Highlights d A proliferating epithelium encapsulated in a hollow sphere spontaneously invaginates d Epithelial proliferation generates compressive stresses that deform the elastic shell d Coupling between stress and folding shape shows that folding arises from buckling d Epithelial elastic moduli are inferred from buckling theory and experiments

Many organs, such as the gut or the spine are formed through folding of an epithelium. Whereas genetic regulation of epithelium folding has been investigated extensively, the nature of the mechanical forces driving this process remain largely unknown. Here we show that monolayers of identical cells proliferating on the inner surface of elastic spherical shells can spontaneously fold. By measuring the elastic deformation of the shell we inferred the forces acting within the monolayer. Using analytical and numerical theories at different scales, we found that the compressive stresses arising within the cell monolayer through proliferation quantitatively account for the shape of folds observed in experiments. Our study shows that forces arising from epithelium growth are sufficient to drive folding by buckling.

In this work we use a computational cell-based model to study the influence of the mechanical properties of cells on the mechanics of epithelial tissues. We analyze the effect of the model parameters on the elasticity and the mechanical response of tissues subjected to stress loading application. We compare our numerical results with experimental measurements of epithelial cell monolayer mechanics. Unlike previous studies, we have been able to estimate in physical units the parameter values that match the experimental results. A key observation is that the model parameters must vary with the tissue strain. In particular, it was found that, while the perimeter contractility and the area elasticity of cells remain constant at lower strains (<20%), they must increase to respond to larger strains (>20%). However, above a threshold of 50% extension, the cells stop counteracting the tissue strain and reduce both their perimeter contractility and area elasticity.

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