Pith. sign in

REVIEW 4 major objections 5 minor 47 references

Boundary-shape driven transitions in vortex and oscillatory dynamics of confined epithelial cells

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A single geometric ratio switches confined epithelial cells between vortex, oscillation, and disorder.

desk verdict Empirical aspect-ratio control is solid and useful; the LA/CIL mechanism claim is model-selected, not experimentally tested. read the letter →

arxiv 2509.06087 v1 pith:QNX33O3B submitted 2025-09-07 cond-mat.soft physics.bio-ph

Ryo Ienaga , Kazuyuki Shigeta , Tatsuya Fukuyama , Kazusa Beppu , Yusuke T. Maeda This is my paper · ORCID
classification cond-mat.softphysics.bio-ph
keywords collectivecellmigrationepithelialmonolayerconfinementaspectratiovortexrotationoscillatorymotioncontactinhibitionoflocomotionself-propelledparticlemodelmicropatterned
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 sets out to show that one number—the aspect ratio of a doublet-shaped confinement, defined as the distance between the centers of two overlapping circles divided by their radius—controls which collective motion an epithelial sheet chooses. In experiments on MDCK cells, small aspect ratios give a stable rotating vortex, intermediate values give back-and-forth oscillatory flow with a period of about six hours, and large aspect ratios give disordered motion. The authors reproduce the same three-state sequence in a self-propelled particle model in which cells align locally and turn away from neighbors on contact, and they identify the balance between those two rules as the cell-level mechanism. If the claim holds, tissue engineers and active-matter physicists get a minimal geometric knob for programming collective behavior without changing any biochemical parameter.

What carries the argument

The argument is carried by two objects. First, the doublet circular boundary: two overlapping circles of fixed radius R whose center separation Δ tunes the confinement aspect ratio Δ/R while preserving the circular boundary conditions known to stabilize vortices; changing Δ/R changes the anisotropy and the collision geometry of the two would-be vortices. Second, the polarity dynamics of the self-propelled particle model (Eq. 3), in which each particle's direction turns under local alignment (LA), which pulls it toward the velocity direction of neighbors, and contact inhibition of locomotion (CIL), which pushes it away from the relative position of neighbors; the strengths μ_a and μ_c set the

What would settle it

Knock down or inhibit contact inhibition of locomotion in MDCK cells confined to doublet circles, then remeasure the vortex order parameter, oscillation period, and disorder threshold across Δ/R. The model predicts that weakening CIL stabilizes vortex pairs and shifts the transition, while strengthening CIL destroys vortices at all aspect ratios; if the experimental transition curve is unchanged, the LA/CIL balance is not the controlling mechanism.

Watch

Extended reading notes

Core claim

The paper identifies the confinement aspect ratio Δ/R of a doublet circular boundary—two equal circles of radius R with centers separated by Δ—as a minimal control parameter for epithelial collective motion. For Δ/R below about 1.33, MDCK cells form a stable co-rotating vortex; above it, the population oscillates, reversing its migration direction along the long axis with a period of about 6 h that peaks near Δ/R≈1.33–1.44 before falling; at larger aspect ratios motion becomes disordered. A self-propelled particle model with local alignment and moderate contact inhibition of locomotion reproduces this sequence, while weak CIL stabilizes counter-rotating vortex pairs and strong CIL destroys o

Load-bearing premise

The explanation assumes that cell behavior is governed by just two local rules—aligning with neighbors and turning away on contact—with the strength of the second rule chosen to match the data; if traction, adhesion, or cell deformability actually drive the switching, the geometric transition could persist while the proposed cell-level mechanism fails.

Editorial extensions

If this is right

  • Collective mode in a confined epithelial sheet can be predicted from geometry alone: measure Δ/R and the state (vortex, oscillation, disorder) follows, without needing cell-type-specific biochemical parameters.
  • The oscillation period grows linearly with Δ up to a maximum near Δ/R≈1.44 because a cell traveling at constant speed needs time proportional to Δ to cross the doublet; beyond that the period drops as order breaks down.
  • Moderate contact inhibition of locomotion is required for oscillatory dynamics; too little CIL locks the system into vortex pairs and too much CIL produces disorder, so perturbations of CIL should shift the transition.
  • Doublet-shaped micropatterns offer a design rule for tissue engineering: by carving the overlap of two circles, one can program rotation, rhythmic pumping, or disorganized migration in a cultured epithelial layer.
  • The results connect epithelial oscillations to vortex-pairing transitions known in bacterial vortices, where two counter-rotating vortices stabilize when Δ/R exceeds √2.

Reading between the lines

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

  • If the geometric rule is generic, the same vortex-oscillation-disorder sequence should appear in other confined active fluids (bacterial suspensions, active nematics, cell extracts) placed in doublet boundaries; testing this would separate geometry-driven physics from MDCK-specific biology.
  • The paper's mechanism could be wrong even if the transition is real: rectangular-confinement oscillations have been explained by traction-driven density waves, and the doublet geometry may simply be another route to the same physics, with LA/CIL being a phenomenological stand-in.
  • A direct test would be to pharmacologically or genetically weaken contact inhibition of locomotion in MDCK cells and remeasure the transition curve; the model predicts the boundary and period maximum should shift systematically.
  • The maximum of the oscillation period near Δ/R≈1.33–1.44 resembles a critical slowing-down signature, suggesting that a hidden ordering transition (possibly vortex-pairing) sits at that aspect ratio; measuring correlation times and fluctuation amplitudes could reveal critical exponents.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript studies MDCK epithelial monolayers confined in a 'doublet' geometry formed by two partially overlapping circles of radius R. Varying the center separation ratio Δ/R from 0 to ~2 changes the collective motion: a stable co-rotating vortex for Δ/R<1.33, oscillatory flow along the long axis with a ~6 h period, and ultimately disordered motion. The authors introduce a self-propelled particle model with local alignment (LA) and contact inhibition of locomotion (CIL), show that with moderate CIL (μ_c=0.5) the simulated sequence matches qualitatively, and sweep CIL strength to argue that an LA/CIL balance is critical. The abstract and conclusion claim that Δ/R is a minimal control parameter and that the LA/CIL balance stabilizes vortex pairs with velocity reversals.

Significance. If established, the paper would provide a simple geometric handle on active turbulence in epithelial sheets and a bridge between circular and rectangular confinement results. The experimental design is clean and the PIV analysis standard. The model is simple and transparent, and the μ_c sweep is a useful exploration. However, the mechanistic conclusion is currently supported only by the model with a calibrated coupling constant, not by experimental perturbation; the quantitative agreement is loose; and the 'minimal control parameter' claim is not tested at multiple R for the order parameter. With those caveats, the empirical transition sequence is a valuable contribution and the model generates falsifiable predictions about CIL strength, although these predictions are not experimentally tested.

major comments (4)
  1. [Eq. (3) and Fig. 5] The mechanistic claim in the abstract and conclusion ('an appropriate balance between LA and CIL is critical') rests entirely on the SPP model. In Eq. (3), polarity evolution contains only LA and CIL; μ_c=0.5 is selected because it reproduces the observed transition (Results, Fig. 5). The μ_c sweep shows that the output changes with this free parameter, but this is not an independent test: no experimental perturbation of CIL or alignment is performed. The Discussion acknowledges omitted traction, adhesion, and mechanical heterogeneity and leaves open active polar-fluid or active-vertex alternatives. Therefore the data do not distinguish the proposed LA/CIL mechanism from, e.g., the traction-driven density-wave mechanism of refs. 41–43. Either add CIL/alignment perturbation experiments or substantially weaken the causal language.
  2. [Results, 'To complement...' and Figs. 3–4] The claim that the model 'successfully reproduced' the experimental transitions is undermined by quantitative mismatches. The simulated vortex-order-parameter transition occurs at Δ/R≈1.17, whereas the experimental transition is Δ/R≈1.33 (Fig. 4(b) vs Fig. 3(b)). The simulated peak period is ~1000 min (600τ), compared to the measured ~6 h (360 min), and describing this as 'comparable' overstates the agreement. In addition, the experimental order parameter is computed in a 20-μm boundary strip while the simulation uses the whole domain, so the matching values (~0.3) are not directly comparable. These discrepancies need to be addressed or the language needs to be qualified to 'qualitative agreement.'
  3. [Discussion] The critical aspect ratio is quoted inconsistently. The Results and Fig. 3(b) state the experimental vortex-order transition at Δ/R≈1.33; the Discussion states 'approximately Δ/R=1.44 in both the experiment and the simulations' and later 'critical value Δ/R=1.44'; the simulation order-parameter transition is Δ/R≈1.17 while the period peak is at Δ/R≈1.44. The authors should define a single estimation procedure for the transition and period maximum and report consistent values with uncertainties.
  4. [Results, doublet geometry] The phrase 'minimal control parameter governing transitions' is too strong given the data. The order-parameter measurements are shown only for R=150 μm; the period measurements for R=100 and 125 μm are reported but no order-parameter transition for these radii. Because vortex stability in circular confinement depends on R (Fig. 1(i)), the claim that Δ/R alone determines the transition requires testing at multiple R for the order parameter or an explicit scaling argument.
minor comments (5)
  1. [Results, doublet boundary definition] The statement 'Δ/R = cos Ψ' cannot hold for Δ/R>1 (the experiments reach 1.97). Either the angle is misdefined or a factor of 2 is missing. This should be corrected.
  2. [Fig. 1(e)] The text says 'a circular boundary with a diameter of R=150 μm' while elsewhere R is the radius; the l_v/2≈150 μm comparison indicates R=150 μm is the radius. Please correct.
  3. [Numerical simulation] The harmonic-potential boundary term introduced in the Methods is not quantified; its strength is a free parameter that could affect the transition. Please specify it or state that it is a numerical regularization.
  4. [Fig. 2] The ordinate in Fig. 2(e) is denoted k_t^{-1}; define this as the oscillation period and state how peak-to-peak intervals are converted.
  5. [General] Several typographical issues: 'ordered vortex rotation was observed' (Introduction), 'IW AKI' for IWAKI, inconsistent reference bracket spacing. Also the definition of the neighbor set A_i via Voronoi tessellation with a 3σ_r cutoff should be clarified (e.g., are Voronoi neighbors within cutoff only?).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Δ/R transition is an independent experimental finding, and the SPP mechanism study, while parameter-calibrated, is not an equation-level reduction.

full rationale

The central experimental claim—that the doublet aspect ratio Δ/R controls the vortex→oscillatory→disordered transition in MDCK monolayers—is measured directly from time-lapse videos and PIV analysis (Figs. 2–3); it does not depend on any fitted parameter or on a model output. The self-propelled particle model is used as a mechanistic probe rather than as the source of the empirical result. Equation (3) contains local alignment and CIL as interaction terms, and μ_c is varied as a control parameter (0.1, 0.5, 1.0); demonstrating sensitivity to that parameter is a standard model exploration, not a circular reduction. The model does not reproduce the transition by construction: the simulated threshold (Δ/R≈1.17) differs from the measured ≈1.33, and the simulated period (~1000 min) is roughly threefold longer than the measured ~6 h, so the match is qualitative rather than identity. The Discussion explicitly acknowledges that the model omits cell–substrate traction and mechanical heterogeneity and that other frameworks (active polar fluid, active vertex models) might also capture the observed transition; this is a limitation of mechanistic inference, not a logical circle. No load-bearing conclusion rests on a self-citation: refs. 32–34 from the same group are invoked only as an analogy to bacterial vortices, and the model itself is based on a prior, independent agent-based framework. Therefore no circular step satisfies the requirement of an explicit equation-level or fitted-parameter reduction.

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

The model has six effectively free parameters (μ_c, μ_a, v0, Φ, σ_r/U0, boundary stiffness). None is fitted by an optimization, but the main mechanistic conclusion is selected from the μ_c sweep, and the experimental comparison relies on a loose parameter mapping (τ=1.67 min) that yields a period 2.8x the measured value. No new entities are introduced; LA and CIL are inherited from ref 45. The axioms are standard particle-model simplifications, of which the exclusion of traction, adhesion, and mechanics is the most load-bearing given that oscillatory motion in rectangular confinement has been attributed to active-polar-fluid mechanics with traction (refs 41-43).

free parameters (6)
  • CIL coupling μ_c = 0.5 (moderate case); swept 0.1 to 1.0
    The main results use μ_c=0.5 because it reproduces the observed vortex-to-oscillation transition; weaker CIL (0.1) stabilizes counter-rotating vortex pairs and stronger CIL (1.0) destroys vortices. The 'moderate CIL is critical' conclusion is a consequence of this choice.
  • LA coupling μ_a = 0.05
    Fixed by hand in every run; the claimed LA/CIL balance is relative to this fixed value.
  • Self-propulsion speed v0 = 0.05 (dimensionless)
    Set from typical MDCK migration speeds; it sets the kinematic time scale invoked to interpret the period increase as travel time across length Δ.
  • Area fraction Φ = 0.6
    Chosen as a confluent-epithelium proxy; SI checks at 0.4 and 0.8 show sensitivity at 0.4, so the working point matters.
  • Repulsion range σ_r and strength U0 = σ_r=10 μm, U0=60 μm^2/min
    Converted to τ=1.67 min to map dimensionless periods to minutes, giving about 1000 min at the peak versus the measured about 360 min; this mapping is the weakest quantitative link.
  • Boundary harmonic potential strength = not reported
    A harmonic confining potential is added at the boundary to stop particles crossing under compression, but its stiffness is never given; an implicit parameter that affects the effective boundary rigidity.
assumptions (6)
  • domain assumption Overdamped dynamics with no inertia, Eq. (1)
    Position update is first-order in time with an instantaneous polarity; standard at cellular Reynolds numbers but not justified in the text.
  • domain assumption Cell-cell interactions consist only of short-range soft repulsion plus polarity alignment and CIL, Eqs. (2)-(3)
    The central mechanism claim assumes adhesion, nematic coupling, traction, and mechanical heterogeneity are irrelevant; the authors admit the model neglects traction and heterogeneity (Discussion).
  • domain assumption Stochastic noise is neglected
    Stated in Methods ('For simplicity, stochastic noise is neglected'); the disordered phase at large Δ/R must therefore emerge deterministically.
  • domain assumption Voronoi-neighbor interactions with cutoff 3σ_r capture all relevant coupling
    The neighbor set and cutoff are a modeling choice, not derived from cell measurements.
  • domain assumption Fixed area fraction Φ=0.6 as boundary area changes
    Holding Φ fixed while the doublet area grows implies the particle number grows with area, mimicking proliferation to confluence; the experiment does not verify that this equivalence holds in the measured monolayers.
  • domain assumption R=150 μm is the relevant confinement scale because l_v/2 about 150 μm
    The radius is calibrated to the measured velocity correlation length; the authors note the correlation length varies across reported cases, so the phenomenology may shift with this scale.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Boundary-shape driven transitions in vortex and oscillatory dynamics of confined epithelial cells." pith.science (2026). https://pith.science/paper/QNX33O3B

@misc{pith2026250906087,
  author       = {Pith},
  title        = {Pith review of: Boundary-shape driven transitions in vortex and oscillatory dynamics of confined epithelial cells},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QNX33O3B}},
  note         = {Machine review of arXiv:2509.06087}
}
read the original abstract

Controlling the collective motion of epithelial cell populations is fundamental for understanding multicellular self-organization and for advancing tissue engineering. Under spatial confinement, cells are known to exhibit either vortex rotation or oscillatory motion depending on boundary geometry, but the mechanisms governing transitions between these states remain unclear. Here, we investigated the collective motion of MDCK cells confined within a doublet circular boundary, where the confinement aspect ratio, defined as the distance between the centers of two circles relative to their radius, can be tuned by varying the degree of overlap. When the overlap is large, cells form a stable vortex. Increasing the confinement aspect ratio destabilizes this vortex and induces oscillatory motion characterized by periodic reversals of migration direction, before ultimately transitioning into disordered dynamics. To elucidate the underlying mechanism, we developed simulations of self-propelled particles incorporating local alignment (LA) and contact inhibition of locomotion (CIL). The model successfully reproduced the experimentally observed transitions from vortices to oscillatory motion and further revealed that an appropriate balance between LA and CIL is critical for stabilizing vortex pairs with velocity reversals. Our findings demonstrate that the confinement aspect ratio serves as a minimal control parameter governing transitions in the collective dynamics of epithelial monolayers.

Figures

Figures reproduced from arXiv: 2509.06087 by the authors.

Figure 1
Figure 1. Collective motion of MDCK cell populations under flat two-dimensional plane and circular confinement conditions. (a) Schematic illustration of unconfined cells. (b) Collective motion of the MDCK epithelial cell population in the unconfined state. (c) Power spectral density (PSD) of the velocity field of MDCK cells. (d) Temporal correlation of collective motion in unconfined MDCK cells. The solid purple line represen… view at source ↗
Figure 2
Figure 2. Oscillation and velocity reversal in the collective motion of MDCK cells in the doublet circular boundary. (a) Schematic illustration of the confinement geometry in the doublet circular boundary. (b) Oscillatory collective motion of MDCK cells confined in the doublet circular boundary with R = 150 µm and ∆/R = 1.44. Scale bar: 100 µm. The white arrow indicated in the lower left corner stands for the averaged directi… view at source ↗
Figure 3
Figure 3. Transition from vortex rotation to oscillatory motion of MDCK cells in the doublet circular boundary. (a) Vorticity patterns of MDCK cells confined in the doublet circular boundary with R = 150 µm. (b) Geometry-dependent change in the vortex order parameter, |⟨ωb⟩|/⟨|ωb|⟩, where ⟨ωb⟩ is the average vorticity within 20 µm of the boundary. The order parameter shows an abrupt change at approximately ∆/R ≈ 1.33. Small d… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Numerical simulation of confined self-propelled particles under LA and moderate CIL interactions (µc = 0.5). (a) Vorticity patterns of self-propelled particles confined within the doublet circular boundary. The cell area is divided by Voronoi tessellation. Top: velocit…
Figure 5
Figure 5. Figure 5: Numerical simulations under weak CIL (µc = 0.1) and strong CIL (µc = 1.0) condi￾tions. (a) Vorticity patterns of self-propelled particles under weak CIL (µc = 0.1) in the doublet circular boundary. Top: velocity vectors of self-propelled particles; bottom: correspondin…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Blanch-Mercader, C.et al.Turbulent dynamics of epithelial cell cultures.Physical Re- view Letters120,208101 (2018). 16

    work page 2018

  2. [2]

    & Feng, X.-Q

    Lin, S.-Z., Zhang, W.-Y., Bi, D., Li, B. & Feng, X.-Q. Energetics of mesoscale cell turbulence in two-dimensional monolayers.Communications Physics4,21 (2021)

    work page 2021

  3. [3]

    Brugu´ es, A.et al.Forces driving epithelial wound healing.Nature Physics10,683–690 (2014)

    work page 2014

  4. [4]

    & Levine, H

    Basan, M., Elgeti, J., Hannezo, E., Rappel, W.-J. & Levine, H. Alignment of cellular motility forces with tissue flow as a mechanism for efficient wound healing.Proceedings of the National Academy of Sciences110,2452–2459 (2013)

    work page 2013

  5. [5]

    Developmental Cell43,305–317 (2017)

    Aoki, K.et al.Propagating wave of ERK activation orients collective cell migration. Developmental Cell43,305–317 (2017)

    work page 2017

  6. [6]

    & Trepat, X

    Alert, R. & Trepat, X. Physical models of collective cell migration.Annual Review of Condensed Matter Physics11,77–101 (2020)

    work page 2020

  7. [7]

    & Joanny, J.-F

    Alert, R., Casademunt, J. & Joanny, J.-F. Active turbulence.Annual Review of Con- densed Matter Physics13,143–170 (2022)

    work page 2022

  8. [8]

    The mechanics and statistics of active matter.Annu

    Ramaswamy, S. The mechanics and statistics of active matter.Annu. Rev. Condens. Matter Phys.1,323–345 (2010)

    work page 2010

Show all 47 references
  1. [9]

    C.et al.Hydrodynamics of soft active matter.Reviews of Modern Physics 85,1143 (2013)

    Marchetti, M. C.et al.Hydrodynamics of soft active matter.Reviews of Modern Physics 85,1143 (2013)

    2013

  2. [10]

    H.et al.Meso-scale turbulence in living fluids.Proceedings of the National Academy of Sciences109,14308–14313 (2012)

    Wensink, H. H.et al.Meso-scale turbulence in living fluids.Proceedings of the National Academy of Sciences109,14308–14313 (2012)

    2012

  3. [11]

    Dunkel, J.et al.Fluid dynamics of bacterial turbulence.Physical Review Letters110, 228102 (2013)

    2013

  4. [12]

    & Dogic, Z

    Needleman, D. & Dogic, Z. Active matter at the interface between materials science and cell biology.Nature Reviews Materials2,1–14 (2017)

    2017

  5. [13]

    T., DeCamp, S

    Sanchez, T., Chen, D. T., DeCamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter.Nature491,431–434 (2012)

    2012

  6. [14]

    J.et al.Topological chaos in active nematics.Nature Physics15,1033–1039 (2019)

    Tan, A. J.et al.Topological chaos in active nematics.Nature Physics15,1033–1039 (2019). 17

    2019

  7. [15]

    Vedula, S. R. K.et al.Emerging modes of collective cell migration induced by geomet- rical constraints.Proceedings of the National Academy of Sciences109,12974–12979 (2012)

    2012

  8. [16]

    G., Duclos, G

    Deforet, M., Hakim, V., Yevick, H. G., Duclos, G. & Silberzan, P. Emergence of col- lective modes and tri-dimensional structures from epithelial confinement.Nature Com- munications5,3747 (2014)

    2014

  9. [17]

    & Silberzan, P

    Duclos, G., Erlenk¨ amper, C., Joanny, J.-F. & Silberzan, P. Topological defects in con- fined populations of spindle-shaped cells.Nature Physics13,58–62 (2017)

    2017

  10. [18]

    Duclos, G.et al.Spontaneous shear flow in confined cellular nematics.Nature Physics 14,728–732 (2018)

    2018

  11. [19]

    & Bonnet, I

    Pricoupenko, N., Marsigliesi, F., Marcq, P., Blanch-Mercader, C. & Bonnet, I. Src kinase slows collective rotation of confined epithelial cell monolayers.Soft Matter20, 9273–9285 (2024)

    2024

  12. [20]

    J., Th¨ uroff, F., Piera Alberola, A., Frey, E

    Segerer, F. J., Th¨ uroff, F., Piera Alberola, A., Frey, E. & R¨ adler, J. O. Emergence and persistence of collective cell migration on small circular micropatterns.Physical Review Letters114,228102 (2015)

    2015

  13. [21]

    Yu, J.et al.Spatiotemporal oscillation in confined epithelial motion upon fluid-to-solid transition.ACS Nano15,7618–7627 (2021)

    2021

  14. [22]

    G., Duclos, G., Bonnet, I

    Yevick, H. G., Duclos, G., Bonnet, I. & Silberzan, P. Architecture and migration of an epithelium on a cylindrical wire.Proceedings of the National Academy of Sciences112, 5944–5949 (2015)

    2015

  15. [23]

    Rupprecht, J.-F.et al.Geometric constraints alter cell arrangements within curved epithelial tissues.Molecular Biology of the Cell28,3582–3594 (2017)

    2017

  16. [24]

    & Teck Lim, C

    Xi, W., Sonam, S., Beng Saw, T., Ladoux, B. & Teck Lim, C. Emergent patterns of collective cell migration under tubular confinement.Nature Communications8,1517 (2017)

    2017

  17. [25]

    Shigeta, K.et al.Collective motion of epithelial cells along a wrinkled 3D-buckled hydrogel.RSC Advances12,20174–20181 (2022). 18

    2022

  18. [26]

    & Roux, A

    Guillamat, P., Blanch-Mercader, C., Pernollet, G., Kruse, K. & Roux, A. Integer topo- logical defects organize stresses driving tissue morphogenesis.Nature Materials21, 588–597 (2022)

    2022

  19. [27]

    & H´ enon, S

    Harmand, N., Huang, A. & H´ enon, S. 3D shape of epithelial cells on curved substrates. Physical Review X11,031028 (2021)

    2021

  20. [28]

    Latorre, E.et al.Active superelasticity in three-dimensional epithelia of controlled shape.Nature563,203–208 (2018)

    2018

  21. [29]

    & Maeda, Y

    Ienaga, R., Beppu, K. & Maeda, Y. T. Geometric confinement guides topological defect pairings and emergent flow in nematic cell populations.Soft Matter19,5016–5028 (2023)

    2023

  22. [30]

    G., Dunkel, J., Kessler, J

    Wioland, H., Woodhouse, F. G., Dunkel, J., Kessler, J. O. & Goldstein, R. E. Con- finement stabilizes a bacterial suspension into a spiral vortex.Physical Review Letters 110,268102 (2013)

    2013

  23. [31]

    G., Dunkel, J

    Wioland, H., Woodhouse, F. G., Dunkel, J. & Goldstein, R. E. Ferromagnetic and antiferromagnetic order in bacterial vortex lattices.Nature Physics12,341–345 (2016)

    2016

  24. [32]

    Beppu, K.et al.Geometry-driven collective ordering of bacterial vortices.Soft Matter 13,5038–5043 (2017)

    2017

  25. [33]

    Proceedings of the National Academy of Sciences118,e2107461118 (2021)

    Beppu, K.et al.Edge current and pairing order transition in chiral bacterial vortices. Proceedings of the National Academy of Sciences118,e2107461118 (2021)

    2021

  26. [34]

    & Maeda, Y

    Beppu, K., Matsuura, K. & Maeda, Y. T. Geometric frustration and pairing-order transition in confined bacterial vortices.Physical Review Research6,033166 (2024)

    2024

  27. [35]

    S., Snezhko, A

    Nishiguchi, D., Aranson, I. S., Snezhko, A. & Sokolov, A. Engineering bacterial vortex lattice via direct laser lithography.Nature Communications9,4486 (2018)

    2018

  28. [36]

    Wu, K.-T.et al.Transition from turbulent to coherent flows in confined three-dimensional active fluids.Science355,eaal1979 (2017)

    2017

  29. [37]

    Opathalage, A.et al.Self-organized dynamics and the transition to turbulence of con- fined active nematics.Proceedings of the National Academy of Sciences116,4788–4797 (2019). 19

    2019

  30. [38]

    Hardo¨ uin, J.et al.Reconfigurable flows and defect landscape of confined active nemat- ics.Communications Physics2,121 (2019)

    2019

  31. [39]

    Araki, S., Beppu, K., Kabir, A. M. R., Kakugo, A. & Maeda, Y. T. Controlling collective motion of kinesin-driven microtubules via patterning of topographic landscapes.Nano Letters21,10478–10485 (2021)

    2021

  32. [40]

    Hardo¨ uin, J.et al.Active boundary layers in confined active nematics.Nature Com- munications13,6675 (2022)

    2022

  33. [41]

    Petrolli, V.et al.Confinement-induced transition between wavelike collective cell mi- gration modes.Physical Review Letters122,168101 (2019)

    2019

  34. [42]

    Peyret, G.et al.Sustained oscillations of epithelial cell sheets.Biophysical Journal117, 464–478 (2019)

    2019

  35. [43]

    P., Pruitt, B

    Parmar, T., Dow, L. P., Pruitt, B. L. & Marchetti, M. C. Spontaneous and Induced Oscillations in Confined Epithelia.PRX Life3,013002 (1 Jan. 2025)

    2025

  36. [44]

    & Jacob, E

    Grossman, D., Aranson, I. & Jacob, E. B. Emergence of agent swarm migration and vortex formation through inelastic collisions.New Journal of Physics10,023036 (2008)

    2008

  37. [45]

    & Feng, X.-Q

    Lin, S.-Z., Ye, S., Xu, G.-K., Li, B. & Feng, X.-Q. Dynamic migration modes of collective cells.Biophysical Journal115,1826–1835 (2018)

    2018

  38. [46]

    & Lin, Y

    Fang, C., Yao, J., Zhang, Y. & Lin, Y. Active chemo-mechanical feedbacks dictate the collective migration of cells on patterned surfaces.Biophysical Journal121,1266–1275 (2022)

    2022

  39. [47]

    L., Henkes, S., Weijer, C

    Barton, D. L., Henkes, S., Weijer, C. J. & Sknepnek, R. Active vertex model for cell- resolution description of epithelial tissue mechanics.PLoS Computational Biology13, e1005569 (2017). 20 Figure 1:Collective motion of MDCK cell populations under flat two-dimensional plane an...

    2017

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.