Steady states of MESSI biological systems

A. DICKENSTEIN

Columbus, Ohio

Workshop; Workshop on Dynamics in Networks with Special Properties; 2016

Mathematical Biosciences Institute

We introduce a general framework for biological systems that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, which we call MESSI systems. Examples of MESSI systems are the sequential distributive or processive multisite phosphorylation networks, phosphorylation cascades, and the bacterial EnvZ/OmpR network. Assuming mass-action kinetics, we simplify the study of steady states and conservation laws of these systems by explicit elimination of intermediate complexes (inspired by [Feliu and Wiuf 2013, Thomson and Gunawardena 2009]).  We also describe an  important subclass of MESSI systems with toric steady states,  for which we give combinatorial conditions to determine multistationarity and the occurrence of relevant boundary steady states. Joint work with Mercedes Pérez Millán.