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.
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
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