Chemical Master Equation for Large Biological Networks: State-space Expansion Methods Using AI

Description

This book highlights the theory and practical applications of the chemical master equation (CME) approach for very large biochemical networks, which provides a powerful general framework for model building in a variety of biological networks. The aim of the book is to not only highlight advanced numerical solution methods for the CME, but also reveal their potential by means of practical examples. The case studies presented are mainly from biology; however, the applications from novel methods are discussed comprehensively, underlining the interdisciplinary approach in simulation and the potential of the chemical master equation approach for modelling bionetworks. The book is a valuable guide for researchers, graduate students, and professionals alike. Preface Acknowledgments Contents Abbreviations Terminology Notations Key Factors and Outputs 1 Introduction 1.1 Chemical Kinetics and Stochastic Processes 1.2 Why Stochastic Processes? 1.2.1 Introduction 1.2.2 Fluctuations in Biological Systems 1.2.3 Experimental Observations 1.2.4 Advantages of Stochasticity 1.2.5 Thermodynamics of Biological Networks Far from Equilibrium 1.2.6 Why Stochastic Fluctuation Modelling? 1.2.7 Stochastic Modelling Methods 1.2.8 Theoretical Thermodynamic Modelling Approaches 1.2.9 Oscillatory Systems 1.3 The Purpose of This Book 1.4 Specific Objectives of the Monograph 1.5 The Organization of the Book References 2 A Review and Challenges in Chemical Master Equation 2.1 Markov Processes 2.2 Derivation of Chemical Master Equation 2.3 Adaptation of CME to Biological Networks 2.4 Generation-Recombination Markov Processes 2.5 Existing State-Space Expansion Methods 2.5.1 R-step Reachability Method 2.5.2 Stochastic Simulation Methods 2.6 Existing Numerical Methods for Approximation 2.6.1 Uniformisation Method 2.6.2 Krylov Subspace 2.7 Toy Biochemical Models 2.8 Conclusions Appendix A: Basic Probability References 3 Visualizing Markov Process Through Graphs and Trees 3.1 Introduction 3.1.1 Definitions and Preliminaries 3.2 Finite State Markov Chains as Sample Space 3.2.1 Sample Space for Biochemical Systems 3.2.2 States Classification of Markov Chain for Biochemical System 3.3 Markov Chain as a Markov Chain Tree 3.4 Problem State-Space Model of Biochemical Networks 3.5 Intelligent Search and Tracking 3.5.1 Artificial Intelligence for CME 3.5.2 Bayesian Likelihood Node Projection Function 3.6 Complexity of Optimal Solutions 3.7 Discussion and Conclusions References 4 Intelligent State Projection 4.1 Introduction 4.2 Derivation of the Method Conditions 4.2.1 Expansion Criterion for States Space 4.2.2 Cease of Criterion After Updating 4.3 Latitudinal Search Strategy 4.3.1 Expansion and Update 4.3.2 Biological Example 4.4 Longitudinal Latitudinal Search 4.4.1 Expansion and Update 4.4.2 Biological Example 4.5 Data Structure Complexity of Operations 4.6 Discussion and Conclusion Appendix A.1 Complexity Based on Operations References 5 Comparative Study and Analysis of Methods and Models 5.1 Study Overview 5.2 Comparison Based on Catalytic Reaction System 5.3 Comparsion Based on the Dual Enzymatic Reaction Network 5.4 Discussion and Conclusion References 6 A Large Model Case Study: Solving CME for G1/S Checkpoint Involving the DNA-Damage Signal Transduction Pathway 6.1 Introduction 6.1.1 What Happens in Normal Conditions? 6.1.2 What Happens in the Presence of a DNA-Damage Signal? 6.2 Model Integration 6.3 Computational Experiments 6.4 Discussion and Summary References 7 An Integrated Large Model Case Study: Solving CME for Oxidative Stress Adaptation in the Fungal Pathogen Candida Albicans 7.1 Introduction 7.1.1 Integrated Model Overview 7.2 Model Integration 7.2.1 Transporter Module 7.2.2 Antioxidant Module 7.2.3 Protein-Thiol Module 7.2.4 Signalling and Gene Expression Module 7.3 Computational Experiments 7.4 Discussion and Summary References