Incorporating Diffusion in Complex Geometries into Stochastic Chemical Kinetics Simulations

A method is developed for incorporating diffusion of chemicals in complex geometries into stochastic chemical kinetics simulations. Systems are modeled using the reaction-diffusion master equation, with jump rates for diffusive motion between mesh cells calculated from the discretization weights of an embedded boundary method. Since diffusive jumps between cells are treated as first order reactions, individual realizations of the stochastic process can be created by the Gillespie method. Numerical convergence results for the underlying embedded boundary method, and for the stochastic reaction-diffusion method, are presented in two dimensions. A two-dimensional model of transcription, translation, and nuclear membrane transport in eukaryotic cells is presented to demonstrate the feasibility of the method in studying cell-wide biological processes.