Stochastic modelling for systems biology
Stage 3 project, 2025/26
Supervisor: Darren Wilkinson
Project outline
At high concentrations, chemical reactions and related processes can be viewed as continuous and deterministic, and be well-described by ODEs and PDEs. However, down at the level of single cells, many biochemical processes take place at such low concentrations that the discreteness of the molecules involved cannot be ignored, and stochastic processes must be used to obtain satisfactory descriptions of the discrete random reaction dynamics. This project will be concerned with computational modelling and stochastic simulation of such continuous-time Markov processes, and the fitting of such models to time course experimental data.
Potential areas for more in-depth study
- Fast exact and approximate simulation algorithms
- Compositional modelling of large reaction networks
- Bayesian inference for stochastic kinetic models
- Simulation of stochastic reaction-diffusion processes
- Detailed modelling and analysis for a real non-trivial genetic/biochemical network
Pre-requisites
You should have a strong background in probability and statistics, and must be comfortable with programming in R and/or Python (Python preferable). MATH3421 (BCM III) is highly recommended as a co-requisite.
Some relevant resources
Books
- Wilkinson, D. J. (2018) Stochastic modelling for systems biology, third edition, Chapman & Hall/CRC Press.
- Erban, R., Chapman, S. J. (2020) Stochastic modelling of reaction-diffusion processes, Cambridge texts in applied mathematics.
Papers
- Wilkinson, D. J. (2025) jax-smfsb: A Python library for stochastic systems biology modelling and inference, The Journal of Open Source Software, 10(106):7491.
- Wilkinson, D. J. (2009) Stochastic modelling for quantitative description of heterogeneous biological systems, Nature Reviews Genetics, 10(2):122-133.
- Golightly, A., Wilkinson, D. J. (2011) Bayesian parameter inference for stochastic biochemical network models using particle MCMC, Interface Focus, 1(6):807-820.
- Salis, H., Kaznessis, Y. N. (2005) Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions, Journal of Chemical Physics, 122(5): 054103.
- Ghosh, A. et al (2015) The spatial chemical Langevin equation and reaction diffusion master equations: moments and qualitative solutions, Theoretical Biology and Medical Modelling, 12:5.
- Smith, S., Grima, R. (2019) Spatial stochastic intracellular kinetics: a review of modelling approaches, Bulletin of Mathematical Biology, 81, 2960-3009.
- Tian, T., Burrage, K. (2006) Stochastic models for regulatory networks of the genetic toggle switch, PNAS, 103(22):8372-8377.
- Arkin, A., Ross, J, McAdams, H. H. (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells, Genetics, 149(4):1633-1648.
- Robb, M. L., Shahrezaei, V. (2014) Stochastic Cellular Fate Decision Making by Multiple Infecting Lambda Phage, PLoS ONE, 9(8): e103636.