Cell Deformation Signatures along the Apical-Basal Axis: A 3D Continuum Mechanics Shell Model

Two-dimensional (2D) mechanical models of confluent tissues have related the mechanical state of a monolayer of cells to the anisotropy or eccentricity of the cell shapes, predicting floppiness or rigidity of the material. For the well-studied system of in-vitro MDCK epithelial cells, however, we find experimentally that cells in mechanically solid tissues display large anisotropy characteristic of a fluid state in 2D models. We hypothesize that this discrepancy is due to mechanical effects in the third (apical-basal) dimension, caused by actin stress fibers near the basal membrane. To fundamentally understand the effect of such additional stress on the shape of a cell, we develop a 3D continuum mechanics model of an epithelial cell as an elastic cylindrical shell, with appropriate boundary conditions reflecting the action of the basal fiber bundles. This formalism yields analytical solutions predicting the resultant cross-sectional shapes at different positions along the cylinder axis. Confocal-slice experimental data confirm the significant and systematic change in cell shape parameters in this apical-basal direction. The approach allows for arbitrary reference cell shapes and takes into account the effect of neighboring cells’ stress states. Its results can be used to augment the 2D modeling with information about the basal fiber stress, explaining the strongly anisotropic cells in rigid tissues and paving the way to a more realistic description of single-layer confluent tissue mechanics.