  It is widely recognized that the shape of epithelial cells is determined by
the tension generated by the actomyosin cortex and the adhesion of cells to the
substrate and to each other. To account for these biological and structural
contributions to cell shape, different physical models have been proposed.
However, an experimental procedure that would allow a validation of a minimal
physical model for the shape of epithelial cells in 3D has not yet been
proposed. In this study, we cultured MDCK epithelial cells on substrates with a
sinusoidal profile, allowing us to measure the shape of the cells on various
positive and negative curvatures. We found that MDCK cells are thicker in the
valleys than on the crests of sinusoidal substrates. The influence of curvature
on the shape of epithelial cells could not be understood with a model using
only differential apical, basal and lateral surface energies. However, the
addition of an apical line tension was sufficient to quantitatively account for
the experimental measurements. The model also accounts for the shape of MDCK
cells that overexpress E-cadherin. On the other hand, when reducing myosin II
activity with blebbistatin, we measured a saturation of the difference in cell
thickness between valleys and crests, suggesting the need for a term limiting
large cell deformations. Our results show that a minimal model that accounts
for epithelial cell shape needs to include an apical line tension in addition
to differential surface energies, highlighting the importance of structures
that produce anisotropic tension in epithelial cells, such as the actin belt
linking adherens junctions. In the future, our experimental procedure could be
used to test a wider range of physical models for the shape of epithelia in
curved environments, including, for example, continuous models.
