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REVIEW 4 major objections 5 minor 34 references

Rosette formations as symmetry-breaking events: theory and experiment

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Rosette assemblies in epithelia are symmetry-breaking responses to local curvature, with probability set by a fluidity–deformability trade-off and stabilized by self-alignment.

desk verdict Simulations are solid and the parameter sweeps are new, but the experimental comparison uses the realized shape factor where the model predicts in target p0, so the central agreement claim is not yet established. read the letter →

arxiv 2505.20543 v2 pith:EGQVYEHJ submitted 2025-05-26 q-bio.CB cond-mat.softcond-mat.stat-mechphysics.bio-ph

Mattia Miotto , Giorgio Gosti , Maria Rosito , Michela Dell'Omo , Viola Folli , Valeria de Turris , Giancarlo Ruocco , Alessandro Rosa
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Matteo Paoluzzi
This is my paper · ORCID
classification q-bio.CBcond-mat.softcond-mat.stat-mechphysics.bio-ph
keywords ActiveVoronoimodelmulticellularrosettestissuefluiditycelldeformabilitycurvaturedefectsself-alignmentneuraliPSCdifferentiation
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

Rosettes—assemblies of five or more cells meeting at a common point—appear in development, wound healing, and cancer, yet the general conditions that favor them have been unclear. This paper argues that rosettes are the natural response of a cell layer to a localized symmetry break: a defect that introduces local curvature, such as a focus of actin tension, a curved surface, or an oversized cell. Using an Active Voronoi model, the paper shows that such a defect creates topological defects in the tissue, and that the probability of assembling a rosette is governed by a trade-off between tissue fluidity and single-cell deformability. Self-alignment of cell motion with cell elongation strongly stabilizes transient rosettes and enlarges lumen-centered ones. Fluorescence time-lapses of iPSC-derived neural cells confirm the prediction: rosettes appear in regions where the average cell shape factor stays above about 3.9, the fluid-like regime.

What carries the argument

The carrying mechanism is the Active Voronoi model: cell centers move under self-propulsion and forces from a vertex energy $$E_v=\frac{1}{2}\sum_i\big[K_p(p_i-p_0)^2+K_A(A_i-A_0)^2\big],$$ so topological rearrangements happen automatically rather than being inserted by hand. Symmetry breaking is imposed by an external harmonic potential $E_h=\frac12 k(\mathbf r_i-\mathbf r_c)^2$ (transient rosettes), a Lennard-Jones potential centered on one point (lumen-centered rosettes), or a leader cell with different target area (pinwheel-like rosettes). A self-alignment term $J\sin(\theta_i-\phi_i)$ in the orientation dynamics couples self-propulsion direction to cell elongation. The argument connects these ingredients to curvature: a localized positive-curvature defect changes the topological-charge balance, making higher-fold vertices energetically favorable; cell motility and deformability then determine whether the defect is stabilized or washed out.

What would settle it

Track the shape factor and motility of cells in many rosette-forming and non-forming regions of a living epithelium; the model predicts rosettes appear only in fluid-like regions with average shape factor above about 3.9 and slow cells, and that flat homogeneous monolayers without any localized defect produce essentially no rosettes. Observing rosettes in stiff, fast-moving, defect-free regions would refute the central claim.

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Extended reading notes

Core claim

The paper's central claim, stated in its own terms, is that rosettes are natural outcomes of geometric and mechanical responses to curvature. In flat space with homogeneous parameters, Euler's relation forces an average of six edges per cell and hexagonal tiling is preferred; higher-fold vertices are unstable and resolve by T1 transitions. Inserting a localized defect—harmonic potential, Lennard-Jones potential, or leader cell of different target area—breaks translational invariance, and the tissue accommodates the induced positive curvature by forming topological defects in which five or more cells meet at a central point. The probability of these transient rosettes increases with cell deformability (target shape index $p_0$) and decreases with self-propulsion speed $v_0$, with an optimal potential strength; self-alignment $J$ boosts the probability and increases the size and polarization of lumen-centered rosettes. The experimental neural-cell data match this picture: rosettes form where the average shape factor is above about 3.9, and single-cell tracks show motion aligned with cell elongation.

Load-bearing premise

The argument rests on the assumption that the localized pull (or barrier) and the oversized leader cell used in the simulations faithfully represent the real biological triggers of rosettes, such as apical actin tension, organoid curvature, or an atypically large cell; if natural rosettes are initiated by something else, the central causal claim loses its basis.

Editorial extensions

If this is right

  • Rosette formation is predictable from tissue-level parameters: deformability (target shape index), self-propulsion speed, persistence time, and alignment strength.
  • Regions with average shape factor above about 3.9 are the ones that form transient rosettes and can mature into lumen-centered rosettes; regions that stiffen over time do not.
  • Turning on self-alignment raises the probability of transient rosettes and increases first-layer and second-layer cell numbers by roughly 30 percent in lumen-centered rosettes.
  • A single oversized leader cell is sufficient to nucleate rosettes without any external potential, showing that a purely mechanical defect can play the role of curvature.
  • Introducing an external potential fluidizes the layer even for low shape index, shifting the rosette-forming region in parameter space.

Reading between the lines

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

  • Beyond the paper: the same curvature-defect logic should apply to other rosette-forming contexts, such as tumor spheroids and organoids, so measurements of shape factor and motility there should predict rosette frequency in the same way.
  • Beyond the paper: because the external potential is a stand-in for apical actin tension, a direct test is to perturb actomyosin contractility and check whether rosette probability moves along the predicted fluidity–deformability map.
  • Beyond the paper: rosette probability could be re-expressed as a function of topological-charge density in microscopy images, giving a quantitative imaging biomarker for tissues about to form rosettes.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper uses the Active Voronoi model to study the formation of multicellular rosettes in epithelial layers. The authors simulate three types of symmetry-breaking perturbations: a harmonic potential localized at a point, a Lennard-Jones potential imitating a lumen, and a leader cell with a different target area. They report that the probability of rosette formation depends on the cell target perimeter p0 and self-propulsion velocity v0, that self-alignment interactions enhance rosette stability and size, and that lumen-centered rosettes grow and polarize with increasing p0. To test the predictions, the authors perform time-lapse fluorescence microscopy on iPSC-derived neural rosettes, estimate v0 and tau from single-cell MSD curves, and find that rosettes appear in regions with measured Voronoi shape factor above 3.95. They conclude that rosettes are natural outcomes of geometric and mechanical responses to curvature.

Significance. The simulation study is systematic: parameter sweeps over p0, v0, J, and potential strengths are accompanied by stationary-state checks, and the use of a Voronoi model avoids hand-implemented topological transitions. The alignment-interaction effect is a plausible mechanism for stabilizing rosettes. However, the experimental validation has a variable-matching problem (realized shape factor vs. target p0), and the rosette propensity proxy is not directly linked to high-order vertices. These issues currently prevent the paper from supporting its stronger causal claims. If the authors can re-analyze the experimental comparison using realized shape factors from the simulations and validate the proxy, the conclusions would be substantially strengthened.

major comments (4)
  1. [Section II.A and Eq. (3); Figures 2-5] The rosette propensity P_r is defined as the frequency of cells with fewer than 5 edges, but the paper's own definition of a rosette is a vertex where five or more cells meet (Introduction). These are distinct observables: a cell's edge count is not the same as the degree of a Voronoi vertex. No validation is shown that P_r tracks the actual number of rosette vertices (e.g., by comparing P_r with direct vertex-degree counts in the same configurations). Because the central phase diagrams and the trade-off claim rely entirely on P_r, the quantitative results would be more convincing if the rosette frequency were measured directly or if the proxy were benchmarked against direct counts. As written, the proxy is an unverified assumption.
  2. [Section II.F and Methods E] The experimental validation compares the measured Voronoi shape factor S_t with the model's phase diagram parameter p0. However, p0 in Eq. (3) is the target perimeter (a model input), whereas S_t is the realized shape factor computed from the experimental Voronoi tessellation. The realized shape factor is not equal to p0 in the model: activity, the external potential, and the rosette itself change the actual cell shapes, and the authors themselves note that the external field fluidifies the layer even at low p0. Therefore the observation that rosette-forming regions have S_t > 3.95 does not place those cells in the high-P_r region of the (p0, v0) maps, and the claimed 'significant agreement' is not established. The authors should compute the realized shape factor from the simulations and compare it with the experimental S_t, or otherwise provide a mapping between S_t and p0.
  3. [Discussion, third paragraph] The statement 'our work proved that rosettes are natural outcomes of geometric and mechanical responses to curvature' overstates the evidence. In the simulations, symmetry breaking is inserted by hand via a harmonic potential, a Lennard-Jones potential, or a leader cell with a different target area; the experiments are correlative. The model demonstrates that such imposed defects can produce rosette-like structures, but it does not prove that biological rosettes originate from a localized curvature defect. I recommend softening the claim to 'consistent with' and explicitly stating the assumption that the external potentials represent biological symmetry-breaking cues.
  4. [Discussion, Euler characteristic/curvature argument] The Discussion argues that the harmonic potential 'inserts the simplest positive correction to the curvature' and changes the Euler characteristic to χ>0. However, the simulations are performed on a flat torus with periodic boundary conditions; Eq. (4) adds a potential energy, not a change in the surface metric. The argument that rosettes are stabilized by an excess of positive topological charge on a curved surface is an analogy, not a property of the simulated model. If the authors wish to support the curvature mechanism, they could simulate cells on an intrinsically curved surface (e.g., a sphere or a bump) and compare with the potential-field results.
minor comments (5)
  1. [Methods E] The text refers to the measured quantity as the 'average target shape factor'; this is a misnomer because the quantity is computed from actual cell geometries, whereas the target shape factor is the model parameter p0. Use 'measured shape factor' instead.
  2. [Section II.F, after Eq. (7)] The phrase 'i. e.,τ≫τ' should read 't≫τ'.
  3. [Section II.F] The sentence 'Thus, l̃p = f·l_p = 10l_c' is confusing; please clarify the notation (l_c vs. 10 l_c) and the scaling factor.
  4. [Figure 4] The text refers to 'Figure 4l' but the caption lists no panel l; the panel labels j-k appear out of order. Please renumber.
  5. [Section II.A] The phrase 'cells with less than 5 edges' is grammatically ambiguous; if the intended proxy is 'fewer than 5 edges,' state it explicitly, or correct to 'more than 5 edges' if that is what was meant.

Circularity Check

1 steps flagged · score 4.0 of 10

Rosette existence around the imposed defect is partly by construction, but the parameter-dependent phase diagrams and the MSD-calibrated experimental test give the paper independent content; score 4.

  1. self definitional [Section II.A-II.B (Eq. 4), Discussion paragraph on curvature; Abstract finding (i)]
    "To induce rosette formation, we modified the topological features of the system in different manners, obtaining transient, lumen-centered, and pinwheel rosettes depending on the adopted defect source ... Introducing the external harmonic field via Eq. 4, we inserted the simplest positive correction to the curvature. To accommodate such curvature, the system tends to introduce topological defects that locally reduce angular excess, forming rosette-like structures."

    The paper's first finding is that breaking spatial symmetry allows rosette formation, but the symmetry breaking is implemented as E_h = sum_i (1/2) k (r_i - r_c)^2, a radial attractive trap centered at r_c. A rosette is defined as five or more cells interfacing at a common center, and the trap supplies exactly that common center while pulling cells toward it. The paper even states it modified the system 'to induce rosette formation,' so the existence of rosettes near the defect is the expected mechanical response to the imposed potential rather than an emergent prediction from tissue parameters.

full rationale

The experimental parameters v0 and tau are fitted from single-cell mean-squared displacement data via Eq. 7, not from rosette occurrence, so the comparison to neural rosette formation is not statistically self-fulfilling. No load-bearing self-citation chain is present: citation [24] supplies the self-alignment term whose rosette-stabilizing effect is recomputed here, and [32] is an algorithmic reference for force computation. The principal circular element is the imposed symmetry-breaking defect: a harmonic potential centered at a point, or an oversized leader cell, is inserted specifically to induce rosettes, and the paper then presents 'curvature causes rosettes' as a finding. That step is partly by construction. The independent content lies in the nontrivial phase diagrams showing how rosette probability, size, and polarization depend on target shape factor, motility, persistence, and alignment, as well as in the experimental observation that rosette-forming regions maintain a high realized shape factor. Note that the experimental validation compares the realized Voronoi shape factor to the model's target perimeter p0, which is a correctness/validity concern rather than a circularity, and it does not warrant a higher circularity score.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The model pulls its mechanical equations and alignment dynamics from prior literature, and the symmetry-breaking defect is inserted by hand as a potential or a leader cell. The experimental calibration supplies v0 and tau from MSD fits, but the rosette probabilities themselves are not fitted to the data, which keeps the main prediction partially independent.

free parameters (8)
  • Target perimeter p0 (shape index) = 3.0 to 4.0 in sweeps
    Control parameter in Vertex energy Eq. 3 that sets preferred cell perimeter and controls solid-to-fluid behavior; varied by hand.
  • Self-propulsion velocity v0 = 0.2 to 1.5 in simulations; 0.4 +/- 0.1 um/s measured in iPSCs
    Active speed in Eq. 1; experimental value fitted from MSD via Eq. 7; simulation value rescaled to match persistence length.
  • Persistence time tau = 50 in simulations; 260 +/- 50 s measured in iPSCs
    Rotational relaxation time in the angular dynamics; experimental value fitted from the ballistic-to-diffusive crossover in MSD.
  • Harmonic potential strength k = 0.2 and 0.3
    Strength of the external symmetry-breaking field in Eq. 4; hand-chosen to create a curvature-like defect.
  • Alignment interaction strength J = 0 to 10
    Nematic alignment rate in Eq. 5; hand-chosen sweep to test stabilization of rosettes.
  • Lennard-Jones depth epsilon_0 = 0.5, 1.0, 3.0
    Attraction strength of the lumen-centered potential in Eq. 6; hand-chosen.
  • Lennard-Jones radius sigma_0 = 0.5, 1.0, 3.0
    Effective lumen size in Eq. 6; hand-chosen.
  • Leader cell target area A0^L = 0.05 to 9.99
    Target area of the leader cell in Figure 5; hand-chosen to create a topological defect without a potential term.
assumptions (5)
  • domain assumption The Vertex energy Eq. 3 with Kp = Ka = A0 = 1 and preferred perimeter p0 describes the mechanics of confluent tissue.
    Adopted from the self-propelled Voronoi model of Bi et al. [17]; this is the base mechanical model for all simulations.
  • standard math In flat space, hexagonal tilings and 3-fold vertices are energetically optimal, and positive curvature stabilizes higher-fold vertices.
    The Euler and Plateau arguments in the Discussion motivate why curvature should induce rosettes.
  • ad hoc to paper The external harmonic potential in Eq. 4 represents biological symmetry-breaking cues such as apical actin networks, diffusing chemoattractants, or organoid curvature.
    This is the key modeling assumption connecting the inserted potential to real biological rosette triggers; it enters in Results B and the Discussion.
  • ad hoc to paper The Lennard-Jones potential in Eq. 6 represents the net mechanical effect of a central lumen on surrounding cells.
    Introduced in Results D to model lumen-centered rosettes; the match to real lumens is assumed rather than derived.
  • domain assumption The self-alignment dynamics in Eq. 5, taken from Paoluzzi et al. [24], captures the experimental observation that cells move along their elongation axis.
    The experimental elongation analysis in Results F supports this assumption qualitatively; the specific form of the alignment torque is borrowed from prior work.

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Pith. "Pith review of Rosette formations as symmetry-breaking events: theory and experiment." pith.science (2026). https://pith.science/paper/EGQVYEHJ

@misc{pith2026250520543,
  author       = {Pith},
  title        = {Pith review of: Rosette formations as symmetry-breaking events: theory and experiment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EGQVYEHJ}},
  note         = {Machine review of arXiv:2505.20543}
}
read the original abstract

Multicellular rosettes are observed in different situations such as morphogenesis, wound healing, and cancer progression. While some molecular insights have been gained to explain the presence of these assemblies of five or more cells around a common center, what are the tunable, global features that favors/hinders their formation is still largely unknown. Here, we made use of a Voronoi dynamical model to investigate the ingredients driving the emergence of rosettes characterized by different degree of stability and organization. We found that (i) breaking the local spatial symmetry of the system, i.e., introducing curvature-inducing defects, allows for the formation of rosette-like structures (ii) whose probability of formation depends on the characteristic of the cellular layer. In particular, a trade-off between tissue fluidity and single cell deformability dictates the assembly of transient rosettes, that are strongly stabilized in the presence of cell alignment interactions. To test our model predictions, we performed fluorescence microscopy experiments on rosette-forming neural populations derived from induced pluripotent stem cells, finding significant agreement. Overall, our work may set the stage to gain an unifying understanding of the plethora of biophysical mechanisms involving the occurrence of rosette-like structure both in physiology and their altered formation in pathology.

Figures

Figures reproduced from arXiv: 2505.20543 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. b). D. Alignment increases the size of lumen-centered rosettes and influences their polarization Transient rosettes can mature in lumen-centered ones [1]. We modeled the net effect of the lumen on nearby cells using a Lennard-Jones potential irradiating from one of the Voronoi cell centers. In particular, we imposed that one of the N cells composing the popula￾tion has zero velocity, vanishingly small target area an… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.