Morphogenetic gradients and the stability of boundaries between neighboring morphogenetic regions

Generating morphogenetic gradients during early development is a fundamental step of positional signaling, which ultimately results in patterning and cell specialization. Based on morphogens propagation from cells to cells, we have presented a biophysical model in Holcman et al. (in press), where gradients and boundaries between different morphogenetic regions can be generated. In that theory, morphogens are transcription factors which induce their own activation and at the same time propagate in a cell ensemble. We analyze here a variant version of the biophysical model proposed in Holcman et al. (in press), where now morphogens can form dimers. As a result, gradients are smoother and borders are much sharper. Because random perturbations of a gradient can affect the precise location of the boundary between two morphogenetic regions, we also analyze these fluctuations and in particular, we obtain an analytic expression for the variance of the boundary location as a function of the variance of the random perturbations. This formula can be used to study the noise intrinsic effect on the boundary position between morphogenetic regions, which can be at the origin of interindividual variations.