Quasi product form approximation for markov models of reaction networks

Abstract

In cell processes, such as gene regulation or cell differentiation, stochasticity often plays a crucial role. Quantitative analysis of stochastic models of the underlying chemical reaction network can be obstructed by the size of the state space which grows exponentially with the number of considered species. In a recent paper [1] we showed that the space complexity of the analysis can be drastically decreased by assuming that the transient probabilities of the model are in product form. This assumption, however, leads to approximations that are satisfactory only for a limited range of models. In this paper we relax the product form assumption by introducing the quasi product form assumption. This leads to an algorithm whose memory complexity is still reasonably low and provides a good approximation of the transient probabilities for a wide range of models. We discuss the characteristics of this algorithm and illustrate its application on several reaction networks. © 2012 Springer-Verlag.