### Parametrizing multistationarity in multisite phosphorylation systems

14 July 2010

Anne Shiu

NSF Postdoc

Department of Mathematics

Duke University

#### Abstract

Multisite phosphorylation systems play key roles in signaling networks. A key property of these systems is their capacity for multistationarity. The focus of this talk is on the number of positive steady states of the n-site phosphorylation system (under the assumptions of a distributive and sequential mechanism) as a function of the rate constants and the conservation relations. Wang and Sontag (2008) reduced this problem of computing the number of steady states to that of counting the number of positive roots (that lie in certain intervals) of a parametrized family of one-variable polynomials. From this formulation, they prove bounds on the number of steady states and characterize certain regions of parameter space as giving rise to systems with one steady state and other regions as having many steady states.

This talk reports on extending the work on Wang and Sontag for the 2-site phosphorylation system. In particular, we highlight how techniques from real algebraic geometry allow us to compute the parameters which give rise to 1, 2 and 3 steady states. This is joint work with Carsten Conradi, Alicia Dickenstein, and Mercedes Pérez Millán.

virtual cell events