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Extracellular signal-regulated kinase (ERK) signaling pathway is one of the mitogen-activated protein kinase (MAPK) signal transduction pathways. This pathway is known as pivotal in many signaling networks that govern proliferation, differentiation and cell survival. The ERK signaling pathway comprises positive and negative feedback loops, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. In this paper, we attempt to model the ERK pathway by considering both of the positive and negative feedback mechanisms based on Michaelis-Menten kinetics. In addition, we propose a fraction ratio model based on the mass action law. We first develop a mathematical model of the ERK pathway with fraction ratios. Secondly, we analyze the dynamical properties of the fraction ratio model based on simulation studies. Furthermore, we propose a concept of an inhibitor, catalyst, and substrate (ICS) controller which regulates the inhibitor, catalyst, and substrate concentrations of the ERK signal transduction pathway. The ICS controller can be designed through dynamical analysis of the ERK signaling transduction pathway within limited concentration ranges.

Dynamical Analysis of Cellular Signal Transduction Pathways with Nonlinear Systems Perspectives