Collective cell polarization and alignment on curved surfaces.

Curvature as an important topological parameter of 3D extra-cellular matrix has drawn growing attention in recent years. But the underlying mechanism that curvature influences cell behaviors has remained unknown. In this study, we seeded cells on semi-cylindrical and hemispheric surfaces and tested cell alignment and polarization. We found that the surface curvature has profound effect on cell behaviors. With the decrease of diameter of the cylinder/sphere (i.e. increase of curvature), the cells would more preferentially align and polarize with large aspect ratio in the axial/peripheral direction. And the behaviors of the alignment and polarization were position-dependent. For example, at the end of the cylinder, the cells preferred to align circumferentially; while in the interior region, the cells preferred to align in the axial direction. We showed that the cell polarization and alignment were closely correlated with the in-plane stresses in cell layer. That is, the cell polarization and alignment were controlled by the maximum shear stress, which drove cells to align and polarize along the maximum principal stress. The curvature could influence the magnitude of the maximum shear stress and thus regulate cell behaviors. This study provided important insights into the mechanisms of surface curvature influencing cell behaviors in tissue morphogenesis. In addition, our theory of the stress dependent cellular polarity provides a generalized interpretation of the curvature and edge effects which might be extended to understand other steric effects in cell behaviors.