Partial Approximation of the Master Equation by the Fokker-Planck Equation

摘要

The chemical master equation (CME) describes the probability for each internal state of the cell or rather the states of a model of the cell. The number of states grows exponentially with the number of chemical species in the model, since each species corresponds to one dimension in the state space. The CME can be approximated by a Fokker-Planck equation (FPE), which can be solved numerically cheaper than the CME. The FPE approximation of the full CME is not always appropriate, while it can be suitable for a subspace in the state space. In order to exploit the lower cost of the FPE approximation a method for splitting the state space in two subspaces where one is approximated by the FPE and one remains unapproximated is presented. A biologically relevant problem in four dimensions is solved as an example.