Coarse-graining stochastic biochemical networks: quasi-stationary approximation and fast simulations using a stochastic path integral technique

TL;DR

This paper introduces a universal stochastic path integral method for coarse-graining stiff biochemical networks, enabling fast, accurate simulations by eliminating fast species while preserving key fluctuations.

Contribution

It develops a quasi-stationary approximation based on stochastic path integrals, providing analytical and computational tools for efficient simulation of complex biochemical systems.

Findings

Coarse-grained simulations are three orders of magnitude faster than Gillespie simulations.

Analytical expressions for moments of chemical fluxes are derived for small reaction networks.

The approach accurately reproduces full system behavior with reduced computational cost.

Abstract

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach, which is similar to the Born-Oppenheimer approximation in quantum mechanics, follows from the stochastic path integral representation of the full counting statistics of reaction events (also known as the cumulant generating function). In applications with a small number of chemical reactions, this approach produces analytical expressions for moments of chemical fluxes between slow variables. This allows for a low-dimensional, interpretable representation of the biochemical system, that can be used for coarse-grained numerical simulation schemes with a small computational complexity and yet high accuracy. As an example, we consider a chain of biochemical reactions, derive its coarse-grained description, and show that the Gillespie simulations of the original stiff system, the coarse-grained simulations, and the full analytical treatment are in an agreement, but the coarse-grained simulations are three orders of magnitude faster than the Gillespie analogue.