Emergent cell migration from cell shape deformations and T1 transitions

Harish P. Jain; Luiza Angheluta; Richard D.J.G. Ho

REVIEW 2 major objections 4 minor 1 cited by

Emergent cell migration from cell shape deformations and T1 transitions

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Although the four-cell neighbor swaps called T1 transitions occur randomly in time for any one cell, the paper shows that their spatial distribution is biased by cell shape, and that this asymmetry gives cells a directional tendency that…

desk verdict A clean new statistical decomposition of successive T1 transitions undermined by a migration claim that no measured cell displacement supports. read the letter →

arxiv 2412.19686 v3 pith:KMIQI4JR submitted 2024-12-27 physics.bio-ph cond-mat.soft

Harish P. Jain , Richard D.J.G. Ho , Luiza Angheluta This is my paper · ORCID

classification physics.bio-phcond-mat.soft

keywords T1transitionsepithelialmonolayerscollectivecellmigrationmulti-phasefieldmodelactiveelasticsolidshapeindextissuefluidizationtopologicalrearrangements

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

T1 transitions, localized four-cell rearrangements that swap neighbors in an epithelial monolayer, look random in time but are spatially organized, and this paper argues that the spatial organization is set by cell shape. Using two complementary simulations, a multi-phase field model that resolves cell contours and an active elastic solid model of self-propelled cells connected by springs, the authors show that losing a neighbor relaxes a cell's shape while gaining a neighbor elongates it. They then track the vertices created and destroyed in successive T1s and find that their locations are non-uniformly distributed around the cell in four distinct loss/gain scenarios. The paper proposes that this geometric bias is what turns isolated topological rearrangements into directed cell migration and, ultimately, into coherent tissue-scale flows.

What carries the argument

The central object is the T1 transition, a four-cell topological rearrangement in which the junction between two cells shrinks away while two other cells form a new junction roughly perpendicular to the old one. The argument is carried by the cell shape index $p=\mathrm{Perimeter}/\sqrt{\mathrm{Area}}$, a measure of elongation, and by the relative orientation $\xi$ between vertices created in the first of two successive T1s and vertices destroyed in the second, measured around the cell's center of mass. Histograms of $\xi$ for the four successive-T1 scenarios are the load-bearing quantity: a non-uniform histogram means the next rearrangement tends to occur on a particular side of the cell, which is the microscopic mechanism proposed for directed migration. The waiting-time distributions and radial distribution functions support the temporal randomness and spatial correlation of the events.

What would settle it

Track the center of mass of each cell through a loser-gainer or gainer-loser pair of successive T1s in the multi-phase field model and average the displacement conditioned on the scenario: if the mean displacement is zero, or points opposite to the direction implied by the relative-orientation histograms, then the non-uniform spatial distribution does not by itself produce directed migration.

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Extended reading notes

Core claim

The paper's central claim is that T1 transitions, random in time for a single cell, are spatially correlated across the tissue and biased by cell shape. Cells that lose neighbors relax toward a rounder shape, while cells that gain neighbors elongate; the paper documents this dual effect with the shape index $p=\mathrm{Perimeter}/\sqrt{\mathrm{Area}}$. For each of the four ways a cell can participate in two successive T1s, losing twice, losing then gaining, gaining then losing, or gaining twice, the authors measure the relative orientation between vertices created by the first T1 and vertices annihilated by the second, and find non-uniform histograms. These non-uniform distributions are the evidence that successive T1s happen preferentially on one side of a cell, giving the cell a directional bias. The paper concludes that such biases chain together into coherent flow patterns at tissue scales.

Load-bearing premise

The load-bearing premise is that the non-uniform spatial distribution of successive T1s actually produces net cell displacement; the simulations measure the geometry of the T1 locations but do not directly measure cell migration or tissue flow.

Editorial extensions

If this is right

T1 events can be described as temporally random with an activity-dependent rate, while their spatial distribution is correlated over several cell diameters.
Neighbor loss relaxes a cell and neighbor gain stretches it, so the same rearrangement has opposite mechanical effects on the cells that shed a contact and those that form a new one.
Successive T1s do not occur uniformly around a cell; the distributions differ between lose-gain and gain-lose, so the order of topology changes matters for the cell's directional response.
The orientation bias persists when the model's activity vector no longer aligns with cell elongation, pointing to cell shape deformation, not polarity alignment, as the source of the spatial organization.
Chains of these biased rearrangements can organize into coherent, tissue-scale flows, linking single-cell topology changes to collective migration.

Reading between the lines

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

Editorial inference: the same relative-orientation histograms could be gathered from live monolayers by tracking tri-cellular vertices; positive results would make the geometric bias a directly observable tissue property rather than a simulation-only statistic.
Editorial inference: if shape deformation is the driver, then suppressing deformation, for example by raising junctional tension or lowering deformability in the model, should weaken the orientation bias and the associated flow coherence; this is a parameter sweep the paper does not report.
Editorial inference: because a gainer-gainer chain implies a neighboring loser-loser chain, the cell-level directional bias may be compensated at the level of neighbor pairs, possibly producing local shear rather than pure translation; quantifying that compensation would test how the coherent flow actually forms.

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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

What to know: the new thing here is the four-scenario decomposition of successive T1 transitions (loser-loser, loser-gainer, gainer-loser, gainer-gainer) and the histograms of relative orientation between created and annihilated vertices. That is a genuinely useful way to characterize the spatial structure of T1 sequences, and the simulations are competently done. The problem is the headline: the abstract says these asymmetric patterns 'promote directed cell migration, and form the backbone for coherent flow patterns,' but the paper never measures migration or flow.

Credit where due: the waiting-time distributions are clean exponentials with activity-dependent rate, and the shape-index evolution separating loser from gainer cells (Fig. 4a) is a nice, clear result. The robustness checks — α=0, varying Ca and v0 — are reassuring, and the AES model provides a consistency check for the Poissonian waiting times. The statistics in Figs. 5f-5i are computed directly from the simulation trajectories, not fitted, so the empirical content is solid.

Where it gets soft: the causal claim. There is no velocity autocorrelation, no mean-squared displacement of cell centers, no flow-field analysis anywhere in the paper. The non-uniform orientation histograms are interpreted in Section VI as suggesting 'an effective directed migration,' and the conclusions escalate that to 'allowing cells to move directionally... potentially forming flow structures.' The stress-test note has it right: the same self-propulsion activity that triggers T1s also moves the cell, so the spatial bias could be a consequence of existing directed motion rather than its cause. The paper's own hedged language doesn't bridge that. A couple of histograms could be correct and still produce no net migration if opposing biases cancel or the cell's own activity dominates its trajectory.

Minor issues: no code or data release, which will slow replication. And the AES model is used only for waiting times and g(r); all the shape-dependent analysis comes from MPF, so the 'two complementary models' framing oversells the AES contribution slightly. Neither of these changes my overall read.

Bottom line: the statistical core deserves a serious referee. The paper should go to review, but the migration/flow claim needs to be either directly measured (MSD, velocity autocorrelation, or tissue-scale flow field) or explicitly softened to a hypothesis. If the authors do that, this becomes a solid contribution to the T1-transition literature.

Who this is for: anyone working on cell rearrangements, shape feedback, and collective migration in epithelia. I'd bring it to a reading group, and I'd cite the four-scenario histograms if I needed a spatial characterization of successive T1s.

Referee Report

2 major / 4 minor

Summary. The paper studies the spatiotemporal statistics of T1 transitions in two complementary models of epithelial monolayers: a multi-phase field (MPF) model with deformable cells and an active elastic solid (AES) model with point-like cells. The authors report three main results: (i) successive T1 transitions involving a given cell follow an exponential waiting-time distribution, i.e., a Poisson process in time; (ii) T1 events are spatially correlated, as quantified by radial distribution functions of T1 epicenters; and (iii) cell shape responds asymmetrically to T1 events, with loser cells relaxing and gainer cells elongating. The central claim is that non-uniform spatial distributions of vertices created and annihilated in successive T1s (Figures 5f-5i) lead to directed cell migration and, through chaining of T1s, to coherent tissue-scale flow patterns. The paper presents these statistics from simulations but does not directly measure cell displacement or flow.

Significance. If the causal link between the observed T1 asymmetry and net cell migration is established, the paper would provide a concrete single-cell topological mechanism for collective migration in epithelia, connecting local junction remodelling to tissue-scale flow. The strengths are that the exponential waiting-time distributions, the radial distribution functions, and the shape-index statistics are computed directly from simulations, and the authors include robustness checks for the alpha = 0 case and for varying activity and deformability. The two-model approach (MPF and AES) strengthens the generality of the temporal Poisson statistics. However, the headline claim about directed migration and coherent flow currently rests on geometric orientation histograms rather than on measured cell displacements or flow fields, so the paper's significance is conditional on additional direct evidence.

major comments (2)

[Section VI, Figs. 5f-5i; Abstract and Conclusions] The central claim that asymmetric spatial patterns of successive T1 transitions 'promote directed cell migration, and form the backbone for coherent flow patterns at tissue scales' is not directly supported by the data shown. The paper never presents cell-center displacements, velocity autocorrelations, mean-squared displacements, or tissue-scale velocity fields. The non-uniform orientation histograms of vertices in Figures 5f-5i are geometric biases of where rearrangements occur, but they do not by themselves establish net cell motion. Moreover, in the MPF model, T1 transitions are triggered by the same self-propelled activity that moves cells (Eqs. A1, A4-A5), so the observed spatial bias could be a consequence of an already-directed motion selecting where T1s occur rather than the T1s generating the motion. A concrete test would be to compute the mean-squared displacement or velocity autocorrelation of cells conditioned on the four scenarios in Figure 5, or to measure the tissue-scale velocity field and its correlation with the T1 orientation histograms.
[Section VI, paragraph after Fig. 5k] The statement that 'these distributions remain similar even if activity and deformability are varied suggesting a universal emergent behaviour' is not supported by any displayed figure or quantitative comparison. The supplemental material shows only the alpha = 0 case (Supp. Fig. 2), not variations of v0 and Ca for the relative-orientation histograms. To make the universality claim, the authors should either include the histograms for varied v0 and Ca or provide a quantitative similarity measure (e.g., histogram overlap or a distance metric).

minor comments (4)

[Section VI] In the paragraph discussing Figure 5, the text refers to 'Figure 5g' for both the loser-gainer and the gainer-loser scenarios; the second reference should likely be Figure 5h.
[Introduction] The word 'emply' should be 'employ' in the sentence 'we emply two complementary modeling approaches'.
[Appendix B] The neighbor criterion is described once as 'cells i and j are considered neighbours if and only if they are closest in distance to their midpoint than any other third cell' and then given explicitly in equations; the verbal phrasing is ambiguous and should be reworded to match the exact mathematical condition.
[Section III, Fig. 2] The claim that waiting times are 'exponentially distributed' is made by eye; providing the mean rates and, if possible, a goodness-of-fit or a log-linear plot would strengthen the statistical statement.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found; the migration/flow claim is an under-supported inference from directly measured T1 statistics, not a fitted or self-defined prediction.

full rationale

The paper is a simulation study with no fitted parameter that is subsequently relabeled as a prediction. The central observables—waiting-time distributions (Fig. 2), radial distribution functions (Fig. 3), shape-index responses (Fig. 4), and relative-orientation histograms of successive T1 vertices (Figs. 5f-i)—are measured directly from the MPF and AES dynamics, and none of them is defined in terms of the migration or flow claim. The sentence "the non-uniform distributions in Figures 5f-5i suggest an effective directed migration of the cells" is an interpretive causal inference, explicitly hedged by "suggest" and "could lead to emergent flow patterns at larger scales." The absence of a direct cell-displacement or flow-field measurement makes the claim under-supported, but under-support is a correctness or validation gap, not a circular reduction: the histogram inputs do not by construction equal the migration output, and no equation in the paper identifies the two. Citations to the authors' prior work ([8], [9], [17], [23], [25]) provide model provenance, the quadrupolar-flow mechanism from T1s, and a reference value for polar order; these are background physics used to interpret the new statistics, not definitions that force the reported result. The paper also acknowledges in the Conclusions that longer chains of successive T1 events are needed to understand emergent fluidization patterns, indicating that the tissue-scale extrapolation is open rather than predetermined. Therefore no specific circular step can be exhibited.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The results rest on two simulation models with hand-chosen parameters, a geometric T1 detection rule from the authors' prior work, and an interpretive leap from vertex-orientation statistics to migration. The models are described fully, so no hidden fitted constants are needed for the statistical observations, but the causal claims add assumptions beyond the simulations.

free parameters (4)

v0 (cell self-propulsion speed) = 0.5 (MPF default; varied in Figs. 2-3)
Controls activity that drives T1 transitions; the paper shows waiting-time and correlation dependence on v0, so the conclusions are parameter-dependent.
Ca (capillarity number / deformability) = 0.2 (default; varied in Supplemental Fig. 1)
Controls cell deformability; the paper states lower Ca reduces T1 frequency and increases duration, affecting shape-index statistics.
alpha (activity-shape alignment rate) = 0.1 (default); 0 in Supplemental Fig. 2
Couples polarity to cell elongation; the paper checks alpha=0 to show the spatial asymmetry is not caused by this alignment, so it is a hand-chosen parameter that could affect interpretation.
Dr (rotational diffusion) = 0.01 (MPF); 0.025/0.15 (AES)
Sets stochastic reorientation of polarity; part of the activity model and influences T1 statistics.

assumptions (4)

domain assumption The MPF free energy functional (Eqs. A2-A3) is a valid representation of epithelial monolayer mechanics, including cortical tension, repulsion, and adhesion.
Invoked throughout the MPF simulations (Appendix A); the entire shape-response analysis rests on this energetics.
domain assumption The AES model with the geometric neighbour rule (r_ij^2 > r_ik^2 + r_jk^2) captures the same T1 physics as the MPF model.
Used in Section II and Appendix B; the universality claim (Poissonian timing in both models) hinges on this equivalence, with the neighbour rule taken from Ref [25] by the same group.
domain assumption Exponential waiting-time distributions are sufficient evidence for a Poisson process.
Section III concludes Poissonian T1 timing from exponential tw distributions alone, without testing independence of successive intervals.
ad hoc to paper The non-uniform vertex-orientation histograms (Figures 5f-5i) are causally related to directed cell migration.
Section VI infers migration from the histograms without measuring cell displacement or flow; this interpretive leap is specific to this paper's argument.

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Cite this review

Pith. "Pith review of Emergent cell migration from cell shape deformations and T1 transitions." pith.science (2026). https://pith.science/paper/KMIQI4JR

@misc{pith2026241219686,
  author       = {Pith},
  title        = {Pith review of: Emergent cell migration from cell shape deformations and T1 transitions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KMIQI4JR}},
  note         = {Machine review of arXiv:2412.19686}
}

read the original abstract

T1 transitions, which are localised cell rearrangements, play an important role in the fluidization of epithelial monolayers. Using a multi-phase field model and an active elastic solid model, we show that although each cell undergoes T1 transitions in time as uncorrelated, random events, the spatial distribution of these events is highly correlated and is dependent on cell shape. T1 transitions have a dual effect. Cells losing neighbours tend to relax their shape, while those gaining neighbours tend to elongate. By analysing the statistics of successive T1 transitions undergone by a deformable cell, we find asymmetric spatial distributions related to how cells lose or gain neighbours. These asymmetric spatial patterns of T1 transitions promote directed cell migration, and form the backbone for coherent flow patterns at tissue scales.

Figures

Figures reproduced from arXiv: 2412.19686 by the authors.

**Figure 2.** a and Figure 2b show the distributions of waiting times tw for varying activity (v0) in the MPF and AES models, respectively. In both cases, the waiting time is exponentially distributed. The average waiting time decreases with increasing activity as cells that move faster are likely to undergo their next T1 sooner. The mean waiting time does not vary significantly with varying deformability Ca (see [PITH_FULL_IM… view at source ↗

**Figure 3.** FIG. 3. Radial distribution function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. For the MPF model: (a) Evolution of mean shape index of cells undergoing a T1 transition. Negative time and positive [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. For the MPF model: (a-d) Four different patterns by which highlighted cell [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 1.** Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p012_1.png]

**Figure 2.** Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p012_2.png]

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Forward citations

Cited by 1 Pith paper

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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Ladoux and R

B. Ladoux and R. M. M` ege, Mechanobiology of collective cell behaviours, Nature Reviews Molecular Cell Biology 18, 743 (2017)

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A. Brugu´ es, E. Anon, V. Conte, J. H. Veldhuis, M. Gupta, J. Colombelli, J. J. Mu˜ noz, G. W. Brod- land, B. Ladoux, and X. Trepat, Forces driving epithelial wound healing, Nature Physics 10, 683 (2014)

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