Epithelial mechanics in a three-dimensional cell vertex model with local junctional constraints
- 1Nagoya University
Abstract
Epithelial monolayers must accommodate deformation while maintaining continuous tissue coverage, but how their material properties emerge from three-dimensional cell mechanics remains incompletely understood. Among several three-dimensional cell vertex formulations, we build on a minimal model that captures experimentally observed features of epithelial monolayers, including shape bistability. The geometric constraint introduced in the model, however, is limited to regular cells undergoing uniform deformation. Here, we extend this model by replacing the original geometric constraint with a local energy based on the geometry of cell-cell junctions, allowing general vertex motions while retaining analytical tractability for regular cell packings and enabling simulations of disordered tissues. Using this framework, we derive analytical expressions for the in-plane elastic moduli and Poisson's ratio and characterize the shear modulus across the tissue thickness. We show that the model reproduces a near-zero Poisson's ratio observed in cultured epithelia. Numerical simulations show that this response persists beyond uniform deformation and remains robust to structural disorder over the timescales examined. Structural disorder also broadens the spectrum of internal relaxation modes and thus introduces slower modes to the frequency-dependent mechanical response. Together, these results establish a tractable three-dimensional framework for understanding how epithelial tissue mechanics emerges from cell-level geometry and interactions under realistic deformations and structural disorder.
Related
- Toll-like receptors in epithelial mechanics and surveillance
- Single cell RNA-seq analysis identifies junctional adhesion molecule two positive endothelial cells aggravate osteoarthritis by mediating vascular permeability and macrophage adhesion
- Depicting External Crown Resorption in Syndromic Amelogenesis Imperfecta Associated With Junctional Epidermolysis Bullosa.
- bioRheoFlow A Rheometric Platform for In Situ Biofilm Mechanics Under Controlled Flow Conditions
- Neuronal lipid composition regulates distinct states of full-length tau assembly, mechanics and membrane interactions
BibTeX
@misc{terada2026epithelial,
title = {{Epithelial mechanics in a three-dimensional cell vertex model with local junctional constraints}},
author = {K. Terada and Y. Kondo},
howpublished = {bioRxiv},
year = {2026},
month = may,
doi = {10.64898/2026.05.15.725329},
url = {https://www.biorxiv.org/content/10.64898/2026.05.15.725329v3},
note = {CC BY-ND},
}
RIS
TY - UNPB
TI - Epithelial mechanics in a three-dimensional cell vertex model with local junctional constraints
AU - K. Terada
AU - Y. Kondo
PY - 2026
DA - 2026/05/15
PB - bioRxiv
DO - 10.64898/2026.05.15.725329
UR - https://www.biorxiv.org/content/10.64898/2026.05.15.725329v3
AB - Epithelial monolayers must accommodate deformation while maintaining continuous tissue coverage, but how their material properties emerge from three-dimensional cell mechanics remains incompletely understood. Among several three-dimensional cell vertex formulations, we build on a minimal model that captures experimentally observed features of epithelial monolayers, including shape bistability. The geometric constraint introduced in the model, however, is limited to regular cells undergoing uniform deformation. Here, we extend this model by replacing the original geometric constraint with a local energy based on the geometry of cell-cell junctions, allowing general vertex motions while retaining analytical tractability for regular cell packings and enabling simulations of disordered tissues. Using this framework, we derive analytical expressions for the in-plane elastic moduli and Poisson's ratio and characterize the shear modulus across the tissue thickness. We show that the model reproduces a near-zero Poisson's ratio observed in cultured epithelia. Numerical simulations show that this response persists beyond uniform deformation and remains robust to structural disorder over the timescales examined. Structural disorder also broadens the spectrum of internal relaxation modes and thus introduces slower modes to the frequency-dependent mechanical response. Together, these results establish a tractable three-dimensional framework for understanding how epithelial tissue mechanics emerges from cell-level geometry and interactions under realistic deformations and structural disorder.
ER -