Date of Award

2018

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Yildirim, Necmettin

Area of Concentration

Applied Mathematics

Abstract

As a means of maintaining homeostasis, a cell must actively respond to external stimuli by employing regulatory mechanisms that may influence the synthesis rate of specific proteins. These regulatory mechanisms are often triggered by external signals that are transmitted between genes, forming genetic interactions. Recurring patterns of interactions within cells are known as genetic motifs. For this study, one such motif, called auto-regulation, was mathematically modeled in order to explore its dynamic response to transient signals. Auto-regulation can be either positive or negative; this study focused on a positive auto-regulatory model, on which transient signals of varying strength and persistence were applied. Depending on where in the network it is applied, the signal can be inhibitory or activatory; inhibitory if the signal decreases the protein abundance, and activatory if it causes increase. To compare the mechanisms, response metrics quantifying different aspects of the model’s deterministic behavior were used. The Gillespie algorithm was also implemented to study the noise dynamics in these mechanisms. It was found that, although the pairs of inhibitory and activatory mechanisms showed an overall decrease or increase in protein levels, each had distinctive response dynamics and stochasticity. These results confirm that the positive autoregulatory model is versatile, and serves an important role in regulating protein synthesis. By computationally studying the autoregulatory response to signals of varying magnitude, one can better understand the genetic interactions of different organisms, and their responses to various environmental stimuli.

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