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arxiv: 2411.07141 · v2 · submitted 2024-11-11 · ⚛️ physics.bio-ph · cond-mat.soft· q-bio.TO

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

Oliver M. Drozdowski , B\"u\c{s}ra Kocame\c{s}e , Kim E. Boonekamp , Michael Boutros , Ulrich S. Schwarz (Heidelberg University , Germany) This is my paper

Pith reviewed 2026-05-23 17:29 UTC · model grok-4.3

classification ⚛️ physics.bio-ph cond-mat.softq-bio.TO
keywords cell extrusionepithelial curvaturevertex modeltopological defectsbulging instabilitybasal tensionorganoidsthree-dimensional tissue
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The pith

Epithelial curvature leads to cell bulging and extrusion at topological defects through amplified interfacial forces.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a three-dimensional bubbly vertex model to examine how curvature interacts with cell extrusion in epithelia. It identifies a generic bulging instability at topological defects that is amplified by the curvature of individual cell interfaces. Data from spherical mouse colon organoids indicate that pentagonal cells increase their basal interfacial tension in response. This local tension stabilizes cell shapes more effectively than tissue-wide mechanisms such as lumen pressure. The findings indicate that curvature in tissues promotes bulged and extrusion-like shapes at defects.

Core claim

In the three-dimensional bubbly vertex model, topological defects in curved epithelial sheets trigger a cellular bulging instability because the interfacial curvature at individual cells strongly amplifies the buckling induced by tissue-scale defects. Increased basal interfacial tension in pentagonal cells, inferred from organoid imaging, stabilizes against this instability and achieves superior cell shape control.

What carries the argument

three-dimensional bubbly vertex model with basal interfacial tension that amplifies defect-induced buckling via cell interface curvature

If this is right

  • Curved epithelial tissues naturally develop bulged and extrusion-like cell shapes at topological defects.
  • Basal tension adjustments in pentagonal cells provide effective local stabilization of cell shapes.
  • Tissue-scale mechanisms such as lumen pressure or spontaneous curvature are less effective for shape control than local basal tension.
  • Extrusion serves as a density control mechanism that is enhanced by curvature in three-dimensional sheets.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same amplification mechanism may operate in other curved epithelia such as lung or intestinal tissues.
  • Direct tension measurements at defects across varying curvatures could test the inferred cellular response.
  • Topological defects likely influence 3D tissue organization more strongly than in flat monolayers.

Load-bearing premise

Increased basal interfacial tension in pentagonal cells inferred from 3D imaging of spherical mouse colon organoids accurately reflects and counters the force conditions at topological defects.

What would settle it

Direct observation of no increased basal tension specifically in pentagonal cells at defects in curved epithelia, or persistent bulging instability despite such tension, would falsify the proposed stabilization.

Figures

Figures reproduced from arXiv: 2411.07141 by B\"u\c{s}ra Kocame\c{s}e, Germany), Kim E. Boonekamp, Michael Boutros, Oliver M. Drozdowski, Ulrich S. Schwarz (Heidelberg University.

Figure 1
Figure 1. Figure 1: FIG. 1. Cell bulging at topological defects in the bubbly ver [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Lowered buckling threshold for icosahdral instability [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Schematic depiction of the defect cell in a mean field [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The core energy for the different defect cell config [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of continuum model with vertex model [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Energy landscapes in configuration space and the resulting defect cell shapes. (a-c) Energy landscapes with coordinates [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Extrusion through lower defect tension in hexagons [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Modulation of instability via luminal pressure and [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Cell bulging as it is observed in mouse small intes [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces a three-dimensional bubbly vertex model for curved epithelial sheets and reports a generic cellular bulging instability at topological defects that is amplified by individual-cell interfacial curvature, stronger than in standard vertex models. From 3D imaging of spherical mouse colon organoids the authors infer increased basal interfacial tension in pentagonal cells. The model is then used to show that this tension stabilizes the instability more effectively than tissue-scale mechanisms such as lumen pressure or spontaneous curvature. The central theoretical claim is that epithelial curvature naturally produces bulged and extrusion-like shapes because cell interfacial curvature at defects amplifies buckling driven by tissue-scale topological defects.

Significance. If the central claims are substantiated, the work would be significant for understanding multi-scale force balance in 3D epithelial morphogenesis, particularly the interplay between topology, curvature, and cell extrusion. The development of the bubbly vertex model and its direct comparison to organoid imaging data constitute clear strengths. The result offers a mechanistic explanation that could be tested in other curved epithelia.

major comments (1)
  1. [Section describing organoid imaging analysis and tension inference] The mapping from organoid shape statistics to an increased basal interfacial tension specifically at pentagonal cells (and its identification as the biologically relevant counter-force at topological defects) is not secured by controls for global curvature, lumen pressure, or cell-density effects. This assumption is load-bearing for the claim that the inferred tension stabilizes the instability better than tissue-scale mechanisms, yet the experimental section provides no direct validation that the observed pentagon bias encodes the local force imbalance present in the model.
minor comments (1)
  1. Figure captions should explicitly state the number of organoids and cells analyzed and include scale bars; model parameter tables would benefit from a column listing which parameters are fixed versus fitted.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review and for highlighting the need to strengthen the experimental inference section. We respond to the single major comment below.

read point-by-point responses

  1. Referee: [Section describing organoid imaging analysis and tension inference] The mapping from organoid shape statistics to an increased basal interfacial tension specifically at pentagonal cells (and its identification as the biologically relevant counter-force at topological defects) is not secured by controls for global curvature, lumen pressure, or cell-density effects. This assumption is load-bearing for the claim that the inferred tension stabilizes the instability better than tissue-scale mechanisms, yet the experimental section provides no direct validation that the observed pentagon bias encodes the local force imbalance present in the model.

    Authors: We acknowledge that the inference of elevated basal tension in pentagons rests on statistical differences in cell shape between pentagons and hexagons without dedicated controls that isolate global curvature, lumen pressure, or density. Global parameters would be expected to affect all cells similarly and therefore cannot account for the topology-specific bias we report. We will add a new paragraph in the revised manuscript that explicitly discusses these assumptions, notes the absence of direct force measurements, and clarifies that the model comparison demonstrates consistency with local tension adjustment rather than tissue-scale alternatives. This constitutes a partial revision focused on improved transparency rather than new data. revision: partial

Circularity Check

0 steps flagged

No circularity: model predictions independent of fitted inputs; imaging inference treated as external constraint

full rationale

The derivation introduces a new 3D bubbly vertex model, derives a bulging instability at defects from its equations, then uses independent 3D organoid imaging to infer a basal-tension adjustment that is inserted as a parameter. No step reduces a claimed prediction to a fit by construction, no self-citation chain bears the central result, and the imaging-to-tension mapping is presented as an external observation rather than derived from the model itself. The overall claim therefore rests on the model's independent mechanics plus separate data, not on re-labeling of its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters and assumptions; the model itself is treated as a domain assumption.

free parameters (1)
  • basal interfacial tension for pentagonal cells
    Inferred from organoid imaging to stabilize against instability, value not specified in abstract.
axioms (1)
  • domain assumption The 3D bubbly vertex model appropriately captures mechanics of curved epithelial sheets including curvature and extrusion
    Core modeling choice used to study interplay between extrusion and curvature.

pith-pipeline@v0.9.0 · 5751 in / 1057 out tokens · 30511 ms · 2026-05-23T17:29:07.160918+00:00 · methodology

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Reference graph

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