Distribution of differentiated cells in a cell sheet under the lateral inhibition rule of differentiation

The distribution of differentiated cells among undifferentiated cells was investigated assuming the lateral inhibition hypothesis of cell differentiation. Computer simulations were undertaken in a planar array of polygonal domains in which homogeneous polygons are all competent to differentiate, and immediate neighbors of a differentiated polygon exert lateral inhibition of differentiation. The simulation showed that the average cell number ratio of undifferentiated to differentiated cells is 3.32, when picking a polygon for differentiation at random from a hexagonal pattern. The ratio decreased when using disturbed polygonal patterns instead of a hexagonal one. A non-random sequence of picking polygons also varied cell number ratio values. Our results show that if there is no control system as a whole, the lateral inhibition rule produced cell distributions whose cell number ratio is around 3. Cell number ratios are discussed in regard to observations of epithelial cell sheets.