The signal-transfer process in the mitogen-activated protein kinase (MAPK) cascade is formulated as a reaction-diffusion system describing the complete three-step phospho-protein reactions and the diffusion process in the direction from the cell membrane to the nucleus. The Simulation analysis of the model demonstrates that MAPK cascade can work as a signal amplifier so as to compensate the signal attenuation due to formation of phospho-protein gradients. It also is found to be attainable for eukaryotic cells that a steep gradient of phosphorylated MAPK is not formed in a certain range of the system parameter values. One of the distinctive features in the formation of phospho-protein gradients is revealed to be its high sensitivity to a change in parameter values such as diffusion distance, diffusion coefficients and enzymatic activities of the phosphatases, Suggesting that these parameters may act as the key factors for regulation of the signal transduction systems. (C) 2005 Elsevier Ireland Ltd. All rights reserved.