Mathematical modeling of the feather follicle morphogenetic wave in birds

During the development of the avian skin, feather follicles are produced in a medio-lateral morphogenetic wave that results in their spatial arrangement in typical patterns. This wave involves the timely acquisition of pattern-forming competence followed by a row-by-row production of feather follicles. While several mathematical models combining self-organizing systems accurately reproduced dynamics of feather follicle pattern formation, the events that control timely parameters of wave propagation remain poorly understood. Here, we built on previous modeling work to theoretically calculate the speed at which tissue competence progresses. Using a weakly non-linear analysis, we calculated the speed at which follicles emerge once competence is attained. We produced numerical simulations of our model to predict the respective influences of competence acquisition and follicle emergence on each other and on wave propagation. Our results show that the theoretical speed of follicle emergence is limited by competence acquisition, but that, in turn, competence acquisition is not constrained by follicle emergence. This modeling work provides an approximation of the timely parameters of the morphogenetic wave, and sheds light on the interplay between competence and patterning events in the developing skin.