Spontaneous elongation of 3D gastruloids from local cell polarity alignment

Dag Kristian Dysthe; Endre J. L. Mossige; Keqing Sunny Dai; Luiza Angheluta; Natalia Smirnova; Richard D.J.G. Ho; Sergei Ponomartcev; Stefan Krauss; Xian Hu

REVIEW 4 major objections 4 minor 27 references

Spontaneous elongation of 3D gastruloids from local cell polarity alignment

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read Local cell polarity alignment alone can drive spontaneous elongation of 3D gastruloids.

desk verdict A credible proof-of-principle model and a suggestive imaging observation, but the paper's headline quantitative claim about bulk quasi-long-range order is not backed by statistics; needs major revision before it can carry the weight. read the letter →

arxiv 2509.08929 v1 pith:RLJPRTPL submitted 2025-09-10 physics.bio-ph cond-mat.soft

Richard D.J.G. Ho , Endre J. L. Mossige , Sergei Ponomartcev , Natalia Smirnova , Xian Hu , Keqing Sunny Dai , Stefan Krauss , Dag Kristian Dysthe

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Luiza Angheluta

This is my paper · ORCID

classification physics.bio-phcond-mat.soft

keywords gastruloidcellpolarityplanaraxialelongationconvergence-extensionquasi-long-rangeordernuclearorientationWntsignaling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that local alignment of cell polarity, without any global gradient or pre-pattern, is sufficient to break symmetry and elongate a 3D cell aggregate. It supports this with light-sheet imaging of mouse gastruloids, where Wnt activation (Chiron) produces coherent nuclear orientation that decays algebraically across the tissue, while untreated controls show only short-range order. A minimal physical model of polarized cells with alignment torques and polarity-mediated adhesion reproduces both the orientational order and the convergence-extension flow that elongates the aggregate. The result matters because it offers an alternative to morphogen-gradient explanations for tissue morphogenesis.

What carries the argument

The central object is a minimal model of interacting polarized cells, each carrying a planar cell polarity vector p and an apical-basal vector q. Cells move under a pairwise potential with isotropic and anisotropic parts, where the anisotropic terms S1, S2, S3 couple polarity orientation to intercellular separation and to each other; polarity reorients under alignment torques and rotational noise. The model requires a crowding rule that limits anisotropic interactions for cells with few neighbors, mimicking surface tension. The experimental key is the pair correlation function of nuclear eigenvectors from 3D segmentation, which distinguishes exponential from algebraic decay.

What would settle it

If a direct marker of cell polarity (such as membrane-localized PCP protein) shows no coherent alignment in Chiron-treated gastruloids at 3–4 dpa, while nuclear axes remain aligned, the link from polarity coherence to elongation would be falsified. Alternatively, if the minimal model with the alignment torques removed (but the same isotropic potential and crowding rule) still elongates, the sufficiency claim would fail.

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Extended reading notes

Core claim

In Chiron-treated gastruloids the longest nuclear axes, used as a proxy for cell polarity, exhibit bulk orientational correlations decaying as ~1/r, a signature of quasi-long-range order, whereas untreated controls decay exponentially with a correlation length of about 10 µm. The same distinction appears in the model: when spatially dependent alignment torques dominate, the pair correlation of planar-cell-polarity orientations decays algebraically and the aggregate elongates perpendicular to the aligned polarity axis. The paper concludes that local cell polarity alignment is a sufficient physical mechanism for spontaneous axial elongation.

Load-bearing premise

The paper treats nuclear elongation and orientation as a direct proxy for cell polarity; if Chiron-induced nuclear alignment instead reflects passive deformation of nuclei by tissue strain, the experimental claim that coherent cell polarity drives elongation would not be established.

Editorial extensions

If this is right

Elongation can emerge from bulk cell dynamics alone; no leader cells at the boundary are required.
Cell proliferation is not necessary for symmetry breaking; the model elongates with constant cell number.
Quasi-long-range orientational order in nuclear axes is a measurable signature that can distinguish polarity-driven from passive-shape morphogenesis.
Wnt activation acts by enhancing the spatially dependent alignment pathway, suggesting a direct link between biochemical signaling and mechanical order.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If nuclear orientation is a faithful readout of cell polarity, then the 1/r decay in Chi-treated gastruloids implies the tissue behaves like an active nematic in three dimensions, with the quasi-long-range order protected by continuous rotational symmetry.
A direct test: immunostaining for planar cell polarity proteins (e.g., Vangl2) in Chi-treated gastruloids should show the same 1/r-aligned domains as the nuclear axes; if it does not, the nucleus is being deformed passively by tissue strain rather than by active polarity.
The model's dependence on the crowding rule suggests that surface tension and neighbor number modulate how far polarity alignment can drive elongation; varying cell-cell adhesion strength experimentally should shift the correlation length.
The same framework could apply to other organoid and embryoid systems that elongate without obvious morphogen gradients, where polarity alignment may be a common driver.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The short version: this paper has two things going for it, and one serious weakness in the middle. The model—polarized cells with alignment torques and polarity-mediated adhesion—convincingly shows that local polarity alignment alone can drive convergence-extension and elongation in a 3D aggregate. That's a useful minimal demonstration, building on the Nissen et al. and Nielsen et al. framework, and the authors are honest about it. They also ship code and data on OSF, which I appreciate.

The new experimental work is the spatial correlation analysis of nuclear orientations in gastruloids. The distinction between surface and bulk is a good idea, and the observation that Chi-treated bulk nuclei show an algebraic tail while controls do not is intriguing. But that observation is not actually supported as presented. Figure 5 shows four curves without error bars, no sample counts, no fitting routine, no model comparison. The text just asserts that +Chi decays as 1/r and −Chi as exponential with lc≈10 µm. The log-log inset covers a narrow range (r≈10–40 µm), and finite-size effects could easily produce an apparent power law. For a claim that carries the title and abstract, that's too thin.

There are also two fixable problems. The abstract says 'quantitatively reproduces,' but the model–experiment comparison is purely qualitative regime matching. The p/q labels are swapped in the Discussion: in the Model section p is PCP and q is AB; in the Discussion they reverse the assignment. A reader who follows the equations will trip on that. And the abstract's statement that 'only Chiron-treated gastruloids exhibit quasi-long-range alignment' ignores Fig. 4, where the surface shows 1/r in controls too. The claim should be restricted to the bulk.

The nuclear-shape proxy is a reasonable first pass, but I'd want the authors to address whether the elongated nuclei are actively polarized or passively deformed by tissue strain. If the latter, the experimental link weakens, even though the model proof-of-principle stands.

Who is this for? People working on gastruloid mechanics, organoid engineering, and active matter models of morphogenesis. It's a plausible candidate mechanism, and the model is clean enough to be worth testing. But in its current form I wouldn't cite it for the quasi-long-range order claim.

Recommendation: send it to peer review—it deserves referee time—but expect the reviewers to insist on error bars, sample sizes, a real fit comparison, and a toned-down abstract. If the authors do that, this could become a solid contribution.

Referee Report

4 major / 4 minor

Summary. This manuscript combines 3D light-sheet imaging of mouse gastruloids with a minimal particle-based model of polarized cells. Experimentally, the authors segment nuclei and use their principal axes as proxies for cell polarity. They report that nuclear elongation occurs with or without Chiron treatment, but that only Chiron-treated gastruloids show persistent bulk orientational correlations decaying algebraically as ~1/r, while untreated controls decay exponentially with a correlation length around 10 µm. In the model, each cell carries two polarity vectors (PCP and apical-basal), with alignment torques and polarity-dependent adhesion. The model exhibits spontaneous symmetry breaking and elongation, and the authors identify parameter regimes producing either exponential or algebraic PCP correlations. The paper claims that local cell polarity alignment alone can drive tissue-scale convergence-extension flows.

Significance. If the central claims hold, the work provides a conceptually appealing mechanism for gastruloid elongation that complements existing reaction-diffusion and differential-adhesion explanations. The minimal model is clearly posed and the paper explicitly links different correlation regimes to distinct alignment torques, which is a useful organizing idea. Strengths include the open data/code repository, the direct measurement of orientational correlations in 3D tissue, and the demonstration that proliferation is not required for elongation in the model. However, the experimental support for the key distinction between algebraic and exponential decay is currently qualitative, the abstract overstates what is shown, and the model is not quantitatively fitted to the experimental curves.

major comments (4)

[Figure 5 and Eq. (1)] The central experimental claim—that Chiron-treated bulk gastruloids show algebraic ~1/r correlations while controls decay exponentially—is not statistically supported. No error bars, number of gastruloids per condition, or fitting procedure are given. The text simply asserts the two functional forms. A comparison of fits (e.g., power law vs exponential with AIC or likelihood ratio), bootstrap confidence intervals on the exponent and correlation length, and the number of independent samples are needed. The log-log inset for +Chi covers only roughly r = 10–40 µm, so finite-size effects near the boundary could mimic a power-law tail. Without this, the 'quasi-long-range order' conclusion is not established.
[Abstract and Introduction, final paragraph] The abstract states that 'only Chiron-treated gastruloids exhibit quasi-long-range alignment of nuclear axes.' This is contradicted by Figure 4, which shows that surface correlations decay as ~1/r both with and without Chi. The claim should be restricted to the tissue interior/bulk. In addition, the Introduction says the model 'quantitatively reproduces this transition,' but the model is never fitted to the experimental correlation curves; the comparison is qualitative regime matching. Either provide a quantitative fit or revise the wording.
[Model section, Eqs. (2)–(5), Fig. 8] No simulation parameter values are reported. The model depends on λ0, β, a0, λ1, λ2, λ3, DT, DR, the neighbor threshold, and the number of particles, but none of these are given. This makes Figures 6–8 irreproducible and prevents the reader from assessing whether the two regimes are robust or fine-tuned. Please provide a parameter table, simulation details, and a sensitivity analysis, especially for the ratio λ2/λ1,3 that controls the exponential vs algebraic correlation regime.
[Experimental section: 'To extract cell polarities from 3D imaging' and Fig. 3] The causal interpretation depends on the assumption that nuclear elongation orientation reflects active cell polarity. If Chiron-induced coherent nuclear orientation is instead a passive response to tissue-scale strain, then the experimental correlation between polarity alignment and elongation would be largely circular. The references [20,21] support a shape–polarity link, but the manuscript does not address this potential confound. A direct test, such as comparing nuclear orientations with a molecular PCP marker or performing live imaging of polarity dynamics, would considerably strengthen the interpretation. At minimum, this limitation should be acknowledged.

minor comments (4)

[Discussion] The polarity labels are swapped: the model section defines p as PCP and q as apical-basal, but the Discussion states that the model includes 'apical–basal (p) and PCP (q).' This should be corrected for consistency.
[Throughout] The term 'quasi-long-range order' is used for algebraic decay in a 3D system. In statistical mechanics, quasi-long-range order typically refers to 2D systems with a continuously broken symmetry. Please define the term operationally or use 'algebraic decay' to avoid confusion.
[Eq. (1)] The normalization uses the absolute value of the dot product, which is appropriate for nematic directors, but the paper sometimes refers to 'alignment' without clarifying whether the order parameter is nematic or polar. This distinction should be explicit, especially since the model uses polar vectors p and q.
[Figure 4 caption / text] The text says surface correlations 'have monotonic dependence on large in-surface distance as ∆C1(r)∼1/r' and that this occurs with or without Chi. The caption of Figure 4 should state this explicitly so that the difference between surface and bulk behavior is clear to the reader.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the model is a proof-of-principle with parameters not fitted to the experimental curves, and the only self-citation is motivational.

full rationale

The paper's central derivation chain runs: (1) measure nuclear-axis correlations in gastruloids with and without Chi; (2) propose a minimal physical model of polarized cells with alignment torques; (3) show by simulation that certain interaction regimes produce either short-range (exponential) or quasi-long-range (1/r) orientational correlations, and that both regimes support elongation; (4) qualitatively associate the Chi condition with the quasi-long-range regime. This chain is not circular. The model parameters λ1, λ2, λ3 are not fitted to the experimental ΔC1(r) data; the paper explicitly explores distinct regimes by tuning these parameters and reports what each regime produces. The 'prediction' of 1/r correlations is a property of the chosen regime, but the choice is not a fit to the experimental curve—it is an exploratory scan, and both regimes yield elongation. Thus the experimental observation and the model output are not equivalent by construction. The only self-citation (Ref. [18], by several of the present authors) is used as background motivation ('This approach has recently been shown to capture key morphological changes in epithelial sheets') and is not load-bearing for the paper's central claim; it does not supply a uniqueness theorem or a forced ansatz. The experimental claim itself lacks error bars and model-selection statistics, but that is a statistical robustness concern, not a circularity. The use of nuclear elongation as a proxy for cell polarity is an explicit assumption, not a definitional equivalence. Overall, the derivation is self-contained and the reported claims, while qualitative, do not reduce to their inputs.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central claim rests on a phenomenological two-polarity-vector model borrowed from prior work (Nissen 2018 et al.), with several hand-tuned coupling constants and an ad hoc crowding rule; the experimental inference additionally assumes nuclear shape is a proxy for cell polarity. No new entities are introduced.

free parameters (8)

λ0 (isotropic adhesion strength) = not reported
Strength of isotropic soft potential V0; hand-tuned, no value reported in text.
β (range ratio in V0) = not reported
Range ratio in isotropic potential; no value reported.
a0 (decay length in V1) = not reported
Decay length of anisotropic interaction potential; no value reported.
λ1, λ2, λ3 (anisotropic coupling strengths) = not reported
Coupling strengths for S1, S2, S3; tuned by hand into two regimes, no values given.
DT (translational diffusivity) = not reported
Noise strength in overdamped position dynamics; no value reported.
DR (rotational diffusivity) = not reported
Noise strength in polarity dynamics; tuned along with λs, no value reported.
Neighbor threshold in crowding rule = not reported
Threshold below which cells feel only isotropic potential; ad hoc, no value reported.
Nuclear inclusion cutoffs (volume, aspect ratio) = volume 65-4189 µm^3; eigenvalue ratio < 2.5
Post-hoc exclusion criteria for segmentation artifacts; may bias orientation statistics but no sensitivity analysis is given.

assumptions (6)

domain assumption Overdamped Langevin dynamics with pairwise forces and Gaussian noise describes cell motion in aggregates.
Standard for cell-scale mechanics; invoked in Eq. 3.
ad hoc to paper Each cell carries two polarity vectors p (PCP) and q (AB), with dynamics given by alignment torques (Eq. 4).
Borrowed from Nissen et al. 2018; the alignment form is chosen, not derived.
ad hoc to paper Anisotropic pairwise potential V^(1) with S1, S2, S3 (Eq. 2) captures polarity-mediated adhesion.
Phenomenological potential; no first-principles derivation.
ad hoc to paper Crowding rule mimicking surface tension: cells with fewer than threshold neighbors experience only isotropic V^(0).
Explicitly introduced to prevent string formation; central to elongation morphology.
domain assumption Nuclear elongation measured by PCA is a proxy for cellular polarity.
Relies on Refs [20,21]; no molecular polarity marker measured.
domain assumption Cell number is held constant; elongation does not require proliferation.
Model scope; authors note division may modulate extent.

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Cite this review

Pith. "Pith review of Spontaneous elongation of 3D gastruloids from local cell polarity alignment." pith.science (2026). https://pith.science/paper/RLJPRTPL

@misc{pith2026250908929,
  author       = {Pith},
  title        = {Pith review of: Spontaneous elongation of 3D gastruloids from local cell polarity alignment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RLJPRTPL}},
  note         = {Machine review of arXiv:2509.08929}
}

read the original abstract

Gastruloids are 3D stem cell aggregate models for early embryogenesis that provide a unique platform to study how collective cell dynamics drive tissue symmetry breaking and axial elongation. Using 3D light sheet imaging, we show that a pulse of Chiron, a Wnt activator, induces coherent alignment of cell polarity during elongation. While nuclear elongation occurs with or without treatment, only Chiron-treated gastruloids exhibit quasi-long-range alignment of nuclear axes, linking cell polarity coherence to tissue-scale remodeling. A minimal physical model of polarized cells, incorporating alignment-dependent torques and polarity-mediated adhesion, reproduces symmetry breaking and elongation, demonstrating that local cell polarity alignment alone can drive tissue-scale convergence-extension flows.

Figures

Figures reproduced from arXiv: 2509.08929 by the authors.

**Figure 3.** illustrates the nuclear orientation vectors corresponding to the cell nuclei on the surface layers of a gastruloid at 4 dpa with Chi. The shortest axes e3 typically align perpendicular to the surface, consistent with an apical-basal polarity. In contrast, the longest axes e1 tend to lie within the surface tissue, similar to planar cell polarities. These surface effects are also seen in gastruloids not treated wit… view at source ↗

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]

**Figure 6.** Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]

**Figure 8.** Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.

[1] [1]

Heisenberg and Y

C.-P. Heisenberg and Y. Bella ¨ ıche, Forces in tissue mor- phogenesis and patterning, Cell153, 948 (2013)

2013

[2] [2]

K. W. Rogers and A. F. Schier, Morphogen gradients: from generation to interpretation, Annual review of cell and developmental biology27, 377 (2011)

2011

[3] [3]

Beccari, N

L. Beccari, N. Moris, M. Girgin, D. A. Turner, P. Baillie- Johnson, A.-C. Cossy, M. P. Lutolf, D. Duboule, and A. M. Arias, Multi-axial self-organization properties of mouse embryonic stem cells into gastruloids, Nature562, 272 (2018)

2018

[4] [4]

Simunovic and A

M. Simunovic and A. H. Brivanlou, Embryoids, organoids and gastruloids: new approaches to understanding em- bryogenesis, Development144, 976 (2017)

2017

[5] [5]

Martyn, T

I. Martyn, T. Kanno, A. Ruzo, E. Siggia, and A. Brivan- lou, Self-organization of a human organizer by combined wnt and nodal signalling, Nature558, 132 (2018)

2018

[6] [6]

Moris, K

N. Moris, K. Anlas, S. C. van den Brink, A. Alemany, J. Schr¨ oder, S. Ghimire, T. Balayo, A. van Oudenaar- den, and A. Martinez Arias, An in vitro model of early anteroposterior organization during human development, Nature582, 410 (2020)

2020

[7] [7]

M. A. de Jong, E. Adegeest, N. M. B´ erenger-Currias, M. Mircea, R. M. Merks, and S. Semrau, The shapes of elongating gastruloids are consistent with convergent extension driven by a combination of active cell crawling and differential adhesion, PLoS Computational Biology 20, e1011825 (2024)

2024

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Fiuza, S

U.-M. Fiuza, S. Bonavia, P. Pascual-Mas, G. Torregrosa- Cortes, P. Casani-Galdon, G. Robertson, A. Dias, and A. Martinez Arias, Morphogenetic constrains in the de- velopment of gastruloids: implications for mouse gastru- lation, bioRxiv , 2024 (2024)

2024