Stochastic Modelling for Systems Biology, Second Edition

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ISBN 9781439837726
Cat# K11715



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  • Provides an accessible introduction to stochastic modeling for systems biology
  • Focuses on computer simulation, with R and SBML code
  • Includes exercises and many biologically motivated examples
  • Presents enhanced material on statistical inference


Since the first edition of Stochastic Modelling for Systems Biology, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Re-written to reflect this modern perspective, this second edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context.

Keeping with the spirit of the first edition, all of the new theory is presented in a very informal and intuitive manner, keeping the text as accessible as possible to the widest possible readership.

New in the Second Edition

  • All examples have been updated to Systems Biology Markup Language Level 3
  • All code relating to simulation, analysis, and inference for stochastic kinetic models has been re-written and re-structured in a more modular way
  • An ancillary website provides links, resources, errata, and up-to-date information on installation and use of the associated R package
  • More background material on the theory of Markov processes and stochastic differential equations, providing more substance for mathematically inclined readers
  • Discussion of some of the more advanced concepts relating to stochastic kinetic models, such as random time change representations, Kolmogorov equations, Fokker-Planck equations and the linear noise approximation
  • Simple modelling of "extrinsic" and "intrinsic" noise

An effective introduction to the area of stochastic modelling in computational systems biology, this new edition adds additional mathematical detail and computational methods that will provide a stronger foundation for the development of more advanced courses in stochastic biological modelling.

Table of Contents

Modelling and Networks
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

Representation of Biochemical Networks
Coupled chemical reactions
Graphical representations
Petri nets
Stochastic process algebras
Systems Biology Markup Language (SBML)

Stochastic Processes and Simulation
Probability Models
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
Quantifying "noise"

Stochastic Simulation
Monte Carlo integration
Uniform random number generation
Transformation methods
Lookup methods
Rejection samplers
Importance resampling
The Poisson process
Using the statistical programming language, R
Analysis of simulation output

Markov Processes
Finite discrete time Markov chains
Markov chains with continuous state-space
Markov chains in continuous time
Diffusion processes

Stochastic Chemical Kinetics
Chemical and Biochemical Kinetics
Classical continuous deterministic chemical kinetics
Molecular approach to kinetics
Mass-action stochastic kinetics
The Gillespie algorithm
Stochastic Petri nets (SPNs)
Structuring stochastic simulation codes
Rate constant conversion
Kolmogorov’s equations and other analytic representations
Software for simulating stochastic kinetic networks

Case Studies
Dimerisation kinetics
Michaelis–Menten enzyme kinetics
An auto-regulatory genetic network
The lac operon

Beyond the Gillespie Algorithm
Exact simulation methods
Approximate simulation strategies
Hybrid simulation strategies

Bayesian Inference
Bayesian Inference and MCMC
Likelihood and Bayesian inference
The Gibbs sampler
The Metropolis–Hastings algorithm
Hybrid MCMC schemes
Metropolis–Hastings algorithms for Bayesian inference
Bayesian inference for latent variable models
Alternatives to MCMC

Inference for Stochastic Kinetic Models
Inference given complete data
Discrete-time observations of the system state
Diffusion approximations for inference
Likelihood-free methods
Network inference and model comparison

SBML Models
Auto-regulatory network
Lotka–Volterra reaction system
Dimerisation-kinetics model


All chapters include exercises and further reading.

Author Bio(s)

Darren Wilkinson is Professor of Stochastic Modelling at Newcastle University in the UK. He was educated at the nearby University of Durham, where he took his first degree in Mathematics, followed by a Ph.D. in Bayesian statistics which he completed in 1995. He moved to a lectureship in statistics at the Newcastle University in 1996, where he has remained since, being promoted to his current post in 2007. Professor Wilkinson is interested in computational statistics and Bayesian inference and in the application of modern statistical technology to problems in statistical bioinformatics and systems biology. He is involved in a variety of systems biology projects at Newcastle, including the Centre for Integrated Systems Biology of Ageing and Nutrition (CISBAN). He recently held a BBSRC Research Development Fellowship on Integrative modelling of stochasticity, noise, heterogeneity and measurement error in the study of model biological systems.

Editorial Reviews

"Each chapter is completed by some training exercises. … In order to satisfy more curious or more advanced readers, the author also proposes further readings in a dedicated section for each chapter, which is in my opinion a really good idea: highlighting a selection of interesting readings is much less disheartening than referring to a bibliography at the end of the book. Note that the book is supplemented by a quite complete website. … the book has been enhanced by an introduction to approximate Bayesian computation, the codes have been updated to SBML Level 3, and the chapters on Markov chains and stochastic differential equations have been reinforced. … a really comprehensible and easy-to-read course."
—Sophie Donnet, Université Paris-Dauphine, CHANCE, 25.4

Praise for the First Edition:
"…designed and well suited as an in-depth introduction into stochastic chemical simulation, both for self-study or as a course text…"
Biomedical Engineering Online, December 2006