Relating cell shape and mechanical stress in a spatially disordered epithelium using a vertex-based model

TL;DR

This study uses a vertex-based model to explore how cell shape correlates with mechanical stress in a disordered epithelial tissue, revealing alignment of stress and shape axes and predicting long-range patterning.

Contribution

It introduces a novel derivation of stress tensors from an energetic model and applies it to experimental data, linking cell shape and mechanical stress in epithelia.

Findings

Principal stress axes align with cell shape axes.

Mechanical interactions produce long-range shape correlations.

Orientation of mechanical and geometric cues are strongly correlated.

Abstract

Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors starting from an energetic formulation of the model, we show that the principal axes of stress for an individual cell align with the principal axes of shape, and we determine the bulk effective tissue pressure when the monolayer is isotropic at the tissue level. Using simulations for a monolayer that is not under peripheral stress, we fit parameters of the model to experimental data for Xenopus embryonic tissue. The model predicts that mechanical interactions can generate mesoscopic patterns within the monolayer that exhibit long-range correlations in cell shape. The model also suggests that the orientation of mechanical and geometric cues for processes such as cell division are likely to be strongly correlated in real epithelia. Some limitations of the model in capturing geometric features of Xenopus epithelial cells are highlighted.