Computational algebraic geometry and biochemical reaction networks.

A DICKENSTEIN

Guanajuato

Congreso; Mathematical Congress of the Americas 2013; 2013

UMALCA - AMS

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. The nonlinearities usually prevent a mathematical analysis of network behaviour, which has largely been studied by numerical simulation and lacks a more comprehensive study of the dependence on the parameters.   The algebraic theory of chemical reaction systems aims to understand their dynamic behavior by taking advantage of the inherent algebraic structure in the kinetic equations, and does not need  a priori determination of the parameters, which can be practically and theoretically impossible. I will present a gentle introduction to the basic concepts and main questions, together with applications to enzymatic mechanisms.