Cell Segregation and Group Diffusion

The dynamics underlying cell migration drives cell segregation which is essential to tissue formation. Since the mid-twentieth century a series of hypotheses for the microscopic mechanism were put to test to explain the evolution observed in experiments. A typical experiment in cell segregation measures the evolution of clusters sizes, or also the size of the interface between the two tissues at stake. In order to appropriately fit the experiment a series of physical constraints must be taken into account, such as the finite size of each cell, the finite number of cells in the process and the scaling of the cluster diffusion with its mass. Here we explore a mean cluster approach that explicitly includes these constraints. In some appropriate limits this mean cluster approach has exact solutions with simple power laws with finite size effects clearly identified. Simulations of cell segregation based on the differential adhesion hypothesis are implemented using simple active matter models. The mean cluster approach solutions
are used to fit the data resulting from the simulations and the power law behavior can be clearly separated out of the minimum and maximum cluster size limits. The relation found between the group diffusion with its mass and the preferential alignment of cell velocities inside clusters impact on the power law exponents with direct consequences to the segregation time scales.