Abstract While many tissues fold in vivo in a highly reproducible and robust way, epithelial folds remain difficult to reproduce in vitro , so that the effects and underlying mechanisms of local curvature on the epithelial tissue remains unclear. Here, we photoreticulated polyacrylamide hydrogels though an optical photomask to create corrugated hydrogels with isotropic wavy patterns, allowed us to show that concave and convex curvatures affect cellular and nuclear shape. By culturing MDCK epithelial cells at confluency on corrugated hydrogels, we showed that the substrate curvature leads to thicker epithelial zones in the valleys and thinner ones on the crest, as well as corresponding density, which can be generically explained by a simple 2D vertex model, leading us to hypothesize that curvature sensing could arise from resulting density/thickness changes. Additionally, positive and negative local curvatures lead to significant modulations of the nuclear morphology and positioning, which can also be well-explained by an extension of vertex models taking into account membrane-nucleus interactions, where thickness/density modulation generically translate into the corresponding changes in nuclear aspect ratio and position, as seen in the data. Consequently, we find that the spatial distribution of Yes associated proteins (YAP), the main transcriptional effector of the Hippo signaling pathway, is modulated in folded epithelial tissues according to the resulting thickness modulation, an effect that disappears at high cell density. Finally, we showed that these deformations are also associated with changes of A-type and B-type lamin expression, significant chromatin condensation and to lower cell proliferation rate. These findings show that active cell mechanics and nuclear mechanoadaptation are key players of the mechanistic regulation of epithelial monolayers to substrate curvature, with potential application for a number of in vivo situations.

Large-scale curvature sensing by epithelial monolayers depends on active cell mechanics and nuclear mechanoadaptation