Stochastic analysis of gene regulatory networks using finite state projections and singular perturbation

Considerable recent experimental evidence suggests that significant stochastic fluctuations are present in gene regulatory networks. The investigation of stochastic properties in genetic systems involves the formulation of a mathematical representation of molecular noise and devising efficient computational algorithms for computing the relevant statistics of the modeled processes. However, the complexity of gene regulatory networks poses serious computational difficulties and makes any quantitative prediction a difficult task. The recently proposed Finite State Projection (FSP) algorithm provides a promising approach to handling these problems, but thus far it has only been demonstrated for a certain class of problems. In this paper we show that the applicability of the finite projection approach can be enhanced by taking advantage of tools from the fields of modern control theory and dynamical systems. In particular, we present an approach that utilizes singular perturbation theory in conjunction with the Finite State Projection approach to improve the computation time and facilitate model reduction. We demonstrate the effectiveness of the resulting slow manifold FSP algorithm on a simple example arising in the cellular heat shock response mechanism.