Time: 13:30-, May 11 (Wednesday), 2016
Speaker: Maya Mincheva (Department of Mathematical Sciences, Northern Illinois University)
Place: Room 435, Main Research Building, RIKEN
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Abstract:
Biochemical reaction networks are often modeled by large nonlinear dynamical systems with many unknown parameters, which complicates the numerical studies. The existence of multiple positive equilibria referred to as multistationarity, or a biological switch related to cell decision making, is an important property of biochemical reaction networks. The potential for multistationarity can be initially determined by the structure of a reaction network. We will discuss a graph-theoretic condition for multistationarity which includes the positive cycle condition as a special case. Similar graph-theoretic approach can be applied for reaction-diffusion models for the existence of Turing patterns, and for time delay models for the existence of oscillations.
An algorithm for finding multistationary parameter regions for dissipative biochemical reaction network models with bounded solutions will be presented. Multistationary and unique equilibrium regions are identified by studying the sign of a multivariate polynomial with coefficients consisting of parameters. Specifically a model for double phosphorylation will be analyzed for multistationarity. A simple parameter inequality splits the parameter space into regions where the existence of multistationarity or the uniqueness of an equilibrium is guaranteed. Other models of dissipative reaction networks analyzed for multistationarity using the same algorithm will be discussed as well.