Stochastic Modelling for Systems Biology

by Wilkinson, Darren James

• ISBN13: 9781584885405
• ISBN10: 1584885408
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-04-18
• Publisher: Chapman & Hall/

Summary

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

1 Introduction to biological modelling	1	(18)
1.1 What is modelling?	1	(1)
1.2 Aims of modelling	2	(1)
1.3 Why is stochastic modelling necessary?	2	(4)
1.4 Chemical reactions	6	(2)
1.5 Modelling genetic and biochemical networks	8	(8)
1.6 Modelling higher-level systems	16	(1)
1.7 Exercises	17	(1)
1.8 Further reading	17	(2)
2 Representation of biochemical networks	19	(26)
2.1 Coupled chemical reactions	19	(1)
2.2 Graphical representations	19	(2)
2.3 Petri nets	21	(10)
2.4 Systems Biology Markup Language (SBML)	31	(5)
2.5 SBML-shorthand	36	(6)
2.6 Exercises	42	(1)
2.7 Further reading	43	(2)
3 Probability models	45	(46)
3.1 Probability	45	(11)
3.2 Discrete probability models	56	(8)
3.3 The discrete uniform distribution	64	(1)
3.4 The binomial distribution	64	(1)
3.5 The geometric distribution	65	(2)
3.6 The Poisson distribution	67	(3)
3.7 Continuous probability models	70	(5)
3.8 The uniform distribution	75	(2)
3.9 The exponential distribution	77	(5)
3.10 The normal/Gaussian distribution	82	(4)
3.11 The gamma distribution	86	(2)
3.12 Exercises	88	(1)
3.13 Further reading	89	(2)
4 Stochastic simulation	91	(18)
4.1 Introduction	91	(1)
4.2 Monte-Carlo integration	91	(1)
4.3 Uniform random number generation	92	(1)
4.4 Transformation methods	93	(4)
4.5 Lookup methods	97	(1)
4.6 Rejection samplers	98	(3)
4.7 The Poisson process	101	(1)
4.8 Using the statistical programming language, R	101	(5)
4.9 Analysis of simulation output	106	(1)
4.10 Exercises	107	(1)
4.11 Further reading	108	(1)
5 Markov processes	109	(30)
5.1 Introduction	109	(1)
5.2 Finite discrete time Markov chains	109	(6)
5.3 Markov chains with continuous state space	115	(6)
5.4 Markov chains in continuous time	121	(12)
5.5 Diffusion processes	133	(2)
5.6 Exercises	135	(2)
5.7 Further reading	137	(2)
6 Chemical and biochemical kinetics	139	(80)
6.1 Classical continuous deterministic chemical kinetics	139	(6)
6.2 Molecular approach to kinetics	145	(2)
6.3 Mass-action stochastic kinetics	147	(2)
6.4 The Gillespie algorithm	149	(1)
6.5 Stochastic Petri nets (SPNs)	150	(3)
6.6 Rate constant conversion	153	(4)
6.7 The Master equation	157	(3)
6.8 Software for simulating stochastic kinetic networks	160	(1)
6.9 Exercises	161	(1)
6.10 Further reading	161	(2)
7 Case studies	163	(18)
7.1 Introduction	163	(1)
7.2 Dimerisation kinetics	163	(5)
7.3 Michaelis-Menten enzyme kinetics	168	(4)
7.4 An auto-regulatory genetic network	172	(4)
7.5 The lac operon	176	(2)
7.6 Exercises	178	(1)
7.7 Further reading	179	(2)
8 Beyond the Gillespie algorithm	181	(16)
8.1 Introduction	181	(1)
8.2 Exact simulation methods	181	(5)
8.3 Approximate simulation strategies	186	(4)
8.4 Hybrid simulation strategies	190	(6)
8.5 Exercises	196	(1)
8.6 Further reading	196	(1)
9 Bayesian inference and MCMC	197	(22)
9.1 Likelihood and Bayesian inference	197	(5)
9.2 The Gibbs sampler	202	(10)
9.3 The Metropolis-Hastings algorithm	212	(4)
9.4 Hybrid MCMC schemes	216	(1)
9.5 Exercises	216	(1)
9.6 Further reading	217	(2)
10 Inference for stochastic kinetic models	219	(18)
10.1 Introduction	219	(1)
10.2 Inference given complete data	220	(3)
10.3 Discrete-time observations of the system state	223	(7)
10.4 Diffusion approximations for inference	230	(4)
10.5 Network inference	234	(1)
10.6 Exercises	234	(1)
10.7 Further reading	235	(2)
11 Conclusions	237	(2)
A SBML Models	239	(8)
A.1 Auto-regulatory network	239	(3)
A.2 Lotka-Volterra reaction system	242	(1)
A.3 Dimerisation-kinetics model	243	(4)
References	247	(4)
Index	251