Improved estimations of stochastic chemical kinetics by finite-state expansion

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations relevant. The master equation provides the evolution of probability distribution across discrete state space consisting vectors population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. deterministic rate (DRE) gives macroscopic approximation as compact system differential equations that estimate average populations species, but it may be inaccurate in case nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an method mediating microscopic and interpretations stochastic network by coupling dynamics chosen subset with mean DRE. An algorithm translates into expanded one represented further distinct This translation exactly preserves dynamics, DRE can interpreted correction original one. effectiveness FSE demonstrated models challenge state-of-the-art techniques due intrinsic noise, multi-scale multi-stability.