Chipot / Pohorille Free Energy Calculations

Theory and Applications in Chemistry and Biology
1. Auflage 2007
ISBN: 978-3-540-38448-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 518 Seiten

This volume offers a coherent account of the concepts that underlie different approaches devised for the determination of free energies. It provides insight into the theoretical and computational foundations of the subject and presents relevant applications from molecular-level modeling and simulations of chemical and biological systems. The book is aimed at a broad readership of graduate students and researchers.

Autoren/Hrsg.

Chipot, Christophe

Pohorille, Andrew

Inhaltsverzeichnis

1;Foreword;6
1.1;Acknowledgments;9
1.2;References;9
2;Contents;10
3;List of Contributors;18
4;1 Introduction;20
4.1;1.1 Historical Backdrop;20
4.2;1.2 The Density of States;33
4.3;1.3 Free Energy;37
4.4;1.4 Ergodicity, Quasi-nonergodicity and Enhanced Sampling;40
4.5;References;43
5;2 Calculating Free Energy Differences Using Perturbation Theory;51
5.1;2.1 Introduction;51
5.2;2.2 The Perturbation Formalism;52
5.3;2.3 Interpretation of the Free Energy Perturbation Equation;55
5.4;2.4 Cumulant Expansion of the Free Energy;58
5.5;2.5 Two Simple Applications of Perturbation Theory;60
5.6;2.6 How to Deal with Large Perturbations;64
5.7;2.7 A Pictorial Representation of Free Energy Perturbation;66
5.8;2.8 ‘Alchemical Transformations’;68
5.9;2.9 Improving the Efficiency of FEP;78
5.10;2.10 Calculating Free Energy Contributions;84
5.11;2.11 Summary;89
5.12;References;90
6;3 Methods Based on Probability Distributions and Histograms;94
6.1;3.1 Introduction;94
6.2;3.2 Histogram Reweighting;95
6.3;3.3 Basic Stratification and Importance Sampling;101
6.4;3.4 Flat-Histogram Methods;109
6.5;3.5 Order Parameters, Reaction Coordinates, and Extended Ensembles;130
6.6;References;133
7;4 Thermodynamic Integration Using Constrained and Unconstrained Dynamics;136
7.1;4.1 Introduction;136
7.2;4.2 Methods for Constrained and Unconstrained Simulations;138
7.3;4.3 Generalized Coordinates and Lagrangian Formulation;140
7.4;4.4 The Derivative of the Free Energy;145
7.5;4.5 The Potential of Mean Constraint Force;148
7.6;4.6 The Adaptive Biasing Force Method;155
7.7;4.7 Discussion of Other Techniques;166
7.8;4.8 Examples of Application of ABF;167
7.9;4.9 Glycophorin A;170
7.10;4.10 Alchemical Transformations;172
7.11;4.11 Conclusion;177
7.12;Appendix;178
7.13;References;184
8;5 Nonequilibrium Methods for Equilibrium Free Energy Calculations;188
8.1;5.1 Introduction and Background;188
8.2;5.2 Jarzynski’s Identity;191
8.3;5.3 Derivation of Jarzynski’s Identity;192
8.4;5.4 Forward and Backward Averages: Crooks Relation;197
8.5;5.5 Derivation of the Crooks Relation (and Jarzynski’s Identity);198
8.6;5.6 Implementation;199
8.7;5.7 Analysis of Nonequilibrium Free Energy Calculations;201
8.8;5.8 Illustrating Example;204
8.9;5.9 Calculating Potentials of Mean Force;208
8.10;5.10 Applications;211
8.11;5.11 Summary;211
8.12;References;212
9;6 Understanding and Improving Free Energy Calculations in Molecular Simulations: Error Analysis and Reduction Methods;216
9.1;6.1 Introduction;216
9.2;6.2 Overview of the FEP and NEW Methods;220
9.3;6.3 Understanding Free Energy Calculations;222
9.4;6.4 Modeling Free Energy Errors;232
9.5;6.5 Optimal Staging Design;243
9.6;6.6 Overlap Sampling Techniques;245
9.7;6.7 Extrapolation Methods;256
9.8;6.8 Concluding Remarks;260
9.9;References;261
10;7 Transition Path Sampling and the Calculation of Free Energies;265
10.1;7.1 Rare Events and Free Energy Landscapes;265
10.2;7.2 Transition Path Ensemble;268
10.3;7.3 Sampling the Transition Path Ensemble;271
10.4;7.4 Free Energies from Transition Path Sampling Simulations;278
10.5;7.5 The Jarzynski Identity: Path Sampling of Nonequilibrium Trajectories;280
10.6;7.6 Rare Event Kinetics and Free Energies in Path Space;286
10.7;7.7 Summary;290
10.8;References;290
11;8 Specialized Methods for Improving Ergodic Sampling Using Molecular Dynamics and Monte Carlo Simulations;293
11.1;8.1 Background;293
11.2;8.2 Measuring Ergodicity;294
11.3;8.3 Introduction to Enhanced Sampling Strategies;295
11.4;8.4 Modifying the Configurational Distribution: Non- Boltzmann Sampling;296
11.5;8.5 Methods Based on Exchanging Configurations: Parallel Tempering and Related Strategies;302
11.6;8.6 Smart Darting and Basin Hopping Monte Carlo;307
11.7;8.7 Momentum-Enhanced HMC;309
11.8;8.8 Skewing Momenta Distributions to Enhance Free Energy Calculations from Trajectory Space Methods;314
11.9;8.9 Quantum Free Energy Calculations;325
11.10;8.10 Summary;330
11.11;References;331
12;9 Potential Distribution Methods and Free Energy Models of Molecular Solutions;339
12.1;9.1 Introduction;339
12.2;9.2 Background Notation and Discussion of the Potential Distribution Theorem;342
12.3;9.3 Quasichemical Theory;352
12.4;9.4 Example;359
12.5;9.5 Conclusions;363
12.6;References;364
13;10 Methods for Examining Phase Equilibria;368
13.1;10.1 Introduction;368
13.2;10.2 Calculating the Chemical Potential;370
13.3;10.3 Ensemble-Based Free Energies and Equilibria;371
13.4;10.4 Selected Applications of Flat Histogram Methods;387
13.5;10.5 Summary: Comparison of Methods;395
13.6;References;397
14;11 Quantum Contributions to Free Energy Changes in Fluids;403
14.1;11.1 Introduction;403
14.2;11.2 Historical Backdrop;406
14.3;11.3 The Potential Distribution Theorem;407
14.4;11.4 Fourier Path Integrals;408
14.5;11.5 The Quantum Potential Distribution Theorem;412
14.6;11.6 The Variational Approach to Approximations;414
14.7;11.7 The Feynman–Hibbs Variational Method;414
14.8;11.8 AWorked Example;417
14.9;11.9 Wigner–Kirkwood Approximations;418
14.10;11.10 The PDT and Thermodynamic Integration for Exact Quantum Free Energy Changes;421
14.11;11.11 Assessment and Applications;423
14.12;11.12 Summary;431
14.13;References;433
15;12 Free Energy Calculations: Approximate Methods for Biological Macromolecules;437
15.1;12.1 Introduction;437
15.2;12.2 Thermodynamic Perturbation Theory and Ligand Binding;439
15.3;12.3 Linear Response Theory and Free Energy Calculations;444
15.4;12.4 Potential of Mean Force and Simplified Solvent Treatments;450
15.5;12.5 Linear Interaction Energy Approaches;457
15.6;12.6 Free Energy Methods Using an Implicit Solvent: PBFE, MM/ PBSA, and Other Acronyms;460
15.7;12.7 Conclusions;468
15.8;References;469
16;13 Applications of Free Energy Calculations to Chemistry and Biology;476
16.1;13.1 Introduction;476
16.2;13.2 Protein–Ligand Association;477
16.3;13.3 Recognition and Association: Following the Binding Reaction;485
16.4;13.4 Free Energies of Solvation;487
16.5;13.5 Transport Phenomena;489
16.6;13.6 Protein Folding and Stability;493
16.7;13.7 Redox and Acid–Base Reactions;494
16.8;13.8 High-Performance Computing;498
16.9;13.9 Conclusions and Future Perspectives for Free Energy Calculations;504
16.10;References;505
17;14 Summary and Outlook;515
17.1;14.1 Summary: A Unified View;515
17.2;14.2 Outlook: What is the Future Role of Free Energy Calculations?;519
17.3;References;523
18;Index;526