Date of Publication

9-2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Angelyn R. Lao
Eduardo R. Mendoza

Defense Panel Chair

Ederlina G. Nocon

Defense Panel Member

Noel T. Fortun
Eduardo R. Mendoza
Editha C. Jose
Bryan S. Hernandez

Abstract/Summary

This thesis examined two models of the gene regulatory system of Mycobacterium Tuberculosis (Mtb) presented as S-system by Magombedze and Mulder (2013). The models are partitioned into three subsystems based on putative gene function and role in dormancy/latency development. This study investigated the chemical reaction network (CRN) representation of the Mtb models and each subsystem to obtain new mathematical results in Chemical Reaction Network Theory. The subsystems are represented as embedded networks (an arc connecting two vertices that represent genes from different subsystems is retained). For the embedded networks of S_system CRNs (with at least two species) are discordant. Analyzing the subsystems as subnetworks, we formed a digraph homomorphism from the corresponding subnetworks to the embedded networks and explored the modularity concepts of digraph. Further analysis of the Mtb S-systems led us to develop different classes of decomposition of reaction networks based on the approach of Feinberg (1987) in decomposing a CRN and were used to correct a deficiency formula of Arceo et al. (2015).

Abstract Format

html

Language

English

Physical Description

104 leaves

Keywords

Mycobacterium tuberculosis--Mathematics; Chemical reactions; Differential equations, Nonlinear

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Embargo Period

10-5-2021

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