We present a technique, called Green's function reaction dynamics (GFRD), for particle-based simulations of reaction-diffusion systems. GFRD uses a maximum time step such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equations are solved analytically using Green's functions, which are used to set up an event-driven algorithm. We apply the technique to a model of gene expression. Under biologically relevant conditions, GFRD is up to 5 orders of magnitude faster than conventional particle-based schemes.

Phys. Rev. Lett.
Biochemical Networks

van Zon, J.S, & ten Wolde, P.R. (2005). Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics. Phys.Rev.Lett., 94(Article number: 128103), 1–4. doi:10.1103/physrevlett.94.128103