Model reduction for stochastic chemical systems with abundant species

TL;DR

This paper develops a hybrid stochastic model for biochemical systems with abundant and scarce species, simplifying analysis and providing exact solutions for certain networks, thus advancing understanding of molecular fluctuations.

Contribution

It introduces a hybrid stochastic framework that reduces complexity by focusing on non-abundant species and proves its accuracy and exact solvability for specific biochemical networks.

Findings

Hybrid model accurately describes non-abundant species fluctuations.

Exact solutions obtained for gene expression and enzyme catalysis networks.

Hybrid and conventional models agree for certain classes regardless of molecule number separation.

Abstract

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. Here we first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently we prove that in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.