Pattern formation of the cone mosaic in the zebrafish retina: a cell rearrangement model

In fish retinas, cone photoreceptor cells are arranged in two-dimensional regular patterns, called cone mosaics. In the zebrafish retina, four subtypes of cone cells, which are maximally sensitive to different wavelengths of light, appear in quasi-periodic patterns. The pattern formation mechanism is unknown. Here, I develop a mathematical model to examine whether cell adhesion can explain the formation of the zebrafish mosaic. I assume that the movement of differentiated cells is responsible for generating the pattern, and that the movement rate is modified by cell adhesion. The pattern is formed if the magnitudes of cell adhesion between cell types are chosen appropriately. I determine the conditions of cell adhesion for generating the pattern. I also compare this cell rearrangement model with a previously studied model in which the pattern is formed by transitions of cell fate. The condition for obtaining the focal pattern is looser in the cell rearrangement model than in the fate transition model.