Math Biosci. 2015 Apr;262:125-37. doi: 10.1016/j.mbs.2014.12.010. Epub 2015 Jan 30.

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

Mathematical biosciences

Mercedes Pérez Millán, Adrián G Turjanski

PMID: 25640872 DOI: 10.1016/j.mbs.2014.12.010

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 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.

Copyright © 2015 Elsevier Inc. All rights reserved.

Keywords: MAPK; Mass-action kinetics; Multistationarity; Signaling networks; Toric steady states

MeSH terms

• Feedback, Physiological
• Humans
• Kinetics
• MAP Kinase Signaling System*
• Mathematical Concepts
• Models, Biological

Publication Types

• Journal Article
• Research Support, Non-U.S. Gov't