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REVIEW 3 major objections 3 minor 73 references

Correlated cell movements drive epithelial finger formation

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Correlated active cell motion alone, without leader cells or signalling, is sufficient to produce the finger-like protrusions at the front of spreading epithelial sheets.

desk verdict Strong sufficiency result: fingers emerge from correlated cell noise plus a soft contractile edge, but the continuum theory's 25x stiffness rescaling and the abstract's causal claims need fixing. read the letter →

arxiv 2508.01046 v1 pith:ILHRKZUH submitted 2025-08-01 cond-mat.soft physics.bio-ph

Sander C. Kammeraat , Yann-Edwin Keta , Paul Appleton , Ian P. Newton , Tanniemola B. Liverpool , Rastko Sknepnek , Inke Näthke , Silke Henkes This is my paper · ORCID
classification cond-mat.softphysics.bio-ph
keywords epithelialmonolayersfingerformationcollectivecellmigrationactivemattercorrelatedvelocityfluctuationsvertexmodelactomyosincablewoundhealing
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

This paper tries to establish a minimal physical explanation for finger-like protrusions at the advancing edge of healing epithelial sheets. It claims that uncorrelated crawling of individual cells, once filtered through elastic and viscous interactions between cells, produces a correlated velocity field in the monolayer interior, and that this field alone drives the contractile actomyosin cable at the edge into long-lived fingers. The authors support the claim by showing that an agent-based model and a continuum theory, with parameters calibrated to measured interior velocity correlations, quantitatively reproduce the tangent-tangent, roughness, and Fourier-spectrum statistics of experimental boundaries. If correct, the result would move finger formation out of the category of specialised biological control and into the generic physics of dense active matter, with leader cells and signalling as modulators rather than triggers.

What carries the argument

The load-bearing object is the advancing edge as a stretched, contractile semiflexible polymer, an effective worm-like chain driven by a correlated active noise field that represents interior cell motion. In the continuum description this becomes a linear height equation for the boundary height $h(x,t)$, whose relaxation is controlled by line tension $\lambda$, bending stiffness $\kappa$, and an internal pair-dissipation coefficient $\eta_h$, and whose driving is the velocity field of a viscoelastic model of the monolayer interior. The analysis shows that the dominant finger length scale is the shear length scale of the interior velocity correlations, $\xi_{\perp,p}=\sqrt{(\mu\tau+\eta)/\zeta_c}$, and that finger lifetimes are set by the slow $q^{-2}$ relaxation of the height modes at that scale. Alongside it, the active vertex model supplies the agent-based testbed: cells crawl as active Brownian particles with persistence time $\tau$, interactions include substrate friction and pair friction, and the boundary is implemented as coupled linear and angular springs that can grow and shrink.

What would settle it

Measure whether the advancing edge is actually passive: if inhibiting actomyosin contractility at the leading edge abolishes fingers while the interior velocity correlations (length scale of about 100 micrometres, persistence of about 1 hour) remain unchanged, the passive-cable picture fails; if fingers persist, the claim that interior correlations alone drive them survives.

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Extended reading notes

Core claim

On its own terms, the paper's central claim is: correlated active cell motion alone suffices to produce fingers; leader cells, signalling, and proliferation modulate, but do not trigger, this pattern. The authors present fingers as long-lived active fluctuations of the boundary rather than the product of a finite-wavelength instability. They demonstrate this by combining in vitro imaging of spreading epithelial monolayers with simulations of an active vertex model whose edge is a contractile semiflexible polymer, and with a linear viscoelastic height-equation theory for the edge driven by correlated noise from the interior. The quantitative match between theory, simulation, and experiment on tangent-tangent correlations, roughness correlations, height spectra, and long finger lifetimes is presented as evidence that no feedback instability is needed.

Load-bearing premise

The load-bearing premise is that the actomyosin cable at the edge can be treated as a passive, very soft elastic string whose line tension and bending stiffness are about 25 times smaller than the values obtained by directly mapping the boundary springs of the simulation.

Editorial extensions

If this is right

  • Leader cells appear at the tips of fingers as a response to the local mechanical environment of a forming protrusion, so they should amplify rather than initiate the pattern.
  • Proliferation and cell flattening contribute to the average border speed but leave the finger statistics unchanged, so division is not the trigger.
  • Finger length and lifetime are predicted to be set by the interior correlation length and cable parameters: changing cell-cell adhesion, friction, crawling speed, or cable line tension should shift both interior and boundary scales in a predictable way.
  • The absence of a peak in the boundary height spectrum over time implies that no finite-wavelength instability is at work; the low-$q$ fluctuations saturate to a steady state.
  • Initial roughness of the border explains the early-time differences between experiment and simulation, and the nonlinear short-scale behaviour shifts the roughness exponent from about 2 to 1.

Reading between the lines

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

  • Inference: the same null model could be tested in other epithelial systems whose interior correlation lengths differ; the theory predicts their finger length scales should track the interior shear length scale rather than any cell-autonomous fingerprint.
  • Inference: if the edge is passive, then transiently suppressing the actomyosin cable should make fingers wider and shorter-lived, while suppressing interior correlations, for example by raising density toward a jammed state, should suppress fingers even with a normal cable; both experiments are directly doable.
  • Inference: because the height correlator contains a leading $1/q^2$ term that dominates at long times and large system sizes, very long experiments should show slowly coarsening roughness even though tangent-tangent correlations saturate; this coarsening is an untested corollary.
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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

3 major / 3 minor

Summary. The paper combines MDCK wound-healing experiments, self-propelled Voronoi/active vertex model (AVM) simulations, and a continuum viscoelastic theory with a boundary height equation and active polymer model to argue that fingers at the edge of expanding epithelial monolayers arise as long-lived active fluctuations driven by correlated interior cell motion, without requiring a finite-wavelength instability or leader-cell feedback. The interior velocity statistics are matched by the AVM and by an active viscoelastic continuum model, while the boundary is modelled as a semiflexible polymer driven by interior noise; the height equation reproduces tangent-tangent, roughness, and temporal correlation functions. The paper concludes that leader cells, signalling, and proliferation modulate but do not trigger finger formation.

Significance. If the mechanism is correct, the paper is significant: it provides a quantitative null model for epithelial fingering, connects finger length and time scales to bulk active-matter correlation lengths, and makes falsifiable predictions about how perturbations to adhesion, friction, crawling speed, and cable properties affect fingers. Strengths include the direct experimental measurement of velocity and boundary correlations, the explicit AVM with a dynamic boundary, the detailed analytical derivations in the SI, and the clear statement of the model as a fluctuation-driven null model. The claim that fingers do not require an instability is supported by the absence of peaks in the Fourier spectra and by the AVM's spontaneous finger formation without division or leader cells. However, the quantitative predictive power of the continuum theory is weakened by an unexplained rescaling of the boundary stiffness, and the dominant-length-scale prediction is partly built into the model construction.

major comments (3)
  1. [SI Appendix II.D and main text Eq. (8)] The continuum theory and the 2D polymer model are not actually obtained from the AVM boundary parameters by dimensional mapping: SI Appendix II.D states that the estimated line tension and bending stiffness on the boundary of the AVM should be taken roughly a factor of 25 smaller to match theory, and the main text admits that a very small value of the spring constant ks had to be fitted. Because finger width, roughness, and lifetime in the height equation depend directly on lambda and kappa, the quantitative agreement shown in Fig. 4c, f, and i is partly a consequence of this tuning rather than an independent validation. As written, the abstract's claim that the model 'quantitatively predicts' the edge statistics is overstated; the authors should either derive the reduction factor from the boundary point addition/removal relaxation process or explicitly treat lambda and kappa as fitted parameters and state how many free parameters the comparison uses.
  2. [SI Appendix II.D] The noise-generating chain modulus for the 2D polymer is set to mu_h/zeta_h = 600 um^2/h 'by hand from fitting the real space spatial correlation of the 2d polymer noise generating chain velocity to the real space velocity correlations of the AVM'. This is an additional free parameter that is not listed in Table I and is calibrated against the same AVM velocity field that was already matched to experiments. This further weakens the claim that the polymer and height-equation simulations are parameter-free descendants of the AVM; mu_h should be listed with its uncertainty, and the sensitivity of the boundary correlation functions to its value should be reported.
  3. [Main text, Eq. (S86) and Discussion] The statement that finger length scales are dominated by the interior shear correlation length q1 = sqrt(zeta/(mu*tau + eta)) is close to a restatement of the model construction: the boundary noise vf in Eq. (S41) is derived from the same viscoelastic interior field with the same mu, eta, zeta, and tau, so the edge inheriting that scale is a consistency check rather than an independent prediction. A stronger, falsifiable test would be a perturbation experiment or simulation, for example varying KP, zeta_pair, or v0 and showing that the finger length and lifetime scales track the predicted q1; the Discussion proposes such dependencies but does not report them. The authors should either perform such a perturbation test or clearly label the dominant-scale result as a self-consistency statement.
minor comments (3)
  1. [Table I] The fitted interval for ks/zeta is reported as 78 +/- 50 h^-1, which is a very large range; the authors should show the sensitivity of the tangent-tangent correlation to ks within this range, for example as a supplemental figure, so that the constraint is visually verifiable.
  2. [Main text, Fig. 2 caption and text near Eq. (3)] The phrase 'again computed using dimensional scaling only' is misleading because the AVM parameters themselves were fitted to the experimental velocity statistics; the continuum theory is parameterized by mapping those fitted AVM parameters, so it is not an independent calculation.
  3. [SI Appendix II.D, Fig. S10] The text states that bond lengths can be approximated by a constant a(t) about a(0) = 5 um, but Fig. S10 shows a(t) growing from about 5 um to about 10 um over 15 h; the approximation should be justified more carefully or its effect on the mapping estimated.

Circularity Check

3 steps flagged · score 6.0 of 10

Quantitative finger-statistics 'predictions' are partly fitted (AVM ks from tangent-tangent; height-equation lambda/kappa rescaled 25x) and the dominant finger scale q1 is built into the 1D noise ansatz.

  1. fitted input called prediction [Results - finger formation (first paragraph) and Table I]
    "We now compare simulated and measured advancing edges quantitatively by defining three boundary correlation functions, which allow us to constrain the remaining parameters of the A VM, the boundary spring constant ks and refine the crawling speed v0. ... After matching the edge stretching stiffness ks and refining v0 (constrained by vrms) to match the amplitude of the temporal decay, it reaches the same steady state value, although not as quickly as in the experiments (Fig. 4b)."

    Table I states that ks is constrained by the 'shape of tangent-tangent correlation'. The AVM tangent-tangent curve in Fig. 4b is therefore the calibration target, not an independent prediction. The abstract's claim that the model 'quantitatively predicts tangent-tangent ... correlation functions' overstates this: for the AVM the match is obtained by fitting ks to that very observable. The qualitative emergence of fingers is independent, but this specific quantitative agreement is forced by construction.

  2. fitted input called prediction [SI Appendix II.D; main text 'Polymer and height equation theory for finger formation']
    "However, we found that the estimated line tension and bending stiffness on the boundary of the A VM should be taken roughly a factor of 25 smaller, to match with theory, likely stemming from the relaxation effects when new points are added to the A VM boundary, see [42] for details. ... Note, however, that we had to fit a very small value of spring constant ks, likely reflecting the effectively viscoelastic relaxation mechanism of the cable in both experiment and A VM (SI Appendix, section II.D)."

    The height equation (Eq. 8) and 2D polymer model (Eq. 7) are presented as derived from the AVM boundary springs by dimensional mapping (SI II.D, Eq. S51: ks/(zeta a^2) = lambda/zeta_h, kb/(zeta a^4) = kappa/zeta_h). The derivation then rescales both lambda and kappa by an undocumented factor of 25 'to match with theory'. Since tangent-tangent, roughness and spectrum predictions all depend on lambda and kappa, the quantitative agreement in Figs. 4c,f,i is obtained by tuning these effective parameters rather than by a parameter-free first-principles mapping; the factor is justified only by a stated but unquantified 'relaxation effects' mechanism.

1 more flagged steps
  1. self definitional [SI Appendix II.C (Eq. S41); main text analysis after Eq. (8)]
    "Therefore, we cannot directly use the fluctuations of the 2d bulk velocity field to inform 1d boundary fluctuations. Therefore, as a matter of simplicity, we will consider that the driving fluctuating velocity field vf is generated by the following chain model ... The largest and dominant of these length scales is for q1 = ..., the same as the shear length scale of the interior velocity correlations."

    The 1D noise chain (Eq. S41) is not derived from the 2D interior theory but posited as the same viscoelastic equation in 1D, carrying the same mu, eta, tau, zeta. Its correlation length xi_perp,p = sqrt((mu tau + eta)/zeta) (Eq. S20) is thus input by ansatz. The subsequent statement that the dominant finger length scale q1 equals 1/xi_perp,p and that finger length scales are 'directly set by the spatiotemporal correlations of the interior' is a restatement of this construction, not an independent prediction. The paper is transparent about the 'matter of simplicity' choice, but the central quantitative scale-selection claim reduces to that input.

full rationale

The paper contains an independent, non-circular core: the AVM is calibrated to bulk velocity correlations (tau, v0, zeta_pair, KP), and fingers emerge spontaneously in that model; the boundary observables are then compared, with ks fitted to the tangent-tangent shape, and roughness/spectrum following. This supports a qualitative sufficiency claim. However, several quantitative 'predictions' in the chain reduce to fitted inputs. (1) The AVM tangent-tangent match is the calibration target for ks (Table I), so the abstract's 'quantitatively predicts tangent-tangent' is an overstatement for the AVM. (2) The height-equation/polymer theory is advertised as dimensionally mapped from AVM boundary springs, but SI II.D rescales lambda and kappa by an unexplained factor of 25 'to match with theory'; the main text admits 'we had to fit a very small value of spring constant ks'. Finger width, roughness, and lifetime scale with lambda and kappa, so the agreement in Figs. 4c,f,i is partly a fit. (3) The dominant finger length scale q1 is built into the model: the 1D noise chain driving the edge is chosen 'as a matter of simplicity' to be the 1D version of the same viscoelastic interior equation, so q1 = sqrt(zeta/(mu tau + eta)) equals the interior shear correlation length by construction; the paper's claim that finger scales are 'directly set by' interior correlations is therefore a model input, not an independent derivation. Self-citation of Ref. [36] is not load-bearing here because the model is re-validated against new experimental velocity-correlation data in this paper. Overall: partial circularity, with the central sufficiency claim retaining independent AVM support, so score 6 rather than 8-10.

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

The central claim rests on a set of fitted parameters and modeling assumptions. The free parameters are calibrated against the experimental interior and boundary statistics, and the boundary line tension is additionally reduced by hand. No new physical entities are introduced; the noise-generating chain is an auxiliary stochastic model for the boundary driving, not a new particle, force, or conserved quantity.

free parameters (8)
  • crawling persistence time tau = 1.0 +/- 0.5 h
    Fitted to the initial decay of the experimental temporal velocity autocorrelation (Table I).
  • crawling speed v0 = 255 +/- 20 µm/h
    Fitted to the experimental root mean square cell velocity (Table I).
  • relative pair friction zeta_pair/zeta = 2.0 +/- 0.5
    Fitted to the initial decay of the spatial velocity correlation (Table I).
  • perimeter modulus KP/zeta = 14 +/- 2 h^-1
    Fitted to the decay length of the spatial velocity correlation (Table I).
  • edge stretching stiffness ks/zeta = 78 +/- 50 h^-1
    Fitted to the shape and steady-state value of the tangent-tangent correlation (Table I); the main text states this is a very small fitted value.
  • effective line tension lambda in height equation = roughly 25x smaller than AVM-mapped value
    Ad hoc reduction needed to make the height-equation theory match the AVM and experiments; SI Appendix II.D.
  • noise-generating chain modulus mu_h/zeta_h = 600 µm^2/h
    Set by hand from fitting the 2D polymer noise-generating chain velocity correlations to the AVM (SI Appendix II.D).
  • target shape index p0 = 3.72
    Chosen to ensure a solid ground state, not fitted to experimental finger data (Table I).
assumptions (6)
  • domain assumption The monolayer interior is a linear, isotropic active viscoelastic solid with bulk and shear elasticity B, mu and bulk and shear viscosities K, eta (Eq. 2).
    Used in the continuum derivation of velocity correlations; assumes small deformations around a homogeneous state.
  • domain assumption Active crawling is spatially uncorrelated on the cell scale and temporally persistent with timescale tau (ABP noise); there is no explicit cell-cell alignment or feedback in the driving.
    This is the core null-model assumption; it enters Eq. (1b) and the active drive in Eq. (2) and is validated only indirectly through the matches to experiments.
  • domain assumption The advancing edge is a passive semiflexible polymer under line tension, with overdamped dynamics and pair dissipation (Eqs. 7 and 8).
    Models the actomyosin cable; the effective line tension must be reduced by a factor of about 25 relative to the AVM mapping to match experiments (SI II.D).
  • domain assumption Boundary fluctuations are small enough that the height function is single-valued and the small-fluctuation expansion of the worm-like chain applies (SI II.B).
    The height equation neglects overhangs, although the experiments and AVM show occasional overhangs; this limits the high-wavenumber predictions.
  • domain assumption The boundary is driven passively by the interior velocity field and does not feed back onto the interior dynamics.
    This is the no-feedback null-model assumption; the paper argues it captures the data, but positive feedback such as leader-cell forces is not included.
  • domain assumption The velocity correlation functions have reached steady state before barrier removal (SI III.B).
    Used to simplify the transient height spectrum and roughness integrals.

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Cite this review

Pith. "Pith review of Correlated cell movements drive epithelial finger formation." pith.science (2026). https://pith.science/paper/ILHRKZUH

@misc{pith2026250801046,
  author       = {Pith},
  title        = {Pith review of: Correlated cell movements drive epithelial finger formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ILHRKZUH}},
  note         = {Machine review of arXiv:2508.01046}
}
read the original abstract

Epithelia form protective barriers in multicellular organisms. To maintain homeostasis, they must be able to regenerate and heal damaged areas. This occurs through collective cell migration, during which finger-like protrusions commonly appear. Whether these protrusions are driven by specialised leader cells, biochemical cues, or generic physical interactions remains unclear. Integrating in vitro imaging, agent-based simulations, and continuum modelling, we show that correlated active cell motion alone suffices to produce fingers. Leader cells, signalling, and proliferation modulate, but do not trigger, this pattern. Our results show that the key mechanism underlying a complex biological process can be understood using a general framework of the physics of dense active matter.

Figures

Figures reproduced from arXiv: 2508.01046 by the authors.

Figure 1
Figure 1. FIG. 1. Experiments and model. ( [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Correlations of the velocity field in the cell sheet for the experiments (black dots), the AVM simulations (green [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Example boundary contours at different times of ( [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Spatial properties of the fingers as a function of time. The left column corresponds to experiments, the middle column [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Temporal properties of the boundary. The shading indicates the standard error of the mean. ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

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    and add pair dissipation. The equation of motion for the displacement field u within the cell sheet reads ζ ˙u(r, t) = ζv 0 ˆn(r, t) + ∇ ·← →σ , (S1) 20 where ζ is a friction coefficient, which we write without the c subscript of the main text for ease of notation, ζv 0 ˆn is ...

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Reviewed August 6, 2026 · model on record in the stance chip above.