Harnessing steady-state parametrizations arising from reaction networks

Reaction networks taken with mass-action kinetics arise in many settings, from epidemiology to population biology to systems of chemical reactions. This talk focuses on certain biological signaling networks, namely, multisite phosphorylation networks. Many of these systems exhibit “toric steady states” (that is, the ODEs generate a binomial ideal), and more generally the set of steady states admits a rational parametrization, that is, the set is the image of a map with rational-function coordinates. We describe how this parametrization allows us to investigate the dynamics of two multisite phosphorylation networks: the emergence of bistability in a network underlying ERK regulation, and the capacity for oscillations in a mixed processive/distributive phosphorylation network. This is joint work with Carsten Conradi and Maya Mincheva.