- •Foreword
- •Preface
- •Contents
- •Introduction
- •Oren M. Becker
- •Alexander D. MacKerell, Jr.
- •Masakatsu Watanabe*
- •III. SCOPE OF THE BOOK
- •IV. TOWARD A NEW ERA
- •REFERENCES
- •Atomistic Models and Force Fields
- •Alexander D. MacKerell, Jr.
- •II. POTENTIAL ENERGY FUNCTIONS
- •D. Alternatives to the Potential Energy Function
- •III. EMPIRICAL FORCE FIELDS
- •A. From Potential Energy Functions to Force Fields
- •B. Overview of Available Force Fields
- •C. Free Energy Force Fields
- •D. Applicability of Force Fields
- •IV. DEVELOPMENT OF EMPIRICAL FORCE FIELDS
- •B. Optimization Procedures Used in Empirical Force Fields
- •D. Use of Quantum Mechanical Results as Target Data
- •VI. CONCLUSION
- •REFERENCES
- •Dynamics Methods
- •Oren M. Becker
- •Masakatsu Watanabe*
- •II. TYPES OF MOTIONS
- •IV. NEWTONIAN MOLECULAR DYNAMICS
- •A. Newton’s Equation of Motion
- •C. Molecular Dynamics: Computational Algorithms
- •A. Assigning Initial Values
- •B. Selecting the Integration Time Step
- •C. Stability of Integration
- •VI. ANALYSIS OF DYNAMIC TRAJECTORIES
- •B. Averages and Fluctuations
- •C. Correlation Functions
- •D. Potential of Mean Force
- •VII. OTHER MD SIMULATION APPROACHES
- •A. Stochastic Dynamics
- •B. Brownian Dynamics
- •VIII. ADVANCED SIMULATION TECHNIQUES
- •A. Constrained Dynamics
- •C. Other Approaches and Future Direction
- •REFERENCES
- •Conformational Analysis
- •Oren M. Becker
- •II. CONFORMATION SAMPLING
- •A. High Temperature Molecular Dynamics
- •B. Monte Carlo Simulations
- •C. Genetic Algorithms
- •D. Other Search Methods
- •III. CONFORMATION OPTIMIZATION
- •A. Minimization
- •B. Simulated Annealing
- •IV. CONFORMATIONAL ANALYSIS
- •A. Similarity Measures
- •B. Cluster Analysis
- •C. Principal Component Analysis
- •REFERENCES
- •Thomas A. Darden
- •II. CONTINUUM BOUNDARY CONDITIONS
- •III. FINITE BOUNDARY CONDITIONS
- •IV. PERIODIC BOUNDARY CONDITIONS
- •REFERENCES
- •Internal Coordinate Simulation Method
- •Alexey K. Mazur
- •II. INTERNAL AND CARTESIAN COORDINATES
- •III. PRINCIPLES OF MODELING WITH INTERNAL COORDINATES
- •B. Energy Gradients
- •IV. INTERNAL COORDINATE MOLECULAR DYNAMICS
- •A. Main Problems and Historical Perspective
- •B. Dynamics of Molecular Trees
- •C. Simulation of Flexible Rings
- •A. Time Step Limitations
- •B. Standard Geometry Versus Unconstrained Simulations
- •VI. CONCLUDING REMARKS
- •REFERENCES
- •Implicit Solvent Models
- •II. BASIC FORMULATION OF IMPLICIT SOLVENT
- •A. The Potential of Mean Force
- •III. DECOMPOSITION OF THE FREE ENERGY
- •A. Nonpolar Free Energy Contribution
- •B. Electrostatic Free Energy Contribution
- •IV. CLASSICAL CONTINUUM ELECTROSTATICS
- •A. The Poisson Equation for Macroscopic Media
- •B. Electrostatic Forces and Analytic Gradients
- •C. Treatment of Ionic Strength
- •A. Statistical Mechanical Integral Equations
- •VI. SUMMARY
- •REFERENCES
- •Steven Hayward
- •II. NORMAL MODE ANALYSIS IN CARTESIAN COORDINATE SPACE
- •B. Normal Mode Analysis in Dihedral Angle Space
- •C. Approximate Methods
- •IV. NORMAL MODE REFINEMENT
- •C. Validity of the Concept of a Normal Mode Important Subspace
- •A. The Solvent Effect
- •B. Anharmonicity and Normal Mode Analysis
- •VI. CONCLUSIONS
- •ACKNOWLEDGMENT
- •REFERENCES
- •Free Energy Calculations
- •Thomas Simonson
- •II. GENERAL BACKGROUND
- •A. Thermodynamic Cycles for Solvation and Binding
- •B. Thermodynamic Perturbation Theory
- •D. Other Thermodynamic Functions
- •E. Free Energy Component Analysis
- •III. STANDARD BINDING FREE ENERGIES
- •IV. CONFORMATIONAL FREE ENERGIES
- •A. Conformational Restraints or Umbrella Sampling
- •B. Weighted Histogram Analysis Method
- •C. Conformational Constraints
- •A. Dielectric Reaction Field Approaches
- •B. Lattice Summation Methods
- •VI. IMPROVING SAMPLING
- •A. Multisubstate Approaches
- •B. Umbrella Sampling
- •C. Moving Along
- •VII. PERSPECTIVES
- •REFERENCES
- •John E. Straub
- •B. Phenomenological Rate Equations
- •II. TRANSITION STATE THEORY
- •A. Building the TST Rate Constant
- •B. Some Details
- •C. Computing the TST Rate Constant
- •III. CORRECTIONS TO TRANSITION STATE THEORY
- •A. Computing Using the Reactive Flux Method
- •B. How Dynamic Recrossings Lower the Rate Constant
- •IV. FINDING GOOD REACTION COORDINATES
- •A. Variational Methods for Computing Reaction Paths
- •B. Choice of a Differential Cost Function
- •C. Diffusional Paths
- •VI. HOW TO CONSTRUCT A REACTION PATH
- •A. The Use of Constraints and Restraints
- •B. Variationally Optimizing the Cost Function
- •VII. FOCAL METHODS FOR REFINING TRANSITION STATES
- •VIII. HEURISTIC METHODS
- •IX. SUMMARY
- •ACKNOWLEDGMENT
- •REFERENCES
- •Paul D. Lyne
- •Owen A. Walsh
- •II. BACKGROUND
- •III. APPLICATIONS
- •A. Triosephosphate Isomerase
- •B. Bovine Protein Tyrosine Phosphate
- •C. Citrate Synthase
- •IV. CONCLUSIONS
- •ACKNOWLEDGMENT
- •REFERENCES
- •Jeremy C. Smith
- •III. SCATTERING BY CRYSTALS
- •IV. NEUTRON SCATTERING
- •A. Coherent Inelastic Neutron Scattering
- •B. Incoherent Neutron Scattering
- •REFERENCES
- •Michael Nilges
- •II. EXPERIMENTAL DATA
- •A. Deriving Conformational Restraints from NMR Data
- •B. Distance Restraints
- •C. The Hybrid Energy Approach
- •III. MINIMIZATION PROCEDURES
- •A. Metric Matrix Distance Geometry
- •B. Molecular Dynamics Simulated Annealing
- •C. Folding Random Structures by Simulated Annealing
- •IV. AUTOMATED INTERPRETATION OF NOE SPECTRA
- •B. Automated Assignment of Ambiguities in the NOE Data
- •C. Iterative Explicit NOE Assignment
- •D. Symmetrical Oligomers
- •VI. INFLUENCE OF INTERNAL DYNAMICS ON THE
- •EXPERIMENTAL DATA
- •VII. STRUCTURE QUALITY AND ENERGY PARAMETERS
- •VIII. RECENT APPLICATIONS
- •REFERENCES
- •II. STEPS IN COMPARATIVE MODELING
- •C. Model Building
- •D. Loop Modeling
- •E. Side Chain Modeling
- •III. AB INITIO PROTEIN STRUCTURE MODELING METHODS
- •IV. ERRORS IN COMPARATIVE MODELS
- •VI. APPLICATIONS OF COMPARATIVE MODELING
- •VII. COMPARATIVE MODELING IN STRUCTURAL GENOMICS
- •VIII. CONCLUSION
- •ACKNOWLEDGMENTS
- •REFERENCES
- •Roland L. Dunbrack, Jr.
- •II. BAYESIAN STATISTICS
- •A. Bayesian Probability Theory
- •B. Bayesian Parameter Estimation
- •C. Frequentist Probability Theory
- •D. Bayesian Methods Are Superior to Frequentist Methods
- •F. Simulation via Markov Chain Monte Carlo Methods
- •III. APPLICATIONS IN MOLECULAR BIOLOGY
- •B. Bayesian Sequence Alignment
- •IV. APPLICATIONS IN STRUCTURAL BIOLOGY
- •A. Secondary Structure and Surface Accessibility
- •ACKNOWLEDGMENTS
- •REFERENCES
- •Computer Aided Drug Design
- •Alexander Tropsha and Weifan Zheng
- •IV. SUMMARY AND CONCLUSIONS
- •REFERENCES
- •Oren M. Becker
- •II. SIMPLE MODELS
- •III. LATTICE MODELS
- •B. Mapping Atomistic Energy Landscapes
- •C. Mapping Atomistic Free Energy Landscapes
- •VI. SUMMARY
- •REFERENCES
- •Toshiko Ichiye
- •II. ELECTRON TRANSFER PROPERTIES
- •B. Potential Energy Parameters
- •IV. REDOX POTENTIALS
- •A. Calculation of the Energy Change of the Redox Site
- •B. Calculation of the Energy Changes of the Protein
- •B. Calculation of Differences in the Energy Change of the Protein
- •VI. ELECTRON TRANSFER RATES
- •A. Theory
- •B. Application
- •REFERENCES
- •Fumio Hirata and Hirofumi Sato
- •Shigeki Kato
- •A. Continuum Model
- •B. Simulations
- •C. Reference Interaction Site Model
- •A. Molecular Polarization in Neat Water*
- •B. Autoionization of Water*
- •C. Solvatochromism*
- •F. Tautomerization in Formamide*
- •IV. SUMMARY AND PROSPECTS
- •ACKNOWLEDGMENTS
- •REFERENCES
- •Nucleic Acid Simulations
- •Alexander D. MacKerell, Jr.
- •Lennart Nilsson
- •D. DNA Phase Transitions
- •III. METHODOLOGICAL CONSIDERATIONS
- •A. Atomistic Models
- •B. Alternative Models
- •IV. PRACTICAL CONSIDERATIONS
- •A. Starting Structures
- •C. Production MD Simulation
- •D. Convergence of MD Simulations
- •WEB SITES OF INTEREST
- •REFERENCES
- •Membrane Simulations
- •Douglas J. Tobias
- •II. MOLECULAR DYNAMICS SIMULATIONS OF MEMBRANES
- •B. Force Fields
- •C. Ensembles
- •D. Time Scales
- •III. LIPID BILAYER STRUCTURE
- •A. Overall Bilayer Structure
- •C. Solvation of the Lipid Polar Groups
- •IV. MOLECULAR DYNAMICS IN MEMBRANES
- •A. Overview of Dynamic Processes in Membranes
- •B. Qualitative Picture on the 100 ps Time Scale
- •C. Incoherent Neutron Scattering Measurements of Lipid Dynamics
- •F. Hydrocarbon Chain Dynamics
- •ACKNOWLEDGMENTS
- •REFERENCES
- •Appendix: Useful Internet Resources
- •B. Molecular Modeling and Simulation Packages
- •Index
ISBN: 0-8247-0455-X
This book is printed on acid-free paper.
Headquarters
Marcel Dekker, Inc.
270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540
Eastern Hemisphere Distribution
Marcel Dekker AG
Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896
World Wide Web
http://www.dekker.com
The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above.
Copyright 2001 by Marcel Dekker, Inc. All Rights Reserved.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher.
Current printing (last digit): 10 9 8 7 6 5 4 3 2 1
PRINTED IN THE UNITED STATES OF AMERICA
Foreword
The long-range goal of molecular approaches to biology is to describe living systems in terms of chemistry and physics. Over the last 70 years great progress has been made in applying the quantum mechanical equations representing the underlying physical laws to chemical problems involving the structures and reactions of small molecules. This work was recognized in the awarding of the Nobel Prize in Chemistry to Walter Kohn and John Pople in 1998. Computational studies of mesoscopic systems of biological interest have been attempted only more recently. Classical mechanics is adequate for describing most of the properties of these systems, and the molecular dynamics simulation method is the most important theoretical approach used in such studies. The first molecular dynamics simulation of a protein, the bovine pancreatic trypsin inhibitor (BPTI), was published more than 20 years ago [1]. Although the simulation was ‘‘crude’’ by present standards, it was important because it introduced an important conceptual change in our view of biomolecules. The classic view of biopolymers, like proteins and nucleic acids, had been static in character. The remarkable detail evident in the protein crystal structures available at that time led to an image of ‘‘rigid’’ biomolecules with every atom fixed in place [2]. The molecular dynamics simulation of BPTI was instrumental in changing the static view of the structure of biomolecules to a dynamic picture. It is now recognized that the atoms of which biopolymers are composed are in a state of constant motion at ordinary temperatures. The X-ray structure of a protein provides the average atomic positions, but the atoms exhibit fluidlike motions of sizable amplitudes about these averages. The new understanding of protein dynamics subsumed the static picture in that the average positions are still useful for the discussion of many aspects of biomolecule function in the language of structural chemistry. The recognition of the importance of fluctuations opened the way for more sophisticated and accurate interpretations of functional properties.
In the intervening years, molecular dynamics simulations of biomolecules have undergone an explosive development and been applied to a wide range of problems [3,4]. Two attributes of molecular dynamics simulations have played an essential role in their increasing use. The first is that simulations provide individual particle motions as a function of time so they can answer detailed questions about the properties of a system, often more easily than experiments. For many aspects of biomolecule function, it is these details
iii
iv |
Foreword |
that are of interest (e.g., by what pathways does oxygen get into and exit the heme pocket in myoglobin? How does the conformational change that triggers activity of ras p21 take place?). The second attribute is that, although the potential used in the simulations is approximate, it is completely under the user’s control, so that by removing or altering specific contributions to the potential, their role in determining a given property can be examined. This is most graphically demonstrated in the calculation of free energy differences by ‘‘computer alchemy’’ in which the potential is transmuted reversibly from that representing one system to another during a simulation [5].
There are three types of applications of molecular dynamics simulation methods in the study of macromolecules of biological interest, as in other areas that use such simulations. The first uses the simulation simply as a means of sampling configuration space. This is involved in the utilization of molecular dynamics, often with simulated annealing protocols, to determine or refine structures with data obtained from experiments, such as X-ray diffraction. The second uses simulations to determine equilibrium averages, including structural and motional properties (e.g., atomic mean-square fluctuation amplitudes) and the thermodynamics of the system. For such applications, it is necessary that the simulations adequately sample configuration space, as in the first application, with the additional condition that each point be weighted by the appropriate Boltzmann factor. The third area employs simulations to examine the actual dynamics. Here not only is adequate sampling of configuration space with appropriate Boltzmann weighting required, but it must be done so as to properly represent the time development of the system. For the first two areas, Monte Carlo simulations, as well as molecular dynamics, can be utilized. By contrast, in the third area where the motions and their development are of interest, only molecular dynamics can provide the necessary information. The three types of applications, all of which are considered in the present volume, make increasing demands on the simulation methodology in terms of the accuracy that is required.
In the early years of molecular dynamics simulations of biomolecules, almost all scientists working in the field received specialized training (as graduate students and/or postdoctoral fellows) that provided a detailed understanding of the power and limitations of the approach. Now that the methodology is becoming more accessible (in terms of ease of application of generally distributed programs and the availability of the required computational resources) and better validated (in terms of published results), many people are beginning to use simulation technology without training in the area. Molecular dynamics simulations are becoming part of the ‘‘tool kit’’ used by everyone, even experimentalists, who wish to obtain an understanding of the structure and function of biomolecules. To be able to do this effectively, a person must have access to sources from which he or she can obtain the background required for meaningful applications of the simulation methodology. This volume has an important role to play in the transition of the field from one limited to specialists (although they will continue to be needed to improve the methodology and extend its applicability) to the mainstream of molecular biology. The emphasis on an in-depth description of the computational methodology will make the volume useful as an introduction to the field for many people who are doing simulations for the first time. They will find it helpful also to look at two earlier volumes on macromolecular simulations [3,4], as well as the classic general text on molecular dynamics [6]. Equally important in the volume is the connection made with X-ray, neutron scattering, and nuclear magnetic resonance experiments, areas in which molecular dynamics simulations are playing an essential role. A number of well-chosen ‘‘special topics’’ involving applications of simulation methods are described. Also, several chapters broaden
Foreword |
v |
the perspective of the book by introducing approaches other than molecular dynamics for modeling proteins and their interactions. They make the connection with what many people regard—mistakenly, in my view—as ‘‘computational biology.’’ Certainly with the announced completion of a description of the human genome in a coarse-grained sense, the part of computational biology concerned with the prediction of the structure and function of gene products from a knowledge of the polypeptide sequence is an important endeavor. However, equally important, and probably more so in the long run, is the biophysical aspect of computational biology. The first set of Investigators in Computational Biology chosen this year demonstrates that the Howard Hughes Foundation recognized the importance of such biophysical studies to which this volume serves as an excellent introduction.
I am very pleased to have been given the opportunity to contribute a Foreword to this very useful book. It is a particular pleasure for me to do so because all the editors and fifteen of the authors are alumni of my research group at Harvard, where molecular dynamics simulations of biomolecules originated.
REFERENCES
1.JA McCammon, BR Gelin, and M Karplus. Nature 267:585, 1977.
2.DC Phillips. In: RH Sarma, ed. Biomolecular Stereodynamics, II. Guilderland, New York: Adenine Press, 1981, p 497.
3.JA McCammon and S Harvey. Dynamics of Proteins and Nucleic Acids. Cambridge: Cambridge University Press, 1987.
4.CL Brooks III, M Karplus, and BM Pettitt. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics. New York: John Wiley & Sons, 1988.
5.For an early example, see J Gao, K Kuczera, B Tidor, and M Karplus. Science 244:1069–1072, 1989.
6.MP Allen and DJ Tildesley. Computer Simulations of Liquids. Oxford: Clarendon Press, 1987.
Martin Karplus Laboratoire de chimie Biophysique, ISIS Universite´ Louis Pasteur Strasbourg, France and
Department of Chemistry and Chemical Biology Harvard University Cambridge, Massachusetts