Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

Handle URI:
http://hdl.handle.net/10754/597550
Title:
Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
Authors:
Erban, Radek; Chapman, S. Jonathan; Kevrekidis, Ioannis G.; Vejchodský, Tomáš
Abstract:
A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
Citation:
Erban R, Chapman SJ, Kevrekidis IG, Vejchodský T (2009) Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model. SIAM Journal on Applied Mathematics 70: 984–1016. Available: http://dx.doi.org/10.1137/080731360.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2009
DOI:
10.1137/080731360
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
Received by the editors July 28, 2008; accepted for publication ( in revised form) June 9, 2009; published electronically August 21, 2009. This work is based on work supported by St. John's College, Oxford; Linacre College, Oxford; Somerville College, Oxford; and by award KUK-C1-013-04, given by King Abdullah University of Science and Technology (KAUST) (RE).
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Full metadata record

DC FieldValue Language
dc.contributor.authorErban, Radeken
dc.contributor.authorChapman, S. Jonathanen
dc.contributor.authorKevrekidis, Ioannis G.en
dc.contributor.authorVejchodský, Tomášen
dc.date.accessioned2016-02-25T12:41:52Zen
dc.date.available2016-02-25T12:41:52Zen
dc.date.issued2009-01en
dc.identifier.citationErban R, Chapman SJ, Kevrekidis IG, Vejchodský T (2009) Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model. SIAM Journal on Applied Mathematics 70: 984–1016. Available: http://dx.doi.org/10.1137/080731360.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/080731360en
dc.identifier.urihttp://hdl.handle.net/10754/597550en
dc.description.abstractA framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipReceived by the editors July 28, 2008; accepted for publication ( in revised form) June 9, 2009; published electronically August 21, 2009. This work is based on work supported by St. John's College, Oxford; Linacre College, Oxford; Somerville College, Oxford; and by award KUK-C1-013-04, given by King Abdullah University of Science and Technology (KAUST) (RE).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectChemical Fokker-Planck equationen
dc.subjectStochastic bifurcationsen
dc.titleAnalysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Modelen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionPrinceton University, Princeton, United Statesen
dc.contributor.institutionAcademy of Sciences of the Czech Republic, Prague, Czech Republicen
kaust.grant.numberKUK-C1-013-04en
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