Solid-fluid transition and cell sorting in epithelia with junctional tension fluctuations

Tissues transition between solid-like and fluid-like behavior, which has major implications for morphogenesis and disease. These transitions can occur due to changes in the intrinsic shape of constituent cells and cell motility. We consider an alternative mechanism by studying tissues that explore the energy landscape through stochastic dynamics, driven by turnover of junctional molecular motors. To identify the solid-fluid transition, we start with single-component tissues and show that the mean cell-shape index uniquely describes the effective diffusion coefficient of cell movements, which becomes finite at the transition. We generalize our approach to two-component tissues, and explore cell-sorting dynamics both due to differential adhesion and due to differential degree of junctional fluctuations. We recover some known characteristic scaling relations describing the sorting kinetics, and discover some discrepancies from these relations in the case of differential-fluctuations-driven sorting. Finally, we show that differential fluctuations efficiently sort two solid-like tissues with a fluid intercompartmental boundary.