Circuits of multistationarity in structured enzymatic networks

MAGALÍ GIAROLI; ALICIA DICKENSTEIN; RICK RISCHTER; MERCEDES PÉREZ MILLÁN

Seminario; Seminar on the Mathematics of Reaction Networks; 2021

In this work we focus on minimal sets of intermediate speciesand their location in the network to allow for multistationarity in thecorresponding mass-action chemical reaction system. This question has alsobeen studied in Feliu and Wiuf (2013) and also in Sadeghimanesh and Feliu(2019) using degree theory techniques. Our results simplify the analysisfor chemical reaction systems with certain structure, called "linearlybinomial networks" [Dickenstein, P.M., Shiu, Tang (2019)]. We apply ourresults on several signaling networks. We also refer to the problem oflifting of multistationarity, and we give easy combinatorial conditionsfor MESSI networks [P.M., Dickenstein (2018)] to be linearly binomial.