Stochastic Modelling for Systems Biology

Published:
April 18, 2006 by Chapman and Hall/CRC - 280 Pages
Author(s):
Darren J. Wilkinson, School of Mathematics and Statistics, Newcastle University, UK
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ISBN 9781584885405
Cat# C5408
 

Features

  • Provides a self-contained introduction to the stochastic modelling of biological and genetic networks
  • Focuses on computer simulation with methods illustrated by concrete example implementations in R
  • Includes an introduction to Bayesian inference for parameter estimation in stochastic kinetic models
  • Covers the latest fast approximate and hybrid simulation techniques
  • Includes example models encoded in SBML and available for downloading from the Web

    • 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

    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
    Exercises
    Further Reading

    REPRESENTATION OF BIOCHEMICAL NETWORKS
    Coupled Chemical Reactions
    Graphical Representations
    Petri Nets
    Systems Biology Markup Language (SBML)
    SBML-Shorthand
    Exercises
    Further Reading

    PROBABILITY MODELS
    Probability
    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
    Exercises
    Further reading

    STOCHASTIC SIMULATION
    Introduction
    Monte-Carlo Integration
    Uniform Random Number Generation
    Transformation Methods
    Lookup Methods
    Rejection Samplers
    The Poisson Process
    Using the Statistical Programming Language, R
    Analysis of Simulation Output
    Exercises
    Further Reading

    MARKOV PROCESSES
    Introduction
    Finite Discrete Time Markov Chains
    Markov Chains with Continuous State Space
    Markov Chains in Continuous Time
    Diffusion Processes
    Exercises
    Further reading

    CHEMICAL AND BIOCHEMICAL KINETICS
    Classical Continuous Deterministic Chemical Kinetics
    Molecular Approach to Kinetics
    Mass-Action Stochastic Kinetics
    The Gillespie Algorithm
    Stochastic Petri Nets (SPNs)
    Rate Constant Conversion
    The Master Equation
    Software for Simulating Stochastic Kinetic Networks
    Exercises
    Further Reading

    CASE STUDIES
    Introduction
    Dimerisation Kinetics
    Michaelis-Menten Enzyme Kinetics
    An Auto-Regulatory Genetic Network
    The Lac operon
    Exercises
    Further Reading

    BEYOND THE GILLESPIE ALGORITHM
    Introduction
    Exact Simulation Methods
    Approximate Simulation Strategies
    Hybrid Simulation Strategies
    Exercises
    Further reading

    BAYESIAN INFERENCE AND MCMC
    Likelihood and Bayesian Inference
    The Gibbs Sampler
    The Metropolis-Hastings Algorithm
    Hybrid MCMC Schemes
    Exercises
    Further reading

    INFERENCE FOR STOCHASTIC KINETIC MODELS
    Introduction
    Inference Given Complete Data
    Discrete-Time Observations of the System State
    Diffusion Approximations for Inference
    Network Inference
    Exercises
    Further reading

    CONCLUSIONS

    A SBML Models
    A.1 Auto-Regulatory Network
    A.2 Lotka-Volterra Reaction System
    A.3 Dimerisation-Kinetics Model

    References
    Index

    Editorial Reviews

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

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