Structure and Rheology in Vertex Models under Cell-Shape-Dependent Active Stresses

Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an active mechanical stress along its axis of elongation. Increasing the active stress amplitude leads to several transitions. An initially hexagonal crystal motif is first destabilized into a solid with anisotropic cells whose shear modulus eventually vanishes at a first critical activity. Increasing activity beyond this first critical value, we find a re-entrant transition to a regime with finite hexatic order and finite shear modulus, in which cells arrange according to a rhombile pattern with periodically arranged rosette structures. The shear modulus vanishes again at a third threshold beyond which spontaneous tissue flows and topological defects of the nematic cell shape field arise. Flow and stress fields around the defects agree with active nematic theory, with either contractile or extensile signs, as also observed in several epithelial tissue experiments.

Automated summary

Cells can adjust their intracellular architecture based on overall shape, and this study investigates the rheological implications of such coupling in a minimal model of dense cellular material. Increasing the active mechanical stress leads to transitions from a hexagonal crystal motif to a solid with anisotropic cells, followed by a re-entrant transition to a regime with finite hexatic order and shear modulus. Further increasing activity results in spontaneous tissue flows and topological defects, consistent with active nematic theory and observations in epithelial tissue experiments.