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Title: Model reduction for stochastic chemical systems with abundant species

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. 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 equationsmore » exactly agree for a class of chemical systems.« less
Authors:
; ;  [1]
  1. School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH93JR, Scotland (United Kingdom)
Publication Date:
OSTI Identifier:
22493286
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 21; Other Information: (c) 2015 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABUNDANCE; CATALYSIS; COMPARATIVE EVALUATIONS; CONCENTRATION RATIO; ENZYMES; FLUCTUATIONS; GENES; HYBRIDIZATION; MOLECULES; NOISE; REACTION KINETICS; REDUCTION; STOCHASTIC PROCESSES