Modeling homeoprotein intercellular transfer unveils a parsimonious mechanism for gradient and boundary formation in early brain development.

Morphogens are molecules inducing morphogenetic responses from cells and cell ensembles. The concept of morphogen is related to that of positional value, as the generation of morphological and physiological characteristics is function of position. Based on the observation that homeoproteins, a category of transcription factors with morphogenetic functions, traffic between abutting cells and, very often, regulate their own expression, we develop here a biophysical model of homeoprotein propagation and study the associated mathematical equations. This mode of cell signaling can generate domains of homeoprotein expression. We study both the transient and steady-state regimes and, in this latter regime, we obtain various morphogenetic gradients, depending on the value of some parameters, such as morphogen synthesis, degradation rates and efficiency of intercellular passage. The same equations, applied to pairs of homeoproteins with auto-activation and reciprocal inhibition properties, account for border formation. They also allow us to compute how specific perturbations can either be buffered or lead to modifications in the position of borders between adjacent areas. The model developed here, based on experimental data, and avoids theoretical obstacles associated with pluricellularity. It extends the idea that Bicoid homeoprotein is a morphogen in the fly embryo syncitium to most homeoproteins and to pluricellular systems. Because the position of borders between brain areas is of primary physiological importance, our model might lead to original views regarding epigenetic inter-individual variations and the origin of neurological and psychiatric diseases. In addition, it provides new hypotheses regarding the molecular basis of brain evolution.