Algebraic methods for the study of biochemical reaction networks

A DICKENSTEIN

Santander

Congreso; Bienal Real Sociedad Matemática Española; 2019

RSME y Universidad de Santander

In recent years, techniques from computational and real algebraic geometry have beensuccessfully used to address mathematical challenges in systems biology. (Bio)chemicalreaction networks dene systems of ordinary differential equations with (in general, un-known) parameters. Under mass-action kinetics, these equations depend polynomiallyon the concentrations of the chemical species. The algebraic theory of chemical reactionsystems aims to understand their dynamic behavior by taking advantage of the inherentalgebraic structure in the kinetic equations, and does not need a priori determination ofthe parameters, which can be theoretically or practically impossible.I will describe general results based on the network structure. In particular, I willexplain a general framework for biological systems, called MESSI systems, that describeModications of type Enzyme-Substrate or Swap with Intermediates, and include manypost-translational modication networks. I will also outline recent methods to addressthe important question of multistationarity.