Models and Algorithms for Biomolecules and Molecular Networks

List of Figures xiii List of Tables xix Foreword xxi Acknowledgments xxiii 1 Geometric Models of Protein Structure and Function Prediction 1 1.1 Introduction, 1 1.2 Theory and Model, 2 1.2.1 Idealized Ball Model, 2 1.2.2 Surface Models of Proteins, 3 1.2.3 Geometric Constructs, 4 1.2.4 Topological Structures, 6 1.2.5 Metric Measurements, 9 1.3 Algorithm and Computation, 13 1.4 Applications, 15 1.4.1 Protein Packing, 15 1.4.2 Predicting Protein Functions from Structures, 17 1.5 Discussion and Summary, 20 References, 22 Exercises, 25 2 Scoring Functions for Predicting Structure and Binding of Proteins 29 2.1 Introduction, 29 2.2 General Framework of Scoring Function and Potential Function, 31 2.2.1 Protein Representation and Descriptors, 31 2.2.2 Functional Form, 32 2.2.3 Deriving Parameters of Potential Functions, 32 2.3 Statistical Method, 32 2.3.1 Background, 32 2.3.2 Theoretical Model, 33 2.3.3 Miyazawa--Jernigan Contact Potential, 34 2.3.4 Distance-Dependent Potential Function, 41 2.3.5 Geometric Potential Functions, 45 2.4 Optimization Method, 49 2.4.1 Geometric Nature of Discrimination, 50 2.4.2 Optimal Linear Potential Function, 52 2.4.3 Optimal Nonlinear Potential Function, 53 2.4.4 Deriving Optimal Nonlinear Scoring Function, 55 2.4.5 Optimization Techniques, 55 2.5 Applications, 55 2.5.1 Protein Structure Prediction, 56 2.5.2 Protein--Protein Docking Prediction, 56 2.5.3 Protein Design, 58 2.5.4 Protein Stability and Binding Affinity, 59 2.6 Discussion and Summary, 60 2.6.1 Knowledge-Based Statistical Potential Functions, 60 2.6.2 Relationship of Knowledge-Based Energy Functions and Further Development, 64 2.6.3 Optimized Potential Function, 65 2.6.4 Data Dependency of Knowledge-Based Potentials, 66 References, 67 Exercises, 75 3 Sampling Techniques: Estimating Evolutionary Rates and Generating Molecular Structures 79 3.1 Introduction, 79 3.2 Principles of Monte Carlo Sampling, 81 3.2.1 Estimation Through Sampling from Target Distribution, 81 3.2.2 Rejection Sampling, 82 3.3 Markov Chains and Metropolis Monte Carlo Sampling, 83 3.3.1 Properties of Markov Chains, 83 3.3.2 Markov Chain Monte Carlo Sampling, 85 3.4 Sequential Monte Carlo Sampling, 87 3.4.1 Importance Sampling, 87 3.4.2 Sequential Importance Sampling, 87 3.4.3 Resampling, 91 3.5 Applications, 92 3.5.1 Markov Chain Monte Carlo for Evolutionary Rate Estimation, 92 3.5.2 Sequentail Chain Growth Monte Carlo for Estimating Conformational Entropy of RNA Loops, 95 3.6 Discussion and Summary, 96 References, 97 Exercises, 99 4 Stochastic Molecular Networks 103 4.1 Introduction, 103 4.2 Reaction System and Discrete Chemical Master Equation, 104 4.3 Direct Solution of Chemical Master Equation, 106 4.3.1 State Enumeration with Finite Buffer, 106 4.3.2 Generalization and Multi-Buffer dCME Method, 108 4.3.3 Calculation of Steady-State Probability Landscape, 108 4.3.4 Calculation of Dynamically Evolving Probability Landscape, 108 4.3.5 Methods for State Space Truncation for Simplification, 109 4.4 Quantifying and Controlling Errors from State Space Truncation, 111 4.5 Approximating Discrete Chemical Master Equation, 114 4.5.1 Continuous Chemical Master Equation, 114 4.5.2 Stochastic Differential Equation: Fokker--Planck Approach, 114 4.5.3 Stochastic Differential Equation: Langevin Approach, 116 4.5.4 Other Approximations, 117 4.6 Stochastic Simulation, 118 4.6.1 Reaction Probability, 118 4.6.2 Reaction Trajectory, 118 4.6.3 Probability of Reaction Trajectory, 119 4.6.4 Stochastic Simulation Algorithm, 119 4.7 Applications, 121 4.7.1 Probability Landscape of a Stochastic Toggle Switch, 121 4.7.2 Epigenetic Decision Network of Cellular Fate in Phage Lambda, 123 4.8 Discussions and Summary, 127 References, 128 Exercises, 131 5 Cellular Interaction Networks 135 5.1 Basic Definitions and Graph-Theoretic Notions, 136 5.1.1 Topological Representation, 136 5.1.2 Dynamical Representation, 138 5.1.3 Topological Representation of Dynamical Models, 139 5.2 Boolean Interaction Networks, 139 5.3 Signal Transduction Networks, 141 5.3.1 Synthesizing Signal Transduction Networks, 142 5.3.2 Collecting Data for Network Synthesis, 146 5.3.3 Transitive Reduction and Pseudo-node Collapse, 147 5.3.4 Redundancy and Degeneracy of Networks, 153 5.3.5 Random InteractionNetworks and Statistical Evaluations, 157 5.4 Reverse Engineering of Biological Networks, 159 5.4.1 Modular Response Analysis Approach, 160 5.4.2 Parsimonious Combinatorial Approaches, 166 5.4.3 Evaluation of Quality of the Reconstructed Network, 171 References, 173 Exercises, 178 6 Dynamical Systems and Interaction Networks 183 6.1 Some Basic Control-Theoretic Concepts, 185 6.2 Discrete-Time Boolean Network Models, 186 6.3 Artificial Neural Network Models, 188 6.3.1 Computational Powers of ANNs, 189 6.3.2 Reverse Engineering of ANNs, 190 6.3.3 Applications of ANN Models in Studying Biological Networks, 192 6.4 Piecewise Linear Models, 192 6.4.1 Dynamics of PL Models, 194 6.4.2 Biological Application of PL Models, 195 6.5 Monotone Systems, 200 6.5.1 Definition of Monotonicity, 201 6.5.2 Combinatorial Characterizations and Measure of Monotonicity, 203 6.5.3 Algorithmic Issues in Computing the Degree of Monotonicity M, 207 References, 209 Exercises, 214 7 Case Study of Biological Models 217 7.1 Segment Polarity Network Models, 217 7.1.1 Boolean Network Model, 218 7.1.2 Signal Transduction Network Model, 218 7.2 ABA-Induced Stomatal Closure Network, 219 7.3 Epidermal Growth Factor Receptor Signaling Network, 220 7.4 C. elegans Metabolic Network, 223 7.5 Network for T-Cell Survival and Death in Large Granular Lymphocyte Leukemia, 223 References, 224 Exercises, 225 Glossary 227 Index 229