Enzyme Kinetics and the Michaelis-Menten Equation

Abstract The concepts presented in this article represent the cornerstone of classical mathematical biology. The central problem of the article relates to enzyme kinetics, which is a biochemical system. However, the theoretical underpinnings that lead to the formation of systems of time-dependent ordinary differential equations have been applied widely to any biological system that involves modeling of populations. In this project, students first learn about the general balance equation, which is a statement of conservation within a system. They then learn how to simplify the balance equation for several specific cases involving chemically reacting systems. Derivations are reinforced with a concrete experiment in which enzyme kinetics are illustrated with pennies. While a working knowledge of differential equations and numerical techniques is helpful as a prerequisite for this set of activities, all of the requisite mathematical skills are introduced in the project, so the methods would also serve as an introduction to these techniques. It is also helpful if students have some basic understanding of chemical concepts such as concentration and reaction rate, as typically covered in high school or college freshman chemistry courses. [Supplementary materials are available for this article. Go to the publisher's online edition of PRIMUS for the following free supplemental resource(s): Appendices and Sample Solution]