Algebraic methods for the study of biochemical reaction networks

A. DICKENSTEIN

Seminario; ICTP Math Seminar; 2017

ICTP

ICTP Math Seminar, Trieste, Italia, 2017. Alicia Dickenstein (UBA-CONICET, Argentina) Title: Algebraicmethods for the study of biochemical reaction networks  Abstract:In recent years, techniquesfrom computational and real algebraic geometry have been successfully used toaddress mathematical challenges in systems biology. (Bio)chemical reactionnetworks define systems of ordinary differential equations with (in general,unknown) parameters. Under mass-action kinetics, these equations dependpolynomially on the concentrations of the chemical species. The algebraictheory of chemical reaction systems aims to understand their dynamic behaviorby taking advantage of the inherent algebraic structure in the kineticequations, and does not need a priori determination of the parameters, whichcan be theoretically or practically impossible. I will first present a gentleintroduction to the basic concepts. I will then describe general results basedon the network structure.  In particular,I will explain a general framework for biological systems, called MESSI systems,that describe Modifications of type Enzyme-Substrate or Swap withIntermediates, and include many post-translational modification networks. Iwill also outline recent methods to detect the capacity for multistationarityand to describe parameters for which multistationarity occurs, allowing formultiple steady states with the same total amounts.