Special Mathematics Department Colloquium|
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.