Anne Shiu, Texas A&M University

Jueves 13/4, a las 16 hs. Sala de Conferencias DM-IMAS (2do piso Pab. I)

ABSTRACT: This talk focuses on the question of how two important dynamical properties, oscillations and bistability, emerge in important signaling networks arising in biology.  Specifically, we consider a mathematical model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We show that oscillations persist even as the model is greatly simplified.  Bistability, however, is much less robust.  We also investigate to what extent these two properties persist in an important limiting model.  Our results are enabled by several algebraic techniques:  a Hopf bifurcation criterion due to Yang, analyses of Newton polytopes arising from Hurwitz determinants, and recent characterizations of multistationarity for networks having a steady-state parametrization.