Flocking and giant fluctuations in epithelial active solids.

The collective motion of epithelial cells is a fundamental biological process which plays a significant role in embryogenesis, wound healing, and tumor metastasis. While it has been broadly investigated for over a decade both in vivo and in vitro, large-scale coherent flocking phases remain underexplored and have so far been mostly described as fluid. In this work, we report an additional mode of large-scale collective motion for different epithelial cell types in vitro with distinctive features. By tracking individual cells, we show that cells move over long time scales coherently not as a fluid, but as a polar elastic solid with negligible cell rearrangements. Our analysis reveals that this solid flocking phase exhibits signatures of long-range polar order, accompanying with scale-free correlations of the transverse component of velocity fluctuations, anomalously large density fluctuations, and shear waves. Based on a general theory of active polar solids, we argue that these features result from massless orientational Goldstone mode, which, in contrast to polar fluids where they are generic, require the decoupling of global rotations of the polarity and in-plane elastic deformations in polar solids. We theoretically show and consistently observe in experiments that the fluctuations of elastic deformations diverge for large system sizes in such polar active solid phases, leading eventually to rupture and thus potentially loss of tissue integrity at large scales.