Multistationarity in Biochemical Reaction Networks

Date Friday November 18, 2016 at 3:00 PM
Location 13-105 CHS, Center for the Health Sciences
Speaker Badal Joshi, Ph.D., Assistant Professor, Department of Mathematics, California State University, San Marcos
Sponsoring Dept UCLA Biomathematics
Abstract The dynamics of a biochemical reaction network are frequently modeled using ordinary differential equations containing numerous unknown parameters (reaction rate constants). The values of these rate constants are difficult to determine experimentally. It is imperative, therefore, to develop theory that can determine the range of qualitative behaviors that a network can possess without requiring detailed knowledge of the parameters. In this talk, I will focus on the existence (or absence) of multiple positive steady states for a reaction network, also known as multistationarity. Existence of multiple positive steady states provides the underpinnings for switching in biochemical reaction networks, while uniqueness of a positive stable steady state is necessary for robust system output. In recent years, there have been multiple advances on the fronts of both ruling out multistationarity and establishing multistationarity in reaction networks. The theoretical results fall under three major areas: (a) deficiency theory, (b) injectivity (Jacobian criteria), (c) lifting/network embedding. I will describe the main ideas in the three areas along with some of the more recent results.
Flyer Badal_Joshi_20161118.pdf