Spatially periodic domain structure in coupled reaction-diffusion equations for segment formation

Segment formation is an important process of pattern formation in the developing vertebrate embryo. The mechanism of such pattern formation is considered to be different from that of Turing instability. We propose reaction- diffusion equations generating traveling pulses and coupled reaction-diffusion equations for two genes that generate a domain structure. Next, we construct a synthetic model for segment formation by combining the coupled reaction- diffusion equations. A spatially periodic domain structure is found in the numerical simulation of the model equation. It is shown that the wavelength of the spatially periodic pattern and the proportion of the sizes of the anterior and posterior domains in each segment can be controlled by adjusting some system parameters.