Date of Award

Spring 2020

Degree Name

Bachelor of Arts

Department

Computer Science & Mathematics; College of Arts & Sciences

First Advisor

Dr. Carlos Ortiz

Abstract

Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in their technical report, “A Continuous Model of Gene Expression”, as wellas past models that inspired theirs. I solve the model by Hunt et al. for variousequilibrium points and analyze those points through eigenvalues and bifurcations to understand the biological relevance.

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Modeling Gene Expression with Differential Equations

Gene expression is the process by which the information stored in DNA is convertedinto a functional gene product, such as protein. The two main functions that makeup the process of gene expression are transcription and translation. Transcriptionand translation are controlled by the number of mRNA and protein in the cell. Geneexpression can be represented as a system of first order differential equations for the rateof change of mRNA and proteins. These equations involve transcription, translation,degradation and feedback loops. In this paper, I investigate a system of first orderdifferential equations to model gene expression proposed by Hunt, Laplace, Miller andPham in their technical report, “A Continuous Model of Gene Expression”, as wellas past models that inspired theirs. I solve the model by Hunt et al. for variousequilibrium points and analyze those points through eigenvalues and bifurcations to understand the biological relevance.

 
 

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