defined as follows:

which is similar to the definition of the residue stability constants except that in this case the probabilities refer to the states in which the amide of residue j is not exposed to the solvent (closed). Residues that are buried from the solvent in the native state (closed) usually become exposed as a result of partial or global unfolding reactions (Bai et aL, 1995). In that sense, the hydrogen exchange protection factors monitor the conformational equilibrium. However, not all protection factors can be equated to residue stability constants since amide groups can become solvent exposed by different mechanisms. The stability constants are thermodynamic quantities defined for all residues. Protection factors, on the other hand, can be affected by nonthermodynamic factors; i.e., an amide can be exposed to the solvent without the residue being unfolded. The most common situations in which a residue is folded but exposed to the solvent occurs when ( 1 ) the amide group of the residue is exposed in the native state and (2)the amide group of the residue becomes exposed by being located in a region of the protein that is structurally complementary to an unfolded region. Despite these constraints, hydrogen exchange protection factors provide good estimates for the residue stability constants of a significant fraction of the protein residues. For a typical globular protein, the fraction of amides whose hydrogen exchange protection factors can be identified with apparent stability constants can be higher than 60%.

Coupling of Residue Stability Constants to Ligand Binding The binding of a ligand affects the statistical weights of conformational states as described by Eqs. (4)and ( 5 ) above. This effect is reflected on the magnitude of the stability constants per residue. In general, for , be written as residues that are part of the binding site, K ~ can C.

( l + KIX1) Kh -

2 2 P",

PJj.br

I

+ 2 PJ~,b, I

(18)

where the first sum in the numerator runs over all the states in which residue j is folded and the binding site is formed (i.e., the remaining

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275

residues that define the binding site are also folded). The statistical weight of all these states is modified by the same factor (1 + K [ X ] ) . The second term in the numerator contains the sum of the probabilities of all the states in which residue j is folded but the binding site is not completely formed and therefore unable to bind. The assumption in Eq. (18) is that all states in which the binding site is formed have the same binding affinity and that a partially formed binding site has no affinity for the ligand. It can be seen in Eq. (18) that the maximal enhancement in K~~ is equal to (1 K [ X ] ) .However, this enhancement will not generally be observed in all the residues that define the binding site. If the binding site is formed by a mixture of residues with high and low stability constants, then the maximal enhancement will be observed only for the residues with the lowest stability constants. For these residues Pj:l,bc 9 PJ,,bE, and therefore reduces to the original stability constant multiplied by the amplitude factor. The stability constants of residues that define the binding site are not the only ones affected by binding. This situation is illustrated in Fig. 8 for a simple situation in which a protein is composed of two folding units. As shown there, the protein has four different accessible states corresponding to the number of ways in which the folding units can be folded or unfolded. In addition, the binding site (located in folding unit 2) is intact in the native state (state 0) and state 1, and therefore those states can be either ligated or unligated. The partition function for this protein is

+

Q=l+Q,Kl+

Q,K2 Q,Kl K2 1+ K[X] + 1+ K[X]

where Q, is the interaction coefficient between folding unit 1 and folding unit 2 (see, e.g., Freire and Murphy, 1991). The interaction coefficient is determined by the interaction energy, AG,,, between folding units, Q, = exp( - A G J R T ) . If the folding units behave independently, then AG,,, = 0 and Q, = 1. Consider the stability constant for residue B, which is located in folding unit 1, away from the binding site; K~~ can be written as

which is a function of the ligand concentration provided that the interaction coefficient @ is not equal to 1. If the two folding units are indepen-

276

ERNEST0 FREIRE

STATE

STATISTICAL WEIGHT

FIG.8. Schematic illustration of the conformational states of a hypothetical protein consisting of two folding units (1 and 2). Region 2 has a binding site for a ligand. The statistical weights are shown on the right panels. It is demonstrated in the text that the effect of a ligand on the residue stability constants is not limited to those residues located directly in the binding pocket (residue A). In fact, the stability constants for residues that are far away from the binding site (residue B) can also be affected by the presence of the ligand even if binding does not induce a conformational rearrangement. The necessary condition is that they are connected by a path of cooperative interactions to the binding site.

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dent of each other, then Eq. (20) reduces to K~~ = l/Kl and the residue stability constant is equal to the intrinsic statistical weight of that folding unit and independent of ligand concentration. The situation is different if the two folding units are linked by cooperative interactions (i.e., Q, # 1). In this case K p will depend on the ligand concentration in a manner that depends on the magnitude of CP. If the interactions are highly cooperative, such as those in protein folding, then @ 6 1 and KJB increases with ligand concentration. The situation is reversed if Q, > 1. In general, if at high ligand concentrations K [ X ] % K2, then K J B = 1/(Kl@);i.e., the stability constant for residue B becomes larger than the intrinsic statistical weight of that folding unit by an amount that reflects the cooperative interactions of that folding unit with the rest of the protein. The foregoing discussion demonstrates that the effect of ligands is not limited to those residues located directly in the binding pocket; in fact, stability constants for residues that are far away from the binding site can also be affected by the presence of the ligand even if binding does not induce a conformational rearrangement. The necessary condition is that they be connected by a path of cooperative interactions to the binding site. Previously,Hilser and Freire (Hilser et al., 1997) have shown that similar long-range effects occur for amino acid mutations even if the mutations do not induce structural changes. Since a subset of the residue stability constants is directly related to hydrogen exchange protection factors, these results indicate that ligand binding effects should be observed in protection factors that are far away from the binding site. In this respect, Williams et al. (1996) have shown that the binding of anti-lysozyme antibodies to lysozyme does in fact reduce the rate of exchange of amide groups that are distant from the binding epitope despite the absence of any observed changes in the crystal structure.

D. Function-Specijic Probabilities The statistical thermodynamic formalism can also be used to define function-specific probabilities that describe a functional property of a protein. These probabilities are defined in much the same way as other macroscopic averages. For example, the average activity of an enzyme can be expressed by an equation similar to Eq. ( 1 2), where ai represents the degree of activity of state i and where Pi denotes the probability of that state. If certain conformations are assigned certain biological properties, the linkage equations between binding and conformational equilibrium provide a way of quantitatively accounting for a functional

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property. In this case, the limits to functionality are dictated by the same energetic constraints discussed for stabilization.

XI.

Conclusions

The conformational equilibrium in proteins represents a delicate balance within a large ensemble of conformations. The statistical nature of the equilibrium requires a description based upon the tools of statistical thermodynamics. Under a given set of conditions, the protein is characterized by a probability distribution of states in which each state is populated according to its Gibbs energy. The most probable distribution of states in the ensemble can be modulated by ligands in a way that can be predicted by a set of linkage equations. From an energetic point of view, only a miniscule fraction of the ensemble has a reasonable chance of being stabilized to significant population levels by ligand binding. Those conformations are expected to be the ones that are biologically relevant from the point of view of folding and from the point of view of Eunction.

ACKNOWLEDGMENT This work is supported by grants from the National Institutes of Health (RR04328 and GM51362). The author acknowledges many helpful discussions with Dr. VincentJ. Hilser.

REFERENCES Bai, Y., Sosnick, T. R., Mayne, L., and Englander, S. W. (1995). Srimre269, 192-197. Bardi, J. S., Luque, I., and Freire, E. (1997). Biochemistry 36, 6588-6596. D’Aquino, J. A., Gornez, J., Hilser, V. J., Lee, K. H., Amzel, L. M., and Freire, E. (1996). Proteins: Struct., Funct., Genet. 25, 143-156. Freire, E. (1995a). In “Protein Stability and Folding” (B. Shirley, ed.), Vol. 40, pp. 191-218. Humana Press, Totowa, NJ. Freire, E. (1995b). In “Methods in Enzymology” (M. L.Johnson and G. K. Ackers, eds.) Vol. 259, pp. 144-168. Academic Press, San Diego, CA. Freire, E. (1995~).Annu. Reo. Biqbhys. Biomol. Struct. 24, 141-165. Freire, E., and Biltonen, R. L. (1978). Biopolymers 17, 463-479. Freire, E., and Murphy, K. P. (1991).J. Mol. Biol. 222, 687-698. Freire, E., Haynie, D. T., and Xie, D. (1993). Proteins: Stmct., Funct., G a e t . 17, 111-123. Gomez, J., and Freire, E. (1995).J. Mol. Bid. 252, 337-350. Gomez, J.. Hilser, J. V., Xie, D., and Freire, E. (1995). Proteins: Struct., Funct., Genet. 22,404-412. Haynie, D. T., and Freire, E. (1993). Proteins: Struct., Funct., Genet. 16, 115-140. Haynie, D. T., and Freire, E. (1994). Biopolymers 34, 261-271. Hilser, V. J., and Freire, E. (1996).J. Mol. Biol. 262, 756-772. Hilser, V. J., and Freire, E. (1997). Proteins: Stmct., Funct., Genet. 27, 171-183.

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Hilser, V. J., Gomez, J., and Freire, E. (1996).Proteins: Struct., Funct., Genet. 26, 123-133. Hilser, V.J., Townsend, B. D., and Freire, E. (1997).Biophys. Chem. 64, 69-79. Jacobs, M.D., and Fox, R. 0. (1994).Proc. Null. Acad. Sci. U.S.A. 91,449-453. Kim, K.-S., and Woodward, C. (1993).Biochemistly 32, 9609-9613. Kuwajima, K. (1977).J. Mol. Biol. 114, 241-258. Kuwajima, K. (1989).Proteins: Struct., Funct., Genet. 6, 87-103. Loh, S. N.,Prehoda, K. E., Wang,J., and Markley,J. L. (1993).Biochemktly32,11022-11028. Luque, I., and Freire, E. (1997).In “Methods in Enzymology” (in press). LuqLie, I., Mayorga, O., and Freire, E. (1996).Biochemistly 35, 13681-13688. Luque, I., Gomez, J,, Semo, N., and Freire, E. (1998).Proteins: Struct., Funct., Genet. 30, 74-85. Morozova, L. A,, Haynie, D. T., Arico-Muendel, C., Van Dael, H., and Dobson, C. M. (1995).Nut. Struct. Biol. 2, 871-875. Myers,J. K., Pace, C . N., and Scholtz, J. M. (1995).Protein Sci. 4,2138-2148. Peng, Z.-y., and Kim, P. S. (1994).Biochemistry 33, 2136-2141. Radford, S.E.,Buck, M., Topping, K. D., Dobson, C. M., and Evans, P. A. (1992).Proteins: Struct., Funct., Cknet. 14, 237-248. Schulman, B. A,, Redfield, C., Peng, Z., Dobson, C. M., and Kim, P. S. (1995).J. Mol. Biol. 253, 651-657. Shortle, D., and Abergunawardana, C. (1993).Cum Biol. 1, 121-134. Shortie, D., and Meeker, A. K. (1989).Biochemistly 28, 936-944. Swint-Kruse, L., and Robertson, A. D. (1996).Biochaistry35, 171-180. Wang, Y.,and Shortle, D. (1995).Riocherndly 34, 15895-15905. Williams, D. C.,Benjamin, D. C., Poljak, R. J., and Rule, G. S. (1996).J. MoZ. Biol.

257,866-876. Wyman, J. (1948).Adv. Protein Chern. 4, 407-531. Wyman, J. (1964).A d a Protein Chern. 19, 233-286. Wyman, J., and Gill, S. J. (1990).“Binding and Linkage: The Functional Chemistry of Biological Macromolecules.” University Science Books, Mill Valley, CA. Xie, D., and Freire, E. (1994a).Proteins: Struct., Funct., Genet. 19, 291-301. Xie, D.,and Freire, E. (1994b).J. Mol. Biol. 242, 62-80. Xie, D.,Fox, R., and Freire, E. (1994).Protein Sci. 3, 2175-2184.

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ANALYSIS OF EFFECTS OF SALTS AND UNCHARGED SOLUTES ON PROTEIN AND NUCLEIC ACID EQUILIBRIA AND PROCESSES: A PRACTICAL GUIDE TO RECOGNIZING AND INTERPRETING POLYELECTROLYTE EFFECTS, HOFMEISTER EFFECTS, AND OSMOTIC EFFECTS OF SALTS By M. THOMAS RECORD, JR.,12 WENTAO ZHANG,'-* and CHARLES F. ANDERSON' Departments of Chemistry' and Biochemistry: University of Wisconsin-Madison, Madison, Wi 53706

I. Introduction

.....................................................

282

11. Overview of Concentration-Dependent Effects of Perturbing Solutes on

Processes Involving Biopolymers .................................... A. The Thermodynamic Basis for Analyses of Linkage Phenomena . . . . B. Types of Biopolymer Surface and of Interactions with Solutes and Water ....................................................... C. Effects of Solutes on Processes Involving Changes in the Exposure of Biopolymer Surface Area to Water ........................... D. Characteristic Functional Forms of Dependences on Solute Concentration of Equilibrium Constants (Koba)and Transition Temperatures (T,) ........................................... 111. Preferential Interaction Coefficients as Fundamental Measures of Thermodynamic Effects due to Solute-Biopolyrner Interactions ........ A. Background ................................................. B. Uncharged Solutes: Definition of in the Context of Dialysis Equilibrium .................................................. C. Charged Solutes: Preferential Interaction (Donnan) Coefficients for Electroneutral Solute Components and for Single-Ion Species ..... IV. Preferential Interactions of Nonelectrolyte Molecules with an Uncharged Biopolymer ...................................................... A. General Two-Domain Analysis of Preferential Interactions of Nonelectrolytes .............................................. B. Two-Domain Analysis of Interactions of Glycine Betaine with Bovine Serum Albumin (BSA): Preferential Exclusion ................... C. Two-Domain Analysis of Urea-BSA Interactions: Preferential Accumulation ................................................ V. preferential Interactions of Electrolyte Ions with a Charged Biopolymer . . . A. Nucleic Acids as High-Charge Density Cylindrical Polyanions: The Physical Origin of the Polyelectrolyte Effect ..................... B. Distinctive Functional Forms of Preferential Interaction Coefficients for Nucleic Acid Polyelectrolytes and Oligoelectrolytes in 1:l Salt Solutions .................................................... C. Two-Domain Interpretation of Single-Ion and Salt-Component Preferential Interaction Coefficients for Interactions of Electrolytes with Weakly Charged Biopolymers (Hofmeister Salt Effects) . . . . . . .

r5.*

286 286 288 29 1 292 295 295 299 300

303 303 307 309 31 1 31 1

312

317

* Present address: Division of Biochemistry & Molecular Biology, University of CaliforniaBerkeley, 401 Barker Hall, Berkeley, CA 94720-3204. 281 ADVANCES IN PROYEIN CHEMI,STRY, Vol. 51

Copyright 0 1998 by Academic Press. Ail rights of reproduction in any form reserved. 0065-3233/98$25.00

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VI. Use of Three-Component Preferential Interaction Coefficients to Analyze Effects of Solute Concentration on Equilibrium Constants, Transition Temperatures, or Free Energy Changes of Biopolymer Processes . . . . . . . A. Thermodynamic Fundamentals ................................ B. Definition of the Experimentally Observable Equilibrium Constant Kubsand Its Dependence on Solute Activity for Macromolecular Associations ......................................... C. Effects of Changing the Concentration of an Uncharged Sol Equilibria of Uncharged Biopolymers ............................ D. Effects of Changing the Concentration of an Electrolyte Solute on Equilibria of Charged Biopolymers .............................. E. Description of Solute Concentration Effects on AG for a Macromolecular Process ....................................... VII. Two-Domain Predictions of Functional Forms of Effects of Nonelectrolyte Concentration on Equilibria (Kob,)and Transition Temperatures (’&,,) of Uncharged Biopolymers in Aqueous Solution . . . A. Effects on Koh of Addition of a Nonelectrolyte Solute Which Is Completely Excluded from the Local Domains of Water of All Polymeric Reactants and Products . . . . . . . . . . . . . . B. Effects on KO&of Addition of a Nonebctrolyte Solute Weak Accumulated in (or Incompletely Excluded from) the Local Domains of Some or All Polymeric Reactants and Products . . . . . . . . . . . . . . . . C. Effects on T,, of a Biopolymer Conformational Transition from Addition of a Nonelectrolyte Solute ............................... VIII. Polyelectrolyte and Two-Domain Predictions of Functional Forms of Effects of Salt Concentration o n Equilibria (Kabl)and Transition Temperatures (’&,,) of Charged Biopolymers in Aqueous Solution . . . A. General Expressions . . . . . . . . . . B. Approximate Analytical Expressio Form and the Key Variables Determining the Magnitude of the Salt Concentration Dependence of Koh.for Binding of Oligocationic Ligands and Proteins to Nucleic Acid Polyions . . . . . C. Analysis of Effects of Salt Con (T,,) of Nucleic Acid Helices IX. Conclusions and Future Directions ................................. References .......................................................

319 319

319 321 322 324

326

326

327 328

330 330

33’2 344 347 350

I. INTRODUCTION Fifty years have passed since the first of two profoundly influential reviews was contributed byJeffries Wyman to Advances in Protein Chemist?. In the earlier article (Wyman, 1948) basic principles of linked thermodynamic functions are applied to analyze the interrelated effects of variations in the thermodynamic activities of ligands on the Orbinding, conformational, and association-dissociation equilibria of heme proteins. A more comprehensive account of thermodynamic relationships pertaining to various types of linkage phenomena is presented in the later article (Wyman, 1964). Together, Wyman’s reviews effectively formed a

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

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basis for many further developments and applications of linkage principles to analyze solute concentration-dependent effects on various kinds of biopolymer processes. Such studies can yield valuable insights about relationships between structure and function in living systems, as Wyman (1948) was among the first to point out. Cellular processes of course occur at the constant temperature and pressure of the intracellular environment. In vivo control of the extents or rates of these processes therefore cannot involve changes in temperature and pressure as regulatory variables. Instead, cellular processes are controlled by covalent modifications or by changes in concentrations of biopolymers, ligands, other solutes, and/or water, which affect the thermodynamic activities of components in the final (product) and/or initial (reactant) states of the process. In particular, ligand and solute concentrations as control variables constitute a perhaps mundane but nonetheless profound “vital force” for the regulation of both covalent (enzyme-catalyzed)and noncovalent processes in vivo. These regulatory phenomena can be investigated both in vitro and in vivo by applying linkage principles to analyze the appropriate experimental input. The thermodynamic framework developed by Wyman was originally intended for, and subsequently has been applied primarily to, analyses of equilibria affected by the site binding of one or more types of ligands to proteins, such as hemoglobin, that have a small net charge at physiological pH. Some effector ligands are uncharged, or if charged [e.g., H’, biphosphoglycerate (BPGV4-)] they are investigated at relatively high dilution in a solution containing excess 1:l salt. For such systems under typical experimental conditions, linkage expressions pertaining to uncharged biopolymers and solutes may suffice. However, such expressions are not applicable as a basis for the quantitative analysis and interpretation of effects due to changes in the concentration of salt (or of ionic ligands present at high concentration) on processes involving charged biopolymers (Record et aL, 1976, 1978). In reviewing the expressions needed to analyze linkage effects such as the solute-concentration dependences of biopolymer equilibria, we emphasize that these expressions can exhibit significant (perhaps surprising) differences, depending on whether the solute and biopolymer are charged or uncharged. Substantial solute effects on biopolymer processes are observed also in systems where the solute does not bind with high affinity to sites on the biopolymer. We designate these solutes as perturbing solutes, because they affect the biopolymer process without being a direct stoichiometric participant (i.e., reactant or product). Perturbing solutes may be nonelectrolytes (e.g., urea, glycerol, sugars, and other polyols), dipolar ions (e.g., glycine betaine, proline, and other amino acids), or electro-

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lytes [e.g., common salts, guanidinium chloride and the spectrum of “Hofmeister salts”; see von Hippel and Schleich (1969a,b)]. “Preferential interactions” (relative to water) of these perturbing small ions or uncharged solutes with the accessible surface of a biopolymer afYect its nonideality to an extent depending on the concentration of the perturb ing solute and hence cause any equilibrium involving the biopolymer to depend on the concentration of this solute. In a review that immediately follows Wyman’s (1964) incisive “second look” at linked functions, Casassa and Eisenberg (1964) provide a comprehensive account of the thermodynamic relationships needed to analyze the results of various experimental methods of characterizing preferential interactions in multicomponent biopolymer solutions, particularly those containing polyelectrolyte and excess electrolyte components. Timasheff and collaborators (see the last chapter in this volume) have investigated the preferential interactions of proteins with a wide variety of nonelectrolyte and electrolyte solutes (including osmolytes, Hofmeister salts, and other solutes of biochemical interest). Coulombic preferential interactions of salt ions with high-charge density polyelectrolytes such as nucleic acids produce nonuniform distributions of these ions in the vicinity of the polyanion surface and cause processes involving polymeric nucleic acids to exhibit very large dependences on salt concentration, which extend to low salt concentration and display a characteristic functional form unlike those that describe most other effects of ligands or solutes on biopolymer processes. These molecular and thermodynamic effects of coulombic interactions can be described with reasonable accuracy by Monte Carlo (MC) simulations for relatively simple structural models (see Anderson and Record, 1990, 1995, for reviews). At least for nucleic acids and 1:l salts, under typical conditions of interest the more approximate Poisson-Boltzmann (PB) analytic polyelectrolyte theory agrees well with MC simulations for the same structural model. The success of these theoretical approaches can be attributed largely to the predominance of coulombic interactions between the salt ions and the polyion over other types of interactions (such as those involving water) that are more difficult to describe accurately in terms of painvise additive interaction potentials. Manning (1969) introduced a counterion condensation hypothesis to obtain a set of analytic limiting law (low salt) expressions for thermodynamic coefficients in solutions containing a cylindrical polyelectrolyte and excess salt. These expressions, subsequently validated as limiting laws by more general PB and MC thermodynamic analyses (Anderson and Record, 1983; Mills et aL, 1986), allowed the explicit incorporation of key polyelectrolyte structural variables (especiallyaxial charge density)

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into analytic thermodynamic descriptions of the effects of salt concentration on nucleic acid denaturation (Manning, 1972) and on oligocationnucleic acid binding (Record et al., 1976).This approach was developed further to arrive at a more general formulation of the salt concentration dependence of biopolymer equilibria that incorporates not only coulombic salt ion-polyion interactions but also ion binding interactions and osmotic effects due to the thermodynamic linkage of salt and water activities (Record et al., 1978). This chapter expands the foundations and updates aspects of this comprehensive review of effects of salt concentration on protein and nucleic acid processes. We summarize the current status of the thermodynamic formulation whereby effects of changes in the concentration of a perturbing solute on biopolymer equilibria, in general, and salt effects on equilibria involving nucleic acids, in particular, are analyzed on the basis of thermodynamic linkage and interpreted in terms of preferential interactions (accumulation, exclusion) of solute ions or molecules vs. water. Polyelectrolyte, Hofmeister, and osmotic effects of salt on these equilibria and processes all exhibit different dependences on the concentration and/or nature of the salt ions. These three fundamentally different classes of effects of changes in salt concentration on equilibria (characterized by equilibrium quotients Koh) and on conformational transitions (characterized by midpoint temperatures, T,,) of nucleic acids and proteins are the primary focus of this article. In brief, “polyelectrolyte effects” of salt concentration, as exhibited by conformational and binding equilibria involving polyanionic nucleic acids, are relatively independent of the nature of the salt, except for the valences of its constituent ions, especially the cation (i.e., the counterion), and are most clearly manifested in solutions containing low to moderate concentrations of excess salt. “Hofmeister” salt effects on conformational and binding equilibria involving proteins and other biopolymers (see von Hippel and Schleich 1969a,b;Collins, 1996; Baldwin, 1996) depend critically on both the nature and concentration of the salt ions (especially the anion) and are most clearly manifested in solutions containing moderate to high salt concentrations. Changes in salt concentration also affect equilibria involving proteins and/or nucleic acids by changing the thermodynamic activity of water. These osmotic effects, which become significant at high concentrations of any salt, typically in the molar range, depend only on the thermodynamic activity of the salt and hence are otherwise independent of its chemical nature. As defined, none of the three effects involve any strong noncoulombic binding interactions of salt ions with the biopolymer participants, nor can any of them be analyzed rigorously using “ionic strength” as a composition variable.

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A primary objective of this review is to illustrate and explain how polyelectrolyte, Hofmeister, and osmotic effects can be analyzed on the basis of thermodynamic linkage principles, interpreted in terms of molecular models, and-where feasible-simulated in detail by calculations that incorporate the molecular information needed to characterize preferential interactions. We present both established and novel expressions, based on differences in preferential interactions, that can be used to quantify effects of solutes on various biopolymer processes. The intent here is to clarify the general physical and mathematical principles with selected examples, rather than to present a comprehensive survey of results that have been reported for numerous individual systems. Section I1 provides a qualitative overview of the magnitude and significance of effects of perturbing solutes on processes involving biopolymers and motivates the subsequent quantitative treatment. Section I11 and references therein provide more detailed commentary on the definitions and physical significances of preferential interaction coefficients in solutions containing a biopolymer and a relatively small solute, present in large excess. Sections IV and V review the characteristics of preferential interaction coefficients as measures of the thermodynamic consequences of interactions of solute molecules or ions with biopolymers, uncharged and charged. Sections VI-VIII provide a practical guide to the use of preferential interaction coefficients to analyze effects of perturbing solutes on equilibria and processes involving biopolymers. In particular, Section VIII focuses on the significant distinctions between polyelectrolyte, Hofmeister, and osmotic effects of salt concentration on processes involving proteins and nucleic acids, and provides a prescription for separating and individually quantifjmg these effects on systems where they occur together, as is often found at least for Hofmeister and osmotic effects of salt concentration.

EFFECTSOF PERTURBING 11. OVERVIEW OF CONCENTRATION-DEPENDENT SOLUTES ON PROCESSES INVOLVING BIOPOLYMERS

A. The Thermodynamic Basis for Analyses of Linkage Phenomena The term “linkage,” as used by Wyman, refers to the mathematical interdependence of thermodynamic functions, in general, and chemical potentials, in particular. For each ion or molecule in a solution, the corresponding chemical potential is a different function of the same set of variables, such as molalities, that specify composition. Consequently, a change in any of these composition variables at constant temperature

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and pressure produces linked changes in the chemical potentials of all constituents of the solution (including water), and concomitant linked changes in any equilibria established among these species. For the purpose of analyzing and interpreting different types of molecular effects manifested by various kinds of linkage, substantial advances have been made, and continue to be, in developing the thermodynamic formulation, the statistical mechanical underpinning, and the associated molecular theory. Thorough accounts of much of this progress have been given in recent books (Wyman and Gill, 1990; Di Cera, 1995). Section V ofwyman’s earlier (1948) review presents a concise summary of relationships that can be used to analyze, for example, the pH dependence of hemoglobin oxygenation. This “Bohr effect” is representative of a large-but not the only-class of biologically significant linkage phenomena. Another common type, considered in Wyman’s later review (1964), is manifested when an equilibrium is driven toward reactants or products by changing the concentration of a perturbing solute that is present in large excess but is not itself a reactant or product. If this solute produces different effects on the stoichiometric combinations of reactant and product activitycoefficients,then a change in concentration of the perturbing solute will shift the reactant-product equilibrium. For systems where none of the solute species bears a net charge, Wyman’s (1964) review includes analyses of two types of solute concentration-dependent effects on a complexation equilibrium of the type A + B AB. In Section 4 of that review, the response of this equilibrium to a change in the thermodynamic activity of a strongbinding uncharged solute (ligand) is attributed entirely to a change in the number of ligands bound to A and/or B as AB is formed. Therefore, the resulting expression [Wyman’s Eq. (4.5)] does not allow for the possibility that any of the activity coefficients of the reactant or product species could depend on the ligand concentration as a result of interactions with unbound ligands. Section 7 of Wyman (1964) addresses the more general situation where any type of preferential interactions between solute molecules and the uncharged participants in the complexation equilibrium may determine its sensitivity to a change in the solute activity. As a result of an uncharged solute binding to and/or its solvent-mediated interactions with A, B, and/or AB,Wyman’s Eq. (7.5) shows that the response of the complexation equilibrium to a change in the thermodynamic activity of the perturbing solute can be described in terms of preferential interaction coefficients. For the case where the interacting sites on A and B are charged and where the perturbing solute is an electrolyte, Record et al. (1976, 1978) used a polyelectrolyte and binding-polynomial analysis to obtain a distinctivelydifferent expres-

*

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M. THOMAS RECORD, JR.,ET AL.

sion from that presented by Wyman (1964) for the nonelectrolyte case. Anderson and Record (1993) developed a more general thermodynamic analysis of effects on the association of A and B due to changes in the concentration of excess salt. The equation describing these effects is expressed in terms of three-component preferential interaction coefficients that characterize the interactions of the perturbing solute with each of the individual participants in the complexation reaction (A, B, and AB, which may be either charged or net neutral). Defined explicitly in Section I11 below, preferential interaction coefficients, which can be represented as partial derivatives in various ways (Eisenberg, 1976), are the basic elements in a complete description of linkage effects manifested by the solute-concentration dependence of any type of biopolymer equilibrium, as reviewed in Sections VI-VIII below. Under typical experimental conditions (when the perturbing solute is in large excess over the biopolymer) , each of these preferential interaction coefficients can be recast either in a form that can be calculated independently from the relevant intersolute potentials, or in a form that can be evaluated by some experimental technique (Anderson and Record, 1993, 1995). To date, rigorous a priori theoretical calculations of preferential interaction coefficients for models intended to describe systems of biological interest have been reported only for coulombic interactions between charged biopolymer and solute species in solution (Olmsted et al., 1991; Bond et al., 1994; Zhang et al., 1996a). The characteristics of solute-biopolymer interactions that determine the sign, magnitude, and solute-concentration dependence of a preferential interaction coefficient also determine the dependence on solute concentration of processes and equilibria involving the biopolymer. Thus, to understand the physical bases for these effects, experimental and theoretical characterizations of preferential interactions are essential.

B. Types of Biopolymer Suqace and of Interactions with Solutes and Water Noncovalent folding, association, and binding interactions of biopolymers (proteins and nucleic acids) in water typically bury many hundreds or thousands of square angstroms of previously water-accessible biopolymer surface. For association or binding interactions, this burial of the surface often occurs both in the contact interface and in coupled folding or other conformational changes that in many cases create parts of that interface. In these processes, noncovalent interactions between the biopolymer surface and water and/or solutes are replaced by biopolymer-biopolymer interactions. The consequences of this exchange of interactions determine both the thermodynamics of the process and the

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effects of changing the concentration of a perturbing solute on the thermodynamics. As general background about the physical factors that determine effects of solute concentration on processes involvingproteins and nucleic acids, we review in this subsection some relevant characteristics of biopolymer surfaces and in the next (Section I1,C) some observable consequences of changes in the amount of solvent-accessiblebiopolymer surface area that are induced by changes in solute concentration. Biopolymer surface may be classified as nonpolar (C), polar (uncharged N, 0, S), or charged. According to model calculations based on this classification, the water-accessible surface of the average native protein is primarily nonpolar (55% nonpolar, 30% polar, and 15% charged; Miller et al., 1987), whereas the water-accessible surface of the DNA double helix is primarily charged (45% charged, 39% nonpolar, and 17%polar; Alden and Kim, 1979). A highly charged polyelectrolyte, such as polymeric helical DNA, has both a large number and a high average axial density of like charges. In contrast, a weakly charged polyelectrolyte or polyampholyte has a smaller density (and number) of total and net charges, as do most proteins. Processes that effectively reduce the axial charge density of nucleic acid polyanions, including conformational changes (e.g., DNA denaturation) and the association of ligands with complementary, positively charged binding surfaces, become increasingly favorable with decreasing salt concentration as a result of changes in the thermodynamic effects of salt ion-polyion (coulombic) preferential interactions. These effects can be predicted or analyzed on the basis of fundamental linkage relationships with input from the appropriate polyelectrolyte theory. The characteristic functional forms and large magnitudes of the effects of salt concentration on transition temperatures ( T , ) and equilibrium quotients (Kob) of nucleic acid processes at low salt concentration provide a unique thermodynamic signature, called the polyelectrolyte effect, which is one principal focus of the present chapter. Reductions in the amount of nonpolar biopolymer surface exposed to water (by coalescence with other nonpolar surface) are intrinsically favorable (Reynolds et al., 1974; Richards, 1977) and exhibit another distinctive thermodynamic signature called the hydrophobic effect (a large negative AG and its consequences for AH", AS",AGO, and Kob) (e.g., see Tanford, 1980; Spolar and Record, 1994, and references therein). When the exposure of polar biopolymer surface to water is reduced by pairing with complementary polar surfaces, hydrogen bonds to water are replaced by hydrogen bonds to complementary polar groups. Neither the thermodynamics of the interactions of biopolymer surface with water nor the effects of the nature or concentration of solutes on

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processes that change the amount of water-accessible nonpolar or polar biopolymer surface can be calculated a priori using molecular theory with the same level of accuracy as can polyelectrolyte effects of salt concentration on processes involving highly charged biopolymers. The latter effects are due primarily to coulombic interactions and therefore do not require construction of reliable pair potentials for the interactions between water molecules and various kinds of surface areas on biopolymers. Even without such detailed microscopic information, the role of biopolymer solvation in determining the sign and magnitude of preferential interaction coefficients can be interpreted using the two-domain model, as reviewed in subsequent sections. Local concentrations of small solutes at the surface of a biopolymer in dilute aqueous solution generally differ significantly from their bulk or average values, because preferential interactions cause the solute to be partitioned unequally between bulk water and the local water of hydration surrounding the biopolymer surface. Accumulation or exclusion of a solute near a biopolymer surface can be quantified by comparing the local and bulk values of the ratio of moles of solute to moles of water. If the mole ratio of local solute to water exceeds that of the bulk solution, the solute is said to be accumulated. The frequently large thermodynamic consequences of solute accumulation in, or exclusion from, the local domain (which appears to correspond to a monolayer of water of macromolecular hydration; see Zhang et al., 1996b, and references therein) are described by solute-polymer preferential interaction coefficients, which are the principal thermodynamic functions of interest in this chapter. Dramatic examples of preferential interactions at the molecular level are provided by accumulation of cations near, and exclusion of anions from, the surface of a highly charged polyanion such as double-helical DNA. At a bulk salt concentration of 1 mM, polyelectrolyte theories predict that the local concentration of a univalent cation exceeds 1 M. In contrast, the local concentration of a univalent anion near DNA is predicted to be less than 1 p M . [These predictions are consistent with PB analyses of scattering measurements (Wu el al., 1988; Chang et al., 1990; Groot et al., 1994).] Because Kf and putrescine2+ions in solution are accumulated near nucleic acid surfaces, they are highly effective perturbants of nucleic acid processes in vitro (e.g., see Capp et al., 1996, and references therein). Surprisingly, amounts and free concentrations of Kt and putrescine in the cytoplasm of Escherichia coli vary over wide ranges in response to changes in growth osmolarity without affecting most intracellular processes. This seemingly paradoxical in uiuo situation, and possible explanations for it, have recently been reviewed (Record

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et al., 1998). Other osmotically regulated cytoplasmic solutes of E. coli (e.g., glutamate, trehalose, proline, or glycine betaine) are excluded to some extent from the local water of hydration of protein surface (Arakawa and Timasheff, 1982; Low, 1985; Zhang et al., 199613).Of these, the apparently high degree of exclusion of glycine betaine is thought to be correlated with its action as the most effective “osmoprotectant” [i.e., the solute whose presence in the cytoplasm results in the highest growth rate at high osmolarity (Cayley et al., 1992; Record et al., 1998)l.

C. Effects of Solutes on Processes Involving Changes in the Exposure of Biopolymer Suqace Area to Water In vitro, ion or nonelectrolyte solute concentrations are key variables that influence both covalent and noncovalent processes involving biomolecules. Changes in the concentrations of these solutes in general affect the thermodynamic activities of both water (the osmotic effect) and biopolymers (preferential interactions). In a process (e.g., conformational change, association or dissociation, or ligand binding) that transforms a biopolymer from an initial to a final state, the difference in the extent of solute accumulation or exclusion between the final and initial states (closelyrelated to the difference in solute-biopolymer preferential interaction coefficients) provides a quantitative prediction of the effect of solute concentration on the observed free energy difference between the final state and the initial state, and hence on the equilibrium extent of conversion of those states. Differences in preferential interactions are of fundamental importance as determinants of the direction and driving force for any process that entails a change in the amount and/or molecular nature of the biopolymer surface in contact with the solution. Such processes therefore may be regulated as effectively by changes in the concentration (and hence the thermodynamic activity) of accumulated or excluded solute as by changes in the concentration of a ligand that can bind strongly to sites on one or more of the participants in the process. Effects of salt concentration on processes involving polyanionic nucleic acids are especially large. For example, midpoint temperatures ( T , ) of conformational transitions and equilibrium concentration quotients ( Kobs)of ligand-binding interactions of polymeric nucleic acids are strongly affected by changes in concentrations of K+, Mg’+, or polyamine salts even when these are at very low concentrations (50.01 M ) (see the reviews by Record et al., 1978, 1981, 1991; Record and Spolar, 1990; Lohman and Mascotti, 1992). Small changes in the concentrations of either K+ or putrescine in this range have very large effects on protein-

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DNA binding equilibria (e.g., see Capp et al., 1996, and references therein). Smaller but still very significant effects of changes in salt concentration in this low salt range are observed on processes involving short nucleic acid oligoelectrolytes (Olmsted et al., 1991; Zhang et al., 1996a). At relatively high concentrations (>0.1 M) , most solutes (whether electrolytes or nonelectrolytes) have a perturbing effect, which may be stabilizing or destabilizing, on the conformational transitions and binding interactions of all types of biopolymers. For electrolytes, these are called Hofmeister effects (see von Hippel and Schleich, 1969a,b;Arakawa et al., 1990; Collins, 1996; Baldwin, 1996, and references therein). Processes which increase the amount of protein surface exposed to the electrolyte solution (including dissolving and unfolding a native protein and dissociating a multimeric protein assembly) all exhibit similar rank orders of effects of different anions and cations. Compared at a fixed salt concentration, locally accumulated anions like I- or Br- favor processes in which additional protein surface is exposed to water, whereas locally excluded anions like F- favor processes that reduce the amount of protein surface exposed to water. Changes in the nature or concentration of the anion typically have more significant effects than do changes in the nature or concentration of the cation. In general, effects of high solute concentrations on biopolymer processes can have several origins. Increasing the concentration of any solute above 0.1 M (i.e., increasing the osmolarity of the solution) significantly reduces the thermodynamic activity of water, and thereby favors processes in which water of hydration is displaced from biopolymer surfaces (Tanford, 1969; Record et al., 1978; Colombo et al., 1992; Timasheff, 1993; Parsegian et al., 1995; Record and Anderson, 1995, and references therein). The analysis of solute concentrationdependent effects on such processes is particularly simple when the solute is completely excluded from the vicinity of both product and reactant biopolymer surfaces, in which case only the osmotic effect of the solute (i.e., its effect on water activity) is involved. If the solute is not completely excluded from both products and reactants, then changes in its preferential interactions in the process must also be taken into account. Quantitative treatments of effects on biopolymer processes of both excluded and accumulated perturbing solutes are reviewed in Sections VI-VIII. D. Characteristic Functional Forms of Dependences on Solute Concentration of Observed Equilibn'um Constants (Koba)and Transition Temperatures (T,n)

Changes in the concentration of a perturbing solute (or ligand) cause variations in the stoichiometric quotients of product and reactant con-

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centrations (Kobs)that characterize biopolymer equilibria and in midpoint transition temperatures ( T,) that characterize biopolymer conformational changes. The dependences of these thermodynamic variables on solute concentration exhibit a variety of characteristic functional forms and magnitudes, especially when the perturbing solute concentration is relatively low (4 1 M) .These functional forms depend on whether the solute is a nonelectrolyte or electrolyte and on whether the regions of the biopolymer affected by the conversion of reactants to products are part of a high-charge density polyelectrolyte (such as DNA) or are part of a low-charge (and/or low-charge density) short oligonucleotide, short oligopeptide, or protein. The dependence of Kobson solute concentration is particularly simple when the solute is a strongly site-bound ligand L, which binds to different numbers of sites on the reactants and products of a biopolymer equilibrium. If the ligand concentration is sufficiently large so that all the binding sites are fully saturated but is still small enough so that nonligating interactions of unbound solute molecules with products or reactants make negligible contributions to the solute-concentration dependence of & , s , then Kobsexhibits a power-law dependence on ligand activity uL (Kobs u ! “ ~ ) ,where uL may often be approximated by the free ligand concentration. Here the exponent ANL is the (stoichiometrically weighted) difference between the numbers of ligand-binding sites on the biopolymer product(s) and reactant(s). For this situation, In Kobs is a linear function of In uLwith slope ANL. At low enough ligand activities, the ligand-binding sites on one or more of the biopolymer participants in the equilibrium of interest will not be saturated and the power-law dependence of K o b s on ul. will no longer be observed. In contrast to this effect of a strongly site-bound ligand, consider processes involving only uncharged (or weakly charged) biopolymers, perturbed by a solute that does not site-bind but is locally accumulated at or excluded from the surface(s) of reactants or products. If the amount of biopolymer surface area that interacts with this solute changes in the process, then In K o b s for the corresponding equilibrium typically is found to be an approximately linear function of the concentration or activity of this perturbing solute. At low concentrations of the perturbing solute (below -0.1 M ) , the variation of &,,with solute concentration is typically undetectably small. “Hofmeister” effects of the nature and concentration of salts on protein processes exhibit this behavior. Another contrasting example of a solute effect is provided by processes involving only small ionic species with small numbers of charges, investigated in the presence of an excess of a 1:l electrolyte. Use of the Debye-Hiickel approximation [in linearized Poisson-Boltzmann (PB) theory] predicts

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that In Kohsvaries linearly with the square root of the ionic strength (i.e., with the square root of the 1:l salt concentration). This effect is predicted to become undetectably small at low salt concentrations. In striking contrast to both Hofmeister and Debye-Huckel effects of salt concentration on Kobsfor processes that involve low-charge density or weakly charged species, equilibria in which the axial charge density of highly charged nucleic acid polyions is locally or globally affected exhibit strong power-law dependences of Kobron salt concentration (typically investigated over a portion of the range 10-3-10-’ M ) . The exponents characterizing these power-law dependences often are large in magnitude and relatively constant over the range of low salt concentrations investigated. In these situations, In Kohs is a strong and approximately linear function of the logarithm of the salt concentration (or activity),and the effect of a given percentage change in salt concentration is almost equally large over the entire experimentally accessible range. Even though the ions of the salt do not site-bind to the nucleic acid (cf. Braunlin, 1995, for a review), the magnitude and functional form of the salt concentration dependence of Kohsare equivalent to the effects on Kohs that would be expected to be produced by changes in the concentration of a ligand that is bound with high affinity and high stoichiometry to sites on the higher axial charge density state of the nucleic acid and is displaced in any process which reduces that axial charge density locally (e.g., by oligocation binding) or globally (e.g., by strand dissociation). These effects of salt concentration on equilibria involving polyanionic nucleic acids are therefore distinct from Hofmeister and Debye-Huckel (ionic strength) salt effects, both in their functional form and in their persistence at low salt concentrations. Even in systems where the concentration of some excess 1:l electrolyte is numerically indistinguishable from the ionic strength, as calculated by the classic Debye-Huckel formula, salt effects on biopolymer equilibria cannot be analyzed accurately on the basis of Debye-Huckel (linearized PB) theory. Ionic strength should never be assumed to be a relevant composition variable for interpreting polyelectrolyte, Hofmeister, and osmotic effects of salt concentration on biopolymers, because all these effects result from preferential interactions that cannot be accurately approximated by Debye-Huckel theory. The use of “ionic strength” as a composition variable in analyzing salt effects on biopolymer equilibria has no fundamental theoretical basis and therefore can lead to serious quantitative errors. For example, two solutions-one containing NaC1, the other MgCl,-at equal ionic strengths are not equivalent with regard to the effects that are produced by these strong electrolytes of different charge types on processes involving biopolymers (see, e.g., Record et al., 1977, 1978, 1981; Lohman, 1985).

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Conformational transitions of high-charge density nucleic acid polyions and of weakly charged globular proteins exhibit characteristic differences in the effects of salt concentration on midpoint temperatures, T,. The effect of salt concentration on order-disorder transitions (denaturation) of nucleic acids persists even at very low (lo-* M) salt concentration (e.g., Record, 19’75).For a variety of order-disorder transitions that reduce the average axial charge density of polyanionic nucleic acids, T, is found to increase linearly with the logarithm of the concentration (or mean ionic activity) of the salt, from M to concentrations in the range 0.1-1 M (e.g., Krakauer and Sturtevant, 1967;Privalov et al., 1969). By contrast, Hofmeister effects of salts on T, for the denaturation of globular proteins become significant only above -0.1 M, and T, exhibits an approximately linear, rather than logarithmic, dependence on salt concentration [increasing or decreasing, depending on the nature of the salt (von Hippel and Schleich, 1969a,b;Baldwin, 1996,and references therein)]. At salt concentrations above 1 M, where polyelectrolyte behavior is suppressed by screening of coulombic interactions, salt effects on DNA denaturation analogous to the Hofmeister salt effects on protein denaturation are observed (Hamaguchi and Geiduschek, 1962). In summary, ligand-binding equilibria and conformational transitions of nucleic acid polyelectrolytes exhibit characteristic functional forms and magnitudes of dependences of Kobsor T, on electrolyte concentration, which differ significantlyfrom those observed for the corresponding processes involving short nucleic acid oligoelectrolytes, protein polyampholytes, or small ions. These differencesjustify the applicability of the term “polyelectrolyte effect” (Record et aL, 1991; Zhang et aL, 1996a) to describe the characteristic thermodynamic signature (i.e., the typically large magnitude and distinctive functional form) of the effect of salt concentration on processes that affect the axial charge density of polyanionic nucleic acids. This usage parallels that of the term “hydrophobic effect,” which describes the distinctive thermodynamic signature (i.e., the large IACil and its consequences for AH”, AS”, AGO, and Kob) of processes that alter the amount of nonpolar surface exposed to water (Tanford, 1980; Spolar and Record, 1994). 111. PREFERENTIAL INTERACTION COEFFICIENTS AS FUNDAMENTAL MEASURES OF THERMODYNAMIC EFFECTS DUE TO SOLUTE-BIOPOLYMER INTERACTIONS A.

Background

The definitions, thermodynamic relationships, and molecular interpretations of preferential interaction coefficients,represented in various

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forms, have been extensively discussed from various perspectives (Eisenberg, 1976; Schellman, 1990; Timasheff, 1992; Record and Anderson, 1995). Experimental determinations of these coefficients have been implemented using different kinds of thermodynamic control variables and constraints (Timasheff, 1992, 1993; Eisenberg, 1994; Schellman, 1990; Zhang et al., 1996b, and references therein). In uitro methods have been applied generally to an aqueous solution containing a biopolymer and an excess of some relatively small perturbing solute, in order to evaluate the solute-biopolymer preferential interaction coefficient pertaining to the limit of infinite dilution of the biopolymer over a range of solute concentrations. Knowledge of the sign, magnitude, and concentration dependence of a preferential interaction coefficient forms a firm basis for constructing physical interpretations and for testing theoretical calculations of the observable effects of solute-biopolymer interactions (Schellman, 1990; Timasheff, 1992; Record and Anderson, 1995; Anderson and Record, 1995, and references therein). These coefficients also provide the most direct route to analyzing and interpreting how changes in the concentration of the perturbing solute (which may also act as a ligand) cause changes in the equilibrium distribution of reactants and products in processes involving biopolymers (Wyman, 1964; Record et al., 1978; Anderson and Record, 1993, 1995; Record and Anderson, 1995). The simplest and most frequently investigated type of system that exhibits preferential interactions contains only three components: solvent water (component 1); a dilute solute (component 2), consisting of either an uncharged biopolymer or a charged biopolymer together with a charge-balancing number of oppositely charged small ions; and a solute (component 3) of much lower molar mass, consisting of either molecules or dissociated salt ions that are much more abundant than the biopolymer in solution. [The physically uninformative numerical designations 1,2,3,which were introduced by Scatchard (1946), have become conventional (Eisenberg, 1976)l. Here component 2 generally is referred to as a polymer, but the discussion in the following sections pertains equally well to systems where it is an oligomer, or any other type of nondiffusible solute whose concentration is sufficiently dilute in comparison to that of component 3. Thermodynamic analyses and molecular interpretations can be constructed most readily for the preferential interaction coefficient defined as the following partial derivative (Anderson and Record, 1993; Record and Anderson, 1995).

r,q*=mlim (~m,/~m,)T,P,,, e 0

(1)

In Eq. ( l ) ,m3 and m2 are the molal analytical concentrations of solute

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297

and biopolymer, respectively, and p3 is the solute chemical potential. Henceforth in this article the superscript “0” denoting the limit of infinite dilution of component 2 will not be shown, because in all situations of interest here m2 is sufficiently dilute that the limiting value of r 3 , 2 , which does not depend on m2, has been attained. [The constraints of constant temperature (T) and pressure (P) also are subsequently not explicitly indicated except where necessary for clarity.] The definition of r3,2 given by Eq. (1) may not appear obviously related to solutebiopolymer interactions. The connection may be clarified by recognizing that, although in general m3and m2could be varied independently, the constraints specified by the partial derivative that defines r 3 , 2 [Eq. (1)] require that m3and m2must be changed together in a way that maintains the constancy of p3 at constant T and P. Consequently, this coefficient reflects all concentrationdependent sources of nonideality due to solute-biopolymer interactions, ranging from site binding to the weaker interactions that cause the local concentration of mobile solute ions or molecules near the biopolymer surface to differ from the corresponding bulk concentration. Particular values of r 3 . 2 can be interpreted at the molecular level in terms of the “twodomain” model (e.g., see Timasheff, 1992;Record and Anderson, 1995) depicted schematicallyin Fig. 1,where for simplicity the biopolymer is shown as a sphere. The two domains are a “local” region of solution surrounding the surface of each biopolymer, and a “bulk” region whose thermodynamic characteristics are defined on the basis of the fundamental properties of a macroscopic membrane dialysis equilibrium (Record and Anderson, 1995). Mathematical details of the twodomain model for nonelectrolyte and electrolyte solutes are reviewed in Sections N a n d V, respectively. If a solute is preferentially accumulated in the local domain relative to its concentration in the bulk, r3,* is positive. In this case, according to Eq. (I), addition of biopolymer to a solution containing an accumulated solute requires concomitant addition of the solute (i.e., an increase in m3)to maintain the constancy of its chemical potential ( p 3 ) Negative . values of I?3,2 indicate preferential exclusion of solute (preferential solvation) so that its local concentration is less than its bulk concentration. In this case, addition of biopolymer would require a concomitant reduction in m3to keep p3constant. For the (uncommon) situation where the local and bulk solute concentrations happen to be identical, r3,2 = 0. This quasi-ideal condition does not imply the absence of solute-biopolymer interactions, but rather that they are effectively balanced by solvent-biopolymer interactions. Such a balance cannot persist at all compositions of a real solution.

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4

-

-

0

'

Localdomain

\

\

n

I II

\

,o /

I

. \

/

\

\ I I I

Biopolymer

\

\

\

B3solute molecules B, solvent molecules

bulk

bulk

Bulk domain: n3 moles solute; n, moles solvent /

0

/

-

. \

Localdomain

/

I I I \

-

\

\

0

\

\

I I

Biopolymer

', \

B3solute molecules B, solvent molecules

I

/

FIG.1. Schematic of the two-domain model of uncharged solute-uncharged biopolymer interactions in solution. The local domain surrounding each biopolymer contains (on average) Bs molecules of solute and Bl molecules of solvent (per molecule of biopolymer). The bulk domain contains @Ik mol of solute and n:"Ik mol of solvent. If B , / B , > > 0). nplk/nplk,the solute is preferentially accumulated

The thermodynamic consequences of preferential interactions are perhaps most readily understood by considering a dialysis equilibrium between two solutions separated by a semipermeable membrane, because in this situation p3, Tand (at low polymer concentration) P c a n be held constant, as specified by the definition of r3,2 given in Eq. (1).Concepts from equilibrium dialysis also prove of central importance in the formulation of the two-domain model (reviewed in Sections IV and V), though in practice dialysis is less satisfactory as an experimental means of determining Ts2 than are other thermodynamic methods (e.g., densimetry, osmometry) (see Eisenberg, 1994; Zhang et aL, 1996b). Of the two solutions equilibrated across a dialysis membrane, one (designated P ) contains only the membrane-permeable solute (component 3) and sol-

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vent; the other (designated a ) contains also the membrane-impermeable solute (component 2), which generally has a higher molar mass and larger molecular surface area than does the other solute component. The thermodynamic analysis of a dialysis equilibrium reviewed in the following subsections depends in detail on whether solute components 2 and 3 are uncharged or charged.

B.

Uncharged Solutes: DeJinition in the Context of Dialysis Equilibrium

Provided that the osmotic pressure difference across a membrane at dialysis equilibrium is small enough (at low enough concentrations of component 2), the condition of dialysis equilibrium can be expressed by equating the thermodynamic activities of the membrane-permeable uncharged solute component in the two solutions:

Here m!$$ is the total molal concentration of uncharged component 3 in solution a (including bound and locally accumulated as well as bulk solute). The experimentally accessible thermodynamic distribution coefficient r;;!‘characterizes solute-polymer interactions in a solution containing a finite polymer concentration at dialysis equilibrium:

From Eqs. (2) and (3), we have

where

At dilute polymer concentrations, 7 3 . 2 may be interpreted as the contribution to the nonideality of solute 3 in solution a arising from its interactions with the biopolymer. At sufficiently small values of m2,rS ceases to be a function of m2 and hence equals the limiting value r3,2 [as defined in Eq. (l)].In this

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M. THOMAS RECORD, JR, ET A L

limit the transmembrane quotient of differences Am3/Am, [Eq. (3)] may be equated to the derivative [eq. (l)]:

In a dialysis equilibrium experiment, F ~rather , than P, is maintained constant while the composition of the three component solution (a)is changed. Under the conditions of interest here, the justification for replacing pl with P, the constraint specified by the partial derivative in Eq. (l),has been considered in detail (Eisenberg, 1976; Schellman, 1990). Accumulation (relative to solution p ) of component 3 in the polymer-containing solution (a)reflects preferential accumulation of that solute in the vicinity of polymer molecules; exclusion of component 3 from the polymer-containing solution (equivalent to preferential accumulation of solvent) reflects exclusion of that solute from the vicinity of each polymer molecule.

C. Charged Solutes: Preferential Interaction (Donnan) Coefficientsfor Electroneutral Solute Components and fm Single-Ion Species The Donnan membrane equilibrium provides a useful experimental means of characterizing the thermodynamics of interactions of ions with charged polymers. Thermodynamic analysis of the Donnan equilibrium is analogous to that of equilibrium dialysis involving uncharged polymers and solutes (see Section II1,B above). New effects arise, however, because the membrane-permeable component (3) consists of dissociated ions and the membrane-impermeable polymer is charged. For a charged polymer-salt solution, at dialysis equilibrium, these effects include ( 1) equilibrium transmembrane differences in concentrations of the low molar mass salt ions (M+ and X-), determined by the most random mixture of these diffusible species that is consistent with the thermodynamic effects of all intersolute interactions and with (virtually exact) electroneutrality of the solutions on both sides of the dialysis membrane; (2)an equilibrium membrane potential, resulting from otherwise negligible deviations from electroneutrality in each of the solutions separated by the semipermeable membrane; and (3) an equilibrium osmotic pressure difference, which arises from the unequal chemical potentials of the nondiffusible polymer component on the two sides of the membrane. In analyses of the Donnan ion distribution that begin with the transmembrane equilibrium condition for the electroneutral salt component, the Donnan osmotic pressure difference and any microscopic deviations

[SALT] AM) [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

30 1

from electroneutrality can be neglected, provided that the concentration of the nondiffusible component is sufficiently low. Then the Donnan equilibrium condition is

where (Y and p designate the polyioncontaining and polyion-free compartments, respectively, as in the previous treatment of nonelectrolyte solutes. When the concentration of salt is in sufficient excess over the concentration of charges on the polyanion, to an excellent approximation the condition of electroneutrality can be applied to each solution:

where 2, is the net structural charge on the polyion and mJ is its molal concentration, which is equal to the molal concentration of the electroneutral component, mZJ.Consistent with the notation in Anderson and Record (1993), the subscript 25 is used in the present chapter exclusively to designate the electroneutral poly-(or oligo-)electrolyte component, defined to consist of a poly-(or oligo-)ionic species J and an equivalent number of counterions, in this case univalent. [Use of this notation in Record and Anderson (1995) was unfortunately ambiguous, and we have attempted to be consistent in the present chapter.] Often the monomeric molal concentration = 12,1mJis used intead of mJ,because thermodynamic properties of “linearchain” polyelectrolytes typically become independent of the degree of polymerization when it is sufficiently large that oligoelectrolyte behavior is no longer detectable. By the definition of components,

From Eqs. (7-9), one obtains the following Donnan equilibrium condition, where differences between and ytCs,generally cannot be neglected:

From Eq. ( l o ) , at low mJ, it follows that

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M. THOMAS RECORD, JR.,ET AL..

where [cf. Eq. (5)]

To obtain Eq. (11) from Eq. ( l o ) , truncation of the expansion of the radical requires excess salt ( m3(a) lZ,l mJ) . In Eq. (12),as in the nonelectrolyte case [Eq. ( 5 ) ] , y3,2may be interpreted as the contribution to the nonideality of the electrolyte in compartment a that arises from interactions of electrolyte cations and anions with the charged polymer. The experimental thermodynamic salt-distribution coefficient (the Donnan quotient), which characterizes solute concentrationdependent nonideality due to electrolyte-charged polymer interactions, is defined by analogy to Eq. (3) for the nonelectrolyte case:

+

c$

As in the development of Eq. ( 6 ) ,the quotient of transmembrane concentration differences becomes .equal to a derivative at sufficiently small polyion concentration, so

The thermodynamic saltdistribution coefficient TsZJ, called the Donnan coefficient, is an experimentally accessible quantity which, under all conditions of interest in this review, is numerically indistinguishable from the preferential interaction coefficient defined in Eq. ( 1 ) .Justification for the approximation implied by replacing the constraint of constant p1with constant Pfor the partial derivative in Eq. (14) has been discussed (for example) by Anderson and Record (1993). From Eqs. (9-12).

In the ideal limit of Eq. (15) where Y ~= ,1, r"g' ~ = -0.5lZJl. (The ideal value of the Donnan coefficient may be approached in solutions containing weakly charged polyions at sufficiently low salt concentrations.) Generally Y ~< ,1 (i.e., ~ the net effect of ion-polyion interactions is favorable) and > -O.SlZ,l.

r-,J

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBIUA

303

For the counterion (here a positive ion):

exp where lim,,8wol?t,J = TtJ. In the ideal limit, where 73.2 = 1, P$’ = 0.512$. Generally 1 51 2 T+J 2 0.5151. On the basis of these single-ion preferential interaction coefficients, counterion accumulation in and coion exclusion from the polyion-containing compartment are specified relative to the usual ideal reference state for a Donnan equilibrium (the most random electroneutral mixture). Because the solution is macroscopically electroneutral, and r- are always related:

r+

Expressed per polymer charge, Eqs. (13) and (17) are

Iv.

PREFERENTIAL INTERACTIONS OF NONELECTROLWE MOLECULES WITH AN UNCHARGED BIOPOLYMER A.

General Two-Domain Analysis of Preferential Interactions of Nonelectrolytes

Record and Anderson (1995) analyzed a two-domain model for preferential interactions of an unchargedsolutewith a dilute uncharged polymer in solution. In this model, as depicted in Fig. 1, a “local” domain containing only solute (component 3) and solvent surrounds each polymer molecule, and a “bulk” domain, generally characterized by a different ratio of solute to solvent, separates all local domains. The two-domain model assumes that the distribution of solute and solvent within the vicinity of a given polymer is not affected by interactions with any other polymer. To meet this condition the solution must be sufficiently dilute in the polymer. By definition the local domain contains (on average) & molecules of solute and B, molecules of solvent per polymer molecule. The bulk domain contains mol of solvent and f l mol of solute. Any preferential interactions with component 2 experienced by compo-

304

M. THOMAS RECORD, JR.,ET AL.

nents 3 and 1, including but not limited to site binding of component 3 and solvation (e.g., hydration) by component 1, cause their mole ratio in the local domain (&/Bl) to differ from their mole ratio in the bulk domain ( n y / n p ) ,which in a sufficient excess of solute is indistinguishable from their overall ratio of molalities (m3/ml). (For water, ml = 55.5 mol/kg). If component 3 is preferentially accumulated in [excluded from] the local domain, B3/BI is greater [less] than m 3 / m l ,and accordingly r3,2 is positive [negative]. The (generally observed) inequality of &/BI and m 3 / m l is the microscopic counterpart of the macroscopic observation (at dialysis equilibrium) of unequal mole ratios of components 3 and 1 in two solutions separated by a dialysis membrane impermeable only to component 2. As reviewed in the preceding section, this analogy has been exploited to derive explicit expressions for r3,2 for uncharged and for charged species (Record and Anderson, 1995). Explicit expressions for preferential interaction coefficients that characterize nonelectrolyte solutebiopolymer nonideally are reviewed in the remainder of this section, and the corresponding expressions for electrolyte solutes and charged biopolymers are reviewed in Section V. In the polymer solution, the total molal concentration of solute 3 is

The bulk concentration of solute component 3, m y , is given by bulk

n3 m y=m l m nl A thermodynamic criterion for distinguishing the local from the bulk domain can be introduced. Consistent with the specification on the bulk domain given above, an ideal dialysis equilibrium condition is used to equate the molality of solute in the bulk domain to the value it would have in a polymer-free solution (0) in dialysis equilibrium with the polymer-containing solution ( a ):

Therefore

According to Eq. (22), the contribution to nonideality of component 3

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

305

due to interactions with component 2 ( Y ~ ,is~ accounted ) for entirely by the accumulation or exclusion (relative to the composition of the bulk solution) of component 3 in the local domain surrounding each polymer. The molal concentration of polymer in solution a is

From Eqs. (3) and (21-23), the following twodomain expression for

ril;pis obtained:

If water is the solvent, ml = 55.5. Equation (24) is perfectly general with respect to the concentration of solute component 3, but the solution must be sufficiently dilute in polymer component 2 so that the osmotic pressure contribution to Eq. (2)can be neglected and so that a bulk polymer-free domain can exist. As m2 --* 0,

This expression formally is the same as presented by Timasheff and Inouye (1968) and Inouye and Timasheff (1972) for the nonelectrolyte case. A similar expression was derived by Schellman (1990) for a particular site-binding model of local solute-solvent exchange. Equation (25) may be recast to recognize explicitly the interdependence of B, and due to solute-solvent exchange in the local domain. Let ,P, be the maximum number of solvent molecules in the local domain of an isolated molecule of component 2. When mS = 0, & = B y , provided that solvation of component 2 is not increased by introducing solute component 3 into the solution. The positive exchange coefficient Sl,3= ( B Y - I l l ) / & is defined as the cumulative stoichiometry of solvent displaced per solute accumulated in the local domain:

= For a completely excluded solute, 4 = 0 and r3,2

-4 ( m 3 / m l ) .For

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M. THOMAS RECORD, JR.,El’ AL

strongly excluded solutes (such as glycine betaine, reviewed below in Section IV,B), BS = 0 over at least some finite range of m3, and hence vs. m3. BYmcan be evaluated directly as the slope of a linear plot of r3,* For accumulated solutes under typical conditions, BY’m3/ml cannot be neglected and 4 varies with m3. Separate evaluation of & and B y may still be feasible by applying Eq. (26) to experimental values of T3,ndetermined for the accumulated solute, but only if B4is not simply proportional to m3 when S1,3m3/ml 1. However, m3-dependent values of & for an accumulated solute can be determined most reliably via the twodomain model if By” has been evaluated independently for a completely excluded solute. An application of this approach to analyze the preferential interactions of the accumulated solute urea, with the value of BI;,, determined for the excluded solute glycine betaine, is reviewed in Section IV, C. In the context of the twodomain picture, further analysis of the m3 dependence of B3 requires additional model assumptions. An explicit as a function of m3 has been developed from a parameterization of detailed model for preferential interactions assumed to arise from a competitive one-for-one (1 : 1) “interchange” of two different types of solvent species (Schellman, 1990). Either the primary solvent, component 1, or the (less abundant) “cosolvent,” component 3, is bound independently at sites that comprise the entire accessible surface of the highly dilute polymeric component 2. These sites need not all be thermodynamically equivalent (have the same relative affinity for components 1 and 3). In particular, some may be occupied only by the principal solvent. However, each site must cover the same amount of surface area on component 2, because the “independent binding” stipulated by this model requires that the identity of the species located at any site does not affect that of the species located at any other site. Despite the presumed equality of site sizes, the model does not require that the individual molecules of components 1 and 3 have equal sizes. [Possible structural scenarios that meet this condition are shown in Fig. 1 of Schellman (1990).] In the simplest situation where the 1 : 1 interchange model can be applied, all N sites are thermodynamically equivalent (have the same affinity for component 3 relative to component 1),and any site occupied by the principal solvent in the total absence of cosolvent is open to occupancy by this component when it is added to the system. More generally,some subset ( N l )of the total number of sites ( N ) on the surface of component 2 that are occupied by the principal solvent (usually water) are not accessible to occupation by component 3 (Timasheff, 1992). If all of the remaining sites, here designated Nl.3have the same binding

+

r9,2

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

307

affinity for component 3 relative to water, then the dependence of r3,2 on m3 can be represented, according to the 1 : 1 interchange model, as

r3,2 = &(K-

1/55.5)m3/(l

+ Km3) - N1m3/55.5

(27)

Here the “practical” equilibrium quotient, K, expressed in units of reciprocal molality, generally has some dependence on solution composition, because it incorporates the stoichiometric quotient of activity coefficients. Note that, for consistency with the notation adopted in this chapter, some of the symbols in Eq. (27) differ from those appearing in expressions published previously [cf. Eqs. (7) and (12) of Schellman (1990), Eq. (21) of Timasheff (1992), and Eq. (6) of Zhang et al. (1996b).] According to the 1 : l interchange model from which Eq. (2’7) was derived, in general K, N,, and Nl,3all may have a role in determining the sign and magnitude of l?3,2.At a given m3, the minimum (most is - (Nl,3+ Nl)m3/ml, which corresponds negative possible) value of r3,2 to total exclusion of component 3, or an infinite preferential affinity for water (i.e., K = 0) at all sites on component 2. If component 3 is strongly but not totally excluded, K may be small enough so that the total number of sites accessible to water (Nl,3+ Nl) can be evaluated vs. m3. The affinity of component from the slope of a linear plot of r3,* 3 relative to component 1 at the Nl.3 sites may be so strong in some systems that K is much larger than both l / m l and l/m3. Nevertheless, in this situation component 3 is preferentially accumulated (r3,2 > 0) only if the number of sites for which it has strong affinity is large enough > Nlm3/ml). This requirement arises because is a measure of net preferential interactions with the entireaccessible surface of component 2 (Timasheff, 1992). Equations (26) and (27) are consistent if 4 = N,,&m,/(l + Km,), Bf” = Nl,3+ Nl and SlS3= 1. These equalities do not uniquely validate the 1 : 1 interchange model, because some form of exact mathematical correspondence must follow from the thermodynamic generality of the twodomain description. If the interchange is not 1 : 1 and/or if site occupancy is not strictly independent, Sl,3may differ from 1 and depend on m3. In any case, the expression for r3,2 given by Eq. (26) is general, provided that the basic requirements for applicability of the two-domain model are fulfilled.

r3,2

B.

Two-Domain Analysis of Interactions of Glycine Betaine with Bovine Serum Albumin (BSA): PreferentialExclusion

Glycine betaine, an osmoprotectant found at significant levels in many prokaryotic and eukaryotic cells, appears to be preferentially excluded

308

M. THOMAS RECORD, JR.,ET AL.

from thevicinity of protein surfacesboth in vitro (Arakawaand Timasheff, 1983; Zhang et aL, 1996b) and in vivo (Cayley et al., 1992). In particular, densimetry (Arakawa and Timasheff, 1983) and vapor pressure osmometry (VPO; Zhang et al., 1996b) measurements demonstrate that glycine betaine is highly excluded in BSA solutions at all m3 examined and that rg,2 is directly proportional to glycine betaine concentration. As shown in Fig. 2, r3,2 = -49( 2 4 ) m3 for betaine concentrations in the range 01.6 M. From a twodomain interpretation of the VPO results summarized in Fig. 2, Zhang et al. (1996b) concluded that glycine betaine is completely excluded from the local domain of water surrounding BSA and that this local domain is composed of a monolayer of water on the protein surface, as indicated by comparisons with predictions of calculations based on structural models. For a completely excluded solute in water, the term in Eq. (26) is by definition zero, so that r3,2 is proportional to m3 with a proportionality constant of -By"/m,. If glycine betaine were completely excluded from BSA, the slope of the plot of l?&vs. mg (-49 5 4) indicates that the hydration of BSA, is 2700 2 200 mol H20/mol protein (on a weight basis, B y = 0.74 2 0.06 g H20/g protein). If exclusion of glycine betaine were incomplete, the true hydration would exceed this estimate, which lies above the average,

m",

m3 (m)

r3,2

FIG.2. Solute concentration dependences of preferential interaction coefficients defined by Eq. ( 1 ) for interactions of BSA with urea and glycine betaine, calculated from vapor pressure osmometry data. (Modified from Zhang et al., 1996b.)

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

309

but within the range, of values for protein hydration calculated from hydrodynamic measurements: 0.12-1.04 g H20/g protein, with an average value of 0.53 ? 0.26 g H,O/g protein (Squire and Himmel, 1979). A previous study of protein hydration based on the preferential interactions of glycerol with proteins (Gekko and Timasheff, 1981) reports hydration numbers smaller than those deduced from hydrodynamic measurements, probably because glycerol is not completely excluded from the proteins considered in that study. Osmometric measurements indicate that glycerol is accumulated near BSA to a greater extent than is glycine betaine (E. Courtenay, unpublished results). To test the hypothesis of complete exclusion of glycine betaine and to provide a molecular picture of the local domain surrounding BSA, the thermodynamic extent of hydration of BSA may be compared with a prediction of its water-accessible surface area. From the observation (Janin, 1976;Teller, 1976;Miller et al., 1987) that water-accessible surface areas of native proteins increase as a power function of the protein molecular weight, Zhang et al. (1996b) estimated the water-accessible If the 2700 ? 200 surface area of native BSA to be 2.0 (20.1) X lo4 H 2 0 molecules of hydration (i.e., B Y ) constitute a surface layer, the surface density of water molecules on BSA is 0.14 5 0.01 H20/Az.This result is plausible, as it lies between the densities predicted for hexagonal closest packing of 1.4 radius water molecules on the protein surface (-0.15 H 2 0 per Az)and for a less dense packing with the same crosssectional area per water as in bulk water (0.11 H 2 0 per Az;Gill et al., 1985). The complete exclusion of glycine betaine from protein surfaces is in accord with the proposed osmoprotective mechanism of glycine betaine in E. coli K-12 cells, where the greater osmotic effect of uptake of glycine betaine suggests that it is more excluded from cytoplasmic biopolymer surfaces than are other osmolytes (Cayley et al., 1992). Most natural osmolytes and amino acids are found to be excluded from proteins to some degree (Liu and Bolen, 1995; Arakawa and Timasheff, 1983).

Az.

A

C.

TweDomain Analysis of Urea-BSA Interactions: Preferential Accumulation

Urea, an osmolyte in some organisms (Lin and Timasheff, 1994), is widely used as a protein denaturant at high concentrations. The destabilizing effect of urea on protein structure generally is thought to be due to its preferential accumulation in the vicinity of amides and other polar functional groups, more of which are exposed to the solution when the protein is denatured (Simpson and Kauzmann, 1953; Schellman, 1990;

310

M. THOMAS RECORD, JR., ET AL.

Liepinsh and Otting, 1994). Studies by various experimental methods indicate that the preferential interactions of most (uncharged) solutes with proteins are intermediate between those exhibited by glycine bemine and urea (Arakawa and Timasheff, 1983; E. Courtenay, u n p u b lished) . As in the case of glycine betaine, values of for urea from W O measurements shown in Fig. 2 are proportional to urea concentration in the range examined [ <1.6 molal (m)] : T3,n/m3 = 6 2 1. The positive sign of r32indicates that the I& term in Eq. (13) is sufficiently large to result in net preferential accumulation of urea. Assuming that B Y / 55.5 = 49 2 4, from the twodomain analysis of betaine-BSA preferential interactions, Zhang et al. (1996b) obtained &/m3 = 54 2 5 for urea-BSA interactions [if S1,3m3Q 55.5 in Eq. (26)] in the urea concentration range investigated (up to 1.6 M ) . Clearly, in this situation independent knowledge of the hydration term, By”, is essential for a correct evaluation of 4. On the basis of some more detailed model assumptions, B3 could be expressed in terms of additional parameters, for example, by introducing the number of urea-water interchangeable sites, Nl,3and the average binding constant, K, as in Eq. (27). However, because the plot of r3,* vs. m3 is linear in the range of urea concentrations investigated by Zhang et al. (1996b), individual values for Nl,3and K were not resolved. With N,,3 = 2700 5 200 mol H,O/mol BSA determined the value B$, = from betaine-BSA interactions, the product Nl,3Kis estimated to be 54 +- 5 m-’. The preferential accumulation of urea near protein surfaces generally is thought to result from favorable interactions with solventaccessible amides and possibly with other polar groups (Robinson and Jencks, 1965; Nozaki and Tanford, 1970; Liepinsh and Otting, 1994). Previous studies using various methods to quantify urea-protein and urea-peptide interactions at urea concentrations up to 8 M have reported estimates of site binding constants (defined in various but similar ways) ranging from 0.04 to 0.3 m-l (Makhatadze and Privalov, 1992; Sijpkes et al., 1993; Liepinsh and Otting, 1994; Scholtz et al., 1995). Zhang et al. (1996b) assumed that at relatively low urea concentrations (0-1.6 M ) , & is determined by urea-amide group interactions, which are among the strongest urea-protein interactions. They then used the molar mass of BSA and correlations based on structural data for other native proteins to estimate that the number of accessible amide groups in native BSA (&) is -220. If Nl,3= 220, then K = 0.25 m-I, a value similar to those that have been deduced from nuclear magnetic resonance (NMR) measurements (Liepinsh and Otting, 1994).

r3,’L

+

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

31 1

V. PREFERENTIAL INTERACTIONS OF ELECTROLWE IONSWITH A CHARGED BIOPOLYMER

A. Nucleic Acids as High-Charge Density Cylindrical Polyanions: The Physical origin of the Polyelectrolyte Effect The distinctive effects on molecular and thermodynamic properties that arise from the interactions of a polymeric nucleic acid with salt ions are due to the combination of a large number 121, of like charges (phosphates) and a high average axial charge density on the polymeric nucleic acid. (For ease of notation, the subscript J is omitted in this section.) Regardless of detailed structural features, the axially averaged charge density of any rodlike polyion can be characterized analytically by the dimensionless parameter:

Here b is the average axial distance between charges projected onto the cylindrical axis of the polyion; e, the electron charge; E , the dielectric constant of pure solvent; and kT has the usual meaning. (In water at -25"C, 6 = 7.146-', if b is expressed in angstroms.) The sufficiency of 6 as the only structural parameter needed to characterize the limiting laws for thermodynamic and transport properties of solutions containing cylindrical polyions is the cornerstone of counterion condensation (CC) theory (Oosawa, 1957; Manning, 1969). In independent studies based on the cylindrical Poisson-Boltzmann (PB) equation, the magnitude of 6 was pointed out as the critical determinant of alternative limiting functional forms of the PB potential (Fuoss et al., 1951) and hence of some thermodynamic properties of solutions containing cylindrical polyions (Gross and Strauss, 1966; Anderson and Record, 1980, 1983). Various theories predict, and experiments have generally confirmed, distinctive molecular and thermodynamic characteristics of solutions that contain rodlike polyions having 121 1 and 6 2 1, together with excess uniunivalent salt whose concentration is not too high ([NaCl] 5 0.5 M, for example) (reviewed by Anderson and Record, 1990, 1995). The high local concentrations and steep concentration gradients of counterions in the vicinity of a polyion surface are strong functions of 6 but are relatively insensitive to changes in salt concentration. These gradients persist with increasing dilution (within the range of experimental accessibility), in marked contrast to the situation in ordinary salt solutions. The accumulation of counterions in the vicinity of a highcharge density polyion (as described by MC or PB theory) or the "con-

+

312

M. THOMAS RECORD, JR.,ET AI..

densed” or “territorially bound” counterions postulated by the approximate molecular CC theory (Manning, 1978) might drive counterion binding to specific sites (if any) on a polyion (Grossand Strauss, 1966),but no evidence exists for the site binding of common univalent cations to DNA (Braunlin, 1995). Interactions with salt ions cause the logarithm of the activity coefficient of the DNA polyanion to exhibit an approximately logarithmic dependence on salt concentration and a significant dependence on 6. Consequently, processes involving nucleic acids that reduce 6 globally or locally, such as denaturation or binding of an oligocationic ligand, are driven by relatively small reductions in the concentration of excess added salt (Manning, 1972, 1978; Record et al., 1976, 1978). Small oligoions and proteins, which generally are polyampholytes, do not have a large number of like charges whose density is high over any significant distance in one direction. Therefore, the typical molecular and thermodynamic effects attributable to ion-ion or to protein-protein interactions are neither so large in magnitude nor so persistent with reductions in salt concentration as are those characteristic of solutions containing a polymeric nucleic acid (Record et al., 1978;Warshel, 1991). The onset of the distinctive molecular and thermodynamic characteristics of polynucleotides is exhibited by a homologous series of oligonucleotides, all having the same axial charge density 6, so that their lengths are proportional to 121.Along the surface of any charged rodlike molecule of finite length, the magnitude of the electric field diminishes steadily in the axial direction as either end is approached. If 121 is small enough, the nonuniform axial profile of the electric field at the surface of the oligomer produces observable coulombic end effects. For example, the average number of counterions accumulated at the surface of a short oligoion per structural charge is significantly less than for the corresponding polyion. The magnitudes of coulombic end effects and their distinctive dependences on I ZI have been quantified from comparative (oligomer vs. polymer) experimental studies of ion distributions (Braunlin, 1995; Stein et al., 1995), conformational transitions (Scheffler et al., 1970), and oligocation binding (Zhang et al., 1996a), and by MC and PB theoretical calculations as a function of oligomer length (Olmsted et al., 1989, 1991, 1995; Zhang et al., 1996a). B. Distinctive Functional F m s of Preferential Interaction CoefJicientsfm Nucleic Acid Polyelectrolytes and Oligoelectrolytes in 1:l Salt Solutions At sufficientlyhigh dilutions of both salt and cylindrical polyelectrolyte, both the PB cell model without the condensation hypothesis (Gross and Strauss, 1966; Anderson and Record, 1980) and the counterion-

313

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

condensation theory (Manning, 1969) predict that T3,uhas the following “limiting law” form:

where 6 is defined by Eq. (28)and C, is the concentration of 1:l salt on the molar scale. According to Eq. (29),W,,, is directly proportional to b and is independent of a or any other structural parameters. More generally, Anderson and Record (1983) used the PB cylindrical cell model to show that at sufficient dilution of the polyion and in a sufficient excess of salt the following equation is obtained:

In Eq. (30), the saltdependent term S, is proportional to the sum of the local concentrations of electrolyte ions at the polyion surface: S, = 25x[C+(a)+ C-(a)]. Here = NA7r$b/103 is the volume per polyion monomer excluded at contact between a small ion (modeled as a hard sphere) and the polyion (modeled as a hard cylinder); NAis Avogadro’s number, and C+(a) and C- (a)denote the local “contact” molar concentrations (at a) of univalent cations and anions, respectively. As C3 is reduced toward zero (while remaining in large excess over G,) , S,approaches either of two limiting values, depending on the magnitude of 6. For 6 > 1, S, + (6 - 1)2, so that Eq. (30) acquires the is directly proportional to b and simple form of Eq. (29),wherein r3,+ independent of a (Anderson and Record, 1980).At very high salt concentrations the contact concentrations of both cations and anions approach the bulk molar salt concentration C3, so that S, + 45vuC,and + -C3qh. Thus for this case also rg; at sufficiently high C3 is directly proportional to b, but now it has a quadratic dependence on a as well. In the experimental salt concentration range, C3vucontributes significantly to r3,u, but becomes dominant only at high salt concentrations. As calculated from solutions of the cylindrical PB equation, the quantity rs; - C3v,also depends significantly on C,. The accuracy of the PB equation as a basis for calculating thermodynamic effects due to the interactions of salt ions with ds DNA is demonstrated in Fig. 3. Donnan data for T,,. are compared with the corresponding results of PB calculations for a model cylindrical polyion with the axial charge density and radius of ds DNA. In general, for a high-charge density (6 > 1) cylindrical polyion either PB or MC calculations of the

vu

r:

314

M. THOMAS RECORD, JK.,ET AL.

0.6-

I

I

I

I

I

I

I

I

0.5 -

< =.

0.40.30.2 -

0.1

0.0

dependence of Ta,uon by the expression

-

5 and on salt concentration can be represented

where in a PB analysis the salt concentration-dependent correction to limiting law (low salt) behavior, a, is defined as the difference between S,,at a specified salt concentration and its low-salt (limiting law) value [SkL= (6 - 1)*]. Among the theoretical methods currently available to calculate TS," for a given model of a nucleic acid solution, the two most frequently used are based either on some form of the PB equation (Stigter, 1975, for example) or on grand canonical Monte Carlo (GCMC) simulations (Mills et al., 1986; Vlachy and Haymet, 1986). Four distinct approaches from solutions of the PB equation and/ have been taken to evaluate r3,,, or MC simulations. For an isolated cylindrical polyion the second virial coefficient can be evaluated by integrating ion distributions calculated either from MC simulations ( H . Ni, unpublished) or from numerical solutions of the cylindrical PB equation (Stigter, 1975). An analytic relationship derived from the PB cell model for a cylindrical polyion by Anderson and Record (1980) can be differentiated directly, under the constraints of constant electrolyte activity and temperature, to obtain ) , ~ , , C, is the molar concentration an expression,:?I = ( I ~ C , / I ~ C , ,where

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRlA

315

of polyion monomer (Anderson and Record, 1983). Alternatively,under the constraints of constant a, and T [and if variations in pressure are negligible (Anderson and Record, 1993)], ion distribution functions generated by solving the cylindrical PB equation can be integrated numerically to determine C, as a function of C,. At sufficiently low C,, where this functionality becomes linear, rit or can be evaluated directly as the slope of a plot of C, vs. C, (Mills et al., 1986). For model systems represented with varying degrees of structural detail, the excess electrostatic free energy attributable to the interactions of mobile salt ions with the multiple charges on some rigid model nucleic acid can be evaluated by appropriate numerical integrations and then differentiated (again numerically) with respect to salt concentration to obtain a function that is approximately equivalent to (Misra et al., 1994a,b;Sharp et al., 1995). All calculations based on the PB equation, for any model, are potentially subject to error insofar as certain interionic correlations are neglected a priori in the statistical mechanical formulation of this equation. At sufficiently high dilutions of salt solutions containing cylindrical polyions, this “PB approximation” does become exact (Fixman, 19’79). Its accuracy over the usual experimental range of concentrations can be assessed best from a theoretical standpoint by comparisons with the results of MC simulations for systems modeled using the same assumptions. The accuracy of the PB approximation and of the underlying model assumptions for which the PB equation is solved varies considerably with the system, the solution conditions, and the property to be calculated (Anderson and Record, 1990,1995; H. Ni, unpublished). The ultimate criterion for the reliability of any theoretical calculation must be based on comparisons with experimental measurements. The acquisition of data appropriate for such comparisons merits high priority, because it will advance our understanding of the physical factors that govern the thermodynamic consequences of preferential interactions. Mills et al. (1986) and Olmsted et al. (1989, 1991, 1995) developed methods based on GCMC simulations to calculate TS,,for cylindrical models of polymeric and oligomeric electrolytes. By analogy to the third described above, r?: = (a C,/a C,) can be evaluway of calculating ated as the slope of a plot of C, vs. C,, as determined by an appropriate series of GCMC simulations.For any model that neglects the molecularity of the solvent, neither osmolarity nor pressure can be explicitly controlled while C,, is varied. Thus, certain approximations are entailed in the identification of (or rC) with These have been discussed in detail by Anderson and Record (1993), who examined the thermody-

rt:

rgt

rgt

:!r

rS,,.

316

M. THOMAS RECORD, JR, ET AL.

namic foundation for the use of GCMC simulations as a means of calculating preferential interaction coefficients for a three-component poly-(or oligo-)electrolyte-salt solution, modeled according to the standard set of assumptions, which neglect the molecularity of solvent water. The GCMC simulations reported by Olmsted et al. (1989) for a homologous series of oligoelectrolytes (model DNA oligomers, designated N mers, having I&,[ = Ncharges) predict that the positive quantity - r 3 , u ( N ) (the negative of the preferential interaction coefficient of the Nmer expressed per oligomer charge) decreases with increasing N. For large enough values of N, r5,J N> approaches the corresponding polyelectrolyte value [here designated r 3 , u ( w ) ]as a linear function of N ‘ ,as shown in Fig. 4 for simulations at two salt activities (1.8 and 12.3 mM):

Here the Nindependent parameter a depends on a+ and on the structural characteristics common to each (model) Nmer in the series (Olmsted et al., 1991, 1995). The magnitude of (Y is a measure of the oligo “end effect” on T,,(N) (expressed per monomer), which causes deviations from the value characteristic of the corresponding polymer.

0.35 i

I

1

I

0.10

0.00 0.01

I

I

I

I

I

I

i

0.02 0.03 0.04 0.05 1/N

FIG.4. Grand canonical Monte Carlo predictionsof the percharge preferential interaction coefficient [plotted as -r3,“(N), where N = lZl] of model EDNA oligomers in univalent salt, as a function of 1/Nat two salt activities: a, = 1.8 mM ( O ) ,and at = 12.3 mM (0). The solid lines were obtained by linear regression. (Modified from Olmsted et al., 1995.)

[SALT] AND [SOLUTE] EFFXCTS ON BIOPOLYMER EQUILIBRIA

317

As noted in Section 111, values of for interactions of nonelectrolyte solutes with weakly charged proteins are observed to be proportional to solute concentration and hence approach zero at 9-+ 0. In contrast, experimental observations indicate that r3,u, predicted by Eqs. (29)- (31), approaches a nonzero limiting law value as the salt concentration is reduced, and that at higher salt concentrations it exhibits a moderate dependence on electrolyte concentration that is more complicated than simple proportionality. In marked contrast, values of for “Hofmeister-like” interactions of electrolytes with weakly charged protein polyampholytes (discussed further in the following subsection) generally are found to be directly proportional to the electrolyte concentration, like the coefficients that characterize the preferential interactions of uncharged solutes with proteins.

C. Two-Domain Interpretation of Single-lon and Salt-Component R#erential Interaction CoefJients for Interactions of Ehctrolytes with Weak4 Charged Biopolymers (Hofmeister Salt Effects) Using a twodomain (local-bulk)model of electrolyte-polymer preferential interactions, Record and Anderson (1995) interpreted the singleion Donnan distribution coefficients I‘-,and rtJdefined by Eqs. (15) and (16).The number of moles of cations (Bt ) and anions ( B - ) associated per mole of charged polymer in the twodomain model each are related to differences between total and bulk quantities: ,lo,

Bt -

+(a)-

n2

,,ptal +(a)

nbulk +(a)

m2

n2

and

- rn!‘$) _ -n?“ & n? =A (a)- (33) n2 m2 n2

where, by analogy to Eqs. (20) and (23), n$’$ = n?$t m$’$/ml, n!!’$, = n?$\ m’l”l,k)/ml,and n2 = n??;! %(m, - B 1 w ) - l . For the nonelectrolyte case, an ideal dialysis equilibrium condition was used to equate the molality of solute in the bulk domain to its molality in a polymer-free solution ( p ) in dialysis equilibrium with the polymer-containing solution (a)[cf. Eq. (21) above]. This analogy was extended to charged solutes in order to relate ion concentrations in the bulk phase in a and in the “reference” solution (0) by using an ideal Donnan dialysis equilibrium condition (i.e., -y!$!j = y 3 ( p ) )[cf. Eqs. (10)-(12)]: &3)

=

( m y $ )( m y $ )

(34)

By incorporation of this thermodynamic condition into the twodomain

318

M. THOMAS RECORD, JR., ET AI.

model, the contribution to nonideality from electrolyte-polymer interactions [ Y ~ cf. , ~Eq. ; (12)] is interpreted entirely in terms of the extent of accumulation of salt ions in the local domain surrounding the protein. Application of the electroneutrality condition to the entire solution (a) -but not to the local or bulk domains individually-and expansion of the square root of Eq. (34) for the condition of excess salt yield, in the limit of low m2 (where my?:) = mVk (a) = m d ,

r+,,= 0.5(12,1 + B- + B,)

BImS/ml T-,,= -0.5(lZ,l - B- - B,) - B I m 3 / m l= TS,* -

(35)

Equations (35)demonstrate that the thermodynamic two-domain model of ion-polymer nonideality describes the difference between each singleion preferential interaction coefficient and its “ideal” value in terms of the following: (1) the modification of the polymer structural charge by the net thermodynamic effect of accumulation (exclusion) of salt anions and cations; and ( 2 ) a hydration term, which contributes significantly only at moderate to high salt concentrations. The molecular picture implied by this two-domain expression, while certainly not literally descriptive of the long-range concentration gradients that characterize interactions of salt ions with highly charged polyions at low salt concentration, should be appropriate for short-range interactions between ions and biopolymers such as those likely to be responsible for Hofmeister salt effects at high salt concentration. The sum of single-ion preferential interaction coefficients for cation and anion is independent of 12,:l

Tt.j + r-,,= B,

+ B- - 2B1m3/m,

(36)

Both T+,, and T-,,,as well as their sum, depend on both B, and B-. As an interesting special case, potentially applicable to the treatment of Hofmeister salt effects on proteins near their isoelectric point, the protein may be uncharged in the absence of the salt (151 = 0) but the cation and anion of the salt may interact differently with the protein, so that B, # B-. Equation (35) for this case becomes

Since Eq. (36) is independent of

151, its form is unaffected if lZJl = 0.

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

319

VI. USEOF THREECOMPONENT PREFERENTIAL INTERACTION COEFFICIENTS TO ANALYZE EFFECTS OF SOLUTE CONCENTRATION ON EQUILIBRIUM OR FREEENERGY CHANGES OF CONSTANTS, TRANSITION TEMPERATURES, BIOPOLYMER PROCESSES

A. Thermodynamic Fundamentals In a solution containing only two solutes (designated 2 and 3) the following partial derivatives or combinations thereof, all taken at constant temperature and pressure, are equal to r3.2:

Equation (38) relates the solute-biopolymer preferential interaction coefficient directly to the dependence of the thermodynamic nonideality of the biopolymer (component 2) on the activity of the solute (component 3). Based on Eq. (38), evaluated at sufficiently low m,the effects of solute concentration on many biopolymer processes may be analyzed quantitatively, subject to certain approximations, generally valid when m3 %- m2, as discussed in detail by Anderson and Record (1993). If components 2 and 3 are, respectively, a biopolyelectrolyte or polyampholyte and an electrolyte, the activities a2and a3refer to the corresponding electroneutral solute components. In particular, if component 2 consists of a polyanionJ with 151charges and its charge-balancingcomplement of univalent cations, M+,then a2and y2in Eq. (38) can be expressed by a?, = a51 a/ and y2/ = 721yJ,respectively. Here the single-ion activity of the polyion is a/ = yJmj = yJm2/and that of its counterion is a d = yM+( mS + l a m J ) .If component 3 is a 1:l electrolyte (M+X-) then

+ li$mJ)

a3 = adax- = a9 = yqm3(m3

(39)

B. Definition of the Experimentally Observable Equilibnum Constant KdS and Its Dependence on Solute Activity fm Macromolecular Associations To avoid the complexity of a more generalized notation, the analysis reviewed here addresses explicitly effects of excess solute concentration

320

M. THOMAS RECORD, JR.,ET AL.

on the thermodynamics of an association process (involving one or more biopolymers) of the form

A+B+A The following analysis of this process exhibits all the essential features encountered in analyzing solute effects on any type of biopolymer process, including conformational changes, multimerization, and dissolving or precipitating the biopolymer. For the corresponding association process at equilibrium,

The thermodynamic equilibrium constant Ke, is obtained from the equilibrium condition p2 = piq p$q and defined as K,, = ( U ~ / U ~ ~a ) function only of temperature and pressure. The experimentally accessible equilibrium quotient Kobsis defined in terms of the molalities of the reactants and products:

+

Experimental values of K o bs typically are reported as quotients of the corresponding molarities. However, under the conditions of interest here and at this stage of the derivation, the distinction between molality and molarity can be ignored, not simply because of approximate numerical equality, but for reasons explained in detail elsewhere (Anderson and Record, 1993). The quotient Kobsis related to Keq by the corresponding quotient of activity coefficients K,:

Under typical in vitro (and, in some cases, in vivo) conditions, the concentrations of A, B, and AB are all sufficiently low, and the concentration of the perturbing solute 3 is sufficiently greater than those of A, B, and AB, so that the only significant contributions to the nonideality of these species, as reflected by yA,yB,ym, are due to various kinds of interactions of A, B, and AB with ions or molecules of the perturbing solute. There-

, ~ ,

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

32 1

fore, three-component preferential interaction coefficients of the type defined in Eq. ( 1 ) can be used to characterize the dependences of yA, yB,and yAB, and hence of 4, on the solute activity (Anderson and Record, 1993, 1998). This dependence can be represented by the derivative:

(a In Kobs/a In %)(m2)

=

-(a In K y / a In @3)(m9)

(42)

As elsewhere in this chapter, the subscripts T and P are omitted to simplify notation and the subscript {m2}indicates that mA, q,and mAB can be regarded as fixed when the dependences of Kobs(and K,) on a, are determined. This approximation can be justified, for example, when the perturbing solute is present in sufficient excess so that the actual changes in mA, %, and mm that must accompany a shift in the complexation equilibrium have no significant effect on yA,yB,and yABor on the activity coefficient of the perturbing solute (Anderson and Record, 1993). For a cooperative macromolecular conformational change, the derivative that expresses the solute-concentration dependence of Kc,bscan be related, using the Gibbs-Helmholtz equation, to the derivative that expresses the effect of solute concentration on the transition temperature T, of that conformational change (as explained, e.g., by Privalov et al., 1969):

AHEb dT, RP, dln a,

(43)

where AH,",, is evaluated at T,. For at least some biopolymer transitions (e.g., protein folding), is a strong function of temperature. At T,,

AHEbs = Accg,obs(Tm - TH)

(44)

Here Tl, is the characteristic temperature where A H o = 0 for the process (Baldwin, 1986; Schellman, 1987), and the heat capacity change ACP",obs is assumed to be independent of temperature. Both Ac,",ob,and Tl, may be functions of a?.

C. E f f t s of Changzng the Concentration of an Uncharged Solute on Equilibria of Uncharged Biopolymers Changes in the equilibrium extent of conversion of uncharged biopolymer reactants to products (i.e., in Kobs)that are driven by changes in

322

M. THOMAS RECORD, JR., ET AL.

the concentration of an uncharged perturbing solute can be analyzed directly in terms of the appropriate solute-biopolymer preferential interaction coefficients. To establish this relationship, the final expression for TS2in Eq. (38) is applied to each biopolymer activity coefficient in K y , as shown in Eq. (42):

Here ATs2is the stoichiometricallyweighted difference between values of T3,.. for products and reactants. When solute component 3 is in sufficient excess so that all macromolecular activity coefficients ( y 2 ) depend on m3 but on none of the m2,Eq. (45) implies that threecomponent preferential interaction coefficients of the type defined by Eqs. (1) and (38) suffice as a basis for the analysis of the dependence of Kohson for an equilibrating system involving four (or more) components. A version of Eq. (45) (expressed in terms of preferential interaction coefficients represented in a different form) was presented [as Eq. (7.5)]by Wyman (1964). For a conformational transition of an uncharged biopolymer, the dependence of T, on the concentration of an uncharged solute can be deduced from Eqs. (43)- (45),

D. E f f t s of Changing the Concentration of an Elech.olyte Solute on Equilibria of Charged Biopolymers For situations where some or all of the reactant(s) and product(s) are charged polymers (either polyelectrolytes or polyampholytes) and/ or where component 3 is an electrolyte, the form of Eq. (45) is not applicable to describe the effects of an electrolyte component 3 on Kobsfor every type of biopolymer equilibrium. Each of the preferential interaction coefficients of the type defined in Eq. (38) can be represented more explicitly by the following equation:

This expression, which follows from Eq. (39) and the analogous expres-

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

323

sion for a?/, incorporates an approximation, a+ a+, expected to be reasonable in excess 1:1 electrolyte ( m , m2). By substituting Eq. (47) for each single-ion activity coefficient derivative (I3 In yJ/d In u+)? in the derivative ( d In K,/d In u+)(,,+ we obtain

*

The derivation of Eq. (48) is expedited by the approximation embedded in Eq. (47), but no assumption about single-ion activity coefficients is required for the rigorous derivation of Eq. (48)(Anderson and Record, 1993). The preferential interaction coefficients for electroneutral components that appear in Eq. (48) can be calculated from GCMC simulations (Mills et al., 1986); in some cases they can be measured by appropriate methods such as osmometry (Zhang et al., 1996a).For typical experimental conditions, where m3 S m2 and where y2Jis a function of m3 but not of any of the m y Eq. (48) generally is applicable for the analysis and interpretation of effects of salt concentration on any process involving charged molecules, including polyelectrolyte, Hofmeister, and osmotic effects. With minor modification, an analogous equation can be derived to describe ionic strength salt effects on equilibria involving only charged solutes of low molar mass. For the situation where AlZ,l = 0, as when all reactants and products are uncharged, or more generally when the sum of 141for products is equal to the sum of 151for reactants, Eq. (48) reduces to Eq. (45) because d In a3 = 2d In a, for a 1:l salt. For example, for DNA helix formation from two complementary strands, AIZ,\ = 0. However, for binding of an oligocation ( L z + )to a DNA poly# 0, and in this case Eq. (48) must be used to analyze effects anion, of salt activity (or concentration) on Kobs. The relationship between Eq. (48), for the effects of a charged solute on equilibria involving charged polymers, and Eq. (45), for the nonelectrolyte case, is further clarified by transforming Eq. (48) using singleion preferential interaction coefficients (Record and Richey, 1988; Record and Anderson, 1995). Incorporation of r+J and r-J from Eq. (17) into Eq. (48)yields

For comparison, the nonelectrolyte expression [Eq. (45)] is (d In Kbs/ a In an)(m,) = AT,,. Changing the concentration of an electrolyte of

324

M. THOMAS RECORD, JR.. ET AL.

course changes both cation and anion concentrations, and Eq. (49) indicates that the resulting effect on Kohscan be expressed as a stoichiometric combination of contributions, each being a sum of cation and anion single-ion preferential interaction coefficients. Corresponding to Eqs. (43) and (48) or (49), the effect of mean ionic activity a, on T, of a biopolymer conformational change involving charged biopolymers can be expressed as

The functional form of Eq. (50) is directly applicable to analyses of effects of salt concentration ( S O . 1 M ) on conformational transitions of nucleic acids and other polyelectrolytes, whereas that of Eq. (51) a p pears to be directly applicable to analyses of Hofmeister effects of salts (20.1 M ) on conformational transitions of biopolymers.

E. Description of Solute Concentration Effects on AG for a Macromolecular Process The relevance of in vitro investigations of solute effects on equilibria to in vivo processes that are not at equilibrium has occasionally been questioned. Some cellular processes occurring at constant P and T a r e not at equilibrium with regard to reactant and/or product concentrations, but rather are in a steady state in which the concentration of each of the reactants and products involved in one process is maintained at a nonequilibrium level by other cell processes. In principle this condition can also be achieved in an in vitro reactor which adds reactants and removes products. At constant P and T, the free energy difference between initial and final states of the system determines whether a process converting the initial to the final state is favorable (i.e., is spontaneous and can be harnessed to do useful work) or unfavorable (i.e., requires coupling to a favorable process in order to occur). For the isothermal, isobaric association process

A+B+AB the free energy change AGis given by the difference in chemical potentials

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

where (for i = A, B, or AB) p i= p: (41), Eq. (52) can be expressed as

325

+ RT In yimi.On the basis of Eq.

In Eq. (53), Qobs and Qy represent stoichiometricallyweighted quotients of product and reactant concentrations and of activity coefficients, respectively, in the specified nonequilibrium steady state of the reacting system:

and &,s and Ky represent the corresponding ratios at equilibrium. In an in uitro reactor, Qobs is not a function of the concentration of a perturbing solute. (Each of the reactant and product molalities appearing in the definition of Qobscan be fixed at any arbitrary value, either in the presence or absence of the perturbing solute.) In contrast, from Eqs. (45) and (48) Kobsis a function of the concentration of the perturbing solute. If the process A + B + AB occurs under conditions of excess perturbing solute where the activity coefficients in Qy and Ky depend on the activity of this solute (%) but not on the concentrations of reactants or products (here A, B, or AB), then

Therefore, for an uncharged solute,

If the solute is an electrolyte, an analogous expression relates derivatives with respect to In a, of AGand In Kobs to A(lZ,l + 2Ts,2J).Consequently, for the system and conditions considered here, changes in solute concentration that would shift the position of equilibrium (and hence change

326

M. THOMAS RECORD, JR.,

ET AL.

Kobs)have the same effect on the thermodynamics (AG) for the corresponding process under the nonequilibrium, steady state conditions. PREDICTIONS OF FUNCTIONAL FORMS OF EFFECTS OF VII. TWO-DOMAIN NONELECTROLWE CONCENTRATION ON EQUILIBRIA (K<,,,JAND TRANSITION TEMPERATURES (Tn)OF UNCHARGED BIOPOLYMERS IN AQUEOUS SOLUTION A. Effects on Kobsof Addition of a Nonekctrolyte Solute Which Is Completely Excluded from the Local Domains of Water of Hydration of All Polymeric Reactants and Products For a completely excluded solute, from Eq. (13),B3 = 0, and therefore for the conversion of polymeric reactants to products

AT3,n=

- msAB;;a;b/55.5

(completely excluded nonelectrolyte only)

(57)

Then

(completely excluded nonelectrolyte only) To simplify Eq. (58), the dependence of aJ on m3 at constant T a n d P may be expressed more compactly as

(s) = 1 + cg

(nonelectrolyte solute only)

(59)

where c3 = (a In y3/d In m3). For a solution containing the biopolymer and a sufficient excess of solute (m3 9 m2),e3 and its dependence on m3 are the same as can be determined independently by osmometry or other colligative measurements on the corresponding two-component (solute 3-water) system. In many cases, c3is relatively small in magnitude compared to unity and relatively independent of m3, within at least a moderate range. From Eqs. (58)- (59)

(completely excluded nonelectrolyte only)

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

327

On integration of Eq. (60):

In Kobs= In K,i,

-

ABTO 5 5.5 (1 +

m3[

$1:”

e3d m 3 ) ]

(61)

(completely excluded nonelectrolyte only)

If the total amount of water of hydration (in the local domains of the reacting species) is reduced in the conversion of reactants to products, then AB;? is negative and In Kobsis predicted to increase approximately linearly with m3 (provided that E is not a strong function of m3).As noted in Section IV,glycine betaine appears to be completely excluded from the local domain of native BSA. Whenever glycine betaine is found to be excluded from native (and denatured) proteins and other biopolymers, this solute will be useful, as explained above, for determining changes in hydration in protein processes. To date no other uncharged solute has been shown to be completely excluded from any type of biopolymer. Equations (60) and (61) constitute two-domain analogs of the “osmotic stress” relationships of Parsegian et al. (1995) and demonstrate that unambiguous quantitative interpretations can be obtained only when a completely excluded solute is used as the osmotic stress agent. An analysis of this osmotic effect for equilibria involving uncharged biopolymers and nonelectrolyte solutes was first performed by Tanford (1969) using binding polynomials. This approach was extended by Record et al. (1978) to equilibria of charged biopolymers affected by changes in the concentration of an excess electrolyte solute (see Section VIII,A,2 below).

B. E f f t s on Kobsof Addition of a Nonelectrolyte Solute Weakly Accumulated in (or Incompletely Excluded ji-om) the Local Domains of Some or All Polymeric Reactants and Products For interactions of weakly accumulated solutes such as urea with proteins, l?3.2 typically is found (or inferred) to be proportional to m3, as for excluded solutes, but with a slope less negative than that characteristic of a completely excluded solute. In such cases, an approximate form of Eq. (27) may be the appropriate two-domain description of r3.2 for analyses of solute effects on equilibria:

Ar3.*= m3A(N,,3K- NJ55.5)

(nonelectrolyte only) (62)

328

M. THOMAS RECORD, JR.,ET AL.

Here N1,3is the number of sites on a polymer occupied either by solute or by water, and N1 is the number of sites on the polymer that can be occupied only by water (N1,3+ N1 = B Y ) . Then

(' 'ym?)

=

(1 + e3)A ( N l , 3 K- N 1 / 5 5 . 5 ) (nonelectrolyte only)

(63)

and

In Kobs= In Kf:To+ m3 A(",$-

NJ55.5) (1

+

$10""

E~

dm3)]

(nonelectrolyte only)

(64)

In this case also, In K o b s is predicted to vary approximately linearly with m3provided that E~ is not strongly dependent on m3. Both Nl,3Kand Nl may change in the conversion of reactants to products. Consequently, for this situation unambiguous interpretation of the m3 dependence of Kobrrequires information from independent determinations of the preferential interaction coefficients pertaining to one or more of the individual reactants and products. Such data must be acquired not only for the accumulated solute but also for some other solute that is completely excluded from the regions of interest (i.e., one for which K = 0 and Nl,3= 0, if such a solute can be found). C. E f f t s on T,,,of a Biopolymer Conformational Transition )om of a Nonelech.olyte Solute

Addition

As discussed in Section VI,B above, for an uncharged polymer and a nonelectrolyte that is either excluded or weakly accumulated, r3.2 often is observed to be proportional to m3 (at least when m3 5 1-2 molal). Hence r 3 , 2 / m 3is independent of mg,and application of Eqs. ( 4 3 ) - ( 4 5 ) yields the following alternative expressions:

(i) If AC; = 0, (nonelectrolyte only)

--

dm3

In integrated form

AEbs

(65a)

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

329

(nonelectrolyte only)

(65b)

(nonelectrolyte only)

(66a)

(ii) If Ac;,,bs # 0, then dT;'

-- -

dms

R(l

AC;,obs(

+ Tm

A(

E)

-

TH)

2)

If AI?;,,,~ is independent of temperature, and if it and THare independent of m3,then

(nonelectrolyteonly)

(66b)

For sufficiently small increases or decreases in T,, Eqs. (65b) and (66b) both may be approximated by

(nonelectrolyte only)

(67)

where AHEb, is the enthalpy of transition at Ti. In this case, because r3,2 is often found to be proportional to m3, AT,,, is approximately proportional to m3 unless the nonideality term E~ is a strong function of m3. [Equations (57) or (62) as appropriate may be inserted for Ar3.2.]Both the physical content and the derivation of Eq. (67) are closely analogous to the two-component thermodynamic relationships that are derived in introductory texts to analyze the effects of solute concentration on the freezing point and boiling point of a solvent. An extensive literature demonstrates linear (or near-linear) dependences of T, or In Kobson concentrations of nonelectrolyte solutes such as urea (eg., Pace, 1986; Makhatadze and Privalov, 1992) and osmolytes (e.g., Santoro et al., 1992). Systematic studies such as these, analyzed using the two-domain model as embodied in Eqs. (63)-(67), should allow correlations to be drawn between solute effects on T, or In Knbs and changes in nonpolar and polar biopolymer surface for systems where structural data are available.

330

M. THOMAS RECORD, JR.,ET AL.

AND TWO-DOMAIN PREDICTIONS OF FUNCTIONAL VIII. POLELECTROLYTE FORMS OF EFFECTSOF SALT CONCENTRATION O N EQUILIBRIA (Kohs) AND TRANSITION TEMPERATURES (T,) OF CHARGED BIOPOLYMERS IN AQUEOUS SOLUTION

A.

General Expressions

1 . Polyelectrolyte Effects of Salt Concentration on Equilibria Involving HighCharge-Density (6 > 1 ) Cylindrical Polyions Double-helix formation from single-stranded polynucleotides is an example of an association equilibrium that involves only high-charge density polyions (in both native and denatured forms, 5, > 1 ) . Such an equilibrium can in principle be characterized by an equilibrium concentration quotient &hs, whose dependence on In a , can be represented by

Because in DNA helix formation A141 = 0, (a In Kobs/dIn a , ) = -A{I41(2t$-l(l uj)}. At sufficiently low (but excess) salt concentrations [limiting law (LL) conditions], all uj += 0 and Eq. (68) becomes

+

Even at low salt concentrations, Kobsfor these polyion processes is predicted to exhibit a strong power dependence on salt concentration. Theoretical (PB, MC) calculations for cylindrical polyions (reviewed by Anderson and Record, 1995) indicate that the limiting law expression in Eq. (69) is expected to be valid only at submillimolar salt concentrations. But in many systems Eq. (69) exhibits a greatly extended range of validity as a consequence of compensating changes in the preferential interaction coefficients of reactants and products with salt concentration, as discussed by Bond et al. (1994) and in Section VII1,C below, where we review GCMC results for nucleic acid conformational transitions. For a conformational transition involving only high-charge density (6 > 1 ) polyions that is characterized by the midpoint temperature T, we obtain from Eqs. (43) and (68),

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

33 1

Again AlZ,l = 0 and dT,,,/dln a , = (RT$/AEIzbs) A(lZJl(SsJ)-'(l+ oj). At very low salt concentrations (limiting law conditions, where oj = 0) , T,, is predicted to vary strongly and approximately linearly with the logarithm of the salt concentration; compensating effects (cf. Section VII1,C below) cause T, for a polynucleotide conformational transition to remain a linear function of In a, over a very wide range of a,.

2. Hofmeister Effects of Salt Concentration on KobsOT Tmof Biopoly mer Processes The general functional forms that characterize Hofmeister salt effects on Kohsand/or T, of biopolymer processes in aqueous solution are obtained from Eqs. (36) and (48):

(E) + =

AB+

2AB,cJ

AB-

-

ABt

+ AB- - 2ABH20 m 3 ) 55.5

~

55.5

m3

and dT;' dln a ,

-

1 dTm T2,dln a,

-

AH&

(72)

If ABt and AB- are proportional to m3, as observed for preferential interactions of nonelectrolytes, and if ABHZ0is independent of m3, then integration of Eq. (71) yields

where &* = (a I n ?,/a In m3).For small changes in T,,,from the transition temperature determined in the absence of the perturbing salt (T:) , integration of Eq. (72) yields

332

M. THOMAS RECORD, JR., ET AL.

Equations (73) and (74) should be useful in the analysis of Hofmeister salt effects, where effects of the cation and anion typically are found to be additive and In Kobsor T, are approximately linear functions of salt concentration. To analyze the extant body of Hofmeister data and obtain values of AB+ and AB- as functions of m3 for different biopolymers and salt ions, the nonideality correction (integrationover E + ) should be applied, the temperature dependence of A H & (in ATn, studies) should be taken into account where it is significant, and, if possible, differential hydration effects (AllH2<)) should be determined independently for the processes of interest by appropriate experiments using an excluded nonelectrolyte solute (Zhang et al., 1996b). If AB+/m3and AB-/m3 are found to be correlated with changes in the accessible biopolymer surface, a structure-thermodynamic predictive capability may evolve for Hofmeister salt effects.

B. Approximate Analytical Expressions That Predict the Functional Form and the K q Variables Determining the Magnitude of the Salt Concentration Dependence of KohR for Binding of Oligocationic Ligands and Proteins to Nucleic Acid Polyanions Equilibrium and kinetic parameters that characterize the noncovalent binding interactions of nucleic acid polyanions with positively charged ligands and proteins often vary as a constant power of the (uniunivalent) salt concentration in the range typically examined (from -0.01 to -0.2 M ) (see Record et al., 1976,1978,1991; Lohman, 1985; Record and Spolar, 1990; Lohman and Mascotti, 1992; Anderson and Record, 1995). Examples are given in Fig. 5. More complicated functional behavior is observed in mixed-salt systems that contain both multivalent and univalent cations (see Capp et al., 1996, and references therein).] Power-law salt dependences have been observed almost universally in studies of the binding interactions of oligocationic intercalating, groove-binding, and phosphate-binding ligands, as well as of both site-specific and nonspecific binding of proteins, with nucleic acids. For all these systems under typical experimental conditions, changes in salt concentration affect the equilibrium extent of complexation much more profoundly than do comparable changes (on a percentage basis) in any of the reactant or product concentrations. At low (but excess) salt concentrations, effects of changing salt concentration on equilibria and rate processes involving nucleic acids are typically much larger than those observed for processes involving only low molecular weight solutes or polyampholytic proteins. 1. Oligocation (Lzt) Binding to Polyanionic DNA: Demonstration of the Dominance of the Polyekctrolyte Contribution to th,e Salt Effect Record et al. (1976, 1977, 1978) proposed that the power-law effects of salt concentration on binding of oligocations to polyanions have a

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

333

polyelectrolyte origin, which differs fundamentally from effects due to mass-action driven competitive site binding of ions, from Hofmeister effects (weakaccumulation or exclusion of salt ions), and most especially from any general “ionic strength” effects that would be predicted by an (unjustifiable) application of classical Debye-HQckel (linearized PB) theory. Key aspects of the model and analysis included (1 ) the proposal of two large asymmetries in the physical origins of these salt effects, namely, that they are primarily cation rather than anion effects and that they originate primarily from the nucleic acid polyelectrolyte (not the oligocationic ligand); and (2) the simplifylng assumption that the only charged groups on the nucleic acid whose interactions with salt ions are affected are those that are neutralized by binding the ligand. In terms of a simple physical picture, the binding of the oligocation was pointed out to be thermodynamically like a cation exchange process. However, this interpretation does not require that exactly one thermodynamically accumulated cation be released per charge on Lz+when it binds to DNA. For the association equilibrium Lz++ DNA site (D) + complex (LD) the effect on Kobsof changing the mean ionic activity of excess 1:l salt is given in terms of preferential interaction coefficients of electroneutral components by (Anderson and Record, 1993)

+

Each term (lZ,I 2r3,2J) in Eq. (75) maybe interpretedas the “thermodynamic extent of association” of electrolyte ions with the indicated oligoor polyelectrolyte species (nucleic acid, ligand, or complex) (Anderson and Record, 1983,1993;Record and Anderson, 1995). The terminology “thermodynamic extent of association” includes, but is not limited to, any site-bound or territorially bound (as defined by Manning, 1978) counterions on the polyion and is equal to the sum of the single-ion interaction coefficients r+J + r-J. For the DNA polyion at low to moderate salt concentrations, this sum is dominated by the single-ion preferential interaction coefficient of the cation > The thermodynamic extent of association is descriptive of the combined thermodynamic nonideality, which originates in the coulombic (preferential) interactions responsible for the counterion and coion gradients in the vicinity of L, D, or LD. For the binding of a simple oligocation L (e.g., an oligolysine, but not a protein), all of whose charges are

(lr+Jl Ir-JI).

3 34

M. THOMAS RECORD, .JR.,ET AL.

neutralized in the LD complex, the difference (IZLDl +2r9,LD) - (lZDl + 2Ts,0) appearing in Eq. (75) may be identified as the thermodynamic extent of ion release from the nucleic acid that accompanies complexmay be identified as the corresponding ation, and the term (1 ZLI 2r3,L) extent of ion release from the ligand. To obtain an approximate analytical expression for the derivative (a In Kobs/d In a,) in terms of the important polyelectrolyte and structural variables, Record et al. (1976) proposed that the oligocationpolyanion complex (LD) differs from the uncomplexed polyanion (D) in its interactions with salt ions primarily in the region occupied by an (isolated) bound ligand where, according to the model, I ZLI phosphate charges have been eliminated. With this approximation for the LD complex, the groups of terms that appear in Eq. (75) can be expressed + on a monomer basis as follows: for the uncomplexed DNA, 2r3,D) = ( 1 + Zr3.u(D)); for the LD complex, ( I Z L D l + 2 r 3 , I . D ) (lZDl - [&I) (1 + 2r3,u(D)); and for the uncomplexed ligand, (lZ,l + 2r3,L) = lZ1~l(l+ 2r3,,,(~.)). Hence, Eq. (75) becomes

+

At sufficiently low salt concentrations in the range where the PB/CC limiting law (LL) expressions are applicable, the oligocation ligand must + -0.5); therefore, Eq. (76) reduces to the behave ideally (2r&,(L) expression originally derived by Record et al. (1976) :

In applications of Eq. (77) to DNA processes, 1 - (25,)-' is 0.88 for ds DNA (5 = 4.2) and 0.7'7 for ss DNA (5 = 2.1). On the basis of either PB or CC limiting law polyelectrolyte thermodynamic theory, Eq. (77) correctly predicts both the observed power-law functional form of the salt concentration dependence of Kobsand the observed dependences of the power-law exponent on both the positive charge ZL of the ligand and the DNA axial charge density 6 (as demonstrated by results reviewed by Lohman and Mascotti, 1992; Anderson and Record, 1995). Remarkably, despite the theoretical restriction to low salt (limiting law) conditions, analyses based on Eq. (77) have been found in quantitative agreement with a wide variety of L"-DNA binding data obtained at salt

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

335

concentrations well above the expected limiting law range, as illustrated by the linearity and the absolute and relative slopes of the log-log plots shown in Fig. 5 for binding of oligolysines with net charge ZL = 3-8 to ds poly(A) * poly(U) (Fig. 5A) and for binding of polyanions (Z, = 2-4) to ds DNA (Fig. 5B). The extended applicability of Eq. (’7’7) has been examined in recent studies using PB calculations (Zhang et aL, 1996a) and MC simulations (Olmsted et al., 1995) that investigate effects of salt concentration on

6 4 v)

n

xo m 2 0

J

0

0

0.5

1.5

1.0

2.0

- Log “a+]

4.0-

B

-

‘ In

n

m

3.0

-

2.0

-

0 1

I

0

0.5

I

I

I

1.0 1.5 2.0 - Log “a+]

1

2.5

3.0

FIG.5. (A) Log-log plot of observed binding constants Kos, for the interaction of poly(A) .poly(U) with oligolysines of the type E-DNP-Lys(lys)., where DNP is 2,Miiodo4nitrophenol and 3 I n 5 8, as functions of the Nat concentration. (Values of n, which correspond to the net charge on the oligocation, are indicated on the figure.) (From Record et al., 1976.) (B) Plots of log KO,,.vs. -log “at] for the binding to DNA of the following polyamines: spermine (+4) (El); spermidine (+3) (0); and putrescine (+2) (0).(The charge on the polyamine is indicated on the figure.) (Modified from Braunlin et al., 1982.)

336

M. THOMAS RECORD. JR.. ET A L

the individual thermodynamic ion association terms (121 + 2r3,J for an octacationic ligand (LRt),oligoanionic or polyanionic DNA (ds, ss) and a centrally bound LD complex. Monte Carlo computational studies at low salt concentrations, summarized in Fig. 4, predict that preferential interaction coefficients (and therefore lZJl + 2r3,2J) increase with increasing salt concentration for La+ and for small DNA oligoelectrolytes (lZ,l 5 48) but decrease with increasing salt concentration for longer DNA oligoelectrolytes. Partial compensations between these opposing salt-concentration dependences of preferential interaction coefficients for oligoions and polyions may explain why values of (I3 In Kobs/13 I n a,) for binding of LR+to polymeric DNA do not deviate greatly from the limiting law predictions even at typical experimental salt concentrations. PB calculations (Zhang et al., 1996a) indicate that effects of salt concentration on binding of an oligocation to a DNA polyanion originate primarily from the local reduction in axial charge density of the DNA polyion. Release of thermodynamically accumulated ions from LRtupon binding to polyanionic DNA is predicted to contribute less than 30% of the total. A “molecular picture” helpful in visualizing the thermodynamic consequences of coulombic preferential interactions is provided by MC calculations of ion distributions (Olmsted et al., 1995). In Fig. 6, axial profiles of surface concentrations of univalent counterions (at a, = 1.8 mM) are plotted for a range of oligomer lengths (8-34 charges, with the axial spacing of ds D N A Fig. 6A) and for central complexes of an octacation (LRt)with two long ds DNA oligomers (110, 250 phosphates; Fig. 6B). Figure 6A demonstrates that the local counterion concentration at the surface of a short oligoion is much smaller than that characteristic of the interior region of a longer oligoion or polyion [less than 0.1 M for an 8-mer vs. 1.3 M near the center of a 34mer, and vs. 1.7 M for the corresponding polyion (cf. Fig. 6B)]. This calculation is applicable both to an oligocation, where the axial profile is that of X-, and to a short DNA oligoanion, where the axial profile is that of M+. The thermodynamic consequences of this coulombic end effect for r3,u are shown in Fig. 4. Figure 6B demonstrates the local reduction in surface concentration of M+ that occurs upon binding of LR+to a centrally located region of 8 phosphates of a long ds DNA oligoion. Comparison with the axial profile for an 8-mer in Fig. 6A clearly illustrates the physical origin of the large asymmetry in the effect of salt concentration on this interaction; it is a “polyelectrolyte effect” originating from local reduction in polyelectrolyte (DNA) axial charge density upon binding the octacation. Figure 6B provides a molecular picture illustrating the

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMEK EQUILIBRIA

1.50

f

v

I

I

,

I

I

337

,

1.25

K 0 ._

p

c

1.00

C

a,

0.75 0

a,

2

't

0.50

3

cn

0.25

0.00 Axial location (monomers)

-E

2.0

.g

1.5

c

s c g c

c

1.0

0

m

0.5

't

0.0

' 0

50 100 150 200 Axial location (monomers)

250

FIG.6. (A) Grand canonical Monte Carlo predictions (at a, = 1.76 mM) of surface concentrations of a univalent counterion (e.g., Na+) as a function of axial location (in monomer units, where 1 is the location of a terminal charge) along cylindrical models of short DNA oligomers: N = 8 (V),13 (H), 24 (A),34 (0).The N = 8 profile also represents the surface concentrations of C1- along a Ls+oligocation. (From Olmsted et nl., 1995.) (B) Grand canonical Monte Carlo predictions (at a, = 1.76 mM) of the surface concentration of a univalent counterion (e.g., Na+) as a function of axial location (in monomer units) along cylindrical models of central complexes of La' with 110-mer (0) and 250-mer ( 0 )DNA. Both oligomers are centered at axial location 125.5; eight central changes are eliminated from each to simulate binding of La+.(From Olmsted et al., 1995.)

cation exchange character of the (L6+-DNA) binding interaction (i.e., release of M+ on binding of La+to DNA). Several other recent computational thermodynamic studies, all based on solutions of a PB equation formulated for structurally detailed models, also have addressed the question of the origins of the salt concentration dependence of oligocation-polyanion binding. Presenting analyses of this effect on the binding of various divalent cationic ligands to DNA,

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M. THOMAS RECORD, JR.,ET A L

Misra et al. (1994a) and Sharp el al. (1995) contend that detailed threedimensional charge distributions on the DNA and on the ligand must be built into the model for which the PB equation is solved, and hence (by inference) that the salt concentration dependence of processes involving nucleic acids should be characterized not as a polyelectrolyte effect but rather as an effect due to local charge distributions for which in general the spatial coordinates differ significantly from system to system. According to this point of view, the contributions of ligand and DNA to the observed salt dependence of Kobswould be expected to be much less asymmetric than proposed by Record et al. (1976). Evidence, both experimental and computational, bearing on the physical origins of observed effects of salt concentration on processes involving nucleic acids has been reviewed by us elsewhere (Anderson and Record, 1995). More recent results concerning the importance of the polyelectrolyte effect are summarized in the remainder of this section. Zhang et al. (1996a) reported the first direct experimental confirmation that polyelectrolyte-salt preferential interactions make the dominant contribution to the magnitude of d In Kobs/d In a , for oligocation-DNA polyanion binding. They compared the effects of salt concentration on Kobsfor the binding of LBtto a small ss DNA oligoanion [dT(pdT) I:-] and to polymeric ss DNA poly(dT). These results are summarized in Fig. 7, where log Kobsis plotted as a function of log a,. 7

I

I

I

1

6

g 5 Y 0)

0

-I

4

3

-1.0

-0.8

-0.6

-0.4

Log a?

FIG.7. Salt concentration dependences of Kohsfor KWK,;-NH? binding to poly(dT)

(0) and to dT(pdT) (0) illustrated by log Kllh,vs. log a, plots. The fitted curves are based on Poisson-Boltzmann calculations for cylindrical models. (From Zhang et nl., 1996a.)

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

339

Values of Kobsfor binding of LBt to a site on dT(pdT)loor poly(dT) are similar at salt concentrations 1 0 . 3 M. For example, Kobsis about lo3M-I for the binding of La+ to a site on either dT(pdT)loor poly(dT) at 0.3 M salt. However, differences in both Kobsand in (a In Kobs/a In a+) for L*+binding to poly(dT) and to dT(pdT)lobecome increasingly significant as the salt concentration is reduced from 0.3 M. Although Kobs increases with decreasing salt concentration for both lengths of DNA, K o b s for poly(dT) is found to be much more strongly dependent on salt for poly(dT) concentration than is Kobsfor dT(pdT)lo.At 0.2 Msalt, Kobs exceeds that for dT(pdT)loby more than 10-fold (-5.4 X lo4 M-I vs. -4.3 X lo3 M I ) . At 0.1 M salt, Kobsfor poly(dT) exceeds that for dT(pdT),,, by more than 70-fold (-3.5 X lo6 vs. -4.6 X lo4 M-'). At 0.2 M salt (a, = 0.15 M ) , (a In Kobs/aIn a,) is -6.5 2 0.2 for binding to poly(dT) and -3.5 ? 0.1 for binding to dT(pdT)lo. On the basis of the following reasoning, Zhang et al. (1996a) conclude that (a In Kobs/aIn a,) for binding of LR+to polymeric DNA is dominated by the release of cations that had been thermodynamically associated with the DNA polyanion. Because both L8+and dT(pdT) ;:- have similar axial charge densities and differ only by 20% in numbers of charges, contributions to [(a In Kobs/aIn a,)l for binding of L8+ to dT(pdT)lo from cation and anion release can be plausibly assumed to make equal contributions: -1.8 at 0.2 M salt. [This estimate is also in the range of calculated values for L*+at 1.8 mM 5 a , 5 12.3 mM (Olmsted et al., 1995).] Comparison of these predicted values for anion release from La+with the experimental value of (a In Kobs/d In a,) for binding of La+ to polymeric DNA indicates that the contribution from cation release (4.7 at 0.2 M salt) constitutes more than 70% of the total effect. The extent of release of thermodynamically accumulated cations from poly(dT) upon binding L8+ is almost threefold larger than from dT(pdT)loin the salt range investigated. If an initially lower charge density oligocation (with the same number of charges) had been used and/or if the oligocation adopted a higher charge density conformation on binding to the nucleic acid (Padmanabhan et al., 1997), an even larger difference in contributions to (a In Kobs/aIn a,) from the oligocation and the DNA polyanion would be expected. Concurring that the salt concentration-dependent effects on oligocation binding to a polymeric nucleic acid are due to the polyelectrolyte character of the latter, Stigter and Dill (1996) analyze this effect by an approach substantially different from that reviewed here, which is based on Eq. (75).They report PB calculations of the salt concentration dependence of a thermodynamic function, also designated KOh,which differs significantly from that defined in Eq. (40).Approximately equivalent to

340

M. THOMAS RECORD, JR., ET AL.

a four-component preferential interaction coefficient (as defined, e.g., in Eisenberg, 1976),the function Kobsdefined by Stigter and Dill provides a measure of the effect of 1:l salt concentration on the total extent of thermodynamic accumulation of Lzt , calculated subject to the condition that LZt is distributed in a potential gradient surrounding the nucleic acid that is determined solely by the interactions of nucleic acid phosphates (modeled as a uniform continuum of charge) with the excess univalent salt ions. For the usual experimental situation, in which L”+, DNA, and complex all are present at high dilution in comparison to the concentration of 1:l salt, and if the binding assay detects only complexation rather than total thermodynamic accumulation of Lz+, the use of three-component preferential interaction coefficients o b tained from MC or PB calculations (Anderson and Record, 1993) is the appropriate method of analysis. Quantitative comparisons between calculations based on the method of Stigter and Dill (1996) and those based on Eq. (75) or the more approximate Eq. (76) are in progress (H. Ni, unpublished). 2. Spec@ and Nonspecajic Binding of Proteins to Polyanionic DNA Both specific and nonspecific protein-DNA interactions also exhibit power-law dependences of KObSon at (in the absence of competitive effects of multivalent cations such as Mg2+,which can be substantial even at low concentrations of the competitor cation relative to that of 1:l salt; see Capp et al., 1996, and references therein). The exponents of these power dependences (i.e., values of d In Kobs/d In a,) are negative and often surprisingly large in magnitude (approximately -20 for specific binding of E. coli Eu”’ RNA polymerase to the AP, promoter (Roe et al., 1985), and also approximately -20 for nonspecific binding of core RNA polymerase (lacking the u7’specificity subunit) to ds DNA (deHaseth et al., 1977). Are these salt concentration dependences also polyelectrolyte effects, arising primarily from the reduction in DNA axial charge density due to interactions with positively charged functional groups in the contact interface of the protein? By analogy with the oligocation-DNA polyanion binding data reviewed above, the generally large magnitudes and the power-law functional form of the salt concentration dependence of KobSfor specific and nonspecific binding of proteins to polymeric double-helical DNA strongly argue for a polyelectrolyte interpretation, as originally proposed by deHaseth et al. (19’77)and Record et al. (1978). However, this conclusion has been challenged in some studies (Misra et al., 1994b; Sharp et aL, 1995) that have instead emphasized coulombic ion-protein interactions on the basis of some

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

341

PB calculations that include structural details. At present, detailed highresolution structures of all reactants and products in solution are not available for any biopolymer systems, and the structure of the complex can be used to model the binding sites on the uncomplexed species only if complexation is not accompanied by a significant coupled conformational change. Therefore, challenges to the polyelectrolyte effect as the common denominator and (in general) primary contributor to the salt concentration dependence of Kobsappear premature (see Anderson and Record, 1995,for a more detailed commentary). Although effects of the choice of anion on the magnitude of Kobaat a specified salt concentration and, in some cases, on the derivative (dln Kobs/dIn a,) can be very significant (e.g., see Barkley et al., 1981; Overman et al., 1988;Ha et al., 1992,and references therein), the extent to which these effects can be described by purely coulombic calculations (e.g., via the PB equation) is presently unclear. Noncoulombic site-bindingor Hofmeister preferential interactions of anions with the protein may be involved. These effects may be analyzed on the basis of the formalism reviewed below. Record et al. (1978)used generalized binding polynomials (including biopolymer activity coefficients) in conjunction with concepts from CC polyelectrolyte theory to extend the thermodynamic analysis of oligocation-polyanion nonspecific binding (reviewedin Section VIII,B,2,a) and thereby derive a general equation applicable to analyses of the effects of salt concentration on Kobsfor specific or nonspecific binding of proteins to nucleic acids. The resulting equation, expressed in the present notation [analogous to Eq. (71),obtained from preferential interaction coefficients interpreted using the twodomain model] is

(E) + = AB+

AB-

-

27% -ABHtO 55.5

To identify and quantify the most important contributions to the effect of salt concentration on Kohl for protein-nucleic acid interactions, Record et al. assumed that the coulombic component of (a In Kobs/dIn a,) could be treated by analogy to oligocation-polyanion binding [cf. Eq. (71)] and obtained the following approximate result (expressed in the present notation) :

342

M. THOMAS RECORD, JK.,ET AL.

In Eq. (79), ZL,lis defined as the net number of (positive) charges on the protein ligand that are located in the protein-DNA interface and therefore reduce the local axial charge density of DNA. Both here and as formulated originally (deHaseth et al., 1977;Record et al., 1977, 1978), Zl.,, does not refer to the net charge on the entire protein, but rather to the net charge on the groups making up the protein interface with DNA. In Eq. (79), coulombic contributions to AB, and to AB- [both approximated as in Lzt binding; cf. Eq. (71)] have been grouped together in the first term. The term ABI refers to the portion of the anion contribution to (8 In K,,,/d In a,) that arises from effects other than direct neutralization of the ZL,Icharges. [These direct effects are de.] scribed by the oligoelectrolyte term ZL,,(1 + 2r3,u(L,1)) The solute concentration dependence of ABI is expected to be proportional to m3at sufficiently low solute concentrations, because it arises primarily from a reduction in weak (e.g., Hofmeister-type) anionprotein interactions (see Section IV,D above) caused by reductions in solvent-accessible protein surface that are due either to coupled folding (or to other conformational changes upon binding) or to the burial of uncharged regions of the protein in the DNA contact interface. The term ABH20reflects changes in hydration of both DNA and protein that accompany formation of the protein-DNA interface and also may result from coupled conformational changes. The magnitude of AB,,, is ' expected to be much larger for specific binding than for nonspecific binding of a given protein (see Ha et al., 1992; Sidorova and Rau, 1994; Frank et al., 1997, and references therein), both because the protein and DNA surfaces of the specific interface should be more complementary and because in general a larger amount of biopolymer surface is removed from contact with the solution in the specific binding process as a result of coupled folding or other coupled conformational changes unique to specific binding. Coupled folding of the protein appears to create a substantial portion of the protein-DNA interface in many specific protein-DNA interactions (Spolar and Record, 1994). In these examples, much more surface appears to be buried by coupled folding than in the protein-DNA contact interface, so both AB! and ABH20 may be dominated by the effect of reductions in protein surface that result from coupled protein folding, rather than from interactions with the DNA surface in the binding interface. The observed power-law dependences of Kohsrequire that the dominant term on the right-hand side of Eq. (79) be relatively independent of salt concentration. Unless the coulombic interactions of anions (and/ or cations) with the relevant regions of nucleic acid binding proteins

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

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have unusually strong thermodynamic effects that differ dramatically from those manifested by anion-oligopeptide interactions and by Hofmeister-type ion-protein preferential interactions, the precedents regarding functional forms and magnitudes of salt concentration dependences of K o b s provided by studies of Lzt oligocation-nucleic acid polyanion binding and by the large body of literature on Hofmeister salt effects on biopolymer processes strongly imply that the large magnitudes and relative salt concentration independence of (13 In Kobs/dIn a,) for protein-nucleic acid interactions are due to a polyelectrolyte effect that originates primarily from the reduction in local charge density of the DNA polyanion. To the extent that the origins of salt concentration dependences of protein-DNA interactions are analogous to those of oligocation-DNA interactions, for which the limiting law polyelectrolyte expression exhibits an extended range of validity as a result of compensation between the salt concentration dependences of the terms on the right-hand side of Eq. (75), the more approximate form of Eq. (79) obtained by introducing the limiting law functional form of the coulombic term may be of use:

In integrated form, Eq. (80) was applied by Ha et al. (1992) to interpret the large effects of replacing chloride by glutamate on &S, of specific and nonspecific binding of lac repressor. At a qualitative level, the proportionality to Z,,, of the polyelectrolyte term in Eqs. (79) and (80) was examined by Capp et al. (1996) for specific binding of lac repressor protein to lac operator DNA. They deduced from the high-resolution NMR structure of the DNA binding domain (DBD) of lac repressor (Chuprina et al., 1993) and the crystal structures of operator complexes of lac and purine repressors (Lewis et al., 1996; Schumacher et al., 1995) that the net charge on the interface region of each DBD is approximately + 3 (i.e., four positive and one negative charge). The corresponding estimate for the interaction of 2 DBD with one operator DNA site is Z,,, = 6, which, at least in the case, is consistentwith that estimatedfrom (a In Kobs/dIn a+) = -5.3forbinding of lac repressor to a centrally located operator site ( O F ) in a 40 bp ds DNA (Frank et al., 1997). A larger magnitude of (a In Koh/ d In a,) characterizes binding to operator sites embedded in longer DNA fragments or plasmids at low salt concentrations (Whitson and

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M. THOMAS KECORD, JR.,ET AL.

Matthews, 1986; see also Levandoski et al., 1996; Frank et al., 1997). Tsodikov et al. (1998) demonstrate that these differences arise from extended binding modes that involve wrapping and looping of flanking regions of nonoperator DNA on the lac repressor tetramer. C. Analysis of Efects of Salt Concentration on Transition Temperature (T,) of Nuckic Acid Helices

Denaturation and other conformational transitions of polymeric nucleic acids exhibit characteristically large effects of salt concentration: T, typically varies linearly with the logarithm of the salt concentration over a wide range (which can extend from to lo-' M or greater). = 0 and therefore from Eq. (69) In these transitions,

where Ah:,,, = AH& /lZpl is the enthalpy change per charged monomer unit (nucleotide) that undergoes the cooperative transition. Studies of effects of salt concentration on a variety of nucleic acid conformational transitions demonstrate that the quality P,/hh& is relatively independent of T,, so that an alternative expression for analysis of nucleic acid denaturation data is

According to the theoretical (MC) calculations of Bond et al. (1994), uJis a significant, salt concentration-dependent correction to the PB/ 1 However, differCC limiting (low salt) expression (I'&= - 1 ~ ~ (26J)-'). ences in the quantity ( -I'i,u= (25J)-'(1 + aJ)for conformational transitions of nucleic acid helices are predicted to be similar in magnitude to the corresponding differences in the limiting law quantity (25J)-'(see Fig. 8A). Therefore the quantity -AI'3,u is relatively independent of salt concentration (see Fig. 8B) and hence the PB/CC limiting law analytical expression for -ATa,,, is apparently useful even at salt concentrations approaching 1 M, far exceeding its expected range of applicability ( 5 1 mM). Fittings of Eqs. (81) or (82) to describe the salt concentration dependences of T, of a variety of order-disorder transitions, using the cylindrical PB equation to evaluate the vJ terms, are shown in Fig. 9 (Bond et al., 1994).

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Denatured

z 0.2 0.1

0.10

0.06

1 ‘

1

I

-2.0

I

1

-1.5

-1.o

-0.5

log c3

FIG.8. (A) Preferential interaction coefficients r3,,, calculated from the cylindrical Poisson-Boltzmann equation for native (ds) and denatured (ss) DNA as a fuaction of log C,. Structural parameters used for native DNA were a = 9.4 A and b = 1.7 A (cf. Fig. 3); those for denatured DNA were determined by nonlinear least squares analysis to be a = 6.9 A and b = 3.4 A. (From Bond et al., 1994.) (B) Differences in preferential interacbetween denatured and native phage T2 DNA (at the melting tion coefficients (Ar3,+) temperature) as a function of log C3. Values of Ar3,” (plotted points) were determined from the data of Privalov et al. (1969; replotted in Fig. 9A below) using Eqs. (81) or (82) and from the Poisson-Boltzmann calculations in panel A (plotted curve). (From Bond et al., 1994.)

Double-helical oligonucleotides exhibit very different trends in dTm/ d In a , with helix length, depending upon whether the helix is formed from two complementary strands (a “dimer” helix) or by a “hairpin” bend in a self-complementary strand. For hairpin helices, d T m / d In a , decreases in magnitude as helix length decreases (Elson et al., 1970). For even relatively short dimer helices, however, dT,/d In a, is found to be similar to the polymer (polyelectrolyte) value (Braunlin and Bloomfield, 1991; Williams et al., 1989). Olmsted et al. (1991) demonstrated that these apparently conflicting experimental results for hairpin and dimer denaturation are both consistent with theoretical predictions of the onset of oligoelectrolyte behavior of short nucleic acid oligomers.

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M. THOMAS RECORD, JR.,ET AL.

360 355 350 t-

E

I

X

345

2.85

340

2.80

\I

$

335 I I I I I I I 2.75 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5

In a+

80

' E

70 60 50 DS + 112 TS + 1/2

40 30 20 -4.5

-3.5

-2.5 In a+

- 1.5

-0.5

FIG.9. (A) Dependences of midpoint transition temperature T , (m) and of Ti,'( 0 ) for phage T2 (B form) DNA (Privalov et al., 1969) as a function of the logarithm of the NaCl mean ionic activity (In a+) at pH 7.0. Fits to a linear (-) function of In a, are shown. (From Bond et al., 1994.) (B) Phase diagram of thermal stability (7:J of doublestranded (DS) and triple-stranded (TS) ordered states of poly(rA) and poly(rU) relative to single strands (SS) in aqueous NaCl solutions. The dependences of melting temperatures T", on the logarithm of NaCl activity (In a + ) for the indicated transitions were determined calorimetrically (0)or spectrophotometrically (0, m) by Krakauer and Sturtevant (1967). The slopes of solid lines are predictions of the cylindrical PoissonBoltzmann thermodynamic analysis. (From Bond et al., 1994.)

-r3,u

Figure 10A and B display GCMC calculations of for native and denatured states of hairpin helices (panel A) where the number of phosphates per helical oligomer (N) is unchanged on denaturation, and for dimer helices (panel B), where N is halved upon denaturation. Differences ATs,+, displayed in Fig. 1OC and as the vertical offset between the pairs of curves in Fig. 10A and B, clearly exhibit qualitatively

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different dependences on chain length ( N ) of the helical form for transitions of hairpin and dimer helices, and these differences correspond to those observed experimentally.Hence, the observed behavior of dT,/d In a, for denaturation of both hairpin and dimer oligonucleotide helices is completely consistent with calculations for model oligoelectrolytes. In particular, the similarity of values of dT,/d In a, observed for dimer helices of short oligoelectrolytes to values of dT,/d In a, for the corresponding polyelectrolytes should not be interpreted to mean that these short oligoelectrolytes are behaving as polyelectrolytes, despite some contrary claims (or implications) based on applications of more approximate theoretical calculations (Fenley et al., 1990; Dewey, 1990). For the conversion of oligomeric ds DNA dimer helices to two smaller ss DNA oligomers (each with one-half the original number of charges and a p proximately one-half the original axial charge density), the difference in salt ion-oligonucleotide preferential interaction coefficients (Ar3,J happens to be, coincidentally, about as large as for the polymeric case (see Fig. 10B and C) . For the conversion of oligomeric DNA hairpin double helices to denatured strands with the same number of charges and approximately one-half the original axial charge density, dT,,/ d In a, (Elson et al., 1970) and therefore the magnitude of AT3,u(Olmsted et al., 1991; cf. Fig. 1OA and C) both decrease with decreasing chain length. For sufficiently long oligomers Ar3,u varies linearly with 1/N (Record and Lohman, 1978; Olmsted et al., 1991; cf. Fig. 1OC). The variation of d T , / d In a, as a function of chain length for hairpin helices (Elson et al., 1970) directly exhibits the changeover from polyelectrolyte to oligoelectrolyte behavior with decreasing degree of polymerization of the nucleic acid (cf. Fig. 1OC) and is consistentwith both MC/PB calculations and with the oligoelectrolyte behavior of Lz+ oligocations in the DNA binding studies reviewed above. Further physical inferences based on experimental and theoretical investigations of oligoelectrolyte end effects have been considered in detail in the concluding portion of the review by Anderson and Record (1995). IX. CONCLUSIONS AND FUTUREDIRECTIONS In this chapter we have reviewed the development and some representative applications of thermodynamic analyses based on solutebiopolymer preferential interaction coefficients, which provide a framework for the quantitative analysis and molecular interpretation of effects of solute concentration on biopolymer equilibria and processes. In par-

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1/yN

1

[SALT] AND [SOLUTE] EFFECTS ON BIOPOLYMER EQUILIBRIA

349

ticular, we have focused on the development of the thermodynamic descriptions of the preferential interactions of electrolyte solutes with charged biopolymers and on the molecular interpretations of these interactions deduced by applying polyelectrolyte theory for high-charge density nucleic acids and the twodomain model for weakly charged proteins. Results for these systems are compared and contrasted with those for systems where both solutes and biopolymers are uncharged. In the future, we anticipate that quantitative analyses based on correlations of solute-biopolymer preferential interactions with nonpolar, polar, and charged regions of biopolymer surfaces will allow a systematized interpretation of the tremendous body of experimental results both for individual solute-biopolymer preferential interactions and for solute effects on biopolymer processes. The development of a structure-based predictive capability can be foreseen. Conversely, where structural data are incomplete or where significant differences exist between the conditions under which the structural information was obtained and those of experimental interest, quantitative analyses of the functional forms and magnitudes of the concentrationdependent effects produced by a spectrum of excluded and accumulated solutes on biopolymer equilibria should reveal any involvement of coupled conformational changes (e.g., protein folding) and/or of coupled association-dissociation by the effects of these solutes on the coupled process. Such thermodymamic studies with solutes can be expected to yield quantitative information ~~~~~~

~

FIG.10. Grand canonical Monte Carlo determinations of dependences of -Ts,. on the reciprocal number of phosphate charges (1/N) for cylindrical models of native (ds) DNA (0)and denatured (ss) DNA (0)at a, = 1.76 mM, suitable to interpret the Ndependence of dT,,/d In a, of denaturation of hairpin helices (where Ndoes not change in denaturation). The magnitude of the difference Ar3,+ (i.e., the vertical displacement between the two curves) decreases with decreasing N. (B) Alternative representation of the Monte Carlo results of Fig. 1OA ( u , = 1.76 mM) suitable to interpret the relatively small dependence of dT,/d In al for denaturation of dimer helices on N, the number of phosfor ds DNA as a function of N-'; phate charges in the dimer. Filled circles represent open circles represent Ts,. for ss DNA as a function of (0.5IV-I. where 0.5Nis the number of phosphates in each denatured strand of the Nphosphate dimer helix. The vertical distance between the two curves yields the magnitude of Ar3," for denaturation of an Nmer helix to two (0.5w-mer single strands. (C) The extent of ion release per phosphate denatured (-A2rs,.) vs. the reciprocal of the number of phosphates in the denatured state (yN)-' for transitions of hairpin helices ( y = 1; open symbols) and dimer helices ( y = 0.5; filled symbols) at a, = 1.76 mM (circles), 7.07 mM (squares), and 12.26 mM (diamonds). The polymer limit ( N - 00) of (-AZrs,.) is shown as the intercept (l/yN+ 0). As observed experimentally, -A2r5,. and dT,/d In a, for denaturation of dimer helices are predicted to vary much less stronglywith Nthan for denaturation of hairpin helices. (From Olmsted et aL, 1991.)

rs,.

350

M. THOMAS RECORD, JR.,ET AL.

regarding the extent of coupled folding and other coupled protein processes in protein-nucleic acid binding interactions, to complement results obtained from quantitative analyses of the heat capacity and entropy changes of these interactions, which (like solute effects) provide thermodynamic signatures of the amounts of nonpolar and polar biopolymer surface removed from water as a result of the binding interactions (Spolar and Record, 1994; Frank et al., 1997, and references therein).

ACKNOWLEDGMENTS We are grateful to Professor Enrico Di Cera for the invitation and encouragement to write this review, and in addition thank him and Professor Tim Lohman for their comments on the manuscript. Research from this laboratory described here and the preparation of this review were supported primarily by NIH grants GM34351 and GM47022.

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Dewey, T. G. (1990). Biopolymers 29, 1793-1 799. Di Cera, E. (1995).“Thermodynamic Theory of Site-SpecificBinding Processes in Biological Macromolecules.” Cambridge University Press, Cambridge, UK. Eisenberg, H. (1976). “Biological Macromolecules and Polyelectrolytes in Solution,” pp. 48-59. Oxford University Press (Clarendon), Oxford. Eisenberg, H. (1994). Biophys. Chem.53, 57-68. Elson, E. L., Scheffler, I. E., and Baldwin, R. L. (1970).J. Mol. Biol. 54, 401-415. Fenley, M. O., Manning, G. S., and Olson, W. K. (1990). Biopolymers30, 1191-1203. Fixman, M. (1979).J. Chem. Phys. 70, 4995-5005. Frank, D. E., Saecker, R. M., Bond, J. P., Capp, M. W., Tsodikov, 0. V., Melcher, S. E., Levandoski, M. M., and Record, M. T., Jr. (1997).J. Mol. Biol. 267, 1186-1206. Fuoss, R. M., Katchasky, A., and Lifson, S. (1951). Proc. Natl. Acad. Sci. U.S.A.37,579-589. Gekko, K., and Timasheff, S. N. (1981). Biochemistly 20, 4667-4676. Gill, S. J., Dec. S. F., Olofsson, G., and Wadso, I. (1985).J. Phys. Chem. 89, 3758-3761. Groot, L. C. A., Kuil, M. E., Leyte,J. C., van der Maarel,J. R. C., Cotton,J. P., and Jannink, G. (1994).J. Phys. Chem. 98, 10167. Gross, L. M., and Straws, U. P. (1966). In ”Chemical Physics of Ionic Solutions” (B. E. Conway and R. G. Barradas, eds.), pp. 361-389. Wiley, New York. Ha,J.-H., Capp, M. W., Hohenwalter, M. D., Baskerville, M., and Record, M. T., Jr. (1992). J. Mol. Biol. 228, 252-264. Hamaguchi, K, and Geiduschek, E. P. (1962).J. Am. Chem. SOC.84, 1329-1338. Inouye, H., and Timasheff, S. N. (1972). Biopolymms 11, 737-743. Janin, H. (1976).J. Mol. Biol. 105, 13-14. Krakauer, H., and Sturtevant, J. M. (1967). Biopolymers 6, 491-512. Levandoski, M. M., Tsodikov, 0. V., Frank, D., Melcher, S., Saecker, R. M., and Record, M. T., Jr. (1996).J. Mol. Biol. 260, 697-717. Lewis, M., Chang, G., Horton, N. C., Kercher, M. A., Pace, H. C., Schumacher, M. A., Brennan, R. G., and Lu, P. (1996). Science271, 1247-1254. Liepinsh, E., and Otting, G. (1994).J. Am. Chem. SOC. 116, 9670-9674. Lin, T. Y., and Timasheff, S. N. (1994). Biochemistry 33, 12695-12701. Liu, Y., and Bolen, D. W. (1995). Biochemistly 34, 12884-12891. Lohman, T. M. (1985). CRC Crit. Rev. Biochem. 19, 181. Lohman, T. M., and Mascotti, D. P. (1992). In “Methods in Enzymology” (D. M. J. Lilley and J. E. Dahlberg, eds.), Vol. 212, pp. 424-458. Academic Press, San Diego, CA. Low, P. S. (1985).In “Transport Processes, Ion- and Osmoregulation: Current Comparative Approaches” (R. Gilles and M. Gilles-Baillen, eds.), pp. 469-477. SpringerVerlag, Berlin. Makhatadze, G. I., and Privalov, P. L. (1992).J. Mol. Biol. 226, 491-505. Manning, G. S. (1969).J. Chem. Phys. 51, 924-933. Manning, G. S. (1972). Annu. Rev. Phys. Chem. 23, 117-140. Manning, G. S. (1978). Q. Rev. Biophys. 11, 179-246. Miller, S., Janin, J., Lesh, A. M., and Chothia, C. (1987).J. Mol. Biol. 196, 641-656. Mills, P., Anderson, C. F., and Record, M. T., Jr. (1986).J. Phys. Chem. 90, 6541-6548. Misra,V. K., Sharp, K. A., Friedman, R. A., and Honig, B. (1994a).J. Mol. Biol. 238,246-263. Misra, V. K., Sharp, K. A., Friedman, R. A., and Honig, B. (1994b). J. Mol. Biol. 238, 264-280. Ni, H. (1998). In preparation. Nozaki, Y., and Tanford, C. (1970).J. Biol. Chem. 245, 1648-1652. Olmsted, M. C., Anderson, C. F., and Record, M. T., Jr. (1989).Proc. Natl. Acad. Sci. U.S.A. 86, 7766-7770.

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Olmsted, M. C., Anderson, C. F., and Record, M. T.,Jr. (1991). Biopolymers31,1593-1604. Olmsted, M. C., Bond, J. P., Anderson, C. F., and Record, M. T., Jr. (1995). Biophys. ,I. 68, 634-647. Oosawa, F. (1957). J. Polym. Sci. 23, 421-430. Overman, L. B., Bujalowski, W., and Lohman, T. M. (1988). Biochemistly 27, 456-471. Pace, C. N. (1986). In “Methods in Enzymology” (C. H. W. Hirs and S. N. Timasheff, eds.), Vol. 131, pp. 266-280. Academic Press, New York. Padmanabhan, S., Zhang, W., Capp, M. W., Anderson, C. F., and Record, M. T.,Jr. (1997). Biochemistly 36, 5193-5206. Parsegian, V. A., Rand, R. P., and Rau, D. C. (1995). In “Methods in Enzymology” (M.L. Johnson and G. K. Ackers, eds.), Vol. 259, pp. 43-94. Academic Press, San Diego, CA. Privalov, P. L., Ptitsyn, 0. B., and Birshtein, T. M. (1969). Biopolymers 8, 559. Record, M. T.,Jr. (1975). Biopolymers 14, 2137-2158. Record, M. T., Jr., and Anderson, C. F. (1995). Biqphys. J. 68, 786-794. Record, M. T., Jr., and Lohman, T. M. (1978). Biopolymers 17, 159-166. Record, M. T., Jr., and Richey, B. (1988). In “ACS Sourcebook for Physical Chemistry Instructors” (T.Lippincott, ed.), pp. 145-159. American Chemical Society, NewYork. Record, M. T.,Jr., and Spolar, R. S. (1990). In “Nonspecific DNA-Protein Interactions” (A. Revzin, ed.), p. 33. CRC Press, Boca Raton, FL. Record, M. T.,Jr., Lohman, T. M., and DeHaseth, P. L. (1976).J. Mol. Biol. 107,145-158. Record, M. T.,Jr., deHaseth, P. L., and Lohman, T. M. (1977). Biochemistly 16,4791-4796. Record,M.T.,Jr.,Anderson,C.F.,andLohman,T. M. (1978). Q.REV.Biophys. 11,103-178. Record, M. T., Jr., Mazur, S. J., Melancon, P., Roe, J.-H., Shaner, S. L., and Unger, L. (1981). Annu. Rev. Biochem. 50, 997-1024. Record, M. T., Jr., Ha, J.-H., and Fisher, M. (1991). In “Methods in Enzymology” (R. T. Sauer, ed.), Vol. 208, pp. 291-343. Academic Press, San Diego, CA. Record, M. T., Jr., Courtenay, E. S., Cayley, D. S., and Guttman. H. J . (1998). 7rends Biochem. Sci. (in press). Reynolds,J. A., Gilbert, D. B., andTanford, C. (1974). R o c . Natl. Arad. Sci. U.S.A.71,29252927. Richards, F. M. (1977). Annu. Rev. Biophys. Bioeng. 6, 151-176. Robinson, D. R., and Jencks, W. P. (1965).J. Am. Chem. Sac. 87, 2462-2470. Roe, J.-H., Burgess, R. R., and Record, M. T., Jr. (1985).J. Mol. Biol. 184, 441-453. Santoro, M. M., Liu, Y., Khan, S. M.,Hou, L. X., and Bolen, D. W. (1992). Biochemistry 31, 5278-5283. Scatchard, G . (1946). J. Am. Chem. Sac. 68, 2320. Scheffler, I. E., Elson, E. L., and Baldwin, R. L. (1970).J Mol. Biol. 48, 145-171. Schellman, J. A. (1987). Annu. Rev. Biophys. Biophys. Chem. 16, 115-137. Schellman, J. A. (1990). Biophys. Chem. 37, 121-140. Scholtz, J. M., Barrick, D.,York, E. J., Stewart,J. M., and Baldwin, R. L. (1995). Proc. Nutl. Acad. Sci. U.S.A. 92, 185-189. Schumacher, M. A., Choi, K. Y., Zalkin, H., and Brennan, R. G. (1995). Sriencf266, 763. Sharp, K. A., Friedman. R. A., Misra, V., Hecht, J., and Honig, B. (1995). Biopolymers 36,227-243. Sidorova, N. Y., and Rau, D. C. (1994). Biopolymers 35, 377-384. Sijpkes, A. H., van de Kleut, G. J., and Gill, S. C. (1993). Biophys. Chem. 46, 171-177. Simpson, R. B., and Kauzmann, W. (1953).J. Am. Chem. Sac. 75, 5139-5152. Spolar, R. S., and Record, M. T., Jr. (1994). Science 263, 777-784. Squire, P. G., and Himmel, M. E. (1979). Arch. Biochem. Biqphys. 196, 165-177.

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CONTROL OF PROTEIN STABILITY AND REACTIONS BY WEAKLY INTERACTING COSOLVENTS: THE SIMPLICITY OF THE COMPLICATED

.

By SERGE N TIMASHEFF Department of Biochemistry. Brmdels Universlty. Waltham. Massachusetts 02254-9110

“To conceive. understand. and grasp the whole symmetry of the scientific edifice . . . is equivalent to tasting that enjoyment only conveyed by the highest forms of beauty a n d truth’’ -Dmitri Mendeleev (1887) I . Introduction .................................................... A. Linked Functions: The Wyman Statement ...................... B. Preferential Interaction Means Competition between Ligand and Water .................................................. I1. Preferential Interactions .......................................... A. Definitions .................................................. B. Meaning of Dialysis Equilibrium Binding in Terms of Transfer Free Energy ................................................. C. Preferential Exclusion and Preferential Binding Are Specific Perturbations of the Cosolvent Activity by the Protein . . . . . . . . . . . . D . Preferential Binding Is the Balance between Site Occupancy by Water and Cosolvent Molecules ............................... E. Exchange at Sites ............................................ F. Additivity; Compensation ..................................... 111. Wyman Linkages in Preferential Interactions ........................ A. General Considerations ....................................... B. Control Is Exercised by the Difference in Preferential Interactions Whatever Their Sign ......................................... C. Specific Systems Controlled by Weak Interactions with Cosolvents . N . Linkage Control of Protein Stability ................................ A . Protein Stabilization ......................................... B. Protein Destabilization ....................................... V . Linkage Control of Protein Reactions .............................. A. Modes of Analysis ............................................ B. “Osmotic Stress” or Cosolvent Potential Stress or Preferential Interaction Stress? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. The Geometric Approach ..................................... VI. Sources of Exclusion ............................................. VII . Osmolytes ...................................................... VIII . Conclusion ..................................................... References ......................................................

355 ADVANCES IN PROTEIN CHEMISTRY. Vol. 51

356 356 357 360 360 362 363 370 373 375 378 380 381 383 387 387 403 409 409 411 415 416 423 425 428

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I. INTRODUCTION A . Linked Functions: The Wyman Statement For the better part of a century, it has been known that some substances such as sucrose or glycerol, when present at a high concentration ( 2 1 M ) , protect from deterioration the activity of isolated biological entities and maintain proteins in a functional state. Other reagents such as urea and guanidine hydrochloride (Hopkins, 1930; Neurath et al., 1944) act as protein denaturants. A classical protein precipitating agent has been ammonium sulfate (Northrop et al., 1948). These practices were purely empirical, and the phenomena were regarded as unrelated. Yet, if one reflects about these observations, it becomes clear that, in each case, the added substance acts as an agent that controls some process(es). What is the basis of these controls? Just as in any system of biological controls, be it that of the function of complex enzymes, regulation of gene expression, transmittal of neuronal signals, or oxygen transport, the controls are exercised through more or less complicated networks of coupled interdependent reactions. And while the patterns of coupling can be most diverse, all are governed by a simple general phenomenon- that of linkedfunctions, first described by Wyman in 1948. This chapter will be devoted to showing that the weakly acting proteinstructure stabilizing, denaturing, protein precipitating, and biochemical reaction modulating agents are all members of a single family. All function in an identical manner and are governed by a single mechanism that can be described with amazing simplicity in terms of a single law, the Wyman concept of linked functions, as applied to solutions in terms of the multicomponent thermodynamic theory, described by Scatchard (1946), Kirkwood (Kirkwood and Coldberg, 1950), and others (Stockmayer, 1950; Casassa and Eisenberg, 1964). The basic statement of the Wyman linked function theory (Wyman, 1964; Wyman and Gill, 1990) is the linkage relation:

where K is the equilibrium constant of a reaction, React Prod, which is modulated by a ligand, x (small or large); V , is the binding of this ligand in the Scatchard (dialysis equilibrium) sense to the entity (molecule, organelle, etc.) that is undergoing the reaction; T, P, and a, are the thermodynamic (Kelvin) temperature, pressure, and activity of component j , respectively. The meaning of this statement for biological controls is simply this: if a biological process, i.e., a biochemical reaction,

CONTROL OF PROTEIN STABILITY AND REACTIONS

357

is controlled by some factor x (which we may call the allosteric effector, cofactor, coenzyme, cosolvent, etc.), then the extent of binding of x will change during the course of the reaction; i.e., binding will be different to the reactant and to the product. The two processes-the React + Prod equilibrium and the binding of the ligand-are linked, and a change in one must necessarily induce a change in the other. In this sense, there is reciprocity between the two processes. In his classical article, Wyman (1964) makes an alternate statement of linkage which encompasses multicomponent thermodynamics: (aAGo/apx) T,P,n,+ = [ ( a p R e a c t / a % )

-

T,P,nlFX ( a ~ ~ r o d / a % )~

, ~ , n ~ , , l / ( a ~ x / 7;P,nItx a ~ )

(2)

where AGO is the standard free energy change of the reaction; p iis the chemical potential of component i, with p, = RTln a, (Ris the universal gas constant); and ni is the concentration of component i. In this form, the right-hand side of Eq. (2) states that the reaction is controlled by a change in preferential interactions between the reacting system and the surrounding medium. What does the term preferential interactions mean?

B. Preferential Interaction Means Competition between Ligand and Water When a protein dissolved in aqueous medium binds a ligand, the L PL, with a binding equilibrium is expressed customarily as P equilibrium constant K = [PL]/[PI [L] and a corresponding free energy change, AGL. Let us consider this reaction in full with the help of Fig. 1, in which the binding process is decomposed into steps. Consider site S. Dissolution of the dry protein in water leads necessarily to occupancy of the site by water molecules, with a free energy of contact A&. If conversely pure ligand were to be added to the dry protein at site S , the free energy of the protein-ligand contact would be AGL. Addition of the ligand to the aqueous protein solution with binding at site S requires that first the water molecules in contact with this site must be displaced with the loss of their free energy of interaction, -A&. This is followed by occupation of the site by the ligand with free energy AGL. The resulting free energy of the overall binding process is (Katz, 1950; Kronman and Timasheff, 1959)

+

This, of course, is the same as the free energy of binding measured

medium: H20

medium: H20

t

Cosolvent

medium: Vacuum

medium: H20

+

medium: Cosolvent

Cosolvent

= Water in ‘solvation layer‘

@I

= Cosolvent in “solvationlayer’

FIG.1. Schematic representation of surface interactions formed in the dissolution of a protein in a mixed solvent and of the exchange of water (W) molecules with a cosolvent molecule (singled out as L) at a site S on the surface of the protein molecule.

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359

when the protein is simply dissolved in an aqueous solution of the ligand. The overall binding equilibrium can be expressed as lu,,

P * ( H 2 0 ) "+ L + P * L + nH20

(4)

and the measured binding constant is an exchange constant K,, (Schellman, 1987, 1990):

Equations (3) and (5) have the practical meaning that a binding affinity measured at equilibrium is the difference between the affinities of the binding site on the protein for the ligand and for water.' If the affinity is greater for ligand, then, as a time average, the site will be occupied more frequently by ligand than by water; i.e., ligand will be bound preferentially over water. If the converse is true, then water will be bound preferentially over ligand; in other words, there will be preferential hydration at site S. This is the meaning of the terms prejerential binding, prejiimtial hydration, and preferential interactions. For weakly or very weakly interacting ligands, the affinities of the site for water and the ligand are of similar magnitude, AGL 2: A&, and interaction with water must be taken into account explicitly. This is true of all the substances which are used to stabilize in solution the native structure of proteins or the biological activity of an isolated organelle, as well as to modulate various biochemical reactions. These include sucrose, other sugars, glycerol, inositol, sorbitol, other polyols, amino acids, and methyl amines. All of these can act as osmolytes and cryoprotectants. The same is true of the general denaturants, such as urea and guanidine hydrochloride, as well as of salting-out salts and polyethylene glycols (PEGS).All of these substances, generally known as cosolvents, can be regarded as allosteric regulators of biochemical reactions (Lee and Timasheff, 1981). To perform their function, these substances must be used at high concentration (0.5-10 M, or 5-60%). This means that the interactions are weak and nonspecific. In other words, these substances act not at specific sites but over large spans of the surface of the protein molecule, where they interact with nonidentical affinities with

' Since biological systems normally operate in an aqueous medium, we have taken water explicitly as the solvent. In fact, these arguments apply to any solvent system, so the displaced molecules are those of the principal solvent. For example, in a benzene solution of polystyrene, benzene would be the principal solvent and any ligand would displace benzene niolecules in the exchange reaction.

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the mosaic of the heterogeneous surface loci. Hence, for cosolvents, the measured interaction is the summation of the interactions at all the n surface loci over the entire protein molecule. For these substances, the measured free energy of interaction is

where each (AG, - A&), can have a negative value (preferential binding of cosolvent at site i), a positive value (preferential binding of water at site i ) , or be equal to zero (indifference of site i for contact with water or ligand). For the weakly interactingsystems, then, the Wyman statement of linkages, as expressed by Eqs. (1) and (2), means that the overall effect of a cosolvent on protein stability or any protein reaction is defined by the sum of the change in interaction with water and cosolvent at each protein surface locus as the protein undergoes its transition from the starting state to the end state in a biochemical reaction, e.g., from the folded to the unfolded state. This includes all the sites originally in contactwith solvent,as well as newly exposed ones and newly buried ones. 11.

PREFERENTIAL INTERACTIONS A. DeJinit ions

The interaction of a protein with the solvent system in which it is immersed can be considered with respect to either of two reference states: pure water or solvent of the given composition. These will be taken in turn. In this analysis, components will be designated according to the Scatchard (1946) notation that component 1 is water, component 2 is protein, and component 3 is cosolvent. 1. The reference state is pure water. The free energy of interaction is given by the transfer free energy, A P ~ , , ~which , is the change in the chemical potential of the protein when it is transferred from pure water into the solvent system, Akp,,,= p2 (in cosolvent system) - p2 (in water). This is identical with the total free energy of interaction of the protein with the cosolvent in aqueous medium, i.e., Ap2,u= AG. 2. The reference state is the solvent system in which the protein is dissolved. When protein and cosolvent are mixed in aqueous medium, each perturbs the chemical potential of the other. This perturbation is expressed ) = (ap3/dm2) T,p,n,s, by the p-eferential interaction parameter, ( a p 2 / a m 3T,P,m2

2

CONTROL OF PROTEIN STABILITY AND REACTIONS

361

where mi is the molal concentration of component i. It is the gradient of the transfer free energy with cosolvent concentration or with protein concentration and a measure of the thermodynamic interaction at the given solvent composition, m3.If (ap3/am2) rp,m3 is not zero, the addition of protein to the system disturbs the thermodynamic equilibrium. To restore equilibrium it is necessary that cosolvent or/and water be added to (or removed from) the vicinity of the protein molecules. Thermodynamically this quantity is expressed by the pefmential binding parameter, (am,/a?) T,p,p3. Within the negligible approximation that (am,/a?) T,p,p3 = (am,/a?) T,p,,p3 (Stigter, 1960), the preferential binding parameter is the binding measured experimentally by dialysis equilib rium, V3 (mol ligand/mol protein) in Scatchard notation. It is the true expression of thermodynamic binding. Measurement of this quantity permits us to calculate the two free energy expressions of the interac-

where (ap3/am3)7;P,mz = n R T [ l / m 3+ (a In in this equation y3 is the activity coefficient of the cosolvent, and n is the number of particles into which the cosolvent dissociates in water. Here Ap3,&is the transfer free energy of the cosolvent into an aqueous protein solution. Depending on the relative global affinities of solvent and water for the protein, preferential binding may assume positive, negative, or zero values, which manifest themselves in measured stoichiometries of dialysis equilibrium binding, V3, that are positive, negative, or zero. Negative F3, i.e., preferential exclusion, indicates preferential hydration. Application of the Gibbs-Duhem equation to Eq. (7) gives the corresponding preferential hydration (Timasheff, 1963):

The relation of the preferential interaction parameter to preferential hydration is

362

SERGE N. TIMASHEFF

(ap!2/am3)T,P,,,,~ = n ( R T / 5 5 . 5 6 )( a m , / a m d T , ~ , , ~ ~ [1 + (a In ~ 3 / aIn

m3)T,P,rn,l

(10)

From Eqs. (7) and ( l o ) , it is clear that “binding” as measured by dialysis equilibrium is simply the observable manifestation of the mutual perturbations of the chemical potentials of the protein and the ligand, (am,/dm,) T,p,ps = - ( dp2/dps) T,P,n2. Rigorously valid comparisons of the strengths of interaction of different ligands may be made only through (aps/dm2)Tp,9or Ap2,,,.2The measured extents of “binding” or “hydration” at a given concentration, m3, do not contain the self-interaction of the ligand, and hence they do not give a true expression of the strength of the interaction.

B. Meaning of Dialysis Equilibn‘um Binding in Terms of Transfer Free Energy The two thermodynamic parameters that express the strength of the interactions, namely, the transfer free energy, and the preferential interaction at a given solvent composition, ( d p 3 / a m 27;P,rn, ) = (dpn/dma)T,P,rn2,are related exactly since preferential interaction is simply the gradient of the free energy of interaction at any given concentration of cosolvent, m3. This is expressed by Eq. (8),from which it is clear that knowledge of one parameter at a single solvent composition gives no information on the other. In fact, the preferential interaction parameter and the transfer free energy may have opposite signs. This is illustrated in Fig. 2A (see p. 3 6 4 ) , which presents the preferential interactions of MgCl, with p-lactoglobulin at pH 3.0. The relation between the three parameters is complex, as they follow totally different variations with cosolvent concentration. The experimental observation is a bell-shaped dependence of dialysis equilibrium binding on cosolvent concentration. Below 2.5 M NaCl, the preferential binding is negative. The exclusion reaches a maximal value at 1 M salt and becomes positive Frequently i t is convenient to compare the preferential interation parameters in concentration units of grams of component i per gram water, g,.These are easily related to the molal quantities, since g, = (m,/M,)/1000.The pertinent relations are

(ags/ag2)T,,,,r9 = W s /

M2) (amdam2)T,,,,p”

(agl/ag2)T.r,.,,= -(l/gs)(ag3/ag2)Tr,,~~

(94

( a ~ d h d= ~ [(nRTM,)/(IOOOgs)l((dgs/ag,)T,,,.,,[l ; ~ , ~ ~ + (a In rs)/(aIn mA:p..l (104 (ags/ag2)r,P,,7= As

- (l/gs)A,

(124

CONTROL OF PROTEIN STABILITY AND REACTIONS

363

after crossing zero at 2.5 M. This experimental binding curve is the manifestation of the variation of (dpu,/dm3) T,p,,,2with cosolvent concentration. The interaction is diminishingly unfavorable at low salt concentrations. It becomes favorable above 2.5 M salt. Although the sign of the thermodynamic effect of the addition of the cosolvent to the system changes with concentration, this does not occur for the transfer free energy. It is unfavorable at all solvent compositions. Thus, at high cosolvent concentrations, Ap2,&and( d p 2 / a m 3Tp,,2 ) are opposite in sign. While at first glance this might appear contradictory, this simply reflects the fact that the latter is the gradient of the former. A very important result is that the point at which the experiment gives the result of no binding, the binding free energy, Ap2,,,, is at a maximum. This means simply that, at that composition, an infinitesimal change in composition has no thermodynamic consequences: the thermodynamic interactions of the protein with cosolvent and water, expressed by Eq. (6), are balanced, with the consequence that the solvent compositions in the immediate domain of the protein and in the bulk are identical. This, however, does not mean thermodynamic indifference. Thermodynamic indifference requires that be zero at all solvent compositions, which leads automatically to zero values of (dpJdm3) T,p,,, and (dm3/dm2)Tp,p9.An example of a “well-behaved” system is shown in Fig. 2B, which depicts the interactions of sucrose with a-chymotrypsin. Here, the negative preferential binding increases monotonely with sugar concentration. This, in fact, reflects a variation almost sugar concentration independent of the chemical potential perturbation, (dp2/dm3)TP,m2, which in its turn reflects the monotonely increasing unfavorable interaction between the protein and the sugar solution, A P ~ , ~ , .

C. Preferential Exclusion and Prejimential Binding Are Specijic Perturbations

of the Cosolvent Activity by the Protein A measured positive stoichiometryin a dialysis equilibrium experiment (binding) is easy to understand. A negative stoichiometry may, at first, be not easy to accept. Yet, thermodynamically the two are mirrorimage manifestations of the same phenomenon, which is the perturbation of the excess chemical potential of the cosolvent by the protein, ( d p d d m d 7 ; ~ , =~ ~(dpui/dm2)T,P,,, = RT(a In Y d d % ) T , p , m 3 . If introduction of the protein into an aqueous solution of the cosolvent raises the activity coefficient of the cosolvent, the interaction will be unfavorable and (dp3/dm2)7;P,ms = RT(d In a3/dmp).I;om, will be positive. By Eq. (7), the preferential binding will be negative and the experimental finding in dialysis equilibrium will show a negative stoichiometry. The converse is

364

SERGE N. TIMASHEFF

A

, 40

-

n

0

20 N-

5

O

E

‘2.

0

0

E

0

30

u

W

-

c-

E

‘1. 10

0 N

V Y

A

E

U

Il

E

rg

h

20

o

-5

-10

2

1

0

3

MgCI, Concentration (M)

B

I

1

I

1

sucrose (M)

I

1

h Y

a

m

W

5

2

(D

E

E

‘2. 0

Y

10

0

CONTROL OF PROTEIN STABILITY AND REACTIONS

365

true when the protein lowers the chemical potential of the cosolvent. The experimental observation is that of a positive stoichiometry of binding. By the Gibbs-Duhem equation, this is reflected by a lowering of the chemical potential of water in the first case and by a raising of it in the second. This does not imply, however, that the effects of cosolvents on proteins are exercised necessarily through their effect on water activity, i.e., the chemical potential of water, (i3pl/i3m,),, = RT(i3 In al/i3m3)T,P Preferential binding and pefkrential exclusion (pejimential hydration) are the consequence of interactions of the cosolvent with the protein that are specijic to each given cosolvent. To make this statement clear, let us examine three typical cosolvents: one that is preferentially excluded, one that is preferentially bound, and one that is neutral (inert), i.e., for which dialysis equilibrium gives a stoichiometry of -0. These could be sucrose, urea, and an alkyl urea. Addition of a cosolvent to water or to an aqueous solution of protein has two consequences. The first is the general totally nonspecific osmotic effect that in a binary solution, at identical values of 9 4 ( 4is the osmotic coefficient), all solutes lower the activity of water by identical extents, which can be expressed through a colligative property such as the osmotic pressure, 7~"'s. The chemical potential of water in the presence of any cosolvent is p,, = po- V,IT, where pois the standard chemical potential of water and & is its partial molal volume (Tanford, 1961b). Superimposed on this universal and totally nonspecific effect are effects specific to each cosolvent (or other solute), manifested in dialysis equilibrium as preferential exclusion and preferential binding. The nature of the interactions is determined b~ the cosolwent. To demonstrate this, let us examine phenomenologically the process of solvation on a molecular, mechanistic level. Let us take a protein surface element and immerse it into water and into three aqueous cosolvents-one that preferentially binds, one that is preferentially excluded, and one that is

FIG.2. Variation of the thermodynamic interaction parameters with cosolvent concentration:preferential binding (drn,/drnz)T,,,,,,, (0); preferential interaction parameter ( 0 ) ; and transfer free energy (A).(A) PLactoglobulin in aqueous MgC12 solution at pH 3.0 [plotted from the data of Arakawa et al. (1990b)l. Note that ApZc is at its peak (maximalfor the unfavorably interacting MgClZ)at the point where the binding measured by dialysis equilibrium is zero. (B) Chymotrypsinogen in aqueous sucrose solution (plotted from data of Lee and Timasheff, 1981). [Figure 2A reprinted from Timasheff (1993) with permission from the Annual Review of Biophysics and Biomolecular Structure,Vol. 22, 1993, by Annual Reviews Inc.]

366

SERGE N. TIMASHEFF

neutral, all three present at activities that lower the activity of water by identical extents. Then, any difference in the observed interactions must reside in the chemical and physical nature of each cosolvent. It may be attracted to the protein surface, repelled from it, or be indifferent to it, leading respectively to the observations of binding, exclusion, or neutrality (no effect), Thermodynamically this reflects the difference in affinity of each cosolvent with that of water for sites on the protein [Eq. (3)], i.e., interactions with the protein, the nature of which is specific for each cosolvent and independent of its effect on the activity of water. In the three cosolvents, the interaction will be described thermodynamically by the transfer free energy, Ap2,,,or Ap3,1r, which is O for preferential exclusion. Binding of cosolvent molecules to a protein or their exclusion from the domain3of the protein may have a variety of chemical and physical causes. In the case of exclusion, bulky cosolvents can be excluded sterically; 2-methyl9,Cpentanediol (MPD) is repelled from charges on the protein surface; trehalose is repelled from surfaces because it raises the surface tension of water; glycerol is solvophobic, and so it is repelled from nonpolar areas on the protein surface. All of these repulsive forces can be expressed by appropriate potentials, the nature of which is determined by the cosolvent since the protein remains unaltered. It presents a surface with certain characteristics. Each cosolvent molecule reacts to this surface with the consequence that its molecules redistribute themselves in the vicinity of the protein. In the case of repulsion, the physical result is a micro phase separation which is thermodynamically unfavorable, i.e., (dp3/dm2) > 0, and, at a set of protein and cosolvent concentrations, Ap2,1r= Ap3,h > 0. This redistribution of the cosolvent molecules, i.e., their inability to form contacts with the protein, leaves in the protein vicinity an excess of water molecules which interact in identical fashion with the immutable protein surface no matter what the cause of cosolvent exclusion. Hence, mechanistically water might be regarded as essentially a passive agent: it reacts to the action of the cosolvent. In the case of the total exclusion of a cosolvent, the number of water molecules in contact with the surface remains the same as when the solvent is pure water. This might at first appear as a neutral event, since water remains in place and cosolvent does not touch the protein. As a consequence, at times, such excluded cosolvents have been referred to as inert. This

’ In the context of preferential interactions the term “domain of the protein” refers to the volume of solvent around a protein molecule in which its presence is “felt” by solvent component molecules so that their freedom of motion (translationalor rotational)

is affected by the protein. It in no way means a defined compartment or shell around the protein molecule.

CONTROL OF PROTEIN STABILITY AND REACTIONS

367

is totally false. A major change does occur in the system. The medium in which the protein is dissolved changes, since the bulk solvent now contains cosolvent molecules in addition to water. The maintenance of the status quo at the protein surface (only water, no cosolvent) requires, therefore, that a redistribution of solvent components take place at that surface. This costs the expenditure of free energy, which is the free energy of cosolvent exclusion, A P ~ It, ~is clear, therefore, that an excluded cosolvent cannot be inert, because this would violate the laws of thermodynamics. Let us now address formally protein hydration in various environments by constructing the proper thermodynamic box. This analysis will also demonstrate the symmetry of preferential binding and preferential exclusion about the point of neutrality. This thermodynamic scheme, presented in Fig. 3, gives the relative levels of the chemical potential of

w a t e r

o n

t h e

p r o t e i n

s u r f a c e

water in cosolvcnt FIG. 3. Thermodynamic scheme of the hydration of a protein surface in pure water and in water-cosolvent systems. The variation is that of the chemical potential of water. For an explanation see the text.

368

SERGE N. TIMASHEFF

water, p l , in the processes of hydration of a protein surface and addition of cosolvents. Let us carry out these processes stepwise. For this, let us take again a dry protein surface element of defined area which will be maintained unaltered in its physical and chemical characteristics over the several operations. Let us immerse it in water and then introduce, in turn, cosolvents with different interaction characteristics into the system-one that is inert, one that is preferentially excluded, and one that is preferen tially bound. The free energy changes related to the various operations of Fig. 3 are as follows: 1. Hydration of the d v protein suface element. When it is immersed into water, it becomes hydrated and the chemical potential of the water in contact with the protein surface rises to a level p p ,which gives a free energy of hydration: AG; = pp - po. 2. Addition of any cosolvent to pure water. The chemical potential of water is lowered to the level p, = RT In al, where al is the activity of water at a cosolvent activity a3 = m(iy3. The transfer free energy of water from pure water into the cosolvent system is ApKZCS = pcs- po = - Kr. This is the osmotic effect. 3. Addition of an inert cosolvent to the protein suqace element-water system. Since the cosolvent is inert, i.e., thermodynamically neutral, at any site on the protein surface element, it is indifferent whether the site is in contact with water or cosolvent, and the composition of the solvent in contact with the protein surface element will be identical with that of the bulk solvent. This lowers the chemical potential of water on the protein surface to the level P;(~"), and the transfer free energy of the water on the protein surface is Ap;+CS(in) = - pp.The thermodynamic indifference to protein contacts with-water or cosolvent has the = A p f rw+cs ee = - V,n. Therefore, the free enconsequence that Ap;+cs(in) - p,,, is identical to that in water and ergy of hydration, AG&in) = SAGh = AG&i,,, - AG: = 0. 4. Addition of a preferential4 excluded cosolvent to the protein suface elementwatersystem. In this situation, the protein surface element makes contact overwhelmingly with water, even though the medium is a mixed solvent. Let us analyze this in steps. First, addition of the cosolvent has the general nonspecific osmotic effect of lowering water activity to the level P;(~"). In addition to this, there is superimposed the e f f t of exclusion that is specijic to the given cosolvent. This creates the state that only water molecules are in contact with the protein surface. This deficiency of cosolvent on the protein surface can be pictured as the removal of cosolvent molecules from the protein surface element and their replace-

CONTROL OF PROTEIN STABILI'R AND REACTIONS

369

ment by water. Such a process requires the expenditure of free energy, the amount of which is equal to the free energy of cosolvent exclusion, AG,,. Then, the free energy of hydration is AG&,,, = AGk(in)+ AG,,. The transfer free energy of the water molecules on the protein surface from water to the excluded cosolvent system is Ap;+cs(ex) =

- PP. 5 . Addition Ofapreferential4 bound cosolvent to the protein suqace elementwater system. In this situation the protein surface element becomes enriched in cosolvent molecules with respect to the bulk solvent. The cosolvent speczjic $&ct of binding is accompanied by a favorable free energy change, A&, which is negative in sign. The number of water molecules on the protein surface is now smaller than would be the case in an inert cosolvent. This leads to a transfer free energy of water, Apw+cs(bd)= p;'bd)- pp = p;Ci") + A& - pp.This, in turn, lowers the free energy of hydration from its value in an inert cosolvent by the free energy of binding, SO that AG,h,,,,) = AG?s(in) + A&. If we apply this analysis to a protein reaction, i.e., if we equate the dry protein surface element to be hydrated to the creation of a new protein surface increment during a conformational change, e.g., the opening of a cleft, then the measured free energy of hydration will be equal to the solvent contribution to the process. All the experimental approaches in which the cosolvent exists in disperse solution with the reacting system give (AG:s - AG;) ,whichis theeffectofacosolvent (oranyotheradditive) on the reaction, It is evident that (1)an inert cosolvent will have no effect on the reaction even though it exerts its osmotic effect; (2) apreferentially bound cosolventwill beapromoterofthe reaction; and (3) apreferentially excluded cosolventwillbe an inhibitor. Preferential exclusion imposes on any system the stress of the unfavorable free energy, AG,,. This can be relieved by reducing the surface that makes contact with solvent by, e.g., a conformational transition that closes a cleft. For the reverse reaction, it is evident that the influences will be reversed. Finally, it must be stressed that the free energy of hydration of a newly exposed protein surface, AG; of Fig. 3, cannot be measured by any approach in which a cosolvent is present in disperse solution together with the reacting system. The information that such approaches can give is limited to the free energy of exchange between water and cosolvent molecules at sites on the protein surface as defined by Schellman (1987, 1990). The only information obtained is Z(AG, - AGw) of Eqs. (3) and (6); AG; = AGw is the reference point, and all measurements give only departures from it that are induced by the cosolvent.

370

SERGE N. TIMASHEFF

D. Pr$mential Binding Is the Balance between Site Occupancy by Water and Cosolvent Molecules

As stated above [Eq. (S)], the transfer free energy is the sum of the interactions between solvent components and protein at all the surface loci of the latter. Then

where the terms on the right-hand side are the contributions to the perturbation of the chemical potential of the protein by cosolvent (L) and water (w) in equilibrium with each other. If the two terms on the right-hand side of Eq. (11) are formally identified with contributions of ligand and water binding to the measured preferential interaction parameter at any given solvent composition, then combination of Eq. (1 1) with Eqs. (7) and (9) permits us to identify formally the two terms on the right-hand side of Eq. (11) with perturbations of the chemical potential of the protein by occupancy of sites by ligand (3) and by water (1 ) , respectively, although this operation has no physical meaning (1) (Tanford, 1969), and ( a p p / a m 3T,P,,, ) = ( a p d a m d F)P,m, - ( a ~ . ~ 2 / a T,P,rn,* md This leads heuristically to a formal relation between preferential binding measured by dialysis equilibrium and the effective total numbers of ligand and water molecules in contact with sites on the protein surface, 4 and B,, respectively:

The same derivation has been given by Tanford (1969), who expressed the interactions in terms of equilibrium constants of ligand and water with empty (dry) sites on the protein surface. This relation has been derived by various heuristic approaches (Timasheff and Inoue, 1968; Tanford, 1969; Aune et al., 1971; Inoue and Timasheff, 1972; Kupke, 1973; Reisler et al., 1977). It must be stressed that the parameters B, and 4 are not thermodynamic quantities and do not represent any physical reality, since they are in equilibrium with each other and cannot be separated (Timasheff, 1992; Schellman, 1994). They are simply a description of the experimental results in terms of a model in which ligand and water molecules occupy discrete loci on the protein surface.

CONTROL OF PROTEIN STABILITY AND REACTIONS

371

In the case of weakly interacting systems, the two terms on the righthand side of Eq. (11) are of similar magnitude and always & > (dmddmJT,p,,s. The effective site occupancy numbers, Bl and 4 [V, and V, in Tanford’s (1969) notation], must not be equated with numbers of water and cosolvent molecules actually in contact with the protein (or with a particular patch on a protein, such as an active site on an enzyme or the locus of the binding of a ligand). Equations (11) and (12) state that 4 and B, stem from the summation of a broad spectrum of thermodynamic perturbations of cosolvent and water molecules by the protein. These may range from actual site occupancy with its exchange free energy, or a strong repulsion from a locus on the protein surface, to a momentary perturbation of the rotational or translational motions of solvent molecules which never come into contactwith the protein surface (Lee et al., 1979). Each of these events makes a contribution to the free energy of interaction, i.e., for each solvent molecule, i: ( d p J d 9 ) ’ = (dAG/d%) and - ( q / m l ) ( d p l / d q ) ’ = (dAC&/dq). Each, when multiplied by (dps/d%),turns in a value of 4 or 4,which may be a small fractional number. By Eq. ( l l ) , the parameters & and B1 of Eq. (12) are summations of all of these numbers and, as such, are only descriptive parameters. Preferential binding is an expression of the thermodynamic interactions of the protein with solvent components. It is measured by equilib rium techniques such as equilibrium dialysis (Scatchard, 1946),isopiestic equilibrium (Hade and Tanford, 1967), light scattering (Katz, 1950), X-ray scattering (Timasheff, 1963), or sedimentation equilibrium (Kielley and Harrington, 1960).It does not give the number of protein-ligand contacts. That information must be obtained from nonthermodynamic techniques, such as calorimetric titration or the perturbation of a spectral property, which respond to contacts between protein and ligand molecules. Conversely the effective number of water molecules that hydrate a protein may be calculated by, e.g., the NMR (nuclear magnetic resonance) approach of Kuntz (1971). These contactdetecting techniques, in turn, cannot give a thermodynamic description of the interactions of a protein with a solvent system, nor can they detect cosolvent molecules that do not make contacts with the protein surface but are weakly perturbed by its proximity. A pictorial description of the process can be given in terms of a simple model which, however, does not correspond to the actual numbers of interacting sites nor to their occupancy. Such a simple model is presented in Fig. 4,in which the surface of the protein is depicted as a mosaic of loci that interact with water and ligand with various affinities. In this model, the contacts have been grouped into

372

SERGE N. TIMASHEFF

/

FIG.4. Schematic representation of the thermodynamic state relative to bulk solvent of the surface of a protein dissolved in a mixed solvent. The total protein surface must make contact with water or cosolvent molecules. Depending on the free energy of interaction with the cosolvent system, three types of interactions may occur: (crosshatching) the cosolvent exchanges with water (these areas will be occupied by water or cosolvent depending on their relative affinities); (dotted areas) the cosolvent is excluded; (hatching, ////) thermodynamic indifference-the ratio of cosolvent to water molecules is the same as in the bulk-solvent medium at all solvent compositions. [Reprinted with permission from Timasheff (1992). Copyright 1997 American Chemical Society.]

three categories: (1) Those that have a significant affinity for ligand and undergo water-ligand exchange; they may manifest preferential binding, B3/B1 > m 3 / m l , or preferential exclusion, B3/B1 < m 3 / m 1 , depending on the relative affinities for water and the ligand. (2)Those that have essentially no affinity for ligand; they do not undergo waterligand exchange and are occupied predominantly by water, B3/B1 < -/ml; they always display negative values of (dm3/dm2)T,p,,9. (3) Those that are indifferent to contact with water or cosolvent; for them B 3 / B 1 = m3/ml and ( d - / 1 3 % ) ~ , ~ , ~= ~ 0 (thermodynamic neutrality); it must be noted, however, that contact-detecting techniques will report these last sites. The affinities of the various sites for the solvent components vary with solvent composition because of the nonideality of the cosolvents

CONTROL OF PROTEIN STABILITY AND REACTIONS

373

(Schellman, 1990, 1993). Hence their distribution will change with solvent composition. Each site of the first kind will be occupied at any moment either by ligand or by water, depending on the relative affinities. As a time average, the occupancy of the n exchangeable sites, which may have nonidentical ligand affinity, will be & molecules of ligand and B Y h molecules of water. The sites of the second category make no contribution to B,; these will be occupied by water molecules that are not exchangeable with ligand, B p . Sites of the third category will not be detected by any equilibrium thermodynamic approach, whether they are occupied by water or cosolvent. The measured dialysis equilibrium binding being the sum of all three occupancies, Eq. (12) becomes

How can these types of sites be resolved? At present there is no way of sorting out these weak surface interactions. A description of the situation for any real protein-cosolvent system can be obtained, however, from a combination of dialysis equilibrium binding results with those of a protein-ligand contact-detecting technique with the unrealistic assumption that the affinity of all n exchangeable sites is identical. Then the contact-counting techniques yield an apparent value of CB,. If the values so obtained as a function of cosolvent concentration are plotted in terms of a Scatchard or similar plot, it is possible to obtain values of n, the descriptive number of exchangeable sites, and of an apparent binding constant, KaPP, which will differ greatly from the true values (Schellman, 1994). Assignment of a model of exchange, such as the number, r, of water molecules displaced by each cosolvent molecule, gives effective values of B Y h = T( n - 4).Combination with the dialysis equilibrium binding results gives, by Eq. (13),BP. Alternately, the effective number of water molecules that interact with the protein (ZBYh+ BNex 1 ) can be estimated by the NMR technique of Kuntz (1971; see also Kuntz and Kauzmann, 1974) or the vapor pressure measurements of Bull and Breese (1974). Combination with measured values of ( d m , / d m , ) T,p,c3 gives, by Eq. (13), the value of &. Examples of such calculations are given in what follows (Sections IV,B,2 and IV,B,3) for the urea denaturation of RNase A.

E. Exchange at Sates While combination of preferential binding with counting of effective contacts gives a descriptive value of B3 and Bl within the model of

374

SERGE N. TIMASHEFF

identical exchangeable sites, further classification of the effective water molecules into exchangeable and nonexchangeable requires a model for the exchange at sites. The question of exchange has been addressed by Schellman (1987,1990,1993,1994)in aseries ofimportant theoretical papers. Treating explicitly the simple model in which one ligand molecule replaces one water molecule at totally independent loci on the protein surface, Schellman has derived the relation between the exchange constant, & [see Eq. ( 5 ) ] , and preferential binding:

where K:, is the exchange constant in mole-fraction units; K,,, the constant in molal units; and X3, the mole fraction of cosolvent. The values of the exchange constants as expressed in Eq. (14) vary with solvent composition because of nonideality. The relation to the intrinsic exchange constant is K:, = Killu(fi/fs), where fi and fs are the activity coefficients of water and cosolvent, respectively. Hence, the cosolvent concentration dependence of preferential binding, which may change sign while Kin[,remains the same (Schellman, 1990). Summation over all the n exchangeable sites of identical K , and the nonexchangeable sites and combination of Eqs. (13) and (14) gives

Equation (15) indicates that neglect of the nonexchangeable sites must always give values that are greater than or equal to the measured preferential binding. The concept of exchange gives a ready explanation for the observed negative stoichiometries of binding measured by dialysis equilibrium for a large number of structure stabilizing and salting out cosolvents. The exchange equilibrium of Eq. (4) is described in molecular terms by Eqs. (12) and (13). The Schellman exchange analysis of Eq. (14) shows how a positive interaction constant, K,,, can result in negative dialysis equilibrium stoichiometries of binding. Classical treatment leads to the absurd conclusion that there must be a negative equilibrium constant, as first pointed out by von Hippel et al. (1973). The introduction of ( K e x- l / m l ) in the numerator of Eq. (14) takes into account specifically the binding of water at the exchangeable sites. This satisfies the require-

375

CONTROL OF PROTEIN STABILITY AND REACTIONS

ment that an equilibrium constant must be positive, even though the measured thermodynamic binding is negative. The exchange equilibrium criterion, for the model treated by Schellman, is established by Eq. (14). It is the magnitude of K,, relative to l/ml. Since ml = 55.56 mol of H 2 0 per 1000 g, l / m l = 0.018 rn-l This means that when K,, < 0.018 m-I, there is preferential hydration, i.e., a negative binding stoichiometry; when K,, > 0.018 m-l, the observation is that of positive binding; K,, = 0.18 m-l is the point of no dialysis equilibrium binding. If we return to Fig. 2, this means that within this model, for the MgC12 system, K,, < 0.018 m-l below 2.5 M salt, and K,, > 0.018 m-l above that concentration, with K,, = 0.018 m-l at 2.5 MMgC12.For cosolvents, the exchange equilibrium at sites corresponds to free energy changes of 51501 cal when expressed on the molal scale.

F. Additivity; Compensation The observed dialysis equilibrium binding is the summation of interactions at a large number of sites, each characterized by its own set of affinities for water and the cosolvent. In this sense, the preferential interactions are additive. Additivity is found also when the cosolvent system contains more than one type of particle. This is true of all salts which dissociate into their cations and anions, as well as of mixed cosolvents. Analysis of the preferential interactions of salts has shown that they follow the Hofmeisterseriesbothfor anions and cations. The induction of preferential hydration decrease in the orders SOq- > CH3CO; > C1- > SCN- for anions and Na+ > X2+ > Gua+ for cations (Arakawa and Timasheff, 1984b). When paired in a salt, the effects are additive, as shown in Table I. For example, guanidinium ions are preferentially TABLE I Hofmeiter Progression ofPrt$iential Hydration of BSA in I M Salts at 20°C (PH 4.5-5.6)" Anion Cation Nat M$+, Ca2+,Ba2+ Gua+

c1OAcsoq[(dgl/8g.Jrp,,pa g r a m s of water per gram of protein] 0.24 0.04 to -0.04 -0.24

"Data from Arakawa and Timasheff (1984b).

0.31 0.11 to 0.18 0.08

0.52 0.34 0.21

376

SERGE N. TIMASHEFF

bound to proteins; C1- is weakly excluded; the pair GuaHCl is preferentially bound. Yet, in 1 M salt, Gua+ is not capable of overwhelming the effect of SO:-, which is strongly excluded. As a consequence, Gua,S04 is preferentially excluded, although to a lesser extent than Na2S04. The progression of salt preferential hydration is reflected in their effects on macromolecules. Thus, Na2S04is a strong salting-out agent, while NaSCN is a protein solubilizer (von Hippel and Schleich, 1969); GuaHCl and GuaSCN are among the best protein denaturants; Gua2S04 stabilizes the native structure of RNase A. The additivity is strikingly evident in the two examples of Fig. 5. Figure 5A shows that the ability of Gua+ salts to denature proteins follows the Hofmeister series, as do

A 'OI

-u

L

E

L

40

-

30-

20

0

I

I

I

1

1

2

3

4

Concwwarlon Imol~s/ll~rrl

FIG.5. See facing page for legend.

CONTROL OF PROTEIN STABILITY AND REACTIONS

377

their preferential interactions (von Hippel and Wong, 1965). In the other example, the effect of salts on the solubility of acetyltetraglycine ethyl ester is found to be totally additive between cations and anions (Robinson and Jencks, 1965a,b). As shown in Fig. 5B, LiBr is a saltingin agent for this model tetrapeptide; NaCl is a salting-out salt. Both NaBr and LiCl had no effect, as each ion compensated for the effect of the other one in an additive manner. Two particularly interesting salts are MgC12and Gua2S04.As shown in Fig. 2,MgC12is strongly excluded from P-lactoglobulin at pH 3. This becomes reversed at 3 M salt. In the case of Gua2S04,the situation is just the opposite (see Table I1 below, in

..

I .o

.

0.8

0.6

0.5

t I

2

MOLARITY FIG.5. Additivity and compensation of Hofmeister ions. (A) Effect of guanidinium salts and urea on the transition temperature of RNase A (pH 7.0, 0.013 M sodium cacodylate, 0.15 M NaC1). (B) Salting in and salting out of acetyl tetraglycine ethyl ester (ATGEE) by varying concentrations of halide salts at 25"C, expressed as the ratio of the pentapeptide solubility (S) in water to that in salt. [Figure 5A reprinted with permission from von Hippel and Wong (1965).Copyright 1997 The American Society for Biochemistry & Molecular Biology. Figure 5B reprinted with permission from Robinson and Jencks (1965a). Copyright 1997 American Chemical Society.]

378

SERGE N. TIMASHEFF

Section IV,A,l). At 0.5 M, it is preferentially bound to BSA, but it is excluded above that concentration. The two observations may be explained in terms of compensation. Both the Mg2+and Gus+ ions have affinity for sites on protein molecules. Yet both C1- and SO:- ions promote preferential exclusion, SO$- doing so more strongly than C1-. Nevertheless, at high MgC12 concentration, MgZt ion binding becomes sufficientlyhigh to overcome the opposing effect. In the case of Gua2S04, the SO$- anion is very strongly excluded and overcomes the attractive interaction of Gua+, the net result being preferential exclusion. Compensation and additivity are also found in mixtures of neutral cosolvents. An example of this is the mixture urea-trimethylamine-N oxide (TMAO). Following the observation that some fish store urea and methylamines (principally TMAO) as osmolytes (Somero, 1986),Yancey and Somero (1979, 1980) have examined their effects individually and in a mixture on the K , of some fish enzymes, as well as on the stability (T,) of ribonuclease A. In both studies, urea and TMAO had opposite effects on the observed properties, while their mixture in the 2 : 1 urea/ TMAO molar ratio, as found in the fish, gave full compensation: K,,, maintained its dilute buffer values. The compensation between these two cosolvents is shown in Fig. 6A for the melting of RNase A (Yancey and Somero, 1979). It is seen that the two cosolvents displace T, in opposite directions. The effect of their mixture on T,, however, is the arithmetic sum of the individual effects. Similar results were obtained with RNase TI (Lin and Timasheff, 1994). Figure 6B shows the preferential binding of urea to native and unfolded RNase TI in the absence and the presence of TMAO (Lin and Timasheff, 1994). The lack of effect of the methylamine on the preferential binding of urea indicates that the two cosolvents interact with the protein in an additive noncooperative manner.

111. W

w LINKAGES IN PREFERENTIAL INTERACTIONS The very weak interactions of cosolvents with proteins and other biological systems can modulate a vast spectrum of biochemical reactions and transitions undergone by biological macromolecules and assembled organelles. This is the consequence of the additivity of interactions at multiple sites (Schellman, 1975, 1987, 1990). These reactions can be classified under five general categories: (1) effect on protein stability (stabilization-denaturation) ; (2) solubility (salting in-salting out) ; (3) self-assembly of subunit systems; (4) modulation of enzymic and other biochemical reactions: ( 5 ) binding of ligands.

I

200

0

400

600

800

I 400

lUreal (mM)

I

I

I

I

I

0

100

200

300

IOthcr solutes] (mM)

"

I

.

0.00 0.03

"

.

I

l

"

1

.

0.06

"

.

I

.

0.09

.

I

.

0.12

.

0.15

93

FIG.6. Compensation of the effects of urea and TMAO. (A) Midpoint of the thermal unfolding transition of RNase A at pH 7: control (0);urea (A); TMAO (0); betaine (M); palanine (A);sarcosine (0); taurine (e); urea and trimethylamine N-oxide (0).(B) Cosolvent concentration dependence of the preferential binding of cosolvent to protein: RNase TI in urea (0);RCMTI in urea ( 0 ) ;RNase TI in TMAO (0);RCM-TI in TMAO (M); RNase TI in solutions of urea and TMAO with a molar ratio of 2:l (V); RCM-TI in solutions of urea and TMAO with a molar ratio of 2:l (v).The gsvalues for the ternary solvents indicate the concentration of urea. In the mixed cosolvents experiments the preferential binding of urea only is detected. It is seen to be identical whether TMAO is present or not. [Figure 6A reprinted from Yancey and Somero (1979). Figure 6B reprinted with permission from Lin and Timasheff (1994). Copyright 1997 American Chemical Society.]

380

SERGE N. TIMASHEFF

A. General Considerations The effect of a cosolvent on any reaction in equilibrium can be examined with respect to two reference states: (1) a solvent of the given composition and (2) water (in practice dilute buffer). When the reference state is a solvent of the given composition used in the experiment, the following question is asked: In what direction will the addition of an infinitesimal amount of cosolvent orient the reaction? The control exercised by the cosolvent is given by the Wyman linkage equation [Eq. (1)3, expressed in terms of preferential binding [Eq. (16a)] or of effective site occupancy [Eq. (16b)l (Tanford, 1969; Aune et aL, 1971):

When the reference state is water, i.e., the equilibrium in cosolvent of concentration m3 is compared to that in water, then the influence of the cosolvent on the reaction is expressed by the difference between the transfer free energies of the products and the reactants:

where AG; and AG; are the standard free energies of the reaction in solvent of composition m3 and in water, respectively. Equation (17) is the integral of the Wyman linkage relation [Eq. (16a)l if the last is expressed as the perturbation of the chemical potential of the protein by addition of the solvent. Then, by Eq. (7),

Integration of Eq. (18) gives (Schellman, 1975; Vlachy and Lapanje, 1978)

CONTROL OF PROTEIN STABILITY AND REACTIONS

381

If the preferential interactions are expressed in terms of the effective site occupancies, Eqs. (19b and c) become, by introduction of Eq. (121,

B.

Control Is Exercised @ the Difference in Prejkrerential Interactions Whatever Their Sign

As stated above, cosolvents can exert an action on a protein reaction only as a consequence of the fact that their action reflects the sum of interactions at a multitude of sites on the protein, as depicted on Fig. 4.For the I sites on the protein surface, the changes in Wyman slope [Eq. (IS)] and transfer free energy [Eq. (17)] are summations of the changes at each site, i:

Therefore, additivity and compensation are functional also in the control of biochemical reactions. Equations (21a) and (21b) tell that the local interactions at each individual site can favor one or the other end state of the reaction, or they may be neutral. The overall effect, however, is the final balance of the many weak local linkages. It is the opposing driving forces at different sites that frequently lead to the

382

SERGE N. TIMASHEFT

requirement that effectors must be present at very high concentration (e.g., 8 M urea). What are the consequences of these relations? If we take the linkage equation [Eq. (16a)l and plot the equilibrium constant logarithmically as a function of the cosolvent activity, the slope at any point defines the direction in which a cosolvent displaces the equilibrium at that solvent composition: if 6(dms/dm2) is po~itive,~ the cosolvent is an activator of the reaction; if it is negative, the cosolvent is an inhibitor of the reaction; if it is zero, the cosolvent has no effect on the reaction-it is inert. If the reference state is water, the requirement is that there must be a change in transfer free energy during the course of the reaction. These relations are illustrated in Fig. 7A and B (see p. 384) for three possible situations: panel A presents the dependence of the linkage slopes on cosolvent concentration; panel B gives the corresponding change in transfer free energy. In the first case, the Wyman slope is positive at all concentrations of cosolvent. This means that at any solvent composition, addition of an infinitesimal amount of cosolvent will enhance the reaction. The corresponding change in transfer free energy shows a monotone increase in enhancement relative to water. Hence, addition of the cosolvent will drive the reaction at all concentrations. The second case is the converse, i.e., increasing inhibition with cosolvent concentration, whether at any individual point or relative to water. The third case illustrates what might strike one as an apparent contradiction between the two types of analyses. In it, the slope is positive at low ligand concentrations, which means activation. It increases up to a maximal point, then passes through zero and assumes negative values. The corresponding change in transfer free energy, however, indicates that, relative to water, the cosolvent activates the reaction at all concentrations. This activation attains a maximal value and then starts weakening. This is reflected by the changes in the slope shown in Fig. '7A. The point at which the Wyman slope seems to indicate maximal activation is only the point of the maximal increase in activation relative to water. The maximal activation occurs at the concentration at which the Wyman slope is zero.At higher concentrations, the negative values of S( drn3/dm2) indicate that each infinitesimal addition of cosolvent progressively weakens the reaction; i.e., the strength of activation relative to water becomes smaller. Reversal of the signs of the ordinate for the dotted lines (example 3) would describe the converse situation, in which the cosolvent acts as an inhibitor of the process relative to water at all solvent compositions but becomes an activator in the differential form at high concentrations. From this point on, the subscripts on the partial derivativeswill be dropped in the text.

CONTROL OF PROTEIN STABILITY AND REACTIONS

383

The difference between the preferential binding of the cosolvent to the reactant and to the product may be generated in a variety of ways. Since this seems to induce some confusion when dealt with in terms of preferential interactions, we shall now list some possibilities, as depicted in Fig. 7C and D. Specifically, let us take the inhibition of a reaction, e.g., protein stabilization by cosolvents, i.e., inhibition of the native P denatured ( N 8 D) equilibrium. Inhibition requires that 6(dm3/dmz) be negative. A positive value means promotion. Since stabilizing cosolvents are preferentially excluded from proteins at 20"C,the first case is the one expected. In it, the preferential exclusion is increasingly greater for the denatured state than for the native protein. This is the expected situation with sugars at 20°C (Lee and Timasheff, 1981; Arakawa and Timasheff, 1984a),although preferential binding values for the unfolded proteins can only be inferred. The same result can be obtained when both end states of the protein preferentially bind the cosolvent, binding to the end state (denatured) being less than that to the starting material (case 2); the change in (dm3/amz)is negative, hence the process is inhibited even though dialysis equilibrium gives preferential binding. In some situations the preferential exclusion from the native protein has been found to decrease with cosolvent concentration and actually to change to preferential binding at high concentration (case 3). This is the case of MgClZinteraction with P-lactoglobulin at pH 3.0, shown in Fig. 2.Nevertheless the cosolvent acts as a protein structure stabilizer, i.e., an inhibitor of the N D equilibrium (Arakawa et al., 1990b). The inference is that exclusion from the denatured end state of the equilibrium is greater, or binding to it is smaller. An interesting situation, described by pattern 4, is when a cosolvent reverses its action on the equilibrium. This is akin to the dashed line of Fig. 7A. In the example depicted here, cosolvent preferentially binds at all concentrations to both end states of the reaction. However, at low concentration, the binding is greater to the native than to the denatured state. This results in inhibition of the equilibrium. As cosolvent concentration is raised, the pattern reverses itself, binding becomes stronger to the end state of the protein, and the cosolvent becomes a promoter of the reaction. Similar variations can be described for a single cosolvent concentration, but with temperature as the variable parameter.

*

C. Specajic Systems Controlled

Weak Interactions with Cosolvents

The influence of a cosolvent on a reaction relative to water is expressed by the change in standard free energy, A G O , and by Eq. (17),in transfer free energy, Ap2,,,.For the sake of analysis, a convenient way to express

384

SERGE N. TIMASHEFF

A

Inhibitor

octivnlor 1

octivotor

111

FIG.7. Patterns of preferential interactions in modulating biochemical reactions. (A,B) Variations of the change in preferential interactions linked to an equilibrium: (A) slope in Wyman linkage relation [Eq. (16A)l; (B) corresponding variations of the transfer free energy (BAp?,,).Case 1, activator with respect to water at all cosolvent concentrations (m3); case 2, inhibitor relative to water at all m?;case 3, activator with respect to water, with a bell-shaped dependence on cosolvent concentration. At the inaximal value of C S A ~ the ~ . ~ sign , of the slope in the log K vs. log as plot reverses from positive (activation) to negative (inhibition); note that the zero point in the linkage plot corresponds to maximal activation relative to water, while the maximal slope of the linkage plot corresponds to the maximal rate of increase of - B A P ~ , ~ ~ .

CONTROL OF PROTEIN STABILITY AND REACTIONS

..

385

+

.h

2 L ' A

1

D

D

D

N

1 ni3 (or Icmpcnlure)

FIG.7. (continued) (C,D) Combinations of preferential binding of the two end states ofan equilibrium, here denoted for the inhibition of the N D reaction. The dependence is either on cosolvent concentration (ms) or temperature. Case 1, preferential exclusion is greater from the product than the reactant: case 2, preferential binding is greater to the native than to the denatured protein; case 3, for the native protein the interaction changes from exclusion to binding, and for the denatured form there is exclusion at all ms (or temperature); case 4, preferential binding is first smaller to the denatured than the native protein, but this relation reverses above a crossover point-there is inhibition at low m3 or temperature and promotion at high m, or temperature (e.g., stabilization changes to denaturation).

386

SERGE N. TIMASHEFF

Eq. (17) is through the thermodynamic cycle. For any equilibrium that is modulated by a cosolvent, that is the classical thermodynamic box [Eq. (2211:

4

4

ACLZ1

AFE1

(22)

\

\

1. Stabilization (denaturation) ( N P D) :

2. Self-assembly (P,

+ P * P,,+,):

where P refers to a protein subunit freely dispersed in solution, and P,,+, refers to the same subunit incorporated into the assembled structure, say, a microtubule o r a subunit enzyme. 3. Confmational transition (P P*):

*

Here the equilibrium refers to, say, the activation of an enzyme, with P being the inactive form and P* the active form whose formation is affected (promoted or inhibited) by the cosolvent. 4. Solubility [protein dispersed in solution (Sol) P precipitate (Pr)]:

where S2is the protein solubility. For salting-out salts, at high salt concentration solubility follows the empirical equation (Green, 1932):

CONTROL OF PROTEIN STABILITY AND REACTIONS

387

where p and K,$are empirical constants. The slope of this plot gives K,, the salting-out constant. Combination of Eqs. ( 2 6 ) and (8) shows that K , is a Wyman linkage description of the process of precipitation, as (Arakawa and Timasheff, 1985b; Timasheff and Arakawa, 1988)

It must be stressed that this describes only the phase separation and has no bearing on protein crystallization, which is a different, post-phase separation process that involves nucleation and growth. 5 . Ligund binding (P 3- L PL):

*

In this case the thermodynamic effect of the cosolvent on the free ligand must be taken into consideration explicitly. This can be measured either by vapor phase equilibrium or by solubility, as

where yt;- and y i are the activity coefficients of the ligand in water and in the cosolvent system, respectively.

IV. LINKAGE CONTROL OF PROTEIN STABILITY A. Protein Stabilization 1. Preferential Exclusion

The influence of cosolvents on protein stability has been known for many decades. Itwas accepted, however, that there were two distinct classes of effectors: protein structure stabilizers and protein denaturants (i.e., structure destabilizers),which operated by unrelated mechanisms. It was accepted that denaturants such as urea or GuaHCl act by binding in the classical sense to proteins. The rationale for stabilization by sucrose, glycerol, and other stabilizers was quite vague, and diverse explantations were proposedsuch as binding to some key sites on the protein or the formation

388

SERGE N. TIMASHEFF

of a protective shell around the protein molecule. In fact, as outlined in the preceding sections, whether a particular cosolvent will stabilize or destabilize proteins is a function strictly of its differential interactions with protein groups in contact with solvent in the two end states of the general N P D equilibrium. The general observation has been that those cosolvents that stabilize protein structure are preferentially excluded from the protein surface at 20°C, whereas those that induce unfolding in general interact favorably with the unfolded state of the protein. The converse, however, may not be necessarily true. A selected list of the interaction parameters of cosolvents with proteins is given in Table 11. The phenomenon of preferential exclusion and its interpretation in terms of multicomponent thermodynamics has been known' for a long time, both for the interaction of salts with DNA (Timasheff, 1963; Hearst, 1965; Cohen and Eisenberg, 1968) and with proteins (Cox and Shumaker, 1961; Ifft and Vinograd, 1962, 1966; Hade and Tanford, 1967; Aune and Timasheff, 1970). In an elegant study, von Hippel et al. (1973) have found that the binding of neutral salts to polyacrylamide columns gave negative values of the elution equilibrium constant. This led them to the conclusion that surface groups in the column were preferentially hydrated in the presence of the salts, which were unable to displace water molecules from the amide dipole. These early observations eventually found theoretical interpretation in the principles of exchange developed by Schellman (1978, 1987, 1990, 1993) and the classification of water molecules into nonexchangeable and exchangeable ones. A detailed analysis of preferential hydration at 20°C in a variety of solvent systems has led to the classification of preferentially excluded cosolvents into two general classes (Arakawa et al., 1990b). In the first class, the preferential hydration is essentially independent of cosolvent concentration and solvent pH. These cosolvents have always been o b served to stabilize the structure of proteins and to reduce protein solubility. In the second class, the preferential hydration is strongly dependent on cosolvent concentration or pH, or both. Their effect on protein stability cannot be predicted from their preferential interactions with the native protein, even though they may be good protein precipitants. The first class of cosolvents consists of sugars, some polyols including glycerol, small amino acids, and certain salting-out salts such as Na2S04, MgS04,and NaCl. Many of the neutral compounds are found in nature as osmolytes and cryoprotectants. The second class includes MgC12,some amino acid salts, PEGS, and MPDa5 It must be noted that errors of measurement of preferential interactions, under the best circumstances, are 50.004-0.010 in (ags/agJ).This, for the interaction of a protein of molecular weight 64,000 with,e.g., 1 M glucose, gives errors of 21 in B, [of Eq. (12)] and 255 in B,, i.e., the effective number of water molecules in contact with the protein surface.

389

CONTROL OF PROTEIN STABILITY AND REACTIONS

TABLE I1 Thermodynamics of Protein-Solvent Interactions in Weakly InteractinR Systemf

1M 3 M

CTGen PH 2

Glucoseb -0.080 0.394 0.205 -0.168

0.4 M 0.4 M

BSA, pH 6 BSA,pH 3

Lactose -0.048 -0.100

20% 40%

CTGen PH 2

5% 10%

BSA

20% 40 % 50%

RNase A pH 5.8 25°C

10%

BSA

50%

25°C. pH 2

25°C

PLg

0.4 M 1.5 M 0.2 M 1.0 M 1.5 M

Lysozyme PH 7

0.5 M 1.5 M

BSA

PH 2

BSA

pH 5.7

6.6 23.2

0.321 0.665

12.7 26.4

2.1 4.8

Glycerol' -0.081 -0.161

0.258 0.195

3.9 2.9

13.9 32.6

Inositold -0.021 -0.041

0.407 0.387

16.4 15.6

4.6 9.4

2-Methyl-2,4pentanediol (MPD)' -0.045 0.196 -0.474 0.810 -0.943 1.03

10% 20% 30%

pH 5.7

6.2 3.7

Propylene glycol' 0.138 -1.25 0.409 -0.44

Polyethylene glycol (PEG) 6009 -0.069 0.627 -0.112 0.464 -0.093 0.232

1.04 1.73 1.24

-50.3 -17.5

10.1 11.1 9.4

0.9 6.2 10.2

-70 -360

1.8 4.1 6.8

Arginine HClh -0.027 0.305 0.230 -0.093 0.010 -0.218 -0.028 0.114 -0.070 0.173

3.7 2.6 13.9 5.7 9.2

3.0 5.0 -3.4 -4.0 3.0

Sodium glutamate' -0.045 0.513 -0.133 0.457

40.6 36.2

22 67 ( continues)

390

SERGE N. TIMASHEFF

TABLE I1 (continued) Solvent concentration

Protein

BSA

(dgda&) (dg)

( a P da 4

/dg2) (g/g)

Arginyl glutamateh -0.024 0.361 -0.114 0.387

0.2 M 0.77 M

pH 5.7

0.25 M 1.0 M 0.25 M 1.0 M

Trimethylamine-Noxide ( T W O ) RNase T, 0.001 -0.044 pH 7; 25°C -0.045 0.553 RCM-Ti -0.024 1.25 pH 7; 25°C -0.007 0.084

kcal/mol'

Aktr (kcal/mol)

23.3 24.2

5 20

-0.3 3.0 8.2 0.5

-0.34 1.2 2.6 5.3

J

Na2SOt -0.021 -0.067

0.287 0.459

21.5 33.6

RNase pH 2.8 pH 5.5

MgSO," -0.047 -0.028 -0.066 -0.032

0.388 0.384 0.452 0.440

17.7 3.1 5.1 3.5

0.5 M 2.0 M 0.5 M 2.0 M

PLg pH 2.0 pH 5.1 pH 5.1

MgC12" -0.015 0.304 -0.030 0.148 0.002 -0.051 0.002 -0.007

21.6 23.9 - 3.6 - 1.2

13 47 -3.5 -2.5

2M 6M 8M 2M 6M 8M

pLg" pH 5.5

- 7.0

-15 -49 -60 4.4 13.0 16.1

0.5 M 1.0 M 2.0 M

BSA

0.5 M 1.0 M

BSA

1.0 M 0.6 M 1.2 M 0.6 M

BSA, pH 4.5

3.0 M 5.2 M 6.3 M

pH 4.5

Myoglobin" pH 7.0

pH 4.5

Urea 0.05 0.18 0.16 -0.03 -0.07 -0.05

-0.40 -0.36 -0.22 0.24 0.14 0.07

Gudnidine sulfate! 0.008 -0.071 -0.052 0.21 1 -0.184 0.316

Guanidine hydrochloride BSAI 0.200 -0.55 25°C 0.134 -0.17 0.1 MDTT 0.038 -0.035

-5.8 -3.4 1.9 1.0 0.5

-4.6 8.7 15.7

-22.4 -5.7 -0.9

-6.6

-5.1 19.1

- 127 - 181 -189 (continues)

CONTROL OF PROTEIN STABILITY AND REACTIONS

39 1

TABLEI1 (continued)

0.8 M 1.3 M 3.5 M 6.5 M

RNase A' pH 7.0

-0.013 0.004 0.044 0

0.141 -0.03 -0.099 0

0.82 -0.15 -0.38 0

0.92 1.05 -0.56 -1.15

"All values are 20"C, unless specified otherwise, extrapolated to zero protein concentration. Key: BSA = bovine serum albumin; DTT = dithiothreitol; P L g = plactoglobulin; RCM-T, = reduced and carboxylate form of RNase T,. "Arakawa and Timasheff. 'Arakawa and Timasheff, "Arakawa et al., 1990a. 1982a. 1985a. Poklar and Lapanje, 1992. 'Gekko and Timasheff, Kita et al., 1994. "Zerovnik and Lapanje, 1981. 'Arakawa and Tirnasheff, 1986. "Gekko and Morikawa, 1984c. P Arakawa and Timasheff, 1981. Lin and Timasheff, 1994. 1984b. Pittz and Timasheff, 1978. Arakawa and Timasheff, q Reisler et al., 1977. 'V. Prakash and S. N. Tima'Gekko and Koga, 1984. 1982b. 'Arakawa et al., 1990b. sheff, unpublished. J

2. Families of Preferentially Excluded Agents a. Sugars. Among sugars, preferential'interaction studies have been carried out on sucrose, trehalose, glucose, and lactose. The preferential hydration in the presence of sucrose between 0.1 and 1.0 M was found to be invariant with sugar concentration, with (ag,/agi) values of 0.32, 0.25, 0.45, and 0.24 g water per gram protein for chymotrypsinogen (CTGen), a-chymotrypsin, RNase A, and tubulin (Lee and Timasheff, 1981;Lee et al., 1975).When the (dgs/ag2)data were plotted as a function of g3 [Eq. (12a)], the straight line fits extrapolated to zero values of AS (and B s ) . This means that, in an aqueous sucrose solution within experimental error, the sugar does not occupy sites on the protein surface other than at thermodynamically indifferent loci. Hence, observably, there is total preferential exclusion, although neutral contacts are formed. The same was found for trehalose in its interactions with RNase A (pH 2.8 and 5.5) (Lin and Timasheff, 1996; Xie and Timasheff, 1997c) and for lactose in its preferential interactions with RNase A (pH 8.8), CTGen (pH 2.0), and bovine serum albumin (BSA) (pH 6.0) (Arakawa and Timasheff, 1982a). For BSA at pH 3.0 the preferential hydration was twice that measured at pH 6.0. This reflects the well-known expansion of BSA at acid pH (Yang and Foster, 1954; Tanford et d.,1955) and emphasizes the fact that preferential interactions are the sum of all site occupancies over the entire surface in contact with solvent. The same

392

SERGE N. TIMASHEFF

is not true of glucose (Arakawa and Timasheff, 1982a). Of the sugars that have been studied, glucose is the only one that shows decreasing values of (dgJdgi) over the concentration range between 0.5 and 2.0 M for four proteins. The values for CTGen are listed in Table 11. This indicates gradual formation of contacts between the sugar and the protein surface as the glucose concentration is increased. Integration of the preferential interactions to obtain Apz,lrgave monotonely increasing functions of sugar concentration for the totally excluded sugars. In the was also positive, but it tended to a maximal case of glucose, A/.L~,,~ value at high sugar concentration, above which contacts should become less unfavorable. b. Glycerol. Glycerol presents a complicated pattern of interactions. The preferential hydration was found to have invariant low values for four proteins, a-chymotrypsin, RNase A, b-lactoglobulin (p-Lg), and tubulin (Gekko and Timasheff, 1981), with (dgl/dgl) values of 0.18, 0.15, 0.14, and 0.24 g water per gram protein, respectively. The one exception was CTGen, for which the preferential hydration decreased with glycerol concentration (Table 11).The low values of the preferential hydration relative to the total hydration measured by Bull and Breese (1974) or calculated by the NMR method to Kuntz (1971) suggest some penetration of glycerol molecules to the surface of the protein. This was scrutinized in terms of Eq. (12) with the assumption that the protein hydration is the same as in pure water, since glycerol does not significantly affect the activity of water (Scatchard, 1946; Kozak et al., 1968). The increasing glycerol concentration dependence of the resulting values of & indicates increasing penetration with glycerol concentration, which is consistent with the Law of Mass Action for the formation of contacts at surface sites.

c. Polyols. Gekko and Morikawa (1981) have measured the preferential interactions of BSA with a series of polyols (ethylene glycerol, glycerol, xylitol, mannitol, sorbitol, and inositol). All except for inositol gave low values of preferential hydration. The strong preferential hydration of inositol (Table 11) was attributed to its strongly hydrophilic nature and high degree of hydration (Suggett, 1975). Gekko and Morikawa (1981) found a low preferential hydration of BSA in the presence of sorbitol (0.21 g water per gram protein). In contrast, when the protein was the highly polar RNase A, the preferential hydration was high but decreased with concentration (Xie and Timasheff, 1997a).The complexity of the correlation between cosolvent structure and preferential interactions is clearly seen in the difference between the values obtained for

CONTROL OF PROTEIN STABILITY AND REACTIONS

393

the interactions of BSA with ethylene glycol (Gekko and Morikawa, 1981) and propylene glycol (Gekko and Koga, 1984). Ethylene glycol was preferentially excluded up to a 60%concentration, with an invariant preferential hydration of 0.14 g water per gram protein. Propylene glycol, on the other hand, manifested strong preferential binding (Table 11). Yet, the more hydrophobic MPD was strongly preferentially excluded (Table 11) (Pittz and Timasheff, 1978). d. Salts. The two magnesium salts, MgS04 and MgC12,even though they share the same cation, belong to different classes. MgSO, is a good structure stabilizer,and its preferential hydration values are usually high. The complexity of the variation of the preferential interactions of MgC1, with its own concentration has been described above (Fig. 2). It is generally regarded as a salting-in agent and a structure destabilizer (von Hippel and Schleich, 1969; Collins and Washabaugh, 1985). Nevertheless, at some limited conditions of concentration and pH, it can salt out proteins (Arakawa et d.,1990a). At acid pH MgC12 raises the value of T, of RNase A, but to a much smaller extent than does MgS04. At pH 5.5, addition of MgC12has no effect on the stability. In fact the T, values of RNase A in MgC12and MgS04follow parallel variations with pH, the T, values in MgS04being higher by -6°C (Xie and Timasheff, 1997b). This is clearly a consequence of the difference in the preferential exclusion capacities of the SO!- and C1- ions that can compensate to different extents for the weak binding of Mg2+ions to negatively charged loci on the protein. Comparison of the Mg2+salts with the corresponding Na+ salts (Table 11) shows an increase in preferential hydration with salt concentration for both Na,S04 and MgSO,, while for MgC12,there is a strong decrease. The good protein solubilizer, CaC12, is preferentially bound to BSA, which reflects the favorable interaction free energy. e. PEG and MPD. Of particular interest are the PEGSand MPD. Both of these organic molecules are used as effective proteincrystallizing agents (McPherson 1982,1985; King et aL, 1956). In fact, at room temperature, MPD is used at concentrations as high as 60%. Yet, when the temperature is increased, both promote protein unfolding. Both PEG and MPD are hydrophobic in nature (Hammes and Schimmel, 1967;Pittz and Bello, 1971) and can interact with the additional protein nonpolar groups exposed on unfolding. Consistent with this is the finding by Lee and Lee (1987) that the decrease of T, induced by 15% PEG 1000 at pH 3.0 was linearly proportional to protein hydrophobicity. For 20% PEG 1000, these authors found that at 20°C, dialysis equilibrium gave a preferential exclusion of (de/dm.J = -1.0 mol PEG 1000 per mol

394

SERGE N. TIMASHEFF

of native CTGen and preferential binding of 1.3 mol PEG 1000 per mol of unfolded protein. As expected from the Wyman linkage relation, this change in preferential binding leads to the observed decrease in T,. A similar study carried out with MPD showed that addition of 30% cosolvent to an aqueous solution of RNase A lowered T, by 10°C (Arakawa et al., 1990b). Yet at 20"C, RNase A is preferentially hydrated in 30% MPD to the extent of 0.6 g H 2 0 per gram protein (Pittz and Timasheff, 19'78) (Table 11). Although there are no preferential interaction data for the denatured protein, the inference is that on unfolding the free energy of interaction should become stronger by GAp2,tr= -3.4 kcal mol-'.

6 Amino Acids, Amino Acid Salts, and Methylamines. Small neutral amino acids belong to the first category of stabilizing agents (Arakawa and Timasheff, 1983). Glycine, a-alanine, and Palanine display an essentially concentration independent degree of preferential hydration. The amino acid salts present a particularly interesting family of agents. Both sodium glutamate and potassium aspartate are strongly excluded (Arakawa and Timasheff, 1 9 8 4 ~ )The . data for the NaGlu-BSA system at pH 7.0 is given in Table 11. The preferential hydration is weakly concentration dependent. With lysozyme, the preferential hydration is lower. This reflects some attraction between the anionic amino acid and the positively charged protein. Similar observations were made with potassium aspartate (Kita et al., 1994). Lysine hydrochloride displays an exactly opposite picture. Preferential exclusion from lysozyme is now much greater than from BSA (Arakawa and Timasheff, 1984~). Arginine hydrochloride is drastically different (Etaet al., 1994). The data (shown in Table 11) indicate preferential binding to BSA at 0.2 M salt and an increasing preferential hydration above 0.7 M salt. This reflects a monotonely decreasing favorable free energy of interaction, as Ap2,tr changes from -3.4 kcal mol-' at 0.2 M salt to +3.0 kcal niol-' at 1.5 M Arg HCI. When the protein is the positively charged lysozyme, the interaction is that of preferential hydration at all salt concentrations. These observationscan be interpreted in terms of compensation between binding and exclusion. ArgHCl raises the surface tension of water (Kita et al., 19941, which leads to preferential hydration (Lee and Timasheff, 1981). On the other hand, the Arg+ ion should enter into favorable interactions with amide and peptide groups on the protein. Arginyl glutamate provides a striking example of compensation. As seen in Table 11, the interaction is that of a salt concentration independent preferential hydration, but the values are smaller than those characteristic of NaGlu. Glutamate is a protein structure stabilizing agent, as shown for tubulin and the tubulin-colchicine complex (Wilson, 1970), and it en-

CONTROI. OF PROTEIN STABILITY AND REACTIONS

395

hances tubulin self-association into microtubules (Hamel and Lin, 1981; Hamel et al., 1982). Its strong preferential exclusion from the protein surface evidently can compensate completely for the binding tendency of Arg+. Thus, its action is akin to that of the SO$- ion when coupled to Gua+. Hence, the close parallel between the Gua2S04-GuaC1 and ArgGlu-ArgC1 pairs. Methylamines such as sarcosine, betaine, and TMAO are known to stabilize the structure of proteins (Arakawa and Timasheff, 1985c) and to act as osmolytes in living systems (Yancey et al., 1982). Their patterns of preferential interactions may, however, be complex. Betaine induces a high level of preferential hydration with a small concentration dependence (Arakawa and Timasheff, 1983). Sarcosine, 1 M, was strongly excluded from lysozyme (Arakawa and Timasheff, 1 9 8 5 ~ )A. study has been carried out on the interactions of TMAO with RNase TI and the reduced and carboxymethylated form of the enzyme (RCM-TI) (Lin and Timasheff, 1994), which exists in a fully unfolded state (Oobatake et al., 1979; Pace et al., 1988). The preferential interaction values, given in Fig. 6B, show opposite trends with TMAO concentration. Preferential exclusion increases for the native protein and decreases for the unfolded form. While it is not known what forces cause methylamines to be excluded from the surface of proteins, unfolding causes the exposure to solvent both of nonpolar residues and peptide bonds.

3. Linkage Controls of Protein Stabilization A full understanding of the effect of preferential interactions on protein stability requires a knowledge of (dm,/dm,) and Appst,at both ends of the N P D equilibrium. Until recently, values of preferential interactions and transfer free energies in stabilizing cosolvents were known only for native proteins, and all inferences on the change in those interactions during the unfolding reaction were based on the statement of the Wyman linkage relation [Eqs. (16) and (17)]. The performance of preferential interaction measurements on the RNase A-sorbitol and RNase A-trehalose systems with the protein in the two end states of the N D equilibrium has permitted a complete linkage examination of structure stabilizing systems to be done with respect to both water and cosolvent of any given concentration as reference states (Xie and Timasheff, 1997a,c). The 6AG& values were determined for both systems via thermal transition experiments. The proper determination of 6Ap2requires that the preferential interactions be measured with both the native and denatured forms of the protein at identical temperature, which means that another solution variable must be different. In both systems, this was

*

396

SERGE N. TIMASHEFF

chosen as pH. Thermal transition experiments showed that in the case of sorbitol at 48°C RNase was native at pH 5.5 and denatured at pH 2.0. For trehalose, the same situation was true at 52°C;the protein was native at pH 5.5 and denatured at pH 2.8.The results of the dialysis equilibrium experiments in the two solvent systems at both temperatures and both values of pH are presented in Fig. 8.The demonstration that the interactions of the cosolvents with the native protein were indistinguishable at the acid pH and pH 5.5 at 20°C was the basis for the assumption that the native states of this protein at the two pH values are identical. At the high temperatures, the results obtained for the two solvent systems follow closely parallel patterns. If we take sorbitol as the example, the observations are as follows: at 48°C and at pH 2.0 (denatured protein), the (d m 3 / d m 2 )conform to weakly increasing preferential exclusion with cosolvent concentration, accompanied by a sharp decline in preferential hydration, at 48°C and pH 5.5 (native protein), the preferential binding is negative up to 1.3 m sorbitol, above which it becomes positive (i.e., there is a shift from preferential exclusion to preferential binding-in other words, the interaction changes from unfavorable to favorable). This is reflected by the change in sign of (dm,/dm2) (Fig. 8B).Integration under the preferential binding results, according to Eq. (19), gave the Apn,t,curves of Fig. 8C. For sorbitol, at both pH 2.0 and pH 5.5 and both temperatures (20°Cand 48"C),the values are positive at all concentrations, meaning that the interactions are thermodynamically unfavorable (Xie and Timasheff, 1997a). The shift in sign of (dm3/dmz)at 48°C for the native protein had no qualitative effect on the stabilization since SAp2,JD-N) and S(dm,/dm,) (D-N) are positive. As shown in Fig. 9A,

FIG.8. Preferential interactions of sorbitol and trehalose with RNase A at 20°C and at high temperature at pH 5.5 and low pH. The dialysis equilibrium binding results are presented as preferential binding (A and D) and preferential hydration (B and E). The variations of the transfer free energy, A P ~ , , ~are , derived from the preferential binding by integration as described in the text. For both cosolvents the unfavorable interactions are identical at 20"C, pH 5.5 and low pH. At high temperature, the low pH values (denatured protein) display more unfavorable interactions than d o the pH 5.5 (native protein) values. It is seen that in 1 M sorbitol stabilization is afforded by an increase in preferential exclusion on unfolding, whereas in trehalose the stabilization is due to lower dialysis equilibrium binding to the denatured protein than to its native form. The interactions relative to water ( A P ~ , , ~are ) unfavorable for both the native and denatured protein with sorbitol at 48°C and favorable for both forms of the protein with trehalose at 52°C. The symbols in all the plots refer to the conditions given in panels A and D (Xie and Timasheff, 1997a,c.)

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FIG.9. Thermodynamic boxes of the stabilization of RNase A by (A) 30% sorbitol at 48°C (Xie and Timasheff, 1997a) and (B) 0.7 M trehalose at 52°C (Xie and Timasheff, 1 9 9 7 ~ )(The . values are in kcdl/mol.)

in 30% sorbitol at 48"C, the thermodynamic box closes within 0.11 kcal mol-I. A similar situation prevails with the RNase A-trehalose system. The variation of the parameters with sugar concentration for the native and denatured forms of the protein are shown in Fig. SD, E, and F. In this case, however, at 52°C trehalose is preferentially bound both to the native and denatured protein at all sugar concentrations used. The key observation is that the binding is always greater to the native than to the denatured protein. For example, in 0.5 M trehalose, S ( d m 3 / d m 2 )= 1.56 - 3.01 = -1.45. The slope of the Wyman linkage plot (log K vs. log a:\) at the same conditions is -1.40. Hence, the change in the directly measured preferential binding can account for the trend in the equilibrium. The thermodynamic box presented for 0.7 M trehalose in Fig. 9B closes within 0.21 kcal mol-' (Xie and Timasheff, 1 9 9 7 ~ ) . The closing of the thermodynamic box for both the sorbitol and trehalose systems signifies that the stabilization of RNase A by both agents is due to a strictly nonspecific thermodynamic effect, namely, the

CONTROL OF PROTEIN STABILIlY AND REACTIONS

399

weak interactions of exchanging water and cosolvent molecules with protein loci exposed to solvent in both states of the protein. There is no evidence of any specific reactions such as a local conformational change induced by the cosolvent. The shift in preferential binding in the case of sorbitol from negative at 20°C to positive at 48°C does not have any dramatic significance. It is a trivial reflection of subtle shifts in the relative affinities of water and trehalose for some loci on the protein surface (by less than 0.05 kcal mol-I), defined by the exchange enthalpies at individual sites. Similarly, the finding that at high temperature stabilization is determined by a decrease in preferential binding on denaturation for trehalose and a shift from preferential binding to preferential exclusion for sorbitol, whereas at low temperature stabilization is determined by an increase in preferential exclusion on denaturation, does not imply any change in the mechanism of stabiliztction. Referring to Fig. 7C and D, we note that the stabilization of RNase A by sorbitol and trehalose at 20°C is an example of case 1, that by trehalose at 52°C represents case 2, and that by sorbitol at 48°C represents case 3. All three conform to the criterion of the Wyman (1964) linkage relation [Eq. ( l ) ] that what matters is not the sign of thep-eferential binding but the sign of the difference in p-eferential bindings between the two end states. An interesting system is represented by RNase T, in GuaHCl (Mayr and Schmid, 1993). This protein is stabilized by 0.1 M GuaHCl (ATm = 0.4”C),but it is destabilized at higher GuaHCl concentrations. Although there are no preferential interaction measurements, these observations point to a smaller preferential binding of the salt to the denatured than the native protein at 0.1 M, with the trend reversing itself as the GuaHCl concentration increases and as preferential binding to the denatured form overcomes that to the native protein. This would render this system an example of case 4 of Fig. 7D. 4. Thermodynamics of Preferential Exclusion

A complete understanding of the thermodynamics of denaturation requires knowledge of the transfer enthalpies and transfer entropies. Equation (21) for the change in transfer free energy may be rewritten in terms of the transfer enthalpies, APz,,,, and transfer entropies, AS2.,,.,if it is recalled that A F ~ is, ~the ~ change in the partial molal free energy of the protein, A?&, when the protein is transferred from water to the cosolvent system. Then,

and

400

SERGE N. TIMASHEFF

The Wyman linkage relation is given by combining Eq. (32) with Eqs. (16) and (18). A complete analysis requires knowledge of the preferential interactions as a function of temperature at a number of cosolvent concentrations for both the native and the denatured states of the protein. Such an analysis has been carried out with the limited data available for the RNase-sorbitol and RNase-trehalose systems (Xie and Timasheff, 1997b,c). Figure 10 gives the variation of the preferential binding as a function of temperature for the 0.5 M trehalose system at pH 2.8 and 5.5. Up to 35"C, the two sets of values coincide and ( a m 3 / d m p )remains essentially invariant with temperature. Above that temperature at pH 5.5 (native protein), the preferential binding increases, assuming positive values above 45°C. At pH 2.8, the same upturn takes place, but only at 48°C. At that pH, the protein undergoes the denaturation transition, as 8 n

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FIG.10. Temperature dependence of the preferential binding of cosolvent to RNase A in 0.5 M trehalose solution: (0) pH 5.5, native protein; (0)pH 2.8 (the protein is native up to 35°C where the N + D transition starts; it is in the denatured form above 50°C) (Xie and Tirnasheff, 1 9 9 7 ~ ) .

CONTROL OF PROTEIN STABILIlY AND REACTIONS

40 1

T,, = 45°C. Hence, at pH 2.8 the values are characteristic of native protein below 35°C and of denatured protein at high temperature. The same pattern was obtained with sorbitol, MgClz, and MgS04 (Xie and Timasheff, 1997a,b). The variation of the partial molal enthalpy of the protein with cosolvent concentration was calculated from the temperature dependence of the variation of the partial molal free energy by applying the truncated form of the integrated van't Hoff equation (Glasstone, 1947; Xie and Timasheff, 1997b). The results for native RNase in 30% sorbitol are presented in Fig. 11. Figure 11A shows the van't Hoff plot of the preferential interaction parameter. Figure 11B gives the resulting values of ( d R , / d m 3 )7;cL,,p3,which are increasing with temperature with a slope of ca. 2.0 kcal deg-' (mol protein)-' (mol coso1vent)-'. Calculation of the transfer enthalpy requires knowledge of (dB,/ am,) 7;p,,ay as a function of concentration, since

This, in turn, requires knowledge of the concentration dependence of (d_cLz/am3)T.p,m,at several temperatures. Approximate values of mz,tr and calculated from the limited data available, are shown in Figure 11D and F (Xie and Timasheff, 1997b). While these numbers must be regarded as illustrative, they nevertheless indicate that the transfer of RNase A from water into aqueous sorbitol is characterized by positive enthalpy and entropy changes. Similar results were obtained from native RNase in aqueous trehalose, MgSO.,, and MgC12. Gekko and Morikawa (1981) have performed the same measurements for the interactions of sorbitol and glycerol with native BSA. They also obtained positive values of ( d R 2 / d m 3 ) 7 ; p ,and m , (d3z/dm3)7;p,9.The similarity of the values of the transfer parameters is remarkable, since they encompass five systems, namely, a sugar, two polyols, and two salts. The availability of these values, albeit approximate, renders possible an evaluation of the relative contribution of the cosolvents to the enthalpy of denaturation of proteins [see Eq. (31)]. For RNase in 30% sorbitol at 48°C (pH 5.5), = 11.3 kcal mol-' (Xie and Timasheff, 1997a), whereas = 131 kcal mol-' (from Fig. 11D). Similar values characterize the RNase A-trehalose system (Xie and Timasheff, 1997~).This leads to the conclusion that the increment of the standard enthalpy of denaturation due to the transfer of the protein from water to the cosolvent system is small relative to both the change in the standard enthalpy of denaturation in water and the transfer enthalpy of the native protein from water to the aqueous sorbitol-or trehalose-medium. The small

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FIG.11. Thermodynamics of the preferential interactions of aqueous sorbitol solutions with native RNase A. (A) The vaii't Hoff plot of the transfer free energy variation with sorbitol concentration: 10% sorbitol (V);20% sorbitol ( V ) ; 30% sorbitol (0);40% (B) Temperature dependence of the variation of the transfer enthalpy with sorbitol (0). sorbitol concentration at 10% 20% (V),30% (O), 40% (0) sorbitol. Numbers on

(v),

CONTROL OF PROTEIN STABILITY AND REACTIONS

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m2,rr

increment in on denaturation suggests that, on unfolding, either the number of new solvent-protein contacts made is small or the newly formed contacts are characterized by a high degree of compensation of the transfer enthalpies between individual sites. B. Protein Destabilization 1. Preferential Binding

The principal protein denaturants are urea and guanidine hydrochloride, which induce a random coil state in proteins (Tanford et al., 1967; Nozaki and Tanford, 1967; Tanford, 1968, 1970). Sodium dodecyl sulfate, alcohols, and some other organic solvents induce a transition into structures rich in a-helices (Tanford et aL, 1960; Tanford and De, 1961; Inoue and Timasheff, 1968; Reynolds and Tanford, 1970). Some early measurements on the preferential interactions of denaturants with proteins have shown positive values of ( d m , / a m , ) for the interaction of various proteins with 2-chloroethanol and methoxyethanol ( Inoue and Timasheff, 1968), GuaHCl with BSA (Noelken and Timasheff, 1967) and with aldolase (Reisler and Eisenberg, 1969), and urea with @-lactoglobulin and chymotrypsinogen (Span and Lapanje, 1973). In their studies of the preferential interactions of 6 M GuaHCl with a number of proteins, Hade and Tanford (1967) have found that the values of preferential binding are very small. They have interpreted these results in terms of the difference in relative affinities of the various amino acid side chains for water and GuaHCl, since in 6 M GuaHCl all of the proteins examined were fully unfolded. 2. Urea The preferential interactions of urea with proteins have been examined in detail by Lapanje and colleagues (see Span and Lapanje, 1973;

the figure are the slopes, which represent (d~p,2/dm3)zp,mj in cal deg-' mol-I, where Ep,p.2 is the partial molal heat capacity of the protein at constant pressure. (C) Dependence on sorbitol concentration of the transfer enthalpy variation with sorbitol concentration at 20°C and 48°C. The dotted line is the parameter calculated at 48°C for the denatured protein. (D) Dependence of the transfer enthalpy on sorbitol concentration at 20°C and 48°C. The dotted line is the parameter calculated at 48°C for the denatured protein. (E) Temperature dependence of the variation of the transfer entropywith sorbitol concentration at 30% sorbitol. (F) Dependence of the transfer entropy on sorbitol concentration at 20°C and 48°C. [From Xie and Timasheff (1997b). Reprinted with the permission of Cambridge University Press.]

404

SERGE N. TIMASHEFF

Zerovnik and Lapanje, 1986; Poklar and Lapanje, 1992; and Prakash et al., to be published). Representative values of the interaction parameters are listed in Table 11. It is clear that urea can be both preferentially bound to and preferentially excluded from proteins. Thus, for /3-Lg and CTGen, (d-/dm) has positive values at all urea concentrations up to 8 M (Span and Lapanje, 1973; Poklar and Lapanje, 1992).For myoglobin, on the other hand, urea is preferentially excluded at all concentrations (Zerovnik and Lapanje, 1986). A particularly interesting case is found in RNase A, since its interactions shift from preferential hydration to preferential binding. Figure 12 shows the preferential binding of urea to RNase A. The pattern of interactions is complex: ( d m 3 / d m 2 )is negative at low urea concentration; it assumes positive values at higher concentrations, which pass through a maximum before falling to zero at ca. 8.0 M urea. In the case of lysozyme, the preferential binding increases monotonely up to ca. 5 M urea, at which point it seems to reach a plateau value, followed by a weak decline. The complex pattern found with RNase A cannot be attributed to the effect 20

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11

CONTROL OF PROTEIN STABILITY AND REACTIONS

405

*

of denaturation alone. The N D transition sets in at 5 Murea (Greene and Pace, 1974). Hence, the observed pattern is characteristic of the native protein. These preferential binding patterns reflect the variation of the transfer free energy with urea concentration shown in Fig. 12B. With native RNase in water as the reference state, it is seen that App,tr remains positive right up to 9.3 M urea. For the native protein, the unfavorable thermodynamic interaction is an increasing function which reaches a maximum at 3.8 Murea. In the transition region, the measured free energy of interaction is complex, since

where fN and j ,are the fractions of protein in the native and denatured states. The term 6 AGZ(N’D) reflects the fact that the reference state for the experimental values is native protein in water whereas that of Ap&, is denatured protein in water. Above 8 M urea, fN = 0. Since at pH 7.0, 6AG,”(N”D)= 7.7 kcal mol-’ (Greene and Pace, 1974), Ap& = 2.0 - 7.7 = -5.5 kcal mol-’, which indicates a significant favorable interaction, even though the preferential binding, (dm,/dm,) 7;a,,p, = 0. In the case of lysozyme at pH 7.0, the situation is much simpler. The protein is native throughout the measurement. Hence, the positive values of ( drn3/drn2), which signify favorable interaction, represent the variation of A&, which is increasingly favorable with urea concentration. The shape of the interaction parameters of urea with lysozyme may be attributed in large part to the variation of urea nonideality, as the pattern mimics closely a theoretical one calculated by Schellman (1990; see Fig. 4A therein). The RNase pattern cannot be reproduced in terms of the variation of the activity coefficient of urea. It must reflect changes with urea concentration of the exchange affinity at some sites. Lapanje and co-workers have examined the preferential interactions of some alkylureas with /?-Lg (Poklar and Lapanje, 1992) and myoglobin (Zerovnik and Lapanje, 1986). The interesting observations are that with p-Lg as protein, methylurea is preferentially bound, whereas for ethylurea and N,N’dimethylurea preferential binding at low concentrations shifts to preferential exclusion at high concentration. The pattern is just the opposite with myoglobin. The alkyl ureas are preferentially excluded at low concentrations. At high concentration, the interaction is that of preferential binding. For the p-Lg systems, the calculated transfer free energies were found to be negative for urea and all the alkyl ureas. Transfer enthalpies measured calorimetrically for the P L g system (Lapanje and Kranjc, 1982) were negative for urea and mostly positive for the alkyl ureas, which gave the same pattern for the transfer

406

SERGE N. TIMASHEFF

entropies. This was interpreted in terms of the hydrophobic nature of the alkyl groups. What do these measured values of low positive or negative preferential binding mean in terms of site occupancy? Referring to Eqs. (12) and (13), it is evident that the values of Table I1 and Fig. 12 are much smaller than the total number of surface sites on the protein molecule, as well as the number of sites with which ligand molecules make contacts. The $fictive number of ligand molecules that make contact with the protein has been determined in a careful calorimetric titration study by Makhatadze and Privalov (1992) for several proteins in the urea and GuaHCl systems. This contact-detecting technique, being nonthermodynamic in nature, cannot give equilibrium thermodynamic binding, but only effective values of site occupancy, i.e., B3 of Eq. (12). Furthermore, these authors have used classical binding theory to analyze their results, neglecting the concepts of exchange and preferential binding. Therefore, their reported values of AGare only descriptive and their thermodynamic significance is uncertain. Nevertheless, within the assumption that all the exchangeable sites are characterized by identical contact enthalpies and have identical exchange affinities, these results are a descriptive representation of site occupancy. It therefore seems useful to carry this descriptive analysis further by calculating effective values of & and B1. The resulting picture can convey a qualitative appreciation of what is occurring, though it cannot uncover the actual physical situation (Schellman, 1994; Schellman and Gassner, 1996). As an illustration, let us take native RNase A at pH 7.0 in 1.0 M urea. The pertinent parameters are as follows: ( d w ~ . J d r n ~ ) ~ ; ~= , , +-3.8 (Fig. 12); the effective total number of exchangeable sites, n = 122, and the site occupancy by urea, B3 = 7, are the values deduced by Makhatadze and Privalov (1992) from a Scatchard analysis of their calorimetric data. We must note that the site occupancy and thermodynamic binding stoichiometries carry opposite signs. These values lead to B, = 570, i.e., 5 water molecules per putative available site, if all are exchangeable. However, if the number of water molecules replaced by one urea molecule is less than 5, e.g., if it is 3, then the protein surface would contain effectively 345 exchangeable water molecules ( B y h ) and 225 nonexchangeable ones (Br]’”).

3. Urea Denaturation Keeping in mind the difference between the thermodynamic, exchange concepts of binding and the site occupancy, classical concept, it is possible to explain the fact that urea and GuaHCl are required at very high concentrations to denature proteins. If we take RNase at pH 7.0 as an example, the denaturation occurs with a midpoint at 7.0 M

CONTROL OF PROTEIN STABILIIY AND REACTIONS

407

urea. The slope of the Wyman plot [Eq. (16a)l is Anurea= 12, and the urea contribution to the free energy of denaturation in 7 M urea is SAG" = -7.7 kcal mol-' (Greene and Pace, 1974). Classical analysis, which is still frequently used, would attribute a binding free energy SAG"/An = -0.64 kcal mol-' for each additional urea molecule bound during unfolding. This would correspond to a classical binding constant of ca. 3 M-', and the expectation that denaturation should occur at between 0.3 and 1 M urea, not at 7 M. The answer to this apparent contradiction is that in classical analysis exchange is neglected. This is illustrated schematicallyin Fig. 13, which describes the change of surface contacts during any conformational change, including protein unfolding (denaturation). It is shown that the formation of a newly exposed surface or, on the contrary, removal of a surface from contact with solvent is accompanied by changes in contacts with both water and cosolvent on the surface of the protein molecule. The slope of the linkage plot [Eq. (16a)l is the difference between preferential interactions, which is the summation of the changes in contacts depicted in Fig. 13. Let us take the Wyman linkage relation expressed in terms of site occupancy [Eq. (16b)l and carry out an illustrative calculation. The Makhatadze and Privalov (1992) values of effective site occupancy on denatured and native ribonuclease in 8 M urea give (B: - B t ) = 41 additional urea molecules occupying sites on an RNase molecule when it unfolds. This leads to (By - By) = 131 additional effective water molecules coming into contact with an RNase molecule. The site occupancy value renders the SAG" contribution 0.21 kcal mol-I per additional urea molecule "bound," or 0.05 kcal mol-* per additional site available to exchange, if the calculation is done in terms of the one-to-one exchange model.

Statc I

State 11

FIG.13. Schematic representation of the redistribution of solvent components on the surface of a protein during a conformational transition (including denaturation). The dashes represent water; the spirals represent cosolvent.

408

SERGE N. TIMASHEFF

It is evident that the need for a high concentration of urea is caused by the compensation between interactions of the same ligand with different sites on the protein. At each newly exposed site at which additional urea molecules are preferentially bound, they favor destabilization of the protein. On the other hand, newly exposed sites for which urea has little affinity and which are occupied by water make a positive free energy contribution and therefore stabilize the structure. This means that urea molecules act simultaneously both as destabilizers and stabilizers of the protein structure. The direction in which each urea molecule drives the reaction depends on the protein surface locus with which it is interacting. By the additivity principle they compensate each other’s action, which leads to the need for a high concentration of denaturant to induce protein unfolding. 4. Guanidinium Salts

The preferential interactions of 6 M GuaHCl with a variety of proteins (Hade and Tanford, 1967; Lee and Timasheff, 1974) were all found to be small, many approaching zero, even though GuaHCl is a strong denaturing agent. The values are listed in Table 111. A similar situation is true of proteins in 8 M urea (Prakash et al., 1981). This reflects the exchange with water and a near balance between sites favoring occupancy by GuaHCl and sites favoring water. In an attempt to explore the nature of the sites with which GuaHCl interacts (Lee and Timasheff, 1974), B3 values were calculated with Eq. (12) for the proteins of Table 111, with the application of B, values calculated by the NMR method of Kuntz (1971). The best correlation of B3 was found with the summation of [(total number of peptide bonds/2) total aromatic amino acids]. This

+

TABLE I11 Prejkrential Binding of 6 M GuHCl to Proteins at 20°C” Protein RNase A Lysoqme Tubulin Chymotrypsinogen a-Chyrnotrypsin BSA Carboxypeptidase A

Protein 0.00 (0.00) 0.09 (0.09) 0.10 0.15 0.17 0.06 (0.06) 0.05

Lactate dehydrogenase Catalase PLactogIobulin Lima bean trypsin inhibitor a-Lactalbumin Aldolase Ovalbumin

(dg?,/%z)

T .r ,,I”<

0.03 0.01 0.08 (0.09) 0.01 0.03 (0.08) (0.11)

The values are those measured by Lee and Timasheff (1974) by equilibrium dialysis. The values in parentheses are those measured by Hade and Tanford (1967) by isopiestic vapor pressure equilibrium.

CONTROL OF PROTEIN STABlLIn AND REACTIONS

409

is in accord with the postulate of Robinson and Jencks (1965a,b) that each GuaHCl molecule interacts with two peptide bonds, and that of Nozaki and Tanford (1970) that aromatic amino acid side chains are good candidates for the binding of GuaHC1. The differences in the concentration dependences of ( d m 3 / d m p ) , ( d p z / d m 3 ) ,and Apz,u of GuaHCl and GuaS04 are compared in Table 11. For GuaHCl, the data of Reisler et al. (1977) were obtained for BSA reduced with dithioerythritol (DTE). For Gua2SO4,the data are for the native protein (Arakawa and Timasheff, 1984b). The two sets of dependences are strikingly different. In GuaHC1, (dm3/dmz) is a sharply decreasing positive function which tends toward zero at 7 M GuaHCl. For Gua2S04,this parameter has a small positive value at 0.5 M salt and then decreases, reaching a high value of preferential hydration at 2 M salt. Both of these curves are consistent with the variation of the activity coefficients of the Gua+salts when compared with the theoretical curves calculated by Schellman (1993) for GuaHCl. The free energies of interaction for the two salts are drastically different. For GuaHCl the interaction is always favorable relative to water, whereas for GuanSOlAp2,=is favorable up to ca. 1.4 M salt and then becomes unfavorable. In fact, the GuapS04 interactions are a mirror image of those of MgC12with P L g at pH 3.0 (Fig. 2); MgCl2stabilizes protein structure at low salt concentration but has no effect above 2 M (Arakawa et al., 1990b). In contrast, GuazS04 is an increasingly strong stabilizer of the structure of RNase A (von Hippel and Wong, 1965). When the protein is RNase, the preferential binding of GuaHCl follows a complex pattern similar to that found with urea: preferential exclusion at low GuaHCl concentration; then preferential binding, which passes through a maximum and descends to zero at 6 M salt (V. Prakash and S. N. Timasheff, unpublished).

v.

LINKAGE CONTROL OF PROTEIN REACTIONS A. Modes of Analysis

It has been known for a long time that any protein reaction can be modulated by weakly interacting cosolvents. The sole requirement is that the preferential interactions with the reactant and product be different, whether expressed by the Wyman (1964) linkage relation or by a thermodynamic box (Tanford, 1961a). Some 30 years ago in their examination of the GuaHCl denaturation of lysozyme, it was realized by Aune and Tanford (1969; Aune, 1968) that linkage could be interpreted in terms of changes in the numbers of water as well as ligand molecules that

410

SERGE N. TIMASHEFF

interact with a protein during the course of the reaction. Tanford (1970) stated that this is not caused by the effect of the ligand on water activity. The relation, as derived by Tanford (1969), is

where V , and F, are B3 and B, of Eq. (20); m, = mg and m, = m l . The effect of solvent components on the free energy of a reaction, S(AG"), can be expressed by the integration of changes in either preferential binding o r preferential hydration [Eqs. (19b), (19c), and (35)]:

Decomposition of preferential interactions into effective site occupancies, B1and B3 [Eqs. (20a), (20b), and (35)], gives

All of these are exact relations, although it must be stressed once again that the "bindings" of cosolvent and water, B , and B3, are only effective nonthermodynamic numbers (Schellman, 1993; Timasheff, 1992). The earliest application of these concepts was the interpretation in terms of Eq. (35) of the dimerization of a-chymotrypsin (a-Ct) by Aune et al. (1971).A Wyman linkage analysis of the dependence of the equilibrium constant of the 2a-Ct 2 a-Ct, equilibrium on salt concentration, gave 6 ( d m , / m m , ) = 6 ( m 3 / d m 2 )= 1.0 for NaCl and 0.5 for CaC12. This was interpreted in terms of Eq. (35),with the conclusion that 125 water molecules leave the domain of the contact region of each monomer when the dimer is formed if there is no change in the binding of salt, i.e., by setting SFx = SB, = 0. Conversely, the same data can be expressed in terms of the change in the binding of only salt by setting SV," = SBI = 0. In another early application of Eq. (35) the promotion by MgC1, of the formation of tubulin double rings was ascribed to the change in binding of one effective MgC12 (Frigon and Timasheff, 1975). This analysis was also applied to the promotions of microtubule self-

CONTROL OF PROTEIN STABILITY AND REACTIONS

41 1

assembly by glycerol (Lee and Timasheff, 1977) and PEG (Lee and Lee, 1979), to the effect of ethylene glycol on oxygen binding to hemoglobin (Haire and Hedlund, 1983),and in the interpretation of protein stabilization by sucrose (Lee and Timasheff, 1981), glycerol (Gekko and Timasheff, 1981), polyols (Gekko and Morikawa, 1981), and salts (Arakawa and Timasheff, 1982b). Most recently, exactly the same principles have been applied in a number of studies in which the effects of cosolvents have been interpreted in terms of a much more restricted restatement of preferential interactions (Colombo et al., 1992, 1994; Colombo and Bouilla-Rodriguez, 1996; Rand, 1992; Rand et al., 1993), namely, that 6B3 = 0 and that 6B1 is independent of cosolvent concentration. This case has been singled out as a special phenomenon, which has been called "osmotic stress" (Rand, 1992; Rand et al., 1993; Colombo et al., 1994; Colombo and Bouilla-Rodriguez, 1996).

B.

"Osmotic Stress" or Cosoluent Potential Stress or Preferential Interaction Stress?

Let us examine the implications of constraining 6(dm3/dm2)or 6(dml/ am,) by various assumptions. Application of the constraint that either S(dm3/dm,) or 6(dml/dm2) is constant gives, on integration of the reduced Eqs. (36a) and (36b),

6AG" = -6(dm3/dm2)pf3 = -6(dm3/dm2)RTln Q%

(38a)

6AG" = -6(dml/dm2)pT;19= -6(dml/dm2)RTln a?

(38b)

The further constraint that 6BI of Eq. (37a) or 6B3 of Eq. (37b) is equal to zero, followed by integration, leads in turn to the results that

6AG" = - 6B3pf3=

- 6B3RTIn &s

6AG" = -6BlpT;19 = -6BlRTln a?

(394 (39b)

The expressions on the right-hand side of Eqs. (38) and (39) state the work involved in the change of the preferential interactions, i.e., the change in transfer free energy during the course of the reaction. They express the driving force of the reaction by addition of cosolvent in terms of either the chemical potential of the cosolvent (pf3)or that of water (pr3) at cosolvent concentration m3. The two are symmetrical since, by Eq. (12), SBI = - ( m3/ml) 6B3, whether in actuality the change is that of protein-cosolvent or protein-water contacts or both.

412

SERGE N. TIMASHEFF

In the “osmotic stress” studies, the aim of which was the measurement of the number of water molecules involved in a reaction (Rand, 1992; Rand et al., 1993; Colombo and Bouilla-Rodriguez, 1996), the effects of cosolvents have been ascribed to water alone and the role of the cosolvent has been described as that of an inert excluded molecule which lowers the activity of water outside the zone of exclusion, thus facilitating removal of water from the domain of the protein. The term “osmotic stress” stems from the elegant technique invented by Parsegian (see Parsegian et al., 1986) in which the reacting system and an osmotic pressure (water activity) adjusting “osmolyte” are separated by a membrane. This raises the following question: Is “osmotic stress” a special phenomenon in the case that a reaction takes place in a medium that consists of water mixed with a preferentially excluded cosolvent? The answer is no. Under such circumstances “osmotic stress”is simply uparticular restricted case of preferential interactions. In this approach all changes in free energy induced by addition of the cosolvent have been assigned to changes in the volume of water that makes contact with the protein during the course of the reaction, AV,,,,, and hence to the changes in the number of water molecules. The basic relation of “osmotic stress,” presented in various forms, is (Rand et al., 1993)

where ~ ‘ is~ the 3 osmotic pressure due to the presence of cosolvent. The term on the right-hand side is defined as the “osmotic work” involved in removing the water from the protein into the cosolvent system. Let us scrutinize this equation. Introduction into Eq. (40) of the definition of osmotic pressure, IP= - ( R T f l l )In ays, gives

SA Go = - (R T f l l ) A V,,,, In a?

(41)

which is identical with Eqs. (39b) or (38b), since AV/v, = 6Bl or 6 ( a m l / am,), depending on the restriction used, and Eq. (40) reduces to a restricted form of preferential interactions. The term “osmotic stress” conveys the implication that what is needed to drive the reaction is an increase in osmotic pressure. This is incorrect. As discussed in Section II,C, addition of any cosolvent has the nonspecific general consequence that the osmotic pressure is raised. A neutral (inert) cosolvent raises T but cannot exert any effect on a reaction. What is required is a change in preferential interactions, S(am,/am,) # 0. In the case of an inert cosolvent, the sites in question will be occupied by cosolvent and wa-

CONTROL OF PROTEIN STABILIW AND REACTIONS

413

ter molecules in the same proportion as they exist in the bulk solvent, i.e., BS/B, = m S / m l .Then ( d m , / d m z ) = 0 and 6(dm,/am2) = 0, and 6AG" = 0 at any value of 7 r m 3 [Eq. (38b)l. As explained in Section II,C, the drive is provided by the change in the perturbation of the chemical which potential (activity) of the cosolvent by the protein, ( d p 3 / d m 2 ) causes the solvent component redistribution in the vicinity of the protein. Then, a more accurate name for the phenomenon might be cosolvent potential stress. An even more appropriate name, in fact, is p-eferential interaction stress. This corresponds exactly to the statement of the Wyman linkage relation, and the most appropriate name would seem to be stress by Wyman linkage. The use of Eq. (40) in the interpretation of experimental results imposes the restrictions (1) that, during a reaction that involves a change in protein surface area in contact with solvent, the only change be that of the number of water molecules in contact with protein at the reaction site, SB, (6B3 = 0), and (2) that there be no thermodynamically neutral loci involved in the transformation of protein surface-solvent contacts. Let us examine the implications of the restricting assumptions. First, the preferential& excluded cosolvent is not inert. Full exclusion from contacts with the protein does not mean thermodynamic indifference. As discussed in Section II,C, exclusion means the play of repulsive forces between the protein and the cosolvent, the nature of which are determined by the cosolvent. This is reflected in a positive increment of the chemical potential of the cosolvent, ( d p 3 / d m z )> 0, detected experimentally as preferential hydration. By the Le ChAtelier principle, these thermodynamically unfavorable forces can be reduced by, e.g., contraction of the protein with loss of surface exposed to the cosolvent. A logical locus would be one prone to undergo transitions, such as the site of a conformational change or of ligand binding. A reduction of protein surface will necessarily be reflected in a reduction of solvent component molecules that make contact with the protein. If that surface is predominantly in contact with water, then water molecules will leave in excess. Relief can also be provided by the binding of cosolvent molecules to the protein. The assumption that the cosolvent makes no contacts with the protein surface, i.e., B3 = 0 and SB3 = 0, is hazardous. This is based on preferential interaction values measured at 20°C and extrapolated to zero cosolvent concentration, with an error in measurements that can correspond to t 5 0 water molecules. Preferential interactions are known to vary with temperature and cosolvent concentration (see Table I1 above, in Section IV,A,l; also Section IV,B),as well as cosolvent nonideality (Schellman, 1990).Specificallythe PEGSand glucose bind to proteins at finite concentrations, whereas sucrose has been shown to have an affinity for amino

414

SERGE N. TIMASHEFF

acid side chains (Liu and Bolen, 1995) and there is evidence for thermodynamically neutral protein-sucrose contacts (Lee and Timasheff, 1981). In view of these uncertainties, it would seem more cautious to interpret any observations that give a constant value of S ( d m l / d m 2 )in a linkage plot in terms of Eq. (38b). Its combination with Eq. (41) gives the quantity S ( d m l / d m 2 )which , is the effective volume change of preferential hydration that involves both water and cosolvent molecules. In a mixed solvent, AV,,,, of Eq. (40) can be expressed as

v,

This states that the volume change measured by a plot of SAG" vs. nrn3 (or In a l ) is the difference of the actual changes in the volume of water SB,) and that of the cosolvent expressed as the equivalent volume of water. Therefore, A V,,,,, is an indeterminate parameter. Its value can SB1 depending on the variations of SB,. be greater or smaller than The change in the apparent site occupancies by both water and cosolvent is expressed by Eq. (35) (Tanford, 1969; Aune et aL, 1971). The assumption that the site occupancies are independent of solvent composition permits the fitting of S(dm,/d&) data by Eq. (35) to certain values of Sv," (SB,) and Sv, (SB,) (Colombo and Bouilla-Rodriguez, 1996). These values, however, are simply fitting parameters. They can correspond to a large set of actual water and cosolvent molecules involved, as has been pointed out by Tanford (1969). Therefore, SB1 and 6B3 are indeterminate parameters. The main reason for this is that, thermodynamically, neutral sites are detected neither by preferential interaction measurements nor by Wyman linkage plots (Timasheff, 1992). As an example, let us examine the glycerol promotion of the selfassembly of tubulin into microtubules. Direct application of the Wyman linkage plot to the experimental data gave S(dm,/dm,) = + l ; i.e., assembly is accompanied by the addition of one glycerol molecule preferentially bound per tubulin dimer (Lee and Timasheff, 1977). This corresponds to a decrease of the preferential hydration by 13.5 water molecules. If the linkage plot were interpreted in terms of Eq. (40), this result would mean the leaving of 13.5 water molecules, which could correspond to 135 Az of protein surface being removed from contact with solvent. This value is unrealistically low, since microtubule assembly involves the formation of multiple protein-protein contacts. However, if neutral sites are involved and the departure of water is accompanied by that of glycerol at a ratio of -13.5, then many more water molecules

(v,

vl

CONTROL OF PROTEIN STABILITY AND REACTIONS

415

might be leaving tubulin on incorporation into a microtubule, which would correspond to a much more realistic contact area. These multicomponent thermodynamic considerations demonstrate the precarious nature of the conclusion that the change in standard free energy induced by a cosolvent measures the changes in the volume of water that hydrates a protein during a biochemical reaction, as well as in the number of water molecules involved. Therefore, when the system is a multicomponent solution that contains both the reacting system and a weakly interacting cosolvent, any deduced values of AV,,, or SBI must be approached with extreme caution and regarded as descriptions of the observations. To obtain a real value of the volume of water displaced during a reaction, true “osmotic stress” as originally invented by Parsegian et al. (1986) must be used; i.e., the reacting system and osmotic pressure adjusting “osmolyte” must be separated by a membrane. In that case, any cosolvent, whether bound, excluded, or inert, will equally lower the chemical potential of free water to p,,. As a consequence, all additives will exert an identical effect on a protein reaction. The same is true when the area perturbed is inaccessible to solute (cosolvent) molecules in both end states of a reaction (e.g., a channel). Finally, when the reaction studied is the binding of a ligand, the situation becomes complicated by effects of the cosolvent on the chemical potential of the ligand, which make contributions to 6AG” expressed through cross terms in multicomponent thermodynamics (Casassa and Eisenberg, 1964).

C. The Geometric Approach An alternate attempt to estimate the protein surface involved in a reaction (Arakawa and Timasheff, 1984c) is based on the assumption that the preferential interactions are statistically distributed over the entire protein surface. This is a very unlikely situation. It might be approximated for reactions where very large patches of protein surface are involved. The relation between the preferential interactions of the protein in the end (Prod) and starting (React) states can be expressed by the relations between the transfer free energies and changes in the equilibrium constants:

where K , and K, are the equilibrium constants for the equilibrium

41 6

SERGE N. TIMASHEFF

React Prod in the cosolvent system and in water, and Xis the fractional decrease in surface area. As an example, let us use again the promotion of microtubule assembly by glycerol (Lee and Timasheff, 1977). The values of K9 in 30% (4.11 m) glycerol and K , (by extrapolation) at 37°C are K9 = 1 X lo5 m-’ and K , = 1 X M I , which gives 6Ap2,, = -1.4 kcal mol-’. The transfer free energy of the monomer (Reactant) at 20”C, Ap&, has been measured (Na and Timasheff, 1981) to be 95.4 kcal mol-’ (see Table 11),givingfor that of one tubulin molecule incorporated into the polymer (Prod), ApgfY = 94.0 kcal mol-’. Application of Eq. (43) leads to the result that X = 0.015. The surface area of a tubulin a-/3dimer has been estimated to be 9.7 X 10” cm2per mol of protein (Lee and Timasheff, 1981). Hence, the effective reduction of protein-solvent contact is 240 Az per molecule when a tubulin molecule becomes incorporated into a microtubule. Once again this value is unrealistically low. It is evident that the numbers of water molecules involved in a reaction, deduced by application of a model, be it that of the “osmotic stress” constraints or of the geometric constraint, must be qualified by extreme caution. It seems more reasonable to stop the analysis at the level of changes in preferential interactions and to regard any extensions in terms of models as strictly intended to give a qualitative view of the process on the molecular level, but not to attach exact quantitative meaning to the numbers.

VI. SOURCES OF EXCLUSION The binding of cosolvent molecules to loci on the protein surface is an easily accepted concept. For example, urea and GuaHCl are believed to form weak hydrogen bonds with peptide groups on a protein (Robinson and Jencks, 1965a,b) and to have an affinity for aromatic residues (Nozaki and Tanford, 1970); nonpolar molecules interact with hydrophobic patches on the protein surface; ions bind to charged loci. Exclusion, on the other hand, seems less evident. Thermodynamically, it is the consequence of an unfavorable effect of the protein on the chemical potential of the cosolvent, ( d p 3 / d m J 9 > 0. The causes of preferential exclusion can be grouped into two general categories: ( 1 ) Those in which the proteins are chemically inert; they only present a surface to which the cosolvent reacts. As a consequence, the preferential hydration has little dependence on the concentration of the cosolvent. (2) Those in which the chemical nature of the protein surface plays a role; i.e., there are chemical interactions (attractive or repulsive) between loci on the protein surface and cosolvent molecules. It must be stressed that

417

CONTROL OF PROTEIN STABILITY AND REACTIONS

the heterogeneous nature of the protein surface frequently leads to a combination of exclusion and binding of the same cosolvent by different loci on the protein. These are additive and therefore compensatory in the measured preferential interaction parameters (dialysis equilibrium binding). The first category consists essentially of two mechanisms: steric exclusion and perturbation of the surface free energy [work of making a cavity (Bransted, 1931)] of water. Steric exclusion was first proposed by W. Kauzmann in 1949, as cited by Schachman and Lauffer (1949). It is based on the difference in size between molecules of water and cosolvents. As depicted in Fig. 14A, the cosolvent molecules are limited in their approach to the protein by the effective radius of the bulky cosolvent molecule (Arakawa and Timasheff, 1985a). This effective shell, which is impenetrable to the cosolvent for mechanical reasons, is filled with the smaller water molecules. The resulting excess of water in the vicinity of the protein is observed in dialysis

%

1.5

0

10

w/v

20

30

40

I

I

1

A I .o

-

4

a

I\

O

M3

W

0.5

0

I 0

I

I

I

I

0.2

0.4

0.6

g3

FIG.14. (A) Schematic representation of the steric exclusion nonspecific mechanism of preferential exclusion of cosolvents from proteins. Rp is the radius of the protein; R, is the radius of exclusion (effective radius of the cosolvent); is the volume in which for PEG there is an excess of water. (B) PEG concentration dependence of (dgl/dgz)P,, 200 (0),400 (A),600 (O), and 1000 (a).(Inset) Dependence of (dg,/dgz)&,,, on PEG molecular weight; (8gl/dge)$'L,,p, was obtained by extrapolation of ( a p J d r n , ) re5. [Figure 14A and B reprinted with permission from Arakawa and Timasheff (1985a). Copyright 1997 American Chemical Society.]

418

SERGE N. TIMASHEFF

equilibrium measurements as preferential hydration, i.e., preferential exclusion of the cosolvent. Effectively, a micro phase separation takes place on the protein surface and (apL,/dmz),h > 0. Within this simple model, the volume of the shell, is equal to the volume of the water where , P ~ ~& , is the of preferential hydration, K = ( M 2 / ~ ) ( a g , / a g z ) ~ density of water and (dgl/dg2) is the preferential hydration parameter extrapolated to zero concentration. The resulting free energy of interaction is

x,

This mechanism has been shown to be the source of the preferential exclusion of the PEGs from proteins (Lee and Lee, 1979,1981;Arakawa and Timasheff, 1985a; Bhat and Timasheff, 1992). Hydrodynamic analysis of the radius of exclusion, R e , as a function of PEG concentration for PEGs varying from 400 to 6000, has given a good correlation with the radius of gyration, Rg,of the PEG molecules expressed as stiff coils (Arakawa and Timasheff, 1985a; Bhat and Timasheff, 1992). The inset of Fig. 14B shows the strong dependence on PEG molecular weight of (ag,/dg,) extrapolated to zero concentration, which reflects the increase in steric exclusion of PEG with increasing R, (Arakawa and Timasheff, 1985a; Bhat and Timasheff, 1992). An almost identical dependence of 6(dg1/dg2)on the molecular weight of PEG during the conformational transition of hexokinase has been reported recently (Reid and Rand, 1997). This report confirms that the steric exclusion of PEG not only determines the extent of preferential hydration of a protein but also provides the driving energy to reduce the surface of protein contact with solvent by relieving the stress imposed by cosolvent exclusion (see Section 11,C). As shown in Fig. 14B, PEG solutions display a strong nonideality. For example, for PEG 1000,preferential hydration decreases by a factor of 3.8 between 0 and 30% PEG. At finite concentrations, the PEGs which are nonpolar polymers (Hammes and Schimmel, 1967) can assume compact structures that can bind to hydrophobic sites on the protein (Arakawa and Timasheff, 1985a). Therefore, the measured values of the preferential exclusion at finite PEG concentrations should contain contributions from PEG contacts with loci on the protein surface. The perturbation of the surfacefree energy reflects the fact that introduction of a protein molecule into an aqueous medium creates a cavity. At the protein-solvent interface there must be interfacial tension. Gibbs (1878) has shown that perturbation of the surface tension of water by the

CONTROL OF PROTEIN STABILITY AND REACTIONS

419

addition of a small solute must lead to an excess or deficiency of the additive in the surface layer. Adapted to protein molecules in the notation of three-component thermodynamics, the Gibbs adsorption is+ therm assumes the form (Lee and Timasheff, 1981)

where u is the surface tension; sp is the surface area of the protein molecule; and NAYis Avogadro's number. Lowering of the surface tension by a cosolvent must lead to an increase in preferential binding, and an increase in amust lead to preferential exclusion. Sugars, salts, and amino acids are known to raise the surface tension of water (Landt, 1931; Lee and Timasheff, 1981; Melander and Horvath, 19'7'7; Bull and Breese, 1974; Kita et al., 1994). Hence they are expected to be preferentially excluded. Yet, the PEGS, MPD, and TMAO lower a (Eta et al., 1994). This means that their effect on surface free energy favors their accumulation on the protein surface. Since they are preferentially excluded, the surface tension effect must be compensated by repulsive forces, according to ( a p 3 / a m 2 ) 2=

2 (ap3/amz)Bind + 2 (aps/amp)Excl i

i

(46)

The measured preferential exclusion of compounds that raise the surface tension of water has been compared with values calculated by Eq. (45) from surface tension measurements. The protein-solvent interface is curved, whereas surface tension measurements are done at flat water-air interfaces. This requires a correction of the values for the curvature (Choi et al., 19'70; Tanford, 1979; Nicholls et al., 1991; Sharp et al., 1991). Measurements on strongly excluded molecules have led to an empirical correction factor R = 0.5-0.7, where R is the ratio of the experimentally measured value of ( a p n / a m , ) to that calculated by Eq. (45) from surface tension data (Arakawa and Timasheff, 1982a, 1983, 1984a;Kita et al., 1994; Lin and Timasheff, 1996). These empirical values of R are similar to those calculated from geometric considerations by Honig and co-workers (Nicholls et al., 1991; Sharp et al., 1991). While cosolvents which increase the surface tension of water are expected to be preferentially excluded, this may be compensated by weak binding to loci on the protein surface. A comparison of the interactions of RNase A with trehalose and ArgHCl (Lin and Timasheff, 1996) has shown that, while the preferential binding of trehalose can be accounted for by that calculated from the surface tension increment and (app/amz)exPis

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independent of sugar concentration, with ArgHCl both (dm3/dm2)'"P and (dp2/dmn)'"Pdecrease with cosolvent concentration, so that at 1.0 MArgHCl the expected preferential exclusion of 8.1 molecules ArgHCl from one molecule of protein is compensated by the binding of 5.2 ArgHCl per molecule of RNase A. Nevertheless the measured total exclusion of, e.g., sucrose and trehalose from proteins does not exclude the penetration of sugar to the protein surface with the formation of active contacts at some loci, while neutral sites are not detectable. The effect of salts on protein solubility and stability has been the subject of extensive studies over many years (Green, 1932; Cohn and Edsall, 1943;von Hippel and Schleich, 1969;Baldwin, 1996).Hofmeister, in 1888, discovered that the effect of salts on protein solubility follows a well-defined order known as the Hofmeister series. This order is amazingly immutable over a broad spectrum of protein reactions (von Hippel and Schleich, 1969). The rationale for the Hofmeister series seems to reside in the interactions of the ions with water. This has been discussed in detail by Collins and Washabough (1985), who give a comprehensive bibliography on this subject. A very insightful analysis of the Hofmeister ion interactions has been given by Baldwin (1996). The characteristic features of these interactions, listed by Baldwin (1996), are that (1) the interactions are weak and conform to the Schellman (1987, 1990) exchange model; (2) these interactions are specific to the ions in the sense that they follow a defined order; and (3) these interactions conform to the Setchenow (1892) equation. In an examination of the effect of salts on protein solubility, Melander and Horvath (1977) have concluded that protein solubility is a function of the surface tension increment of water induced by addition of salts. The surface tension increment, in turn, follows the Hofmeister series (Jarvis and Scheiman, 1968; Baldwin, 1996). The preferential interactions of the ions with proteins conform to the Setchenow (1892) equation, and their order of preferential binding (exclusion) follows the Hofmeister series (Arakawa and Timasheff, 1982b, 1984a,b).All of these observations point to the role of the surface tension increment in the preferential exclusion of salts. This, however, can be counteracted by attractive forces between some ions, such as Mg2+,and charged loci on the protein surface, as has been pointed out in Section I1,E. The increase in the free energy of cavity formation when a protein unfolds has been proposed as a source of the stabilization of proteins by sucrose (Lee and Timasheff, 1981), trehalose (Lin and Timasheff, 1996), and other surface-tension raising cosolvents (Arakawa and Timasheff, 198213, 1984a; Timasheff, 1995a,b), in analogy to the proposal of Sinanoglu and co-workers for the stability of DNA molecules (Sinanoglu

CONTROL OF PROTEIN STABILIlY AND REACTIONS

42 1

et ab, 1964;Sinanoglu and Abdulnur, 1964,1965).This has found support in the observations that T, of the thermal unfolding of RNase A, CTGen, and CT in sucrose and that of RNase A in trehalose occur at constant values of the surface tension, independent of sugar concentration (Lee and Timasheff, 1981;Lin and Timasheff, 1996).Surface tension increases with sugar concentration and decreases with temperature (Landt, 1931):

uT= uo+ (au/um,)m3+ ( a u / a T ) (AT:@r - Pter m ) (47) where uTand uoare the values at T, in the presence of cosolvent and in water, respectively. The unfolding at such combinations of ms and AT, that uTremainsconstant has been interpreted in terms of unfolding occurring at a constant value of the cavity free energy and hence of the work done by the protein on expansion of the surface of the cavity during unfolding (Lee and Timasheff, 1981). In the case of ArgHCl, the surface tension at T, increases with ArgHCl concentration. This has been ascribed to a compensatory gain in free energy due to the increase of ArgHCl binding to the protein as new peptide groups are made available during unfolding (Lin and Timasheff, 1996). This is consistent with the finding by Breslow and Guo (1990) that cosolvents can affect the energy required to produce a cavity in the solvent by solvating the solute. Thus, the role of compensation of two opposing actions of the same cosolvent is evident again, the exclusion due to a general surface effect being compensated by attractive forces at specific sites. The second categoly of preferential exclusion comprises those cosolvents that recognize the chemical nature of sites on the protein surface. It has been shown that MPD is repelled from the surface charges of protein (Pittz and Timasheff, 1978), although the cause of this repulsion is not known. The most prominent phenomenon that belongs to this category is the solvophobic effect exhibited by glycerol and other polyols. Polyols are polar molecules that are capable of forming hydrogen bonds with water, as well as polar residues on the surface of the protein. Glycerol has been found to repel nonpolar substances effectively (Sinanoglu and Abdulnur, 1965) and to interact favorably with water (Scatchard et al., 1938). It fits well into the fluctuating network of water hydrogen bonds that is referred to as the “water structure” (McDuffie et aL, 1962) and can strengthen this network, i.e., increase the hydrophobicity.Therefore, glycerol is a solvophobic agent. Since, contact with nonpolar regions on a protein surface of glycerol-modulated “water structure” is even more unfavorable than that of water, it can be expected that glycerol will be preferentially repelled from the nonpolar groups on the surface of the protein. This causes water and glycerol molecules to redistribute them-

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selves around these groups in such a manner as to minimize unfavorable contacts. In other words, the exchange reaction at hydrophobic loci is favorable to water. On the other hand, the polar nature of glycerol favors its interactions with polar groups on the surface of the protein. This is supported by the correlation between B3 values calculated from preferential interaction measurements (Gekko and Timasheff, 1981) and the polarity (Bigelow, 1967) of the proteins. Therefore, the source of the preferential hydration in aqueous glycerol is the solvophobic (enhanced hydrophobic) effect, compensated by the favorable exchange with water at polar sites on the surface of the protein molecule. An analysis of the preferential interactions of proteins with a number of polyols (xylitol, mannitol, sorbitol, inositol) have led Gekko and Morikawa (1981) to the same conclusion, The preferential exclusion of urea from the highly polar myoglobin found by Zerovnik and Lapanje (1986), while it is preferentially bound by /3-lactoglobulin (Vlachy and Lapanje, 1978), has led these authors to propose that preferential exclusion occurs mostly from the highly hydrated surface charged residues. This could also explain the preferential exclusion from native RNase A (Fig. 12), which is greater at pH 7.0 than at pH 2.8 (Prakash et al., to be published). It is expected that the ionized carboxylate groups at pH 7.0 would be more strongly hydrated than the protonated ones at pH 2.8. Such hydrating water molecules would extend to layers beyond the first layer of contact with the protein. Finally, the source of preferential interactions has been probed by measurements of the effects of cosolvents on individual amino acid residues and peptide groups. This has been done by solubility measurements for a large number of denaturants (Tanford, 1968, 1970). For preferentially excluded cosolvents, such measurements have been performed on polyols (Gekko and Morikawa, 1981; Gekko, 1982; Gekko and Koga, 1984) and salts (Arakawa and Timasheff, 1984a). Liu and Bolen (1995) have examined the transfer free energies of amino acids in two osmolytes, sucrose and sarcosine, which differ greatly in chemical structure. It is striking that the two osmolytes interact similarly with amino acid side chains and peptide groups. Both have weak affinities for polar groups and some nonpolar residues. Both have lower affinity than water for peptide groups. This unfavorable interaction with newly exposed peptide groups on unfolding may make a major contribution to their stabilization of proteins (Liu and Bolen, 1995). Most recently, Wang and Bolen (1997) have shown that the transfer free energy of most amino acid side chains from water to 1 MTMAO is neutral whereas that of the peptide groups is strongly positive. Since protein unfolding is accompanied by the exposure of a large number of peptide groups,

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this observation can account for the stabilizing action of TMAO. The transfer tree energy variations open the possibility that stabilization of globular proteins against unfolding, while thermodynamically caused by the increase in preferential exclusion of cosolvent during the reaction, may reflect different mechanisms of exclusion in the two end states. For example, in the case of sucrose, preferential exclusion due to the surface tension increment from the native protein may shift to preferential exclusion due to unfavorable interactions with groups newly exposed on unfolding. This process would be the converse of that occurring with salting-out cosolvents, such as PEG or MPD, which are excluded from the native structure, but bind to the unfolded protein and, as a result, act as denaturants. VII. OSMOLWES When it needs $0 maintain the osmotic pressure of living cells, nature has (through evolutionary selection) opted to do this by incorporating into the cells a number of compounds known as osmolytes. It is remarkable that the small number of these compounds span cellular organisms, plants, and animal vertebrates and invertebrates (Yancey et aL, 1982; Somero, 1986;Yancey and Somero, 1979). These compounds comprise polyols, sugars, methylamines, amino acids, and some derivatives, and in some cases urea in combination with methylamines.All are electrically neutral, without major nonpolar moieties, and-with the exception of urea-they are “compatible solutes” (Brown and Simpson, 1972; Clark, 1985) in that they do not interfere with cellular structure and function. Compounds that perturb biochemical processes, such as arginine and lysine or amino acids with large hydrophobic side chains, are not used. When an incompatible molecule is used, it is compensated by some compatible ones, such as methylamines. As shown above, the effects of urea are compensated by TMAO [see Yancey and Somero (1979) and Fig. 61, while betaine has been found to compensate the deleterious action of some salts (Pollard and Wyn-Jones, 1979) and of urea (Yancey and Burg, 1990). All of the compounds used as osmolytes that have been examined have been found to stabilize the native structure of proteins and to be preferentially excluded from contact with proteins at 20°C (Arakawa and Timasheff, 1985c; Santoro et al., 1992). In fact, preferential exclusion has been proposed as the basis of their selection (Low, 1985; Somero, 1986). Many of the same compounds are found to be cryoprotectants in that they protect plants and animals (e.g., frogs) from being damaged by freezing (Carpenter and Crowe, 1988).In studies in vitro, they have been shown to protect protein structure in the frozen

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state by being preferentially excluded (Carpenter et al., 1993). In fact, in the frozen state, they can compensate for the protein structure damaging effects of protein destabilizers,as has been shown for the sucrose-NaSCN aqueous system (Allison et al., 1996). The small selected number of compounds used as osmolytes are all compatible protein structure stabilizers. It is evident, therefore, that one of the criteria in their selection by nature is the ability to provide thermodynamic stabilization. Furthermore, since stabilization is determined by the difference between the preferential interactions with the native and denatured states of the proteins, none of these compounds show any significant binding to proteins at 20°C; all are preferentially excluded. Why this need of exclusion? And what is the most favorable relation between structural stabilization and maintenance of the osmotic pressure? For a neutral nondissociable solute at concentration m3, the osmotic pressure, n, is defined by

where TI is the partial molal volume of the principal solvent (in living cells, water) and is the osmotic coefficient [+ = - (ml/m3) In all, so that

+

Differentiation and application of the Gibbs-Duhem equation gives

Combination with the preferential interaction relation [Eq. (7)], expressed as preferential hydration, results in

This shows that the degree of preferential hydration (or preferential binding) is inversely proportional to the departure of the osmotic pressure from the ideal van’t Hoff law. For preferentially excluded cosolvents, the parameter (dp3/i)m2)”s = (apn/i)m,), is a measure of the repulsion of the cosolvent from a protein surface and can be regarded as a measure of stabilization. If we generalize this equation to the interior of a cell, this parameter should also give a measure of the repulsion from the

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surface of a cellular compartment. Therefore, the difference in osmotic pressure gradients with concentration of different cosolvents leads to different degrees of preferential hydration for a given repulsion from the cell surface. This is illustrated in Table IV,in which preferential hydration and preferential exclusion have been calculated for osmolytes at a 1 molal concentration and a constant value of ( d p 3 / d m 2 ) K R m=3 4000 cal/mol‘. The sixth column shows that the preferential hydration varies by a factor of 1.65 between glycine and the hypothetical “superosmolyte.” It is clear that the perturbation of the solvent composition at a surface decreases as the deviation from ideality becomes more positive. For a cellular compartment, this means less redistribution of solvent components; i.e., the higher the osmotic pressure gradient, the smaller will be the volume of cellular fluid perturbed. This situation, which is advantageous to the integrity of the organism, might explain the evolutionary selection of “superosmolytes” by a variety of organisms. VIII. CONCLUSION Weak interactions of cosolvents with proteins can modulate almost any biochemical reaction or biological process. The criterion for this was first established by Jeffries Wyman 50 years ago in the concept of linked functions. What is required is that the preferential interactions

TABLE IV Relation between Osmotic Pressure Increment and Solvent Exclwiona,b

Ideal Glycine Sucrose Betaine “Superosrnolyte”

24.1 21.1 29.6 32.1 34.8

583 514 716 777 843

0 -0.118 0.229 0.333 0.447

-6.86 -7.78 -5.59 -5.15 -4.74

0.48 0.54 0.39 0.36 0.33

Reproduced from Tirnasheff (1992). bAll calculations were done for 20°C, m, = 1.0, and a constant value of ( 8 ~ 2 / 8 m S ) 1 ~ , p=, :4000 n 2 cal/rno12. ‘Calculated for lysozyme, molecular weight = 14,300; = 0.70; radius = 15.8 A.

426

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between the aqueous cosolvent medium and the reacting system change during the course of the reaction; i.e., the thermodynamic, dialysis equilibrium binding of the cosolvent must be different to the two end states of the reaction. The measured dialysis equilibrium binding may give stoichiometries which are either positive or negative: a positive stoichiometry means preferential binding; a negative stoichiometry means preferential exclusion of the cosolvent, i.e., preferential hydration. The requirement that cosolvent molecules be at a high concentration, 2 1 M, means that the free energies of interaction at loci on the protein surface are similar to those of water molecules. Hence, in the case of cosolvents, exchange with water must be considered explicitly. The vast amount of knowledge acquired on the interactions of cosolvents with proteins has characterized them into strongly excluded, weakly excluded, and preferentially bound ones. The criterion is simply the values of the exchange constant, K,,, in the P.H20, + L S P-L + nHPO reaction, in which a cosolvent molecule replaces n water molecules on a protein site when it binds. When (Kex-1) (on a mole fraction scale) is positive, there is preferential binding; when ( K e x- 1) is negative, there is preferential exclusion. This criterion, in turn, reflects the direction in which a protein shifts the chemical potential of the cosolvent when it comes into contact with it: if it raises the activity of the cosolvent, there will be preferential exclusion; if it lowers it, the result will be preferential binding. It is clear, therefore, that the weakly interacting cosolvents can all fit along a single spectrum which spans from strong preferential binding to strong preferential exclusion. Their position is determined by their exchange constants with water and their values of ( d p 3 / d m 2 T,p,q. ) In this way, one finds GuaHC1, urea, and NaSCN at one end of the spectrum, while sucrose, Na2S04,glycerol, and glycine are found at the other end. In between, the ribbon is filled out with GuaOAc, Gua2S04,TMAO, and other weakly interacting or “chameleon” cosolvents, i.e., those the sign of whose preferential interactions depends on circumstances, such as MgC12, NaBr, LysHC1, ethylene glycol, and the PEGS. The measured preferential binding (positive or negative), or the change in preferential interactions during the course of a reaction, reflects changes in occupancy of loci on the protein surface both by cosolvents and water molecules. These may be decomposed empirically into numbers of water and cosolvent molecules that occupy sites. These site occupancy values are not thermodynamic numbers, but rather are effective values that correspond to the summation of many weak interactions. Hence, they must be regarded strictly as descriptions of the data, not as true stoichiometries.

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The sign of the preferential interaction of any cosolvent with a protein in one end state of the equilibrium, State I C State 11, is totally immaterial in determining the direction in which the cosolvent drives the reaction. The only criterion is the difference in values between the interactions with State I and State 11. Thus, during protein denaturation (unfolding), for example, stabilization may occur if the preferential binding to the unfolded state is less than that to the native state of the protein. Conversely, if a cosolvent is excluded to a smaller degree from the denatured protein than from the native one, it will be a denaturant. Vast studies carried out at 20°C have given the result that most compounds which stabilize proteins and enhance self-assembly are preferentially excluded from native proteins at that temperature. Those that denature proteins may be either preferentially bound to or excluded from the native protein. At higher temperatures, preferential exclusion of some stabilizing cosolvents has been observed to change to preferential binding. This did not affect stabilization, since this was true of both end states of the reaction. The surface of a protein molecule is a heterogeneous mosaic of sites with different affinities for any given cosolvent. In fact, there may be sites favorable to binding a given cosolvent and other sites favorable to exclusion. This leads to compensation in the global interaction, which is the observed quantity, since what is measured by dialysis equilibrium is the summation over all sites. In the case of reactions that occur at a limited portion of the protein surface, such as the binding site of a ligand or the locus of a conformational transition during the activation of an enzyme, the interactions with cosolvents may be highly different from the global ones over the entire protein molecule, and site-specific effects may become the controlling factors. This provides the possibility of manipulating reactions by the addition of weakly interacting cosolvents. While the Wyman linkage relation is frequently taken as the criterion of the effect of a ligand on an equilibrium, it expresses only the direction into which the cosolvent system drives the reaction at the given solvent composition. The effect relative to water is given by the integrated form of the Wyman linkage relation, which is the “thermodynamic box.” Thus, the promotion of a reaction by a cosolvent (or any ligand) relative to water as the medium may reach an optimal value at some solvent composition, above which the promotion will be decreasing. This manifests itself as an inhibition in the Wyman linkage relation slope, which represents the rate of decrease of the promotion. As a consequence, the signs of the transfer free energy, GAP^.^, and the Wyman linkage slope, 6 ( d p 2 / d m 3 ) may , be opposite.

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Over decades, vast amounts of empirical information have accumulated on the effects of various weakly interacting agents on biological and biochemical phenomena. The advent of the Wyman concept of linked functions in 1948 and the later application to it of multicomponent thermodynamics, developed by G. Scatchard and J. G. Kirkwood at about the same time, have made it possible to group all of these apparently unrelated observations and, in fact, biological controls in general under a single statement of truth, a truth that fishes, frogs, and cactuses have abided by for eons, as witnessed by their selection of osmolytes and cryoprotectants in the course of evolution, and that Wyman’s genius led him to realize half a century ago. Dmitri Mendeleev in 1887 wrote, “Without the material, the plan alone is but a castle in the air; whilst the material without a plan is but useless matter.” The accumulated observations are that material; Wyman discovered the plan, and what had appeared as chaos has turned out to be part of a “scientific edifice” that is beautiful in its simplicity.

ACKNOWLEDGMENT I am most grateful to John Schellman, Kirk Aune, Charles Tanford, Robert Baldwin, Wayne Bolen, and Chris Miller for their insightful comments over many years which have helped to clarify in my mind many of the issues discussed in this chapter. I also wish to thank Mrs. Patricia Murray and Dr. Guifu Xie for their invaluable assistance with the preparation of this manuscript. But most of all I wish to acknowledge my indebtedness to the bright postdoctorals whose scientific inquisitiveness and enthusiasm provided the drive for the studies described here. Finally, my gratitude goes out to my two great teachers, John G. Kirkwood and Jeffries Wyman. From Jeffries Wyman, I absorbed many a point of wisdom, as we discussed science and the Russian Revolution, be it during our walks in Liguria or o n a Greek island, or while we were drinking tea under the plum tree in his summer home in Burgundy under the watchful care of the unforgettable Olga Aleksandrovna.

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AUTHOR INDEX Numbers in italics refer to pages on which the complete references are listed.

A Abdulnur, S., 420, 421, 431 Abeles, R. H., 66, 118 Aberg, C., 81, 115 Abergunawardana, C., 264, 279 Abraham, D. J., 189, 248 Abrams, C. C., 39, 40, 41, 47, 49, 50, 51, 52, 55 AbuChazaleh, R., 39, 42, 55 Acharya, K. R., 188, 248 Ackers, G. K, 69, 75, 115, 117, 186, 189, 191, 192, 193, 196, 197, 199, 200, 201, 202, 203, 204, 205, 207, 209, 210, 211, 212, 213, 215, 216, 217, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 236, 237, 238, 239, 240, 241, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253 Adair, C. S., 3, 54, 198, 248 Adams, C., 172, 177 Adelman, J. P., 141, 171, 184 Adelman, M. B., 393, 430 Adelsberger-Mangan,D. M., 168, 173 Adler, L. E., 172, 177 Akabas, M. H., 124, 173, 179 Akk, G., 122, 157, 173, I75 Alden, C . J., 289, 350 Allen, D. W., 186, 253 Allison, S. D., 424, 428 Altichieri, L., 95, 115 Amador, M., 163, 183 Amiconi, G., 11, 54 Amit, D. J., 168, 173 Ampulski, R. S., 238, 248 Amzel, L. M., 264, 267, 278 Anand, R., 173, 181 Anderson, C. F., , 284, 285, 287, 288, 291, 292, 294, 295, 296, 297, 298, 300, 302,

303, 304, 307, 308, 309, 310, 31 1, 312, 313, 314, 315, 316, 317, 319, 320, 321, 323, 327, 330, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 345, 346, 347, 349, 350, 351, 352, 353 Anderson, C. M., 221, 249 Anderson, P., 174 Anderson, S., 64, 71, 115 Angliker, H., 83, 88, 118 Antonini, E., 198, 202, 248, 251, 253 Antosiewicz, J., 2, 11, 17, 19, 22, 26, 28, 54 Aqvist, J., 50, 54 Arakawa, T., 291,292, 308, 309, 310, 350, 365, 375, 383, 387, 388, 391, 392, 393, 394, 395, 409, 411, 415, 417, 418, 419, 420, 422, 423, 424, 428, 429, 430, 432 Archontis, G., 43, 55 Arcus, V. L., 56 Aricc-Muendel, C . , 255, 279 h o n e , A., 188, 190, 192, 248, 250, 252 Aruga, R., 86, 1 I7 Ascenzi, P., 11, 54, 55 Atha, D. H., 201,204,212, 217, 248 Auerbach, A, 122, 126, 132, 154, 156, 157, 171, 173, 175, 183, 184 Aune, K C., 370,377, 380, 388, 409, 410, 414, 429 Auzat, I., 248 Ayala,Y. M., 82, 83, 86, 88, 115, 116 Ayers, V. E., 188, 238, 248 Aylwin, M. L., 141, 144, 173

B Bai, Y., 255, 274, 278 Bailey, M., 210, 246, 252 Baldwin, J., 188, 248 Baldwin, R. L., 285, 292, 295, 310, 312, 321, 345, 347, 350, 351, 352, 420, 429 433

434

AUTHOR INDEX

Balliano, G., 11, 55 Ballivet, M., 124, 126, 141, 142, 147, 149, 151, 166, 171, 172, 174, 175, 176, 182, 183 Banaszak, L. J., 188, 250 Banfield, D. R, 86, 99, 115 Barbone, F. P., 65, 118 Bardi, J. S., 264, 278 Bardsley, W. G., 149, 151, 152, 176 Barkas, T., 124, 176 Barkley, M. D., 341, 350 Barmat, L., 69, 117 Barnett, B. J., 395, 431 Barot, S., 171, 174 Barr, P. J.. 80, 92, 115 Barradas, R. G., 351 Barrett, A. J., 79, 86, 117 Barrett, R. W., 65, 81, 115, 118 Barria, A,, 170, 173 Barrick, D., 310, 352 Barry, P. H., 141, 142, 146, 180, 182 Bartik, R,13, 23, 25, 54 Bartol, T. M., 168, 174 Bartsch, H. H., 86, 92, 115 Bartunik, H. D., 86, 92, 115 Bashford, D., 1, 4, 5, 13, 18, 19, 22, 28, 55, 57, 66, 115 Baskemille, M., 341, 342, 343, 351 Bauer, C., 205, 251 B a t , B., 39, 55, 56 Bear, M. F., 169, 174 Beeson, D., 171, 183 Bekkers, J. M., 168, 174 Bello, J., 393, 431 Belsham, G. J., 39, 40, 41, 47, 49, 50, 51, 52, 55 Benazzi, L., 192, 193, 219, 220, 222, 239, 240, 245, 252 Bencherif, M., 173, 180 Benesch, R., 238, 248 Benesch, R. E., 238, 248 Benjamin, D. C., 277, 279 Bennett, E. L., 66, 116 Berg, D. R,122, 124, 163, 175, 182, 183 Berg, D. T., 83, 115 Berg, J. M., 186, 251 Berger, A,, 80, 118 Berger, R. L., 219, 222, 252 Berkovic, S. F., 172, 183 Berliner, L. J., 82, 115

Bernstein, F. C., 28, 42, 55 Beroza, P., 5, 19, 20, 42, 55 Berry, A., 69, 118 Bertrand, D., 124, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 149, 151, 154, 156, 157, 163, 165, 166, 167, 171, 172, 174, 175, 176, 177, 178, 181, 182, 183 Bertrand, S., 124, 126, 141, 142, 143, 144, 145, 146, 147, 149, 151, 156, 157, 163, 171, 172, 175, 176, 177, 178, 181, 182, 183 Bessis, A,, 173, 181 Bettati, S., 229, 231, 248 Betz, A. J., 65, 115 Betz, H., 141, 142, 144, 146, 174, 179, 182 Bezeaud, A., 86, 117 Bhat, R., 292, 350, 365, 383, 388, 391, 393, 394, 409, 418, 429 Bienenstock, E. L., 166, 168, 169, 174 Bigelow, C. C., 422, 429 Biltonen, R. L., 271, 273, 278 Binder, E. P., 95, 117 Binzoni, T., 124, 149, 181 Birshtein, T. M., 295, 321, 345, 346, 352 Bishop, G. A., 199, 209, 250 Blackstone, C. D., 170, 182 Blakemore, W., 39, 42, 55 Blanchard, M. H., 66, 116 Blankenship, D. T., 81, 117 Blanquet, S., 66, 115 Blinder, M., 95, 117 Blomback, B., 81, 115, 118 Blombick, G., 81, 82, 115 Blombick, M., 81, 115, 118 Bloom, F. F., 174 Bloomfield, V. A., 345, 350 Blough, N. V., 188, 248 Blount, P., 126, 174 Bock, E., 173, 174 Bode, W., 81, 83, 87, 88, 95, 115, 117, 118 Boelens, R., 343, 350 Bohler, S., 126, 156, 157, 175 Bohn, B., 199, 252 Bolen, D. W., 309, 329, 351, 352, 414, 422, 423, 430, 431, 432 Bolognesi, M., 11, 54, 55 Bond, J. P., 288, 290, 291, 292, 295, 296, 298, 307, 308, 309, 310, 312, 314, 315,

435

AUTHOR INDEX

316, 323, 330, 332, 335, 336, 337, 338, 339, 342, 343, 344, 345, 346, 350, 351, 352, 3553

Bontems, F., 126, 175 Booth, C., 69, 116 Borchardt, D., 188, 248 Bormann, J., 141, 142, 146, 174, 179 Bouet, F., 142, 177 Bouilla-Rodriguez, 0.. 411, 412, 414, 429 Boulter, J., 124, 177 Bouzat, C., 152, 153, 154, 155, 156, 157, 171, 181, 183 Bowie, J., 186, 252 Bowlus, R. D., 395, 423, 432 Boyer, P. D., 251 Bragg, J. K., 199, 253 Braun, P. J., 84, 116 Braunlin, W., 294, 312, 335, 345, 350 Breese, C. R., 172, 177 Breese, K., 373, 392, 419, 429 Bren, N., 122, 126, 132, 151, 153, 154, 155, 157, 171, 180, 181, 183 Brengman,J. M., 127, 151, 152, 154, 155, 157, 171, 181 Brennan, R. G., 343, 351, 352 Breslow, R., 421, 429 Brezniak, D. V., 84, 115 Brice, M. D., 28, 42, 55 Brocklehurst, K., 12, 55 Bronsted, J. N., 417, 429 Brooks, B. R., 23, 28, 43, 55 Brower, M. S., 84, 115 Brown, A. D., 423, 429 Brown, B. M., 64, 70, 71, 117 Brown, F., 39, 40, 41, 47, 52, 55, 56, 57 Broze, G. J., 82, 116 Bruccoleri, R. E., 23, 43, 55 Bruix, M., 13, 56 Bnllet, P., 173, 181 Brdnger, A. T., 28, 55 Brunori, M., 198, 248 Brussard, A. B., 122, 174 Brzovic, P. S., 188, 248 Brzozowski, A,, 188, 248 Buck, M., 26, 34, 55, 255, 279 Buisson, B., 166, 172, 174 Bujalowski, W., 341, 352 Bujo, H., 124, 179 Bull, C., 211, 250 Bull, H. B., 373, 392, 419, 429

Bunn, H. F., 189, 199, 200, 210, 237, 248 Buonomano, D. V., 168, 174 Burg, M. B., 423, 432 Burgess, R. R,340, 352 Burrage, T. G., 40, 41, 47, 52, 57 Burroughs, J. N., 39, 55 Bursaux, E., 209, 251 Burseaux, E., 199, 252 Busch, C., 124, 179 Butko, P., 411, 412, 431 Butler, P. J. G., 239, 252 Buzzell, J. G., 391, 432 Byerley, W., 172, 177

C Caflisch, A., 26, 55 Calvin, M., 66, 116 Campo, A. A., 395, 429 Campos, R. H., 39, 55 Cantor, C. R., 199, 249 Capp, M. W., 290, 291, 292, 296, 298, 307, 308, 309, 310, 312, 332, 339, 341, 342, 343, 344, 350, 351, 352, 353 Cardin, A. D., 81, 117 Carpenter, J. F., 423, 424, 428, 429 Carrasco, L., 39, 56 Camllo, E.C., 39, 55 Carter, P. J., 65, 67, 69, 75, 115 Cartwright, B., 39, 40, 55 Casale, E., 11, 55 Casassa, E. F., 284, 350, 356, 415, 429 Case, D. A, 13, 55, 190, 250 Castro, M. J. M.,64, 115 Cayley, D. S., 290, 291, 292, 332, 340, 343, 350, 352

Cayley, S., 291, 308, 309, 350 Chalfie, M., 151, 172, 183 Chang, G., 343, 351 Chang, H. W., 173, 174 Chang, J. Y., 124, 178 Chang, R., 65, 118 Chang, S. I., 290, 350 Chang, Y., 171, 172, 174 Changeux, J.P., , 60, 78, 117, 122, 123, 124, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 154, 155, 156, 157, 158, 159,

436

AUTHOR INDEX

160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182, 187, 188, 189, 200, 209, 210, 251 Chatrenet, B., 126, 175 Chemouilli, P., 122, 175 Chen,J., 122, 157, 173, 175, 184 Chen, S., 210, 246, 252 Chen, S.-H., 290, 353 Chen, S. J., 290, 350 Cheng, Q.-L., 71, 119 Chiancone, E., 202, 251, 253 Chien, J. C. W., 192, 211, 249 Choi, D. S., 419, 429 Choi, K. Y.,343, 352 Choi, W., 188, 248 Chothia, C., 188, 248, 289, 309, 351 Chu, A. H., 193, 200, 201, 202, 203, 205, 212, 213, 215, 217, 220, 239, 247, 249 Chu, 2. T., 4,20, 22, 24, 56 Chuprina, V. P., 343, 350 Church, W. R., 82, 117 Churchland, P. S., 168, 175 Churg, A. K., 21, 22, 57 Clackson, T., 64, 65, 70, 71, 115 Claeson, G., 81, 115 Clark, M. E., 395, 423, 429, 432 Claudio, T., 126, 157, 167, 182, 183 Clementi, E., 350 Clements,J. D., 122, 175 Cohen, G., 388, 429 Cohen, J. B., 126, 127, 181 Cohn, E. J., 206, 249, 420, 429 Coleman, P., 64, 118 Coletra, M., 11, 54 Collins, K., 285, 292, 350 Collins, K. D., 393, 420, 429 Collyer, C., 11, 55 Colombo, M. F., 292, 350, 411, 412, 414, 429

Colosimo, A., 220, 222, 245, 252 Colquhoun, D., 122, 126, 132, 133, 134, 155, 157, 159, 162, 166, 167, 175, 176 Colter, J. S., 39, 56 Connolly, A. J., 82, 116 Conroy, W. G., 124, 163, 175, 183 Conway, B. E., 351 Coombs, G. S., 81, 116 Coon, H., 172, 177 Cooper, E., 124, 175

Cooper, L. N., 166, 168, 169, 174 Corey, D. R., 81, 116 Cornblath, D. R.,126, 171, 172, 178 Cornish, V. W., 64, 115 Corringer, P..J., 156, 157, 163, 172, 174, 175, 178

Cotton, J. P., 290, 351 Coughlin, S. R.,82, 116, 118 Courrsge, P., 168, 175 Courtenay, E. S., 291, 310, 352 Coutre, S. E., 65, 86, 116, 118 Couturier, S., 124, 175, 176 Cowan, W. M., 175 Cox, D. J., 388, 429 Cox, M. M., 13, 15, 56 Craik, C. S., 79, 80, 92, 115, 117 Crawford, T. O., 127, 151, 181 Creighton, T. E., 56, 72, 115 Cremonesi, L., 219, 222, 252 Crepeau, R. H., 211, 250 Crowe, J. H., 423, 429 Crowther, J. C., 39, 40, 41, 47, 49, 50, 51, 52, 55 Croxen, R.,171, 18? Cuchillo, C. M., 56 Cull, P., 168, 178 Cullis, A. F., 188, 210, 252 Cunningham, B. C., 64, 69, 115 Curry, S., 39, 40, 41, 42, 47, 49, 50, 51, 52, 54, 55, 57

Cwirla, S. E., 81, 115 Czajkowski, C., 126, 176

D Dahlberg, J. E., 351 Dalessio, P. M., 189, 196, 215, 220, 232, 233, 234, 236, 237, 238, 251 Dalvit, C., 13, 55 Danchin, A., 168, 174, 175 Dang, Q. D., 65, 79, 81, 82, 83, 84, 86, 88, 89, 92, 93, 95, 99, 102, 115, 116, 118 Dani,J.A., 122, 163, 173, 176, 178, 183 D’Aquino,J. A., 264, 267, 278 Daugherty, M. A., 189, 193, 197, 204, 207, 212, 213, 216, 220, 222, 223, 226, 229, 231, 239, 240, 243, 246, 247, 248, 249 Davie, E. W., 80, 82, 115, 116 Davis, A., 172, 177

437

AUTHOR INDEX

Davis, M. E., 4, 5, 18, 22, 55, 56 De, P. K, 403, 432 Deatherage, J. T., 221, 249 Dec, S. F., 309, 351 Decker, H., 188, 249, 252 De Filippis, V., 95, 115 Dehaene, S., 168, 169, 175, 176 DeHaseth, P. L., 283, 285, 294, 312, 332, 334, 335, 340, 341, 342, 350, 352 Del Castillo,J., 126, 176 Delcour, A. J., 166, 179 de Llorens, R., 56 Dernchuk, E., 21, 22, 55 Denisov, I., 219, 245, 248, 251 Dennis, M., 124, 172, 178 Dennis, S., 65, 118 Derkach, D., 170, 173 Denvenda, Z.,188, 248 Desphande, P., 126, 141, 171, 179 Devillers-Thi&ry,A., 122, 124, 126, 141, 142, 143, 144, 145, 146, 147, 149, 151, 156, 171, 172, 174, 175, 176, 177, 178, 182 Devlin,J. J., 81, 115 Devlin, P. E., 81, 115 de Vos, A. M., 64, 11 7 Dewey, T. G., 347, 351 DeYoung, A., 202, 204, 249 Di Cera, E., 60, 61, 65, 66, 75, 76, 77, 78, 79, 81, 82, 83, 84, 86, 88, 89, 92, 93, 95, 97, 98, 99, 102, 110, 113, 114, 115, 116, 117, 118, 119, 199, 202, 205, 209, 214, 249, 250, 287, 351 Dickerson, R. E., 233, 249 Dickinson, C. D., 64, 65, 70, 71, 116 Dickinson, L. C., 192, 211, 249 Dill, K A., 72, 73, 116, 339, 340, 353 Ding, L., 81, 116 Dobson, C. M., 13, 23, 25, 26, 32, 34, 54, 55, 255, 279 Dodson, G., 188, 248 Dolman, D., 199, 249 Dong, A., 424, 428 Doolittle, R. F.,79, 82, 116, 118 Dower, W. J., 65, 81, 115, 117, 118 Downing,J. E. G., 166, 183 Doyle, J. P., 122, 174 Doyle, M. L., 189, 193, 197, 200, 201, 202, 203, 204, 205, 207, 209, 212, 213, 215, 216, 217, 219, 220, 221, 222, 223, 224,

226, 227, 228, 229, 230, 238, 243, 245, 246, 247, 248, 249, 250, 253 Dudel, J., 133, 134, 137, 139, 167, 177 Dunn, K E., 64, 65, 86, 116, 118 Dunn, M., 188, 248 D y e r , J. J., 64, 116

E Eaton, D., 82, 116 Eaton, W. A., 131, 176, 178, 202, 229, 230, 231, 248, 249, 250, 252 Edelman, G., 168, 175, 176 Edelstein, S. J., 122, 123, 126, 127, 128, 129, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 154, 155, 156, 157, 158, 159, 160, 161, 162, 165, 167, 172, 174, 175, 176, 178, 205, 209, 211, 229, 249, 250, 251 Edman, L., 157, 176 Edrnonds, B., 122, 126, 132, 15’7, 162, 166, 176

Edsall,J. T., 60, 66, 116, 186, 198, 199, 206, 249, 420, 429 Edwards, B. F. P., 83, 88, 89, 117 Ehrenberg, M., 166, 177 Ehrenfeld, E., 56 Eichele, G., 25, 56 Eigen, M., 123, 157, 166, 177 Eisele, J.-L., 124, 143, 156, 163, 175, 176, 177

Eisenberg, H., 284, 288, 296, 298, 300, 340, 350, 351, 356, 370, 388, 391, 403, 409, 415, 429, 431 Elgoyhen, A. B., 124, 177 ElMary, N. F., 26, 55 Elson, E. L., 166, 177, 180, 312, 345, 347, 351, 352

Engel, A. G., 122, 126, 127, 132, 151, 152, 153, 154, 155, 156, 157, 171, 177, 180, 181, 183 Englander, J. J., 188, 251 Englander, S. W., 188, 251, 255, 274, 278 Erickson,J. O., 356, 430 EIying, H., 419, 429 Esmon, C., 81, 117 Evans, M. G., 66, 116 Evans, P. A., 255, 279 Everse, J., 249, 251

438

AUTHOR INDEX

F Faber, D. S., 168, 177 Farnum, M., 69, 116 Farrell, F. X., 65, 118 Fasano, M., 11, 55 Fasman, G. D., 353, 432 Fayet, G., 66, 115 Fehler, G., 5, 19, 20, 42, 55 Feng, D. F., 79, 116 Fenley, M. O., 347, 351 Fenton, J. W., 11, 82, 84, 115, 116 Fermi, G., 188, 192, 196, 211, 215, 249, 251, 252

Fersht, A. R., , 8, 10, 13, 15, 25, 26, 50, 55, 56, 64, 66, 67, 69, 75, 76, 78, 115, 116, 117, 131, 177, 206, 249 Fiebig, K . M., 26, 34, 55 Fields, B. N., 56 Filatov, G. N., 126, 171, 177 Filmer, D., 60, 77, 117, 122, 179, 186, 187, 209, 251 Fine, R. F., 431 Fischbeck, K. H., 127, 151, 181 Fisher, M., 291, 295, 352 Fisher, R. G., 211, 250 Fishman, M. C., 170, 183 Fixman, M., 315, 351 Flanagen, M. A,, 25, 56 Fleischer, S., 252 Fletcher, T., 80, 92, 115 Fletterick, R. J., 80, 92, 115, 117 Flory, P.J., 199, 249 Fogg, J. H., 239, 252 Foldiak, P., 168, 177 Fontana, A., 95, 115 Fordham, W. D., 79, 117 Forget, G. B., 189, 199, 200, 237, 248 Forman, S. A., 167, 177 Foster, D., 82, 116 Foster, J. F., 391, 432 Foundling, S., 81, 11 7 Fox, R. O., 255, 264, 270, 279 France, L. L., 40, 41, 47, 52, 57 Francis, G., 411, 412, 431 Francisco, J. S., 131, 183 Frank, D. E., 342, 343, 344, 350, 351 Franke, C., 133, 134, 137, 139, 167, 177 Franks, F., 431 Fredkin, D. R., 5, 19, 20, 42, 55

Freedman, R., 172, 177 Freier, S. M., 345, 353 Freire, E., 262, 264, 267, 268, 269, 270, 271, 273, 274, 275, 277, 278, 279 French, C. R., 141, 142, 146, 182 Friedman, R. A,, 315, 338, 340, 351, 352 Frigon, R. P., 391, 410, 429, 430 Fry, E., 39, 40, 41, 42, 47, 49, 50, 51, 52, 55 Fu, D. X., 126, 177 Fujikawa, K., 80, 82, 115 Fukuda, R, 124, 179 Fukudome, T., 153, 154, 155, 157, 180 Fuller, N. L., 411, 412, 415, 431 Fuoss, R. M., 311, 351 Fuxe, K., 173, 182

Gailani, D., 82, 116 Galacteros, F., 189, 202, 219, 253 Gall, W. E., 168, 175, 176 Galzi, J.-L., 122, 123, 124, 126, 141, 142, 143, 144, 145, 146, 147, 148, 149, 151, 156, 163, 171, 172, 174, 175, 176, 177, 178, 182

Gamble, T. R., 64, 117 Gammack, J. T., 126, 171, 172, 178 Garcia-Moreno, B., 64, 67, 117 Garcia-Moreno, E. B., 25, 56, 64, 1I6 Garel, J. R., 188, 248 Gassner, N. C., 406, 431 Gaud, H., 200, 251 Geiduschek, E. P., 295, 351 Geis, I., 233, 249 Gekko, K., 309, 351, 371, 391, 392, 393, 401, 411, 422, 429, 430 Gellin, B. R., 189, 195, 215, 237, 249 Gerzanich, V., 173, 181 GhelichKhani, E., 205, 249 Giachetti, C., 39, 55 Gibb, A. J., 122, 126, 132, 157, 162, 166, 176

Gibbs, C. S., 64, 65, 86, 116, 118 Gibbs, J. W., 59, 116, 418, 429 Gibson, Q. E., 205, 249 Gibson, Q. H., 131, 182, 211, 219, 250, 251 Gierasch, L. M., 186, 249 Gilbert, D. B., 289, 352 Gill, S. C., 310, 352

439

AUTHOR INDEX

Gill, S. J., 1, 2, 3, 10, 12, 54, 57, 60, 61, 119, 186, 187, 188, 198, 199, 200, 202, 206, 207, 209, 249, 250, 251, 252, 253, 256, 279, 287, 309, 351, 353, 356, 432 Gilles, R.,351, 429, 430 Gilles-Baillien, M., 351, 429, 430 Gilson, M . K., 2, 5, 11, 17, 19, 20, 21, 22, 26, 28, 54, 55, 66, 1 I6 Gingrich, D., 192, 201, 204, 219, 221, 224, 249, 252 Giraudat, J., 124, 172, 178 Gittelman, M. S., 69, 117 Gittis, A. G., 64, 116 Glasstone, S., 401, 429 Goeldner, M. P., 126, 142, 175, 177 Goldbeck, R. A., 205, 249 Goldberg, R.J., 356, 4?0 Goldsmith, L. C., 370, 377, 410, 414, 429 Gomez, C. M., 126, 171, 172, 178 Gbrnez,J., 264, 267, 273, 274, 278, 279 Gonzalez, C., 13, 56 Gorbunoff, M. J., 408, 431 GOUZI~, J.-L., 168, 178 Grabharn, P. W., 82, 116 Grabowski, M., 188, 248 Grand, R . J . A., 82, 116 Grant, F. J., 82, I16 Grant, G. A., 188, 250 Gray, C. L., 82, 116 Gray, R., 122, I78 Green, A. A,, 386, 420, 429 Green, S. M., 64, 67, 69, 116 Greene, R. F., Jr., 405, 407, 429 Greengard, P., 163, 166, 170. 179 Greenstein, J. P., 356, 430 Gregory, R.,432 Griffith, L. C., 170, 173 Griffon, N., 202, 251 Grimsley, G. R.,395, 431 Grinnell, B. W., 81, 82, 83, 115, 116 Groot, L. C. A,, 290, 351 Gross, L. M., 311, 312, 351 Guarneri, M., 11, 54 Guidotti, G., 210, 248 Guillin, M. C., 86, 117 Guinto, E. R.,65, 83, 84, 86, 93, 97, 98, 99, 115, 116, 119 Gunner, M . R., 17, 19, 22, 57, 66, 119 Guo, T., 421, 429 Gurd, F. R. N., 25, 56

Gustafsson, B., 165, 169, 184 Gutfreund, H., 198, 199, 206, 219, 249, 250 Guttman, H. J., 290, 291, 292, 332, 340, 343, 350, 352

H Ha, J.-H., 291, 295, 341, 342, 343, 351, 352 Hade, E. P. IL, 371, 388, 403, 408, 429 Hagen, F. S., 82, 116 Hahn, A. F., 146, 182 Haik, Y., 370, 391, 409, 431 Haire, R. N., 411, 429 Haley, P., 82, 117 Hall, J. A., 95, 117 Halvorson, H. R.,191, 199, 200, 201, 202, 212, 217, 219, 248, 250 Hamaguchi, IL, 13, 23, 25, 55, 295, 351 Hamel, E., 395, 429 Hamer, W. J., 421, 4?1 Hammes, G. G., 393, 418, 429 Hand, S. C., 395,423, 432 Handford, C. A., 142, 180 Hangartner, R D., 168, 178 Harber, J., 39, 56 Harker, D., 393, 430 Harper, M. C., 127, I81 Harrington, W. F., 371, 430 Hart, C. E., 82, 116 Hase, W. L., 131, 183 Hassard, S., 40, 41, 47, 52, 57 Hawkes, A. G., 155, 159, 175 Hawkins, R. D., 170, 183 Hawrot, E., 141, 144, 183 Haymet, A. D. J., 314, 353 Haynie, D. T., 255, 262, 268, 269, 278, 279 Hazzard, J. H., 193, 248 Hearst, J. E., 388, 429 Hebb, D. O., 168, 178 Hecht, J., 315, 338, 340, 352 Hedlund, B., 189, 202, 219, 253 Hedlund, B. E., 411, 429 Hedstrom, L., 80, 116 Heidmann, T., 122, 124, 127, 139, 142, 165, 168, 172, 175, 178 Heinemann, S., 124, 173, 176, 177 Helfgott, C., 353 Hendrickson, T. F., 21, 55 Henry, E. R.,122, 126, 127, 128, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140,

440

AUTHOR INDEX

141, 154, 157, 165, 167, 176, 178, 202, 229, 230, 231, 248, 250, 252 Hernandez, M.G.,124, 176 Herriott, R. M., 356, 431 Herz, A,, 168, 178 Herz, J. M., 141, 178 Hess, G. P., 166, 179 Hill, A. V., 206, 250 Hill, T. L., 66, 116, 198, 250 Hiker, V. J., 264, 267, 270, 273, 274, 277, 278, 279 Himmel, M. E., 309, 352 Hirs, C. H. W., 56, 352, 428, 430 Hirth, C. G., 126, 142, 175, 177 Ho, C., 188, 210, 239, 250, 251, 253 Ho, N., 239, 253 Hof, P., 81, 117 Hoff, M., 172, 177 Hoffman, B. M., 188, 192, 201, 204, 211, 212, 219, 221, 224, 240, 248, 249, 250, 251, 252 Hofmeister, F., 420, 429 Hofrichter, J., 131, 176, 178, 202, 230. 249, 250 Hofsteenge, J., 65, 84, 115, 116, 118 Hohenwalter, M . D., 341, 342, 343, 351 Hokfelt, B., 174 Holik, J., 172, 177 Holler, E., 66, 116 Holt, J. H., 200, 201, 203, 205, 213, 215, 217, 220, 249 Holt, J. M., 189, 193. 219, 248, 250 Honig, B. H., 2, 5, 11, 17, 18, 19, 21, 22, 26, 50, 55, 56, 57, 66, 119, 315, 338, 340, 351, 352, 419, 430, 431 Hopfield, J. J., 168, 178 Hopkins, F. G., 356, 429 Hopkins, J., 172, 177 Hori, H., 221, 253 Horovitz, A., 64, 66, 69, 75, 76, 78, 116 Horton, N. C., 343, 351 Horvath, C., 419, 420, 430 Hou, J., 71, 119 HOU,L.-X., 329, 352, 423, 431 Hovav, G., 133, 134, 137, 139, 167, 177 Howell, E. E., 69, 116 Huang, P. L., 170, I83 Huang, Y. H., 193, 197, 207, 213, 216, 219, 224, 230, 238, 239, 240, 241, 243, 245, 246, 248, 250

Huber, R.,81, 83, 88, 95, 117, 118 Hucho, F., 124, 126, 172, 179, 180 Huck, S., 122, I74 Huganir, R. L., 163, 166, 170, 179, 182 Hnnenberger, P. H., 26, 55 Hung, D. T., 82, 118 Hussy, N., 126, 141, 142, 144, 145, 147, 149, 151, 171, 172, 174, 178, 182 Hutchison, D. O., 152, 153, 155, 171, 181 Hvalby, O., 174 Hwang, J. K., 57, 79, 118

I Ifft, J. B., 388, 429, 430 Ikeda-Saito, M., 200, 210, 211, 221, 250 Imai, K., 198, 199, 200, 202, 205, 210, 211, 214, 221, 250, 252 Imoto, K., 122, 124, 179 Imoto, T., 25, 55 Innbushi, T., 210, 252 Inoue, H., 305, 351, 353, 370, 403, 430, 432 Insley, M., 82, 116 Ip, S. H. C., 202, 215, 219, 238, 250 Ishihara, H., 82, 116 Ishimori, K., 214, 250 Itzhaki, L. S., 26, 55 Iwanaga, S., 86, I 1 7

J Jackson, C. M., 95, 11 7 Jackson, M . B., 122, 157, 159, 167, 179, 186, 250 Jackson, S. E., 69, 116 Jackson, T., 39, 42, 55 Jacob, F., 60, 117, 251 Jacobs, M . D., 255, 279 Jahr, C. E., 122, 175 Jain, A. U., 64, 65, 86, 116, 118 Janin, H., 309, 351 Janin, J., 289, 351 Jannink, G., 290, 351 Janis, N. L., 420, 430 Jayaraman, V., 188, 237, 250 Jean-Charles, A., 21, 55 Jencks, W. P., 62, 117, 131, 179, 186, 250, 310, 352, 377, 409, 416, 431

AUTHOR INDEX

Jenny, R. J., 82, 117 Jensen, L. H., 23, 28, 56 Jhon, M. S., 419, 429 Johnson, D. A,, 141, 178 Johnson, D. L., 65, 117, 118 Johnson, D. S., 124, 177 Johnson, J. A., 193, 220, 222, 249 Johnson, L., 188, 248 Johnson, M. L., 199, 200, 201, 202, 204, 205, 209, 210, 212, 213, 215, 217, 219, 223, 231, 248, 250, 251, 278, 352 Jolliffe, L. K., 65, 117, 118 Jones, C., 202, 230, 250 Jones, C. M., 131, 178 Judice, J. K., 64, 11 7 Judson, H., 186, 250 Jurman, M., 141, 144, 183

Kaarsholm, N. C., 188, 248 Kahn, M. L., 82, 116 Kandel, E. R., 170, 171, 180, 183 Kantrowitz, E. R., 188, 250 Kaptein, R., 343, 350 Karlin, A., 122, 124, 126, 146, 163, 173, 1 76, 179, 182 Karlson, L., 374, 388, 432 Karplus, M., 1, 2, 4, 5, 7, 8, 11, 12, 13, 17, 18, 19, 20, 21, 22, 23, 26, 28, 43, 49, 50, 54, 55, 56, 57, 66, 115, 195, 200, 205, 209, 210, 215, 237, 241, 246, 249, 251, 253 Karshikov, A., 81, 83, 87, 88, 95, 115 Kashyap, A. K., 65, 118 Katchasky, A., 311, 351 Katz,B., 126, 132, 139, 176, 179 Katz, S., 357, 371, 430 Kaufmann, C., 126, 176 Kauzmann, W., 309, 352, 373, 392,417, 430 Kavanaugh,J. S., 190, 250 Kawahara, K., 403, 432 Keating, S., 76, 11 7 Kellett, G. L., 219, 250 Kellog, G. E., 188, 189, 248 Kelly, C. R., 64, 65, 70, 71, 116 Kennard, O., 28, 42, 55 Kercher, M. A,, 343, 351 Kerker, M., 432

441

Kerszberg, M., 168, 179 Kestner, N. R., 420, 431 Khan, S. M . A., 329, 352, 423, 431 Khorana, H. G., 64, 118, 186, 251 Kiebler, M., 170, 183 Kielley, W. W., 371, 430 Kierzek, R., 345, 353 Kilmartin,J. V., 188, 239, 251, 252 Kim, C., 186, 251 Kim, K . 5 , 255, 279 Kim, P. S., 64, 67, 117, 119, 255, 269, 279 Kim, S. H., 289, 350 King, A. M., 39, 40, 41, 42, 47, 49, 50, 51, 52, 55 King, G., 21, 22, 57 King, J. A., 186, 249 King, M. V., 393, 430 Kirkwood, J. G., 4, 22, 24, 55, 57, 356, 430 Kirsch,J. F., 23, 28, 56 Kisiel, W., 80, 81, 82, 115, 116, 117 Kister, J., 202, 230, 251 Kita, Y., 391, 394, 419, 430 Kittel, C., 122, 175 Kleinfeld, A. M., 70, 71, 118 Kliger, D. S., 205, 249 Knight, W. S., 392, 430 Knipe, D. M., 56 Knowles, J., 2, 12, 55 Koestner, M. L., 193, 224, 241, 243, 244, 250 Koetzle, T. F., 28, 42, 55 Koga, S., 391, 393, 422, 429 Komives, E. A., 84, 88, 114, 118. Konno, T., 122, 124, 179 Korant, B. D., 39, 55 Korn, H., 168, I77 Koshland, D. E., 60, 77, 117, 122, 179, 186, 187, 209, 251 Kozak, J. J., 392, 430 Krakauer, H., 295, 351 Kranjc, 2.. 405, 430 Kraut, J., 69, 116 Krem, M. M., 86,92,98,99, 117 Krishnaswamy, S.,82, 117 Kronman, M. J., 357, 430 Kruglyak, L., 172, 177 Kufller, S. W., 122, 179 Kuhn, R., 168, 178 Kuil, M. E., 290, 351 Kuliopulos, A., 69, 75, 11 7

442

AUTHOR INDEX

Kuncl, R. W., 126, 171, 172, 178 Kunitz, M., 356, 430 Kuntz, I. D.,Jr., 371, 373, 392,408, 430 Kupke, D. W., 370, 431 Kurachi, K , 82, 116 Kuramitsu, S., 13, 23, 25, 55 Kurganov, B. I., 188, 251 Kurz, A., 205, 251 Kushe, J., 141, 144, 182 Kuwajima, K., 262, 264, 279 Kwiatkowski, L., 202, 204, 249

L Labarca, C., 126, 141, 171, 179 Lagrutta, A., 141, 171, 184 Lallemand, Y., 173, 181 Lamerichs, R. M. J. N., 343, 350 Land, B. R.,168, I74 Landt, E., 419, 421, 430 Langosh, D., 141, 142, 146, 174,179 Lapanje, S., 380, 391, 403, 404, 405, 422,

430,431,432 Lardy, H., 251 Largman, C., 80, 92, 115 Lasalde, J., 124, 126, 171, 172, 178,I80 L~ST,J.-M., 168, 178 Lattman, E. E., 64, I26 Lau, F. T.-K, 64, 69, I17 Laube, B., 141, 142, 146, 179 Lauffer, M. A., 417, 431 Law, V. S., 65, 86, 116 Lazaridis, T., 43, 55 Lea, S., 39, 42, 55 Leach, S. J., 430 Leatherbarrow, R.J., 131, 177 LeBras, G., 188, 248 Lee, A., 189, 195, 209, 210, 237, 241, 249, 251 Lee, C.-P., 64, 118 Lee, D. W., 64, 118 Lee, J. C., 359, 365, 371, 383, 391, 393, 408, 411, 414, 416, 418, 419, 420, 421, 430 Lee, K H., 264, 267, 278 Lee, L. L. Y., 411, 418, 430 Lee, L. Y., 393, 430 Leffler, J. E., 131, 180 Legendre, P., 168, 177 Lehar, M., 126, 171, 172, 178

Lehninger, A. L., 13, 15, 56 Lena, C., 122, 126, 151, 163, 164, 171, 173,

180,181,182 Le Novere, N., 123, 124, 163, 173, 180,181 Leonard, S., 172, 177 Lesk, A. M., 79, 117,289, 309, 351 Leslie, A. G. W., 188, 251 Lester, H. A., 126, 141, 171, 179 Lester, R. A. J., 122, 175 Leung, L. L. K, 64, 65, 86, 116,118 Leutje, C. W., 146, 180 Levandoski, M. M., 342, 343, 344, 350, 351 Levitan, I. B., 163, 180 Levitski, A., 188, 251 Levitt, M., 22, 57 Levy, W. B., 168, 173 Lew, G., 201, 202, 204, 249 Lewis, B. A., 308, 309, 350 Lewis,J. W., 205, 249 Lewis, M., 343, 351 Lewis, P. A., 291, 341, 350 Leyte, J. C., 290, 351 Li, L., 124, 173, 180,181 Li, W.-X., 65, 86, 116,118 Li,Y. H., 124, 180 LiCata,V. J., 69, 75, 117,189, 192, 193, 196, 201, 204, 215, 219, 220, 221, 222, 224, 230, 232, 233, 234, 236, 237, 238,

249,250,252 Liddington, B., 188, 251 Liddington, R.,188, 248 Liddington, R. C., 196, 211, 215, 252 Liepinsh, E., 310, 351 Lifson, S., 311, 351 Lilley, D. M. J., 351 Lim, C., 186, 252 Lin, C. M., 395, 429 Lin, J. S., 290, 309, 350,353 Lin, T.-Y., 67, 117,351,378, 379, 391, 394, 419, 421, 430 Lindstrom, J., 124, 173, 180,181 Lingle, C.J., 122, 126, 132, 157, 162, 180 Lippincott, T., 352 Lipscomb, W. N., 188, 250,251 Lisman, J., 169, 171, 180 Litovitz, T. A,, 421, 430 Liu, X., 64, 118 Liu, Y., 309, 329, 351,352,414, 422, 423,

430,431 Livnah, O., 65, I17

AUTHOR INDEX

Llinas, R. R., 174 Lo, D. C., 124, 180 Lockhart, D. J., 50, 56 Loe, R. S., 192, 212, 221, 249, 251 Loh, S. N., 255, 279 Lohman, T. M., 283, 285, 287, 288, 291, 292, 294, 295, 296, 312, 323, 332, 334, 335, 336, 338, 339, 340, 341, 342, 347, 350, 351, 352, 353 Lonberg-Holm, K, 39, 55 Longfellow, C. E., 345, 353 Lottenberg, R., 95, 117 Lottspeich, F., 124, 172, 179 Loucheux, C., 408, 431 Louie, G., 188, 251 Low, P. J., 70, 71, 118 Low, P. S., 291, 351, 423, 430 Lowe, M. C., 395, 429 Lu, P., 343, 351 Luecke, H., 50, 54 Luetje, C. W., 163, 183 Luigi-Rossi, G., 229, 231, 248, 252 Luisi, B., 188, 196, 211, 215, 251, 252 Lukas, R. J., 173, 180 Lumry, R., 186, 251 Luque, I., 264, 267, 278, 279 Luty, B. A,, 5, 18, 22, 55, 56 Lynch,J. W., 141, 142, 146, 180, 182 Lyster, R. L. J., 198, 252

Maccallum, P. H., 26, 56 McCammon,J. A., 2, 4, 5, 11, 17, 18, 19, 22, 26, 28, 54, 55, 56 McDonald, M., 211, 250 1 McDuffie, G. E, Jr., 421, 430 MacGillivray, R. T. A,, 86, 99, 115 McGourty,J. L., 188, 248 McGrath, M. E., 92, I1 7 Machold, J., 125, 126, 180 MacKerell, A,, Jr., 7, 8, 12, 21, 28, 49, 56 McLaughlin,J. T., 141, 144, 183 McLendon, G., 210, 246, 252 McNamee, M., 124, 126, 171, 172, 173, 178, 180, 181 Maconochie, D., 122, 126, 132, 157, 162, 180 McPherson, A,, 393, 430

443

Madison, E. L., 81, 116 Madura, J. D., 5, 18, 22, 55 Magde, D., 166, 177, 180 Magdoff, B. S., 393, 430 Magnusson, A., 172, 183 Magnusson, D., 174 Mak, T. W., 39, 56 Makhadatze, G. I., 67, 117, 310, 329, 406, 407, 430 Makino, N., 238, 251 Malcolm, B. A., 23, 28, 56 Malenka, R. C., 171, 180 Malinow, R., 171, 180 Mann, K G., 82, 117 Manning, G. S., 284, 285, 311, 312, 313, 333, 347, 351 Mao, C. T., 65, 86, 116, 118 March, K. L., 25, 56 Marden, M. C., 202, 230, 251 Mark, A. E., 26, 55 Markley, J. L., 255, 279 Marti, T., 64, 118 Martin, K., 170, 183 Martin, P. D., 83, 88, 89, 117 Marubio, L. M., 173, 182 Mascotti, D. P., 291, 332, 334, ?51 Maselli, R., 126, 171, 172, 178 Mason, P. W.,39, 56 Masson, C., 168, 179 Mather, T., 81, 117 Matsumura, S. Y.,65,86, 116, 118 Matter, J.-M., 124, 176 Matteucci, M. D., 65, 118 Matthew,J. B., 25, 56 Matthews, B. W., 23, 28, 56, 64, 66, 67, 11 7 Matthews, C. R., 69, 117 Matthew, D. J., 71, 119 Matthews, J. M., 26, 55 Matthews, K S., 344, 35? Mayford, M., 170, 171, 180 Mayne, L., 255, 274, 278 Mayorga, O., 264, 279 Mayr, I., 83, 88, 118 Mayr, L. M., 399, 430 Mazur, S. J., 291, 294, 352 Meeker, A. K., 64, 67,69, 70, 71, 75, 116, 117, 118, 264, 279 Mehler, E. L., 25, 56 Mejza, S. J., 65, 86, 116 Melancon, P., 291, 294, 352

444

AUTHOR INDEX

Melander, W., 419, 420, 430 Melcher, S. E., 290, 292, 332, 340, 342, 343, 344, 350, 351, 352 Mendeleev, D., 430 Menegatti, E., 11, 54, 55 MCnez, A., 126, 142, 175, 177 Merlie, J. P., 126, 174 Merlo Pich, E., 173, 181, I82 Merzenich, M. M., 168, 174 Metropolis, N., 19, 56 Mets, U., 157, 166, 176 Meyer, G. J . B., Jr., 28, 42, 55 Meyer-Almes, F.-J., 123, 157, 166, 182 Middleton, S. A., 65, 11 7 Mildvan, A. S., 69, 75, 117 Milla, M. E., 64, 70, 71, 117 Milla, P., 11, 55 Millar, N., 124, 176 Miller, K. W., 167, 177 Miller, S., 289, 309, 351 Mills, F. C., 200, 201, 202, 203, 205, 212, 213, 215, 217, 238, 248, 251 Mills, P., 284, 314, 315, 323, 351 Milner-White, E. J., 26, 56 Milone, M., 127, 151, 152, 153, 154, 155, 156, 157, 171, 180, 181, 183 Minton, A., 210, 251 Mishina, M., 122, 124, 179 Misra, V. K., 315, 338, 340, 351, 352 Miura, S., 210, 251 Miyata, T., 86, 117 Miyazaki, G., 221, 253 Moffat, K., 212, 251 Moffatt, K., 192, 221, 249 Monod, J., 60, 78, 117, 123, 128, 181, 186, 187, 188, 200, 209, 251 Montague, P. R., 168, 169, 181 Moo-Penn, W., 189, 202, 219, 253 M o d , S. A., 238, 248 Morgan, R. S., 25, 57 Mori, Y., 124, 179 Morikawa, T., 391, 392, 393, 401, 411, 422, 429 Morimoto, H., 210, 221, 222, 229, 252, 253 Morishima, I., 214, 250 Morozova, L. A., 255, 279 Mozzarelli, A., 229, 231, 248, 252 Muirhead, H., 188, 210, 252 Mukeji, I., 188, 237, 250, 251 Mulcahy, L. S., 65, 117, 118 Mulle, C., 126, 141, 142, 147, 149, 151, 163, 164, 171, 172, 174, 181, 182

Muller, D., 170, 173 Muller-Hill, B., 186, 188, 251 Mulley,J. C., 172, 183 Munro, P. W., 166, 168, 169, 174 Murdin, A., 39, 56 Murphy, E. C., 64, 117 Murphy, K. P., 275, 278 Myers, D. M., 189, 193, 197, 199, 201, 204, 205, 207, 212, 213, 216, 220, 222, 223, 226, 229, 231, 243, 246, 247, 248, 249 Myers, J. K , 262, 279 Myrback, K., 251

Na, G. C., 416, 430 Nadal, J.-P., 168, 169, 176 Nagel, R. L., 219, 251 Nakai, J., 124, 179 Nakano, S., 151, 157, 171, 181 Nakken, K. 0.. 172, 183 Narahashi, T., 180 Naray-Szabo, G., 57, 79, 118 Navre, M., 81, 116 Neet, K. E., 188, 251 Neher, E., 123, 142, 157, 166, 181, 182 Neira, J. L., 13, 56 Nelson, D. L., 13, 15, 56 Nemethy, G., 60, 77, 117, 122, 179, 186, 187, 209, 251 Nesheim, M. E., 82, 117 Neuberger, A,, 66, 117 Neubig, R. R.,127, 181 Neumann, E., 157, 166, 182 Neurath, H., 79, I1 7, 356, 430 Newland, C., 171, 183 Newman, J., 39, 42, 55 Newman, J. F., 40, 41, 47, 52, 57 Ni, F., 89, 117 Ni, H., 314, 315, 351 Nicholls, A., 21, 55, 419, 430, 431 Nicholls, P., 411, 412, 431 Nicoll, R. A., 171, 180 Nishikura. K, 239, 252 Noble, J., 39, 55 Noble, R. W., 202, 204, 249 Noelken, M. E., 403, 430 Nogues, M. V., 56 North, A. C. T., 188, 210, 252 North, R. A., 141, 171, 184 Northrop, J. H., 356, 431

AUTHOR INDEX

Nowak, M. W., 126, 141, 171, 179 Nozaki, Y., 13, 15, 56, 310, 351, 403, 409, 416, 4?1 Numa, S., 122, 124, 179 Nyles-Worsley, M., 172, 177

0 Oberthur, W., 124, 172, 179 O’Callaghan, D. J., 39, 56 Ochoa, E. L. M., 173, 181 O’Connell, P., 146, 182 O’Dell, T. J., 170, 171, 180 Oganessyan, V., 81, 117 Ogata, R. T., 70, 71, 118 Ogden, D. C., 167, 175 O’Hara, P., 82, 116 Ohno, K., 122, 126, 127, 132, 151, 152, 153, 154, 155, 156, 157, 171, 180, 181, 18? Okamura, M. Y., 5, 19, 20, 42, 55 Olafson, B. D., 23, 43, 55 O’Leary, M. E., 141, 144, 181 Olincy, A,, 172, 177 Oliveberg, M., 56 Olmsted, M. C., 288, 292, 312, 315, 316, 336, 337, 339, 345, 347, 349, ?51, 352 Olofsson, G., 309, 351 Olson, S. T., 83, 117 Olson, W. K., 347, ?51 Olsson, P., 81, 115, 118 Onuffer, J. J., 69, 117 Oobatake, M., 395, 431 Ooi, T., 395, 431 Oosawa, F., 311, 352 Orme, A., 66, 116 Orr-Urtreger, A., 172, 177 Ortiz-Miranda, S. I., 124, 180 Oschkinat, H., 83, 88, 118 Oswald, R. E., 126, 181 Otis, A., 198, 252 Otting, G., 310, 351 Owen, D. E., 26, 55 Overman, L. B., 341, ?52

Paborsky, L. R.,65, 86, 116, 118 Pace, C. N., 69, 118, 262, 279, 329, 352, 395, 405, 407, 429, 431

445

Pace, H. C., 343, ?51 Packer, L., 252 Padmanabhan, K, 81, 117 Padmanabhan, K. P., 81, 117 Padmanabhan, S., 339, 352 Palma, E., 124, 149, 172, 174, 181 Palmenberg, A,, 49, 56 Panganiban, L. C., 81, 115 Pao, L., 127, 151, 181 Pappone, P., 124, 180 Pares, X., 56 Park, C. H., 81, 117 Parnas, H., 133, 134, 137, 139, 167, 177 Parsegian, V. A., 292,327, 350, 352, 411, 412, 415, 429, 431 Patel, N., 64, 118 Patlak, j.,123, 142, 157, 166, 182 Patrick, J., 146, 163, 180, 183 Patterson, D., 172, 177 Patthy, L., 79. 117 Pauling, L., 186, 251 Paulsen, O., 174 Pedersen, S. E., 126, 181 Peng, X., 173, 181 Peng, Z., 255, 279 Peng, Ly., 269, 279 Perez, L., 39, 56 Perham, R.N., 69, 118 Perin, F., 124, 163, 182 Perona, J. J., 79,92, 117 Perrella, M., 192, 193, 210, 219, 220, 222, 231, 239, 245, 248, 251, 252 Perry, K. M., 69, 117 Perutz, M. F., 123, 181, 187, 188, 189, 192, 195, 196, 200, 210, 211, 215, 239, 240, 241,246, 249, 252 Peters, E. A., 81, 115 Peticolas, V., 374, 388, 432 Petrenko, V. A., 81, 118 Pettigrew, D. W., 189, 202, 203, 219, 252, 253

Pfeil, W., 26, 28, 31, 32, 33. 56 Phillips, H. A., 172, 183 Piattoni, M., 146, 180 Picciotto, M. R., 173, 181, 182 Pierce, K D., 141, 142, 146, 180, 182 Pink, H., 353 Pinkham, J. L., 124, 180 Pittz, E. P., 391, 393, 394, 421, 431 Poet, R.,26, 56 Poiret, M., 66, 115

446

AUTHOR INDEX

Poklar, N., 391, 404, 405, 431 Polanyi, M., 66, 116 Poljak, R. J., 277, 279 Pollard, A., 423, 431 Polymeropoulos, M., 172, 177 Poyart, C., 189, 199, 202, 209, 210, 230, 251, 252 Prakash, V., 391, 404, 408, 409, 422, 431 Prehoda, K. E., 255, 279 Prestrelski, S.J., 424, 429 Prince, R. J., 126, 181 Privalov, P. L., 26, 28, 31, 32, 33, 56, 67, 72, 117, 295, 310, 321, 329, 345, 346, 351, 352, 406, 407, 430 Propping, P., 172, 183, 184 Pruitt, J. N., 151, 153, 154, 155, 156, 157, 171, 180, 181, 183 Pruitt, J. N., 11, 127, 151, 181 Ptitsyn, 0. B., 34, 56, 295, 321, 345, 346, 352 Pullman, B., 431 Punch, D. L., 251 Purves, D., 174 Putnam, F. W., 356, 430

Qu, X., 124, 163, 182 Quinn, R. G., 421, 430 Quiocho, F. A,, 50, 54 Quiram, P., 127, 151, 157, 171, 181

R Radcliffe, K. A., 122, 178 Radford, S. E., 255, 279 Raiuey, P., 66, 116 Rajan, A. S., 122, 178 Rajbhandary, U. L., 64, 118 Rajendrd, s., 141, 142, 146, 180, 182 Ramanadham, M., 23, 28, 56 Ramirez-Latorre, J., 124, 163, 182 Ramols, D. G., 391, 432 Rand, R. P., 292, 327, 352, 411, 412, 415, 418, 431 Randrup, A,, 39, 56 Rang, H. P., 139, 182 Rathouz, M. M., 163, 182

Rau, D. C., 292, 327, 342, 350, 352, 411, 412, 415, 429, 431 Rauer, B., 157, 166, 182 Rawlings, R. D., 79, 86, I 1 7 Raymond, L. A., 170, 182 Record, M. T., Jr., 283, 284, 285, 287, 288, 289, 290, 291, 292, 294, 295, 296, 297, 298, 300, 302, 303, 304, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 319, 320, 321, 323, 327, 330, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 349, 350, 351, 352, 353 Redfield, C., 13, 23, 25, 54, 255, 279 Reed, C. A., 221, 246, 252 Reeke, G . N., 168, 176 Reid, C., 418, 431 Reimherr. F., 172, 177 Reisler, E., 370, 391, 403, 409, 431 Revah, F., 126, 141, 142, 143, 144, 147, 149, 151, 171, 172, 174, 177, 182 Revzin, A,, 352 Reynolds, J. A., 289, 352, 403, 431 Rezaie, A. R., 83, 84, 1 I7 Richards, F. M . , 289, 352 Richey, B., 188, 252, 323, 352 Richieri, G. V., 70, 71, 118 Rico, M., 13, 56 Riggs, A. F., 201, 204, 212, 217, 238, 248, 252 Rigler, R., 123, 157, 166, 176, 177, 182 Rill, R. I., 290, 350 Rimondi, R., 173, 182 Ripamonti, M., 220, 222, 231, 239, 245, 252 Ripoll, D. R., 89, 117 Ritter, J. M., 139, 182 Rivietti, C., 231, 252 Robert, C. H., 188, 202, 205, 209, 249, 250, 252 Robertson, A. D., 255, 279 Robertson, W., 83, 88, 117 Robinson, C . R., 69, 118 Robinson, D. R., 310, 352, 377, 409, 416, 431 Roczniak, S., 80, 92, 115 Rodgers, J. R., 28, 42, 55 Rodgers, K. R., 188, 237, 250 Rodriguez, H., 82, 116 Roe, J.-H., 291, 294, 340, 352 Rogers, P., 188, 190, 192, 248, 252

AUTHOR INDEX

Rogers, P. H., 190, 250 Rojas, L., 124, 180 Rojas, M. E., 64, 65, 118 Role, L. W., 122, 124, 163, 166, 174, 182, 183

Rollema, H. S., 239, 252 Romeo, P. H., 203, 252 Rosenbluth, A. W., 19, 56 Rosenbluth, M. N., 19, 56 Rosenthal, J., 172, 177 Ross, P. D., 252 Rossi-Bernardi, L., 198, 202, 210, 219, 220, 222, 239, 245, 251, 252, 253 Rossman, M. G., 188, 210, 252 Rothschild, K. J., 64, 118 Roughton, F. J. W., 198, 252 Rovida, E., 69, 117, 204, 219, 222, 230, 251 Rowlands, D. J., 39, 42, 55 Roxby, R., 1, 8, 20, 26, 28, 29, 30, 32, 56, 57

Rubin, M. M., 148, 149, 151, 175, 182 Rucknagel, D. L., 189, 202, 219, 249, 253 Rueckert, R. R., 39, 56 Ruf, W., 64, 65, 70, 71, 116 Rule, G. S., 277, 279 Rullmann, J. A. C., 343, 350 Rundstrbm, N., 141, 142, 146, 174, 179 Russell, S. T., 21, 22, 56, 57 Rutter, W. J., 80, 92, 115, 116 Ryan, S. G., 146, 182 Rydel, T. J., 95, 118

Saari, G. C., 82, 116 Sabetta, M., 84, 115 Saccia, S., 222, 231, 245, 252 Saecker, R. M., 290, 292, 332, 340, 342, 343, 344, 350, 351, 352 Saigo, S., 210, 222, 229, 252 Sakmann, B., 122, 123, 124, 126, 132, 133, 134, 142, 157, 166, 175, 179, 181, 182 Salpeter, E. E., 168, 174 Salpeter, M. M., 168, 174 Sampogna, R., 17, 19, 22, 57, 66, 119 Sancho, J., 50, 56 Sandberg, W. S., 69, 118 Sangar, D. V., 39, 55 Santoro, J., 13, 56

447

Santoro, M. M., 329, 352, 423, 431 Sargent, P. B., 124, 182 Sarma, R., 350 Sauer, R., 186, 252 Sauer, R. T., 64, 70, 71, 117, 352 Sawicki, C. A., 131, 182 Scatchard, G., 296, 352, 356, 360, 371, 392, 421, 431 Schaad, O., 122, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 151, 154, 157, 158, 159, 160, 161, 162, 165, 167, 176 Schachman, H. K., 188,211, 252, 417, 431 Schack, L., 374, 388, 432 Schaefer, M., 2, 11, 17, 19, 20, 23, 28, 54, 56,57 Schechter, I., 80, 118 Schemer, I. E., 172, 312, 345, 347, 352 Scheidt, R. W., 221, 246, 252 Scheiman, M. A., 420, 430 Schellman, J. A., 1, 5, 6, 56, 67, 118, 296, 300, 305, 306, 307,309, 321, 352, 359, 369, 371, 373, 374, 378, 380, 388, 405, 406, 409, 410, 413, 420, 431 Scheufele, S., 408, 431 Schimanouchi, T., 28, 42, 55 Schimmel, P. R.,199, 249, 393, 418, 429 Schirmer, R. H., 26, 56 Schleich, T., 284, 285, 292, 295, 353, 376, 393, 420, 432 Schmid, F. X., 399, 430 Schmieden, V., 141, 142, 144, 146, 179, 182 Schofield, P. R., 141, 142, 146, 180, 182 Scholes, C., 210, 246, 252 Scholler, D. M., 252 Scholtz, J. M., 262, 279, 310, 352 Schuller, D. J., 188, 250 Schulman, B. A, 255, 279 Schulten, K., 2, 57 Schulu, P. G., 64, 115, 117 Schulz, G. E., 26, 56 Schumacher, M. A,, 343, 351, 352 Schumaker, V. N., 388, 429 Schwalbe, H., 26, 34, 55 Schwille, P., 123, 157, 166, 182 Scott, J. K., 81, 118 Scrutton, N. S., 69, 118 Sejnowski, T. J., 168, 169, 175, 181 Semler, B. L., 56 Semo, N., 267, 279

448

AUTHOR INDEX

Serrano, L., 50, 56, 64, 116 Setchenow, M., 420, 431 Seydoux, F. J., 188, 253 Sham, Y. Y., 4, 20, 22, 24, 56 Shaner, S. L., 291, 294, 352 Shannan, B., 211, 215, 252 Shapiro, S., 202, 219, 248 Sharp, K A., 5 , 17, 18, 19, 21, 22, 50, 55, 56, 57, 66, 119, 315, 338, 340, 351, 352, 419, 430, 431 Shea, M. A., 192, 193, 219, 220, 222, 239, 240, 249, 252 Shiang, R., 146, 182 Shiao, D. F., 252 Shibayama, N., 188, 210, 221, 222, 229, 251, 252, 253 Shih, L. B., 290, 353 Shire, S. J., 25, 56 Shirley, B. A,, 69, 118 Shortle, D., 64, 66, 67, 69, 70, 71, 75, 116, 117, 118, 264, 279 Shrager, R. J., 199, 201, 205, 249 Sidorva, N. Y., 342, 352 Sieker, L. C., 23, 28, 56 Sigurdson, W., 122, I73 Sigworth, F. J., 155, 157, 159, 160, 167, 182, 183 Sijpkes, A. H., 310, 352 Silva, A. J., 170, 182 Silva, M., 190, 192, 252 Simmons, R , 192, 252 Simolo, K., 210, 246, 252 Simpson, J. R., 423, 429 Simpson, R. B., 309, 352 Sinanoglu, O., 420, 421, 431 Sine, S. M., 122, 126, 127, 132, 151, 152, 153, 154, 155, 156, 157, 159, 160, 167, 171, 173, 175, 177, 180, 181, 182, 183 Sitkoff, D., 21, 50, 56 Skarzyuski, T., 188, 248 Sligar, S. G., 69, 118 Smith, F. R., 75, 115, 186, 189, 191, 192, 193, 202, 204, 210, 212, 213, 217, 219, 220, 240, 248, 252, 253 Smith, G. P., 81, 118 Smith, L. J., 26, 34, 55 Smith, M., 63, I18 Smith, M. L., 203, 252 Soderling, T. R., 170, 173 Somero, G. N., 379, 395, 423, 431, 432

Sommer, M. S., 2, 7, 8, 11, 12, 17, 19, 20, 21, 23, 28, 54, 56 Son, H., 170, 183 Sonar, S., 64, 118 Sosnick, T. R., 255, 274, 278 Span, J., 403, 404, 431 Spencer, D. S., 64, 116 Speros, P. C., 69, 117, 192, 193, 201, 204, 219, 221, 222, 224, 230, 249, 250, 252 Spiro, T . G., 188, 237, 238, 250, 251 Spolar, R. S., 289, 291, 295, 332, 342, 350, 352 Sporns, O., 168, 176 Spudich, J. L., 64, 118 Squire, P. G., 309, 352 Stanssen, P., 69, 118 Stasne, J. T., 39, 55 States, D. J., 21, 23, 43, 55, 56 Stein, V., 312, 353 Steinbach, J. H., 122, 126, 132, 157, 162, 180 Steinfeld, J. I., 131, 183 Steinlein, 0. K, 172, 183, 184 Steitz, T . A., 186, 188, 253 Sternberg, M. J . E., 25, 55 Sterner, R., 188, 249 Stevens, C. F., 124, 170, 180, 182, 183 Stewart, J. M., 310, 352 Steyaert, J., 69, 118 Stigter, D., 361, 431 Still, W. C., 21, 55 Stirling, Y., 81, 118 Stites, W. E., 64, 67, 70, 71, 116, 118 Stitger, D., 314, 339, 340, 353 Stockmayer, W. H., 356, 431 Stone, S. R., 65, 83, 84, 88, 115, 116, 118 Stoodl, J., 172, 183 Strandberg, L., 81, 116 Strauss, U. P., 311, 312, 351, 353 Strick, T . J., 335, 350 Stuart, D. I., 39, 40, 41, 42, 47, 49, 50, 51, 52, 55, 248 Stubbe, J . A., 66, 118 Stubbs, M., 83, 88, 118 Stucky, G., 210, 246, 252 Sture, E. A,, 65, I 1 7 Sturtevant, J. M., 252, 295, 351 Subramanian, S., 252 Suggett, A,, 392, 431 Sugita, Y., 238, 251

449

AUTHOR INDEX

Sullivan, G. E., 341, 350 Sulzer, B., 168, 178 Summers, L. J., 86, 92, 115 Sun, D. P., 239, 253 Sussman, D., 79, 118 Sussman, F., 21, 22, 57 Sutherland, G. R., 172, 183 Svendsen, L., 81, 115, 118 Swaminathan, S., 23, 43, 55 Swanson, S. A., 391, 432 Swint-Kruse, L., 255, 279 Szabo, A., 1, 5 , 11, 57, 131, 183, 189, 200, 205, 209, 253 Szilagyi, L., 80, 116

T Taggart, V. G., 403, 432 Takagi, T., 82, 118 Takahashi, S., 395, 431 Talbot, P., 39, 55 Tamamizu, S., 126, 171, 172, 178 Tanford, C., 1 , 4, 8, 13, 15, 20, 22, 24, 25, 26, 28, 29, 30, 32, 56, 57, 289, 292, 295, 310, 327, 351, 352, 353, 365, 370, 371, 377, 380, 388, 391, 403, 408, 409, 410, 414, 416, 419, 422, 428, 429, 431, 432 Tang, L., 126, 141, 171, 179 Tanokura, M., 13, 15, 57 Tasumi, M., 28,42, 55 Taylor, P., 141, 178 Teller, A. H., 19, 56 Teller, D. C., 309, 353 Teller, E., 19, 56 Tempczyk, A,, 21, 55 Tennant, L., 13, 55 Terwilliger, T. C., 69, 118 Thesleff, S., 132, 139, 179 Thikry, J.-P., 122, 175 Thillet, J., 203, 252 Thomson, J. A,, 395, 431 Tidor, B., 50, 57 Timasheff, S. N., , 291, 292, 296,297, 305, 306, 307, 308, 309, 310, 350, 351, 352, 353, 357, 359, 361, 365, 370, 371, 372, 375, 378, 379, 383, 387, 388, 391, 392, 393, 394, 395, 396, 398, 400, 401, 403, 404, 408, 409, 410, 411, 414, 415, 416,

417, 418, 419, 420, 421, 422, 423, 425, 428, 429, 430, 431, 432 Timmons, C., 82, 116 Tomaselli, G. F., 141, 144. 183 Tonegawa, S., 170, 182, 183 Tong, G., 122, 175 Tononi, G., 168, 176 Topping, K D., 255, 279 Townsend, B. D., 264, 277, 279 Tram, T., 82, 116 Tran, T., 188, 251 Treinin, M., 151, 172, 183 Tremeau, O., 126, 175 Tsapis, A., 203, 252 Tsetlin, V., 125, 126, 180 Tsiang, M., 64, 65, 86, 116, 128 Tsodikov, 0.V., 342, 343, 344, 350, 351, 353 Tsu, C. A., 92, 117 Tsuneshige, A., 214, 229, 231, 240, 248, 250 Tulinsky, A., 81, 86, 88, 95, 98, 116, 117, 118, 119 Tung, T., 122, 175 Turk, D., 81, 83, 87, 88, 95, 115, 117 Turnell, A. S., 82, 116 Turner, B. W., 189, 193, 200, 201, 202, 203, 205, 209, 210, 212, 213, 215, 217, 219, 220, 239, 247, 249, 250, 252, 253 Turner, D. H., 345, 353 Turner, G. J., 189, 193, 202, 219, 220, 249, 253 Turner, G. L., 193, 220, 222, 249 Twomey, T., 40, 41, 47, 52, 57

U Umeyama, H., 86, 11 7 Unger, L., 291, 294, 352 Unwin, N., 124, 125, 126, 183 Unzai, S., 221, 253 Utkin, Y., 125, 126, 180

v Valdes, R., 202, 205, 217, 253 Valenta, D. C., 166, I83 Valera, S., 124, 166, 176, 183 Vallely, D., 188, 248

AUTHOR INDEX

van Boom, J. H., 343, 350 Van Dael, H., 255, 279 Vandegriff, K. D.,249, 251 van d e Kleut, G. J., 310, 352 van der Maarel, J. R. C., 290, 351 van Gunsteren, W. F., 26, 55 Van Holde, K. E., 188, 253 van Vlijmen, H. W. T., 54, 57 Varvill, K. M., 188, 248 Vehar, G. A., 82, 116 Vernallis, A. B., 124, 163, 175, 183 Vernino, S.,163, 183 Verzilli, D., 211, 221, 250 Vesely, S., 219, 222, 252 Vetter, D. E., 124, 177 Viggiano, G., 219, 222, 252 Vijayaraghavan, S., 163, 182 Villarroel, A., 172, 184 Vincent, A., 171, 183 Vincent, P., 173, 181 Vindigni, A., 65, 83, 84, 86, 88, 89, 92, 93, 95, 102, 114, 115, 116, 118 Vinogard, J., 388, 429,430 Viola, F., 11, 55 Viratelle, 0. M., 188, 253 Vlachy, V., 314, 353,380, 422, 432 von Hippel, P. H., 284, 285, 292, 295, 353, 374, 376, 377, 388, 393, 409, 420, 432 Vu, T. K H., 82, I18

W Wade, R., 21, 22, 55 Wadso, I., 309, 351 Waldo, M. C.,172, I77 Wallace, A., 65, 118 Wallace, R. H., 172, 183 Waller, J.P., 66, I15 Walz, D. A., 84, 115 Wang, A.,422, 432 Wang, H.-L., 122, 126, 127, 132, 151, 153, 154, 155, 157, 171, 180, 181, 183 Wang, J.. 170, 171, 180,255, 279 Wang, L., 77, 118 Wang, M. Y. R., 252 Wang, R., 171, 174 Wang, Y., 170, 182, 183,264, 279 Warren, M. S., 69, 116 Warshel, A., 2, 4, 20, 21, 22, 24, 50, 54, 56, 57,79, 118,312, 353

Warwicker, J., 5, 25, 51, 52, 57 Washabaugh, M. W., 393, 420, 429 Wasmuth, J. J., 146, 182 Watson, H. C.,5, 25, 57 Waxman, P. G.,395, 429 Webb, W., 166, 180 Weber, D. J., 69, 75, 117 Weber, G., 62, 118,186, 200, 253 Wegscheider, R., 66, 118 Weiland, S., 172, 183, 184 Weise, C.,125, 126, I80 Weiss, D. S., 171, 174 Weissman, J. S., 64, 119 Wells, C. M., 83, 118 Wells, J. A.,64, 65, 67, 69, 70, 88, 92, 93, 115, 118 Wells, T. N. C., 131, 177 Wender, P., 172, 177 Westbrook, G. L., 122, 175 Wheaton, V. I., 82, 118 White, C. E., 84, 88, 114, 118 White, M. M., 126, 141, 144, 171, 173, 177, 181 Whiting, P. J., 173, 181 Whitson, P. A.,343, 353 Widengren, J., 157, 166, 182 Wierzba, A., 202, 204, 249 Wigsuorn, H., 165, 169, 184 Wiley, M. R.,83, I15 Wilkinson. A. J., 67, 69, 75, 115 Will, G., 188, 210, 252 Williams, A. P., 345, 353 Williams, D., 168, 176 Williams, D. C., 277, 279 Williams, T. F., 28, 42, 55 Wilson, A. C.,23, 28, 56 Wilson, I. A.,65, 117 Wilson, K. P., 23, 28, 56 Wilson, L., 394, 432 Wimmer, E., 39, 56 Windemuth, A,, 2, 57 Winslow, R. M., 249, 251 Winter, G.,67, 69, 75, 115 Witting, J. I., 84, 115 Witzemann, V., 172, 184 Wonacott, A. J., 188, 251 Wong, K-Y., 377, 409, 432 Wonnacott, S., 122, 173, 184 Wood, S. E., 421, 431 Woodbury, R. G.,116

45 1

AUTHOR INDEX

Woodrow, G. V., 210, 211, 221, 253 Woodward, C., 255, 279 Wright, P. E., 13, 55 Wrighton, N. C., 65, 117, 118 Wu, C. F., 290, 353 Wuyi, M., 86, 116 Wyckoff, H. W., 428 Wyman, J., 1, 2, 3, 5, 6, 10, 12, 54, 57, 59, 60, 78, 83, 113, 116, 117, 119, 122, 123, 128, 181, 184, 186, 187, 188, 198, 200, 206, 207, 209, 249, 251, 252, 253, 256, 279, 282, 283, 284, 287, 288, 296, 322, 353, 356, 432 Wyman, J., Jr., 356, 357, 409, 432 Wyn-Jones, R. G., 423, 431

X Xie, D., 264, 267, 268, 269, 270, 278, 279 Xie, G., 391, 392, 393, 395, 396, 398, 400, 401, 403, 404, 422, 431, 432

Y Yakehiro, M., 122, 178 Yakel, J. L., 141, 171, 184 Yamamoto, H., 200, 210, 211, 221, 250, 253 Yancey, P. H., 377, 378, 379, 395, 423, 432 Yang, A.S., 2, 5, 11, 17, 19, 22, 26, 57, 66, 119

Yang, J. T., 391, 432 Yang, X., 122, 174 Yaw, J., 172, 177

Yellen, C., 141, 144, 183 Yonetani, T., 192, 193, 200, 205, 210, 211, 219, 221, 222, 229, 231, 240, 248, 250, 252, 253

York, E. J., 310, 352 Yoshikami, D., 122, 179 You, T. J.. 22, 57 Young, D. A., 172, 177 Young, D. C., 71, 119 Young, W. S., 168, 177 Yu, C. R., 124, 163, 182 Yu, M.-H., 64, 119

z Zalkin,J., 343, 352 Zauhar, R. J., 25, 57 Zeng, D., 82, 116 Zerovnik, E., 391, 404, 405, 422, 432 Zhan, H., 71, 119 Zhang, E., 86, 88, 98, 119 Zhang, H., 126, 141, 171, 175, 179 Zhang, W., 288,290,291, 292,295,296, 298, 307, 308, 309, 310, 312, 323, 332, 335, 338,339,340, 343, 350, 352, 353 Zhang, Y., 157, 184 Zheng, Y. W., 82, 116 Zhou, F., 2, 57 Zhu, Y. Z., 146, 182 Zimm, B. H., 199, 253 Zippelius, A., 168, 179 Zlotnik, A., 52, 57 Zoli, M., 124, 163, 173, 180, 181, 182 Zou, M., 239, 253

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SUBJECT INDEX

A Acetylcholine receptor agonist binding by, 136 allosteric effectors and coincidence detection in, 163-166 allosteric transitions of, 121-184 allosteric-type model for, 127-129, 166 binding-site nonequivalence in, 157-163 conformational states of, 123, 127-131, 142, 154, 160, 173 “cyclic” model of, 137 desensitization of, 132-141, 166 in diseases and dependency, 126, 127, 149, 151-153, 156, 171-173 dose-response analysis of, 137-142 evolutionary relationships in subunits of, 124 four-state allosteric kinetic mechanism for, 134, 137, 142 free energy profile of, 133, 135 “gain of function” mutations affecting, 151 y-phenotype of, 142, 143, 146-147, 148, 172 homotropic interactions in, 123 hyperresponsive system of, 148-149 ion channel domain of, 141 kinetic properties of, 126 K phenotype of, 142, 143-144 ligand-binding domain of, 141 linear free energy relations of, 129-132 “loss of function” mutations affecting, 151 L phenotype of, 142, 143, 144-146 mechanistic models for, 127-133. 166-1 67 Monod-Wyman-Changeux model applied to, 126, 128, 132, 171 in multiple phenotypes, 141-149 mutations affecting, 123, 125, 126-127, 141-157, 171

oligomeric structure of, 123 pharmacologic agents affecting, 163 pleiotropic phenotypes of, 123, 141, 142-143 presynaptic effects of, 122 properties of, 123 pseudosymmetric oligomeric structure of, 123-126 sequential-type model of, 126, 132, 166 similarities to other allosteric proteins, 121-123 single
454

SUBJECT INDEX

P-Alanine, protein interactions with, 394-395 Alanine-scanning mutagenesis applications of, 64-65 of coagulation factor VIla, 65 epitope assignment by, 72 of erythropoietin receptor, 65 of hirudin-thrombin reaction, 65 of human growth hormone receptor, 65 limitations of, 69-73 principles of, 64, 65-66, 69 site-site transition modes in, 75-76 of structural epitopes, 68 of thrombin, 65 Aldolase, guanidinium hydrochloride interaction with, 408 Alkyl urea, effects on protein, 365 Allosteric effectors, 357 Allosteric model analysis, 209-210 Allosteric theory, 60 Allosteric transitions of acetylcholine receptor, 121-184 Monod-Wyman-Changeu (MWC) model of, 78, 122, 126, 128, 132 Allostery of hemoglobin, molecular code for, 185-253 tetrameric, 205 Amides in proteins, role in preferential accumulation, 309, 310 solvent effects on, 274 Amino acid, side chains, pKo, 13 Amino acids as osmolytes, 423 as perturbing solutes, 283 pK.’s of, 11 in preferential hydration, 388 protein exclusion of, 309 protein interactions with, 394-395 as protein stabilizers, 359 replacement in sitedirected mutagenesis, 63-64 replacements in thrombin, 92-95 side chains of in hemoglobin, 239 sucrose binding, 413-414 unnatural, use in protein structure manipulation, 64

Amino acid salts, protein interactions with, 394-395 Ammonium sulfate, as protein precipitant, 356 AMPA-type glutamate receptors, phosphorylation of, 170 Antibiotics, affecting human rhinovirus, 39 Anticoagulants, thrombin mutations as, 65 Antithrombin 111, thrombin interaction with, 84 Arc repressor alanine-scanning mutagenesis studies on, 71 stability of, 70 Arginine in fibrinogen, 83 in foot-and-mouth disease virus capsid, 43, 44, 45, 46, 51 in lysozyme, 26 pK. of, 14 in serine proteases, 80 in thrombin, 92, 94, 96, 97, 102 Arginine hydrochloride, protein interactions of, 389, 394, 395, 419-420 Arrhenius activation energy, of hemoglobin tetramer-dimer dissociation, 202 Aspartate transcarbamylase (ATCase), characterization by PALA analog, 21 1 Aspartic acid in acetylcholine receptor, 144 in foot-and-mouth disease virus capsid, 43, 44, 46, 51 in lysozyme, 26 pK. of, 14 in protein C, 83 in thrombin, 81 Association-dissociation processes, in biopolymers, 291, 350 A10 serotype of foot-and-mouth disease virus, 39, 40 crystal structure of, 42 helix backbone and side chains in, 50-51 solvation and binding free energy of, 43,44 A22 serotype of foot-and-mouth disease virus, 39, 40 crystal structure of, 42 helix backbone and side chains in, 50-51 solvation and binding free energy of, 43, 44

455

SUBJECT INDEX

A24 serotype of foot-and-mouth disease virus, 39, 40 Autolysis loop, of thrombin, 84, 87 Axial charge density of DNA, 334-335, 336, 340-341 as polyelectrolyte structural variable, 284, 294 of rodlike polyions, 311

B Backbone entropy, of protein partially folded state, 267 “Background atoms,” of titrating site, 13 “Background charges,” of titrating site, 13 Benzene, polystyrene dissolved in, 359 P-Barrels in serine proteinase conformation, 79 in staphylococcal nuclease conformation, 270 in thrombin conformation, 84, 86, 98-99 Betaine as osmolyte, 423, 425 as protein stabilizer, 395 Beta model of lysozyme, 26, 27, 28, 29, 30, 31, 32, 33, 34 absolute electrostatic stability of, 34, 37 electrostatic free energy for, 35, 36 relative electrostatic stability of, 31 titration curve of, 29, 30, 31, 33 PSheet extension, adjacent to histidines in human rhinovirus and poliovirus, 52 Binding cascade, of hemoglobin, 192, 230, 242 Binding constants derivation of, 359 theoretical evaluation of, 1 Binding equilibria, thermodynamic linkage to conformational equilibria, 255-279 Binding free energies, pH dependence of, 2 Binding polynomials, 3 use in osmotic effect studies, 327 Binding sites, in native and subensemble states, 260-261 Biopolymers equilibria of, 288 solute concentration effects, 321-322

preferential interactions of, see Preferential interaction coefficients; Preferential interactions surface types of, 288-291 water exposure of, 291-292 Blood coagulation, serine protease role in, 79, 82 Bohr effect, 60, 231, 287 “remainder Bohr effect,” 239, 241 “tertialy Bohr effect,” 241 Bohr protons release in hemoglobin binding, 199, 216, 239-241 role in CN-met cascade, 242 Boltzmann exponents, 257 Boltzmann weight factor, in rewriting of binding polynomial, 3-4 “Born term” energy, 18, 21 Bovine serum albumin (BSA) amino acid interaction with, 394 glycine betaine interaction with, 307-309, 327 guanidinium hydrochloride interaction with, 408 salt interaction with, 378 solvent interactions with, 389, 390, 392-393 urea interaction with, 309-310 water-accessible surface area of, 309 BPTI alanine-scanning mutagenesis studies on, 71 trypsin binding of,70, 71 Bromide ion, effects on protein surface, 292

C Caenmhabditis elegans, acetylcholine receptor mutation in, 172 Calcium chloride, protein interactions with, 393 Calcium ion in trypsin and chymotrypsin binding loops, 83 uptake by acetylcholine receptor, 152, 163-165, 171 CaM kinase 11, role in synaptic plasticity, 169-170

456

SUBJECT INDEX

Capsid stability, of foot-and-mouth disease virus, 2, 20, 39-53 Carbon dioxide, effect on hemoglobin oxygenation, 188 Carboxyhemoglobin binding interactions in, 233 cooperative free energies of, 244 intermediates of, molecular code partitition function for, 243-246 microstate cooperativity components of, 197- 198 structure of, 190 Carboxyl groups, in unfolded lysozyme structure, 30 Carboxypeptidase A, guanidinium hydrochloride interaction with, 408 Cascade, of hemoglobin binding, 192, 230 Catalase, guanidinium hydrochloride interaction with, 408 Catalytic triad, of serine proteases, 79 Cellular processes, ligand and solute concentration role in, 283 Central processing (CPU) time, for electrostatic free energy calculations, 19, 20 “Chameleon” cosolvent5, 426 “Charge-solvent energy,” 22 CHARMM program, 21, 43 foot-and-mouth disease capsid studies using, 43, 49 lysozyme studies using, 23, 28 Chemical potentials, in linkage phenomena, 287 Chemo-electrical transduction, acetylcholine receptor role in, 121 Chloride ion effect on hemoglobin oxygenation, 188, 241 protein exclusion of, 378 P-Chloroethanol, protein interaction with, 403 Chromium, hemes substituted with, 21 1 Chymotrypsin calcium-binding loop of, 83 guanidinium hydrochloride interaction with, 408 solvent interactions with, 391, 392 specificity of, 80 sucrose interaction with, 363

Chymotrypsinogen guanidinium hydrochloride interaction with, 408 solvent interactions with, 391 Cluster method, for electrostateic free energy, 20 CN-met hemoglobin, 219, 220 binding cascade of, 192, 242 cooperative response parameters for, 240 cysteine sulfhydlyl groups in, 238 oxygen binding by, 227, 230 properties of, 221 Coagulation factor VIIa Ala-scanning rnutagenesis of, 65, 70 tissue factor binding to, 70, 71 Cobalt, heme substitution with, 211, 219, 243, 244, 246 oxygen binding in, 221, 223, 224, 229 subunit assembly in, 204 Coincidence detectors, synaptic triads as, 169 “Compatible solutes,” osmolytes as, 423 Complement fixation, serine protease role in, 79 “Concerted transition,” in hemoglobin, 186- 187 “Condensed” counterions, 31 1-312 Conformations electrostatic free energy difference between, 7-8,9, 53 equilibria of, thermodynamic linkage to binding equilibria, 255-279 Gibbs energy effect on distribution of, 263-266 Gibbs energy scale of, 269-271 most probable distribution of, 257 of proteins, 186 statistical descriptors of ensemble of, 271-278 Conformation transition, 187, 291, 322, 324, 330-331, 344-345, 407 ligand-induced, 263 solute effects on, 350 thermodynamic relation for, 386 Consensus partition function of hemoglobin analogs, 224-226, 243 oxygen binding tests of, 227 Continuum model, for solvent and solute, 4, 17-18, 22

457

SUBJECT INDEX

Cooperative free energy definition of, 201 of hemoglobin oxygenation, 201, 216 of oxyhemoglobin analogs, 221-226 T quaternary form of hemoglobin, 236-237 Cooperativity enthalpic and entropic components of, in hemoglobin, 238-239 of ligand binding, mechanisms, 78 Cooperativity constant, derivation of, 213 Cooperativity effect, in hemoglobin oxygen binding, 215-216 CORE algorithm, for protein conformations, 264 Cosolvents in twodomain model, 306 weakly interacting in protein stability control, 355-432 systems controlled by, 383-387 Coulomb energies, calculation of, 9 Coulombic preferential interactions, of salts with nucleic acids, 284, 285 Coulomb plus “Born” energy, 18 Coulomb plus “chargesolvent energy,” 18 Counterion condensation (CC) theory, 312-313 Counterions, “condensed” or “territorially bound,” 311-312 Coupled conformation changes, solute effects on, 350 Coupled folding, of proteins, 342 Coupling free energy direct, 77 indirect, 78 measurements of, 63, 67, 74 properties of, 76-77 in reference cycle, 62 between two mutations, 77 Cryogenic isoelectric focusing method, application to hemoglobin microstate species, 219, 221-222, 232 Cryogenic quenching procedure, CN-met studies using, 222 Cryoprotectants examples of, 359 natural occurrence of, 388,423-424 Crystallography,of tetrameric molecules, 187, 188

GS8Cl serotype of foot-and-mouth disease virus, 39, 40 crystal structure of, 42 Gterminal carboxyl group, pK,, of, 13, 15 Gterminus in foot-and-mouth disease virus capsid, 43,44 in lysozyme, 26 Cyanide, release from CN-met hemoglobin, 222 “Cyclic” model, of acetylcholine receptor, 137 Cylindrical cell model, application to nucleic acid-oligoelectrolyte interaction, 313 Cysteine in foot-and-mouth disease virus capsid, 43,45 in hemoglobin, sulfhydryl groups in, 238 in lysozyme, 26 pK, of, 15

D Debye-Hiickel approximation, 23, 293, 294, 333 Denaturants, 29, 67, 309 effects on modulation of state distribution, 262-263 Denaturation of globular proteins, 295 of lysozyme, 26, 38 of nucleic acids, 285, 295, 344 of proteins, 295 thermodynamics of, 399-403 by urea, 67, 356,359, 373, 387, 403-409 Densimetry, in studies of preferential exclusion, 308 Deoxyhemoglobin active site analogs of, 211 binding interactions in, 233 structure of, 190 tetramer-dimer dissociation rate of, 202 Destabilization of foot-and-mouth disease virus capsid, 52 as increase of relative free energy, 46 of proteins, 403-409 stabilization related to, 408

458

SUBJECT INDEX

Dialysis equilibrium binding, 363-364, 373, 375-377, 417-418 transfer free energy and, 362-363 Dielectric constant, of protein, 21-25 Differential scanning calorimetry, use in conformational ensemble studies, 271 Digestion, serine protease role in, 79 Dihydro-krythroidine, as acetylcholine receptor antagonist, 141, 147 2,&Diiodo4nitrophenoI (DNP), 335 “Dimer” helix, helix formation from, 345-346, 347 Dimer-tetramer assembly, use to evaluate energy costs of binding cooperativity, 201 2,3Diphosphoglycerate, effect on hemoglobin-oxygen binding, 188 Dipolar ions, as perturbing solutes, 283 Dismutation free energy, 62-63 Dissociation constant, of molecular complex, 12 4,4’-Dithiophyridine,use in hemoglobin sulfhydryl group studies, 238 DNA axial charge density of, 334-335, 336, 340-341 binding equilibria of, 292 cationic ligand binding to, 337-338, 339 denaturation of, 289, 345, 348-349 double helix of formation, 323, 330 preferential interactions of, 290 water-accessible surface of, 289 oligocation binding to, 333-340 polyamine binding of, 335, 336 preferential interaction coefficients of, 345 protein binding to, 340-344 salt interactions with, 312, 388 sodium bromide interaction with, 314 solute effects on, 293 stability of, 420-421 triplet combinations of base pairs of, in genetic code, 185-186 DNA binding domain (DBD), of Inc repressor, 343-344 “Domain of the protein,” definition of, 366 Donnan coefficient, derivation of, 302

Donnan dialysis equilibrium condition, 317 Donnan membrane equilibrium, of ions with charged polymers, 300-303, 313 Donnan quotient, derivation of, 302 Dose-response analysis, of acetylcholine receptor, 137-142 Double helix, formation of, 323 as association equilibrium, 330 Double mutants of proteins, 73-75, 78 of thrombin, 86 Drug design enzyme specificity importance in, 81 structural mapping of energetics in, 63

Effective pK.’s, of titrating site, 13-16 E helix, in hemoglobin, 237-238 Elastase, specificity of, 80 Electrolytes, as perturbing solutes, 283-284 Electrostatic contributions, to molecular free energies, 1-57 Electrostatic coupling, of ligands, 73 Electrostatic free energy absolute vs. relative, 8, 11 of association of foot-and-mouth disease protomers, 42 calculation of, 4, 17-19 of protonation state, 4, 8, 10, 16-17 Electrostatic interaction, between sites, 18 Electrostatic potential, dependence on solute charges, 18 ELISA assay, of foot-and-mouth disease virus subtypes, 39-40 Endosomal acidification, of picornavirus cell entry, 39 Energetics sitespecific structural perturbations and, 66-69 structural mapping of, 63-73 Enzyme catalysis, ionizable group role in, 2 Enzymes activation of, 427 Ala-scanning mutagenesis studies on, 65 allosteric, 123 “macromolecular switches” of, 186 specificity sites of, 80 Wyman linkage role in modulation of, 378

SUBJECT INDEX

Epilepsy, inherited, acetylcholine receptor mutation in, 172 Epitopes, Ma-scanning mutagenesis use in characterization of, 64 ~T264Pmutant, of acetylcholine receptor, 127, 153, 154, 155, 171-172 Equilibirum constants, twodomain predictions of, 326-329 Equilibrium constants, 307 Hofmeister salt effects on, 331-332 nonelectrolyte solute effects on, 327-328 solute effects on, 292-295 threecomponent preferential interaction coefficients for, 319-326 transfer free energy and, 415-416 Equilibrium dialysis, preferential binding measurement by, 371 Equilibrium quotient, derivation of, 320 Erythropoietin receptor, Ma-scanning mutagenesis of, 65 Eschm’chiacoli binding of RNA polymerase of, 340 cation effects on cytoplasm of, 290-291 Ethylene glycerol, protein interactions with, 392 Ethylene glycol as “chameleon” cosolvent, 416 protein interactions with, 393 E217 residue, of thrombin, Ala-scans of, 65 Exchange, at sites in preferential binding, 373-375 Exchange constant, relation to preferential binding, 374 Ex72 model of lysozyme, 26, 27, 28, 29, 30, 31, 32, 33, 34 absolute electrostatic stability of, 34, 37 electrostatic free energy for, 35, 36 pHdependent stability of, 32, 33 relative electrostatic stability of, 31 titration curve of, 29, 30, 31, 33 Exosite I, of thrombin, 83, 84

F Factor V activation of, 82 thrombin cleavage site in, 82 Factor Va, cleavage and inactivation of, 82 Factor VII, thrombin cleavage site in, 82

459

Factor VIII activation of, 82 thrombin cleavage site in, 82 Factor Xa structure and specificity of, 80-81 thrombin double-mutant mimic of, 86 trypsin inhibitor binding of, 11-12 Factor XI, activation of, 82 Factor XIII, fibrin clot stabilization of, 82 FGR tripeptide, thrombin specificity for, 89, 103 F-helix, of hemoglobin, 190 Fibrinogen conversion into fibrin clot, 82 thrombin binding of, 87 Ma-scans, 65 thrombin cleavage site in, 82 thrombin interaction with, 84 Fibrinolysis, serine protease role in, 79 Fibrinopeptide A, use in activesite thrombin inhibitor synthesis, 81 Finitedifference algorithm, PoissonBoltzmann equation solution by, 18, 20 Finitedifference method, 5 for calculation of continuum electrostatic free energies, 25 Finiteelement method, for calculation of continuum electrostatic free energies, 25 Fluorescence correlation spectroscopy, of ligand-binding events, 123, 157-158 Fluoride ion, effects on protein surface, 292 Foot-and-mouth disease virus (FMDV) absolute electrostatic free energy of binding of, 43-44 capsid stability of, 2, 20, 39-53 infection mechanism of, 39 pH effects on, 41,53 ~K.’s, 13-16 relative electrostatic free energy of binding of, 44-46 subtypes of, pH effects on, 39-40 titration curves of, 48 VP chains of, 39, 40, 41, 46, 48, 49, 50, 51-52 Foot-and-mouth disease virus (FMDV), linked function theory applied to, 39-53

460

SUBJECT INDEX

Four-site binding system, for tetrameric hemoglobin, 198 FPR tripeptide, thrombin specificity for, 88-89, 90,97, 101, 102, 110 Free energy changes, threecomponent preferential interaction coefficients for, 319-326 Free energy contributions, to cooperativity, 192, 193 Free energy of binding, measurement of, 357, 359 Free energy of hydration, 368-370 Free energy of interaction, derivation of, 360 Free energy of tertiary constraint, in hemoglobin oxygen binding, 215-216 Free energy simulation methods, 4 Functionspecific probabilities, statistical thermodynamic formalism applied to, 277-278

G “Gain of function” mutations, affecting acetylcholine receptor, 151 y-phenotype, of acetylcholine receptor, 142, 143, 146-147, 148, 172 Gel chromatography of hemoglobin microstate species, 219 use in dimer-tetramer equilibrium studies, 201 Gene regulatory proteins, “macromolecular switches” of, 186 Genetic disease, from acetylcholine receptor abnormalities, 125, 149-157 Geometric approach, to preferential exclusion, 415-416 Gibbs adsorption isotherm, 419 Gibbs approach, use in Wyman linkedfunction theory, 59-60 Gibbs-Duhem equation, 361, 365, 424 Gibbs energy of binding, 256, 263 of conformational states, 256, 257, 263, 278 effect on conformation distribution, 2623-266 of globular proteins, 270 of protein unfolded state, 267-269 of stability, 256

Gibbs energy scale, of conformations, 269-271 Gibbs free energy, 33 Gibbs-Helmholtz equation, 321 Gibbs potential function, of protein conformations, 267-268 Globular proteins, Gibbs energy diagram for, 270 Glucose, protein interactions of, 389, 391, 413 Glutamate as cytoplasmic solute, 291 protein interactions with, 394 Glutamic acid in foot-and-mouth disease virus capsid, 43, 44, 46, 51 in lysozyme, 26 pK, of, 15 Glycerol as perturbing solute, 283 as preferential excluded agent, 392 in preferential hydration, 388 protein interactions with, 309, 366, 389, 392,401, 411, 421-422, 426 as protein stabilizer, 356, 359, 387 role in tubulin self-assembly, 414-415, 416 Glycine in fibrinogen, 83 as osmolyte, 425 as perturbing solute, 283 protein interactions with, 394-395 as replacement in thrombin, 93, 94, 95, 96, 102, 106 use in Ala-scanning mutagenesis, 64 Glycine betaine bovine serum albumin interaction with, 307-309, 327 as cytoplasmic solute, 291 protein interactions with, 310 Grand canonical Monte Carlo (GCMC) simulations of counterion surface concentrations, 337 of hairpin helices, 347 of nucleic acid conformation transitions, 330 of preferential interaction coefficients, 314, 315-316, 323

SUBJECT INDEX

Granulocyte colony stimulating factor (GCSF), alanine-scanning mutagenesis studies on, 70, 71 Guanidine hydrochloride effects on modulation of state distribution, 262-263 hydrogen bond formation by, 416 as lysozyme denaturant, 29 as protein denaturant, 67, 356, 359, 387, 403,406, 408-408 protein interactions with, 375-376, 387, 390-391, 395, 399,426 Guanidine sulfate, protein interactions with, 376, 377, 378, 390, 409 Guanidine thiocyanate, as protein denaturant, 376 Guanidinium ion, protein-site affinity of, 378 Guanidinium salts as denaturants, 408-409 protein interactions with, 426 Guanosine monophosphate, ribonuclease T, binding to, 7, 12

“Hairpin” helices, 346 denaturation of, 349 Haptoglobin trapping kinetics of dimer-tetramer equilibria, 202 of hemoglobin microstate species, 219 HBUILD command, in CHARMM, 28, 43 HEK cells acetylcholine receptor mutation expression in, 152-153 human muscle acetylcholine receptor expression in, 157 a-Helix effect on histidine in foot-and-mouth disease virus capsid, 50-51, 52 in W chains of foot-and-mouth disease virus capsid, 40 Helix-coil transitions, in proteins, 61 Helix dipole, acid lability of virus capsid and, 20-21 Hemes, metal substitution in, 196-197 Hemocyanins, “macromolecular switches” of, 186

461

Hemoglobin(s), see Carboxyhemoglobin; CN-met hemoglobin; Deoxyhemoglobin; Oxyhemoglobin Adair constants for, see under Adair constants “allosteric core” of, 189 allosteric properties of, 123, 185-253 binding cascade of, 192, 230, 242 chemical modification of, 202, 203, 234 conformational states of, 131 cooperativity constants of intermediates of, 209 cooperativity within dimeric half-tetramer Of, 230-231 dimer-dimer interface of, 232-237 four-site binding system for, 198 hybridization techniques applied to, 218-220 linkage relationships for, 122, 186, 282, 287 “macromolecular switches” of, 186 microstate cooperativity of, 202 microstate energetics of, 196 microstate resolution in, 210-21 1 molecular code for allostery of, 185-253 mutations of, 189, 202, 203, 204, 210, 232-237 oxygenation analogs of, 211-212 oxygen binding by cooperative, 188 curves for, 198-206 ligand roles, 282, 287 pH effects on, 60 site-specific aspects, 206-21 1 partially ligated intermediates of, 212-216 quaternary enhancement of, 202 quaternaly form of, 189 site-specific cooperativity terms for, 211-220 stereochemisny of, 196 structural probe studies on, 196 subunit structure of, 187 tertiary conformation of, 189, 195 tertiary constraint effect in, 195, 196, 233-237 tetramer binding function of, 216-218 tetramer dissociation in, 212 Henderson-Hasselbach equation, 8, 10,53 Heparin, drug alternates to, 81

462

SUBJECT INDEX

Hill coefficient, 143, 144, 167 application to hemoglobin binding sites, 205-206, 207 derivation of, 205 as descriptor of cooperativity, 201 Hirudin-thrombin reaction binding free energy of, 65 binding site in, 83, 84 Histidine in foot-and-mouth disease virus capsid, 40, 43, 46-51, 52 in hemoglobin, 190 in lysozyme, 26 pK, of, 14, 15 proton of active site of, 83 unprotonated state of, 2 Hofmeister effects on biopolymers, 292, 293, 294, 317-318, 342, 343, 375, 377,420 on equilibrium constants, 331-332 on transition temperatures, 331-332 Hofmeister ions, additivity and compensation of, 377 “Hofmeister-like” interactions, of electrolytes with protein polyampholytes, 317 Hofmeister salts effects on conformational and binding equilibria, 285 effects on protein denaturation, 295 as perturbing solutes, 283-284 thermodynamic linkage principles applied to, 286 Horovitz-Fersht approach, to site-site interaction, 78 Human growth hormone, alanine-scanning mutagenesis studies on, 70, 71 Human growth hormone receptor, binding energy in, 65 Human rhinovirus (HRV), 40 k h e e t extension in, 40 infection mechanism of, 39 Hybridization techniques, applied to hemoglobin microstate species, 218-220, 232 Hydration, of proteins, 367-368 Hydrogen bonds role in hemoglobin oxygenation, 188 role in lysozyme pH stability, 38

role in preferential exclusion, 416 role in water-biopolymer interaction, 289 Hydrogen exchange protection, in proteins, 255, 264, 273-274, 277 Hydrophobic cores, of proteins, 64 Hydrophobic effect on nonpolar surfaces, 295 of water-biopolymer interaction, 289 Hyperekplexia mutations, of glycine receptor, 141-142. 146

I “Independent binding,” in twodomain model, 306 Independent sites (IS) model, 2, 8-12 Induced-fit mechanism, for ligand gating, 122 Inositol protein interactions of, 389, 392 as protein stabilizer, 359 “Interchange,” of solvent species, 306 Intestinal fatty acid binding protein (I-FABP) alanine-scanning mutagenesis studies on, 71 binding studies on, 70, 71 Intrinsic pK.’s, of titrating site, 13-16 Iodide ion, effects on protein surface, 292 Ion channels, ligand-gated, 168 Ionic interactions, in amino acid residues, 64 Ionic strength as composition variable, 285 of salts, effects on biopolymers, 294 Iron, in hemoglobin molecule, 190 king lattice model, 76, 77 Isopiestic equilibrium, preferential binding measurement by, 371

Kansas mutant, of hemoglobin, 204 Karplus model, for hemoglobin oxygenation, 189, 191, 209, 246 Koshland-Nemethy-Filmer (KNF) model of ligand binding cooperativity, 77, 186, 188, 246

SUBJECT INDEX

Monod-Wyman-Changeux model conipared to, 209-210 K phenotype, of acetylcholine receptor, 142, 143-144

L lac repressor, DNA binding domain of, 343-344 a-Lactalbumin Gibbs energy of conformations in, 269 guanidinium hydrochloride interaction with, 408 mild denaturation of, 263 partially folded states in, 264, 265, 269 Lactate dehydrogenase, guanidinium hydrochloride interaction with, 408 &Lactoglobulin alkylurea interactions with, 405 guanidinium hydrochloride interaction with, 408 magnesium chloride interaction with, 383, 390 solvent interaction with, 392, 422 Lactose as preferentially excluded agent, 391 protein interactions of, 389 Lennard-Jones potential, van der Waals radii of, 28 Leucine in acetylcholine receptor, 171, 172 in foot-and-mouth disease virus capsid, 46 in hemoglobin, 190 Ligand binding, thermodynamic relation for, 386-387 Ligand gating, Wyman theory applied to, 122 Ligands activity coefficients for, 387 binding processes of, in biopolymers, 61-62, 114, 291, 378 conformational changes induced by, 263, 277 coupling of statistical weights to, 257-259 electrostatic coupling of, 73 modulation of state distribution by, 259-262 protein recognition by, 67-68, 72, 75, 78 residue stability constants and, 274-277

463

role in conformational equilibria, 256 site-bound, of biopolymers, 293 van der Waals coupling of, 73 Light scattering, preferential binding measurement by, 371 “Linear-chain” polyelectrolytes, thermodynamic properties of, 301 Linear free energy relations of acetylcholine receptor, 129-132 in ligand gating, 122 Linked function theory (Wyman) application to foot-and-mouth disease virus capsid, 39-53 application to hemoglobin, 122, 186, 202,247,283 application to preferential interactions, 378-381 application to protein stability, 387-409 application to site-specific analysis of mutational effects, 59-1 19 application to statistical ensembles, 256 basic principles of, 59-60, 286-287, 356, 357 electrostatic free energies and, 2 multiple ligands and allosteric effects on, 54 original articles on, 282-283, 287 osmotic stress and, 413 in protein reaction control, 409-416 solute-concentrationdependent effects in, 287 thermodynamic basis of, 282-283, 286-288 thrombin catalysis and, 83, 113-114 Linolate, binding to intestinal fatty acid binding protein, 70 Lithium chloride, 377 Long-term depression (LTD), in synaptic plasticity, 169, 170 Long-term potentiation (LTP), in synaptic plasticity, 169, 170 “Loss of function” mutations, affecting acetylcholine receptor, 151 Low-temperature electrophoresis methods, of hemoglobin microstate species, 219 L phenotype, of acetylcholine receptor, 142, 143, 144-146, 147-149, 171 L247T mutant, of acetylcholine receptor, 126, 147, 171

464

SUBJECT INDEX

Lysine in foot-and-mouth disease virus capsid, 43, 44, 45, 46, 51 in hemoglobin, 190 in lysozyme, 26 pK. of, 14 as replacement in thrombin, 92, 94, 96, 97,102 in serine proteases, 80 Lysine hydrochloride, as “chameleon” cosolvent, 416 Lysozyme absolute electrostatic stability of, 34-38, 53 amino acid interaction with, 394 anti-lysozyme antibody binding to, 277 backbone conformation of, 26, 28 Beta model of, see Beta model of lysozyme conformations of, 53-54, 266 crystal structures of, 23 denaturation of, 26, 38,404, 409 Ex72 model of, see Ex72 model of lysozyme Gibbs potential function and Gibbs energy for, 267, 268 guanidinium hydrochloride interaction with, 408, 409 linked function theory applied to, 20-39 native state structure of, 26, 27, 38 null model of, 28, 29, 31, 32 lhel model of, see lhel model of lysozyme pH stability of, 2, 8, 20, 25-39, 53 pK.’s, 2, 20, 25 relative electrostatic stability of, 31-34 solvent interactions with, 389 stability and structural perturbation link in, 67 titratable sites of, 24, 26, 29 titration curve of, 25, 29-31 21zt model of, 27 wire graph of, 27

M “Macromolecular switches,” of proteins, 186 Macroscopic membrane dialysis equilibrium, properties of, 297, 298, 299, 300

Magnesium chloride effects on biopolymers, 294 Plactoglobulin interaction with, 383, 390 in preferential hydration, 388 protein exclusion of, 377, 378 protein interactionswith, 393,401,410,426 Magnesium ion effect on protein surface, 420 effects on nucleic acid ligand binding, 291, 340 protein-site affinity of, 378 Magnesium sulfate, protein interactions with, 388, 390, 393, 401 Manganese, hemes substituted with, 21 1, 219, 223 Mannitol, protein interactions with, 392 Maxwell’s principle, 59 MC titration program, 7 Mean field approximation, cluster method combined with, 20 Membrane ion channels, “macromolecular switches” of, 186 Mengovirus, infection mechanism of, 39 Metabotropic receptors, 168 Methoxyethanol, protein interaction with, 403 Methylamines as osmolytes, 423 protein interactions with, 394-395 as protein stabilizers, 359 2-Methyl-2,4pentanediol (MPD), protein interactions with, 366, 388, 389, 393-394, 419, 421 Mice, transgenic, use in drug addition studies, 173 Microstate tetramers, of hemoglobin, 192 Model-independent site-specific formalism, 77 “Molecular choreography,” of hemoglobin analogs, 227 Molecular code of hemoglobin allostery, 185-253 deciphering of, 221-224 quaternary assignments and, 241-243 of site-specific Adair constants, 243 symmetry rule in, 193, 195 Molecular complex, dissociation constant of, 12 Molecular free energies, electrostatic contributions to, 1-57

SUBJECT INDEX

“Molecular picture,” of coulombic preferential interactions, 336 Molecular stability and assembly, ionizable group role in, 2 Monod-Wyman-Changeux (MWC) model application to acetylcholine receptor, 126, 128, 132, 171 application to hemoglobin, 188, 191, 205, 209, 246 application to hemoglobin analogs, 223 of concerted allosteric transitions, 78, 122 Koshland-Nemethy-Filmer model compared to, 209-210 “sequential” concept in, 186, 1888 “symmetry consemtion” rule of, 188 as “twostate model,” 186-187, 209 Monte Carlo (MC) simulations, see also Grand canonical Monte Carlo (GCMC) simulations of coulombic interactions, 284 of counterion activity, 311-312 of cylindrical polyions, 313-314, 315, 330 of DNA binding studies, 347, 348-349 prediction of preferential interaction coefficients by, 336 of salt effects on transition temperatures, 344 Monte Carlo titration, 19-20 in studies of foot-and-mouth disease virus, 42 Multicomponent thermodynamic theory applied to preferential exclusion, 388 applied to Wyman linked function principles, 356 Muscle, acetylcholine receptor kinetics in, 126, 132, 144, 153, 154, 157, 162, 167 Mutagenesis, Ala-scanning method, 64 Mutations absolute electrostatic free energy and, 8 of acetylcholine receptor, 123, 125, 126-127, 141-157, 171 double, 73-75 energetic cost of, 75-76 of foot-and-mouth disease virus, effects on pH stability, 52-53 of hemoglobins, 189, 202, 203, 204, 209, 210, 232-237 involving alanine, see Alanine-scanning mutagensis

465

MWC model, see Monod-WymanChangeux (MWC) model Myasthenic syndrome, acetylcholine receptor mutation in, 126, 127, 149, 151-153, 156, 172 Myoglobin, solvent interactions with, 390, 422

N Neuromuscular junctions electric impulses in, 122 myasthenic syndrome affecting, 149, 151 synaptogenesis in, 168 Neurons, acetylcholine receptors in, 162 Neurotransmitters, release of, 122 Nicotine addiction to, 172-173 pharmacology of, 137, 156-157 Nicotinic ligands, binding sites for, 126 pNitroanilide, attachment to tripeptides in thrombin specificity library, 89 Noncovalent bonds, role in hemoglobin oxygenation, 188-189 Nonelectrolytes, binding by, linked function theory applied to, 287-288 N-terminal ammonium group, pK. of, 13, 14 N-terminus in foot-and-mouth disease virus capsid, 43 in lysozyme, 26, 27 Nuclear magnetic resonance (NMR) spectroscopy of CN-met hemoglobin, 26, 221 of DNA binding domain, 343 of hydrogen exchange protection, 255 of lysozyme in solution, 26 of partially folded protein conformations, 264 of protein hydration, 371, 373 of urea-bovine serum albumin interaction, 310 use in conformational ensemble studies, 271, 273 use in structural mapping of energetics, 63 Nucleic acids conformational transitions of, 295 denaturation of, 285, 295,344 electrolyte ion interactions with, 311-312 oligocation binding by, 285

466

SUBJECT INDEX

oligocationic ligand binding to, 332-344 order-disorder transitions of, 295 protein binding to, 332-344, 350 salt interactions with, 284 Null model of lysozyme, 28 of unfolded protein state, 11

0 OIBFS serotype of foot-and-mouth disease virus, 39, 40, 48 crystal structure of, 42 helix backbone and side chains in, 50-51 mutation effects on, 49, 52-53 pH stability of, 45, 51 Oligocations binding of, 294, 312, 332-344 nucleic acid binding of, 285, 343 Oligoelectrolytes, effects on nucleic acid binding, 292 Oligo “end effect,” 316 Oligoions, as polyampholytes, 31 2 Oligolysines, binding to polyanionic DNA, 335 Oligonucleotides double-helical, transition temperatures Of, 345-346 solute effects on, 293 Oligopeptides, solute effects on, 293 lfod serotype of foot-and-mouth disease virus, solvation and binding free energy of, 43, 44 1he1 model of lysozyme absolute electrostatic stability of, 34, 37 electrostatic free energy of, 35, 36 pK. of, 28 titration curve of, 29 Order-disorder transitions, of nucleic acids, 295 Osmolytes, 284, 412 examples of, 359 fish storage of, 378 natural occurrence of, 388 properties of, 423-425 protein exclusion of, 309 Osmoprotectants, effectiveness of, 291 Osmotic effects of solutes on biopolymers, 292, 294, 327

thermodynamic linkage principles applied to, 286 of water, 291 “Osmotic stress,” 411-415 twodomain analogs of, 327 Ovalbumin, guanidinium hydrochloride interaction with, 408 Oxyanion hole, in serine proteases, 79 Oxyhemoglobin binding cascade of, 192, 230 intermediates of, molecular code partitition function for, 243-246 microstate cooperativity components of, 197-198 site-specific binding parameters for, 229-231 Oxyhemoglobin analogs consensus partition function, 222-224 cooperative free energies, 221-226 microstate distributions of, 222-226

P Partition function, 258 derivation of, 3 thermodynamic properties of titration system from, 5 Pauling model, for ligand-induced conformation changes, 186 Peptides, binding to proteins, perturbations from, 78-79 Perturbing solutes concentrationdependent effects of, 286-295 definition of, 283 effects on free energy change, 324-326 examples of, 283-284 Perutz model, for hemoglobin oxygenation, 188, 191, 246 PH effects on foot-and-mouth disease capsid, 39-41 effects on hemoglobin oxygen binding, 287 electrostatic free energy dependence on, 5, 7 system properties dependent on, 13 theory of stability of, 53 Phage display, peptide method based on, 81

SUBJECT INDEX

Phenylalanine in hemoglobin, 190 in thrombin, 94, 95, 102 in VP chains of foot-and-mouth disease virus subtypes, 40 Phosphate charges, for DNA cylindrical models, 348-349 N(Phosphonacety1)-L-aspartate (PALA), use in aspartate transcarbamylase characterization, 21 1 Phosphorylation, role in long-term potentiation and depression, 170 Picornavirus, foot-and-mouth disease virus as, 39 pK’s effective, 13-16 of foot-and-mouth disease virus capsid, 13-16 intrinsic, 13-16 of lysozyme, 2, 20, 25, 28 of poliovirus, 52 of protein titratable sites, 2, 13-16 standard, 13-16 pK,’s, pH dependence of, 12 Point mutations of acetylcholine receptor, 123 of OIBFS serotype of foot-and-mouth disease virus, 49 Poisson-Boltzmann (PB) analytic electrolyte theory, 26, 333 application to nucleic acid-oligocation interactions, 284, 290, 312 application to nucleic acid-salt interactions, 284, 290, 312 cylindrical cell model and, 313, 314, 330 prediction of equilibrium constant by, 293-294 prediction of power-law functional form of salt concentration, 334 Poisson-Boltzmann (PB) equation, 4, 311, 337, 338, 345 f i n i t a e r e n c e program (UHBD) for, 19 solution by finitedifference algorithm, 18, 24 Poliovirus, 39, 40 acid stability of, 52 P-sheet extension in, 40 Polyacrylamide columns, salt binding to, 388 Polyamines, DNA binding of, 335

467

Polyamine salts, effects on nucleic acid ligand binding, 291 Polyampholytes, oligoions and proteins as, 312 Polyelectrolyte effect origin of, 311-312, 336, 338 of salts, 295 Polyelectrolytes binding-polynomial analysis and, 287-288 effects on cylindrical polyanion equilibria, 330-331 salts as, 281-353 thermodynamic linkage principles applied to, 286, 349 Polyethylene glycols (PEGS) as allosteric regulators, 359 as “chameleon” cosolvent, 416 protein interactions of, 388, 389, 393-394, 411, 413,418,419 Polyols as osmolytes, 423 as perturbing solutes, 283 in preferential hydration, 388 protein interactions with, 392-393 as protein stabilizers, 359 Polypeptides, of thrombin, 83 Polystyrene, benzene solution of, 359 Postsynaptic membrane, ionotropic receptors in, 122 Potassium aspartate, protein interactions with, 394-395 Potassium cyanide, effects on CN-met hemoglobin, 221 Potassium ion, effects on nucleic acids, 290, 29 1 Preferential accumulation, twodomain analysis of, 309-310 Preferential binding definition and description of, 359, 370-373 measurement of, 371 in protein-cosolvent interaction, 363-370, 380, 383 in protein destabilization, 403 Preferential binding parameter, 361-362 Preferential exclusion families of agents for, 391-399 in protein-cosolvent interaction, 363-370, 383 shift to preferential binding, 396

468

SUBJECT INDEX

sources of, 416-423 thermodynamics of, 399-403 twodomain analysis of, 307-309 Preferential hydration cosolvent classification by, 388 definition of, 359 derivation of, 361, 365 Hofmeister progression of, 375 linkage control of, 387-391 Preferential interaction coefficients charged solutes, 300-303 derivation of, 296 of DNA, 345 for electrolytes with weakly charged biopolymers, 317-318 of electroneutral components, 333 as measures of thermodynamic effects, 295-303 for nucleic acids and oligoelectrolytes, 312-31 7 representation of, 288 sign and magnitude of, 290 threecomponent, 319-326 twodomain model of, 290, 297, 298 for uncharged solutes, 299-300 use in analysis of perturbing solute effects, 286 Preferential interaction parameter, 360-362 Preferential interactions, 360-377 of biopolymers, 291 definitions of, 360-362 description of, 284, 357-360 of electrolytes with charged biopolymers, 311-318 Hofmeister, 341 of nonelectrolytes with uncharged biopolymers, 303-310 twc-domain model applied to, 303-310, 34 1 Wyman linkages in, 378-381 “Prepulse” concentrations, of agonist, in acetylcholine receptor studies, 139-141 “Probability density function” (pdf), for acetylcholine receptor, 159 Probability distribution of states, in proteins, 278 Proline as cytoplasmic solute, 291 in lysozyme, 31 as perturbing solute, 283

in thrombin, 93, 94, 96, 102, 106 use in Ala-scanning mutagenesis, 64 Propylene glycol, protein interactions of, 389, 393 Protein C activated, structure and specificity of, 80-81 thrombin cleavage site in, 82-83 thrombomodulin-assisted activation of, 82 Protein data bank, native lysozyme structures from, 28 Protein S, role in blood coagulation, 82 Proteins binding to nucleic acid polyanions, 332-344 binding to polyanionic DNA, 340-344 conformational changes in, 22 conformational equilibria in, 255-279 conformational flexibility of, 21 coupled folding of, 342 destabilization of, 403-409 dielectric constant of, 21-25 dissolution of, surface interactions, 358 double-mutant cycles of, 73-75, 76 helix-coil transitions in, 61 hydration of, 367-368 hydrogen exchange protection, 255 hydrophobic cores of, 64 ionization properties of, 66 ligand-binding processes in, 61-62 ligand interactions in, 59-60 ligand recognition of, 67-68, 72, 75, 78 “macromolecular switches,” 186 mixedsolvent dissolution of, 372 mutations effects in, 73-79 mutations in, site-specific analysis, 59-119 nucleic acid binding to, 332-344, 350 partially folded conformations in, 264 polar interior of, 22 as polyampholytes, 312 protonation of bindable sites in, 1 reversible thermal denaturation of, 67 self-assembly of subunits of, 378 stability of, see Protein stability structure-function correlations in, 64 unfolded-state model of, 11, 67 unfolded states and unfolding of, 267-269,422-423

469

SUBJECT INDEX

Protein stability, 64-65, 72 interaction additivity role in, 378 linkage control of, 387-409 salt effects on, 420 by weakly interacting cosolvents, 355-432 Protein titration as example of multiple ligand binding, 1 multiple conformation role in, 54 theory of, 53 Prothrombinase complex, role in blood coagulation, 82 Protonation, equilibria of, 53 Protonation state electrostatic free energy of, 16-17 of a protein, 2 Protons binding sites for, 1 bound to titrating system, 6 Purine repressor, DNA binding domain of, 343 Putrescine DNA binding of, 335 effects on nucleic acid binding, 290, 291

Q Quaternary conformations of hemoglobin, structure-sensitive probes for, 231-241 of proteins, 186 Quaternary enhancement, of assembled hemoglobin molecules, 204-205 Quaternary transitions, in hemoglobin analogs, 222-223, 224 QX222, as channel blocker, 141

Recognition sites, multiple, of proteins, 80 Recombinant DNA technology, use to study energetics and regulatory interactions, 60, 63, 65-66 “Reduced site” approximation, Monte Carlo titration compared to, 19 Reference cycle application to linked-function principles, 61, 66, 74 purpose of, 62

Ribonuclease guanidinium hydrochloride interaction with, 408, 409 solvent interactions with,390, 400, 401 urea denaturation of, 407-408 Ribonuclease A guanidine sulfate as stabilizer for, 376, 377 guanidinium hydrochloride interaction with, 408, 409 solvent interactions with, 391, 392, 395, 398, 399, 402, 419-420, 422 urea denaturation of, 373, 378,404-405 Ribonuclease T, guanosine monophosphate binding to, 7, 12 solvent interactions with, 390 urea binding of, 378, 379 RNA, of foot-and-mouth disease virus, 39 RNA polymerase, binding of, 340 R quaternary form of hernoglobin, 188, 189 Ruthenium carbonylporphyrin hemoglogin, 214

S Salakta thrombin mutant, 86 Salt bridges, role in hemoglobin oxygenation, 188, 189, 215 Salting-out agents, for proteins, 376, 377, 378, 388 Salts effect on DNA denaturation, 295 effects on protein and nucleic acid equilibria, 281-353 Hofmeister effects of, 281-353 osmotic effects of, 281-353 polyelectrolyte effects of, 285 protein interactions with, 393 Sarcosine, as protein stabilizer, 395 Scatchard notation, for preferential interactions, 360, 361, 373 Schellman exchange analysis, 374 Schizophrenia, acetylcholine receptor mutation in, 172 Scissile bond, in serine proteases, 80 Sedimentation equilibrium, preferential binding measurement by, 371 Sew-assembly, thermodynamic relation for, 386

470

SUBJECT INDEX

Sequential model(s) of acetylcholine receptor, 132, 133 of ligand gating, 122, 186 Serine in chymotrypsin, 80 in fibrinogen, 83 in lysozyme, 26 pK. of, 13, 15 Serine proteases, see also Thrombin catalytic triad of, 79 conformation of, 79 specificity of, 80, 81-82 substrate recognition by, 79-82 Sidechain entropy, of protein partially folded state, 267 Sidechain reorientations, in proteins, 22 Signal transduction cascades, “macromolecular switches” of, 186 Silica gels, hemoglobin binding studies in, 231 Sitedirected isotope labeling, of protein amino acid residues, 64 Site-site interaction, mechanism of, 77 Site-specific mutations in proteins, 59-1 19 alanine substitutions in, 64 Sitespecific structural perturbations, 63-66 energetics and, 66-69 Sliding threshold model, for visual cortical development, 169 Smoking, nicotine addiction in, 172-173 Sodium bromide, 377, 426 Sodium chloride effects on biopolymers, 294 in preferential hydration, 388 Sodium glutamate, protein interactions with, 394-395 Sodium ion protease binding of, 79 as thrombin ligand, 83, 84-86, 87-88, 97,98-100 Sodium sulfate in preferential hydration, 388 protein interactions with, 376, 390, 426 Sodium thiocyanate, as protein protectant, 376, 424, 426 Solubility, thermodynamic relation for, 386-387 Solutes, perturbing, see Perturbing solutes

Solvation free energies calculation of, 9 of small molecules, 21 Sorbitol protein interactions with, 392, 395, 397, 398, 400, 401, 402 as protein stabilizer, 359 Specificity sites, of enzymes, 80 Spermidine, DNA binding of, 335 Spermine, DNA binding of, 335 Stability constants, of protein residues, 273-277 Stabilization, thermodynamic relation for, 386 Staphylococcal nuclease alanine-scanning rnutagenesis studies on, 71 Gibbs energy of conformations in, 269-270 mutation effects on, 67 partially folded states in, 264, 265-266 stability of, 70 Startle disease, acetylcholine receptor mutation in, 126-127 Statistical thermodynamic formalism applied to conformational and binding equilibria, 255-279 function-specific probabilities defined by, 277-278 Steric exclusion, role in preferential exclusion, 417-418 Steroids, effects on acetylcholine receptors, 166 Stopped-flow kinetics of dimer-tetramer equilibria, 202 of hemoglobin microstate species, 219 Strand dissociation, in biopolymers, 294 Structural mapping, of energetics, 63-73 Sucrose amino acid side chain binding of, 413-414 a-chymotrypsin interaction with, 363 effects on proteins, 365, 387, 424, 426 as osmolyte, 425 as preferentially excluded agent, 391 as protein stabilizer, 356, 387 Sugars as osmolytes, 423 as perturbing solutes, 283 preferential hydration by, 388

SUBJECT INDEX

as preferentially excluded agents,

391-392 as protein stabilizers, 359 Sulfate ion, protein exclusion of, 378 Sulfhydryl groups, in hemoglobin cysteines,

238 “Superosmolytes,” 425 Surface free energy, perturbation of,

418-419 Surface tension increment, role in protein solubility, 420 “Symmetqwonserved” transitions, in conformations, 187-188 Symmetq rule, application to hemoglobin binding, 191-196,220 Synaptic plasticity, acetylcholine receptor activity and, 168-171

T Tanford-Kirkwood model of protein titration, 22,24,30 modification of, 25 “Territorially bound” counterions, 312 “Tertiary Bohr effect,” in hemoglobin tetramers, 241 Tertiary conformations, of proteins, 186 Tertiary constraint effect, in hemoglobin conformation changes, 195,196,

233-237,239,242 “Tertiary constraint energy,” in hemoglobin oxygen binding, 215 Tertiary transitions, in hemoglobin analogs,

222-224 Tetramer Adair function, of hemoglobin,

202-203 Tetrameric molecules, R quaternary form,

187,188 Tetramers, Adair equation for, 198 Thermodynamic box, for cosolvent modulation equilibria, 386,398 “Thermodynamic distances,” between hemoglobin microstate tetramers,

213-214 Thermodynamic effects, in solute-biopolymer interactions,

295-303 “Thermodynamic extent of association,” definition of, 333-334

471

Thermodynamic linkage, in CN-met hemoglobin dimer-tetramer assembly,

228 Thermodynamics, of protein hydration,

367-368 “Thermodynamic transformation,” in hemoglobin analogs, 243-244 Three-component preferential interaction coefficients, 319-326 Threonine in lysozyme, 26 pK. of, 13,15 Thrombin Ala-scanning mutagenesis, 65 allostenc mechanism for high-order coupling of, 103-113,114 anticoagulant derivatives of, 65 coupling in perturbations of, 94,95-96 inhibitors affecting active site of, 87 mutants affecting, 86 natural substrates for, 82 perturbation at Pl-P3 sites of, 91-96,

.

106-113 polypeptide chains of, 83,84 possible active-site inhibitors of, 81 procoagulant-anticoagulant switch of, 83 site-specificprobes for, 87-91 slow and fast forms of, 83,88,90,91,

92-93,94,96-102, 104-105,109, 112 sodium ion as ligand of,83 specificity of, sitespecific studies, 79-87 structure and function of, 81,82-87 substrate library for, 89,90,114 Thrombin-hirudin reaction, Ala-scanning mutagenesis of, 65 Thrombin receptors 1 and 3,thrombin cleavage sites in, 82 Thrombomodulin binding to trypsin and chymotrypsin, 83 wild-type thrombin energetics and, 114 Tissue factor, binding to coagulation factor MIa, 70, 71 Titrating sites, numerous, 53 Titration, calculation of, 5-7 Titration curve definition of, 6 of lysozyme, 25,29-31 T+edo, acetylcholine receptor of, 124,125,

126,146

472

SUBJECT INDEX

T quaternary form of hemoglobin, 188 cooperative free energy in, 236-237 intradimeric cooperativity within, 189- 190 transition to R quaternary form, 188, 189, 191, 196, 201, 212, 221, 242, 247 Transfer free energy changes in, 381 derivation of, 360, 370 dialysis equilibrium binding and, 362-363 equilibrium constants and, 415-416 Transition temperatures biopolymer conformation effects on, 328-329 Hofmeister salt effects on, 331-332 salt concentration effects on, 344-348 solute effects on, 292-295 threecomponent preferential interaction coefficients for, 319-326 twodomain predictions of, 326-329 Tre halose as cytoplasmic solute, 291 protein interactions with, 366, 391, 395, 397, 398, 399, 400, 401, 419, 421 protein repulsion of,366 Trimethylamine-Noxide (TMAO) as fish osmolyte, 378 protein interactions of, 390, 395, 419, 422-423, 426 urea compensation with, 378, 379 Trypsin calcium-binding loop of, 83 specificity of, 79, 80 structure of, 86 Trypsin inhibitor factor Xa binding of, 11-12 guanidinium hydrochloride interaction with, 408 Tryptophan in acetylcholine receptor, 143 in hemoglobin, 237 Tubulin guanidinium hydrochloride interaction with, 408 self-assemblyof, 414-415, 416 solvent interactions with, 391, 392, 394, 410-41 1 21zt model of lysozyme, 27, 28 absolute electrostatic stability of, 34, 37

electrostatic free energy for, 35, 36 pHdependent stability of, 31 py, of, 28 titration curve of, 29 Twodomain model in biopolymer surface studies, 329 in preferential accumulation analysis, 309-310 in preferential exclusion analysis, 307-309, 317-318, 326-329 of preferential interaction coefficients, 290, 297, 303-307, 341 schematic of, 298 for weakly charged proteins, 349 Twmtate model, of protein sites, 2, 220, 255 Tyrosine in acetylcholine receptor, 143 in foot-and-mouth disease virus capsid, 43,45 in hemoglobin, 237 in lysozyme, 26 pKo of, 15 in VP chains of foot-and-mouth disease virus subtypes, 40

U program, as finitedifference Poisson-Boltzmann program, 19, 23 Ultraviolet resonance Raman (UVRR) spectroscopy, of hemoglobin ligation intermediates, 237-238 Urea betaine protection against, 423 bovine serum albumin interaction with, 307-309 effects on modulation of state distribution, 262 effects on proteins, 310, 365, 377, 378, 387, 426 hydrogen bond formation by, 416 as perturbing solute, 283 as protein denaturant, 67, 356, 359, 373, 387,403-409 UHBD

v “Valency exchange,” in CN-met hemoglobin, 222

473

SUBJECT INDEX

Valine, as replacement in thrombin, 94, 95, 102 Van der Waals coupling, of ligands, 73 Van der Waals radii, of Lennard-Jones potential, 28 van? Hoff law, 424 Vapor pressure osmornetry (WO) in studies of preferential exclusion, 308, 309 in studies of preferential interactions, 310, 373 VGK tripeptide, thrombin specificity for, 89, 102 Visual cortical development, sliding threshold model for, 169 W chains, of foot-and-mouth disease virus capsid, 39, 40, 41, 46, 48, 49, 50, 51-52

Warfarin, drug alternates to, 81 Water biopolymer interactions in, 288, 289 in cosolvent reactions, 383, 384 role in polyelectrolyte binding, 285 role in preferential interactions, 360, 362, 370-373 in sodium-binding site of thrombin, 84-84 Water of hydration, of protein surface, 291, 292

“Water structure,” water hydrogen bonds in, 421 Weakly interacting cosolvents, role in protein stability, 355-432 Wire graph, of lysozyme, 27 Wyman linkage relation, 377, 380, 382, 384, 395, 400,407,417 in cooperative free energy approach, 201 Wyman linked function theory, see Linked function theory (Wyman) Wyman slope, 381, 382, 384,427

X X-ray crystallography of lysozyme in solution, 26 of partially folded protein conformations, 264 use in structural mapping of energetics, 63 X-ray scattering, preferential binding measurement by, 371 Xylitol, protein interactions with, 392

z “Zero interaction” model, of unfolded protein state, 11 Zinc, heme substitution with, 211, 243, 245-246 Zinc protoporphyrin IX, structure of, 246

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