Collective curvature sensing and fluidity in three-dimentional multicellular systems*

Collective cell migration is an essential process throughout the lives of multicellular organisms, for example in embryonic development, wound healing, and tumor metastasis. Substrates or interfaces associated with these processes in situ are typically curved in three-dimensions (3D), with radii of curvatures comparable to many cell lengths, yet the role of substrate curvature at this scale in regulating collective cell migration remains virtually unknown. Using both fabricated hemispherical geometries and lung alveolospheres derived from human induced pluripotent stem cells, here we show that cells sense substrate curvature in a collective manner. As substrate curvature increases, cells reduce their collectiveness and the multicellular flow field becomes more dynamic. Furthermore, hexagonally shaped cells tend to aggregate in solid-like clusters surrounded by non-hexagonal cells that act as a background fluid. We propose a physical mechanism in which cells naturally form hexagonally organized clusters to minimize free energy, where the size of these clusters is limited by an elastic bending energy penalty induced by substrate curvature. Indeed, we observe that cluster size grows linearly as sphere radius increases, which further stabilizes the multicellular flow field and increases cell collectiveness. As a result, increasing curvature tends to promote the fluidity in multicellular monolayer. Together, these findings highlight the potential for a fundamental role of substrate curvature in regulating both spatial and temporal characteristics of three-dimensional multicellular systems in development, wound healing, and tumor formation.