Alex Galarce

Date of Award

2016

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Yildirim, Necmettin

Area of Concentration

Applied Mathematics

Abstract

G-protein signaling pathways are conserved among many different kinds of organisms. They are important for a vast array of cellular activities. Among them is the transduction of extracellular signals into intracellular responses. These pathways have been experimentally studied extensively, but their system-level regulation is still poorly understood. One of the first attempts to study the system-level dynamic regulation of this pathway using real-time experimental data is the Yi-Kitano model. The model, making use of ordinary differential equations, takes the free receptor, active receptor, inactive G-protein, and active G-protein dynamics into account. Although the model includes both receptor and G-protein dynamics, it ignores a key negative regulator of the system due to Sst2, whose upregulation by pheromone has previously been shown experimentally. In this work, the Yi-Kitano model has been modified by including Sst2 as a dynamic variable. In addition, to make this model biologically more realistic, a time delay required for the transcription and translation of Sst2 has been added to the model. The new model is a six-dimensional nonlinear delay differential equation system. This model was numerically solved and compared with the experimental data collected by Yi-Kitano. It was seen that the model better captures the experimentally-observed dynamics of the active G-protein when compared to the Yi-Kitano model, particularly for the early part of the response before pheromone-induced Sst2 production begins. Furthermore, in order to study the effect of a transcriptional and translational time delay on the response dynamics, a reduced model was developed for the system. It was shown that the time delay can force the system into a regime of damped oscillation.

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