Cut it out: Out-of-plane stresses in cell sheet folding of Volvox embryos

The folding of cellular monolayers pervades embryonic development and disease. It results from stresses out of the plane of the tissue, often caused by cell shape changes including cell wedging via apical constriction. These local cellular changes need not however be compatible with the global shape of the tissue. Such geometric incompatibilities lead to residual stresses that have out-of-plane components in curved tissues, but the mechanics and function of these out-of-plane stresses are poorly understood, perhaps because their quantification has proved challenging. Here, we overcome this difficulty by combining laser ablation experiments and a mechanical model to reveal that such out-of-plane residual stresses exist and also persist during the inversion of the spherical embryos of the green alga Volvox. We show how to quantify the mechanical properties of the curved tissue from its unfurling on ablation, and reproduce the tissue shape sequence at different developmental timepoints quantitatively by our mechanical model. Strikingly, this reveals not only clear mechanical signatures of out-of-plane stresses associated with cell shape changes away from those regions where cell wedging bends the tissue, but also indicates an adaptive response of the tissue to these stresses. Our results thus suggest that cell sheet folding is guided mechanically not only by cell wedging, but also by out-of-plane stresses from these additional cell shape changes.