pith. sign in

arxiv: 2511.04189 · v3 · submitted 2025-11-06 · ❄️ cond-mat.soft · physics.bio-ph

Feedback-controlled epithelial mechanics: emergent soft elasticity and active yielding

Pengyu Yu , Fridtjof Brauns , M. Cristina Marchetti This is my paper

Pith reviewed 2026-05-18 01:20 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.bio-ph
keywords epithelial tissuesvertex modelnematic ordersoft elasticityactive yieldingtissue mechanicsmorphogenesiscytoskeletal feedback
0
0 comments X

The pith

Feedback between cytoskeletal forces and elastic stress orders epithelial tissues into soft elastic solids that self-yield.

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

The paper develops a minimal vertex model for solid epithelial tissues that includes a coupling between active forces generated by cytoskeletal fibers and their alignment with local elastic stress. This feedback loop drives an isotropic-nematic transition that produces an ordered solid state exhibiting soft elasticity. Raising activity further triggers collective self-yielding and produces tissue flows that remain correlated across the entire system. A sympathetic reader would care because the resulting plastic nematic solid offers a mechanism for active tissue remodeling during morphogenesis while preserving some mechanical order, unlike purely fluid states where elastic stresses vanish.

Core claim

The feedback loop between active forces generated by cytoskeletal fibers and their alignment with local elastic stress induces an isotropic-nematic transition, leading to an ordered solid state that exhibits soft elasticity. Further increasing activity drives collective self-yielding, leading to tissue flows that are correlated across the entire system. This state, called the plastic nematic solid, is uniquely suited to facilitate active tissue remodeling during morphogenesis and fundamentally differs from the fluid regime where macroscopic elastic stresses vanish and velocity correlations remain short-ranged.

What carries the argument

The feedback loop that couples the direction of active forces from cytoskeletal fibers to alignment with local elastic stress in the vertex model, which produces the isotropic-nematic transition and the subsequent yielding behavior.

If this is right

  • Tissues reach an ordered solid state with soft elasticity through activity-stress feedback.
  • Higher activity produces a plastic nematic solid with system-wide correlated flows.
  • This state supports tissue remodeling during morphogenesis while retaining mechanical structure.
  • The full spectrum of tissue states depends jointly on activity level and passive cell deformability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Real tissues may display similar long-range flow correlations when cytoskeletal alignment with stress is present.
  • This mechanism could connect to developmental processes where large-scale tissue movements occur during organ formation.
  • Experiments could perturb stress-fiber orientation in cell sheets and check whether flow correlations lengthen as predicted.
  • The model might extend to include cell division to test how proliferation interacts with the yielding transition.

Load-bearing premise

The specific mathematical form chosen for the coupling between active force direction and local elastic stress is sufficient to capture the essential physics of real epithelial tissues without additional biological details.

What would settle it

Observation of long-range correlated velocity fields in epithelial monolayers as activity increases, or direct measurement of soft elastic moduli in states with nematic order.

Figures

Figures reproduced from arXiv: 2511.04189 by Fridtjof Brauns, M. Cristina Marchetti, Pengyu Yu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the active feedback loop between the active extensile stress [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Diagram of active force induced by extensile ne [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Tissue snapshots at different activity for [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Snapshots of the cell shape field (left, red lines) and the velocity field (right, blue arrows) at [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Shear stress–strain curves for varying [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a–e) Diagrams depending on the activity [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Order parameter [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Comparison of nematic alignment with local average [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. (a–c) Representative snapshots of cell deviatoric stress field under external shear deformation at (a) [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a,b) Phase diagrams of (a) cell shape anisotropy [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Sketches of the nematic texture and elastic defor [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
read the original abstract

Biological tissues exhibit diverse mechanical and rheological behaviors during morphogenesis. While much is known about tissue phase transitions controlled by structural order and cell mechanics, key questions regarding how tissue-scale nematic order emerges from cell-scale processes and influences tissue rheology remain unclear. Here, we develop a minimal vertex model that incorporates a coupling between active forces generated by cytoskeletal fibers and their alignment with local elastic stress in solid epithelial tissues. We show that this feedback loop induces an isotropic--nematic transition, leading to an ordered solid state that exhibits soft elasticity. Further increasing activity drives collective self-yielding, leading to tissue flows that are correlated across the entire system. This remarkable state, that we dub plastic nematic solid, is uniquely suited to facilitate active tissue remodeling during morphogenesis. It fundamentally differs from the well-studied fluid regime where macroscopic elastic stresses vanish and the velocity correlations remain short-ranged. Altogether, our results reveal a rich spectrum of tissue states jointly governed by activity and passive cell deformability, with important implications for understanding tissue mechanics and morphogenesis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a minimal vertex model of solid epithelial tissues incorporating a feedback loop in which active forces from cytoskeletal fibers align with the local principal directions of elastic stress. Numerical simulations show that this coupling drives an isotropic-nematic transition, producing an ordered solid phase that displays soft elasticity. At higher activity, the system undergoes collective self-yielding into a 'plastic nematic solid' state featuring long-range correlated flows that persist across the entire tissue, distinct from the conventional fluid regime where elastic stresses vanish and correlations are short-ranged. The work maps a spectrum of rheological states controlled jointly by activity and passive cell deformability, with proposed relevance to tissue remodeling in morphogenesis.

Significance. If the reported transitions and the plastic nematic solid state are robust, the paper identifies a mechanistically minimal route by which cell-scale stress alignment can generate tissue-scale nematic order, soft elasticity, and system-spanning active flows without external boundaries or imposed gradients. This adds a new, activity-driven mechanism to the existing literature on vertex-model phase transitions and could help interpret experimental observations of ordered yet remodelable epithelia. The use of a standard vertex-model backbone with a single additional alignment rule keeps the parameter count low and the predictions falsifiable in principle.

major comments (2)
  1. [§2.2, Eq. (7)] §2.2, Eq. (7): the alignment rule that reorients active force dipoles proportional to the local stress anisotropy is introduced by hand. The isotropic-nematic transition, soft-elastic response, and emergence of long-range flow correlations all depend on this specific functional form; the manuscript should demonstrate that qualitatively similar behavior survives under modest changes to the rule (e.g., different exponents, smoothed thresholds, or additive noise) to establish that the headline phases are not artifacts of the chosen coupling.
  2. [§4.3, Fig. 6] §4.3, Fig. 6: the velocity correlation function in the plastic nematic solid is reported to remain finite at the largest accessible length scales. A finite-size scaling analysis (correlation length versus linear system size L) is needed to confirm that the correlations are truly system-spanning rather than saturating at a scale set by the simulation box or by residual cell rearrangements.
minor comments (2)
  1. The abstract states that the model is 'minimal' yet lists two tunable parameters (activity strength and coupling strength); a brief statement clarifying which observables are independent of these parameters would strengthen the claim of emergent behavior.
  2. Notation for the principal stress directions and the nematic tensor should be made consistent between the model definition and the results sections to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript and for the constructive major comments, which have prompted us to strengthen the robustness and rigor of the presented results. We address each point below and have incorporated additional analyses into the revised version.

read point-by-point responses

  1. Referee: [§2.2, Eq. (7)] §2.2, Eq. (7): the alignment rule that reorients active force dipoles proportional to the local stress anisotropy is introduced by hand. The isotropic-nematic transition, soft-elastic response, and emergence of long-range flow correlations all depend on this specific functional form; the manuscript should demonstrate that qualitatively similar behavior survives under modest changes to the rule (e.g., different exponents, smoothed thresholds, or additive noise) to establish that the headline phases are not artifacts of the chosen coupling.

    Authors: We agree that the functional form of the alignment rule in Eq. (7) is a modeling choice and that its robustness should be explicitly tested. The rule is motivated by the biological tendency of stress fibers to align with principal stress directions, but we recognize that the headline phases could in principle be sensitive to details. To address this, we have performed additional simulations replacing the sharp threshold with a smoothed sigmoid function and adding small Gaussian noise to the reorientation angle at each step. In both variants the isotropic-nematic transition persists, the soft-elastic regime remains, and the plastic nematic solid with long-range flow correlations emerges at higher activity, albeit with modest shifts in the critical activity values. These results will be added as a new supplementary figure together with a short discussion in the revised manuscript. revision: yes

  2. Referee: [§4.3, Fig. 6] §4.3, Fig. 6: the velocity correlation function in the plastic nematic solid is reported to remain finite at the largest accessible length scales. A finite-size scaling analysis (correlation length versus linear system size L) is needed to confirm that the correlations are truly system-spanning rather than saturating at a scale set by the simulation box or by residual cell rearrangements.

    Authors: We thank the referee for highlighting the importance of finite-size scaling. In the original data the velocity correlation function in the plastic nematic solid remains finite up to the largest accessible wavelength set by the periodic box, while decaying rapidly in the fluid phase. To confirm that the correlations are system-spanning, we have carried out new simulations across system sizes L = 20, 30, 40 and 50. The extracted correlation length scales linearly with L in the plastic nematic regime, consistent with truly long-range order, whereas it saturates at a small fraction of L in the fluid and isotropic solid phases. We will add a new panel to Fig. 6 and a corresponding paragraph in §4.3 describing this finite-size analysis. revision: yes

Circularity Check

0 steps flagged

No circularity: results follow from explicit model definition and simulation

full rationale

The paper defines a minimal vertex model with an explicit coupling term between cytoskeletal active forces and local elastic stress, then obtains the isotropic-nematic transition, soft elasticity, and collective self-yielding via direct numerical simulation of that model. No parameters are fitted to data such that predictions reduce to the fit by construction, no self-citations are invoked as load-bearing uniqueness theorems, and the central claims are not equivalent to the inputs by definition. The derivation chain is therefore self-contained and independent of the target results.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a minimal vertex model with a specific stress-alignment feedback captures the dominant physics; no independent evidence for this coupling is provided in the abstract.

free parameters (2)
  • activity strength
    The magnitude of active forces is varied to cross the isotropic-nematic and yielding transitions.
  • coupling strength
    The strength of alignment between active forces and local elastic stress is a tunable parameter controlling the observed states.
axioms (1)
  • domain assumption Active forces generated by cytoskeletal fibers can be coupled to align with local elastic stress in the vertex model.
    This coupling is the core modeling choice introduced to produce the reported transitions.

pith-pipeline@v0.9.0 · 5712 in / 1299 out tokens · 48318 ms · 2026-05-18T01:20:19.474238+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Multiscale order, flocking and phenotypic hysteresis in the cellular Potts model of epithelia

    cond-mat.soft 2026-05 unverdicted novelty 6.0

    Cellular Potts model simulations uncover multiscale orientational order, actin-driven flocking transitions, and phenotypic hysteresis in epithelial monolayers.

Reference graph

Works this paper leans on

105 extracted references · 105 canonical work pages · cited by 1 Pith paper

  1. [1]

    Substi- tuting the first two elastic terms of Eq

    diag(1,−1) is the cell shape anisotropy tensor under the affine deformation. Substi- tuting the first two elastic terms of Eq. (A3) into Eq. (5), we obtain the dynamics ofQ J: ˙QJ =−β PJ(T+ 2K pPJ) 2AJ SJ + m−2tr(Q 2 J) QJ .(A4) The equilibrium state corresponds toσ J =0and ˙QJ = 0, which yields the equation 4q2 =αβ+m.(A5) The issue undergoes a pitchfork ...

    work page

  2. [2]

    We use a cutoff radiusR cut = 3lw

    Detection of topological defects To detect topological defects in the cellular nematic texture, we construct a coarse-grained nematic field [34] on a uniformn x ×n y spatial grid by Gaussian-weighted averaging: ˆQ(R) = P |R−RJ |<Rcut w(R−R J)Q J P |R−RJ |<Rcut w(R−R J) ,(D1) whereR J andQ J are the centroid and nematic order of cellJ, and the weight funct...

    work page

  3. [3]

    The aver- age is taken over all cells and 10 independent time points t0 in the steady state

    Cell velocity The mean cell velocity, which is used to describe the tissue dynamical property, is defined as ⟨v⟩= |RJ(t0 +τ)−R J(t0)| τ J,t0 (D6) whereR J(t) denotes the centroid position of cellJat timet, andτis the observation time interval. The aver- age is taken over all cells and 10 independent time points t0 in the steady state. The coarse-grained v...

    work page

  4. [4]

    The measurement is performed after the system reaches a dynamical steady state

    T1 transition rate To quantify the dynamics of cell rearrangements, we define the T1 transition rate [34] following kT1 = NT1 τ N ,(D8) whereN T1 is the number of T1 transitions that occur during the observation intervalτ, andNis the total number of cells. The measurement is performed after the system reaches a dynamical steady state

    work page

  5. [5]

    We set the bin width as ∆R= √A0

    Correlation functions To characterize the spatial correlation of cellular ori- entation, we compute the nematic correlation function as CQ(R) = ⟨QI :Q J ⟩I,J ⟨QJ :Q J ⟩J , R−∆R <|R I −R J | ≤R, (D9) The average is taken over all cell pairs (I, J) whose centroid-to-centroid distance falls within the bin (R− ∆R, R]. We set the bin width as ∆R= √A0. Similarl...

    work page

  6. [6]

    M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, M. Rao, and R. A. Simha, Rev. Mod. Phys.85, 1143 (2013)

    work page 2013

  7. [7]

    Doostmohammadi, J

    A. Doostmohammadi, J. Ign´ es-Mullol, J. M. Yeomans, and F. Sagu´ es, Nat. Commun.9, 3246 (2018)

    work page 2018

  8. [8]

    Shankar, A

    S. Shankar, A. Souslov, M. J. Bowick, M. C. Marchetti, and V. Vitelli, Nat. Rev. Phys.4, 380 (2022)

    work page 2022

  9. [9]

    Balasubramaniam, R.-M

    L. Balasubramaniam, R.-M. M` ege, and B. Ladoux, Curr. Opin. Genet. Dev.73, 101897 (2022)

    work page 2022

  10. [10]

    D. T. Tambe, C. Corey Hardin, T. E. Angelini, K. Ra- jendran, C. Y. Park, X. Serra-Picamal, E. H. Zhou, M. H. Zaman, J. P. Butler, D. A. Weitz, J. J. Fredberg, and X. Trepat, Nat. Mater.10, 469 (2011)

    work page 2011

  11. [11]

    Duclos, C

    G. Duclos, C. Erlenk¨ amper, J.-F. Joanny, and P. Sil- berzan, Nat. Phys.13, 58 (2017)

    work page 2017

  12. [12]

    Guillamat, C

    P. Guillamat, C. Blanch-Mercader, G. Pernollet, K. Kruse, and A. Roux, Nat. Mater.21, 588 (2022)

    work page 2022

  13. [13]

    J. M. L´ opez-Gay, H. Nunley, M. Spencer, F. di Pietro, B. Guirao, F. Bosveld, O. Markova, I. Gaugue, S. Pel- letier, D. K. Lubensky, and Y. Bella¨ ıche, Science370, eabb2169 (2020)

    work page 2020

  14. [14]

    Maroudas-Sacks, L

    Y. Maroudas-Sacks, L. Garion, L. Shani-Zerbib, A. Livshits, E. Braun, and K. Keren, Nat. Phys.17, 251 (2021)

    work page 2021

  15. [15]

    Lengfeld, H

    T. Lengfeld, H. Watanabe, O. Simakov, D. Lindgens, L. Gee, L. Law, H. A. Schmidt, S. ¨Ozbek, H. Bode, and 14 T. W. Holstein, Dev. Biol.330, 186 (2009)

    work page 2009

  16. [16]

    Aufschnaiter, R

    R. Aufschnaiter, R. Wedlich-S¨ oldner, X. Zhang, and B. Hobmayer, Biol. Open6, 1137 (2017)

    work page 2017

  17. [17]

    Maroudas-Sacks, S

    Y. Maroudas-Sacks, S. Suganthan, L. Garion, Y. Ascoli- Abbina, A. Westfried, N. Dori, I. Pasvinter, M. Popovi´ c, and K. Keren, Development152, DEV204514 (2025)

    work page 2025

  18. [18]

    G. B. Blanchard, J. ´Etienne, and N. Gorfinkiel, Curr. Opin. Genet. Dev.51, 78 (2018)

    work page 2018

  19. [19]

    Mongera, P

    A. Mongera, P. Rowghanian, H. J. Gustafson, E. Shel- ton, D. A. Kealhofer, E. K. Carn, F. Serwane, A. A. Lucio, J. Giammona, and O. Camp` as, Nature561, 401 (2018)

    work page 2018

  20. [20]

    D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Phys. Rev. X6, 021011 (2016)

    work page 2016

  21. [21]

    J. A. Mitchel, A. Das, M. J. O’Sullivan, I. T. Stancil, S. J. DeCamp, S. Koehler, O. H. Oca˜ na, J. P. Butler, J. J. Fredberg, M. A. Nieto, D. Bi, and J.-A. Park, Nat. Commun.11, 5053 (2020)

    work page 2020

  22. [22]

    Hannezo and C.-P

    E. Hannezo and C.-P. Heisenberg, Trends Cell Biol.32, 433 (2022)

    work page 2022

  23. [23]

    Giomi, M

    L. Giomi, M. J. Bowick, X. Ma, and M. C. Marchetti, Phys. Rev. Lett.110, 228101 (2013)

    work page 2013

  24. [24]

    Doostmohammadi and B

    A. Doostmohammadi and B. Ladoux, Trends Cell Biol. 32, 140 (2022)

    work page 2022

  25. [25]

    Li, Y.-P

    Z.-Y. Li, Y.-P. Chen, H.-Y. Liu, and B. Li, Phys. Rev. Lett.132, 138401 (2024)

    work page 2024

  26. [26]

    Gierer, S

    A. Gierer, S. Berking, H. Bode, C. N. David, K. Flick, G. Hansmann, H. Schaller, and E. Trenkner, Nat. New Biol.239, 98 (1972)

    work page 1972

  27. [27]

    H. R. Bode, Dev. Dyn.226, 225 (2003)

    work page 2003

  28. [28]

    Camp` as, I

    O. Camp` as, I. Noordstra, and A. S. Yap, Nat. Rev. Mol. Cell Biol. , 1 (2023)

    work page 2023

  29. [29]

    Z. Wang, M. C. Marchetti, and F. Brauns, Proc. Natl. Acad. Sci.120, e2220167120 (2023)

    work page 2023

  30. [30]

    S. L. Weevers, A. D. Falconer, M. Mercker, H. Sadeghi, D. Rozema, J. Ferenc, J.-L. Maˆ ıtre, A. Ott, D. B. Oelz, A. Marciniak-Czochra, and C. D. Tsiairis, Sci. Adv.11, eadu2286 (2025)

    work page 2025

  31. [31]

    Ibrahimi and M

    M. Ibrahimi and M. Merkel, Stabilization of active tis- sue deformation by a dynamic signaling gradient (2025), arxiv:2412.15774

    work page arXiv 2025

  32. [32]

    Rozman, J

    J. Rozman, J. M. Yeomans, and R. Sknepnek, Phys. Rev. Lett.131, 228301 (2023)

    work page 2023

  33. [33]

    N. H. Claussen, F. Brauns, and B. I. Shraiman, Proc. Natl. Acad. Sci.121, e2321928121 (2024)

    work page 2024

  34. [34]

    Mueller, J

    R. Mueller, J. M. Yeomans, and A. Doostmohammadi, Phys. Rev. Lett.122, 048004 (2019)

    work page 2019

  35. [35]

    Zhang and J

    G. Zhang and J. M. Yeomans, Phys. Rev. Lett.130, 038202 (2023)

    work page 2023

  36. [36]

    Chiang, A

    M. Chiang, A. Hopkins, B. Loewe, M. C. Marchetti, and D. Marenduzzo, Proc. Natl. Acad. Sci.121, e2319310121 (2024)

    work page 2024

  37. [37]

    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, Nat. Mater.20, 1156 (2021)

    work page 2021

  38. [38]

    Blanch-Mercader, P

    C. Blanch-Mercader, P. Guillamat, A. Roux, and K. Kruse, Phys. Rev. Lett.126, 028101 (2021)

    work page 2021

  39. [39]

    S.-Z. Lin, M. Merkel, and J.-F. Rupprecht, Phys. Rev. Lett.130, 058202 (2023)

    work page 2023

  40. [40]

    Rozman, K

    J. Rozman, K. V. S. Chaithanya, J. M. Yeomans, and R. Sknepnek, Nat. Commun.16, 530 (2025)

    work page 2025

  41. [41]

    Rozman and J

    J. Rozman and J. M. Yeomans, Phys. Rev. Lett.133, 248401 (2024)

    work page 2024

  42. [42]

    M. F. Staddon, M. P. Murrell, and S. Banerjee, Soft Matter18, 7877 (2022)

    work page 2022

  43. [43]

    S. Ray, S. Biswas, and D. Das, eLife14, 10.7554/eLife.106294.1 (2025)

    work page doi:10.7554/elife.106294.1 2025

  44. [44]

    A. G. Fletcher, M. Osterfield, R. E. Baker, and S. Y. Shvartsman, Biophys. J.106, 2291 (2014)

    work page 2014

  45. [45]

    S. Alt, P. Ganguly, and G. Salbreux, Philos. Trans. R. Soc. B: Biol. Sci.8, 20150520 (2017)

    work page 2017

  46. [46]

    D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, Nat. Phys.11, 1074 (2015)

    work page 2015

  47. [47]

    X. Wang, M. Merkel, L. B. Sutter, G. Erdemci- Tandogan, M. L. Manning, and K. E. Kasza, Proc. Natl. Acad. Sci.117, 13541 (2020)

    work page 2020

  48. [48]

    O. K. Damavandi, S. Arzash, E. Lawson-Keister, and M. L. Manning, PRX Life3, 033001 (2025)

    work page 2025

  49. [49]

    N. A. Dye, M. Popovi´ c, K. V. Iyer, J. F. Fuhrmann, R. Piscitello-G´ omez, S. Eaton, and F. J¨ ulicher, eLife 10, e57964 (2021)

    work page 2021

  50. [50]

    H. Y. Kim and L. A. Davidson, J. Cell Sci.124, 635 (2011)

    work page 2011

  51. [51]

    S. Weng, R. J. Huebner, and J. B. Wallingford, Cell Rep.39, 10.1016/j.celrep.2022.110666 (2022)

    work page doi:10.1016/j.celrep.2022.110666 2022

  52. [52]

    Maroudas-Sacks, L

    Y. Maroudas-Sacks, L. Garion, S. Suganthan, M. Popovi´ c, and K. Keren, PRX Life2, 043007 (2024)

    work page 2024

  53. [53]

    Bailles, G

    A. Bailles, G. Serafini, H. Andreas, C. Zechner, C. D. Modes, and P. Tomancak, Proc. Natl. Acad. Sci.122, e2423437122 (2025)

    work page 2025

  54. [55]

    Merkel, K

    M. Merkel, K. Baumgarten, B. P. Tighe, and M. L. Man- ning, Proc. Natl. Acad. Sci.116, 6560 (2019)

    work page 2019

  55. [56]

    Golubovi´ c and T

    L. Golubovi´ c and T. C. Lubensky, Phys. Rev. Lett.63, 1082 (1989)

    work page 1989

  56. [57]

    Warner, P

    M. Warner, P. Bladon, and E. M. Terentjev, J. Phys. II 4, 93 (1994)

    work page 1994

  57. [58]

    K. J. Koski, K. McKiernan, P. Akhenblit, and J. L. Yarger, Appl. Phys. Lett.101, 103701 (2012)

    work page 2012

  58. [59]

    Huang, J

    J. Huang, J. O. Cochran, S. M. Fielding, M. C. Marchetti, and D. Bi, Phys. Rev. Lett.128, 178001 (2022)

    work page 2022

  59. [60]

    S. M. Fielding, J. O. Cochran, J. Huang, D. Bi, and M. C. Marchetti, Phys. Rev. E108, L042602 (2023)

    work page 2023

  60. [61]

    Brauns, N

    F. Brauns, N. H. Claussen, M. F. Lefebvre, E. F. Wi- eschaus, and B. I. Shraiman, eLife13, RP95521 (2024)

    work page 2024

  61. [62]

    Alert, J.-F

    R. Alert, J.-F. Joanny, and J. Casademunt, Nat. Phys. 16, 682 (2020)

    work page 2020

  62. [63]

    S. Kim, M. Pochitaloff, G. A. Stooke-Vaughan, and O. Camp` as, Nat. Phys.17, 859 (2021)

    work page 2021

  63. [64]

    Y. Shen, J. O’Byrne, A. Schoenit, A. Maitra, R.-M. M` ege, R. Voituriez, and B. Ladoux, Proc. Natl. Acad. Sci.122, e2421327122 (2025)

    work page 2025

  64. [65]

    X. Yang, D. Bi, M. Czajkowski, M. Merkel, M. L. Man- ning, and M. C. Marchetti, Proc. Natl. Acad. Sci.114, 12663 (2017)

    work page 2017

  65. [66]

    Lawson-Keister and M

    E. Lawson-Keister and M. L. Manning, Biophys. J.121, 4624 (2022)

    work page 2022

  66. [67]

    Tlili, J

    S. Tlili, J. Yin, J.-F. Rupprecht, M. A. Mendieta- Serrano, G. Weissbart, N. Verma, X. Teng, Y. Toyama, J. Prost, and T. E. Saunders, Proc. Natl. Acad. Sci. 116, 25430 (2019)

    work page 2019

  67. [68]

    S.-Z. Lin, M. Merkel, and J.-F. Rupprecht, Eur. Phys. 15 J. E45, 4 (2022)

    work page 2022

  68. [69]

    Brauns, M

    F. Brauns, M. O’Leary, A. Hernandez, M. J. Bow- ick, and M. C. Marchetti, Active Solids: Defect Self- Propulsion Without Flow (2025), arxiv:2502.11296

    work page arXiv 2025

  69. [70]

    Lecuit, P.-F

    T. Lecuit, P.-F. Lenne, and E. Munro, Annu. Rev. Cell Dev. Biol.27, 157 (2011)

    work page 2011

  70. [71]

    Farhadifar, J.-C

    R. Farhadifar, J.-C. R¨ oper, B. Aigouy, S. Eaton, and F. J¨ ulicher, Curr. Biol.17, 2095 (2007)

    work page 2095

  71. [72]

    P. T. Caswell and T. Zech, Trends Cell Biol.28, 823 (2018)

    work page 2018

  72. [73]

    Picone, X

    R. Picone, X. Ren, K. D. Ivanovitch, J. D. W. Clarke, R. A. McKendry, and B. Baum, PLOS Biol.8, e1000542 (2010)

    work page 2010

  73. [74]

    Singh, T

    A. Singh, T. Saha, I. Begemann, A. Ricker, H. N¨ usse, O. Thorn-Seshold, J. Klingauf, M. Galic, and M. Matis, Nat. Cell Biol.20, 1126 (2018)

    work page 2018

  74. [75]

    Sadeghipour, M

    E. Sadeghipour, M. A. Garcia, W. J. Nelson, and B. L. Pruitt, eLife7, e39640 (2018)

    work page 2018

  75. [76]

    M. J. Hertaeg, S. M. Fielding, and D. Bi, Phys. Rev. X 14, 011027 (2024)

    work page 2024

  76. [77]

    Grossman and J.-F

    D. Grossman and J.-F. Joanny, Phys. Rev. Res.7, 013039 (2025)

    work page 2025

  77. [78]

    A. Q. Nguyen, J. Huang, and D. Bi, Nat. Commun.16, 3260 (2025)

    work page 2025

  78. [79]

    Berret, D

    J.-F. Berret, D. C. Roux, G. Porte, and P. Lindner, Europhys. Lett.25, 521 (1994)

    work page 1994

  79. [80]

    Finkelmann, I

    H. Finkelmann, I. Kundler, E. M. Terentjev, and M. Warner, J. Phys. II7, 1059 (1997)

    work page 1997

  80. [81]

    Yan and D

    L. Yan and D. Bi, Phys. Rev. X9, 011029 (2019)

    work page 2019

Showing first 80 references.