Computational biochemistry and biophysics

Cover 1 Foreword 4 Preface 8 Contents 10 Introduction 14 Oren M. Becker 14 Alexander D. MacKerell, Jr. 14 Benoi t Roux 14 Masakatsu Watanabe* 14 I. INTRODUCTION 14 II. OVERVIEW OF COMPUTATIONAL BIOCHEMISTRY 15 AND BIOPHYSICS 15 III. SCOPE OF THE BOOK 17 IV. TOWARD A NEW ERA 18 REFERENCES 18 Atomistic Models and Force Fields 20 Alexander D. MacKerell, Jr. 20 I. INTRODUCTION 20 II. POTENTIAL ENERGY FUNCTIONS 21 A. Potential Energy Functions for the Treatment of 21 Biological Molecules 21 B. All- Atom Versus Extended- Atom Models 24 C. Extensions of the Potential Energy Function 24 D. Alternatives to the Potential Energy Function 25 III. EMPIRICAL FORCE FIELDS 26 A. From Potential Energy Functions to Force Fields 26 B. Overview of Available Force Fields 26 C. Free Energy Force Fields 27 D. Applicability of Force Fields 28 IV. DEVELOPMENT OF EMPIRICAL FORCE FIELDS 29 A. Philosophical Considerations Behind Commonly Used 29 Force Fields 29 B. Optimization Procedures Used in Empirical Force Fields 30 C. Explicit Solvent Models and the Importance of Balancing the 35 External Interactions 35 D. Use of Quantum Mechanical Results as Target Data 35 E. Extension of Available Force Fields: Application to CHARMM 36 V. FUTURE DIRECTIONS 47 VI. CONCLUSION 48 REFERENCES 48 Dynamics Methods 52 Oren M. Becker 52 Masakatsu Watanabe* 52 I. INTRODUCTION 52 II. TYPES OF MOTIONS 53 III. THE STATISTICAL MECHANICS BASIS OF MOLECULAR 54 DYNAMICS 54 IV. NEWTONIAN MOLECULAR DYNAMICS 55 A. Newton’s Equation of Motion 55 B. Properties of Newton’s Equation of Motion 56 C. Molecular Dynamics: Computational Algorithms 57 V. MOLECULAR DYNAMICS: SIMULATION PRACTICE 61 A. Assigning Initial Values 61 B. Selecting the Integration Time Step 62 C. Stability of Integration 63 D. Simulation Protocol and Some Tricks for Better Simulations 64 VI. ANALYSIS OF DYNAMIC TRAJECTORIES 66 A. Time Series 66 B. Averages and Fluctuations 67 C. Correlation Functions 67 D. Potential of Mean Force 68 E. Estimating Standard Errors 69 VII. OTHER MD SIMULATION APPROACHES 69 A. Stochastic Dynamics 69 B. Brownian Dynamics 70 C. Molecular Dynamics in Alternative Ensembles 70 VIII. ADVANCED SIMULATION TECHNIQUES 75 A. Constrained Dynamics 75 B. Multiple Time Step Methods 76 C. Other Approaches and Future Direction 78 REFERENCES 79 Conformational Analysis 82 Oren M. Becker 82 I. BACKGROUND 82 II. CONFORMATION SAMPLING 83 A. High Temperature Molecular Dynamics 83 B. Monte Carlo Simulations 84 C. Genetic Algorithms 86 D. Other Search Methods 87 III. CONFORMATION OPTIMIZATION 90 A. Minimization 90 B. Simulated Annealing 95 IV. CONFORMATIONAL ANALYSIS 96 A. Similarity Measures 97 B. Cluster Analysis 98 C. Principal Component Analysis 99 V. CONCLUSION 102 REFERENCES 102 Treatment of Long- Range Forces and Potential 104 Thomas A. Darden 104 I. INTRODUCTION: BASIC ELECTROSTATICS 104 II. CONTINUUM BOUNDARY CONDITIONS 111 III. FINITE BOUNDARY CONDITIONS 113 IV. PERIODIC BOUNDARY CONDITIONS 117 V. STRENGTHS AND WEAKNESSES OF VARIOUS APPROACHES 125 REFERENCES 126 Internal Coordinate Simulation Method 128 Alexey K. Mazur 128 I. INTRODUCTION 128 II. INTERNAL AND CARTESIAN COORDINATES 128 III. PRINCIPLES OF MODELING WITH INTERNAL COORDINATES 132 A. Selection of Variables 132 B. Energy Gradients 134 IV. INTERNAL COORDINATE MOLECULAR DYNAMICS 135 A. Main Problems and Historical Perspective 135 B. Dynamics of Molecular Trees 136 C. Simulation of Flexible Rings 138 V. PRACTICAL EXAMPLES 140 A. Time Step Limitations 140 B. Standard Geometry Versus Unconstrained Simulations 141 VI. CONCLUDING REMARKS 142 REFERENCES 143 Implicit Solvent Models 146 Benoi t Roux 146 I. INTRODUCTION 146 II. BASIC FORMULATION OF IMPLICIT SOLVENT 148 A. The Potential of Mean Force 148 B. Relative and Absolute Values: Reversible Work 150 III. DECOMPOSITION OF THE FREE ENERGY 151 A. Nonpolar Free Energy Contribution 152 B. Electrostatic Free Energy Contribution 153 IV. CLASSICAL CONTINUUM ELECTROSTATICS 153 A. The Poisson Equation for Macroscopic Media 153 B. Electrostatic Forces and Analytic Gradients 155 C. Treatment of Ionic Strength 155 D. Treatment of a Transmembrane Potential 156 V. MISCELLANEOUS APPROACHES 157 A. Statistical Mechanical Integral Equations 157 B. Solvent Boundary Potentials and Implicit/ Explicit Mixed Schemes 158 C. Solvent- Accessible Surface Area Models 159 D. Knowledge- Based Potentials 160 VI. SUMMARY 161 REFERENCES 161 Normal Mode Analysis of Biological Molecules 166 Steven Hayward 166 I. INTRODUCTION 166 II. NORMAL MODE ANALYSIS IN CARTESIAN COORDINATE SPACE 167 III. NORMAL MODE ANALYSIS OF LARGE 169 BIOLOGICAL MOLECULES 169 A. Determination of the Eigenvalues and Eigenvectors of 169 a Large Hessian 169 B. Normal Mode Analysis in Dihedral Angle Space 171 C. Approximate Methods 172 IV. NORMAL MODE REFINEMENT 173 A. Normal Mode X- Ray Refinement 174 B. Normal Mode NMR Refinement 174 C. Validity of the Concept of a Normal Mode Important Subspace 175 V. NORMAL MODE ANALYSIS AND REALITY 176 A. The Solvent Effect 176 B. Anharmonicity and Normal Mode Analysis 176 VI. CONCLUSIONS 178 ACKNOWLEDGMENT 179 REFERENCES 179 Free Energy Calculations 182 Thomas Simonson 182 I. INTRODUCTION 182 II. GENERAL BACKGROUND 183 A. Thermodynamic Cycles for Solvation and Binding 183 B. Thermodynamic Perturbation Theory 185 C. Dummy Atoms and Endpoint Corrections 190 D. Other Thermodynamic Functions 193 E. Free Energy Component Analysis 194 III. STANDARD BINDING FREE ENERGIES 194 IV. CONFORMATIONAL FREE ENERGIES 197 A. Conformational Restraints or Umbrella Sampling 197 B. Weighted Histogram Analysis Method 199 C. Conformational Constraints 200 V. ELECTROSTATIC FREE ENERGIES 201 A. Dielectric Reaction Field Approaches 201 B. Lattice Summation Methods 204 VI. IMPROVING SAMPLING 205 A. Multisubstate Approaches 205 B. Umbrella Sampling 207 C. Moving Along 207 VII. PERSPECTIVES 208 REFERENCES 209 Reaction Rates and Transition Pathways 212 John E. Straub 212 I. INTRODUCTION 212 A. Defining Reactant and Product ‘‘ States’’ 212 B. Phenomenological Rate Equations 213 II. TRANSITION STATE THEORY 214 A. Building the TST Rate Constant 214 B. Some Details 216 C. Computing the TST Rate Constant 217 III. CORRECTIONS TO TRANSITION STATE THEORY 217 A. Computing Using the Reactive Flux Method 218 B. How Dynamic Recrossings Lower the Rate Constant 220 C. An Efficient Method for Computing Small Values of 221 IV. FINDING GOOD REACTION COORDINATES 222 V. GLOBAL SEARCHES FOR IMPORTANT TRANSITION PATHWAYS 223 A. Variational Methods for Computing Reaction Paths 224 B. Choice of a Differential Cost Function 224 C. Diffusional Paths 226 D. Onsager– Machlup Paths 226 VI. HOW TO CONSTRUCT A REACTION PATH 227 A. The Use of Constraints and Restraints 227 B. Variationally Optimizing the Cost Function 228 VII. FOCAL METHODS FOR REFINING TRANSITION STATES 228 VIII. HEURISTIC METHODS 230 IX. SUMMARY 231 ACKNOWLEDGMENT 232 REFERENCES 232 Computer Simulation of Biochemical Reactions with QM– MM Methods 234 Paul D. Lyne 234 Owen A. Walsh 234 I. INTRODUCTION 234 II. BACKGROUND 235 A. QM– MM Methodology 235 B. The Quantum/ Classical Boundary 239 III. APPLICATIONS 240 A. Triosephosphate Isomerase 241 B. Bovine Protein Tyrosine Phosphate 243 C. Citrate Synthase 244 IV. CONCLUSIONS 247 ACKNOWLEDGMENT 247 REFERENCES 247 X- Ray and Neutron Scattering as Probes of the Dynamics of Biological Molecules 250 Jeremy C. Smith 250 I. INTRODUCTION 250 II. BASIC EQUATIONS RELATING ATOMIC POSITIONS TO X- RAY 252 AND NEUTRON SCATTERING 252 III. SCATTERING BY CRYSTALS 253 A. Bragg Diffraction 254 B. X- Ray Diffuse Scattering 255 IV. NEUTRON SCATTERING 257 A. Coherent Inelastic Neutron Scattering 258 B. Incoherent Neutron Scattering 259 V. CONCLUSIONS 263 REFERENCES 264 Applications of Molecular Modeling in NMR Structure Determination 266 Michael Nilges 266 I. INTRODUCTION 266 II. EXPERIMENTAL DATA 266 A. Deriving Conformational Restraints from NMR Data 266 B. Distance Restraints 268 C. The Hybrid Energy Approach 268 III. MINIMIZATION PROCEDURES 270 A. Metric Matrix Distance Geometry 271 B. Molecular Dynamics Simulated Annealing 274 C. Folding Random Structures by Simulated Annealing 275 IV. AUTOMATED INTERPRETATION OF NOE SPECTRA 277 A. Recognition of Incorrect Restraints: The Structural 277 Consistency Hypothesis 277 B. Automated Assignment of Ambiguities in the NOE Data 278 C. Iterative Explicit NOE Assignment 278 D. Symmetrical Oligomers 279 V. TREATMENT OF SPIN DIFFUSION 280 VI. INFLUENCE OF INTERNAL DYNAMICS ON THE 282 EXPERIMENTAL DATA 282 VII. STRUCTURE QUALITY AND ENERGY PARAMETERS 284 VIII. RECENT APPLICATIONS 284 REFERENCES 285 Comparative Protein Structure Modeling 288 Andra´ s Fiser, Roberto Sa´ nchez, Francisco Melo, and Andrej S ali 288 I. INTRODUCTION 288 II. STEPS IN COMPARATIVE MODELING 290 A. Identifying Known Protein Structures Related to the Target 290 Sequence 290 B. Aligning the Target Sequence with the Template Structures 292 C. Model Building 293 D. Loop Modeling 298 E. Side Chain Modeling 299 III. AB INITIO PROTEIN STRUCTURE MODELING METHODS 302 IV. ERRORS IN COMPARATIVE MODELS 303 V. MODEL EVALUATION 307 VI. APPLICATIONS OF COMPARATIVE MODELING 308 A. Ligand Specificity of Brain Lipid- Binding Protein 310 B. Finding Proteins Remotely Related to the E. coli Subunit 311 VII. COMPARATIVE MODELING IN STRUCTURAL GENOMICS 311 VIII. CONCLUSION 314 ACKNOWLEDGMENTS 314 REFERENCES 314 Bayesian Statistics in Molecular and Structural Biology 326 Roland L. Dunbrack, Jr. 326 I. INTRODUCTION 326 II. BAYESIAN STATISTICS 327 A. Bayesian Probability Theory 327 B. Bayesian Parameter Estimation 329 C. Frequentist Probability Theory 330 D. Bayesian Methods Are Superior to Frequentist Methods 333 E. Setting Up Bayesian Models 335 F. Simulation via Markov Chain Monte Carlo Methods 339 G. Mixture Models 340 H. Explanatory Variables 342 III. APPLICATIONS IN MOLECULAR BIOLOGY 343 A. Dirichlet Mixture Priors for Sequence Profiles 343 B. Bayesian Sequence Alignment 345 C. Sequence– Structure Alignment 349 IV. APPLICATIONS IN STRUCTURAL BIOLOGY 351 A. Secondary Structure and Surface Accessibility 351 B. Side- Chain Conformational Analysis 352 V. CONCLUSION 357 ACKNOWLEDGMENTS 357 REFERENCES 357 Computer Aided Drug Design 364 Alexander Tropsha and Weifan Zheng 364 I. INTRODUCTION 364 II. RELATIONSHIPS BETWEEN EXPERIMENTAL AND THEORETICAL 365 APPROACHES TO STUDYING DRUG– RECEPTOR INTERACTIONS 365 III. COMPUTATIONAL APPROACHES TO MODELING 367 LIGAND– RECEPTOR INTERACTIONS 367 A. Ligand- Based Approaches 367 B. Quantitative Structure– Activity Relationship Method 371 C. Structure- Based Drug Design 374 D. Chemical Informatics and Drug Design 376 IV. SUMMARY AND CONCLUSIONS 377 REFERENCES 378 Protein Folding: Computational Approaches 384 Oren M. Becker 384 I. INTRODUCTION 384 II. SIMPLE MODELS 387 III. LATTICE MODELS 389 IV. OFF- LATTICE MINIMALIST MODELS 392 V. ATOMISTIC MODELS 395 A. Unfolding/ Folding Simulations 395 B. Mapping Atomistic Energy Landscapes 396 C. Mapping Atomistic Free Energy Landscapes 401 VI. SUMMARY 402 REFERENCES 402 Simulations of Electron Transfer Proteins 406 Toshiko Ichiye 406 I. INTRODUCTION 406 II. ELECTRON TRANSFER PROPERTIES 406 III. CALCULATION TECHNIQUES FOR ELECTRON 408 TRANSFER PROTEINS 408 A. Quantum Chemistry of the Redox Site 408 B. Potential Energy Parameters 409 C. Molecular Mechanics and Electrostatics Calculations 411 of the Protein 411 IV. REDOX POTENTIALS 412 A. Calculation of the Energy Change of the Redox Site 413 B. Calculation of the Energy Changes of the Protein 413 V. DIFFERENCES IN REDOX POTENTIALS 417 A. Calculation of Differences in the Energy Change 417 of the Redox Site 417 B. Calculation of Differences in the Energy Change of the Protein 417 VI. ELECTRON TRANSFER RATES 421 A. Theory 421 B. Application 423 REFERENCES 424 The RISM- SCF/ MCSCF Approach for Chemical Processes in Solutions 430 Fumio Hirata and Hirofumi Sato 430 Seiichiro Ten- no 430 Shigeki Kato 430 I. SOLVENT EFFECT ON CHEMICAL PROCESSES 430 A. Continuum Model 431 B. Simulations 431 C. Reference Interaction Site Model 432 II. OUTLINE OF THE RISM- SCF/ MCSCF METHOD 433 III. SOLVATION EFFECT ON A VARIETY OF CHEMICAL PROCESSES 435 IN SOLUTION 435 A. Molecular Polarization in Neat Water* 435 B. Autoionization of Water* 436 C. Solvatochromism* 439 D. Conformational Equilibrium* 440 E. Acid– Base Equilibrium 441 F. Tautomerization in Formamide* 445 G. The SN2 Reaction* 446 IV. SUMMARY AND PROSPECTS 449 ACKNOWLEDGMENTS 451 REFERENCES 451 Nucleic Acid Simulations 454 Alexander D. MacKerell, Jr. 454 Lennart Nilsson 454 I. INTRODUCTION 454 II. OVERVIEW OF COMPUTATIONAL STUDIES 455 ON OLIGONUCLEOTIDES 455 A. DNA 455 B. RNA 459 C. Dynamics and Energetics of Oligonucleotides 460 D. DNA Phase Transitions 461 E. Modified Oligonucleotides 461 F. Alternative Secondary and Tertiary Motifs of Oligonucleotides 462 III. METHODOLOGICAL CONSIDERATIONS 462 A. Atomistic Models 462 B. Alternative Models 464 IV. PRACTICAL CONSIDERATIONS 465 A. Starting Structures 465 B. System Configuration, Solvation, and Ion Placement 467 C. Production MD Simulation 469 D. Convergence of MD Simulations 469 E. Analysis of MD Simulations 470 V. CONCLUSION 472 WEB SITES OF INTEREST 472 REFERENCES 472 Membrane Simulations 478 Douglas J. Tobias 478 I. INTRODUCTION 478 II. MOLECULAR DYNAMICS SIMULATIONS OF MEMBRANES 480 A. System Size and Construction 480 B. Force Fields 481 C. Ensembles 483 D. Time Scales 484 III. LIPID BILAYER STRUCTURE 484 A. Overall Bilayer Structure 484 B. Density Profiles 484 C. Solvation of the Lipid Polar Groups 486 D. Water Orientational Polarization and the Membrane 487 Dipole Potential 487 IV. MOLECULAR DYNAMICS IN MEMBRANES 489 A. Overview of Dynamic Processes in Membranes 489 B. Qualitative Picture on the 100 ps Time Scale 489 C. Incoherent Neutron Scattering Measurements of Lipid Dynamics 490 D. Comparison of MD and Neutron Scattering Results 492 on Lipid Dynamics 492 E. Lipid Center- of- Mass ‘‘ Diffusion’’ 498 F. Hydrocarbon Chain Dynamics 501 G. Water Dynamics 504 V. SUMMARY AND CONCLUSIONS 506 ACKNOWLEDGMENTS 507 REFERENCES 507 Appendix: Useful Internet Resources 510 A. Internet Resources for Topics in Selected Chapters 510 B. Molecular Modeling and Simulation Packages 511 C. Molecular Visualization Software 512 D. Computational Biophysics Related at the National Institutes of 513 Health (NIH) 513 E. Molecular Biology Software Links 513 F. Online Tutorials 513 G. Additional Resource List for Computational Chemistry and 513 Molecular Modeling Software 513 H. Databases of Biological Molecules 514 Index 516 Cover......Page 1 Foreword......Page 4 Preface......Page 8 Contents......Page 10 I. INTRODUCTION......Page 14 AND BIOPHYSICS......Page 15 III. SCOPE OF THE BOOK......Page 17 REFERENCES......Page 18 I. INTRODUCTION......Page 20 Biological Molecules......Page 21 C. Extensions of the Potential Energy Function......Page 24 D. Alternatives to the Potential Energy Function......Page 25 B. Overview of Available Force Fields......Page 26 C. Free Energy Force Fields......Page 27 D. Applicability of Force Fields......Page 28 Force Fields......Page 29 B. Optimization Procedures Used in Empirical Force Fields......Page 30 D. Use of Quantum Mechanical Results as Target Data......Page 35 E. Extension of Available Force Fields: Application to CHARMM......Page 36 V. FUTURE DIRECTIONS......Page 47 REFERENCES......Page 48 I. INTRODUCTION......Page 52 II. TYPES OF MOTIONS......Page 53 DYNAMICS......Page 54 A. Newton’s Equation of Motion......Page 55 B. Properties of Newton’s Equation of Motion......Page 56 C. Molecular Dynamics: Computational Algorithms......Page 57 A. Assigning Initial Values......Page 61 B. Selecting the Integration Time Step......Page 62 C. Stability of Integration......Page 63 D. Simulation Protocol and Some Tricks for Better Simulations......Page 64 A. Time Series......Page 66 C. Correlation Functions......Page 67 D. Potential of Mean Force......Page 68 A. Stochastic Dynamics......Page 69 C. Molecular Dynamics in Alternative Ensembles......Page 70 A. Constrained Dynamics......Page 75 B. Multiple Time Step Methods......Page 76 C. Other Approaches and Future Direction......Page 78 REFERENCES......Page 79 I. BACKGROUND......Page 82 A. High Temperature Molecular Dynamics......Page 83 B. Monte Carlo Simulations......Page 84 C. Genetic Algorithms......Page 86 D. Other Search Methods......Page 87 A. Minimization......Page 90 B. Simulated Annealing......Page 95 IV. CONFORMATIONAL ANALYSIS......Page 96 A. Similarity Measures......Page 97 B. Cluster Analysis......Page 98 C. Principal Component Analysis......Page 99 REFERENCES......Page 102 I. INTRODUCTION: BASIC ELECTROSTATICS......Page 104 II. CONTINUUM BOUNDARY CONDITIONS......Page 111 III. FINITE BOUNDARY CONDITIONS......Page 113 IV. PERIODIC BOUNDARY CONDITIONS......Page 117 V. STRENGTHS AND WEAKNESSES OF VARIOUS APPROACHES......Page 125 REFERENCES......Page 126 II. INTERNAL AND CARTESIAN COORDINATES......Page 128 A. Selection of Variables......Page 132 B. Energy Gradients......Page 134 A. Main Problems and Historical Perspective......Page 135 B. Dynamics of Molecular Trees......Page 136 C. Simulation of Flexible Rings......Page 138 A. Time Step Limitations......Page 140 B. Standard Geometry Versus Unconstrained Simulations......Page 141 VI. CONCLUDING REMARKS......Page 142 REFERENCES......Page 143 I. INTRODUCTION......Page 146 A. The Potential of Mean Force......Page 148 B. Relative and Absolute Values: Reversible Work......Page 150 III. DECOMPOSITION OF THE FREE ENERGY......Page 151 A. Nonpolar Free Energy Contribution......Page 152 A. The Poisson Equation for Macroscopic Media......Page 153 C. Treatment of Ionic Strength......Page 155 D. Treatment of a Transmembrane Potential......Page 156 A. Statistical Mechanical Integral Equations......Page 157 B. Solvent Boundary Potentials and Implicit/ Explicit Mixed Schemes......Page 158 C. Solvent- Accessible Surface Area Models......Page 159 D. Knowledge- Based Potentials......Page 160 REFERENCES......Page 161 I. INTRODUCTION......Page 166 II. NORMAL MODE ANALYSIS IN CARTESIAN COORDINATE SPACE......Page 167 a Large Hessian......Page 169 B. Normal Mode Analysis in Dihedral Angle Space......Page 171 C. Approximate Methods......Page 172 IV. NORMAL MODE REFINEMENT......Page 173 B. Normal Mode NMR Refinement......Page 174 C. Validity of the Concept of a Normal Mode Important Subspace......Page 175 B. Anharmonicity and Normal Mode Analysis......Page 176 VI. CONCLUSIONS......Page 178 REFERENCES......Page 179 I. INTRODUCTION......Page 182 A. Thermodynamic Cycles for Solvation and Binding......Page 183 B. Thermodynamic Perturbation Theory......Page 185 C. Dummy Atoms and Endpoint Corrections......Page 190 D. Other Thermodynamic Functions......Page 193 III. STANDARD BINDING FREE ENERGIES......Page 194 A. Conformational Restraints or Umbrella Sampling......Page 197 B. Weighted Histogram Analysis Method......Page 199 C. Conformational Constraints......Page 200 A. Dielectric Reaction Field Approaches......Page 201 B. Lattice Summation Methods......Page 204 A. Multisubstate Approaches......Page 205 C. Moving Along......Page 207 VII. PERSPECTIVES......Page 208 REFERENCES......Page 209 A. Defining Reactant and Product ‘‘ States’’......Page 212 B. Phenomenological Rate Equations......Page 213 A. Building the TST Rate Constant......Page 214 B. Some Details......Page 216 III. CORRECTIONS TO TRANSITION STATE THEORY......Page 217 A. Computing Using the Reactive Flux Method......Page 218 B. How Dynamic Recrossings Lower the Rate Constant......Page 220 C. An Efficient Method for Computing Small Values of......Page 221 IV. FINDING GOOD REACTION COORDINATES......Page 222 V. GLOBAL SEARCHES FOR IMPORTANT TRANSITION PATHWAYS......Page 223 B. Choice of a Differential Cost Function......Page 224 D. Onsager– Machlup Paths......Page 226 A. The Use of Constraints and Restraints......Page 227 VII. FOCAL METHODS FOR REFINING TRANSITION STATES......Page 228 VIII. HEURISTIC METHODS......Page 230 IX. SUMMARY......Page 231 REFERENCES......Page 232 I. INTRODUCTION......Page 234 A. QM– MM Methodology......Page 235 B. The Quantum/ Classical Boundary......Page 239 III. APPLICATIONS......Page 240 A. Triosephosphate Isomerase......Page 241 B. Bovine Protein Tyrosine Phosphate......Page 243 C. Citrate Synthase......Page 244 REFERENCES......Page 247 I. INTRODUCTION......Page 250 AND NEUTRON SCATTERING......Page 252 III. SCATTERING BY CRYSTALS......Page 253 A. Bragg Diffraction......Page 254 B. X- Ray Diffuse Scattering......Page 255 IV. NEUTRON SCATTERING......Page 257 A. Coherent Inelastic Neutron Scattering......Page 258 B. Incoherent Neutron Scattering......Page 259 V. CONCLUSIONS......Page 263 REFERENCES......Page 264 A. Deriving Conformational Restraints from NMR Data......Page 266 C. The Hybrid Energy Approach......Page 268 III. MINIMIZATION PROCEDURES......Page 270 A. Metric Matrix Distance Geometry......Page 271 B. Molecular Dynamics Simulated Annealing......Page 274 C. Folding Random Structures by Simulated Annealing......Page 275 Consistency Hypothesis......Page 277 C. Iterative Explicit NOE Assignment......Page 278 D. Symmetrical Oligomers......Page 279 V. TREATMENT OF SPIN DIFFUSION......Page 280 EXPERIMENTAL DATA......Page 282 VIII. RECENT APPLICATIONS......Page 284 REFERENCES......Page 285 I. INTRODUCTION......Page 288 Sequence......Page 290 B. Aligning the Target Sequence with the Template Structures......Page 292 C. Model Building......Page 293 D. Loop Modeling......Page 298 E. Side Chain Modeling......Page 299 III. AB INITIO PROTEIN STRUCTURE MODELING METHODS......Page 302 IV. ERRORS IN COMPARATIVE MODELS......Page 303 V. MODEL EVALUATION......Page 307 VI. APPLICATIONS OF COMPARATIVE MODELING......Page 308 A. Ligand Specificity of Brain Lipid- Binding Protein......Page 310 VII. COMPARATIVE MODELING IN STRUCTURAL GENOMICS......Page 311 REFERENCES......Page 314 I. INTRODUCTION......Page 326 A. Bayesian Probability Theory......Page 327 B. Bayesian Parameter Estimation......Page 329 C. Frequentist Probability Theory......Page 330 D. Bayesian Methods Are Superior to Frequentist Methods......Page 333 E. Setting Up Bayesian Models......Page 335 F. Simulation via Markov Chain Monte Carlo Methods......Page 339 G. Mixture Models......Page 340 H. Explanatory Variables......Page 342 A. Dirichlet Mixture Priors for Sequence Profiles......Page 343 B. Bayesian Sequence Alignment......Page 345 C. Sequence– Structure Alignment......Page 349 A. Secondary Structure and Surface Accessibility......Page 351 B. Side- Chain Conformational Analysis......Page 352 REFERENCES......Page 357 I. INTRODUCTION......Page 364 APPROACHES TO STUDYING DRUG– RECEPTOR INTERACTIONS......Page 365 A. Ligand- Based Approaches......Page 367 B. Quantitative Structure– Activity Relationship Method......Page 371 C. Structure- Based Drug Design......Page 374 D. Chemical Informatics and Drug Design......Page 376 IV. SUMMARY AND CONCLUSIONS......Page 377 REFERENCES......Page 378 I. INTRODUCTION......Page 384 II. SIMPLE MODELS......Page 387 III. LATTICE MODELS......Page 389 IV. OFF- LATTICE MINIMALIST MODELS......Page 392 A. Unfolding/ Folding Simulations......Page 395 B. Mapping Atomistic Energy Landscapes......Page 396 C. Mapping Atomistic Free Energy Landscapes......Page 401 REFERENCES......Page 402 II. ELECTRON TRANSFER PROPERTIES......Page 406 A. Quantum Chemistry of the Redox Site......Page 408 B. Potential Energy Parameters......Page 409 of the Protein......Page 411 IV. REDOX POTENTIALS......Page 412 B. Calculation of the Energy Changes of the Protein......Page 413 B. Calculation of Differences in the Energy Change of the Protein......Page 417 A. Theory......Page 421 B. Application......Page 423 REFERENCES......Page 424 I. SOLVENT EFFECT ON CHEMICAL PROCESSES......Page 430 B. Simulations......Page 431 C. Reference Interaction Site Model......Page 432 II. OUTLINE OF THE RISM- SCF/ MCSCF METHOD......Page 433 A. Molecular Polarization in Neat Water*......Page 435 B. Autoionization of Water*......Page 436 C. Solvatochromism*......Page 439 D. Conformational Equilibrium*......Page 440 E. Acid– Base Equilibrium......Page 441 F. Tautomerization in Formamide*......Page 445 G. The SN2 Reaction*......Page 446 IV. SUMMARY AND PROSPECTS......Page 449 REFERENCES......Page 451 I. INTRODUCTION......Page 454 A. DNA......Page 455 B. RNA......Page 459 C. Dynamics and Energetics of Oligonucleotides......Page 460 E. Modified Oligonucleotides......Page 461 A. Atomistic Models......Page 462 B. Alternative Models......Page 464 A. Starting Structures......Page 465 B. System Configuration, Solvation, and Ion Placement......Page 467 D. Convergence of MD Simulations......Page 469 E. Analysis of MD Simulations......Page 470 REFERENCES......Page 472 I. INTRODUCTION......Page 478 A. System Size and Construction......Page 480 B. Force Fields......Page 481 C. Ensembles......Page 483 B. Density Profiles......Page 484 C. Solvation of the Lipid Polar Groups......Page 486 Dipole Potential......Page 487 B. Qualitative Picture on the 100 ps Time Scale......Page 489 C. Incoherent Neutron Scattering Measurements of Lipid Dynamics......Page 490 on Lipid Dynamics......Page 492 E. Lipid Center- of- Mass ‘‘ Diffusion’’......Page 498 F. Hydrocarbon Chain Dynamics......Page 501 G. Water Dynamics......Page 504 V. SUMMARY AND CONCLUSIONS......Page 506 REFERENCES......Page 507 A. Internet Resources for Topics in Selected Chapters......Page 510 B. Molecular Modeling and Simulation Packages......Page 511 C. Molecular Visualization Software......Page 512 Molecular Modeling Software......Page 513 H. Databases of Biological Molecules......Page 514 Index......Page 516 Pt. 1. Computational Methods -- Introduction / Oren M. Becker -- Atomistic Models And Force Fields / Alexander D. Mackerell, Jr. -- Dynamic Methods / Oren M. Becker -- Confrontational Analysis / Oren M. Becker -- Treatment Of Long-range Forces And Potential / Thomas A. Darden -- Internal Coordinate Simulation Method / Alexey K. Mazur -- Implicit Solvent Models / Benoit Roux -- Normal Mode Analysis Of Biological Molecules / Steven Hayward -- Free Energy Calculations / Thomas Simonson -- Reaction Rates And Transition Pathways / John E. Straub -- Computer Simulation Of Biochemical Reactions With Qm-mm Methods / Paul D. Lyne -- Pt. 2. Experimental Data Analysis -- X-ray And Neutron Scattering As Probes Of The Dynamics Of Biological Molecules / Jeremy C. Smith -- Applications Of Molecular Modeling In Nmr Structure Determination / Michael Nilges -- Pt. 3. Modeling And Design -- Comparative Protein Structure Modeling / Andrãs Fiser -- Bayesian Statistics In Molecular And Structural Biology / Roland L. Dunbrack, Jr. -- Computer Aided Drug Design / Alexander Tropsha -- Pt. 4. Advanced Applications -- Protein Folding: Computational Approaches / Oren M. Becker -- Simulations Of Electron Transfer Proteins / Toshiko Ichiye -- The Rism-scf/mcscf Approach For Chemical Processes In Solutions / Fumio Hirata -- Nucleic Acid Simulations / Alexander D. Mackerell, Jr. -- Membrane Simulations / Douglas J. Tobias. Edited By Oren M. Becker ... [et Al.]. Includes Bibliographical References And Index.