Topographical curvature is sufficient to control epithelium elongation.

How biophysical cues can control tissue morphogenesis is a central question in biology and for the development of efficient tissue engineering strategies. Recent data suggest that specific topographies such as grooves and ridges can trigger anisotropic tissue growth. However, the specific contribution of biologically relevant topographical features such as cell-scale curvature is still unclear. Here we engineer a series of grooves and ridges model topographies exhibiting specific curvature at the ridge/groove junctions and monitored the growth of epithelial colonies on these surfaces. We observe a striking proportionality between the maximum convex curvature of the ridges and the elongation of the epithelium. This is accompanied by the anisotropic distribution of F-actin and nuclei with partial exclusion of both in convex regions as well as the curvature-dependent reorientation of pluricellular protrusions and mitotic spindles. This demonstrates that curvature itself is sufficient to trigger and modulate the oriented growth of epithelia through the formation of convex "topographical barriers" and establishes curvature as a powerful tuning parameter for tissue engineering and biomimetic biomaterial design.

Curvotaxis directs cell migration through cell-scale curvature landscapes.

Cells have evolved multiple mechanisms to apprehend and adapt finely to their environment. Here we report a new cellular ability, which we term "curvotaxis" that enables the cells to respond to cell-scale curvature variations, a ubiquitous trait of cellular biotopes. We develop ultra-smooth sinusoidal surfaces presenting modulations of curvature in all directions, and monitor cell behavior on these topographic landscapes. We show that adherent cells avoid convex regions during their migration and position themselves in concave valleys. Live imaging combined with functional analysis shows that curvotaxis relies on a dynamic interplay between the nucleus and the cytoskeleton-the nucleus acting as a mechanical sensor that leads the migrating cell toward concave curvatures. Further analyses show that substratum curvature affects focal adhesions organization and dynamics, nuclear shape, and gene expression. Altogether, this work identifies curvotaxis as a new cellular guiding mechanism and promotes cell-scale curvature as an essential physical cue.