Modelling bulk mechanical effects in a planar cellular monolayer

TL;DR

This paper develops a 2D vertex model incorporating bulk effects like cell volume and surface area, revealing mechanisms of rigidity loss and stress distribution in cellular monolayers.

Contribution

It introduces a 3D-to-2D reduced model that captures bulk mechanical effects and distinguishes between bulk and in-plane stresses in epithelial monolayers.

Findings

Bulk effects couple cell area and perimeter energy variations.

Five mechanisms can lead to loss of in-plane rigidity.

Lateral crowding causes cell elongation and rigidity loss.

Abstract

We use a three-dimensional formulation of the cell vertex model to describe the mechanical properties of a confluent planar monolayer of prismatic cells. Treating cell height as a degree of freedom, we reduce the model to a two-dimensional form. We show how bulk effects, associated with cell volume and total surface area, lead to coupling between energy variations arising from changes in cell apical area and apical perimeter, a feature missing from standard implementations of the two-dimensional vertex model. The model identifies five independent mechanisms by which cells can lose in-plane rigidity, relating to variations in total cell surface area, the strength of lateral adhesion, and constrictive forces at the apical cortex. The model distinguishes bulk from in-plane stresses, and identifies two primary measures of cell shear stress. In the rigid regime, the model shows how lateral crowding in a disordered isolated monolayer can lead to cell elongation towards the monolayer centre. We examine loss of in-plane rigidity in a disordered monolayer and connect isolated patches of stiffness that persist during the rigidity transition to the spectrum of a Laplacian matrix. This approach enables bulk mechanical effects in an epithelium to be captured within a two-dimensional framework.