General Prerequisites: Part A Differential Equations II and Probability, and Part B Applied Probability, would also be an advantage, but are not necessary.
Course Overview: Stochastic Modelling of Biological Processes provides an introduction to stochastic methods for modelling biological systems. The course starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods which can be used for analysis of stochastic models. Different models of molecular diffusion (on-lattice and off-lattice models, velocity-jump processes) and their properties are studied, before moving to stochastic reaction-diffusion models. Compartment-based and molecular-based approaches to stochastic reaction-diffusion modelling (Brownian dynamics) are discussed together with stochastic spatially-distributed models (pattern formation).
Lecturer(s):
Prof. Ruth Baker
Learning Outcomes: The student will learn: (i) mathematical techniques for the analysis of stochastic models; (ii) how stochastic models can be efficiently simulated using a computer; (iii) connections and differences between different stochastic methods, and between stochastic and deterministic modelling.
Course Synopsis: Stochastic simulation of chemical reactions in well-stirred systems: Gillespie algorithm, chemical master equation, analysis of simple systems, deterministic vs. stochastic modelling.
Stochastic differential equations: numerical methods, Fokker-Planck equation, first exit time, backward Kolmogorov equation, chemical Fokker-Planck equation.
Compartment-based stochastic reaction-diffusion models: reaction-diffusion master equation, pattern formation, morphogen gradients.
Molecular-based approaches to reaction-diffusion modelling, Brownian dynamics, reaction radius.
Velocity-jump models for biological transport processes.