Ramp function approximations of Michaelis-Menten functions in biochemical dynamical systems

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dc.contributor.authorDore-Hall, Skye
dc.contributor.supervisorEdwards, Roderick
dc.date.accessioned2020-12-23T05:27:26Z
dc.date.available2020-12-23T05:27:26Z
dc.date.copyright2020en_US
dc.date.issued2020-12-22
dc.degree.departmentDepartment of Mathematics and Statisticsen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractIn 2019, Adams, Ehlting, and Edwards developed a four-variable system of ordinary differential equations modelling phenylalanine metabolism in plants according to Michaelis-Menten kinetics. Analysis of the model suggested that when a series of reactions known as the Shikimate Ester Loop (SEL) is included, phenylalanine flux into primary metabolic pathways is prioritized over flux into secondary metabolic pathways when the availability of shikimate, a phenylalanine precursor, is low. Adams et al. called this mechanism of metabolic regulation the Precursor Shutoff Valve (PSV). Here, we attempt to simplify Adams and colleagues’ model by reducing the system to three variables and replacing the Michaelis-Menten terms with piecewise-defined approximations we call ramp functions. We examine equilibria and stability in this simplified model, and show that PSV-type regulation is still present in the version with the SEL. Then, we define a class of systems structurally similar to the simplified Adams model called biochemical ramp systems. We study the properties of the Jacobian matrices of these systems and then explore equilibria and stability in systems of n ≥ 2 variables. Finally, we make several suggestions regarding future work on biochemical ramp systems.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/12485
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectMichaelis–Menten kineticsen_US
dc.subjectRamp functionsen_US
dc.subjectOrdinary differential equationsen_US
dc.subjectPiecewise linearen_US
dc.subjectBiochemical systemsen_US
dc.subjectDynamical systemsen_US
dc.subjectPhenylalanine metabolismen_US
dc.subjectMetabolic pathwaysen_US
dc.subjectLinear algebraen_US
dc.subjectEigenvaluesen_US
dc.subjectEquilibriaen_US
dc.subjectStabilityen_US
dc.titleRamp function approximations of Michaelis-Menten functions in biochemical dynamical systemsen_US
dc.typeThesisen_US

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