Fokker-Planck Approximation of the Master Equation in Molecular Biology

Paul Sjöberg, Per Lötstedt, and Johan Elf

December 2005

Abstract:

The master equation of chemical reactions is solved by first approximating it by the Fokker-Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker-Planck equation is analyzed. The solution of the Fokker-Planck equation is compared to the solution of the master equation obtained with Gillespie's Stochastic Simulation Algorithm (SSA) for problems of interest in the regulation of cell processes. The time dependent and steady state solutions are computed and for equal accuracy in the solutions, the Fokker-Planck approach is more efficient than SSA for low dimensional problems and high accuracy.

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