@TechReport{ it:2010-014,
author = {Stefan Hellander and Per L{\"o}tstedt},
title = {Flexible Single Molecule Simulation of Reaction-Diffusion
Processes},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2010},
number = {2010-014},
month = may,
abstract = {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 its distribution function. 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. }
}