A Density-Independent Flocking Transition in Confluent Tissues

Some of us recently demonstrated a density-independent solid-liquid transition in confluent tissues controlled by cell motility and a cell shape parameter measuring the interplay of cortical tension and cell-cell adhesion. An important insight of this work is that the rigidity and dynamics of cell layers depends sensitively on cell shape. To explore the influence of cell shape on collective states, we have constructed continuum equations that couple a scalar field describing cell-shape anisotropy to cell polarization. The model displays a density independent transition to a polarized state of elongated cells driven by a cellular “shape-index” parameter. We map out the phase diagram using linear stability analysis and numerical solution of the nonlinear hydrodynamic equations. The proposed transition constitutes a density-independent flocking transition.