Algebra and geometry in the study of enzymatic cascades

ALICIA DICKENSTEIN

Berna

Congreso; SIAM AG 19; 2019

In recent years, techniques fromcomputational and real algebraic geometry  have been successfully used toaddress mathematical challenges in systems biology. The algebraic theory ofchemical reaction systems aims to understand their dynamic behavior by takingadvantage of the inherent algebraic structure in the kinetic equations, anddoes not need the determination of the parameters a priori, which can betheoretically or practically impossible.I will give a gentle introduction to general results based on the networkstructure.  In particular, I will describe a general framework forbiological systems,  called MESSI systems, that describe Modifications oftype Enzyme-Substrate or Swap with Intermediates, and include many networksthat model post-translational modifications of proteins inside the cell. I willalso outline recent methods to address the important question ofmultistationarity, in particular in the study of enzymatic cascades, and willpoint out some of the mathematical challenges that arise from this application.