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The coupling of the internal mechanisms of cell polarization to cell shapedeformations and subsequent cell crawling poses many interdisciplinaryscientific challenges. Several mathematical approaches have been proposed tomodel the coupling of both processes, where one of the most successful methodsrelies on a phase field that encodes the morphology of the cell, together withthe integration of partial differential equations that account for thepolarization mechanism inside the cell domain as defined by the phase field.This approach has been previously employed to model the motion of single cellsof the social amoeba Dictyostelium discoideum, a widely used model organism tostudy actin-driven motility and chemotaxis of eukaryotic cells. Besides singlecell motility, Dictyostelium discoideum is also well-known for its collectivebehavior. Here, we extend the previously introduced model for single cellmotility to describe the collective motion of large populations of interactingamoebae by including repulsive interactions between the cells. We performednumerical simulations of this model, first characterizing the motion of singlecells in terms of their polarity and velocity vectors. We then systematicallystudied the collisions between two cells that provided the basic interactionscenarios also observed in larger ensembles of interacting amoebae. Finally,the relevance of the cell density was analyzed, revealing a systematic decreaseof the motility with density, associated with the formation of transient cellclusters that emerge in this system. This model is a prototypical active mattersystem for the investigation of the emergent collective dynamics of deformable,self-driven cells with a highly complex, nonlinear coupling of cell shapedeformations, self-propulsion and repulsive cell-cell interactions.

From single to collective motion of social amoebae: a computational study of interacting cells