Modern methods for the study of biochemical reaction networks

A DICKENSTEIN

Comodoro Rivadavia

Congreso; VI MACI; 2017

Universidad Nacional de la Patagonia San Juan Bosco

In recent years, techniques from computational and real algebraicgeometry  have been successfully used to address mathematical challengesin systems biology. (Bio)chemical reaction networks define systems of ordinarydifferential equations with (in general, unknown) parameters. Under mass-actionkinetics, these equations depend polynomially on the concentrations of thechemical species. 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 a priori determination ofthe parameters, which can be theoretically or practically impossible.I will first present a gentle introduction to the basic concepts. I will thendescribe general results based on the network structure.  In particular, Iwill explain a general framework for biological systems, called MESSI systems,that describe Modifications of type Enzyme- Substrate or Swap withIntermediates, and include many post-translational modification networks. Iwill also outline recent methods to detect the capacity for multistationarityand to describe parameters for which multistationarity occurs, allowing formultiple steady states with the same total amounts.