Reaction-diffusion approach to prevertebrae formation: effect of a local source of morphogen

Periodic structure formation is an essential feature of embryonic development. Many models of this phenomenon, most of them based on time oscillations, have been proposed. However, temporal oscillations are not always observed during development and how a spatial periodic structure is formed still remains under question. We investigate a reaction-diffusion model, in which a Turing pattern develops without temporal oscillations, to assess its ability to account for the formation of prevertebrae. We propose a correspondence between the species of the reaction scheme and biologically relevant molecules known as morphogens. It is shown that the model satisfactorily reproduces experiments involving grafting of morphogen sources into the embryos. Using a master equation approach and the direct simulation Monte Carlo method, we examine the robustness of the results to internal fluctuations.