Curvature induces active matter velocity waves in rotating multicellular spheroids

Collective behavior of cells in 3D curved environements determine the multicellular organization of diverse systems, such as embryos, intestines and tumors. 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. We study 3D collective migration in a mammary cell spheroid, which represents 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 and motion along geodesics. Using a minimal active particle model, we reveal that this collective mode originates from the active flocking behaviour of an incompressible cell layer confined to a curved surface. Our results identify curvature-induced velocity waves as a generic active matter mode, which could manifest in a wide range of 3D curved active systems.