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The migration behavior of colliding cells is critically determined by transient contact-interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface protein-mediated transmission of forces and biochemical signals between cells. While biomolecular details of such contact-interactions are increasingly well understood, it remains unclear what biophysical interaction mechanisms govern the cell-level dynamics of colliding cells and how these mechanisms vary across cell types. Here, we develop a phenomenological theory based on 14 candidate contact-interaction mechanisms coupling cell position, protrusion, and polarity. Using high-throughput micropattern experiments, we detect which of these phenomenological contact-interactions captures the interaction behaviors of cells. We find that various cell types - ranging from mesenchymal to epithelial cells - are accurately captured by a single model with only two interaction mechanisms: polarity-protrusion coupling and polarity-polarity coupling. The qualitatively different interaction behaviors of distinct cells, as well as cells subject to molecular perturbations of surface protein-mediated signaling, can all be quantitatively captured by varying the strength and sign of the polarity-polarity coupling mechanism. Altogether, our data-driven phenomenological theory of cell-cell interactions reveals polarity-polarity coupling as a versatile and general contact-interaction mechanism, which may underlie diverse collective migration behavior of motile cells.

The multicellular organization of diverse systems, such as embryos, intestines and tumours, relies on the coordinated migration of cells in 3D curved environments. In these settings, cells establish supracellular patterns of motion, including collective rotation and invasion. While such collective modes are increasingly well understood in 2D flat systems, the consequences of geometrical and topological constraints on collective cell migration in 3D curved tissues are largely unknown. Here, we study 3D collective migration in mammary cell spheroids, which represent a common and conceptually simple curved geometry. We discover that these rotating spheroids exhibit a collective mode of cell migration in the form of a velocity wave propagating along the equator with a wavelength equal to the spheroid perimeter. This wave is accompanied by a pattern of incompressible cellular flow across the spheroid surface featuring topological defects, as dictated by the closed spherical topology. Using a minimal active particle model, we reveal that this collective mode originates from the active flocking behaviour of a cell layer confined to a curved surface. Our results thus identify curvature-induced velocity waves as a generic mode of collective cell migration, which could impact the dynamical organization of 3D curved tissues., Comment: 45 pages, 16 figures