A biophysical model describing long-range cell-to-cell communication by a diffusiblesignal mediated by autocrine loops in developing epithelia in the presence of amorphogenetic pre-pattern is introduced. Under a number of approximations, the modelreduces to a particular kind of bistable reaction-diffusion equation with strongheterogeneity. In the case of the heterogeneity in the form of a long strip a detailedanalysis of signal propagation is possible, using a variational approach. It is shown thatunder a number of assumptions which can be easily verified for particular sets of modelparameters, the equation admits a unique (up to translations) variational traveling wavesolution. A global bifurcation structure of these solutions is investigated in a number ofparticular cases. It is demonstrated that the considered setting may provide a robustdevelopmental regulatory mechanism for delivering chemical signals across large distancesin developing epithelia.

Cell contact-dependent signaling is a major regulatory mechanism in the organization of developing tissues and in the reorganization (post-injury responses) of specialized tissues in multicellular organisms. In this review we contribute to the further understanding of post-injury recovery processes in adult nervous tissue. We emphasize evidence that supports the involvement of cell contact-inhibition signaling in the cell proliferation, growth and differentiation that occurs during healing and neural reorganization after brain damage.