Publication Date

Spring 2019

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

Advisor

Matthew D. Johnston

Keywords

chemical reaction network theory, dynamical systems, graph theory, multi-stationary, steady states

Subject Areas

Applied mathematics

Abstract

In this paper, we investigate results from chemical reaction network theory and a list of techniques to test for the reaction-coordinates dynamical system to have a partial order induced by a positive orthant cone. A successful result from one of these tests guarantees mono-stationarity (and indeed convergence). We also investigate a recently published algorithmic and computational approach to determine whether a reaction network establishes mono- or multi-stationarity. We test new reactions that have not been previously introduced in the literature for mono- or multi-stationarity using this approach. This includes the two-site phosphorylation reaction network and a modified double phosphorylation reaction network that more accurately models the action of the enzymes of two distinct sites. We also use the enzymatic futile cycle as a running example to illustrate these results. We conclude the two-site phosphorylation reaction network is multi-stationary; while the original double phosphorylation reaction network is also multi-stationary, our modified version is mono-stationary.

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Hernandez_sjsu_6265M_150.zip (6740 kB)
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