A reduced model solution for the chemical master equation arising in stochastic analyses of biological networks

This article introduces the observability aggregated finite state projection (OAFSP) method for use in the stochastic analysis of biological systems. The small chemical populations of such systems have probability distributions that evolve according to a set of linear, time-invariant, ordinary differential equations known as the chemical master equation (CME). The original FSP algorithm directly approximates the full CME solution to within a prespecified error. However, one may be interested only in certain portions of the distribution or certain statistical quantities such as mean or variance, and the full FSP method may provide an excess of information. In these cases, one can define a linear output signal and extract only the reachable and observable regions from the full distribution state space. The unobservable regions of the distribution can be aggregated with no accuracy loss but with less computational cost. This paper presents the resulting OAFSP algorithm and illustrates its benefits on a simple chemical reaction