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

TL;DR

This paper introduces a 3D continuum mechanics shell model for epithelial cells, revealing how apical-basal deformations influence tissue rigidity and challenging prior 2D assumptions about cell mechanics.

Contribution

The authors develop a novel 3D elastic shell model for epithelial cells that incorporates apical-basal effects, providing analytical solutions and experimental validation.

Findings

Cells in rigid tissues have long perimeters similar to floppy states in 2D models.

Active stress and 3D effects significantly influence cell shape and tissue mechanics.

Tissues are more robust against rigidity loss than previously thought.

Abstract

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.