Solid-liquid transitions of deformable active particles

Experiments have established that confluent epithelial tissues exhibit solid-liquid transitions. Although epithelial tissues usually form a cell monolayer, there are situations in which that monolayer structure breaks, such as in cell extrusion and pseudo-stratified epithelia. To describe such situations, we have developed a multi-phase field model where cells are characterized by multiple scalar fields, and interact through steric repulsion. By reducing their deformability, these cells go from being highly-deformable with no overlap to almost-circular with high overlap, which can be thought of as a way to incorporate layering between cells. Using this model we have examined the interplay of cell deformability and cell motility in controlling the solid-liquid transition of ordered lattices. We find that by reducing cell deformability the melting transition changes from continuous to discontinuous: at finite overlap the system develops an intermittent region, alternating between crystalized and liquid states. Finally, by studying the formation of defect pairs in the intermittent region, we find that they correlate with spatial fluctuations of the cell-overlap, suggesting that cell extrusion is correlated with structural defects.