Atsushi Mochizuki, Yasuhiko Takeda, Hiroyuki Ide and Yoh Iwasa
Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812-81, Japan
(Received April 27, 1996; Accepted June 28, 1996)
Keywords: Cell Sorting, Cell-to-Cell Adhesion, Stochastic Cell Sorting, Pattern of Cell Distribution, Inferring Adhesion Force
Abstract. A model of spontaneous sorting out of cells is studied. Cells of two types (black and white) are arranged on a square lattice, and adhesions between cells in contact depend on their types. Cells exchange their location with neighbors randomly with the rate affected by differential cell-to-cell adhesion. At equilibrium, cell distribution pattern show segregation if ratio of differential adhesion to intensity of random movement (A/m) is large. Two statistics quantify degree of sorting:  fraction of black cells in the neighbor of a randomly chosen black cell (qB/B), and  number of isolated black cells (IBC). Their equilibrium values are predicted accurately as functions of A/m and ratio of black cells, by using pair-approximation. These statistics are applied to photographs obtained by cell-sorting experiments mixing cells derived from avian wing buds. Convergence and value of A/m in the experiment was investigated.