Elimination of Intermediate Species in Multiscale Stochastic Reaction Networks

TL;DR

This paper develops a method to simplify complex biochemical reaction networks by eliminating short-lived intermediate species, making analysis and simulation more feasible while maintaining accuracy.

Contribution

It provides conditions and a framework for approximating multiscale stochastic reaction networks with reduced models that exclude intermediates, linking stochastic and deterministic models.

Findings

Reduced models accurately approximate original networks under certain conditions

Establishes a connection between stochastic and deterministic models

Provides a scalable approach for analyzing complex biochemical systems

Abstract

We study networks of biochemical reactions modelled by continuous-time Markov processes. Such networks typically contain many molecular species and reactions and are hard to study analytically as well as by simulation. Particularly, we are interested in reaction networks with intermediate species such as the substrate-enzyme complex in the Michaelis-Menten mechanism. These species are virtually in all real-world networks, they are typically short-lived, degraded at a fast rate and hard to observe experimentally. We provide conditions under which the Markov process of a multiscale reaction network with intermediate species is approximated in finite dimensional distribution by the Markov process of a simpler reduced reaction network without intermediate species. We do so by embedding the Markov processes into a one-parameter family of processes, where reaction rates and species abundances are scaled in the parameter. Further, we show that there are close links between these stochastic models and deterministic ODE models of the same networks.