Algebraic methods for the study of biochemical reaction networks

A DICKENSTEIN

Seminario; Seminar on Nonlinear Algebra; 2017

Max Planck Institute for Mathematics and the Sciences

:  In recent years, techniques from computationaland real algebraic geometry  have beensuccessfully used to address mathematical challenges in systems biology.(Bio)chemical reaction networks define systems of ordinary differentialequations with (in general, unknown) parameters. Under mass-action kinetics,these equations depend polynomially on the concentrations of the chemicalspecies. The algebraic theory of chemical reaction systems aims to understandtheir dynamic behavior by taking advantage of the inherent algebraic structurein the kinetic equations, and does not need a priori determination of theparameters, which can be theoretically or practically impossible. Iwill first present a gentle introduction to the basic concepts. I will thendescribe general results based on the network structure.  In particular, I will explain a generalframework for biological systems, called MESSI systems, that describeModifications of type Enzyme- Substrate or Swap with Intermediates, and includemany post-translational modification networks. I will also outline recent methodsto detect the capacity for multistationarity and to describe parameters forwhich multistationarity occurs, allowing for multiple steady states with thesame total amounts.