A kinetic model of ERK cyclic pathway on substrate control

Extracellular signal-regulated kinase (ERK) is a key factor in the widely used signaling cascade of phosphorylation-dephosphorylation cycles and plays pivotal roles in many aspects of biological processes. Experimental studies in yeast and in Drosophila embryo have suggested that the phosphorylation and spatial localization of ERK are influenced by the level of its downstream substrates. However, the mechanism, through which these substrates control properties of ERK signaling, has been unclear. I propose a mass-action kinetic model of ERK cycle with its substrate, and demonstrate that the substrate can modulate the ERK activity by directly interacting with ERK. The model shows that the addition of substrate controls the level of ERK phosphorylation positively or negatively, depending on the balance between dissociation constants of ERK-substrate interaction and properties of ERK cyclic signaling in the absence of the substrate. In addition, by considering cellular compartments, cytosol and nucleus, the substrate can lead to nuclear accumulation of ERK, suggesting that the substrate can act as a nuclear anchor of ERK. The model gives a possible mechanism that can account for substrate-mediated modulation of ERK signaling.