Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation

Handle URI:
http://hdl.handle.net/10754/598320
Title:
Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation
Authors:
Mélykúti, Bence; Burrage, Kevin; Zygalakis, Konstantinos C.
Abstract:
The Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.
Citation:
Mélykúti B, Burrage K, Zygalakis KC (2010) Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation. J Chem Phys 132: 164109. Available: http://dx.doi.org/10.1063/1.3380661.
Publisher:
AIP Publishing
Journal:
The Journal of Chemical Physics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
2010
DOI:
10.1063/1.3380661
PubMed ID:
20441260
Type:
Article
ISSN:
0021-9606
Sponsors:
The authors wish to thank Thomas G. Kurtz for observing a mistake in an earlier version of this material which has been corrected subsequently. B.M.’s work was funded by the Engineering and Physical Sciences Research Council through a Doctoral Training Centre grant for the Life Sciences Interface Doctoral Training Centre, University of Oxford (Grant No. EP/E501605/1). K. C. Z. was supported by Award No. KUK-C1-013-04 made by the King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorMélykúti, Benceen
dc.contributor.authorBurrage, Kevinen
dc.contributor.authorZygalakis, Konstantinos C.en
dc.date.accessioned2016-02-25T13:18:39Zen
dc.date.available2016-02-25T13:18:39Zen
dc.date.issued2010en
dc.identifier.citationMélykúti B, Burrage K, Zygalakis KC (2010) Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation. J Chem Phys 132: 164109. Available: http://dx.doi.org/10.1063/1.3380661.en
dc.identifier.issn0021-9606en
dc.identifier.pmid20441260en
dc.identifier.doi10.1063/1.3380661en
dc.identifier.urihttp://hdl.handle.net/10754/598320en
dc.description.abstractThe Chemical Langevin Equation (CLE), which is a stochastic differential equation driven by a multidimensional Wiener process, acts as a bridge between the discrete stochastic simulation algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions there is another, simple formulation of the CLE with only m1 + m2 Wiener processes, whereas the standard approach uses 2 m1 + m2. We demonstrate that there are considerable computational savings when using this latter formulation. Such transformations of the CLE do not cause a loss of accuracy and are therefore distinct from model reduction techniques. We illustrate our findings by considering alternative formulations of the CLE for a human ether a-go-go related gene ion channel model and the Goldbeter-Koshland switch. © 2010 American Institute of Physics.en
dc.description.sponsorshipThe authors wish to thank Thomas G. Kurtz for observing a mistake in an earlier version of this material which has been corrected subsequently. B.M.’s work was funded by the Engineering and Physical Sciences Research Council through a Doctoral Training Centre grant for the Life Sciences Interface Doctoral Training Centre, University of Oxford (Grant No. EP/E501605/1). K. C. Z. was supported by Award No. KUK-C1-013-04 made by the King Abdullah University of Science and Technology (KAUST).en
dc.publisherAIP Publishingen
dc.titleFast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equationen
dc.typeArticleen
dc.identifier.journalThe Journal of Chemical Physicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Queensland, Brisbane, Australiaen
kaust.grant.numberKUK-C1-013-04en

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