Differentiation of wing epidermal scale cells in a butterfly under the lateral inhibition model--appearance of large cells in a polygonal pattern.

Cellular pattern formations of some epithelia are believed to be governed by the direct lateral inhibition rule of cell differentiation. That is, initially equivalent cells are all competent to differentiate, but once a cell has differentiated, the cell inhibits its immediate neighbors from following this pathway. Such a differentiation repeats until all non-inhibited cells have differentiated. The cellular polygonal patterns can be characterized by the numbers of undifferentiated cells and differentiated ones. When the differentiated cells become large in size, the polygonal pattern is deformed since more cells are needed to enclose the large cell. An actual example of such a cellular pattern was examined. The pupal wing epidermis of a butterfly Pieris rapae shows a transition of the equivalent-size cell pattern to the pattern involving large cells. The process of the transition was analyzed by using the method of weighted Voronoi tessellation that is useful for treatment of irregularly sized polygons. The analysis supported that the pattern transition of the early stage of the pupal wing epidermis is governed by the lateral inhibition rule. The differentiation takes place in order of largeness, but not smallness, of the apical polygonal area in the differentiating region of the pupal wing.