COMPUTATIONAL METHODS FOR PROTEIN FOLDING A SPECIAL VOLUME OF ADVANCES IN CHEMICAL PHYSICS VOLUME 120 Computational Methods for Protein Folding: Advances in Chemical Physics, Volume 120. Edited by Richard A. Friesner. Series Editors: I. Prigogine and Stuart A. Rice. Copyright # 2002 John Wiley & Sons, Inc. ISBNs: 0-471-20955-4 (Hardback); 0-471-22442-1 (Electronic) EDITORIAL BOARD Bruce J. Berne, Department of Chemistry, Columbia University, New York, New York, U.S.A. Kurt Binder, Institut fu ¨ r Physik, Johannes Gutenberg-Universita ¨ t Mainz, Mainz, Germany A. Welford Castleman, Jr., Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, U.S.A. David Chandler, Department of Chemistry, University of California, Berkeley, California, U.S.A. M. S. Child, Department of Theoretical Chemistry, University of Oxford, Oxford, U.K. William T. Coffey, Department of Microelectronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland F. Fleming Crim, Department of Chemistry, University of Wisconsin, Madison, Wisconsin, U.S.A. Ernest R. Davidson, Department of Chemistry, Indiana University, Bloomington, Indiana, U.S.A. Graham R. Fleming, Department of Chemistry, The University of California, Berkeley, California, U.S.A. Karl F. Freed, The James Franck Institute, The University of Chicago, Chicago, Illinois, U.S.A. Pierre Gaspard, Center for Nonlinear Phenomena and Complex Systems, Universite ´ Libre de Bruxelles, Brussels, Belgium Eric J. Heller, Department of Chemistry, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A. Robin M. Hochstrasser, Department of Chemistry, The University of Pennsylva- nia, Philadelphia, Pennsylvania, U.S.A. R. Kosloff, The Fritz Haber Research Center for Molecular Dynamics and Depart- ment of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Rudolph A. Marcus, Department of Chemistry, California Institute of Tech- nology, Pasadena, California, U.S.A. G. Nicolis, Center for Nonlinear Phenomena and Complex Systems, Universite ´ Libre de Bruxelles, Brussels, Belgium Thomas P. Russell, Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts Donald G. Truhlar, Department of Chemistry, University of Minnesota, Minneapolis, Minnesota, U.S.A. John D. Weeks, Institute for Physical Science and Technology and Department of Chemistry, University of Maryland, College Park, Maryland, U.S.A. Peter G. Wolynes, Department of Chemistry, University of California, San Diego, California, U.S.A. COMPUTATIONAL METHODS FOR PROTEIN FOLDING ADVANCES IN CHEMICAL PHYSICS VOLUME 120 Edited by RICHARD A. FRIESNER Columbia University, New York, NY Series Editors I. PRIGOGINE Center for Studies in Statistical Mechanics and Complex Systems The University of Texas Austin, Texas and International Solvay Institutes Universite Libre de Bruxelles Brussels, Belgium and STUART A. RICE Department of Chemistry and The James Franck Institute The University of Chicago Chicago, Illinois AN INTERSCIENCE PUBLICATION A JOHN WILEY & SONS, INC. PUBLICATION Designations used by companies to distinguish their products are often claimed as trademarks. In all instances where John Wiley & Sons, Inc., is aware of a claim, the product names appear in initial capital or all capital letters. Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration. Copyright # 2002 by John Wiley & Sons, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic or mechanical, including uploading, downloading, printing, decompiling, recording or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the Publisher. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212) 850-6011, fax (212) 850-6008, E-Mail: PERMREQ @ WILEY.COM. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional person should be sought. ISBN 0-471-22442-1 This title is also available in print as ISBN 0-471-20955-4. For more information about Wiley products, visit our web site at www.Wiley.com. CONTRIBUTORS TO VOLUME 120 Benoit Cromp,De ´ partement de Chimie, Universite ´ de Montre ´ al, Montre ´ al, Que ´ bec, Canada; Centre de Recherche en Calcul Applique ´ , Montre ´ al, Que ´ bec, Canada; and Protein Engineering Network of Centers of Excellence, Edmonton, Alberta, Canada R. I. Dima, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, U.S.A. Aaron R. Dinner, New Chemistry Laboratory, University of Oxford, Oxford, U.K. Ron Elber, Department of Computer Science, Cornell University, Ithaca, NY, U.S.A. Volker A. Eyrich, Department of Chemistry and Center for Biomolecular Simulation, Columbia University, New York, NY, U.S.A. Anthony K. Felts, Department of Chemistry, Rutgers University, Wright- Rieman Laboratories, Piscataway, NJ, U.S.A. Christodoulos A. Floudas, Department of Chemical Engineering, Princeton University, Princeton, NJ, U.S.A. Richard A. Friesner, Department of Chemistry and Center for Biomolecular Simulation, Columbia University, New York, NY, U.S.A. Emilio Gallicchio, Department of Chemistry, Rutgers University, Wright- Rieman Laboratories, Piscataway, NJ, U.S.A. John Gunn, Schro ¨ dinger, Inc., New York, NY, U.S.A.; Centre de Recherche en Calcul Applique ´ , Montre ´ al, Que ´ bec, Canada; and Protein Engineering Network of Centers of Excellence, Edmonton, Alberta, Canada Pierre-Jean L’Heureux,De ´ partement de Chimie, Universite ´ de Montre ´ al, Montre ´ al, Que ´ bec, Canada; Centre de Recherche en Calcul Applique ´ , Montre ´ al, Que ´ bec, Canada; and Protein Engineering Network of Centers of Excellence, Edmonton, Alberta, Canada Martin Karplus, New Chemistry Laboratory University of Oxford, Oxford, U.K.; Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, U.S.A.; and Laboratoire de Chimie Biophysique, Institut le Bel, Universite ´ Louis Pasteur, Strasbourg, France v John L. Klepeis, Department of Chemical Engineering, Princeton University, Princeton, NJ, U.S.A. D. K. Klimov, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, U.S.A. Andrzej Kolinski, Laboratory of Computational Genomics, Danforth Plant Science Center, Creve Coeur, MO, U.S.A.; and Department of Chemistry, University of Warsaw, Warsaw, Poland Ronald M. Levy, Department of Chemistry, Rutgers University, Wright-Rieman Laboratories, Piscataway, NJ, U.S.A. E ´ ric Martineau,De ´ partement de Chimie, Universite ´ de Montre ´ al, Montre ´ al, Que ´ bec, Canada; Centre de Recherche en Calcul Applique ´ , Montre ´ al, Que ´ bec, Canada; and Protein Engineering Network of Centers of Excellence, Edmonton, Alberta, Canada Jaroslaw Meller, Department of Computer Science, Cornell University, Ithaca, NY, U.S.A.; and Department of Computer Methods, Nicholas Copernicus University, Torun, Poland Heather D. Schafroth, Department of Chemical Engineering, Princeton University, Princeton, NJ, U.S.A. Jeffrey Skolnick, Laboratory of Computational Genomics, Danforth Plant Science Center, Creve Coeur, MO, U.S.A. Sung-Sau So, Hoffman-La Roche, Inc., Discovery Chemistry, Nutley, NJ, U.S.A. Daron M. Standley, Schro ¨ dinger Inc., New York, NY, U.S.A. D. Thirumalai, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, U.S.A. Anders Wallqvist, Department of Chemistry, Rutgers University, Wright- Rieman Laboratories, Piscataway, NJ, U.S.A. Karl M.Westerberg, Department of Chemical Engineering, Princton University, Princeton, NJ, U.S.A. vi contributors to volume 120 INTRODUCTION Few of us can any longer keep up with the flood of scientific literature, even in specialized subfields. Any attempt to do more and be broadly educated with respect to a large domain of science has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists. This series, Advances in Chemical Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field. I. Prigogine Stuart A. Rice vii PREFACE The first attempts to model proteins on the computer began almost 30 years ago. Over the past three decades, our understanding of protein structure and dynamics has dramatically increased as a result of rapid advances in both theory and experiment. The Protein Data Bank (PDB) now contains more than 10,000 high- resolution protein structures. The human genome project and related efforts have generated an order of magnitude more protein sequences, for which we do not yet know the structure. Spectroscopic measurement techniques continue to increase in resolution and sensitivity, allowing a wealth of information to be obtained with regard to the kinetics of protein folding and unfolding, comple- menting the detailed structural picture of the folded state. In parallel to these efforts, algorithms, software, and computational hardware have progressed to the point where both structural and kinetic problems may be studied with a fair degree of realism. Despite these advances, many major challenges remain in understanding protein folding at both a conceptual and practical level. There is still significant debate about the role of various underlying physical forces in stabilizing a unique native structure. Efforts to translate physical principles into practical protein structure prediction algorithms are still at an early stage; most successful prediction algorithms employ knowledge-based approaches that rely on examples of existing protein structures in the PDB, as well as on techniques of computer science and statistics. Theoretical modeling of the dynamics of protein folding faces additional difficulties; there is a much smaller body of experimental data, which is typically at relatively low resolution; carrying out computations over long time scales requires either very large amounts of computer time or the use of highly approximate models; and the use of statistical methods to analyze the data is still in its infancy. The importance of the protein folding problem—underscored by the recent completion of the human genome sequence—has led to an explosion of theoretical work in areas of both protein structure prediction and kinetic modeling. An exceptionally wide variety of computational models and techniques are being applied to the problem, due in part to the participation of scientists from so many different disciplines: chemistry, physics, molecular biology, computer science, and statistics, to name a few. This has made the field very exciting for those of us working in it, but it also poses a challenge; how can the key issues in state of the art research be communicated to different audiences, given the interdisciplinary nature of the task at hand and the methods being brought to bear on it? ix The objective of this volume of Advances in Chemical Physics is to discuss recent advances in the computational modeling of protein folding for an audience of physicists, chemists, and chemical physicists. Many of the contributors to this volume have their roots in chemical physics but have committed a significant fraction of their resources to studying biological systems. The chapters thus address the target audience but incorporate approaches from other areas because they are relevant to the methods that the various authors have developed in their laboratories. While some of the chapters contain review sections, the principal focus is on the authors’ own research and recent results. When modeling protein folding the key questions are (a) the nature of the physical model to be used and (b) the questions that the calculations are aimed at answering. It is impossible in a single volume to cover all of the different approaches that are currently being used in research on protein folding. Never- theless, a reasonably broad spectrum of computational methods is represented here, as is briefly described below. The volume is organized so as to group together contributions in which similar approaches are adopted. The simplest models of proteins involve representations of the amino acids as beads on a chain (typically taken to be hydrophobic or hydrophilic, depending upon the identity of the amino acid) embedded in a lattice. Primitive models of this type employ a simple lattice such as a cubic lattice, and they use a single center to represent each amino acid. These models are very fast computation- ally, but lack a level of detail (both structurally and in their potential energy function) to permit prediction of protein structure from the amino acid sequence. On the other hand, they can be extremely valuable in providing conceptual insight into the general thermodynamic and kinetic issues as to why and how proteins fold into a unique native state; they can also be profitably used to model folding kinetics, as well as to make testable predictions for such kinetics that can be compared with experimental data. The contributions of Thirumulai et al. and Dinner et al. discuss models of this type, presenting both conceptual insights into the basis of protein folding and results for modeling of specific protein folding events. Reduced models of proteins (i.e., models not containing complete atomic detail) can be used to make structural predictions, either by allowing assessment of the fitness of a protein structure already in the PDB as a model for an unknown sequence (‘‘threading’’) or by carrying out Monte Carlo simulations using the model and a suitable potential energy function. The contribution by Meller and Elber describes a classical threading approach in which the amino acid sequence is ‘‘threaded’’ in an optimal fashion onto a set of candidate template structures using dynamic programming techniques, and the suitability of the template is evaluated by a potential energy function. These authors have worked out new methods for optimizing such functions, which are discussed in detail in their chapter. x preface If a reduced (or other) model is used to predict protein structure via simulation, without direct reference to structures in the PDB, this is referred to as ‘‘ab initio protein’’ structure prediction. Potential energy functions for ab initio prediction can be derived either from physical chemical principles or from a ‘‘knowledge-based’’ approach based on statistics from the PDB (e.g., the probability of observing a residue–residue distance for a given pair of amino acids). For reduced models, the use of knowledge-based potential of some sort is mandated. The contributions of Eyrich et al., Skolnick and Kolinsiki, and L’Heureux et al. derive originally from an ab initio approach using reduced models. However, all of these groups have in the past several years increasingly incorporated empirical elements from threading and other such approaches, so that what is described in these contributions is more of an attempt to integrate reduced model simulations with additional information and techniques that can improve practical structure prediction results. Several of these research groups have entered the CASP (Critical Assessment of Protein Structure Prediction) blind test experiments, which allow a comparative evaluation of the prediction accuracy of the different methods employed by the participants; results from the most recent such experiment, CASP4 (not reported in this volume because the results were available subsequent to submission of most of the chapters), were encouraging with regard to the ability of these hybrid methods to provide improvement in many cases over methods not incorporating simulations. The use of models employing an atomic level of detail (e.g. a molecular mechanics potential function) in addressing the protein folding problem presents significant difficulties for two reasons: (1) A large expenditure of computation time is required to evaluate the model energy at each configuration; (2) the quality of the potential energy functions and solvation model are critical in being able to accurate compare the stability of alternative structures. The contribution by Klepeis et al. discusses both algorithms designed to reduce the required computational effort by sampling phase space more efficiently and a wide variety of applications of atomic level models using these more efficient sampling techniques. The contribution from Wallqvist et al. is more narrowly focused on a single problem: the use of detailed atomic potential functions in conjunction with a continuum solvation model to distinguish native and ‘‘native-like’’ protein structures from ‘‘decoys’’—alternative structures gener- ated by various means and intended to challenge the model’s accuracy. Both of these contributions demonstrate that considerable progress is being made in the application of atomic level models with regard to improving both accuracy and efficiency. In the end, a thorough description of all aspects of protein folding will require the use of the full range of models and methods discussed in this volume. In the simplest hierarchical picture, one can imagine using inexpensive reduced models to generate low-resolution structures that can then be refined preface xi [...]... database of 33 proteins described in Section IV.B [15] and demonstrated that the stability contributes significantly to determining folding rates for a given contact order Moreover, for 14 slow -folding proteins with high contact orders (mixed-a/b and b-sheet proteins), the free energy of unfolding can be used by itself to predict folding rates By contrast, the folding rates of a-helical proteins show... experimentally measured folding kinetics of proteins were hindered by the fact that complex multiphasic behavior was exhibited by most of the proteins for which data were available (e.g., barnase and lysozyme) In recent years, an increasing number of proteins that lack statistical analysis of protein folding kinetics 3 significantly populated folding intermediates and thus exhibit two-state folding kinetics... native structure) Computational Methods for Protein Folding: Advances in Chemical Physics, Volume 120 Edited by Richard A Friesner Series Editors: I Prigogine and Stuart A Rice Copyright # 2002 John Wiley & Sons, Inc ISBNs: 0-471-20955-4 (Hardback); 0-471-22442-1 (Electronic) STATISTICAL ANALYSIS OF PROTEIN FOLDING KINETICS AARON R DINNER New Chemistry Laboratory, University of Oxford, Oxford, U.K SUNG-SAU... the Observed Correlations 1 2 aaron r dinner et al V Unfolding Rates of Proteins VI Homologous Proteins VII Relating Protein and Lattice Model Studies VIII Conclusions Acknowledgments References I INTRODUCTION Experimental and theoretical studies have led to the emergence of a unified general mechanism for protein folding that serves as a framework for the design and interpretation of research in this... sequences The utility of the statistical approach for obtaining a better understanding of the folding rates of proteins is described in the following section statistical analysis of protein folding kinetics IV 9 FOLDING RATES OF PROTEINS In this section we describe statistical analyses of measured rates of protein folding Earlier studies are reviewed and an analysis of currently available experimental... kinetics of particular proteins at the level of individual residues, for which protein engineering [4] and nuclear magnetic resonance (NMR) [5] experiments are very useful, complementary information about the roles played by the sequence and the structure can also be obtained by a statistical analysis of the folding rates of a series of proteins Statistical methods have been applied for many years in attempts... evidence for the physical basis of the model; that is, it provides an ‘‘explanation’’ of the empirical relationship between the folding rate and the contact order However, the improvement appears to be due to the incorporation of the protein stabilities into the model These were introduced by adjusting the pairwise interactions separately for each protein such that the model yielded free energies for folding. .. whereas for those with higher contact orders, the rate increases with ÁG=n As described in Ref 15, a single-input neural network can be trained to predict log kf from ÁG for the 14 proteins with c > 21 (Fig 4); rtrn ¼ 0:81, and rcv ¼ 0:64, which confirms that stability plays a significant role in determining the folding rates of mixed-a/b and b-sheet proteins For these 14 TABLE VII Randomization Tests for. .. the design of fast folding sequences [29] and are consistent with similar studies which focus on exhaustive enumeration of folding paths for two-dimensional chains [7,30] or on the ratio of the folding and the ‘‘glass’’ transition temperatures for the (threedimensional) 27-residue model [8] In a number of subsequent studies of the 27-residue model, it was argued that the kinetic folding behavior is... mandating a certain fraction of longrange contacts, so that the resulting ground states were more appropriate for modeling a helix-coil transition than protein folding Nevertheless, as will be discussed below, native structure does play a role for certain lattice models [10,11] as it does for proteins [12,14,15] Klimov and Thirumalai [32,33] introduced the parameter s ¼ 1 À Tf =Ty, where Tf is the temperature . COMPUTATIONAL METHODS FOR PROTEIN FOLDING A SPECIAL VOLUME OF ADVANCES IN CHEMICAL PHYSICS VOLUME 120 Computational Methods for Protein Folding: Advances in Chemical. Wolynes, Department of Chemistry, University of California, San Diego, California, U.S.A. COMPUTATIONAL METHODS FOR PROTEIN FOLDING ADVANCES IN CHEMICAL PHYSICS VOLUME 120 Edited by RICHARD A. FRIESNER Columbia. presenting both conceptual insights into the basis of protein folding and results for modeling of specific protein folding events. Reduced models of proteins (i.e., models not containing complete atomic detail)