Stochastic Modelling for Systems Biology

 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