Predicting the spatiotemporal dynamics of hair follicle patterns in the developing mouse.

Reaction-diffusion models have been used as a paradigm for describing the de novo emergence of biological patterns such as stripes and spots. In many organisms, these initial patterns are typically refined and elaborated over the subsequent course of development. Here we study the formation of secondary hair follicle patterns in the skin of developing mouse embryos. We used the expression of sex-determining region Y box 2 to identify and distinguish the primary and secondary hair follicles and to infer the spatiotemporal dynamics of the follicle formation process. Quantitative analysis of the specific follicle patterns observed reveals a simple geometrical rule governing the formation of secondary follicles, and motivates an expansion-induction (EI) model in which new follicle formation is driven by the physical growth of the embryo. The EI model requires only one diffusible morphogen and provides quantitative, accurate predictions on the relative positions and timing of secondary follicle formation, using only the observed configuration of primary follicles as input. The same model accurately describes the positions of additional follicles that emerge from skin explants treated with an activator. Thus, the EI model provides a simple and robust mechanism for predicting secondary space-filling patterns in growing embryos.