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  • Letter
  • Open Access

Morphological instability at topological defects in a three-dimensional vertex model for spherical epithelia

Oliver M. Drozdowski and Ulrich S. Schwarz*

  • Institute for Theoretical Physics and BioQuant, Heidelberg University, 69120 Heidelberg, Germany and Max Planck School Matter to Life, 69120 Heidelberg, Germany

  • *Corresponding author: schwarz@thphys.uni-heidelberg.de
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Phys. Rev. Research 6, L022045 – Published 22 May, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L022045

Abstract

Epithelial monolayers are a central building block of complex organisms. Topological defects have emerged as important elements for single cell behavior in flat epithelia. Here we theoretically study such defects in a three-dimensional vertex model for spherical epithelia like cysts or intestinal organoids. We find that they lead to the same generic morphological instability to an icosahedral shape as it is known from spherical elastic shells like virus capsids, polymerized vesicles, or buckyballs. We derive analytical expressions for the effective stretching and bending moduli as a function of the parameters of the vertex model, in excellent agreement with computer simulations. These equations accurately predict both the buckling of a flat epithelial monolayer under uniaxial compression and the faceting transition around the topological defects in spherical epithelia. We further show that localized apico-basal tension asymmetries allow them to reduce the transition threshold to small system sizes.

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Phys. Rev. Research 6, L022045– Published 22 May, 2024
  • Received 15 November 2023
  • Accepted 9 May 2024
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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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