Enzyme Kinetics and the Michaelis-Menten Equation

• Published in: PRIMUS : problems, resources, and issues in mathematics undergraduate studies Vol. 20; no. 2; pp. 148 - 168
• Main Authors: Biaglow, Andrew, Erickson, Keith, McMurran, Shawnee
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis Group 01.02.2010; Taylor & Francis, Ltd; Taylor & Francis Ltd
• Subjects: Biochemistry; Biology; Calculus; Catalysts; Chemistry; College Mathematics; conservation of mass; Difference equations; Differential equations; elementary differential equations; enzyme catalysis; Enzyme kinetics; Enzymes; Equations (Mathematics); Euler's method; Experiments; Kinetics; law of mass action; linearization; mass balance; Mass balance models; Mathematical analysis; Mathematical Concepts; Mathematics Instruction; Michaelis-Menten kinetics; Parameter estimation; Scientific Concepts; Teaching Methods
• ISSN: 1051-1970; 1935-4053
• DOI: 10.1080/10511970903486491

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]