Models and Algorithms for Biomolecules and Molecular Networks

BHASKAR DASGUPTA is a Professor in the Computer Science department at the University of Illinois at Chicago, USA. He has written numerous bioinformatics research papers. Dr. DasGupta was the recipient of the NSF CAREER award in 2004 and the UIC College of Engineering Faculty Teaching award in 2012. JIE LIANG is the Richard and Loan Hill Professor within the Department of Bioengineering and Department of Computer Science at the University of Illinois at Chicago, USA. He earned his Ph.D. in Biophysics. He was an NSF CISE postdoctoral research associate (1994-1996) at the Beckman Institute and National Center for Supercomputing and its Applications (NCSA), as well as a visiting fellow at the NSF Institute of Mathematics and Applications at Minneapolis. He was a recipient of the NSF CAREER award in 2003. He was elected a fellow of the American Institute of Medicine and Biological Engineering in 2007. He was a University Scholar (2010-2012).

• List of Figures xiiiList of Tables xixForeword xxiAcknowledgments xxiii1 Geometric Models of Protein Structure and Function Prediction 11.1 Introduction 11.2 Theory and Model 21.2.1 Idealized Ball Model 21.2.2 Surface Models of Proteins 31.2.3 Geometric Constructs 41.2.4 Topological Structures 61.2.5 Metric Measurements 91.3 Algorithm and Computation 131.4 Applications 151.4.1 Protein Packing 151.4.2 Predicting Protein Functions from Structures 171.5 Discussion and Summary 20References 22Exercises 252 Scoring Functions for Predicting Structure and Binding of Proteins 292.1 Introduction 292.2 General Framework of Scoring Function and Potential Function 312.2.1 Protein Representation and Descriptors 312.2.2 Functional Form 322.2.3 Deriving Parameters of Potential Functions 322.3 Statistical Method 322.3.1 Background 322.3.2 Theoretical Model 332.3.3 Miyazawa--Jernigan Contact Potential 342.3.4 Distance-Dependent Potential Function 412.3.5 Geometric Potential Functions 452.4 Optimization Method 492.4.1 Geometric Nature of Discrimination 502.4.2 Optimal Linear Potential Function 522.4.3 Optimal Nonlinear Potential Function 532.4.4 Deriving Optimal Nonlinear Scoring Function 552.4.5 Optimization Techniques 552.5 Applications 552.5.1 Protein Structure Prediction 562.5.2 Protein--Protein Docking Prediction 562.5.3 Protein Design 582.5.4 Protein Stability and Binding Affinity 592.6 Discussion and Summary 602.6.1 Knowledge-Based Statistical Potential Functions 602.6.2 Relationship of Knowledge-Based Energy Functions and Further Development 642.6.3 Optimized Potential Function 652.6.4 Data Dependency of Knowledge-Based Potentials 66References 67Exercises 753 Sampling Techniques: Estimating Evolutionary Rates and Generating Molecular Structures 793.1 Introduction 793.2 Principles of Monte Carlo Sampling 813.2.1 Estimation Through Sampling from Target Distribution 813.2.2 Rejection Sampling 823.3 Markov Chains and Metropolis Monte Carlo Sampling 833.3.1 Properties of Markov Chains 833.3.2 Markov Chain Monte Carlo Sampling 853.4 Sequential Monte Carlo Sampling 873.4.1 Importance Sampling 873.4.2 Sequential Importance Sampling 873.4.3 Resampling 913.5 Applications 923.5.1 Markov Chain Monte Carlo for Evolutionary Rate Estimation 923.5.2 Sequentail Chain Growth Monte Carlo for Estimating Conformational Entropy of RNA Loops 953.6 Discussion and Summary 96References 97Exercises 994 Stochastic Molecular Networks 1034.1 Introduction 1034.2 Reaction System and Discrete Chemical Master Equation 1044.3 Direct Solution of Chemical Master Equation 1064.3.1 State Enumeration with Finite Buffer 1064.3.2 Generalization and Multi-Buffer dCME Method 1084.3.3 Calculation of Steady-State Probability Landscape 1084.3.4 Calculation of Dynamically Evolving Probability Landscape 1084.3.5 Methods for State Space Truncation for Simplification 1094.4 Quantifying and Controlling Errors from State Space Truncation 1114.5 Approximating Discrete Chemical Master Equation 1144.5.1 Continuous Chemical Master Equation 1144.5.2 Stochastic Differential Equation: Fokker—Planck Approach 1144.5.3 Stochastic Differential Equation: Langevin Approach 1164.5.4 Other Approximations 1174.6 Stochastic Simulation 1184.6.1 Reaction Probability 1184.6.2 Reaction Trajectory 1184.6.3 Probability of Reaction Trajectory 1194.6.4 Stochastic Simulation Algorithm 1194.7 Applications 1214.7.1 Probability Landscape of a Stochastic Toggle Switch 1214.7.2 Epigenetic Decision Network of Cellular Fate in Phage Lambda 1234.8 Discussions and Summary 127References 128Exercises 1315 Cellular Interaction Networks 1355.1 Basic Definitions and Graph-Theoretic Notions 1365.1.1 Topological Representation 1365.1.2 Dynamical Representation 1385.1.3 Topological Representation of Dynamical Models 1395.2 Boolean Interaction Networks 1395.3 Signal Transduction Networks 1415.3.1 Synthesizing Signal Transduction Networks 1425.3.2 Collecting Data for Network Synthesis 1465.3.3 Transitive Reduction and Pseudo-node Collapse 1475.3.4 Redundancy and Degeneracy of Networks 1535.3.5 Random Interaction Networks and Statistical Evaluations 1575.4 Reverse Engineering of Biological Networks 1595.4.1 Modular Response Analysis Approach 1605.4.2 Parsimonious Combinatorial Approaches 1665.4.3 Evaluation of Quality of the Reconstructed Network 171References 173Exercises 1786 Dynamical Systems and Interaction Networks 1836.1 Some Basic Control-Theoretic Concepts 1856.2 Discrete-Time Boolean Network Models 1866.3 Artificial Neural Network Models 1886.3.1 Computational Powers of ANNs 1896.3.2 Reverse Engineering of ANNs 1906.3.3 Applications of ANN Models in Studying Biological Networks 1926.4 Piecewise Linear Models 1926.4.1 Dynamics of PL Models 1946.4.2 Biological Application of PL Models 1956.5 Monotone Systems 2006.5.1 Definition of Monotonicity 2016.5.2 Combinatorial Characterizations and Measure of Monotonicity 2036.5.3 Algorithmic Issues in Computing the Degree of Monotonicity 𝖬 207References 209Exercises 2147 Case Study of Biological Models 2177.1 Segment Polarity Network Models 2177.1.1 Boolean Network Model 2187.1.2 Signal Transduction Network Model 2187.2 ABA-Induced Stomatal Closure Network 2197.3 Epidermal Growth Factor Receptor Signaling Network 2207.4 C. elegans Metabolic Network 2237.5 Network for T-Cell Survival and Death in Large Granular Lymphocyte Leukemia 223References 224Exercises 225Glossary 227Index 229