On a jump Markovian model for a gene regulatory network

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dc.contributor.authorDe La Chevrotière, Michèle
dc.contributor.supervisorReinhard, Illner
dc.date.accessioned2008-05-01T00:26:00Z
dc.date.available2008-05-01T00:26:00Z
dc.date.copyright2008en_US
dc.date.issued2008-05-01T00:26:00Z
dc.degree.departmentDept. of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractWe present a model of coupled transcriptional-translational ultradian oscillators (TTOs) as a possible mechanism for the circadian rhythm observed at the cellular level. It includes nonstationary Poisson interactions between the transcriptional proteins and their affined gene sites. The associated reaction-rate equations are nonlinear ordinary differential equations of stochastic switching type. We compute the deterministic limit of this system, or the limit as the number of gene-proteins interactions per unit of time becomes large. In this limit, the random variables of the model are simply replaced by their limiting expected value. We derive the Kolmogorov equations — a set of partial differential equations —, and we obtain the associated moment equations for a simple instance of the model. In the stationary case, the Kolmogorov equations are linear and the moment equations are a closed set of equations. In the nonstationary case, the Kolmogorov equations are nonlinear and the moment equations are an open-ended set of equations. In both cases, the deterministic limit of the moment equations is in agreement with the deterministic state equations.en_US
dc.identifier.urihttp://hdl.handle.net/1828/933
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectGenetic Oscillatoren_US
dc.subjectCircadian Rhythmen_US
dc.subjectMarkov Processen_US
dc.subjectStochastic Switching Systemen_US
dc.subjectKolmogorov Equationsen_US
dc.subjectMoment Equationsen_US
dc.subject.lcshUVic Subject Index::Sciences and Engineering::Mathematicsen_US
dc.titleOn a jump Markovian model for a gene regulatory networken_US
dc.typeThesisen_US

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