Cell bulging and extrusion in a three-dimensional bubbly vertex model for curved epithelial sheets

TL;DR

This paper introduces a 3D bubbly vertex model to study how cell extrusion and tissue curvature interact, revealing a strong bulging instability at topological defects and how basal tension stabilizes cell shapes.

Contribution

The study develops a novel 3D bubbly vertex model to analyze the interplay between cell extrusion, curvature, and force regulation in epithelial tissues.

Findings

A strong bulging instability occurs at topological defects in the model.

Basal interfacial tension in pentagonal cells stabilizes against the instability.

Tissue curvature naturally promotes bulged and extrusion-like cell shapes.

Abstract

Cell extrusion is an essential mechanism for controlling cell density in epithelial tissues. Another essential element of epithelia is curvature, which is required to achieve complex shapes, like in the lung or intestine. Here we introduce a three-dimensional bubbly vertex model to study the interplay between extrusion and curvature. We find a generic cellular bulging instability at topological defects which is much stronger than for standard vertex models. Analyzing cell shapes in three-dimensional imaging data of spherical mouse colon organoids, we infer that pentagonal cells have an increased basal interfacial tension, suggesting that cells at topological defects react to the different force conditions. Using the bubbly vertex model, we show that such basal tensions stabilize against the predicted instability and result in better cell shape control than tissue-scale mechanisms such as lumen pressure and spontaneous curvature. Our theory suggests that epithelial curvature naturally leads to bulged and extrusion-like cell shapes because the interfacial curvature of individual cells at the defects strongly amplifies buckling effected by tissue-scale topological defects in elastic sheets. Our results highlight the complex interplay of forces across scales in three-dimensional tissue organization.