moments

The study of stochastic biomolecular networks is a key part of systems biology, as such networks play a central role in engineered synthetic biology constructs as well as in naturally occurring cells. This expository paper reviews in a unified way a pair of recent approaches to the finite computation of statistics for chemical reaction networks.

Biochemical reaction networks in cells frequently consist of reactions with disparate timescales. Stochastic simulations of such multiscale BRNs are prohibitively slow due to the high computational cost incurred in the simulations of fast reactions. One way to resolve this problem is to replace fast species by their stationary conditional expectation values conditioned on slow species. While various approximations schemes for this quasi-steady state approximation have been developed, they often lead to considerable errors. This paper considers two classes of multiscale BRNs which can be reduced by through an exact QSS rather than approximations. Specifically, we assume that fast species constitute either a feedforward network or a complex balanced network. Exact reductions for various examples are derived, and the computational advantages of this approach are illustrated through simulations.

We review in a unified way results for two types of stochastic chemical reaction systems for which moments can be effectively computed: feedforward networks and complex-balanced networks.