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

PEREZ MILLÁN, MERCEDES; TURJANSKI, ADRIÁN G.

MATHEMATICAL BIOSCIENCES

elsevier

Lugar: Amsterdam; Año: 2015 vol. 262 p. 125 - 137

0025-5564

Abstract. Mitogen-activated protein kinase (MAPK) signaling pathways playan 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 MAPKextracellular activated protein kinase (ERK) cascade represent attractive targetsfor cancer therapy as their aberrant activation is a frequent event amonghighly prevalent human cancers. MAPK networks are a model for computationalsimulation, mostly using Ordinary and Partial Differential Equations.Key results showed that these networks can have switch-like behavior, bistabilityand oscillations. In this work, we consider three representative ERKnetworks, one with a negative feedback loop, which present a binomial steadystate ideal under mass-action kinetics. We therefore apply the theoretical resultpresent in P´erez Mill´an et al. (2012) to find a set of rate constants thatallow two significantly different stable steady states in the same stoichiometriccompatibility class for each network. Our approach makes it possible to studycertain aspects of the system, such as multistationarity, without relying onsimulation, since we do not assume a priori any constant but the topology ofthe network. As the performed analysis is general it could be applied to manyother important biochemical networks