book

Stochastic Modelling for Systems Biology, Third Edition, 3rd Edition

by Darren J. Wilkinson

December 2018

Intermediate to advanced

404 pages

10h 35m

English

Chapman and Hall/CRC

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1.1 What is modelling?1.2 Aims of modelling1.3 Why is stochastic modelling necessary?1.4 Chemical reactions1.5 Modelling genetic and biochemical networks1.6 Modelling higher-level systems1.7 Exercises1.8 Further reading
2.1 Coupled chemical reactions2.2 Graphical representations2.3 Petri nets2.4 Stochastic process algebras2.5 Systems Biology Markup Language (SBML)2.6 SBML-shorthand2.7 Exercises2.8 Further reading
3.1 Probability3.2 Discrete probability models3.3 The discrete uniform distribution3.4 The binomial distribution3.5 The geometric distribution3.6 The Poisson distribution3.7 Continuous probability models3.8 The uniform distribution3.9 The exponential distribution3.10 The normal/Gaussian distribution3.11 The gamma distribution3.12 Quantifying ‘noise’3.13 Exercises3.14 Further reading
4.1 Introduction4.2 Monte Carlo integration4.3 Uniform random number generation4.4 Transformation methods4.5 Lookup methods4.6 Rejection samplers4.7 Importance resampling4.8 The Poisson process4.9 Using the statistical programming language R4.10 Analysis of simulation output4.11 Exercises4.12 Further reading
5.1 Introduction5.2 Finite discrete time Markov chains5.3 Markov chains with continuous state-space5.4 Markov chains in continuous time5.5 Diffusion processes5.6 Exercises5.7 Further reading
6.1 Classical continuous deterministic chemical kinetics6.2 Molecular approach to kinetics6.3 Mass-action stochastic kinetics6.4 The Gillespie algorithm6.5 Stochastic Petri nets (SPNs)6.6 Structuring stochastic simulation codes6.7 Rate constant conversion6.8 Kolmogorov’s equations and other analytic representations6.9 Software for simulating stochastic kinetic networks6.10 Exercises6.11 Further reading
7.1 Introduction7.2 Dimerisation kinetics7.3 Michaelis–Menten enzyme kinetics7.4 An auto-regulatory genetic network7.5 The lac operon7.6 Exercises7.7 Further reading
8.1 Introduction8.2 Exact simulation methods8.3 Approximate simulation strategies8.4 Hybrid simulation strategies8.5 Exercises8.6 Further reading
9.1 Introduction9.2 One-dimensional reaction–diffusion systems9.3 Two-dimensional reaction–diffusion systems9.4 Exercises9.5 Further reading
10.1 Likelihood and Bayesian inference10.2 The Gibbs sampler10.3 The Metropolis–Hastings algorithm10.4 Hybrid MCMC schemes10.5 Metropolis–Hastings algorithms for Bayesian inference10.6 Bayesian inference for latent variable models10.7 Alternatives to MCMC10.8 Exercises10.9 Further reading
11.1 Introduction11.2 Inference given complete data11.3 Discrete-time observations of the system state11.4 Diffusion approximations for inference11.5 Likelihood-free methods11.6 Approximate Bayesian computation (ABC) for parameter inference11.7 Network inference and model comparison11.8 Exercises11.9 Further reading
A.1 Auto-regulatory networkA.2 Lotka–Volterra reaction systemA.3 Dimerisation-kinetics model
B.1 smfsb R packageB.2 SBML-shorthandB.3 smfsbSBML R packageB.4 scala-smfsb library

Overview

Since its first edition, there have been many interesting developments in the use of "likelihood-free" methods of Bayesian inference for complex stochastic models. Having been thoroughly updated to reflect this, this third edition covers everything necessary for a good appreciation of stochastic kinetic modelling of biological networks in the systems biology context.