Copyright 4
About the Cover 5
Book URLs 8
Preface 9
Prelude 17
Contents 18
List of Figures 30
List of Tables 35
Acronyms, Abbreviations, and Units 37
1 Biomolecular Structure and Modeling: Historical Perspective 42
1.1 A Multidisciplinary Enterprise 43
1.1.1 Consilience 43
1.1.2 What is Molecular Modeling? 44
1.1.3 Need For Critical Assessment 46
1.1.4 Text Overview 47
1.2 The Roots of Molecular Modeling in Molecular Mechanics 49
1.2.1 The Theoretical Pioneers 49
1.2.2 Biomolecular Simulation Perspective 52
Representative Progress 53
Trends 55
1.3 Emergence of Biomodeling from Experimental Progressin Proteins and Nucleic Acids 55
1.3.1 Protein Crystallography 55
1.3.2 DNA Structure 58
1.3.3 The Technique of X-ray Crystallography 59
1.3.4 The Technique of NMR Spectroscopy 61
1.4 Modern Era of Technological Advances 63
1.4.1 From Biochemistry to Biotechnology 63
1.4.2 PCR and Beyond 64
1.5 Genome Sequencing 66
1.5.1 Projects Overview: From Bugs to Baboons 66
Roundworm, C. elegans (1998) 67
Fruitfly, Drosophila (1999) 67
Mustard Plant, Arabidopsis (2000) 68
Mouse (2001, 2002) 69
Rice (2002) 70
Pufferfish, Fugu (2002) 70
Homo Sapiens (2003) 70
Other Organisms 71
1.5.2 The Human Genome 71
Milestones 72
A Triumph of Technology 74
A Gold Mine of Biodata 76
Implications
Some Application Examples 76
Ongoing Challenges and Ramifications 79
2 Biomolecular Structure and Modeling: Problem and Application Perspective 82
2.1 Computational Challenges in Structure and Function 82
2.1.1 Analysis of the Amassing Biological Databases 82
2.1.2 Computing Structure From Sequence 87
2.2 Protein Folding
An Enigma 87
2.2.1 'Old' and 'New' Views 87
2.2.2 Folding Challenges 89
2.2.3 Folding by Dynamics Simulations? 90
2.2.4 Folding Assistants 91
2.2.5 Unstructured Proteins 93
2.3 Protein Misfolding
A Conundrum 94
2.3.1 Prions and Mad Cows 94
2.3.2 Infectious Protein? 94
2.3.3 Other Possibilities 95
2.3.4 Other Misfolding Processes 96
2.3.5 Deducing Function From Structure 97
2.4 From Basic to Applied Research 98
2.4.1 Rational Drug Design: Overview 99
2.4.2 A Classic Success Story: AIDS Therapy 99
HIV Enzymes 99
AIDS Drug Development 101
AIDS Drug Limitations 102
Lurking Virus 103
Vaccine? 104
2.4.3 Other Drugs and Future Prospects 106
Success Stories 106
Impact of Technology and Modeling 106
Declining Productivity 107
2.4.4 Gene Therapy
Better Genes 108
2.4.5 Designed Compounds and Foods 110
2.4.6 Nutrigenomics 113
2.4.7 Designer Materials 115
2.4.8 Cosmeceuticals 115
3 Protein Structure Introduction 117
3.1 The Machinery of Life 117
3.1.1 From Tissues to Hormones 117
3.1.2 Size and Function Variability 118
3.1.3 Chapter Overview 119
3.2 The Amino Acid Building Blocks 122
3.2.1 Basic C Unit 122
3.2.2 Essential and Nonessential Amino Acids 123
3.2.3 Linking Amino Acids 125
3.2.4 The Amino Acid Repertoire: From FlexibleGlycine to Rigid Proline 125
Aliphatic R: Gly, Ala, Val, Leu, Ile 127
Rigid Proline 128
Aliphatic Hydroxyl R: Ser, Thr 128
Acidic R and Amide Derivatives: Asn, Gln, Asp, Glu 128
Basic R: Lys, Arg, His 128
Aromatic R: Phe, Tyr, Trp 128
Sulfur-Containing R: Met, Cys 129
3.3 Sequence Variations in Proteins 129
3.3.1 Globular Proteins 130
3.3.2 Membrane and Fibrous Proteins 130
3.3.3 Emerging Patterns from Genome Databases 132
3.3.4 Sequence Similarity 132
Sequence Similarity Generally Implies Structure Similarity 132
Exceptions Exist 134
3.4 Protein Conformation Framework 137
3.4.1 The Flexible 蠁 and 蠄 and Rigid 蠅 Dihedral Angles 137
3.4.2 Rotameric Structures 139
3.4.3 Ramachandran Plots 139
3.4.4 Conformational Hierarchy 143
4 Protein Structure Hierarchy 145
4.1 Structure Hierarchy 146
4.2 Helices: A Common Secondary Structural Element 146
4.2.1 Classic 伪-Helix 146
4.2.2 310 and 蟺 Helices 147
4.2.3 Left-Handed 伪-Helix 149
4.2.4 Collagen Helix 150
4.3 尾-Sheets: A Common Secondary Structural Element 150
4.4 Turns and Loops 150
4.5 Formation of Supersecondary and Tertiary Structure 153
4.5.1 Complex 3D Networks 153
4.5.2 Classes in Protein Architecture 153
4.5.3 Classes are Further Divided into Folds 154
4.6 伪-Class Folds 154
4.6.1 Bundles 154
4.6.2 Folded Leafs 155
4.6.3 Hairpin Arrays 155
4.7 尾-Class Folds 155
4.7.1 Anti-Parallel 尾 Domains 156
Two-Strand Units 156
Four-Strand Units 156
Eight-Strand Units 156
4.7.2 Parallel and Antiparallel Combinations 156
Sandwiches and Barrels 157
Propellers 157
Other 尾-Folds 157
4.8 伪/尾 and 伪+尾-Class Folds 157
4.8.1 伪/尾 Barrels 157
4.8.2 Open Twisted 伪/尾 Folds 158
4.8.3 Leucine-Rich 伪/尾 Folds 158
4.8.4 伪+尾 Folds 158
4.8.5 Other Folds 158
4.9 Number of Folds 158
4.9.1 Finite Number? 159
4.10 Quaternary Structure 159
4.10.1 Viruses 159
4.10.2 From Ribosomes to Dynamic Networks 163
4.11 Protein Structure Classification 166
5 Nucleic Acids Structure Minitutorial 169
5.1 DNA, Life's Blueprint 170
5.1.1 The Kindled Field of Molecular Biology 170
5.1.2 Fundamental DNA Processes 172
5.1.3 Challenges in Nucleic Acid Structure 173
5.1.4 Chapter Overview 174
5.2 The Basic Building Blocks of Nucleic Acids 175
5.2.1 Nitrogenous Bases 175
5.2.2 Hydrogen Bonds 176
5.2.3 Nucleotides 177
5.2.4 Polynucleotides 177
5.2.5 Stabilizing Polynucleotide Interactions 180
5.2.6 Chain Notation 180
5.2.7 Atomic Labeling 181
5.2.8 Torsion Angle Labeling 182
5.3 Nucleic Acid Conformational Flexibility 182
5.3.1 The Furanose Ring 183
5.3.2 Backbone Torsional Flexibility 185
5.3.3 The Glycosyl Rotation 188
5.3.4 Sugar/Glycosyl Combinations 188
5.3.5 Basic Helical Descriptors 190
5.3.6 Base-Pair Parameters 191
Reference Frame 192
Global Variables (Base Pair Orientations With Respect to Helical Axis) 193
Local Variables (Base-Pair Step Orientations) 194
Deviations Within a Base Pair 194
5.4 Canonical DNA Forms 195
5.4.1 B-DNA 196
5.4.2 A-DNA 197
5.4.3 Z-DNA 200
Biological Significance 201
5.4.4 Comparative Features 201
6 Topics in Nucleic Acids Structure: DNA Interactionsand Folding 203
6.1 Introduction 204
6.2 DNA Sequence Effects 205
6.2.1 Local Deformations 205
6.2.2 Orientation Preferences in Dinucleotide Steps 206
6.2.3 Orientation Preferences in Dinucleotide StepsWith Flanking Sequence Context: TetranucleotideStudies 209
6.2.4 Intrinsic DNA Bending in A-Tracts 209
6.2.5 Sequence Deformability Analysis Continues 213
6.3 DNA Hydration and Ion Interactions 214
6.3.1 Resolution Difficulties 215
6.3.2 Basic Patterns 216
6.4 DNA/Protein Interactions 220
6.5 Cellular Organization of DNA 222
6.5.1 Compaction of Genomic DNA 222
6.5.2 Coiling of the DNA Helix Itself 224
6.5.3 Chromosomal Packaging of Coiled DNA 225
The Nucleosome: DNA + Histones 226
Nucleosome Structure 226
Polynucleosome Assembly 228
6.6 Mathematical Characterization of DNA Supercoiling 235
6.6.1 DNA Topology and Geometry 235
Basic Topological Identity 235
Linking Number 235
Twist 236
Writhe 237
6.7 Computational Treatments of DNA Supercoiling 237
6.7.1 DNA as a Flexible Polymer 238
6.7.2 Elasticity Theory Framework 239
6.7.3 Simulations of DNA Supercoiling 240
7 Topics in Nucleic Acids Structure: Noncanonical Helicesand RNA Structure 245
7.1 Introduction 245
7.2 Variations on a Theme 246
7.2.1 Hydrogen Bonding Patterns in Polynucleotides 246
Classic Watson-Crick (WC) 246
Reverse WC 247
Hoogsteen 247
Reverse Hoogsteen 248
Mismatches and Wobbles 249
Other Patterns 250
7.2.2 Hybrid Helical/Nonhelical Forms 250
Alternative Helical Geometries 250
DNA Triplexes and Quadruplexes 251
DNA Mimics 252
7.2.3 Unusual Forms: Overstretched and UnderstretchedDNA 254
Single-Molecule Manipulations 254
Biological Relevance and Other Applications 254
7.3 RNA Structure and Function 256
7.3.1 DNA's Cousin Shines 256
7.3.2 RNA Chains Fold Upon Themselves 256
7.3.3 RNA's Diversity 257
7.3.4 Non-Coding and Micro-RNAs 261
7.3.5 RNA at Atomic Resolution 262
7.4 Current Challenges in RNA Modeling 265
7.4.1 RNA Folding 265
7.4.2 RNA Motifs 265
7.4.3 RNA Structure Prediction 266
7.5 Application of Graph Theory to Studies of RNA Structureand Function 269
7.5.1 Graph Theory 269
7.5.2 RNA-As-Graphs (RAG) Resource 270
RNA Structure Enumeration 271
RNA-Like Motifs 271
RNA Design 272
8 Theoretical and Computational Approaches to BiomolecularStructure 277
8.1 The Merging of Theory and Experiment 278
8.1.1 Exciting Times for Computationalists! 278
8.1.2 The Future of Biocomputations 280
8.1.3 Chapter Overview 280
8.2 Quantum Mechanics (QM) Foundations of Molecular Mechanics (MM) 281
8.2.1 The Schr枚dinger Wave Equation 281
8.2.2 The Born-Oppenheimer Approximation 282
8.2.3 Ab Initio QM 282
Density Functional Theory (DFT) 283
8.2.4 Semi-Empirical QM 284
8.2.5 Recent Advances in Quantum Mechanics 284
Linear Scaling 284
Biomolecular Applications 285
8.2.6 From Quantum to Molecular Mechanics 287
Mechanical Molecular Representation 287
Early Days 287
8.3 Molecular Mechanics: Underlying Principles 291
8.3.1 The Thermodynamic Hypothesis 291
Does Sequence Imply Structure? 291
8.3.2 Additivity 292
Local Terms 293
Nonlocal Terms 293
Benefits of Separability 293
Multibody Potentials 294
8.3.3 Transferability 294
Functional Variations in Geometry 295
Proliferation of Atom Types 295
8.4 Molecular Mechanics: Model and Energy Formulation 296
8.4.1 Configuration Space 298
A Question of Size 298
The Pseudorotation Description 299
Cartesian Space 299
8.4.2 Functional Form 299
Composition 299
Molecular Geometry 300
8.4.3 Some Current Limitations 302
9 Force Fields 305
9.1 Formulation of the Model and Energy 306
9.2 Normal Modes 307
9.2.1 Quantifying Characteristic Motions 307
Experimental Determination 308
Frequency Units 308
Illustration 308
9.2.2 Complex Biomolecular Spectra 309
9.2.3 Spectra As Force Constant Sources 309
9.2.4 In-Plane and Out-of-Plane Bending 311
9.3 Bond Length Potentials 312
9.3.1 Harmonic Term 313
9.3.2 Morse Term 314
9.3.3 Cubic and Quartic Terms 315
9.4 Bond Angle Potentials 316
9.4.1 Harmonic and Trigonometric Terms 317
9.4.2 Cross Bond Stretch / Angle Bend Terms 318
9.5 Torsional Potentials 321
9.5.1 Origin of Rotational Barriers 321
9.5.2 Fourier Terms 321
9.5.3 Torsional Parameter Assignment 322
Twofold and Threefold Sums 323
Reproduction of Cis/Trans and Trans/Gauche Energy Differences 323
Model Compounds 325
9.5.4 Improper Torsion 326
9.5.5 Cross Dihedral/Bond Angle and Improper/ImproperDihedral Terms 327
9.6 The van der Waals Potential 328
9.6.1 Rapidly Decaying Potential 328
9.6.2 Parameter Fitting From Experiment 329
9.6.3 Two Parameter Calculation Protocols 329
Energy Minimum/Distance Procedure (Vij, r0ij) 329
Slater-Kirkwood Procedure (Aij, Bij) 330
9.7 The Coulomb Potential 331
9.7.1 Coulomb's Law: Slowly Decaying Potential 331
9.7.2 Dielectric Function 332
Sigmoidal Function 332
9.7.3 Partial Charges 334
9.8 Parameterization 335
9.8.1 A Package Deal 335
9.8.2 Force Field Comparisons 335
9.8.3 Force Field Performance 337
10 Nonbonded Computations 339
10.1 A Computational Bottleneck 341
10.2 Approaches for Reducing Computational Cost 342
10.2.1 Simple Cutoff Schemes 342
10.2.2 Ewald and Multipole Schemes 343
10.3 Spherical Cutoff Techniques 344
10.3.1 Technique Categories 344
10.3.2 Guidelines for Cutoff Functions 345
10.3.3 General Cutoff Formulations 346
Truncation 347
Switch/Shift 347
Atoms/Groups 347
Energy/Force Modifications 347
10.3.4 Potential Switch 347
10.3.5 Force Switch 348
Buffer Parameters 349
10.3.6 Shift Functions 349
10.4 The Ewald Method 351
10.4.1 Periodic Boundary Conditions 351
Space-Filling Polyhedra 351
Minimum-Image Convention 351
Choice of Geometry 352
10.4.2 Ewald Sum and Crystallography 354
10.4.3 Mathematical Morphing of a ConditionallyConvergent Sum 356
Coulomb Energy in Periodic Domains 356
Conditional Convergence 356
Ewald's Trick 357
The Screening Gaussian 蟻Gj 358
10.4.4 Finite-Dielectric Correction 360
10.4.5 Ewald Sum Complexity 360
Optimization of 尾 360
Mesh Interpolation 360
Variations 361
10.4.6 Resulting Ewald Summation 361
10.4.7 Practical Implementation: Parameters, Accuracy,and Optimization 362
Gaussian Width 362
Grid Size and Accuracy 363
Computer Architecture Considerations 363
10.5 The Multipole Method 364
10.5.1 Basic Hierarchical Strategy 364
Series Expansion 365
Domain Decomposition 365
Summation Protocol 366
10.5.2 Historical Perspective 369
Hierarchical Refinements 369
Hierarchical Protocol 369
O (N logN) Work 370
Fast Multipole Machinery (O (N)) 370
10.5.3 Expansion in Spherical Coordinates 370
10.5.4 Biomolecular Implementations 372
10.5.5 Other Variants 373
10.6 Continuum Solvation 373
10.6.1 Need for Simplification! 373
10.6.2 Potential of Mean Force 374
Balancing Biophysics with Numerics 374
Electrostatic and Non-Electrostatic Components 374
Variations 374
10.6.3 Stochastic Dynamics 375
The Langevin Equation 375
Langevin Parameters from Hydrodynamic and Other Considerations 376
The Brownian Limit 377
10.6.4 Continuum Electrostatics 378
Gauss' Law for the Electrostatic Potential 378
The Poisson-Boltzmann Equation 379
Linear Approximations to the PB Equation; Debye-H眉ckel Theory 380
General Solutions to the Poisson-Boltzmann Equation 382
Algorithmic Challenges 384
11 Multivariate Minimization in Computational Chemistry 385
11.1 Ubiquitous Optimization: From Enzymes to Weather to Economics 387
11.1.1 Algorithmic Sophistication Demands BasicUnderstanding 387
11.1.2 Chapter Overview 387
11.2 Optimization Fundamentals 388
11.2.1 Problem Formulation 388
11.2.2 Independent Variables 389
11.2.3 Function Characteristics 389
Linear and Quadratic Functions 389
Least-Squares Functions 390
Separable Functions 390
Nonsmooth Functions 390
Potential Energy Functions 390
11.2.4 Local and Global Minima 391
Definitions 391
Convergence 392
11.2.5 Derivatives of Multivariate Functions 393
Gradient 393
Hessian and Curvature 393
11.2.6 The Hessian of Potential Energy Functions 393
Sparsity 393
Memory Intensity 395
Exploitation of Derivatives 396
11.3 Basic Algorithmic Components 396
11.3.1 Greedy Descent 396
Two Frameworks 396
Algorithmic Parameters 396
11.3.2 Line-Search-Based Descent Algorithm 399
Step 2: Descent Direction 399
Steepest Descent 400
Step 3: The One-Dimensional Optimization Subproblem (Line Search) 400
11.3.3 Trust-Region-Based Descent Algorithm 401
Basic Idea 401
11.3.4 Convergence Criteria 402
11.4 The Newton-Raphson-Simpson-Fourier Method 404
A Fundamental Optimization Tool 404
11.4.1 The One-Dimensional Version of Newton's Method 404
Iterative Recipe 404
Geometric Interpretation 405
Performance 405
11.4.2 Newton's Method for Minimization 407
11.4.3 The Multivariate Version of Newton's Method 408
11.5 Effective Large-Scale Minimization Algorithms 409
11.5.1 Quasi-Newton (QN) 410
Basic Idea 410
Recent Advances 410
QN Condition 410
Updating Formula 411
BFGS Method 411
Practical Implementation 411
11.5.2 Conjugate Gradient (CG) 412
CG Search Vector 412
CG Variants 412
CG/QN Connection 413
Recent CG Advances 413
11.5.3 Truncated-Newton (TN) 414
Approximate Solution of the Newton Equations 414
Truncated Outer Iteration; Effective Residual 414
Preconditioning 415
Overall Work 415
Hessian/Vector Products 415
Performance 416
11.5.4 Simple Example 416
11.6 Available Software 418
11.6.1 Popular Newton and CG 418
11.6.2 CHARMM's ABNR 419
11.6.3 CHARMM's TN 419
11.6.4 Comparative Performance on Molecular Systems 419
11.7 Practical Recommendations 420
11.8 Future Outlook 423
12 Monte Carlo Techniques 425
12.1 MC Popularity 426
12.1.1 A Winning Combination 426
12.1.2 From Needles to Bombs 427
12.1.3 Chapter Overview 427
12.1.4 Importance of Error Bars 428
12.2 Random Number Generators 428
12.2.1 What is Random? 428
12.2.2 Properties of Generators 429
Uniformity and Subtle Correlations 429
Long Period 430
Portability 431
Efficiency 431
12.2.3 Linear Congruential Generators (LCG) 432
Basic Recipe 432
Simple Example 433
IBM's SURAND and Unix's rand and drand48 433
Lattice Structure in Linear Congruential Generators 435
12.2.4 Other Generators 436
Fibonacci Series 436
Shift-Register Generators 438
Combination Generators 438
12.2.5 Artifacts 440
12.2.6 Recommendations 441
12.3 Gaussian Random Variates 443
12.3.1 Manipulation of Uniform Random Variables 443
12.3.2 Normal Variates in Molecular Simulations 443
12.3.3 Odeh/Evans Method 444
12.3.4 Box/Muller/Marsaglia Method 445
12.4 Means for Monte Carlo Sampling 446
12.4.1 Expected Values 446
MC Estimate 446
Simple Example: Calculate 蟺 by MC 446
12.4.2 Error Bars 449
Law of Large Numbers 449
Variance 449
Variance Relation to Central Limit Theorem 449
12.4.3 Batch Means 450
12.5 Monte Carlo Sampling 451
12.5.1 Density Function 451
12.5.2 Dynamic and Equilibrium MC: Ergodicity,Detailed Balance 451
Dynamic Process 451
Equilibrium Process 451
12.5.3 Statistical Ensembles 452
Canonical Ensemble and Boltzmann Factor 452
12.5.4 Importance Sampling: Metropolis Algorithmand Markov Chains 453
Markov Chain 454
Metropolis Algorithm 454
Simulated Annealing 455
Metropolis Algorithm Implementation 455
MC Moves 456
12.6 Monte Carlo Applications to Molecular Systems 458
12.6.1 Ease of Application 458
12.6.2 Biased MC 459
12.6.3 Hybrid MC 460
Exploiting Strengths of MC and MD 460
Overall Idea 460
12.6.4 Parallel Tempering and Other MC Variants 461
13 Molecular Dynamics: Basics 464
13.1 Introduction: Statistical Mechanics by Numbers 465
13.1.1 Why Molecular Dynamics? 465
13.1.2 Background 466
13.1.3 Outline of MD Chapters 467
13.2 Laplace's Vision of Newtonian Mechanics 468
13.2.1 The Dream Becomes Reality 468
13.2.2 Deterministic Mechanics 471
13.2.3 Neglect of Electronic Motion 471
13.2.4 Critical Frequencies 472
13.2.5 Hybrid Quantum/Classical Mechanics Treatments 474
13.3 The Basics: An Overview 474
13.3.1 Following the Equations of Motion 474
13.3.2 Perspective on MD Trajectories 475
Force Field Dependency 475
Statics Vs. Dynamics 475
Range of Timescales 475
Challenges 476
13.3.3 Initial System Settings 476
Structure 476
Solvation 476
Velocity 477
Equilibration 478
Illustration 478
13.3.4 Sensitivity to Initial Conditions andOther Computational Choices 479
Chaos and Saturation 479
Statistical View 480
13.3.5 Simulation Protocol 481
13.3.6 High-Speed Implementations 482
13.3.7 Analysis and Visualization 484
13.3.8 Reliable Numerical Integration 484
13.3.9 Computational Complexity 485
Intensive Requirements 485
Less Work Per Step 486
Larger Timesteps: Accuracy vs. Stability 486
Constraining Fastest Motions 486
Splitting Forces in MTS Schemes 487
13.4 The Verlet Algorithm 487
13.4.1 Position and Velocity Propagation 488
Iterative Recipe 488
Position Update 489
Velocity Update 489
13.4.2 Leapfrog, Velocity Verlet, and Position Verlet 490
Leapfrog 490
Velocity Verlet 491
Position Verlet 492
MTS Preference 492
13.5 Constrained Dynamics 492
SHAKE 493
RATTLE 493
Computational Advantage 493
Limitations 493
13.6 Various MD Ensembles 494
13.6.1 Need for Other Ensembles 494
13.6.2 Simple Algorithms 495
Weak Coupling Thermostat for Constant T 495
Weak Coupling Barostat for Constant P 496
13.6.3 Extended System Methods 498
Canonical Ensemble 498
Isothermal-Isobaric Ensemble 499
14 Molecular Dynamics: Further Topics 501
14.1 Introduction 502
14.2 Symplectic Integrators 503
14.2.1 Symplectic Transformation 504
14.2.2 Harmonic Oscillator Example 505
14.2.3 Linear Stability 505
14.2.4 Timestep-Dependent Rotation in Phase Space 507
14.2.5 Resonance Condition for Periodic Motion 508
14.2.6 Resonance Artifacts 509
14.3 Multiple-Timestep (MTS) Methods 510
14.3.1 Basic Idea 510
14.3.2 Extrapolation 511
14.3.3 Impulses 512
14.3.4 Vulnerability of Impulse Splitting to ResonanceArtifacts 513
14.3.5 Resonance Artifacts in MTS 514
Simple Example 515
Extensions to Stochasticity and Nonlinearity 516
14.3.6 Limitations of Resonance Artifacts on Speedup;Possible Cures 516
14.4 Langevin Dynamics 517
14.4.1 Many Uses 517
14.4.2 Phenomenological Heat Bath 518
14.4.3 The Effect of 纬 518
14.4.4 Generalized Verlet for Langevin Dynamics 520
14.4.5 The LN Method 520
Resonance Alleviation 521
Testing and Application 524
14.5 Brownian Dynamics (BD) 525
14.5.1 Brownian Motion 525
14.5.2 Brownian Framework 527
Generalized Friction 527
Neglect of Inertia 527
Transport Properties 528
Algorithms 528
14.5.3 General Propagation Framework 529
Ermak/McCammon 529
14.5.4 Hydrodynamic Interactions 529
Tensor T 530
Oseen Tensor 531
Rotne-Prager Tensor 531
14.5.5 BD Propagation Scheme: Cholesky vs. ChebyshevApproximation 532
14.6 Implicit Integration 534
14.6.1 Implicit vs. Explicit Euler 535
14.6.2 Intrinsic Damping 536
14.6.3 Computational Time 536
14.6.4 Resonance Artifacts 537
IM Analysis 537
A Family of Symplectic Implicit Schemes 539
Perspective 540
14.7 Enhanced Sampling Methods 541
14.7.1 Overview 541
14.7.2 Harmonic-Analysis Based Techniques 541
14.7.3 Other Coordinate Transformations 543
14.7.4 Coarse Graining Models 545
14.7.5 Biasing Approaches 546
14.7.6 Variations in MD Algorithm and Protocol 547
14.7.7 Other Rigorous Approaches for DeducingMechanisms, Free Energies, and Reaction Rates 549
14.8 Future Outlook 551
14.8.1 Integration Ingenuity 551
Many Approaches 551
Resonance 552
14.8.2 Current Challenges 552
PME Protocols 552
Technology's Role 553
Sampling Issues 553
Tip of the Iceberg 554
15 Similarity and Diversity in Chemical Design 556
15.1 Introduction to Drug Design 557
15.1.1 Chemical Libraries 557
15.1.2 Early Drug Development Work 558
15.1.3 Molecular Modeling in Rational Drug Design 560
15.1.4 The Competition: Automated Technology 561
15.1.5 Chapter Overview 563
15.2 Problems in Chemical Libraries 563
15.2.1 Database Analysis 563
15.2.2 Similarity and Diversity Sampling 564
15.2.3 Bioactivity Relationships 566
15.3 General Problem Definitions 569
15.3.1 The Dataset 569
15.3.2 The Compound Descriptors 571
15.3.3 Characterizing Biological Activity 572
15.3.4 The Target Function 573
15.3.5 Scaling Descriptors 573
15.3.6 The Similarity and Diversity Problems 575
15.4 Data Compression and Cluster Analysis 577
15.4.1 Data Compression Based on Principal ComponentAnalysis (PCA) 577
Covariance Matrix and PCs 577
Dimensionality Reduction 578
15.4.2 Data Compression Based on the Singular ValueDecomposition (SVD) 579
SVD Factorization 579
Low-Rank Approximation 580
Projection 581
15.4.3 Relation Between PCA and SVD 581
15.4.4 Data Analysis via PCA or SVD and DistanceRefinement 582
Projection Refinement 582
Distance Geometry 582
15.4.5 Projection, Refinement, and Clustering Example 583
15.5 Future Perspectives 588
Epilogue 591
Appendix A: Molecular Modeling Sample Syllabus 592
Appendix B: Article Reading List 594
Appendix C: Supplementary Course Texts 598
Appendix D: Homework Assignments 605
References 656