The Mathematics of Chemical Reaction Networks
Chemical Engineering & Mathematics, The Ohio State University
There is now quite a bit known about connections between reaction network structure and qualitative properties of the corresponding differential equations, especially when the reaction rates are described by classical mass action kinetics*. In fact, there are powerful theorems that permit deep inferences about qualitative behavior even when parameter values -- e.g., rate constants -- are unknown (the usual situation in biology). It is both fortunate and remarkable that the theorems themselves are easy to understand and easy to apply, even by those without extensive training in higher mathematics.
Approximately the first third of the course will devoted to a description of what is known; for this, a rudimentary acquaintance with linear algebra and ordinary differential equations should suffice. For the remainder of the course, we will begin to do proofs, and the mathematical requirements will deepen. But even then a good grounding in modern linear algebra and advanced calculus should suffice. The aim is not merely to exhibit proofs but, rather, to give students sufficient insight that they might become contributors to chemical reaction network theory.
Except for students who are taking the course for credit, participants should feel free to attend whatever parts of the course are of interest.
*Other canonical reaction rate descriptions, such as Michaelis-Menten kinetics invoked in enzyme chemistry, ultimately derive from mass action kinetics.