Expanding ODE Examples: Introducing Gene Regulation Dynamics through Hill Functions

Authors

Maila Hallare, United States Air Force AcademyFollow
Jane M. Santamore, United States Air Force AcademyFollow

Publication Date

11-3-2025

Keywords

Hill functions, feedback loops, nullclines, cooperative and competitive systems, MATLAB simulation

Disciplines

Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Gene regulation is a fundamental biological process that controls gene expression. It can explain phenomena such as cell differentiation, circadian rhythms, disease progression, and metabolic control, among many others. Despite their importance in mathematical biology, gene regulation models are rarely featured in traditional ODE textbooks, which focus mainly on examples from engineering, physics, chemistry, and population biology. This article introduces gene regulation dynamics as a valuable addition to ODE curricula, presenting the models from a mathematical perspective and building on properties of the Hill function. These models deepen the understanding of biology-inspired ODE applications, provide accessible research opportunities for students, and foster interdisciplinary collaboration for faculty.

Recommended Citation

Hallare, Maila and Santamore, Jane M. (2025) "Expanding ODE Examples: Introducing Gene Regulation Dynamics through Hill Functions," CODEE Journal: Vol. 19, Article 6.
Available at: https://scholarship.claremont.edu/codee/vol19/iss1/6