Hybrid framework for the simulation of stochastic chemical kinetics

Duncan, Andrew, Erban, Radek and Zygalakis, Konstantinos (2016) Hybrid framework for the simulation of stochastic chemical kinetics. Journal of Computational Physics, 326. pp. 398-419. ISSN 0021-9991

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Abstract

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be mod-elled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA)[25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well-mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. Abound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Related URLs:
Depositing User: Billy Wichaidit
Date Deposited: 15 Jun 2017 14:38
Last Modified: 15 Jun 2017 14:50
URI: http://sro.sussex.ac.uk/id/eprint/68621

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