Problems of high dimension in molecular biology

The deterministic reaction rate equations are not an accurate description of many systems in molecular biology where the number of molecules of each species often is small. The master equation of chemical reactions is a more accurate stochastic description suitable for small molecular numbers. A computational difficulty is the high dimensionality of the equation. We describe how it can be solved by first approximating it by the FokkerPlanck equation. Then this equation is discretized in space and time by a finite difference method. The method is compared to a Monte Carlo method by Gillespie. The method is applied to a four-dimensional problem of interest in the regulation of cell processes. This paper was presented at the 19th GAMM-Seminar in Leipzig, January 23–25, 2003.