Radek Erban (Maths, Oxford)

Stochastic modelling of reaction, diffusion and taxis processes in biology

Abstract: Many cellular and subcellular biological processes can be described
in terms of diffusing and chemically reacting species (e.g. genes and
proteins). Several stochastic simulation algorithms suitable for the
modelling of such reaction-diffusion processes will be analysed. The
connections between stochastic simulation algorithms and the deterministic
models (based on reaction-diffusion partial differential equations) will be
presented. We show that the behaviour close to a reactive boundary (e.g. a
membrane with receptors) is model-dependent. We derive the correct choice of
boundary conditions for each stochastic simulation algorithm. The movement of
unicellular organisms can be also viewed as a stochastic process - a biased
random walk. Examples include chemotaxis of bacteria or amoeboid cells and in
both cases, cells detect extracellular signals (attractants or repellents)
and alter their behaviour accordingly. The corresponding macroscopic partial
differential equations describing the behaviour of cellular populations will
be derived.