Solid-liquid transition in layers of deformable active droplets

Layers of epithelial tissue have been modeled either as collections of spherical active particles or via the Vertex Model (VM) that describes cells as irregular polygons tiling the plane. The VM is appropriate to describe confluent layers where there are no gaps between cells and does not incorporate variations in the cell packing fraction that is by construction set to one. In contrast, the particle model can account for variation in packing fraction, but does not allow for deformations of individual cells. Both models predict a solid-liquid transition of cellular tissue tuned either by cell shape (VM) or by cell density (particle model). To bridge between these two models, we describe cells as deformable self-propelled droplets each characterized by a scalar field representing the cell’s density. We then examine the collective behavior of N droplets modeled as N interacting phase fields. Using this model, we examine the interplay of cell deformability, cell density and cell motility in controlling the solid-liquid transition. We quantify the melting of the hexagonal ground state, as well as the stability of metastable states.