Flexible single molecule simulation of reaction–diffusion processes

An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green’s function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.