As I entered graduate school at the University of Illinois, my background in mathematics
became highly important. I was in a research group that studied, among other things,
the kinetic analysis of chemical reactions using pulsed-laser spectroscopy. The task
of analysis involves mathematical modeling of the concentration of key reactants and
products over time - this is a pure application of differential equations.
Because of my background in Mathematics, I became the computer/algorithm guy in the
research group, and I was responsible for most of the programs that were used to analyze
the kinetic results.
This experience in computers/math was primarily responsible for my entry into Computer-aided
Drug Design field. In that field, I use vector calculus, DE, and a good deal of Linear
Algebra. It is surprising how often an Eigen Vector analysis turns out to be the answer
to a drug design problem.
The Directed Tweak and the Tweak-Dock algorithms I have worked on directly use vector
calculus. The Hologram QSAR system is supported by fast Eigen vector analysis. ; The
Convex hull method for drug binding site prediction in fact calculates a convex hull
around the atoms of a drug receptor. Potential binding sites are almost universally
found to be groove, cavities, or other concave features on the protein surface. These
are identified as the volumes outside of the protein but inside the convex hull. This
algorithm works extremely well.
In short, I use my math training all of the time.