Algebraic methods for the study of biochemical reaction networks

A. DICKENSTEIN

Fort Worth, Texas

Congreso; CBMS Conference on ?Applications of Polynomial Systems?; 2018

Texas Christian University

In recent years, techniques from computationaland real algebraic geometry  have been successfully used to addressmathematical challenges in systems biology. The algebraic theory of chemicalreaction systems aims to understand their dynamic behavior by taking advantageof the inherent algebraic structure in the kinetic equations, and does not needa priori determination of the parameters, which can be theoretically orpractically impossible.I will describe general results based on the network structure.  Inparticular, I will explain a general framework for biological systems, calledMESSI systems, that describe Modifications of type Enzyme-Substrate or Swapwith Intermediates, and include many post-translational modification networks.I will also outline recent methods to address the important question ofmultistationarity.