Algebra and geometry in the study of enzymatic cascades

ALICIA DICKENSTEIN

Conferencia; Cattedra Fubini; 2019

Politécnico de Turín

In recent years, techniquesfrom computational 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, and doesnot need the determination of the parameters a priori, which can betheoretically or practically impossible.I will give a gentleintroduction to general results based on the network structure. In particular,I will describe a general framework for biological systems, called MESSIsystems, that describe Modifications of type Enzyme-Substrate or Swap withIntermediates, and include many networks that model post-translationalmodifications of proteins inside the cell. I will also outline recent methodsto address the important question of multistationarity, in particular in thestudy of enzymatic cascades, and will point out some of the mathematicalchallenges that arise from this application.