Stochastic modelling of reaction-diffusion processes in biology

Several stochastic simulation algorithms (SSAs) have been recently

proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this talk, two commonly used SSAs will  be studied. The first SSA is an on-lattice model described by the  reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual  molecules and their reactive collisions. The connections between SSAs  and the deterministic models (based on reaction- diffusion PDEs) will  be presented. I will consider chemical reactions both at a surface  and in the bulk. I will show how the "microscopic" parameters should  be chosen to achieve the correct "macroscopic" reaction rate. This  choice is found to depend on which SSA is used. I will also present  multiscale algorithms which use models with a different level of  detail in different parts of the computational domain