title: Distribution of differentiated cells in a cell sheet under the lateral inhibition rule of differentiation.
abstract: 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.
authors.affiliation: Institute of Statistical Mathematics, Tokyo, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Tanemura
authors.forename: H
authors.initials: H
authors.lastname: Honda
authors.forename: A
authors.initials: A
authors.lastname: Yoshida
mesh_terms: D000818:Animals; D002454:Cell Differentiation; D003198:Computer Simulation; D008954:Models, Biological; D013223:Statistics as Topic