- 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.

** Modelling and NetworksIntroduction 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

Graphical representations

Petri nets

Stochastic process algebras

Systems Biology Markup Language (SBML)

SBML-shorthand

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"

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

Finite discrete time Markov chains

Markov chains with continuous state-space

Markov chains in continuous time

Diffusion processes

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

Dimerisation kinetics

Michaelis–Menten enzyme kinetics

An auto-regulatory genetic network

The

Exact simulation methods

Approximate simulation strategies

Hybrid simulation strategies

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 given complete data

Discrete-time observations of the system state

Diffusion approximations for inference

Likelihood-free methods

Network inference and model comparison

Lotka–Volterra reaction system

Dimerisation-kinetics model

References

Index

*All chapters include exercises and further reading.*

**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.

"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…"

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