Forma, Vol. 12 (No. 2), pp. 107-122, 1997
Original Paper

A Stochastic Model for Cell Sorting and Its Application

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: [1] fraction of black cells in the neighbor of a randomly chosen black cell (qB/B), and [2] 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.