Emergent epithelial elasticity governed by interfacial surface mechanics and substrate interaction

During the life of animals, epithelial tissues undergo extensive deformations--first to form organs during embryogensis and later to preserve integrity and function in adulthood. To what extent these deformations resemble that of non-living elastic materials is not well understood. We derive an elasticity theory of epithelia, supported by a thin layer of extracellular material and the stroma, in which the mechanics of individual cells are dominated by differential interfacial tensions stemming from cell cortical tension and adhesion. Upon coarse-graining a discrete single-cell-level mechanics model, we obtain a harmonic deformation energy and derive the critical conditions for the elastic instability, where an initially flat tissue either buckles out of plane or forms wrinkles. Due to the distinct origin of elasticity, the scaling of the critical load to induce an instability and the wrinkling wavelength with layer thickness is fundamentally different than in solid plates. The theory also naturally describes reversal of the groove-to-crest thickness-modulation phase--a recently observed epithelial shape feature which cannot be explained by the classical elasticity theory. Our work provides a guideline for understanding the relative role of cell surface tensions and the interaction of tissues with substrates during epithelial morphogenesis.