Ratio control in a cascade model of cell differentiation

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a global feedback term. The size ratio of each cell type is controlled by a system parameter in the model. Finally, we extend the model to a cascade model of cell differentiation. A hierarchical spatial structure appears as a result of the cell differentiation. The size ratio of each cell type is also controlled by the system parameter.