Stochastic Modelling for Systems Biology: (Chapman & Hall/CRC Mathematical and Computational Biology)

Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective. Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modelling using examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications. While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source.

Table of Contents:
INTRODUCTION TO BIOLOGICAL MODELLING What is Modelling? Aims of Modelling Why is Stochastic Modelling Necessary? Chemical Reactions Modelling Genetic and Biochemical Networks Modelling Higher-Level Systems Exercises Further Reading REPRESENTATION OF BIOCHEMICAL NETWORKS Coupled Chemical Reactions Graphical Representations Petri Nets Systems Biology Markup Language (SBML) SBML-Shorthand Exercises Further Reading PROBABILITY MODELS Probability Discrete Probability Models The Discrete Uniform Distribution The Binomial Distribution The Geometric Distribution The Poisson Distribution Continuous Probability Models The Uniform Distribution The Exponential Distribution The Normal/Gaussian Distribution The Gamma Distribution Exercises Further reading STOCHASTIC SIMULATION Introduction Monte-Carlo Integration Uniform Random Number Generation Transformation Methods Lookup Methods Rejection Samplers The Poisson Process Using the Statistical Programming Language, R Analysis of Simulation Output Exercises Further Reading MARKOV PROCESSES Introduction Finite Discrete Time Markov Chains Markov Chains with Continuous State Space Markov Chains in Continuous Time Diffusion Processes Exercises Further reading CHEMICAL AND BIOCHEMICAL KINETICS Classical Continuous Deterministic Chemical Kinetics Molecular Approach to Kinetics Mass-Action Stochastic Kinetics The Gillespie Algorithm Stochastic Petri Nets (SPNs) Rate Constant Conversion The Master Equation Software for Simulating Stochastic Kinetic Networks Exercises Further Reading CASE STUDIES Introduction Dimerisation Kinetics Michaelis-Menten Enzyme Kinetics An Auto-Regulatory Genetic Network The Lac operon Exercises Further Reading BEYOND THE GILLESPIE ALGORITHM Introduction Exact Simulation Methods Approximate Simulation Strategies Hybrid Simulation Strategies Exercises Further reading BAYESIAN INFERENCE AND MCMC Likelihood and Bayesian Inference The Gibbs Sampler The Metropolis-Hastings Algorithm Hybrid MCMC Schemes Exercises Further reading INFERENCE FOR STOCHASTIC KINETIC MODELS Introduction Inference Given Complete Data Discrete-Time Observations of the System State Diffusion Approximations for Inference Network Inference Exercises Further reading CONCLUSIONS A SBML Models A.1 Auto-Regulatory Network A.2 Lotka-Volterra Reaction System A.3 Dimerisation-Kinetics Model References Index

Review :
"This book is an excellent introduction to the concepts of stochastic modelling relevant for system biology applications based on stochastic processes . . . strongly recommended for classroom use, especially for computational systems biologists and statisticians." – W. Urfer, in Statistical Papers, 2007, Vol. 48