Frontiers in Mathematics Lecture Series

Date: October 7, 2015

Time: 4:00PM - 5:00PM

Location: Blocker 220

Speaker: Alicia Dickenstein, University of Buenos Aires

Title: Computational algebraic geometry and biochemical reaction networks (Colloquium)

Abstract: In recent years, techniques from computational algebraic geometry have been successfully used to address mathematical challenges in systems biology. (Bio)chemical reaction networks define systems of ordinary differential equations with (in general, unknown) parameters. Under mass-action kinetics, these equations depend polynomially on the concentrations of the chemical species. Biologically-relevant steady states correspond thus to the positive real solutions of a structured system of polynomial equations. I will give a gentle introduction to the subject, based on joint work with C. Conradi, E. Feliu, S. Mueller, M. Perez Millan, G. Regensburger, and A. Shiu.  One of the major questions is to preclude or to guarantee multiple positive steady states.  I will explain this motivation and I will present necessary and sufficient conditions in terms of sign vectors.  I will also describe the structural properties of MESSI biological systems, which include all the popular mechanisms which present modifications of type enzyme substrate or swap with intermediates.