A biophysical model describing long-range cell-to-cell communication by a diffusible
signal mediated by autocrine loops in developing epithelia in the presence of a
morphogenetic pre-pattern is introduced. Under a number of approximations, the model
reduces to a particular kind of bistable reaction-diffusion equation with strong
heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed
analysis of signal propagation is possible, using a variational approach. It is shown that
under a number of assumptions which can be easily verified for particular sets of model
parameters, the equation admits a unique (up to translations) variational traveling wave
solution. A global bifurcation structure of these solutions is investigated in a number of
particular cases. It is demonstrated that the considered setting may provide a robust
developmental regulatory mechanism for delivering chemical signals across large distances
in developing epithelia.