MAPK's networks and their capacity for multistationarity due to toric steady states

TL;DR

This paper explores the capacity for multistationarity in MAPK networks with toric steady states, using a theoretical approach that bypasses simulation and applies to various biochemical networks.

Contribution

It introduces a method to identify multiple stable steady states in MAPK networks based on network topology and toric steady states, without relying on numerical simulations.

Findings

MAPK networks can exhibit multistationarity with appropriate rate constants.

Theoretical approach applies to networks with binomial steady state ideals.

Method enables analysis of multistationarity without simulation.

Abstract

Mitogen-activated protein kinase (MAPK) signaling pathways play an essential role in the transduction of environmental stimuli to the nucleus, thereby regulating a variety of cellular processes, including cell proliferation, differentiation and programmed cell death. The components of the MAPK extracellular activated protein kinase (ERK) cascade represent attractive targets for cancer therapy as their aberrant activation is a frequent event among highly prevalent human cancers. MAPK networks are a model for computational simulation, mostly using Ordinary and Partial Differential Equations. Key results showed that these networks can have switch-like behavior, bistability and oscillations. In this work, we consider three representative ERK networks, one with a negative feedback loop, which present a binomial steady state ideal under mass-action kinetics. We therefore apply the theoretical result present in P\'erez Mill\'an et. al (2012) to find a set of rate constants that allow two significantly different stable steady states in the same stoichiometric compatibility class for each network. Our approach makes it possible to study certain aspects of the system, such as multistationarity, without relying on simulation, since we do not assume a priori any constant but the topology of the network. As the performed analysis is general it could be applied to many other important biochemical networks.