A SHORT COURSE IN THE MODELING OF CHEMOTAXIS

Appendix A
Linear Chemical Reactions
There are several ways that one can translate a chemical schematic into math-
ematical equations. The most common assumption is that the reactions are linear
in the reactants. Here, I think it most instructive to explain this by going through
a typical (albeit fictitious) example. But first a few words about notation.
In the literature, particularly when composed by chemists, a given chemical
species is denoted differently when it appears in a chemical schematic than when it
appears in a differential equation. For example, suppose that the reaction involves
the polymerization of methyl methacrylate. In the chemical schematic, this might
be assigned a variable A (A + B → C) which is a symbol that denotes that methyl
methacrylate is one of the reactants but that has no notion of dimension associ-
ated with it. When translated into a mathematical equation, chemists will typically
denote the concentration of methyl methacrylate, which would have specified di-
mensions of Moles/Liter or perhaps micro Moles/Liter, by the related variable [A]
Thus the mathematical expression would look something like
d[A]
dt
= −k[A][B].
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