Models and Algorithms for Biomolecules and Molecular Networks

Content: 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.