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 average perimeter length of the cell cross sections, 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 rigid tissues display long perimeters characteristic of a floppy state in 2D models. We suggest that this discrepancy is due to mechanical effects in the third (apical-basal) dimension, including those caused by actin stress fibers near the basal membrane. To quantitatively understand cell deformations in 3D, we develop a continuum mechanics model of epithelial cells as elastic cylindrical shells, with appropriate boundary conditions reflecting both the passive confinement of neighboring cells and the active stress of actomyosin contractility. This formalism yields analytical solutions predicting cell cross sections along the entire cylinder axis. Deconvolution microscopy experimental data confirm the significant and systematic change in cell shape parameters in this apical-basal direction. In addition to providing a wealth of detailed information on deformation on the subcellular scale, the results of the approach alter our understanding of how active tissues balance requirements of their stiffness and integrity, suggesting they are more robust against loss of rigidity than previously inferred.