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Cell Bulging and Extrusion in a Three-Dimensional Bubbly Vertex Model for Curved Epithelial Sheets

Oliver M. Drozdowski1,2,3,4, Büşra Kocameşe-Tamgac𝚤5,6, Kim E. Boonekamp5,6, Michael Boutros2,3,5,6, and Ulrich S. Schwarz1,2,3,*

  • *Contact author: schwarz@thphys.uni-heidelberg.de
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Phys. Rev. X 16, 021023 – Published 30 April, 2026

DOI: https://doi.org/10.1103/x82g-cq7n

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 extrusionlike 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.

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Popular Summary

Epithelial cell monolayers are the main barriers between the many different compartments in our body. We used a fully three-dimensional theoretical model to determine where cell extrusion is most likely to occur when these layers are curved. We found that extrusion should be preferred at topological defects, which generate the curvature in such sheets. We complemented this theoretical prediction with experimental observations in spherical mouse colon organoids. Cells at these defects had higher surface tensions, likely in order to stabilize shape and avoid extrusion. Our work highlights the interplay between physical forces and biological responses in curved tissues, which have to be stable and dynamic at the same time.

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Outline

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Phys. Rev. X 16, 021023– Published 30 April, 2026
  • Received 11 November 2024
  • Revised 27 February 2026
  • Accepted 18 March 2026
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