Molecular Modeling and Simulation: An Interdisciplinary Guide

Tamar Schlick

Contents

Important Note: Chapters 1 and 2 were updated May 18, 2003! Remaining parts below correspond to published book.

	Preface  (PDF)
	Prelude  (PDF)
	Table of Contents  (PDF)
1	Biomolecular Structure and Modeling: Historical Perspective   (PDF) - updated 5/18/03
	1.1 A Multidisciplinary Enterprise       1.1.1 Consilience       1.1.2 What is Molecular Modeling       1.1.3 Need For Critical Assessment       1.1.4 Text Overview 1.2 Molecular Mechanics       1.2.1 Pioneers       1.2.2 Simulation Perspective 1.3 Experimental Progress       1.3.1 Protein Crystallography       1.3.2 DNA Structure       1.3.3 Crystallography       1.3.4 NMR Spectroscopy 1.4 Modern Era       1.4.1 Biotechnology       1.4.2 PCR and Beyond 1.5 Genome Sequencing       1.5.1 Sequencing Overview       1.5.2 Human Genome Chapter 1 References (PDF)
2	Biomolecular Structure and Modeling: Problem and Application Perspective (PDF) - Updated 5/18/03
	2.1 Computational Challenges       2.1.1 Bioinformatics       2.1.2 Structure From Sequence 2.2 Protein Folding       2.2.1 Folding Views       2.2.2 Folding Challenges       2.2.3 Folding Simulations       2.2.4 Chaperones       2.2.5 Unstructured Proteins 2.3 Protein Misfolding       2.3.1 Prions       2.3.2 Infectious Proteins?       2.3.3 Hypotheses       2.3.4 Other Misfolding Processes       2.3.5 Function From Structure 2.4 Practical Applications       2.4.1 Drug Design       2.4.2 AIDS Drugs       2.4.3 Other Drugs       2.4.4 A Long Way To Go       2.4.5 Better Genes       2.4.6 Designer Foods       2.4.7 Designer Materials       2.4.8 Cosmeceuticals Chapter 2 References (PDF)
3	Protein Structure Introduction
	3.1 Machinery of Life       3.1.1 From Tissues to Hormones       3.1.2 Size and Function Variability       3.1.3 Chapter Overview 3.2 Amino Acid Building Blocks       3.2.1 Basic C Unit       3.2.2 Essential and Nonessential Amino Acids       3.2.3 Linking Amino Acids       3.2.4 The Amino Acid Repertoire 3.3 Sequence Variations in Proteins       3.3.1 Globular Proteins       3.3.2 Membrane and Fibrous Proteins       3.3.3 Emerging Patterns from Genome Databases       3.3.4 Sequence Similarity 3.4 Protein Conformation Framework       3.4.1 The Flexible phi and psi and Rigid omega Dihedral Angles       3.4.2 Rotameric Structures       3.4.3 Ramachandran Plots       3.4.4 Conformational Hierarchy
4	Protein Structure Hierarchy
	4.1 Structure Hierarchy 4.2 Helices       4.2.1 Classic - Helix       4.2.2 310 and Helices       4.2.3 Left - Handed - Helix       4.2.4 Collagen Helix 4.3 - Sheets: A Common Secondary Structural Element 4.4 Turns and Loops 4.5 Supersecondary and Tertiary Structure       4.5.1 Complex 3D Networks       4.5.2 Classes in Protein Architecture       4.5.3 Classes are Further Divided into Folds 4.6 - Class Folds       4.6.1 Bundles       4.6.2 Folded Leafs       4.6.3 Hairpin Arrays 4.7 - Class Folds       4.7.1 Anti - Parallel Domains       4.7.2 Parallel and Antiparallel Combinations 4.8 / and + - Class Folds       4.8.1 / Barrels       4.8.2 Open Twisted / Folds       4.8.3 Leucine-Rich / Folds       4.8.4 + Folds 4.9 Number of Folds       4.9.1 Finite Number?       4.9.2 Concerted Target Selection: Structural Genomics 4.10 Quaternary Structure       4.10.1 Viruses       4.10.2 From Ribosomes to Dynamic Networks 4.11 Structure Classification
5	Nucleic Acids Structure Minitutorial
	5.1 DNA, Life's Blueprint       5.1.1 The Kindled Field of Molecular Biology       5.1.2 DNA Processes       5.1.3 Challenges in Nucleic Acid Structure       5.1.4 Chapter Overview 5.2 Basic Building Blocks       5.2.1 Nitrogenous Bases       5.2.2 Hydrogen Bonds       5.2.3 Nucleotides       5.2.4 Polynucleotides       5.2.5 Stabilizing Polynucleotide Interactions       5.2.6 Chain Notation       5.2.7 Atomic Labeling       5.2.8 Torsion Angle Labeling 5.3 Conformational Flexibility       5.3.1 The Furanose Ring       5.3.2 Backbone Torsional Flexibility       5.3.3 The Glycosyl Rotation       5.3.4 Sugar/Glycosyl Combinations       5.3.5 Basic Helical Descriptors       5.3.6 Base - Pair Parameters 5.4 Canonical DNA Forms       5.4.1 B-DNA       5.4.2 A-DNA       5.4.3 Z-DNA       5.4.4 Comparative Features
6	Topics in Nucleic Acids Structure
	6.1 Introduction 6.2 DNA Sequence Effects       6.2.1 Local Deformations       6.2.2 Orientation Preferences in Dinucleotide Steps       6.2.3 Intrinsic DNA Bending in A-Tracts       6.2.4 Sequence Deformability Analysis Continues 6.3 DNA Hydration and Ion Interactions       6.3.1 Resolution Difficulties       6.3.2 Basic Patterns 6.4 DNA/Protein Interactions       Supplement to section 6.4 6.5 Variations on a Theme       6.5.1 Hydrogen Bonding Patterns in Polynucleotides       6.5.2 Hybrid Helical/Nonhelical Forms       6.5.3 Overstretched and Understretched DNA 6.6 RNA Structure       6.6.1 RNA Chains Fold Upon Themselves       6.6.2 RNA's Diversity       6.6.3 RNA at Atomic Resolution       6.6.4 Emerging Themes in RNA Structure and Folding 6.7 Cellular Organization of DNA       6.7.1 Compaction of Genomic DNA       6.7.2 Coiling of the DNA Helix Itself       6.7.3 Chromosomal Packaging of Coiled DNA 6.8 Mathematical Characterization of DNA Supercoiling       6.8.1 DNA Topology and Geometry 6.9 Computational Treatments of DNA Supercoiling       6.9.1 DNA as a Flexible Polymer       6.9.2 Elasticity Theory Framework       6.9.3 Simulations of DNA Supercoiling
7	Theoretical and Computational Approaches to Biomolecular Structure
	7.1 Merging of Theory and Experiment       7.1.1 Exciting Times for Computationalists!       7.1.2 The Future of Biocomputations       7.1.3 Chapter Overview 7.2 QM Foundations       7.2.1 The Schrodinger Wave Equation       7.2.2 The Born-Oppenheimer Approximation       7.2.3 Ab Initio       7.2.4 Semi-Empirical QM       7.2.5 Recent Advances in Quantum Mechanics       7.2.6 From Quantum to Molecular Mechanics 7.3 Molecular Mechanics Principles       7.3.1 The Thermodynamic Hypothesis       7.3.2 Additivity       7.3.3 Transferability 7.4 Molecular Mechanics Formulation       7.4.1 Configuration Space       7.4.2 Functional Form       7.4.3 Some Current Limitations
8	Force Fields
	8.1 Formulation of the Model and Energy 8.2 Normal Modes       8.2.1 Characteristic Motions       8.2.2 Spectra of Biomolecules       8.2.3 Spectra As Force Constant Sources       8.2.4 In-Plane and Out-of-Plane Bending 8.3 Bond Length Potentials       8.3.1 Harmonic Term       8.3.2 Morse Term       8.3.3 Cubic and Quartic Term 8.4 Bond Angle Potentials       8.4.1 Harmonic and Trigonometric Terms       8.4.2 Cross Bond Stretch / Angle Bend Terms 8.5 Torsional Potentials       8.5.1 Origin of Rotational Barriers       8.5.2 Fourier Terms       8.5.3 Torsional Parameter Assignment       8.5.4 Improper Torsion       8.5.5 Cross Dihedral/Bond Angle and Improper/Improper Dihedral Terms 8.6 van der Waals Potential       8.6.1 Rapidly Decaying Potential       8.6.2 Parameter Fitting From Experiment       8.6.3 Two Parameter Calculation Protocols 8.7 Coulombic Potential       8.7.1 Coulomb's Law: Slowly Decaying Potential       8.7.2 Dielectric Function       8.7.3 Partial Charges 8.8 Parameterization       8.8.1 A Package Deal       8.8.2 Force Field Performance
9	Nonbonded Computations
	9.1 Computational Bottleneck 9.2 Reducing Computational Cost       9.2.1 Simple Cutoff Schemes       9.2.2 Ewald and Multipole Schemes 9.3 Spherical Cutoff Techniques       9.3.1 Technique Categories       9.3.2 Guidelines for Cutoff Functions       9.3.3 General Cutoff Formulations       9.3.4 Potential Switch       9.3.5 Force Switch       9.3.6 Shift Functions 9.4 Ewald Method       9.4.1 Periodic Boundary Conditions       9.4.2 Ewald Sum and Crystallography       9.4.3 Morphing a Conditionally Convergent Sum       9.4.4 Finite-Dielectric Correction       9.4.5 Ewald Sum Complexity       9.4.6 Resulting Ewald Summation       9.4.7 Practical Implementation 9.5 Multipole Method       9.5.1 Basic Hierarchical Strategy       9.5.2 Historical Perspective       9.5.3 Expansion in Spherical Coordinates       9.5.4 Biomolecular Implementations       9.5.5 Other Variants 9.6 Continuum Solvation       9.6.1 Need for Simplification!       9.6.2 Potential of Mean Force       9.6.3 Stochastic Dynamics       9.6.4 Continuum Electrostatics
10	Multivariate Minimization in Computational Chemistry
	10.1 Optimization Applications       10.1.1 Algorithmic Understanding Needed       10.1.2 Chapter Overview 10.2 Fundamentals       10.2.1 Problem Formulation       10.2.2 Independent Variables       10.2.3 Function Characteristics       10.2.4 Local and Global Minima       10.2.5 Derivatives       10.2.6 Hessian Matrix 10.3 Basic Algorithms       10.3.1 Greedy Descent       10.3.2 Line Searches       10.3.3 Trust Region Methods       10.3.4 Convergence Criteria 10.4 Newton's Method       10.4.1 Newton in One Dimension       10.4.2 Newton's Method for Minimization       10.4.3 Multivariate Newton 10.5 Large-Scale methods       10.5.1 Quasi-Newton (QN)       10.5.2 Conjugate Gradient (CG)       10.5.3 Truncated-Newton (TN)       10.5.4 Simple Example 10.6 Software       10.6.1 Popular Newton and CG       10.6.2 CHARMM's ABNR       10.6.3 CHARMM's TN       10.6.4 Comparative Performance on Molecular Systems 10.7 Recommendations 10.8 Future Outlook
11	Monte Carlo Techniques
	11.1 Monte Carlo Popularity       11.1.1 A Winning Combination       11.1.2 From Needles to Bombs       11.1.3 Chapter Overview       11.1.4 Importance of Error Bars 11.2 Random Number Generators       11.2.1 What is Random?       11.2.2 Properties of Generators?       11.2.3 Linear Congruential Generators       11.2.4 Other Generators       11.2.5 Artifacts       11.2.6 Recommendations 11.3 Gaussian Random Variates       11.3.1 Manipulation of Uniform Random Variables       11.3.2 Normal Variates in Molecular Simulations       11.3.3 Odeh/Evans       11.3.4 Box/Muller/Marsaglia 11.4 Monte Carlo Means       11.4.1 Expected Values       11.4.2 Error Bars       11.4.3 Batch Means 11.5 Monte Carlo Sampling       11.5.1 Probability Density Function       11.5.2 Equilibria or Dynamics       11.5.3 Ensembles       11.5.4 Importance Sampling 11.6 Hybrid MC       11.6.1 MC and MD       11.6.2 Basic Idea       11.6.3 Variants and Other Hybrid Approaches
12	Molecular Dynamics: Basics
	12.1 Introduction       12.1.1 Why Molecular Dynamics?       12.1.2 Background       12.1.3 Outline of MD Chapters 12.2 Laplace's Vision       12.2.1 The Dream       12.2.2 Deterministic Mechanics       12.2.3 Neglect of Electronic Motion       12.2.4 Critical Frequencies       12.2.5 Electronic/Nuclear Treatment 12.3 Basics       12.3.1 Following Motion       12.3.2 Trajectory Quality       12.3.3 Initial System Setting       12.3.4 Trajectory Sensitivity       12.3.5 Simulation Protocol       12.3.6 High-Speed Implementations       12.3.7 Analysis and Visualization       12.3.8 Reliable Numerical Integration       12.3.9 Computational Complexity 12.4 Verlet Algorithm       12.4.1 Position and Velocity Propagation       12.4.2 Leapfrog, Velocity Verlet, and Position Verlet 12.5 Constrained Dynamics 12.6 Various MD Ensembles       12.6.1 Ensemble Types       12.6.2 Simple Algorithms       12.6.3 Extended System Methods
13	Molecular Dynamics: Further Topics
	13.1 Introduction 13.2 Symplectic Integrators       13.2.1 Symplectic Transformation       13.2.2 Harmonic Oscillator Example       13.2.3 Linear Stability       13.2.4 Timestep-Dependent Rotation in Phase Space       13.2.5 Resonance Condition for Periodic Motion       13.2.6 Resonance Artifacts 13.3 Multiple-Timestep (MTS) Methods       13.3.1 Basic Idea       13.3.2 Extrapolation       13.3.3 Impulses       13.3.4 Resonances in Impulse Splitting       13.3.5 Resonance Artifacts in MTS       13.3.6 Resonance Consequences 13.4 Langevin Dynamics       13.4.1 Uses       13.4.2 Heat Bath       13.4.3 Effect of       13.4.4 Generalized Verlet for Langevin Dynamics       13.4.5 LN Method 13.5 Brownian Dynamics (BD)       13.5.1 Brownian Motion       13.5.2 Brownian Framework       13.5.3 General Propagation Framework       13.5.4 Hydrodynamics       13.5.5 BD Propagation 13.6 Implicit Integration       13.6.1 Implicit vs. Explicit Euler       13.6.2 Intrinsic Damping       13.6.3 Computational Time       13.6.4 Resonance Artifacts 13.7 Future Outlook       13.7.1 Integration Ingenuity       13.7.2 Current Challenges
14	Similarity and Diversity in Chemical Design
	14.1 Introduction to Drug Design       14.1.1 Chemical Libraries       14.1.2 Early Days       14.1.3 Rational Drug Design       14.1.4 Automated Technology       14.1.5 Chapter Overview 14.2 Database Problems       14.2.1 Database Analysis       14.2.2 Similarity and Diversity Sampling       14.2.3 Bioactivity 14.3 General Problem Definitions       14.3.1 The Dataset       14.3.2 The Compound Descriptors       14.3.3 Biological Activity       14.3.4 The Target Function       14.3.5 Scaling Descriptors       14.3.6 The Similarity and Diversity Problem 14.4 Data Compression and Cluster Analysis       14.4.1 PCA compression       14.4.2 SVD compression       14.4.3 PCA and SVD       14.4.4 Projection Application       14.4.5 Example 14.5 Future Perspectives
Appendix A Syllabus  (PDF)
Appendix B Article Reading List
Appendix C General Reference List
Appendix D Homeworks
Bibliography
References

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