Numerical Method for Coupling the Macro and Meso Scales in Stochastic Chemical Kinetics

A numerical method is developed for simulation of stochastic chemical reactions. The system is modeled by the Fokker-Planck equation for the probability density of the molecular state. The dimension of the domain of the equation is reduced by assuming that most of the molecular species have a normal distribution with a small variance. The numerical approximation preserves properties of the analytical solution such as nonnegativity and constant total probability. The method is applied to a nine dimensional problem modelling an oscillating molecular clock. The oscillations stop at a fixed point with a macroscopic model but they continue with our two dimensional, mixed macroscopic and mesoscopic model.