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Mitogen-activated protein kinase (MAPK) signaling pathways play an essentialrole in the transduction of environmental stimuli to the nucleus, therebyregulating a variety of cellular processes, including cell proliferation,differentiation and programmed cell death. The components of the MAPKextracellular activated protein kinase (ERK) cascade represent attractivetargets for cancer therapy as their aberrant activation is a frequent eventamong highly prevalent human cancers. MAPK networks are a model forcomputational simulation, mostly using Ordinary and Partial DifferentialEquations. Key results showed that these networks can have switch-likebehavior, bistability and oscillations. In this work, we consider threerepresentative ERK networks, one with a negative feedback loop, which present abinomial steady state ideal under mass-action kinetics. We therefore apply thetheoretical result present in P\'erez Mill\'an et. al (2012) to find a set ofrate constants that allow two significantly different stable steady states inthe same stoichiometric compatibility class for each network. Our approachmakes it possible to study certain aspects of the system, such asmultistationarity, without relying on simulation, since we do not assume apriori any constant but the topology of the network. As the performed analysisis general it could be applied to many other important biochemical networks.

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