A scalable moment-closure approximation for large-scale biochemical reaction networks

Motivation: Stochastic molecular processes are a leading cause of cell-to-cell variability. Their dynamics are often described by continuous-time discrete-state Markov chains and simulated using stochastic simulation algorithms. As these stochastic simulations are computationally demanding, ordinary differential equation models for the dynamics of the statistical moments have been developed. The number of state variables of these approximating models, however, grows at least quadratically with the number of biochemical species. This limits their application to small-and medium-sized processes. Results: In this article, we present a scalable moment-closure approximation (sMA) for the simulation of statistical moments of large-scale stochastic processes. The sMA exploits the structure of the biochemical reaction network to reduce the covariance matrix. We prove that sMA yields approximating models whose number of state variables depends predominantly on local properties, i.e. the average node degree of the reaction network, instead of the overall network size. The resulting complexity reduction is assessed by studying a range of medium-and large-scale biochemical reaction networks. To evaluate the approximation accuracy and the improvement in computational efficiency, we study models for JAK2/STAT5 signalling and NFjB signalling. Our method is applicable to generic biochemical reaction networks and we provide an implementation, including an SBML interface, which renders the sMA easily accessible.