  The shapes of epithelial tissues result from a complex interplay of
contractile forces in the cytoskeleta of the cells in the tissue, and adhesion
forces between them. A host of discrete, cell-based models describe these
forces by assigning different surface tensions to the apical, basal, and
lateral sides of the cells. These differential-tension models have been used to
describe the deformations of epithelia in different living systems, but the
underlying continuum mechanics at the scale of the epithelium are still
unclear. Here, we derive a continuum theory for a simple differential-tension
model of a two-dimensional epithelium and study the buckling of this epithelium
under imposed compression. The analysis reveals how the cell-level properties
encoded in the differential-tension model lead to linear, nonlinear as well as
nonlocal elastic behavior at the continuum level.
