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REVIEW 3 major objections 5 minor 45 references

Amoeboid swimming of active vesicles

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read A vesicle's mean swimming speed equals the winding of its shape cycle in shape space: two shape modes need a forcing threshold, while a third mode gives motion at arbitrarily weak activity.

desk verdict A solid quasi-spherical framework with a clean geometric picture, but the marquee 'arbitrarily small activity' propulsion claim is asserted, not proven, and most quantitative punchlines are deferred to a companion paper. read the letter →

arxiv 2607.14714 v1 pith:OE5NLHN3 submitted 2026-07-16 cond-mat.soft physics.bio-phphysics.flu-dyn

Reiner Kree , Annette Zippelius This is my paper · ORCID
classification cond-mat.softphysics.bio-phphysics.flu-dyn
keywords activevesiclesamoeboidswimmingshapedynamicsmembraneinextensibilitylowReynoldsnumberStokesflowwindingsynchronization
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 studies how a nearly spherical, weakly deflated vesicle swims when active tractions drive its membrane shapes. Because the membrane is locally inextensible, rigid-body translation is suppressed, so migration must come from time-dependent shape changes. The authors show that what matters is whether the deformation cycle encloses a nonzero area in shape space: with only two shape modes, the cycle is confined to a circle, so below a critical forcing the vesicle oscillates in place and the time-averaged speed is zero, while above threshold the cycle winds and the vesicle swims at a speed proportional to its winding number. With a third mode, the dynamics lives on a sphere where even infinitesimal activity produces an area-enclosing cycle and hence finite propulsion. This provides a generic, mechanism-independent route from active tractions arising in the membrane or cortex to autonomous amoeboid swimming.

What carries the argument

The central object is the reduced shape-space trajectory of rescaled deformation amplitudes q_l = f_l sqrt(w_l/Δ). The constant-area constraint forces these amplitudes onto the unit circle (two modes) or unit sphere (three modes). The swimming velocity is an antisymmetric product of neighboring modes, so its cycle average equals C̃2 times the enclosed area. The lifted phase Φ records the cumulative angular progress around the shape space, and its long-time slope defines the winding number ρ = ΔΦ/(2π). The mean swimming speed is then exactly C̃2 ω ρ, reducing the propulsion problem to the synchronization dynamics of a driven phase oscillator, including fixed points of a stroboscopic map, crit

What would settle it

Track a single vesicle's centroid and low-order shape modes simultaneously while driving at fixed frequency and slowly increasing the forcing amplitude: two-mode driving should show zero net drift until a critical amplitude, then a square-root onset, while three-mode driving should show finite drift from the smallest amplitude. Observing finite drift in the two-mode case at any amplitude, or zero drift in the three-mode case at weak forcing, would contradict the central claim.

Watch

Extended reading notes

Core claim

For a force-free vesicle with a locally inextensible membrane, autonomous swimming is generated by non-reciprocal shape deformations. In the quasi-spherical expansion, the propulsion velocity is a sum of antisymmetric products of neighboring deformation modes, so its cycle average is determined by the area enclosed by the trajectory in shape space. Restricting to two adjacent axisymmetric modes, the constant-area constraint confines the dynamics to a circle; weak periodic forcing produces only bounded oscillations with zero net propulsion, while strong forcing makes the phase wind around the circle, giving a long-time mean speed <U> = C̃2 ω ρ, where ρ is the winding number of the lifted phas

Load-bearing premise

The two-mode versus three-mode dichotomy rests on truncating the shape to two or three low-order axisymmetric Legendre modes, with the constant-area constraint as the only nonlinearity; if higher or non-axisymmetric modes couple in at the same order, or if the viscosity contrast differs strongly from unity, the reduced phase-space structure and its thresholds could change qualitatively.

Editorial extensions

If this is right

  • Two-mode driving yields a genuine threshold: below a critical forcing the vesicle oscillates in place with zero net displacement, and above it the mean speed grows continuously with a square-root singularity while phase-slip bursts generate intermittent propulsion.
  • Three-mode driving gives threshold-free propulsion: even arbitrarily small activity produces a periodic, area-enclosing deformation cycle and a finite swimming speed.
  • The mean swimming speed is proportional to the driving frequency times the winding number of the shape cycle, so synchronization plateaus in the winding number translate into plateaus and local extrema in the speed versus frequency curve.
  • A spherical, inextensible vesicle driven by l = 1 tractions does not swim; the polar traction is exactly balanced by the tension field, so shape deformations with l ≥ 2 are essential for autonomous motion.
  • Estimated swimming speeds from the model, 10⁻³ to 10⁻¹ µm/s, fall in the range measured for freely swimming amoeboid cells, supporting the relevance of shape-only swimming mechanisms.

Reading between the lines

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

  • If the winding-number mechanism is generic, cells or synthetic vesicles that actively excite at least three shape modes in the relevant subspace should swim even with very weak activity; an observed threshold would indicate an effectively two-dimensional deformation subspace.
  • The Arnold-tongue structure implies that swimming speed need not be monotonic in driving frequency; local maxima at synchronization plateaus could be directly tested in experiments that vary frequency while holding forcing strength fixed.
  • Extending to non-axisymmetric spherical harmonics would enlarge the shape space and likely permit turning and helical trajectories; the area-enclosure criterion should generalize to closed loops in the larger manifold.
  • Near the two-mode threshold the model predicts a diverging residence time τ* ∝ (s − s*)^(−1/2); stroboscopic shape tracking could reveal this critical slowing down as intermittent bursts of propulsion between long quasi-stationary intervals.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The manuscript studies a nearly spherical, weakly deflated vesicle in Stokes flow, driven by periodic active tractions representing cortex or membrane activity. It derives the coupled shape-dynamics equations from membrane force balance and the constant-area constraint (Eqs. 15-17), reduces the two-mode driving case to a one-dimensional phase dynamics on a circle (Eq. D46), and the three-mode case to motion on a sphere. The central claims are that two-mode driving produces net propulsion only above a critical forcing strength, with a square-root divergence of the residence time at the transition, while three-mode driving produces finite propulsion for arbitrarily small activity. The mean swimming speed is related to a winding number, <U> = C̃2 ω ϱ (Eq. 26), and Arnold-tongue-like synchronization plateaus are reported numerically. The paper closes with order-of-magnitude estimates comparing the predicted swimming speeds to those observed for amoeboid cells.

Significance. If the two-mode/three-mode dichotomy survives, the paper identifies a simple design principle: in a low-dimensional shape space, net swimming requires a non-reciprocal cycle that encloses finite area, and adding a third mode removes the threshold for such cycles. This would be a useful and generic contribution to the theory of amoeboid swimming by active vesicles. The derivation of the shape-dynamics equations and the reduction to the phase equation are transparent and mechanically consistent, and the winding-number representation of the mean speed is elegant and practically useful. The comparison with experimental time and force scales gives concrete, falsifiable estimates. However, the two sharpest quantitative claims — the absence of a threshold for three-mode driving and the critical exponent for two-mode driving — are not proven in the manuscript, and the truncation to a few Legendre modes is the main unresolved caveat.

major comments (3)
  1. [Sec. 4.2, Eq. (27)] The statement that 'three-mode driving gives rise to finite propulsion even for arbitrarily small activity' is asserted without a supporting calculation. A direct small-s expansion is available: around the stable fixed point q2=1, the area constraint forces q2=1+O(s^2), while q3 and q4 satisfy, to leading order, decoupled damped-driven linear equations. The time average of the (3,4) contribution in Eq. (8) is then generically O(s^2) and nonzero if the damping rates and the forcing phases differ. The authors should either present this expansion or show numerically that <U>/s^2 tends to a nonzero constant as s→0. Without this, the central two-mode/three-mode dichotomy is not established.
  2. [Sec. 4.1, Fig. 4 and text near Eq. (24)] The quantitative claims τ* ∼ (s-s*)^(-1/2) and the square-root increase of the mean swimming velocity above threshold are attributed to Ref. [34], an unpublished preprint. If these are intended as results of the present paper, a derivation should be included; if they are imported from [34], the text should clearly mark them as external results. The current sentence 'A detailed analysis shows [34]' is insufficient for a headline quantitative prediction, especially since Fig. 4 shows only a single parameter set and no extraction of the exponent.
  3. [Secs. 4.1-4.2 and Outlook] The sharp threshold/no-threshold dichotomy is a property of the finite-dimensional truncation to l=2,3 or l=2,3,4, with the constant-area constraint as the only nonlinearity. The Outlook acknowledges higher modes and non-axisymmetric deformations, but the abstract and Section 4 present the dichotomy without that caveat. I recommend stating explicitly that the two-mode/three-mode contrast is a result within this truncation, and adding a brief estimate of the corrections from omitted O(f^2) force-balance terms or higher Legendre modes, to show that they do not restore a threshold at the same order.
minor comments (5)
  1. [Appendix D, after Eq. (D46)] The text says 'Recalling the scaling, Z_l ∝ F_l/√Δ, we see that the effective forcing strength is s/Δ.' From the definition of Z_l this should be s/√Δ, i.e. the parameter called ~tilde s in Section 4.1. Please correct this apparent typo.
  2. [Figure captions 1-4 and 6] The symbol ~hat s is used in the captions but never defined. Please clarify its relation to s and ~tilde s = s/√Δ. Also specify the viscosity contrast λ and the spontaneous-curvature value C0 used in the numerics; the text sets C0=2 but the figure captions do not state λ.
  3. [Abstract and Section 2.1] The phrase 'local membrane incompressibility suppresses rigid-body translation' could be misread. The precise statement, from Appendix A, is that a force-free spherical vesicle cannot translate: the l=1 force balance gives U=0 when the total active force vanishes. Please rephrase to avoid implying that shape-changing vesicles cannot translate.
  4. [Eq. (21)] The notation U(τ) for the time-averaged speed over an interval τ is easily confused with the instantaneous speed U(t). Consider writing <U>_τ or ~bar U.
  5. [Appendix A, Eqs. (A19)-(A25)] The propulsion law Eq. (8) is quoted from Ref. [27] without derivation. A one-sentence statement of the perturbation order and the assumptions (small excess area, axisymmetry, viscosity contrast) would make the paper more self-contained.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the shape-dynamics derivation is self-contained, and the imported propulsion law is a parameter-free kinematic result with independent citation.

full rationale

The paper's central derivation—active tractions to shape dynamics to propulsion—does not reduce to its inputs by construction. The shape evolution equation (17) is derived within the paper from membrane force balance (Appendix B) and the Helfrich variation (Appendix C), with the constant-area constraint enforced by Eq. (18). The propulsion law (8) is imported from the authors' prior work [27], but it is a parameter-free kinematic relation, reproduced with explicit coefficients in Appendix A and also supported by citations to Lighthill [28] and Farutin et al. [23]; it does not itself contain the two-mode/three-mode distinction or the winding-number result. The mean-speed formula (26), <U> = C̃2 ω ρ, follows algebraically from Eq. (8) and the definition of the winding number, not from any fitted parameter. Deferrals to the companion paper [34] concern detailed analysis of Arnold tongues, the critical exponent, and the C0 ≠ 2 case; these are extensions, not load-bearing imports. The three-mode 'arbitrarily small activity' claim in Sec. 4.2 is asserted without an explicit small-forcing expansion, and the two-mode threshold is established only within the low-mode truncation—but missing proof or acknowledged truncation is a correctness/rigor concern, not circularity. No step in the derivation is equivalent by definition to the result it is used to predict.

Assumptions & free parameters 7 free parameters · 10 assumptions · 0 invented entities

The paper introduces no new physical entities such as particles, forces, or dimensions beyond standard effective active tractions (cortex and membrane) already common in the field. The central claims rest instead on the low-mode truncation, the small-excess-area expansion, the constant-area constraint as the only nonlinearity, and the implicit numerical choice lambda=1.

free parameters (7)
  • excess area Delta = small (expansion parameter); not numerically specified
    Defines the small parameter epsilon ~ sqrt(Delta); deformations scale as f ~ epsilon. Central to the perturbation expansion and to the rescaled variables q_l = f_l sqrt(w_l/Delta).
  • driving strength s (or s-tilde = s/sqrt(Delta)) = scanned: 5 sqrt(40), 7.75 sqrt(40), 10 sqrt(40), 11 sqrt(40)
    Chosen by hand to illustrate non-propelling, transitional, and propelling regimes; not fitted to data.
  • driving frequency omega = 1.48 in most figures; scanned in Fig. 5
    Control parameter for synchronization plateaus and Arnold tongues; chosen by hand.
  • relative amplitude alpha (two-mode) and alpha_3, alpha_4 (three-mode) = two-mode: 5/sqrt(14); three-mode: sqrt(7/2), sqrt(63/10)
    Chosen by hand to define the illustrative driving scenarios.
  • relative phases delta (two-mode) and delta_3, delta_4 (three-mode) = two-mode: 0.6 pi; three-mode: 1.55, 1.0
    Chosen by hand; phase lags are essential for non-reciprocal shape cycles.
  • viscosity contrast lambda = not stated; implicitly 1 in numerical figures
    Appears in N_l and T_l (Appendix B, Eqs. B30-B31) but is never listed in the figure parameters. This is an unflagged assumption in the numerics.
  • spontaneous curvature C0 = set to 2 (dimensionless, a=1)
    Choice of homogeneous spontaneous curvature equal to the sphere curvature; general C0 != 2 is deferred to companion paper [34].
assumptions (10)
  • standard math Stokes flow at low Reynolds number (Eq. 1)
    Governing fluid equations inside and outside the vesicle; standard for microswimmer theory.
  • domain assumption Local membrane inextensibility: div_S v = 0 (Eq. 3) and constant volume
    Physical model of a lipid membrane; suppresses rigid-body translation for force-free vesicles and generates the area constraint.
  • domain assumption Small excess area: epsilon ~ sqrt(Delta), f ~ epsilon; force balance linearized in f
    Perturbation expansion about a sphere; the propulsion velocity is second order in f while shape dynamics is linear in f plus the quadratic area constraint.
  • ad hoc to paper Axisymmetric deformations truncated to l = 2,3 or 2,3,4 Legendre modes
    The two- and three-mode shape spaces (circle and sphere) are artificial truncations; the paper explicitly acknowledges that general spherical harmonics would allow turning and other motions.
  • domain assumption Total active force vanishes for an autonomous system (Eq. 10)
    Physical requirement that no external force acts on the swimmer; leads to U=0 at linear order.
  • ad hoc to paper Active tractions modeled as harmonic driving with chosen amplitudes and phases (Eqs. 19, 27)
    The microscopic origin of the tractions is not derived; sinusoidal driving is chosen for illustration.
  • domain assumption Propulsion coefficients C_l, B_l taken from Ref. [27]
    Eq. (8) and Appendix A import the propulsion law from the authors' earlier work; not re-derived here.
  • domain assumption Gaussian curvature neglected
    Justified by no topological changes and homogeneous Gaussian bending modulus; standard in vesicle elasticity.
  • domain assumption No feedback from swimming flow onto shape dynamics at leading order
    The propulsion velocity U does not enter the l>=2 deformation equations in the quasi-spherical expansion; shape and migration are effectively one-way coupled.
  • ad hoc to paper Viscosity contrast lambda is taken equal to 1 in numerics
    Not stated in the parameter lists; N_l and T_l depend on lambda, so the figures implicitly assume lambda=1.

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Cite this review

Pith. "Pith review of Amoeboid swimming of active vesicles." pith.science (2026). https://pith.science/paper/OE5NLHN3

@misc{pith2026260714714,
  author       = {Pith},
  title        = {Pith review of: Amoeboid swimming of active vesicles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OE5NLHN3}},
  note         = {Machine review of arXiv:2607.14714}
}
read the original abstract

We investigate the shape dynamics and migration of weakly deflated active vesicles driven by processes acting either directly in the membrane or transmitted by the cytoskeleton. For a force-free vesicle, local membrane incompressibility suppresses rigid-body translation, so that migration arises from time-dependent shape deformations. Assuming small excess area enables a systematic analysis of the coupled deformation and migration dynamics in free space, i.e. in the absence of substrate adhesion or confinement. Depending on the strength and frequency of the activity, the vesicle exhibits several dynamical regimes, including synchronized oscillations, quasiperiodic shape changes, transitions between non-propelling and propelling states, and intermittent motion.

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Works this paper leans on

45 extracted references · 17 canonical work pages

  1. [34]

    preprint (2026)

    Kree, R., Zippelius, A.: Shape dynamics and self-propulsion of area-preserving vesi- cles. preprint (2026)

    2026

  2. [1]

    Wiley Interdiscip Rev Comput Mol Sci.9, 1 (2019)

    Othmer, H.G.: Eukaryotic cell dynamics from crawling to swimming. Wiley Interdiscip Rev Comput Mol Sci.9, 1 (2019)

    2019

  3. [2]

    Paluch, E.K., Aspalter, I.M., Sixt, M.: Focal adhesion-independent cell migration. Annu. Rev. Cell Dev. Biol.32, 469 (2016)

    2016

  4. [3]

    Bergert, M., Erzberger, A., Desai, R.A., Aspalter, I.M., Oates, A.C., Charras, G., Sal- breux, G., Paluch, E.K.: Force transmission during adhesion-independent migration. Nat. cell Biol.17, 524 (2015)

    2015

  5. [4]

    Frontiers in cell and and devel- opmental biology10(2022) https://doi.org/ 10.3389/fcell.2022.1000071

    Callen-Jones, A.: Self-organization in amoe- boid motility. Frontiers in cell and and devel- opmental biology10(2022) https://doi.org/ 10.3389/fcell.2022.1000071

    arXiv 2022

  6. [5]

    Nature physics15, 496– 502 (2019)

    Noselli, G., Beran, A., Arroyo, M., DeSimone, A.: Swimming euglena respond to confine- ment with a behavioural change enabling effective crawling. Nature physics15, 496– 502 (2019)

    2019

  7. [6]

    Biology of the Cell113(1), 28–38 https://doi.org/10.1111/boc.202000084

    Garcia-Seyda, N., Seveau, V., Manca, F., Biarnes-Pelicot, M., Valignat, M.- P., Baj´ enoff, M., Theodoly, O.: Human 14 neutrophils swim and phagocytise bac- teria. Biology of the Cell113(1), 28–38 https://doi.org/10.1111/boc.202000084

    work page doi:10.1111/boc.202000084

  8. [7]

    PNAS107, 11376 (2010)

    Barry, N.P., Bretscher, M.S.: Dictyostelium amoeba and neutophils can swim. PNAS107, 11376 (2010)

    2010

Show all 45 references
  1. [8]

    Develop- mental Cell46(1), 9–224 (2018) https: //doi.org/10.1016/j.devcel.2018.05.029

    O’Neill, P.R., Castillo-Badillo, J.A., Meshik, X., Kalyanaraman, V., Mel- garejo, K., Gautam, N.: Membrane flow drives an adhesion-independent amoeboid cell migration mode. Develop- mental Cell46(1), 9–224 (2018) https: //doi.org/10.1016/j.devcel.2018.05.029

    2018 doi

  2. [9]

    PNAS107, 165 (2010)

    Bae, A.J., Bodenschatz, E.: On the swim- ming of dictyostelium amoeba. PNAS107, 165 (2010)

    2010

  3. [10]

    Biophysical Journal119(6), 1157–1177 (2020) https:// doi.org/10.1016/j.bpj.2020.07.033

    Aoun, L., Farutin, A., Garcia-Seyda, N., N` egre, P., Rizvi, M.S., Tlili, S., Song, S., Luo, X., Biarnes-Pelicot, M., Galland, R., Sibarita, J.-B., Michelot, A., Hivroz, C., Rafai, S., Valignat, M.-P., Misbah, C., Theodoly, O.: Amoeboid swimming is propelled by molec- ular pad...

    2020 doi

  4. [11]

    Andrieu, C., Lee, B.H., Franz, A.: Cell defor- mations generated by stochastic actomyosin waves in vivo random-walk swimming migra- tion

  5. [12]

    Nature438, 590 (2005)

    McMahon, H.T., Gallop, J.L.: Membrane curvature and mechanisms of dynamics cell membrane remodelling. Nature438, 590 (2005)

    2005

  6. [13]

    Dimova, R.: Recent developments in the field of bending rigidity measuerments of mem- branes. Adv. Colloid and Interface Science 208, 225 (2014)

    2014

  7. [14]

    Lang- muir33, 4083–4089 (2017) https: //doi.org/10.1021/acs.langmuir.7b01020

    Pernpeintner, C., Frank, J.A., Lohm¨ uller, T.,et al.: Light-controlled membrane mechanics and shape transitions of photoswitchable lipid vesicles. Lang- muir33, 4083–4089 (2017) https: //doi.org/10.1021/acs.langmuir.7b01020

    2017 doi

  8. [15]

    Communica- tions Materials6:59(2025) https://doi.org/ 10.1038/s43246-025-00773-8

    Pritzl, S.D., Morstein, J., Pritzl, N.A., Lipfert, J., Lohm¨ uller, T., Trauner, D.H.: Photoswitchable phospholipids for the opti- cal control of membrane processes, protein function, and drug delivery. Communica- tions Materials6:59(2025) https://doi.org/ 10.1038/s43246-025-00773-8

    2025 doi

  9. [16]

    Ange- wandte Chemie International Edition57(6), 1621–1626 (2018) https://doi.org/10.1002/ anie.201710374

    Litschel, T., Ramm, B., Maas, R., Hey- mann, M., Schwille, P.: Beating vesi- cles: Encapsulated protein oscillations cause dynamic membrane deformations. Ange- wandte Chemie International Edition57(6), 1621–1626 (2018) https://doi.org/10.1002/ anie.201710374

    2018

  10. [17]

    Soft Matter17, 319–330 (2021) https://doi.org/10.1039/D0SM00790K

    Christ, S., Litschel, T., Schwille, P., Lipowsky, R.: Active shape oscilla- tions of giant vesicles with cyclic closure and opening of membrane necks. Soft Matter17, 319–330 (2021) https://doi.org/10.1039/D0SM00790K

    2021 doi

  11. [18]

    ACS Synthetic Biology9(4), 893–901 (2020) https: //doi.org/10.1021/acssynbio.9b00516

    Jones, T.I., Liu, A., Cui, B.: Light-inducible generation of membrane curvature in live cells with engineered bar domain proteins. ACS Synthetic Biology9(4), 893–901 (2020) https: //doi.org/10.1021/acssynbio.9b00516

    2020 doi

  12. [19]

    Scientific reports6:34146(2016) https://doi.org/10.1038/srep34146

    Paoluzzi, M., Di Leonardo, R., Marchetti, M.C., Angelani, L.: Shape and displacement fluctuations in soft vesicles filled by active particles. Scientific reports6:34146(2016) https://doi.org/10.1038/srep34146

    2016 doi

  13. [20]

    Chinese Physics B26, 100502 (2017)

    Tian, W.-d., Gu, Y., Guo, Y.-K., Chen, K.: Anomolous boundary deformation induced by enclosed active particles. Chinese Physics B26, 100502 (2017)

    2017

  14. [21]

    New Journal of Physics21, 123024 (2019) https: //doi.org/10.1088/1367-2630/ab5c70

    Abaurrea-Velasco, C., Auth, T., Gomp- per, G.: Vesicles with internal active fil- aments: Self-organized propulsion controls shape, motility, and dynamical response. New Journal of Physics21, 123024 (2019) https: //doi.org/10.1088/1367-2630/ab5c70

    2019 doi

  15. [22]

    Soft Matter18(36), 6868–6881 (2022) https://doi.org/10.1039/ D2SM00622G 15

    Iyer, P., Gompper, G., Fedosov, D.A.: Non-equilibrium shapes and dynamics of active vesicles. Soft Matter18(36), 6868–6881 (2022) https://doi.org/10.1039/ D2SM00622G 15

    2022

  16. [23]

    Farutin, A., Rafai, S., Dysthe, D.K., Duper- ray, A., Peyla, P., Misbah, C.: Amoeboid swimming: A generic self-propulsion of cells in fluids by means of membrane deformations. Phys. Rev. Lett.111, 228102 (2013)

    2013

  17. [24]

    Computer Methods in Biome- chanics and Biomedical Engineering16(10), 1085–1095 (2013) https://doi.org/10.1080/ 10255842.2012.757598

    Lim, F.Y., Koon, Y.L., Chiam, K.-H.: A computational model of amoeboid cell migration. Computer Methods in Biome- chanics and Biomedical Engineering16(10), 1085–1095 (2013) https://doi.org/10.1080/ 10255842.2012.757598

    2013

  18. [25]

    Physics of Fluids29(10), 101902 (2017) https://doi

    Campbell, E.J., Bagchi, P.: A computational model of amoeboid cell swimming. Physics of Fluids29(10), 101902 (2017) https://doi. org/10.1063/1.4990543

    2017 doi

  19. [26]

    PLOS ONE15(1), 0227562 (2020) https: //doi.org/10.1371/journal.pone.0227562

    Barrio, R.A., Alarcon, T., Hernandez- Machado, A.: The dynamics of shapes of vesicle membranes with time depen- dent spontaneous curvature. PLOS ONE15(1), 0227562 (2020) https: //doi.org/10.1371/journal.pone.0227562

    2020 doi

  20. [27]

    Soft Matter21, 4241–4255 (2025) https://doi.org/10.1039/ D4SM01504E

    Kree, R., Zippelius, A.: Amoeboid propul- sion of active solid bodies, vesicles and droplets: A comparison. Soft Matter21, 4241–4255 (2025) https://doi.org/10.1039/ D4SM01504E

    2025

  21. [28]

    Lighthill, M.J.: On the squirming motion of nearly spherical deformable bodies through liquids at very small reynolds numbers. Comm. Pure Appl. Math.5, 109 (1952)

    1952

  22. [29]

    Current oppinion in biotechnology23, 758– 765 (2012)

    Vogel, S.K., Schwille, P.: Minimal systems to study membrane-cytoskeleton interactions. Current oppinion in biotechnology23, 758– 765 (2012)

    2012

  23. [30]

    Callen-Jones, A.C., Ruprecht, V., Wieser, S., Heisenberg, C.P., Voituriez, R.: Critical flow- driven shapes of nonadherent cells. Phys. Rev. Lett.116, 028102 (2016)

    2016

  24. [31]

    Soft matter9, 2308 (2013)

    Holderer, O., Frielinghaus, H., Monkenbusch, M., Klostermann, M., Sottmann, T., Richter, D.: Experimental determination of bending modulus and saddle splay modulus in bicon- tinuous microemulsions. Soft matter9, 2308 (2013)

    2013

  25. [32]

    Biophysical Journal102(6), 1403–1410 (2012) https:// doi.org/10.1016/j.bpj.2012.02.013

    Hu, M., Briguglio, J.J., Deserno, M.: Deter- mining the gaussian curvature modulus of lipid membranes in simulations. Biophysical Journal102(6), 1403–1410 (2012) https:// doi.org/10.1016/j.bpj.2012.02.013

    2012 doi

  26. [33]

    Holderer, F.: Direct evaluation of the sad- dle splay modulus of a liquid-liquid interface using the classical mean field lattice model. J. Chem. Physics138, 124103 (2013)

    2013

  27. [35]

    Proceedings of the National Academy of Sciences101(26), 9660–9665 (2004) https://doi.org/10.1073/ pnas.0300552101

    Vallotton, P., Gupton, S.L., Waterman- Storer, C.M., Danuser, G.: Simultaneous mapping of filamentous actin flow and turnover in migrating cells by quantitative fluorescent speckle microscopy. Proceedings of the National Academy of Sciences101(26), 9660–9665 (2004) https://doi...

    2004

  28. [36]

    Annu Rev Biophys.39, 449–470 (2010) https://doi.org/ 10.1146/annurev-biophys-051309-103849

    Bugyi, B., Carlier, M.-F.: Control of actin fil- ament treadmilling in cell motility. Annu Rev Biophys.39, 449–470 (2010) https://doi.org/ 10.1146/annurev-biophys-051309-103849

    2010 doi

  29. [37]

    PLoS Biology5(9), 221 (2007) https://doi

    Weiner, O.D., Marganski, W.A., Wu, L.F., Altschuler, S.J., Kirschner, M.W.: An actin- based wave generator organizes cell motility. PLoS Biology5(9), 221 (2007) https://doi. org/10.1371/journal.pbio.0050221

    2007 doi

  30. [38]

    Current Opinion in Cell Biology25(1), 107–115 (2013) https://doi.org/10.1016/j.ceb.2012

    Allard, J., Mogilner, A.: Traveling waves in actin dynamics and cell motility. Current Opinion in Cell Biology25(1), 107–115 (2013) https://doi.org/10.1016/j.ceb.2012. 08.012

    2013 doi

  31. [39]

    Proceedings of the National Academy of Sci- ences112(44), 6603–6611 (2015) https://doi

    Bement, W.M., Leda, M., Moe, A.M., Kita, A.M., Larson, M.E., Golding, A.E., Pfeuti, C., Su, K.-C., Miller, A.L., Goryachev, A.B., Dassow, G.: Activator–inhibitor coupling between rho signalling and actin assembly makes the cell cortex an excitable medium. Proceedings of the Na...

    2015 doi

  32. [40]

    Biophys J

    Laurent, V.M., Kasas, S., Yersin, A., Sch¨ affer, 16 T.E., Catsicas, S., Dietler, G., Verkhovsky, A.B., Meister, J.J.: Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy. Biophys J. 89(1), 667–675 (2005) https://doi.org/10. 1529/bio...

    2005

  33. [41]

    J Cell Biol.174, 767–772 (2006) https://doi

    Prass, M., Jacobson, K., Mogilner, A., Rad- macher, M.: Direct measurement of the lamel- lipodial protrusive force in a migrating cell. J Cell Biol.174, 767–772 (2006) https://doi. org/10.1083/jcb.200601159

    2006 doi

  34. [42]

    PLoS ONE6(11), 27532 (2011) https: //doi.org/10.1371/journal.pone.0027532

    Van Haastert, P.J.M.: Amoeboid cells use protrusions for walking, gliding and swim- ming. PLoS ONE6(11), 27532 (2011) https: //doi.org/10.1371/journal.pone.0027532

    2011 doi

  35. [43]

    Science345, 1135–1139 (2014)

    Keber, F.C., Loiseau, E., Sanchez, T., DeCamp, S.J., Giomi, L., Bowick, M.J., Marchetti, M.C., Dogic, Z., Bausch, A.R.: Topology and dynamics of active nematic vesicles. Science345, 1135–1139 (2014)

    2014

  36. [44]

    Soft Matter21, 6175– 6185 (2025)

    Willems, V., Baron, A., Fernandez-Matos, D., Wolfisberg, G., Baret, J.-C., Dufresne, E., Alvarez, L.: Run-and-tumble dynamics of active giant vesicles. Soft Matter21, 6175– 6185 (2025)

    2025

  37. [45]

    Chemistry and Physics of Lipids185, 031918 (2015) 17

    Deserno, M.: Fluid lipid membranes: from differential geometry to curvature stresse. Chemistry and Physics of Lipids185, 031918 (2015) 17

    2015

Pith tools

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