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# Some Mathematical and Statistical Aspects of Enzyme Kinetics

## Tilte Page

#### Abstract

Most calculus or differential equations courses utilize examples taken from physics, often discussing them in great detail. Chemistry, however, is seldom utilized to illustrate mathematical concepts. This tendency should be reversed because chemistry, especially chemical kinetics, provides the opportunity to apply mathematics readily. We will analyze some basic ideas behind enzyme kinetics, which allow us to deal with separable and linear differential equations as well as realize the need to use power series to approximate $$e^x$$ and ln(1 + x) close to the origin, and to apply the recently defined Lambert W function.

The models studied in this context require the estimation of parameters based on experimental data, which in turn allows us to discuss simple and multiple linear regression, transformations and non-linear regression and their implementation using statistical software.

#### Author Information

Michel Helfgott (helfgott@etsu.edu) is Associate Professor in the Department of Mathematics, East Tennessee State University. He is interested in the relationship between mathematics and the natural sciences, as well as in the history of mathematics.

Edith Seier (seier@etsu.edu) is Associate Professor in the Department of Mathematics, East Tennessee State University. Her areas of current interest are kurtosis and variability, statistical consulting, and teaching statistics with an active learning approach in the context of biology.

#### Keywords

• chemistry
• enzyme kinetics
• calculus
• differential equations
• statistics
• Lambert W function

#### Publication data

• Published October, 2007; article ID 1611