Directed cell movement and cluster formation : physical principles

(Received 4 November 1993, revised 3 March 1994, accepted 6 April 1994)

Abstract
The cell-cell interaction of migrating human leukocytes (granulocytes) was investigated. We have found that the attractive pair interaction of granulocytes tan be switched-off at high calcium concentrations and switched-on at low calcium concentrations. Through this experiment we established that the cells attracted each other and formed clusters containing actively moving cells : (i) the cluster formation was a function of the mean cell density, (ii) where no clusters were observed for small cell densities, (< 150-300 cells/mm ² ; threshold behaviour), (iii) and the mean cluster size was a function of the mean cell density. (iv) In addition we established that the dynamic process of the cluster formation was a function of the mean cell density, and (v) the migrating cells were oriented towards the cluster's tenter. The cluster formation is discussed in the framework of a droplet model where two dynamic processes are observed : (a) the cells in a cluster attract further cells and (b) the cells at the boundary of the cluster have the possibility to move away. The droplet mode] in connection with the cell conservation law is confirmed by the experiments. The analogy between the liquid-gas transition of interacting molecules and the condensation of interacting cells is shown. The migrating and oriented cells of a cluster are in an orientational liquid crystal state of polar symmetry. The polar order is discussed in the framework of a polar mean field.