Algebra and geometry in the study of enzymatic cascades

ALICIA DICKENSTEIN

Conferencia; Coloquio Departamental; 2019

University of Wisconsin, Madison

In recent years, techniques from computational and real algebraicgeometry have been successfully used to address mathematical challenges insystems biology. The algebraic theory of chemical reaction systems aims tounderstand their dynamic behavior by taking advantage of the inherent algebraicstructure in the kinetic equations, and does not need the determination of theparameters a priori, which can be theoretically or practically impossible.I will give a gentle introduction to general results based on thenetwork structure. In particular, I will describe a general framework forbiological systems, called MESSI systems, that describe Modifications of typeEnzyme-Substrate or Swap with Intermediates, and include many networks thatmodel post-translational modifications of proteins inside the cell. I will alsooutline recent methods to address the important question of multistationarity,in particular in the study of enzymatic cascades, and will point out some ofthe mathematical challenges that arise from this application.