Signal propagation in the MAPK cascade: role of bistability and ultrasensitivity for a mixed problem

TheMAPK signaling cascade is nowadays understood as a networkmodule highly conserved across species. Its main function is to transfer a signal arriving at the plasma membrane to the cellular interior, the nucleus. Current understanding of ’how’ this is achieved involve the notions of ultrasensitivity and bistability which relate to the nonlinear dynamics of the biochemical network, ignoring spatial aspects. Much less, indeed, is so far known about the propagation of the signal through the cytoplasm. In this work we formulate, starting from aMichaelis-Mentenmodel for theMAPK cascade inXenopus oocytes, a reaction-diffusionmodel of the cascade. We study this model in one space dimension. Basing ourselves on previous general results on reaction diffusion models, we particularly study for our model the conditions for signal propagation. We show that the existence of a propagating front depends sensitively on the initial and boundary conditions at the plasma membrane. Possible biological consequences of this finding are discussed.