Vertex modeling of active superelasticity in epithelial tissues

Epithelial tissues often exhibit 3D shapes during development and physiological functions. However, mechanobiology of epithelial tissues in 3D has not been quantitatively explored. We use epithelial domes developed on soft micropatterned substrates, combined with 3D traction microscopy, to extract constitutive behavior of epithelial tissues. A remarkable plateauing of tissue tension is observed as the domes reach areal strains of up to 300%. While the spherical domes are required to maintain uniform tissue tension, the distribution of cellular strains on the domes is highly heterogeneous as some cells exhibit areal strains close to 1000%. A classical vertex model with constant junctional tensions captures the tensional plateau, but not the strain heterogeneity. We develop a 3D vertex model accounting for cellular-softening induced by cortical depletion and re-stiffening at extreme strains, which captures the contrasting observations of tensional plateau and cellular strain heterogeneity. The model reveals non-convex two-well energy landscape of the cells, which permits co-existence of barely-stretched and superstretched cells to accommodate large strains while maintaining a tensional plateau; all of which are landmark features of superelasticity, albeit, of active origin.