Algebraic methods in biochemical reaction networks

M. PÉREZ MILLÁN

CABA

Congreso; Mathematical Methods and Modeling in Engineering and Life Sciences, V International Conference on Applied Mathematics, Design and Control; 2018

Universidad de San Martín

Biochemical reaction networks give rise, through mass-action kinetics, topolynomial dynamical systems. Algebraic methods have proved to be a useful tool to obtain results by exploiting the network structure, regardless of specific values for the kinetic equations parameters. One important aspect to address are the steady states of biochemical systems. I will show how algebraic tools can help to determine whether certain well structured biochemical systems have the capacity for multistationarity, and when then do, it is possible to explicitly find witnesses to multistationarity. This means that we can find parameter values and two different positive solutions for the corresponding polynomial system of equations. I will also focus on a different aspect that can also be approached by algebraic tools: the identifiability of the parameters by measuring a reduced set of biologically relevant species. I will apply these results to a specific biological system: the phosphorylation signaling cascade.