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

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dc.contributor.author Dore-Hall, Skye
dc.date.accessioned 2020-12-23T05:27:26Z
dc.date.available 2020-12-23T05:27:26Z
dc.date.copyright 2020 en_US
dc.date.issued 2020-12-22
dc.identifier.uri http://hdl.handle.net/1828/12485
dc.description.abstract In 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.language English eng
dc.language.iso en en_US
dc.rights Available to the World Wide Web en_US
dc.subject Michaelis–Menten kinetics en_US
dc.subject Ramp functions en_US
dc.subject Ordinary differential equations en_US
dc.subject Piecewise linear en_US
dc.subject Biochemical systems en_US
dc.subject Dynamical systems en_US
dc.subject Phenylalanine metabolism en_US
dc.subject Metabolic pathways en_US
dc.subject Linear algebra en_US
dc.subject Eigenvalues en_US
dc.subject Equilibria en_US
dc.subject Stability en_US
dc.title Ramp function approximations of Michaelis-Menten functions in biochemical dynamical systems en_US
dc.type Thesis en_US
dc.contributor.supervisor Edwards, Roderick
dc.degree.department Department of Mathematics and Statistics en_US
dc.degree.level Master of Science M.Sc. en_US
dc.description.scholarlevel Graduate en_US

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