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  • Open Access

Modeling bulk mechanical effects in a planar cellular monolayer

Natasha Cowley*

Sarah Woolner†

Oliver E. Jensen‡

  • Division of Cell Matrix Biology & Regenerative Medicine, University of Manchester, Oxford Road, Manchester M13 9PT, United Kingdom

  • *Contact author: Natasha.Cowley@manchester.ac.uk
  • †Contact author: Sarah.Woolner@manchester.ac.uk
  • ‡Contact author: Oliver.Jensen@manchester.ac.uk
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Phys. Rev. E 112, 054401 – Published 3 November, 2025

DOI: https://doi.org/10.1103/5l56-wc8f

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 the cell apical area and the 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 it 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 center. We examine the 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.

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Outline

Information

Phys. Rev. E 112, 054401– Published 3 November, 2025
  • Received 30 May 2025
  • Accepted 6 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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