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Recent experiments in epithelial wound healing have demonstrated thenecessity of Mitogen-activated protein kinase (MAPK) for coordinated cellmovement after damage. This MAPK activity is characterized by two wave-likephenomena. One MAPK "wave" that originates immediately after injury, propagatesdeep into the cell layer, and then rebounds back to the wound interface. Afterthis initial MAPK activity has largely disappeared, a second MAPK frontpropagates slowly from the wound interface and continues into the tissue,maintaining a sustained level of MAPK activity throughout the cell layer. Ithas been suggested that the first wave is initiated by reactive oxygen species(ROS) generated at the time of injury. In this paper, we develop a minimalmechanistic diffusion-convection model that reproduces the observed behavior.The main ingredients of our model are a competition between ligand (e.g.,Epithelial Growth Factor) and ROS for the activation of Epithelial GrowthFactor Receptor (EGFR) and a second MAPK wave that is sustained by stressesinduced by the slow cell movement that closes the wound. We explore themathematical properties of the model in connection with the bistability of theMAPK cascade and look for traveling wave solutions consistent with theexperimentally observed MAPK activity patterns.

A mathematical model of intercellular signaling during epithelial wound healing