Effective Biological Science Through Mathematics

Oklahoma State University, Stillwater, OK

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The Effective Biological Science Through Mathematics (EBSM) project is an interdisciplinary effort involving faculty from the departments of Mathematics and Microbiology and Molecular Genetics. The goal is to contribute directly to student success in selected coursework areas in the biological sciences and to student retention in the biological sciences. The purpose of this project is to develop a series of mathematical studies related to quantitative topics that are difficult for students. Here, we focus on one topic: enzyme kinetics. The primary development activities include the development of this instructor- and student-friendly supplement on enzyme kinetics including simple enzyme kinetics, various forms of inhibition, and the effect of gating on Michaelis enzyme kinetics.

EBSM Michaelis-Menten Supplement
(EBSM M-M Supplement)

Enzymes are as indispensable to life as the nucleic acids, DNA, and RNA. As nucleic acids make the memory of a parent's genes available to the daughter generation of organisms, enzymes make the realization of those genetic traits possible. About the time that the cell was being understood to contain lipids, proteins, and nucleic acids the mathematics of enzyme kinetics was under development. Using assumptions later legitimized by J.B.S. Haldane, Michaelis and Menten developed a treatment of enzyme kinetics loosely based on chemical catalysts. In Michaelis and Menten's work, an enzyme is treated as a reacting model independent of the world around except for substrate and product. Surprisingly this elegant treatment has dropped out of many college courses even though it is a favorite target of post-graduate testing including the MCAT and biology GRE.

The Michaelis-Menten Model of Enzyme Saturation has been selected as the initial topic for this project. Several mathematical topics are essential for a quantitative understanding of this model. These include the significance of the concavity of a graph, the interpretation of approximate linearity, and the practical meaning of asymptotes. The unifying concept underlying these is that of a rate of change. The application of this concept in the context of this model is crucial for a quantitative understanding.

Understanding the connections between a scientific theory and the related mathematical model is fundamental. The traditional approach has been to develop a repertoire of mathematical skills in mathematics classrooms that are prerequisite to studying concepts of science. The notion seems simple enough: possessing the prerequisite mathematical skills should enable the science learner to apply these skills when needed in the study of science concept. Unfortunately, we have not had too much success with this approach. We have approached the problem differently. We have selected one essential scientific theory that instructors and students alike perplex over -enzyme kinetics- and have developed this instructor- and student-friendly supplement revisiting the necessary mathematics in the model. We have made this supplement readily available in a CD format at well through the internet.

The EBSM M-M Supplement includes a review of the mathematical content directly related to enzyme kinetics. Presented in this fashion, you can review that specific area of mathematics related to enzyme kinetics. Technology, the graphing calculator specifically, plays a great role in analyzing and summarizing experimental data. We have included a review of some of the more useful functions in this regard for the TI-83 graphing calculator; you should consult the TI-83 Guidebook for general operating procedures.

The components of the EBSM M-M Supplement are: Entering Functions for Graphing
Entering Statistical Data
Creating a List Name
Arranging Lists
Clearing Data from a List
Deleting Lists
Sorting Lists
Viewing Scatter Plots of L1 (X-Values) vs L2 (Y-Values)
Viewing a Box and Whisker Plot L1 (X-Values)
Creating a Histogram of L1 (X-Values)

Good Luck!

Douglas B. Aichele
Alan V. Noell
James T. Blankemeyer

Credits. The Effective Biological Sciences Through Mathematics Michaelis-Menten Supplement is made possible through funding to Oklahoma State University from the Howard Hughes Medical Institute. It is based on work sponsored wholly, or in part, by the Howard Hughes Program for Retention of Undergraduates in the Biological Sciences at Oklahoma State University.

Copyright. 2002 by Oklahoma State University

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This page is maintained by Doug Aichele (aichele@math.okstate.edu)

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