Special Mathematics Department Colloquium Gheorge Craciun Mathematical Biosciences Institute, Ohio State Univesity "Mathematical Models of Neurofilament Transport in Axons" Tuesday January 18, 2005 4:15pm in JWB 335 In nature there are millions of distinct networks of biochemical reactions that might present themselves for study at one time or another. Each reaction network gives rise to its own system of differential equations. These are usually high dimensional, nonlinear, and have many unknown parameters. Nevertheless, each reaction network induces its corresponding differential equations (up to parameter values) in a precise way. This raises the possibility that qualitative properties of the induced differential equations might be tied directly to reaction network structure. We will show that reaction diagrams, similar to those that biochemists usually draw, carry subtle information about a reaction network's capacity to exhibit multiple equilibria. Some of these results suggest interesting new problems in real algebraic geometry and graph theory. We will also discuss implications for the interpretation of experiments in cell biology.