Date of Award

2022

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Yildirim, Necmettin

Area of Concentration

Applied Mathematics with Statistics

Abstract

To maintain cellular homeostasis, cells continuously respond to external stimuli by employing a variety of regulatory mechanisms that often involve up-regulation of some proteins. This study focuses on deterministic and stochastic modeling and analysis of dynamics of a hypothetical protein P with negative autoregulations in E.coli. It assumes that the input signal up-regulates the protein P , and P down-regulates its own production using 2 types of autoregulatory mechanisms. The mathematical models are differential equations that describe the dynamics of mRNA and protein P for 3 scenarios: (1)Simplistic model with no regulation, (2)Model with transcriptional autoregulation, and (3)Model with translational autoregulation. The model parameters are estimated from previous literature for E.coli. The steady state and stability of each of the models are analyzed and the dynamics of P to step-like external transient signals is investigated as the signal amplitude and persistency change. Our analysis shows that the negative autoregulation models produce faster response to the signal compared to the model with no regulation, and they also control unnecessary protein synthesis. The return time to the resting states after removal of the signal is faster in the autoregulation models. Moreover, among all 3 models, only the transcriptional autoregulation model is capable of producing oscillatory dynamics. Gene networks are inherently noisy due to random fluctuations in protein molecules. To study regulatory roles of random fluctuations in the dynamics, we employed the Gillespie algorithm to simulate the models stochastically. At steady state, our stochastic simulations predict that the transcriptional autoregulation model is the noisiest followed by the simplistic model, and the translational autoregulation model has the lowest noise level. The noise level depends on the strength of inhibition. The transcriptional autoregulation model filters out the noise in the input signal for a period of time after the signal application, and this time becomes longer as the strength of the feedback gets stronger. The other two models do not filter out input noise to this extent.

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