Fokker-Planck approximation of the master equation in molecular biology
P. Lötstedt (Uppsala University)
The stochastic character of the molecular devices in single cells cannot be
neglected, since the number of macromolecules of the different species involved
often is limited to tens or hundreds. This makes mesoscale modelling of the
chemical reactions based on the master equation mandatory.
The master equation is a scalar, linear difference-differential equation for how
the probability distribution of the number of molecules of the species in the
reactions varies with time.
Each different molecule species corresponds to one dimension.
The equations are approximated numerically by a finite difference discretization
of the multidimensional Fokker-Planck equation.
The number of grid points for a two dimensional system for the Fokker-Planck
equation is reduced by more than 300 compared to the master equation.
The steady state solution of a four dimensional problem illustrates the
efficiency of the method. Comparisons are made with solutions obtained
with Gillespie's Monte Carlo method.
This talk presents joint work with Johan Elf and Paul Sjöberg.