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.
Recommended Citation
Kuduk, Madison, "Modeling Gene Expression with Differential Equations" (2020). Capstone Showcase. 20.
https://scholarworks.arcadia.edu/showcase/2020/comp_sci_math/20
Included in
Cell Biology Commons, Genomics Commons, Numerical Analysis and Scientific Computing Commons, Ordinary Differential Equations and Applied Dynamics Commons
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.