Models and Algorithms for Biomolecules and Molecular Networks

Contents

List of Figures

List of Tables

Foreword

Acknowledgments

1: Geometric Models of Protein Structure and Function Prediction

1.1 Introduction

1.2 Theory and Model

1.2.1 Idealized Ball Model

1.2.2 Surface Models of Proteins

1.2.3 Geometric Constructs

1.2.4 Topological Structures

1.2.5 Metric Measurements

1.3 Algorithm and Computation

1.4 Applications

1.4.1 Protein Packing

1.4.2 Predicting Protein Functions from Structures

1.5 Discussion and Summary

References

Exercises

2: Scoring Functions for Predicting Structure and Binding of Proteins

2.1 Introduction

2.2 General Framework of Scoring Function and Potential Function

2.2.1 Protein Representation and Descriptors

2.2.2 Functional Form

2.2.3 Deriving Parameters of Potential Functions

2.3 Statistical Method

2.3.1 Background

2.3.2 Theoretical Model

2.3.3 Miyazawa–Jernigan Contact Potential

2.3.4 Distance-Dependent Potential Function

2.3.5 Geometric Potential Functions

2.4 Optimization Method

2.4.1 Geometric Nature of Discrimination

2.4.2 Optimal Linear Potential Function

2.4.3 Optimal Nonlinear Potential Function

2.4.4 Deriving Optimal Nonlinear Scoring Function

2.4.5 Optimization Techniques

2.5 Applications

2.5.1 Protein Structure Prediction

2.5.2 Protein–Protein Docking Prediction

2.5.3 Protein Design

2.5.4 Protein Stability and Binding Affinity

2.6 Discussion And Summary

2.6.1 Knowledge-Based Statistical Potential Functions

2.6.2 Relationship of Knowledge-Based Energy Functions and Further Development

2.6.3 Optimized Potential Function

2.6.4 Data Dependency of Knowledge-Based Potentials

References

Exercises

3: Sampling Techniques: Estimating Evolutionary Rates and Generating Molecular Structures

3.1 Introduction

3.2 Principles of Monte Carlo Sampling

3.2.1 Estimation Through Sampling from Target Distribution

3.2.2 Rejection Sampling

3.3 Markov Chains and Metropolis Monte Carlo Sampling

3.3.1 Properties of Markov Chains

3.3.2 Markov Chain Monte Carlo Sampling

3.4 Sequential Monte Carlo Sampling

3.4.1 Importance Sampling

3.4.2 Sequential Importance Sampling

3.4.3 Resampling

3.5 Applications

3.5.1 Markov Chain Monte Carlo for Evolutionary Rate Estimation

3.5.2 Sequential Chain Growth Monte Carlo for Estimating Conformational Entropy of RNA Loops

3.6 Discussion and Summary

References

Exercises

4: Stochastic Molecular Networks

4.1 Introduction

4.2 Reaction System and Discrete Chemical Master Equation

4.3 Direct Solution of Chemical Master Equation

4.3.1 State Enumeration with Finite Buffer

4.3.2 Generalization and Multi-Buffer dCME Method

4.3.3 Calculation of Steady-State Probability Landscape

4.3.4 Calculation of Dynamically Evolving Probability Landscape

4.3.5 Methods for State Space Truncation for Simplification

4.4 Quantifying and Controlling Errors From State Space Truncation

4.5 Approximating Discrete Chemical Master Equation

4.5.1 Continuous Chemical Master Equation

4.5.2 Stochastic Differential Equation: Fokker–Planck Approach

4.5.3 Stochastic Differential Equation: Langevin Approach

4.5.4 Other Approximations

4.6 Stochastic Simulation

4.6.1 Reaction Probability

4.6.2 Reaction Trajectory

4.6.3 Probability of Reaction Trajectory

4.6.4 Stochastic Simulation Algorithm

4.7 Applications

4.7.1 Probability Landscape of a Stochastic Toggle Switch

4.7.2 Epigenetic Decision Network of Cellular Fate in Phage Lambda

4.8 Discussions and Summary

References

Exercises

5: Cellular Interaction Networks

5.1 Basic Definitions and Graph-Theoretic Notions

5.1.1 Topological Representation

5.1.2 Dynamical Representation

5.1.3 Topological Representation of Dynamical Models

5.2 Boolean Interaction Networks

5.3 Signal Transduction Networks

5.3.1 Synthesizing Signal Transduction Networks

5.3.2 Collecting Data for Network Synthesis

5.3.3 Transitive Reduction and Pseudo-node Collapse

5.3.4 Redundancy and Degeneracy of Networks

5.3.5 Random Interaction Networks and Statistical Evaluations

5.4 Reverse Engineering of Biological Networks

5.4.1 Modular Response Analysis Approach

5.4.2 Parsimonious Combinatorial Approaches

5.4.3 Evaluation of Quality of the Reconstructed Network

References

Exercises

6: Dynamical Systems and Interaction Networks

6.1 Some Basic Control-Theoretic Concepts

6.2 Discrete-Time Boolean Network Models

6.3 Artificial Neural Network Models

6.3.1 Computational Powers of ANNs

6.3.2 Reverse Engineering of ANNs

6.3.3 Applications of ANN Models in Studying Biological Networks

6.4 Piecewise Linear Models

6.4.1 Dynamics of PL Models

6.4.2 Biological Application of PL Models

6.5 Monotone Systems

6.5.1 Definition of Monotonicity

6.5.2 Combinatorial Characterizations and Measure of Monotonicity

6.5.3 Algorithmic Issues in Computing the Degree of Monotonicity 𝗠

References

Exercises

7: Case Study of Biological Models

7.1 Segment Polarity Network Models

7.1.1 Boolean Network Model

7.1.2 Signal Transduction Network Model

7.2 ABA-Induced Stomatal Closure Network

7.3 Epidermal Growth Factor Receptor Signaling Network

7.4 C. Elegans Metabolic Network

7.5 Network For T-Cell Survival and Death in Large Granular Lymphocyte Leukemia

References

Exercises

Glossary

Index

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