Families of Polynomials in the Study of Biochemical Reaction Networks

The standard mass-action kinetics modeling of the dynamics of biochemical reaction networks gives rise to systems of ordinary polynomial differential equations with (in general unknown) parameters. Attempts to explore the parameter space in order to predict properties of the associated systems challenge the standard current computational tools because even for moderately small networks we need to study families of polynomials with many variables and many parameters. These polynomials have a combinatorial structure that comes from the digraph of reactions. We show that different techniques can be strengthened and applied for biochemical networks with special structure.