Stochastic Modelling for Systems Biology

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.

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.

All Chapters include Exercises and Further ReadingModelling and networksIntroduction to biological modellingWhat is modelling?Aims of modellingWhy is stochastic modelling necessary?Chemical reactionsModelling genetic and biochemical networksModelling higher-level systemsRepresentation of biochemical networksCoupled chemical reactionsGraphical representationsPetri netsStochastic process algebrasSystems Biology Markup Language (SBML)SBML-shorthandStochastic processes and simulationProbability modelsProbabilityDiscrete probability modelsThe discrete uniform distributionThe binomial distributionThe geometric distributionThe Poisson distributionContinuous probability modelsThe uniform distributionThe exponential distributionThe normal/Gaussian distributionThe gamma distributionQuantifying "noise"Stochastic simulationIntroductionMonte Carlo integrationUniform random number generationTransformation methodsLookup methodsRejection samplersImportance resamplingThe Poisson processUsing the statistical programming language, RAnalysis of simulation outputMarkov processesIntroductionFinite discrete time Markov chainsMarkov chains with continuous state-spaceMarkov chains in continuous timeDiffusion processesStochastic chemical kineticsChemical and biochemical kineticsClassical continuous deterministic chemical kineticsMolecular approach to kineticsMass-action stochastic kineticsThe Gillespie algorithmStochastic Petri nets (SPNs)Structuring stochastic simulation codesRate constant conversionKolmogorov’s equations and other analytic representationsSoftware for simulating stochastic kinetic networksCase studiesIntroductionDimerisation kineticsMichaelis–Menten enzyme kineticsAn auto-regulatory genetic networkThe lac operonBeyond the Gillespie algorithmIntroductionExact simulation methodsApproximate simulation strategiesHybrid simulation strategiesBayesian inferenceBayesian inference and MCMCLikelihood and Bayesian inferenceThe Gibbs samplerThe Metropolis–Hastings algorithmHybrid MCMC schemesMetropolis–Hastings algorithms for Bayesian inferenceBayesian inference for latent variable modelsAlternatives to MCMCInference for stochastic kinetic modelsIntroductionInference given complete dataDiscrete-time observations of the system stateDiffusion approximations for inferenceLikelihood-free methodsNetwork inference and model comparisonConclusionsSBML ModelsAuto-regulatory networkLotka–Volterra reaction systemDimerisation-kinetics modelReferencesIndex