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Stochastic approximations of higher-molecular by bi-molecular reactions.

Published version
Peer-reviewed

Type

Article

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Authors

Abstract

Reactions involving three or more reactants, called higher-molecular reactions, play an important role in mathematical modelling in systems and synthetic biology. In particular, such reactions underpin a variety of important bio-dynamical phenomena, such as multi-stability/multi-modality, oscillations, bifurcations, and noise-induced effects. However, as opposed to reactions involving at most two reactants, called bi-molecular reactions, higher-molecular reactions are biochemically improbable. To bridge the gap, in this paper we put forward an algorithm for systematically approximating arbitrary higher-molecular reactions with bi-molecular ones, while preserving the underlying stochastic dynamics. Properties of the algorithm and convergence are established via singular perturbation theory. The algorithm is applied to a variety of higher-molecular biochemical networks, and is shown to play an important role in synthetic biology.

Description

Keywords

Chemical master equation, DNA computing, Singular perturbation theory, Stochastic reaction networks, Synthetic biology, Stochastic Processes, Algorithms, Models, Biological, Computer Simulation

Journal Title

J Math Biol

Conference Name

Journal ISSN

0303-6812
1432-1416

Volume Title

86

Publisher

Springer Science and Business Media LLC