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Collective migration and topological phase transitions in confluent epithelia

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Pith's one-line read Active stress turns the onset of collective migration into a defect-driven melting transition.

desk verdict A promising KTHNY-based theory of activity-driven epithelial melting, but the central exponent-spectrum claim is undercut by an internal numerical mismatch and needs revision before it can be taken as quantitative. read the letter →

arxiv 2502.09554 v1 pith:UAI24YYK submitted 2025-02-13 cond-mat.soft cond-mat.stat-mechphysics.bio-ph

Leonardo Puggioni , Dimitrios Krommydas , Luca Giomi This is my paper · ORCID
classification cond-mat.softcond-mat.stat-mechphysics.bio-ph MSC 82B2682B2782B28
keywords KTHNYmeltingconfluentepitheliacollectivecellmigrationT1andT2rearrangementshexaticorderdislocationcoreenergyactivematterrenormalizationgroup
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 the onset of collective migration in a confluent epithelium is an activity-driven version of the two-dimensional Kosterlitz–Thouless–Halperin–Nelson–Young (KTHNY) melting scenario. In this picture active stresses produced by T1 cell intercalation reduce the effective energetic cost of creating 5–7 dislocations, so the dislocation fugacity becomes $y=\exp[-(\epsilon_c+\sigma)a^2/(k_B T)]$. The result is an exponentially divergent correlation length across the solid–hexatic boundary, with an exponent $\bar\nu$ that is not universal but lies in a material-dependent range bounded by $1/2$ and $1$ (and whose lower limit depends on the ratio of T1 to T2 processes). This matters because it converts a qualitative question—when does an epithelium start to migrate?—into a quantitative scaling law that could be compared directly with experiments, and it predicts that tissues with different rates of cell division and extrusion should exhibit measurably different critical behavior.

What carries the argument

The central object is the dislocation gas Hamiltonian $H_D=-\frac{Y}{8\pi k_B T}\sum_{i\neq j} G(\mathbf{r}_i-\mathbf{r}_j):(\mathbf{b}_i\otimes\mathbf{b}_j)+\frac{\epsilon_c+\sigma}{k_B T}\sum_i|\mathbf{b}_i|^2$, where $G$ is the elastic Green function and the active stress $\sigma=2\eta\dot\epsilon$ is derived from the viscous stress of the convergent-extension flow around a T1 event. The constants $c_1$, $c_2$, and $c_3$ encode the statistical weight of one-, two-, and three-dislocation unbinding modes: $c_1$ is always finite, while $c_2$ is tied to T1 processes and $c_3$ to T2 processes, and in closed epithelia $c_3=0$. The renormalization-group flow for the softness $x$ and fugacity $y$, $dx/dl=c_2 y^2$ and $dy/dl=c_1 x y+c_3 y^2$, determines the divergence law for $\xi_+$ and yields the exponent range in Eq. (5).

What would settle it

Measure the density of unbound 5–7 dislocations and the positional correlation length while independently varying the self-propulsion speed and the rate of cell intrusion/extrusion, and check whether the fitted exponent falls in the predicted range and whether the divergence is exponential across the solid–hexatic boundary. More directly, test the equilibrium assumption by measuring the fluctuation–dissipation ratio near criticality: if the effective temperature extracted from that ratio does not match the value used in the Boltzmann fugacity, the equilibrium mapping fails.

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Extended reading notes

Core claim

The paper shows that the onset of collective cell migration in cell-resolved models of epithelial layers takes place via an activity-driven melting transition. Active forces, sourced by the convergent-extension flow of intercalating cells, shift the core energy of 5–7 dislocation pairs from $\epsilon_c$ to $\epsilon_c+\sigma$, so the dislocation fugacity is $y=\exp[-(\epsilon_c+\sigma)a^2/(k_B T)]$. Confluency reduces the degeneracy of dislocation-unbinding modes relative to point-particle crystals: in closed monolayers only T1 processes operate, giving $c_3=0$ and a Kosterlitz–Thouless-type flow, while open monolayers that permit T2 processes recover a finite $c_3$. The correlation length across the solid–hexatic boundary diverges as $\log(\xi_+/a)\sim|\sigma-\sigma_c|^{-\bar\nu}$, with $\bar\nu$ between $\frac{1}{2}\left(1-\frac{c_3}{\sqrt{c_3^2+4c_1c_2}}\right)$ and $1$. In numerical simulations of a multiphase-field model, closed systems give $\bar\nu=1.0\pm0.1$ and open systems give $\bar\nu=0.18\pm0.06$. When T1 processes are suppressed, the transition is replaced by a solid-to-solid transition with power-law divergence $\xi\sim|\sigma-\sigma_c|^{-\nu}$, with $\nu=c_1|x_0|$.

Load-bearing premise

The whole calculation rests on the premise that near the melting point the active, self-propelled cell layer behaves like a thermal equilibrium system, so that the standard equilibrium statistical mechanics of defects applies.

Editorial extensions

If this is right

  • Increasing cell speed drives a two-step melting sequence from crystalline solid to hexatic liquid crystal to isotropic liquid, mediated first by unbinding of neutral 5–7 dislocation pairs and then by their splitting into isolated 5- and 7-fold disclinations.
  • In closed epithelial layers, where only T1 processes are available, the correlation-length exponent sits at the upper bound of the predicted range, $\bar\nu$ near 1, whereas open layers with T2 processes sit near the lower bound, $\bar\nu$ near 0.18, making the critical behavior tunable by controlling cell division and extrusion.
  • If T1 processes are suppressed while T2 processes remain, the transition is no longer of KTHNY type; instead the correlation length diverges as a power law, $\xi\sim|\sigma-\sigma_c|^{-\nu}$ with $\nu=c_1|x_0|$, a transition between two solid phases driven by persistent intrusion and extrusion events.
  • Extensile active stress can produce a negative effective core energy, rendering the crystalline solid unstable to cell intercalation, which is consistent with experimental observations on migrating MDCK monolayers.
  • The exponential divergence $\log(\xi_+/a)\sim|\sigma-\sigma_c|^{-\bar\nu}$ provides a sharp, quantitative signature of the solid–hexatic boundary that can be sought in in vitro experiments.

Reading between the lines

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

  • The exponent $\bar\nu$ measured in experiments could serve as a diagnostic for whether a tissue behaves as a closed monolayer (T1 only), an open monolayer (T1 plus T2), or an intermediate regime, offering a direct link between tissue turnover rates and critical behavior.
  • A decisive test of the equilibrium-like assumption would be to compare the temperature-like parameter extracted from the variance of cell displacements with the value inferred from fitting the dislocation fugacity: if the two disagree, the Boltzmann mapping used here does not hold even near criticality.
  • The predicted solid-to-solid transition when T1 is suppressed suggests that modulating cell intercalation—for instance via drugs that alter junctional tension—could switch a tissue between exponential and power-law correlation-length scaling, a testable pharmacological prediction.
  • Because the multiphase-field model allows T2 rates to be controlled externally, the same simulation framework could be used to map the full $\bar\nu$ versus T2-rate curve predicted by the RG analysis, providing a continuum check between the closed and open limits.
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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 / 6 minor

Summary. The manuscript proposes that the onset of collective migration in confluent epithelia is an activity-driven KTHNY-type melting transition. It argues that active stresses renormalize the dislocation core energy (Eq. 2), that confluency restricts the available dislocation-unbinding modes (leading to c3=0 for closed layers), and that open layers with both T1 and T2 processes yield a material-dependent exponent ν̄ in the range of Eq. (5). The RG analysis is paired with multiphase-field simulations of 1085 cells in closed and open systems, which show a solid-hexatic-liquid phase sequence and an exponentially divergent correlation length across the solid/hexatic boundary. The fitted exponents are ν̄=1.0±0.1 (closed) and ν̄=0.18±0.06 (open). A limiting case with only T2 processes (c2=0) is predicted to show power-law divergence of the correlation length.

Significance. If the quantitative claims held, the paper would establish a concrete and testable connection between topological rearrangements in epithelia and defect-mediated melting, and it would identify T1/T2 availability as a tuning parameter for critical behavior. The numerical evidence for the two-step melting sequence is credible: the authors use three independent realizations, long averaging, and multiple diagnostics (structure factor, orientational correlations, MSD, defect densities), and the analytical flow solution in Supplementary Sec. S1 is a useful standalone contribution. However, the central quantitative claim—the 'well-defined spectrum' of exponents in Eq. (5)—is not actually supported by the simulations as presented. The open-system fitted exponent falls well outside the spectrum computed with the paper's own constants, and the stated escape that the constants are material-dependent makes the spectrum non-predictive without an independent measurement. The equilibrium assumption at criticality is also not directly tested. If these issues are addressed, the work could make a solid contribution; in its present form the central quantitative claim needs substantial revision.

major comments (4)
  1. [Eq. (5) and Fig. 2e] The open-system fit gives ν̄=0.18±0.06, while the lower bound of Eq. (5), computed with the constants stated in the text and in Supplementary Sec. S2 (c1=32π, c2≈2597.84, c3≈38.93), is 0.5[1−c3/(c3²+4c1c2)^1/2]≈0.48. The fitted value is therefore about five standard deviations below the claimed spectrum, not 'close to the lower bound' as stated in the text. Because the manuscript permits c1,c2,c3 to 'shift away from the classic estimate' and treats them as material parameters, the comparison is not a test of Eq. (5); any ν̄ in (0,1] could be rationalized by an appropriate choice of the c's. I request either an independent measurement of c1,c2,c3 for the multiphase-field model, or an explicit statement that the open-system exponent is outside the predicted range, with a discussion of what this implies for the theory.
  2. [Introduction and Supplementary Sec. S2] The RG flow (Eqs. 3 and S21) and the dislocation Hamiltonian (Eq. S19) are imported from equilibrium KTHNY theory with a modified core energy; they are not derived from the active multiphase-field dynamics. The paper assumes that the transition is effectively equilibrium-like at criticality, but the a posteriori evidence—the phase sequence and an exponentially divergent correlation length—does not test whether the fluctuations obey Gibbs-Boltzmann statistics. I ask for a direct diagnostic, such as comparing the measured dislocation pair distribution or static structure factor with the equilibrium predictions of Eq. (S19), or measuring an effective temperature via a fluctuation-dissipation ratio. Without such a check, the central mechanism remains an assumption.
  3. [Main text after Eq. (5); Supplementary Sec. S3B] The mapping between T2 processes and the constant c3 is only qualitative. In the simulations, T2 processes are implemented as random cell extrusion and intrusion events, but neither the rate nor the associated fugacity y0 (or effective core energy) is measured, and c3 is never extracted. Consequently, the claim that open systems 'render melting possible even at low activities' and thereby place ν̄ near the lower bound is not quantitatively connected to Eq. (5). The paper should either report measured T1/T2 rates and relate them to y0, or explicitly treat c3 as a free parameter and show that the fit remains inside the corresponding range.
  4. [Fig. 2e and Methods] The estimate of ξ+ from the defect density via n5-7∼ξ+^{-2}, and the subsequent fit to Eq. (4), are not described in sufficient detail. The number of data points, the fitting range in v0, the weighting of the error bars, and the goodness-of-fit are absent, and the text does not state whether alternative functional forms (e.g., a power law or a pure KT form) were tested. Given that the quantitative claim rests entirely on this fit, please provide these details and, if possible, an independent measure of ξ+ from the decay of g6(r) or S(q).
minor comments (6)
  1. [Abstract and Fig. 1a caption] Typography and language: 'loosing confluency' should be 'losing confluency'; 'KTNHY' in the Fig. 1a caption should be 'KTHNY'; 'multiphase filed' should be 'multiphase field'; and 'experiementally' in the main text should be 'experimentally'.
  2. [Eq. (1)] The same symbol σ is used for the stress tensor and for its magnitude, which makes the derivation hard to follow. Please use a distinct symbol for the tensor (e.g., Σ) and define the scalar explicitly.
  3. [Supplementary Sec. S1] The sentence describing the quadrupole should read 'two +1/6 and two −1/6 disclinations' rather than 'two +1/6 and two +1/6 disclinations'.
  4. [Supplementary Sec. S3A and Eq. (S49)] The relation between the coarse-grained active stress σ(r) in Eq. (S49) and the scalar σ in Eq. (1) of the main text is not stated. Please explain explicitly how σ∼v0 follows from the simulation parameters.
  5. [Main text, paragraph on thermal-like fluctuations] The statement that Gaussian white noise introduced via a Langevin or Monte Carlo thermostat is 'indistinguishable from the thermal noise characteristic of Gibbs ensembles' is too strong; a Langevin thermostat does not automatically guarantee Gibbs statistics for the configurational degrees of freedom in an active system.
  6. [Fig. 2e] Axis labels and units for the horizontal axis are missing. The caption should specify the self-propulsion speed in units of a Dr, where a is the lattice spacing and Dr the rotational diffusivity.

Circularity Check

1 steps flagged · score 4.0 of 10

One load-bearing self-citation (the T1/hexatic dictionary) anchors the derivation; the RG analysis and MPF simulations are otherwise independent, while the broad exponent range is a falsifiability problem rather than a circular reduction.

  1. self citation load bearing [Main text, Introduction (p. 2); Supplementary Sec. S1, opening of the active-flow derivation]
    "Taking advantage of the recently established correspondence between topological rearrangements in epithelia and hexatic defects [21], we show how active forces lead to a renormalization of the so-called defect core energy. ... Due to the correspondence demonstrated in Ref. [21], this active flow is the hydrodynamic flow sourced by a hexatic disclination quadrupole."

    Ref. [21] is Krommydas, Carenza and Giomi, eLife (2024), i.e. prior work by two of the present authors. The dictionary 'T1 = unbinding of an anti-parallel 5-7 dislocation pair' is the load-bearing premise from which Eq. (2) (the active core-energy shift) and the entire RG analysis follow. The current paper does not re-derive or independently test this correspondence; it explicitly defers to [21], and SI S1 bases the active-flow calculation on it. Thus the derivation chain is anchored in a self-citation. Because the cited work is a separate peer-reviewed publication and the RG solution plus MPF simulations add independent content, this is partial circularity rather than a tautology, warranting score 4 rather than 6-8.

full rationale

Apart from the self-citation identified above, the derivation is not circular: Eq. (2) is a physical work estimate; Eqs. (3) and (S21) are the standard Nelson-Halperin-Young recursion relations with c1, c2, c3 treated as material parameters; Eq. (5) and the exponent range are genuine consequences of those equations; and the multiphase-field simulations provide an independent numerical probe of the phase sequence, correlations, defect densities, and the fitted value of nu_bar. The more serious concern is falsifiability rather than circularity: SI S2 states that c1, c2, and c3 'are expected to shift away from the classic estimate' and treats them as material parameters, so Eq. (5) can accommodate almost any fitted nu_bar in (0,1] by unmeasured choices of c2/c3. In particular, the open-system fit nu_bar = 0.18 +/- 0.06 is about five standard deviations below the lower bound 0.48 computed from the paper's own classic constants c1 = 32 pi, c2 = 2597.84, c3 = 38.93, and the text's claim that this is 'close to its lower bound' depends on the untested shifted c-values. That is an internal consistency/predictive-power problem, not a circular reduction, so it is noted but not counted as an additional circular step.

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

The central derivations rest on borrowed equilibrium RG equations and on heuristic identifications (T1 = dislocation unbinding, sigma shift of core energy). The constants c1, c2, c3 and the initial fugacity are free material parameters; the exponents are fitted, so the ledger shows the paper contributes a scenario rather than a closed calculation.

free parameters (5)
  • c1, c2, c3 = c1=32pi, c2=2597.84, c3=38.93 (cited for point particles, stated to shift for cell monolayers)
    The RG flow constants control the exponent range; the paper treats them as free material parameters for epithelia, so the predicted range is not quantitatively fixed.
  • initial fugacity y0 (or core energy epsilon_c and active stress sigma) = not specified; set by model parameters and activity
    The exponent depends on whether y0 is exponentially small or large, which is not predicted from cell properties.
  • critical stress sigma_c = fitted to simulations in Fig 2e
    Needed to test Eq. (4); not predicted by the theory.
  • prefactor in Eq. (4) = not reported
    The logarithmic divergence requires a scale a, but the amplitude is fitted.
  • correlation length estimate from n5-7 ~ xi_+^{-2} = assumed
    The conversion from defect density to correlation length is a standard assumption but adds an uncalibrated constant.
assumptions (5)
  • domain assumption Standard KTHNY RG recursion relations (Eqs. 3) apply to confluent epithelia
    The paper imports the point-particle dislocation gas formalism to cell monolayers without deriving it from the cell model.
  • ad hoc to paper At criticality the active system is equilibrium-like
    Stated in the introduction; only verified a posteriori by the observed phase sequence, not by checking equilibrium relations.
  • ad hoc to paper Active stress enters only as a shift epsilon_c -> epsilon_c + sigma
    Derived heuristically from the Peach-Koehler force with U_eff = -sigma b dot delta r and delta r = -b; the choice of delta r is an assumption.
  • domain assumption In closed epithelia, c3=0 because T2 processes are absent
    Justified by the time-scale separation (cell intercalation faster than division/apoptosis), citing Refs. [28,29].
  • domain assumption The active flow field around a T1 event is a quadrupolar stagnation flow
    Derived in Sec. S1 from the active hexatic stress, but its connection to the actual simulations is not checked.

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Cite this review

Pith. "Pith review of Collective migration and topological phase transitions in confluent epithelia." pith.science (2026). https://pith.science/paper/UAI24YYK

@misc{pith2026250209554,
  author       = {Pith},
  title        = {Pith review of: Collective migration and topological phase transitions in confluent epithelia},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UAI24YYK}},
  note         = {Machine review of arXiv:2502.09554}
}
read the original abstract

Collective epithelial migration leverages on topological rearrangements of the intercellular junctions, which allow cells to intercalate without loosing confluency. In silico studies have provided a clear indication that this process could occur via a two-step phase transition, where a hierarchy of topological excitations progressively transforms an epithelial layer from a crystalline solid to an isotropic liquid, via an intermediate hexatic liquid crystal phase. Yet, the fundamental mechanism behind this process and its implications for collective cell behavior are presently unknown. In this article, we show that the onset of collective cell migration in cell-resolved models of epithelial layers takes place via an activity-driven melting transition, characterized by an exponentially-divergent correlation length across the solid/hexatic phase boundary. Using a combination of numerical simulations and Renormalization Group analysis, we show that the availability of topologically distinct rearrangements - known as T1 and T2 processes - and of a non-thermal route to melting, renders the transition significantly more versatile and tunable than in two-dimensional passive matter. Specifically, the relative frequency of T1 and T2 processes and of the "bare" stiffness of the cell layer affect the divergence of positional correlations within a well-defined spectrum of critical behaviors. Suppressing T1 processes, changes the nature of the transition by preventing collective migration in favor of a cellular analog of surface sublimation.

Figures

Figures reproduced from arXiv: 2502.09554 by the authors.

Figure 1
Figure 1. FIG. 1. (a) The three phases of epithelial layers from nu [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Multiphase field simulations of the onset of collective migration in closed and open systems (a) Structure factor of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

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Works this paper leans on

64 extracted references · 56 canonical work pages

  1. [1]

    Kalluri and R

    R. Kalluri and R. A. Weinberg, The basics of epithelial- mesenchymal transition, J. Clin. Invest. 119, 1420 (2009)

    work page 2009

  2. [2]

    Mongera, P

    A. Mongera, P. Rowghanian, H. J. Gustafson, E. Shelton, D. A. Kealhofer, E. K. Carn, F. Serwane, A. A. Lucio, J. Giammona, and O. Camp` as, A fluid-to-solid jamming transition underlies vertebrate body axis elongation, Na- ture 561, 401 (2018)

    work page 2018

  3. [3]

    Brugu´ es, E

    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, Nat. Phys. 10, 683 (2014)

    2014

  4. [4]

    Zhang and R

    Y. Zhang and R. A. Weinberg, Epithelial-to- mesenchymal transition in cancer: Complexity an- dopportunities, Front. Med. 12, 361 (2018)

    work page 2018

  5. [5]

    D. J. Montell, Emt, one of many morphological tran- sitions in cellular phase space, in The epithelial-to- mesenchymal transition , edited by K. Campbell and E. Theveneau (Springer-Vergal, New York, NY, USA,

    work page

  6. [6]

    D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tis- sues, Nat. Phys. 11, 1074 (2015)

    2015

  7. [7]

    D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biolog- ical tissues, Phys. Rev. X 6, 021011 (2016)

    2016

  8. [8]

    Li and M

    Y.-W. Li and M. P. Ciamarra, Role of cell deformability in the two-dimensional melting of biological tissues, Phys. Rev. Materials 2, 045602 (2018)

    work page 2018

Show all 64 references
  1. [9]

    Durand and J

    M. Durand and J. Heu, Thermally driven order-disorder transition in two-dimensional soft cellular systems, Phys. Rev. Lett. 123, 188001 (2019)

    2019

  2. [10]

    Pasupalak, Y.-W

    A. Pasupalak, Y.-W. Li, R. Ni, and M. Pica Ciamarra, Hexatic phase in a model of active biological tissues, Soft Matter 16, 3914 (2020)

    2020

  3. [11]

    Li and B.-q

    J.-j. Li and B.-q. Ai, Melting of two-dimensional bio- logical tissues containing active ornstein–uhlenbeck cells, New J. Phys. 23, 083044 (2021)

    2021

  4. [12]

    Li, Y.-l

    J.-j. Li, Y.-l. He, and B.-q. Ai, Solid–liquid transition induced by rigidity disparity in a binary mixture of cell tissues, Soft Matter 19, 3849 (2023)

    2023

  5. [13]

    Nemati and J

    H. Nemati and J. de Graaf, The cellular potts model on disordered lattices, Soft Matter 20, 8337 (2024)

    2024

  6. [14]

    J. M. Kosterlitz and D. J. Thouless, Long range order and metastability in two dimensional solids and superfluids, J. Phys. C: Solid State Phys. 5, L124 (1972)

    1972

  7. [15]

    J. M. Kosterlitz, The critical properties of the two- dimensional xy model, J. Phys. C: Solid State Phys. 7, 1046 (1974)

    1974

  8. [16]

    D. R. Nelson and B. I. Halperin, Dislocation-mediated melting in two dimensions, Phys. Rev. B19, 2457 (1979)

    1979

  9. [17]

    A. P. Young, Melting and the vector coulomb gas in two dimensions, Phys. Rev. B 19, 1855 (1979)

    1979

  10. [18]

    J. M. Kosterlitz, Kosterlitz–thouless physics: a review of key issues, Rep. Prog. Phys. 79, 026001 (2016)

    2016

  11. [19]

    Mueller, J

    R. Mueller, J. M. Yeomans, and A. Doostmohammadi, Emergence of active nematic behavior in monolayers of isotropic cells, Phys. Rev. Lett. 122, 048004 (2019)

    2019

  12. [20]

    H. P. Jain, R. D. Ho, and L. Angheluta, Emergent cell mi- gration from cell shape deformations and t1 transitions, arXiv:2412.19686 (2025)

    2025 arXiv

  13. [21]

    Krommydas, L

    D. Krommydas, L. N. Carenza, and L. Giomi, Collec- tive epithelial migration 2 mediated by the unbinding of hexatic defects, eLife (2024)

    2024

  14. [22]

    D. L. Weaire and S. Hutzler, The physics of foams (Ox- ford University Press, Oxford, UK, 1999)

    1999

  15. [23]

    Henkes, K

    S. Henkes, K. Kostanjevec, J. Collinson, R. Sknepnek, and E. Bertin, Dense active matter model of motion pat- terns in confluent cell monolayers, Nat. Commun. 11, 1405 (2020)

    2020

  16. [24]

    Beatrici, C

    C. Beatrici, C. Kirch, S. Henkes, F. Graner, and L. Brun- net, Comparing individual-based models of collective cell motion in a benchmark flow geometry, Soft Matter 19, 5583 (2023)

    2023

  17. [25]

    N. H. Claussen, F. Brauns, and B. I. Shraiman, A geometric-tension-dynamics model of epithelial conver- gent extension, Proc. Natl. Acad. Sci. U.S.A. 121, e2321928121 (2024)

    2024

  18. [26]

    Brauns, N

    F. Brauns, N. H. Claussen, M. F. Lefebvre, E. F. Wi- eschaus, and B. I. Shraiman, The geometric basis of ep- ithelial convergent extension, eLife 13, RP95521 (2024)

    2024

  19. [27]

    Balasubramaniam, A

    L. Balasubramaniam, A. Doostmohammadi, T. B. Saw, G. H. N. S. Narayana, R. Mueller, T. Dang, M. Thomas, S. Gupta, S. Sonam, A. S. Yap, Y. Toyama, R.-M. M´ ege, J. M. Yeomans, and B. Ladoux, Investigating the nature of active forces in tissues reveals how contractile cells can ...

    2021

  20. [28]

    ¨Ozel¸ ci, E

    E. ¨Ozel¸ ci, E. Mailand, M. R¨ uegg, A. C. Oates, and M. S. Sakar, Deconstructing body axis morphogenesis in ze- brafish embryos using robot-assisted tissue micromanip- ulation, Nat. Commun. 13, 7934 (2022)

    2022

  21. [29]

    Aigouy, R

    B. Aigouy, R. Farhadifar, D. B. Staple, A. Sagner, J.- C. R¨ oper, F. J¨ ulicher, and S. Eaton, Cell flow reori- ents the axis of planar polarity in the wing epithelium of drosophila, Cell 142, 773 (2010)

    2010

  22. [30]

    Supplementary information, inclusive of Refs. [58–62]

  23. [31]

    M. J. Bowick, D. R. Nelson, and H. Shin, Interstitial frac- tionalization and spherical crystallography, Phys. Chem. Chem. Phys. 9, 6304 (2007)

    2007

  24. [32]

    Nonomura, Study on multicellular systems using a phase field model, PloS one 7, e33501 (2012)

    M. Nonomura, Study on multicellular systems using a phase field model, PloS one 7, e33501 (2012)

    2012

  25. [33]

    B. A. Camley, Y. Zhang, Y. Zhao, B. Li, E. Ben-Jacob, H. Levine, and W.-J. Rappel, Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns, Proc. Natl. Acad. Sci. U.S.A. 111, 14770 (2014)

    2014

  26. [34]

    Palmieri, Y

    B. Palmieri, Y. Bresler, D. Wirtz, and M. Grant, Multi- ple scale model for cell migration in monolayers: Elastic mismatch between cells enhances motility, Sci. Rep. 5, 11745 (2015)

    2015

  27. [35]

    L¨ ober, F

    J. L¨ ober, F. Ziebert, and I. S. Aranson, Collisions of de- formable cells lead to collective migration, Sci. Rep. 5, 9172 (2015). 7

    2015

  28. [36]

    Marth and A

    W. Marth and A. Voigt, Collective migration under hy- drodynamic interactions: a computational approach, In- terface Focus 6, 20160037 (2016)

    2016

  29. [37]

    Loewe, M

    B. Loewe, M. Chiang, D. Marenduzzo, and M. C. Marchetti, Solid-liquid transition of deformable and over- lapping active particles, Phys. Rev. Lett. 125, 038003 (2020)

    2020

  30. [38]

    Hopkins, M

    A. Hopkins, M. Chiang, B. Loewe, D. Marenduzzo, and M. C. Marchetti, Local yield and compliance in active cell monolayers, Phys. Rev. Lett. 129, 148101 (2022)

    2022

  31. [39]

    Hopkins, B

    A. Hopkins, B. Loewe, M. Chiang, D. Marenduzzo, and M. C. Marchetti, Motility induced phase separation of deformable cells, Soft Matter 19, 8172 (2023)

    2023

  32. [40]

    H. P. Jain, A. Voigt, and L. Angheluta, From cell inter- calation to flow, the importance of t1 transitions, Phys. Rev. Res. 6, 033176 (2024)

    2024

  33. [41]

    Chiang, A

    M. Chiang, A. Hopkins, B. Loewe, D. Marenduzzo, and M. C. Marchetti, Multiphase field model of cells on a substrate: From three dimensional to two dimensional, Phys. Rev. E 110, 044403 (2024)

    2024

  34. [42]

    Chiang, A

    M. Chiang, A. Hopkins, B. L. Loewe, M. C. M. Marchetti, and D. Marenduzzo, Intercellular friction and motility drive orientational order in cell monolayers, Proc. Natl. Acad. Sci. U.S.A. 121, e2319310121 (2024)

    2024

  35. [43]

    Monfared, G

    S. Monfared, G. Ravichandran, J. Andrade, and A. Doostmohammadi, Mechanical basis and topological routes to cell elimination, eLife 12, e82435 (2023)

    2023

  36. [44]

    Monfared, G

    S. Monfared, G. Ravichandran, J. E. Andrade, and A. Doostmohammadi, Short-range correlation of stress chains near solid-to-liquid transition in active monolay- ers, Journal of the Royal Society Interface 21, 20240022 (2024)

    2024

  37. [45]

    Alert and X

    R. Alert and X. Trepat, Physical models of collective cell migration, Annu. Rev. Condens. Matter Phys. 11, 77 (2020)

    2020

  38. [46]

    Wenzel and A

    D. Wenzel and A. Voigt, Multiphase field models for col- lective cell migration, Phys. Rev. E 104, 054410 (2021)

    2021

  39. [47]

    Moure and H

    A. Moure and H. Gomez, Phase-field modeling of individ- ual and collective cell migration, Arch Computat Meth- ods Eng 28, 311 (2021)

    2021

  40. [48]

    Armengol-Collado, L

    J.-M. Armengol-Collado, L. N. Carenza, J. Eckert, D. Krommydas, and L. Giomi, Epithelia are multiscale active liquid crystals, Nat. Phys. 19, 1773–1779 (2023)

    2023

  41. [49]

    Armengol-Collado, L

    J.-M. Armengol-Collado, L. N. Carenza, and L. Giomi, Hydrodynamics and multiscale order in confluent epithe- lia, eLife , 13:e86400 (2023)

    2023

  42. [50]

    Eckert, B

    J. Eckert, B. Ladoux, R.-M. M´ ege, L. Giomi, and T. Schmidt, Hexanematic crossover in epithelial mono- layers depends on cell adhesion and cell density, Nat. Commun 14, Article number: 5762 (2023)

    2023

  43. [51]

    P. Keim, G. Maret, and H. H. von Gr¨ unberg, Frank’s constant in the hexatic phase, Phys. Rev. E 75, 031402 (2007)

    2007

  44. [52]

    Baconnier, D

    P. Baconnier, D. Shohat, C. H. L´ opez, C. Coulais, V. D´ emery, G. D¨ uring, and O. Dauchot, Selective and collective actuation in active solids, Nat. Phys. 18, 1234 (2022)

    2022

  45. [53]

    Y. Tang, S. Chen, M. J. Bowick, and D. Bi, Cell division and motility enable hexatic order in biological tissues, Phys. Rev. Lett. 132, 218402 (2024)

    2024

  46. [54]

    D. A. Matoz-Fernandez, K. Martens, R. Sknepnek, J. L. Barrat, and S. Henkes, Cell division and death inhibit glassy behaviour of confluent tissues, Soft Matter 13, 3205 (2017)

    2017

  47. [55]

    Br´ ezin and J

    E. Br´ ezin and J. Zinn-Justin, Renormalization of the non- linear σ model in 2 + ϵ dimensions—application to the heisenberg ferromagnets, Phys. Rev. Lett.36, 691 (1976)

    1976

  48. [56]

    Br´ ezin and J

    E. Br´ ezin and J. Zinn-Justin, Spontaneous breakdown of continuous symmetries near two dimensions, Phys. Rev. B 14, 3110 (1976)

    1976

  49. [57]

    T. C. Lubensky, Critical exponents for the zero state potts model in 2 + ϵ dimensions, Phys. Lett. A 67, 169 (1978)

    1978

  50. [58]

    P. M. Chaikin, T. C. Lubensky, and T. A. Witten, Prin- ciples of condensed matter physics , Vol. 10 (Cambridge University Press, Cambridge, UK, 1995)

    1995

  51. [59]

    J. D. Jackson, Classical electrodynamics (1999)

    1999

  52. [60]

    Christoffersen, M

    J. Christoffersen, M. M. Mehrabadi, and S. Nemat- Nasser, A micromechanical description of granular ma- terial behavior, J. Appl. Mech. 48, 339 (1981)

    1981

  53. [61]

    H. Li, D. Matsunaga, T. S. Matsui, H. Aosaki, G. Ki- noshita, K. Inoue, A. Doostmohammadi, and S. Deguchi, Wrinkle force microscopy: a machine learning based ap- proach to predict cell mechanics from images, Commun. Biol 5, 361 (2022)

    2022

  54. [62]

    living cell

    L. Bai and D. Breen, Calculating center of mass in an un- bounded 2d environment, J. Graph. Tools 13, 53 (2008). Collective migration and topological phase transitions in confluent epithelia Supplementary information Leonardo Puggioni, 1 Dimitrios Krommydas, 2, 1 and Luca Giom...

    2008 arXiv

  55. [63]

    Positional order Positional order is quantified by means of the structure factor, S(q), defined from the Fourier transform of the correlation function of the cell density ρ(r) = N∑ i=1 δ(r−ri). (S50) Using standard manipulations, one can readily show that S(q) = 1 N N∑ j=1 N∑ ...

  56. [64]

    Orientational order In order to investigate the orientational order and the presence of defects, we tessellate the domain assigning each point to the cell with the large value of the phase field at that point: ra∈i− cell if ϕi (ra) = max ({ϕj (ra)}) j = 1, 2... N . (S53) Such ...

Pith tools

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