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Abstract Collective migration of epithelial cells drives diverse tissue remodeling processes. In many cases, a free tissue edge polarizes the cells to promote directed motion, but how edge-free or closed epithelia initiate migration remains unclear. Here, we show that the rotational migration of follicular epithelial cells in theDrosophilaegg chamber is a self-organizing process. Combining experiments and theoretical modeling, we identify a positive feedback loop in which the mechanosensitive behavior of the atypical cadherin Fat2 synergizes with the rigid-body dynamics of the egg chamber to both initiate and sustain rotation. Mechanical constraints arising from cell–cell interactions and tissue geometry further align this motion around the egg chamber’s anterior–posterior axis. Our findings reveal a biophysical mechanism — combining Fat2-mediated velocity–polarity alignment, rigid-body dynamics, and tissue geometry — by which a closed epithelial tissue self-organizes into persistent, large-scale rotational migrationin vivo, expanding current flocking theories. 

Abstract Coherent structures—flow features that organize material transport and deformation—are central to analyzing complex flows in fluids, plasmas, and active matter. Yet, identifying such structures on dynamic surfaces remains an open challenge, limiting their application to many living and synthetic systems. Here, we introduce a geometric framework to extract Lagrangian and Eulerian coherent structures from velocity data on arbitrarily shaped, time-evolving surfaces. Our method operates directly on triangulated meshes, avoiding global parametrizations while preserving objectivity and robustness to noise. Applying this framework to active nematic vesicles, collectively migrating epithelial spheroids, and beating zebrafish hearts, we uncover hidden transport barriers and Lagrangian deformation patterns—such as dynamic attractors, repellers, isotropic and anisotropic strain—missed by conventional Eulerian analyses. This approach offers a new perspective on soft and living matter, revealing how geometry and activity can be harnessed to program synthetic materials, and how Lagrangian strain and principal deformation directions can help uncover mechanosensitive processes and directional cues in morphogenesis.