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The shapes of epithelial tissues result from a complex interplay ofcontractile forces in the cytoskeleta of the cells in the tissue, and adhesionforces between them. A host of discrete, cell-based models describe theseforces by assigning different surface tensions to the apical, basal, andlateral sides of the cells. These differential-tension models have been used todescribe the deformations of epithelia in different living systems, but theunderlying continuum mechanics at the scale of the epithelium are stillunclear. Here, we derive a continuum theory for a simple differential-tensionmodel of a two-dimensional epithelium and study the buckling of this epitheliumunder imposed compression. The analysis reveals how the cell-level propertiesencoded in the differential-tension model lead to linear, nonlinear as well asnonlocal elastic behavior at the continuum level.

Nonlinear and Nonlocal Elasticity in Coarse-Grained Differential-Tension Models of Epithelia