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dc.contributor.authorPetrides, Andreas
dc.date.accessioned2018-09-03T14:59:46Z
dc.date.available2018-09-03T14:59:46Z
dc.date.issued2018-10-20
dc.date.submitted2018-01-25
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279059
dc.description.abstractThis dissertation is concerned with the potential multistability of protein concentrations in the cell that can arise in biochemical networks. That is, situations where one, or a family of, proteins may sit at one of two or more different steady state concentrations in otherwise identical cells, and in spite of them being in the same environment. Models of multisite protein phosphorylation have shown that this mechanism is able to exhibit unlimited multistability. Nevertheless, these models have not considered enzyme docking, the binding of the enzymes to one or more substrate docking sites, which are separate from the motif that is chemically modified. Enzyme docking is, however, increasingly being recognised as a method to achieve specificity in protein phosphorylation and dephosphorylation cycles. Most models in the literature for these systems are deterministic i.e. based on Ordinary Differential Equations, despite the fact that these are accurate only in the limit of large molecule numbers. For small molecule numbers, a discrete probabilistic, stochastic, approach is more suitable. However, when compared to the tools available in the deterministic framework, the tools available for stochastic analysis offer inadequate visualisation and intuition. We firstly try to bridge that gap, by developing three tools: a) a discrete `nullclines' construct applicable to stochastic systems - an analogue to the ODE nullcines, b) a stochastic tool based on a Weakly Chained Diagonally Dominant M-matrix formulation of the Chemical Master Equation and c) an algorithm that is able to construct non-reversible Markov chains with desired stationary probability distributions. We subsequently prove that, for multisite protein phosphorylation and similar models, in the deterministic domain, enzyme docking and the consequent substrate enzyme-sequestration must inevitably limit the extent of multistability, ultimately to one steady state. In contrast, bimodality can be obtained in the stochastic domain even in situations where bistability is not possible for large molecule numbers. We finally extend our results to cases where we have an autophosphorylating kinase, as for example is the case with $Ca^{2+}$/calmodulin-dependent protein kinase II (CaMKII), a key enzyme in synaptic plasticity.
dc.description.sponsorshipEPSRC (1468514)
dc.language.isoen
dc.rightsAll rights reserved
dc.rightsAll Rights Reserveden
dc.rights.urihttps://www.rioxx.net/licenses/all-rights-reserved/en
dc.subjectMarkov processes
dc.subjectChemicals
dc.subjectMathematical model
dc.subjectSwitches
dc.subjectGenetics
dc.subjectSteady-state
dc.subjectStochastic systems
dc.subjectbimodal stationary distribution
dc.subjectlow feedback gain
dc.subjectsteady state distribution
dc.subjectdiscrete genetic toggle switch phenomena
dc.subjectMarkov chain tree theorem
dc.subjectlow dimensional nonlinear deterministic systems
dc.subjectdiscrete state stochastic systems
dc.subjectbiological systems
dc.subjectgraphical discrete nullcline-like construction
dc.subjectoriginal genetic toggle switch
dc.subjectfeedback interconnection
dc.subjectmutually repressing genes
dc.subjectPratt Tableau
dc.subjectMultistability
dc.subjectRoot locus
dc.subjectCaMKII
dc.titleAdvances in the stochastic and deterministic analysis of multistable biochemical networks
dc.typeThesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnameDoctor of Philosophy (PhD)
dc.publisher.institutionUniversity of Cambridge
dc.publisher.departmentEngineering
dc.date.updated2018-08-27T15:28:56Z
dc.identifier.doi10.17863/CAM.26440
dc.publisher.collegeTrinity College
dc.type.qualificationtitlePhD Engineeering
cam.supervisorVinnicombe, Glenn
cam.thesis.fundingtrue
rioxxterms.freetoread.startdate2018-08-27


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