An improved dynamic Finite State Projection algorithm for the numerical solution of the chemical master equation with applications

Abstract

Recently, Munsky and Khammash suggested the Finite State Projection (FSP) algorithm for the numerical solution of the Chemical Master Equation, which provides a discrete and stochastic modelling framework for chemical kinetics. The important question of whether or not the algorithm is guaranteed to terminate is not addressed in the original work. We show that the well-known explosive birth process provides a counter example. We also give sufficient criteria for a model to be suitable for the FSP technique. We demonstrate the FSP technique on three novel applications. Results are presented for: (i) the Schlogl reactions; (ii) another example from Gillespie's celebrated book; and (iii) models for the role that dimerization plays in reducing noise in simple gene regulatory networks. Finally, we augment the dimerization model to include tetramers and show that this enhances the noise reduction properties of the network.