A higher-order numerical framework for stochastic simulation of chemical reaction systems.

Handle URI:
http://hdl.handle.net/10754/596756
Title:
A higher-order numerical framework for stochastic simulation of chemical reaction systems.
Authors:
Székely, Tamás; Burrage, Kevin; Erban, Radek; Zygalakis, Konstantinos C
Abstract:
BACKGROUND: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system. RESULTS: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. CONCLUSIONS: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.
Citation:
Székely T, Burrage K, Erban R, Zygalakis KC (2012) A higher-order numerical framework for stochastic simulation of chemical reaction systems. BMC Syst Biol 6: 85. Available: http://dx.doi.org/10.1186/1752-0509-6-85.
Publisher:
Springer Nature
Journal:
BMC Systems Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
15-Jul-2012
DOI:
10.1186/1752-0509-6-85
PubMed ID:
23256696
PubMed Central ID:
PMC3529698
Type:
Article
ISSN:
1752-0509
Sponsors:
TSz is supported by the Engineering and Physical Sciences Research Council through the Systems Biology Doctoral Training Centre, University of Oxford. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) /ERC grant agreement No. 239870. RE would also like to thank Somerville College, University of Oxford, for a Fulford Junior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. TSz would like to thank Manuel Barrio for his discussions and help with the simulations. KCZ would like to thank James Lottes for his invaluable comments regarding the global error expansion.
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Full metadata record

DC FieldValue Language
dc.contributor.authorSzékely, Tamásen
dc.contributor.authorBurrage, Kevinen
dc.contributor.authorErban, Radeken
dc.contributor.authorZygalakis, Konstantinos Cen
dc.date.accessioned2016-02-21T08:49:58Zen
dc.date.available2016-02-21T08:49:58Zen
dc.date.issued2012-07-15en
dc.identifier.citationSzékely T, Burrage K, Erban R, Zygalakis KC (2012) A higher-order numerical framework for stochastic simulation of chemical reaction systems. BMC Syst Biol 6: 85. Available: http://dx.doi.org/10.1186/1752-0509-6-85.en
dc.identifier.issn1752-0509en
dc.identifier.pmid23256696en
dc.identifier.doi10.1186/1752-0509-6-85en
dc.identifier.urihttp://hdl.handle.net/10754/596756en
dc.description.abstractBACKGROUND: In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system. RESULTS: By obtaining a global error expansion for a general weak first-order method, we prove that extrapolation can increase the weak order of convergence for the moments of the Euler and the midpoint τ-leap methods, from one to two. This is supported by numerical simulations of several chemical systems of biological importance using the Euler, midpoint and θ-trapezoidal τ-leap methods. In almost all cases, extrapolation results in an improvement of accuracy. As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. CONCLUSIONS: Extrapolation is a general framework for increasing the order of accuracy of any fixed-step stochastic solver. This enables the simulation of complicated systems in less time, allowing for more realistic biochemical problems to be solved.en
dc.description.sponsorshipTSz is supported by the Engineering and Physical Sciences Research Council through the Systems Biology Doctoral Training Centre, University of Oxford. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) /ERC grant agreement No. 239870. RE would also like to thank Somerville College, University of Oxford, for a Fulford Junior Research Fellowship; Brasenose College, University of Oxford, for a Nicholas Kurti Junior Fellowship; the Royal Society for a University Research Fellowship; and the Leverhulme Trust for a Philip Leverhulme Prize. TSz would like to thank Manuel Barrio for his discussions and help with the simulations. KCZ would like to thank James Lottes for his invaluable comments regarding the global error expansion.en
dc.publisherSpringer Natureen
dc.rightsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.en
dc.rights.urihttp://creativecommons.org/licenses/by/2.0en
dc.subject.meshMonte Carlo Methoden
dc.subject.meshModels, Biologicalen
dc.titleA higher-order numerical framework for stochastic simulation of chemical reaction systems.en
dc.typeArticleen
dc.identifier.journalBMC Systems Biologyen
dc.identifier.pmcidPMC3529698en
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionQueensland University of Technology QUT, Brisbane, Australiaen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Southampton, Southampton, United Kingdomen
dc.contributor.institutionEcole Polytechnique Federale de Lausanne, Lausanne, Switzerlanden
kaust.grant.numberKUK-C1-013-04en

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