Pith. sign in

REVIEW 3 major objections 3 minor 1 cited by

Collective filament wrapping and nested spiral formation in active polydisperse systems

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

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

Pith's one-line read Polydispersity in filament length turns single-filament spiraling into cooperative wrapping: long active filaments coil around shorter ones, forming nested spirals that persist at activities where monodisperse nested structures dissolve.

desk verdict Solid simulation study with a plausible new mechanism, but the persistence claim needs a matched monodisperse control before it is fully sold. read the letter →

arxiv 2507.20969 v1 pith:CXT6EA2N submitted 2025-07-28 cond-mat.soft

Caterina Landi , Giulia Janzen , Francesco Sciortino , John Russo , Chantal Valeriani , Daniel A. Matoz-Fernandez This is my paper · ORCID
classification cond-mat.soft
keywords activefilamentspolydispersitynestedspiralsself-propelledsemiflexiblepolymersturningnumbervanHovedistributioncollectivewrappingnonequilibriumself-assembly
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether length polydispersity changes how self-propelled semiflexible filaments organize in two dimensions. It argues that it does: when filaments come in different lengths, longer ones coil around shorter ones and trap them, forming 'nested spirals' that are stable at activity levels where the nested structures seen in monodisperse systems have already fallen apart. The mechanism is length disparity itself, not any added attraction, so the paper identifies filament length as a control parameter for nonequilibrium self-assembly. A careful reader would care because real cytoskeletal and bacterial filament systems are naturally polydisperse, and this gives a minimal route to hierarchical, cooperative confinement in active matter.

What carries the argument

The central object is the nested spiral: a cluster of filaments whose centers of mass all lie within a threshold distance $\bar{r}$ (defined in the Supplementary Material). The paper measures it with the turning number $\psi = (1/2\pi)\sum_j (\theta_{j+1}-\theta_j)$, which counts how many turns a filament makes, and with the self-part of the van Hove distribution of filament center-of-mass displacements, which separates confined from motile populations. These tools together carry the argument: turning number shows length-dependent reentrant spiraling, nested-spiral statistics show the transition from multi-filament to two-filament structures, and the van Hove distribution shows the dynamical signature of confinement.

What would settle it

Run this model at the same packing fraction, stiffness, and activity window with a strictly monodisperse length distribution under identical simulation settings, and count nested spirals with the same $\bar{r}$ criterion; if the polydisperse system does not retain significantly more nested spirals at high $\mathrm{Pe}$, the persistence claim fails. Independently, sweep $\bar{r}$ across the values consistent with the Supplementary Material: if the two-stage decay in the number of nested spirals and the $\langle l_{\min}/l_{\max}\rangle$ trend are not stable to the threshold choice, the structural transition is an artifact of the cluster criterion.

Watch

Extended reading notes

Core claim

In a two-dimensional, dry suspension of active semiflexible filaments with fixed bond lengths and ten discrete lengths, the authors find a collective wrapping mechanism absent in monodisperse systems. At intermediate Péclet number, long filaments wind around shorter ones, producing nested spirals; as activity rises, medium filaments unwind first, leaving two-filament structures of one long filament wrapped around one short filament, and only at still higher activity do these break down. The turning number per filament length shows the same reentrant open-chain/spiral/open-chain behavior as the monodisperse case, but with length-dependent thresholds, so polydispersity shifts when each population transitions and extends the lifetime of nested spirals. The van Hove displacement distributions at $\mathrm{Pe}=110$ are bimodal for short and medium filaments, reflecting coexisting confined and motile populations, and single-peaked for long filaments, which remain trapped in spirals.

Load-bearing premise

The identification of nested spirals depends on a threshold distance $\bar{r}$ that is specified only in the Supplementary Material, and the claim that these structures persist longer than in monodisperse systems is compared against earlier published simulations rather than a matched control simulation in this paper; if the threshold or the comparison parameters differ, the reported trends could change.

Editorial extensions

If this is right

  • Polydispersity alone can stabilize multi-filament spiral assemblies at activities where monodisperse systems have already unwound.
  • The number of filaments per nested spiral drops from many to two as activity increases, and the surviving pairs are strongly length-asymmetric, so filament length disparity becomes the organizing variable.
  • van Hove distributions predict coexisting fast, motile filaments and confined, spiral-trapped filaments within the same system, with the split depending on filament length.
  • The same reentrant spiral behavior seen in monodisperse systems survives polydispersity, but with length-dependent Péclet thresholds, so polydispersity can both destabilize (premature unwinding of medium filaments) and stabilize (wrapping of short filaments by long ones).

Reading between the lines

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

  • Because the mechanism is purely steric and length-based, the same wrapping should appear in other rod-like active particles, granular rods, or colloidal chains whenever a length distribution overlaps with a broad activity window; this could be tested in experiments with mixtures of two rod lengths.
  • The paper's 'nested spiral' definition only uses centers of mass; a topological measure of mutual entanglement, such as linking or winding numbers between filament pairs, might reveal whether the two-filament states are genuinely interlocked or merely coaxial, and would make the persistence claim sharper.
  • Length-dependent propulsion, which the paper suggests as an extension, may reinforce or erase the wrapping depending on whether longer filaments move faster or slower; that is a testable prediction for future simulations.
  • The exponential length distribution test reported as qualitatively similar suggests that the wrapping is not an artifact of the specific uniform mix, but the threshold $\bar{r}$ should be re-derived for each distribution before comparing.
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

3 major / 3 minor

Summary. The manuscript reports molecular-dynamics simulations of a two-dimensional polydisperse suspension of self-propelled semiflexible filaments with fixed bond lengths and ten discrete filament lengths. The authors compute the per-length average turning number as a function of Péclet number, identify 'nested spirals' through a center-of-mass distance threshold, and analyze filament displacements via self-part van Hove distributions. Their central claims are that length polydispersity preserves the reentrant spiral regime of monodisperse systems, that polydisperse systems exhibit a collective wrapping mechanism absent in monodisperse systems, and that this mechanism stabilizes two-filament nested spirals at high activity, promoting persistent confinement. The paper includes a clear model description, standard simulation methodology, and qualitative snapshots of the proposed wrapping mechanism.

Significance. If the central claims are correct, the paper identifies a new and potentially important mechanism for hierarchical self-assembly in active matter: length disparity alone can stabilize multi-filament wrapped structures beyond the activity range where monodisperse spirals dissolve. The study is also potentially useful as a benchmark because the model is described in enough detail to reproduce, the observables (turning number, Péclet number, van Hove distributions) are direct and not fitted, and the simulation package is identified. However, the load-bearing novelty—'collective wrapping absent in monodisperse systems' and 'persistent confinement at high activity'—is established only by comparison with earlier monodisperse simulations using different model parameters, not by a matched control in this manuscript. The quantitative structural statistics also depend on a threshold defined only in the Supplementary Material, and no error bars are shown for the key averages. These issues must be addressed before the claims can be considered fully supported.

major comments (3)
  1. [Section IV and Fig. 3] The central claim that polydispersity enables nested spirals to persist at high Péclet numbers is not tested against a monodisperse control in this manuscript. The comparison is made to Refs. [22] and [23], which use different interaction potentials, stiffness protocols, packing fractions, filament lengths, and activity definitions. For example, this paper fixes ξp/L=1.3, uses the Tether bond potential, ρ=0.3, and a uniform length distribution of 10 discrete lengths; any of these choices could shift the activity at which monodisperse nested spirals dissolve. Please add matched monodisperse simulations with the same model, same ρ, same ξp/L, and the same individual filament lengths at the same Péclet numbers, and compare the nested-spiral statistics and turning-number reentrance directly. Without such controls, the abstract's claim that the collective wrapping mechanism is 'absent in monodisperse systems' is not established.
  2. [Section III B] The identification of nested spirals relies entirely on a threshold distance r̄, stated only as 'provided in the Supplementary Material.' All quantitative trends in Fig. 3—⟨Nf⟩ approaching 2, ⟨lmin/lmax⟩ decreasing toward the minimum ratio, and the two-stage decay of Nnested—depend on this cluster criterion. The manuscript should report the exact value of r̄ in the main text and demonstrate that the reported trends are robust to reasonable variations of r̄ (e.g., a sensitivity analysis over ±20–30%). Without this, a reader cannot assess whether the structural characterization is an artifact of the threshold choice.
  3. [Figs. 1, 3, and 4] Key quantitative claims are made without statistical uncertainty estimates. The average turning number ⟨|ψ|⟩, the nested-spiral statistics ⟨Nf⟩, ⟨lmin/lmax⟩, Nnested, and the van Hove distributions are all plotted without error bars or confidence intervals. The manuscript states that 10 independent simulations are used for the van Hove analysis, but no measure of run-to-run variability is shown. Since the paper's conclusions include shifts in transition Péclet numbers and quantitative comparisons with earlier monodisperse results, the absence of error bars makes it impossible to determine whether the reported differences are significant. Please provide error estimates for all averaged quantities.
minor comments (3)
  1. [Fig. 4 caption] The caption refers to 'l = 11' for the short filament case, while the text and legend define lengths by bead number Nb = 11. Please use consistent notation throughout, either Nb or L.
  2. [Section II] The Péclet number is written as 'P e' with a space, and 'P´eclet' appears with an accented character issue. Please use a uniform notation such as 'Pe' throughout.
  3. [Section III A] The sentence 'at the Pe where filaments form stable spirals in the monodisperse system, the presence of shorter filaments ... promotes their premature unwinding' is a mechanistic claim that appears only with a pointer to the Supplementary Material. Please provide the supporting data or figure in the main text, or state which supplementary figure is relevant.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: all reported quantities are direct observables and the monodisperse comparison rests on external or prior-work simulations, not on fitted parameters or definitions.

full rationale

The paper's quantitative results are direct measurements from the simulations: the turning number (Eq. 2) is computed from bond-angle increments, nested spirals are identified by a center-of-mass threshold r_bar described in the Supplementary Material, and the reported observables (average filament count per spiral, length ratio, total number of spirals, and van Hove distributions) are ensemble averages over these identified structures. No model parameter is fitted to the target claim, and the threshold r_bar, while hand-chosen, is not tuned to produce the observed trends; it therefore does not amount to a fitted input disguised as a prediction. The central claim that polydispersity extends nested-spiral persistence to higher activity is supported by comparing the polydisperse simulations with monodisperse results from Refs. [22] and [23]; Ref. [22] is an external study (Duman et al.) and Ref. [23] is a prior simulation by one of the current authors. Even though the comparison across papers leaves unmatched parameters and thus carries a correctness risk, this is a control-comparison issue rather than a circularity: the polydisperse results are not derived from, nor equivalent to, the monodisperse inputs. The self-citations to Refs. [23], [37], and [42] concern modeling choices (Tether versus FENE, tangential versus push-pull activity, and an exponentially decaying length distribution), but they are methodological continuity statements, not load-bearing steps that make the conclusions equivalent to their premises. No equation is defined in terms of the result it is supposed to establish, and no uniqueness theorem or ansatz is imported from the authors' prior work to force the chosen interpretation. The paper therefore contains no circular step and is self-contained with respect to its own simulation data, with the monodisperse benchmark serving as an external, falsifiable reference rather than as an input that guarantees the reported outcome.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical entities are postulated. The 'nested spiral' is a structural pattern defined by a distance threshold, not a new force, particle, or conserved quantity. All parameters are simulation inputs; none are fitted to external data.

free parameters (3)
  • Nested spiral threshold r_bar = Not stated in main text (deferred to SI)
    Defines which clusters count as nested spirals and therefore directly shapes all composition and count statistics in Fig. 3.
  • Filament length set and equal-number distribution = Equal counts of Nb in {3,11,20,28,37,45,54,62,71,80}
    Choice of polydisperse composition; an exponential distribution is mentioned as qualitatively similar in the SI, but the main results use this uniform set.
  • Fixed persistence ratio xi_p/L = 1.3
    The bending rigidity is chosen so all filaments have the same persistence-to-length ratio; wrapping thresholds may depend on this choice.
assumptions (4)
  • domain assumption Dry limit, no hydrodynamic interactions
    Simulations neglect long-range hydrodynamic coupling; real suspensions may modify wrapping and confinement.
  • domain assumption Filaments are fixed-length and non-breaking
    No polymerization, depolymerization, severing, or annealing; biology involves dynamic length changes, which could alter the mechanism.
  • domain assumption Tangential self-propulsion with no propulsion at end beads
    Model choice from Refs [21,27,40,41]; the paper states that other active polymer models give similar results (Ref [42]).
  • standard math Standard simulation potentials (WCA, Tether, harmonic angle) and BAOAB integration
    These are standard, well-tested ingredients of coarse-grained polymer simulation; they are not derived in the paper but are accepted methodology.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Collective filament wrapping and nested spiral formation in active polydisperse systems." pith.science (2026). https://pith.science/paper/CXT6EA2N

@misc{pith2026250720969,
  author       = {Pith},
  title        = {Pith review of: Collective filament wrapping and nested spiral formation in active polydisperse systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CXT6EA2N}},
  note         = {Machine review of arXiv:2507.20969}
}
read the original abstract

We investigate a two-dimensional polydisperse suspension of self-propelled semiflexible filaments and reveal a collective wrapping mechanism that is absent in monodisperse systems. At intermediate activity levels, long filaments coil around shorter ones, forming nested spiral structures stabilized by filament length disparity. These assemblies generalize the single-filament spiraling seen in active systems into cooperative, multi-filament configurations. As activity increases, the nested spirals undergo structural transitions: medium-length filaments unwind, longer filaments encapsulate shorter ones, and eventually all spiral structures dissolve. This reorganization is reflected in the dynamics, where van Hove distributions uncover coexisting confined and motile filament populations. Our findings identify filament length as a key control parameter for nonequilibrium self-assembly and establish inter-filament wrapping as a minimal mechanism for hierarchical organization in active matter. This mechanism provides a simple model for the cooperative confinement and structural hierarchy observed in both biological and synthetic active systems.

Figures

Figures reproduced from arXiv: 2507.20969 by the authors.

Figure 1
Figure 1. (a) shows the average turning number, ⟨|ψ|⟩, as a function of the P´eclet number for five represen￾tative filament lengths: one short (Nb = 11), three medium (Nb = 28, Nb = 37 and Nb = 54), and one long (Nb = 71). Turning numbers for all other lengths are provided in the Supplementary Material [46]. Here, ⟨·⟩ denotes the ensemble average over all filaments of the same length. Short filaments (Nb = 11) exhibit a turn… view at source ↗
Figure 2
Figure 2. FIG. 2. Snapshots illustrating the typical mechanism of for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Structural properties of nested spirals as a function [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. van Hove distribution for filaments of different lengths [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Locally tuned hydrodynamics of active polymer chains

    cond-mat.soft 2025-08 conditional novelty 6.0 of 10

    Simulations show that the location of the counterforce on the fluid, not just the active monomer, determines whether an active polymer creates pusher or puller flow fields, and that stiff chains transmit forces in a w...

Reference graph

Works this paper leans on

52 extracted references · 51 canonical work pages · cited by 1 Pith paper

  1. [22]

    Duman, R

    O. Duman, R. E. Isele-Holder, J. Elgeti and G. Gompper, Soft matter , 2018, 14, 4483–4494

    work page 2018

  2. [23]

    Janzen and D

    G. Janzen and D. A. Matoz-Fernandez, Soft Matter , 2024, 20, 6618–6626

    work page 2024

  3. [1]

    te Vrugt and R

    M. te Vrugt and R. Wittkowski, The European Physical Journal E , 2025, 48, 12

    work page 2025

  4. [2]

    Sciortino, H

    A. Sciortino, H. A. Faizi, D. A. Fedosov et al. , Nature Physics, 2025, 21, 799–807

    work page 2025

  5. [3]

    Ganguly, L

    S. Ganguly, L. S. Williams, I. M. Palacios and R. E. Gold- stein, Proceedings of the National Academy of Sciences , 2012, 109, 15109–15114

    work page 2012

  6. [4]

    Y. I. Yaman, E. Demir, R. Vetter and A. Kocabas,Nature communications, 2019, 10, 1–9

    work page 2019

  7. [5]

    S. S. Ding, L. J. Schumacher, A. E. Javer, R. G. Endres and A. E. Brown, eLife, 2019, 8, e43318

    work page 2019

  8. [6]

    G. K. Auer, P. M. Oliver, M. Rajendram, T.-Y. Lin, Q. Yao, G. J. Jensen and D. B. Weibel, mBio, 2019, 10, e00210-–19

    work page 2019

Show all 52 references
  1. [7]

    Deblais, A

    A. Deblais, A. Maggs, D. Bonn and S. Woutersen, Phys- ical Review Letters, 2020, 124, 208006

    2020

  2. [8]

    Deblais, S

    A. Deblais, S. Woutersen and D. Bonn, Physical Review Letters, 2020, 124, 188002

    2020

  3. [9]

    Nguyen, Y

    C. Nguyen, Y. Ozkan-Aydin, H. Tuazon, D. I. Goldman, M. S. Bhamla and O. Peleg, Frontiers in Physics , 2021, 9, 734499

    2021

  4. [10]

    J. Yan, M. Han, J. Zhang, C. Xu, E. Luijten and S. Granick, Nature Materials, 2016, 15, 1095–1099

    2016

  5. [11]

    P.-P. Wen, N. Zheng, L.-S. Li, H. Li, G. Sun and Q.-F. Shi, Physical Review E , 2012, 85, 031301

    2012

  6. [12]

    B. W. Soh, I. R. Gengaro, A. R. Klotz and P. S. Doyle, Physical Review Research, 2019, 1, 033194

    2019

  7. [13]

    Marvi, C

    H. Marvi, C. Gong, N. Gravish, H. Astley, M. Travers, R. L. Hatton, J. R. Mendelson III, H. Choset, D. L. Hu and D. I. Goldman, Science, 2014, 346, 224–229

    2014

  8. [14]

    Ozkan-Aydin, D

    Y. Ozkan-Aydin, D. I. Goldman and M. S. Bhamla, Pro- ceedings of the National Academy of Sciences, 2021, 118, e2010542118

    2021

  9. [15]

    Bourdieu, T

    L. Bourdieu, T. Duke, M. B. Elowitz, D. A. Winkelmann, S. Leibler and A. Libchaber, Phys. Rev. Lett. , 1995, 75, 176–179

    1995

  10. [16]

    Schaller, C

    V. Schaller, C. Weber, C. Semmrich, E. Frey and A. R. Bausch, Nature, 2010, 467, 73–77

    2010

  11. [17]

    Sumino, K

    Y. Sumino, K. H. Nagai, Y. Shitaka, D. Tanaka, K. Yoshikawa, H. Chat´ e and K. Oiwa,Nature, 2012, 483, 448–452

    2012

  12. [18]

    Sciortino and A

    A. Sciortino and A. R. Bausch, Proceedings of the Na- tional Academy of Sciences , 2021, 118, e2017047118

    2021

  13. [19]

    J. Chan, G. Calder, S. Fox and C. Lloyd, Nature cell biology, 2007, 9, 171–5

    2007

  14. [20]

    Lin, W.-C

    S.-N. Lin, W.-C. Lo and C.-J. Lo, Soft Matter, 2014, 10, 760–766

    2014

  15. [21]

    R. E. Isele-Holder, J. Elgeti and G. Gompper, Soft Mat- ter, 2015, 11, 7181–7190

    2015

  16. [24]

    K. R. Prathyusha, S. Henkes and R. Sknepnek, Physical Review E, 2018, 97, 022606

    2018

  17. [25]

    A. Shee, N. Gupta, A. Chaudhuri and D. Chaudhuri, Soft Matter, 2021, 17, 2120–2131

    2021

  18. [26]

    S. K. Anand, Journal of Physics: Condensed Matter , 2025, 37, 185101

    2025

  19. [27]

    Bianco, E

    V. Bianco, E. Locatelli and P. Malgaretti, Phys. Rev. Lett., 2018, 121, 217802

    2018

  20. [28]

    J.-X. Li, S. Wu, L.-L. Hao, Q.-L. Lei and Y.-Q. Ma,Phys. Rev. Res., 2023, 5, 043064

    2023

  21. [29]

    R. G. Winkler and G. Gompper, The Journal of Chemical Physics, 2020, 153, 040901

    2020

  22. [30]

    Gopinathan, K.-C

    A. Gopinathan, K.-C. Lee, J. M. Schwarz and A. J. Liu, Physical Review Letters, 2007, 99, 058103

    2007

  23. [31]

    Pavlov, A

    D. Pavlov, A. Muhlrad, J. Cooper, M. Wear and E. Reisler, Journal of molecular biology, 2007, 365, 1350– 1358

    2007

  24. [32]

    Humphrey, C

    D. Humphrey, C. Duggan, D. Saha, D. Smith and J. K¨ as, Nature, 2002, 416, 413–416

    2002

  25. [33]

    J. J. Lietor-Santos, C. Kim, M. L. Lynch, A. Fernandez- Nieves and D. A. Weitz, Langmuir, 2010, 26, 3174–3178

    2010

  26. [34]

    Kumar, A

    M. Kumar, A. Murali, A. G. Subramaniam, R. Singh and S. Thutupalli, Nature Communications, 2024, 15, 4903

    2024

  27. [35]

    J. Li, C. Zhang, Q. Zhang, S. Wang, R. Zhang, Z. Ding and Y. Han, Macromolecules, 2025, 58, 3208–3220

    2025

  28. [36]

    C. A. De Filippo, S. Del Galdo, P. Corsi, C. De Michele and B. Capone, Soft Matter , 2023, 19, 1732–1738

    2023

  29. [37]

    Landi, J

    C. Landi, J. Russo, F. Sciortino and C. Valeriani, Soft Matter, 2025, 21, 45–54

    2025

  30. [38]

    Noguchi and G

    H. Noguchi and G. Gompper, Phys. Rev. E , 2005, 72, 011901

    2005

  31. [39]

    J. D. Weeks, D. Chandler and H. C. Andersen, The Jour- nal of chemical physics , 1971, 54, 5237–5247

    1971

  32. [40]

    Jiang and Z

    H. Jiang and Z. Hou, Soft Matter , 2014, 10, 1012–1017

    2014

  33. [41]

    Foglino, E

    M. Foglino, E. Locatelli, C. A. Brackley, D. Michieletto, C. N. Likos and D. Marenduzzo, Soft Matter , 2019, 15, 5995–6005

    2019

  34. [42]

    Janzen, J

    G. Janzen, J. P. Miranda, J. Mart ´ ın-Roca, P. Malgaretti, E. Locatelli, C. Valeriani and D. A. M. Fernandez, The J. Chem. Phys , 2025, 162, 114905

    2025

  35. [43]

    Sknepnek, SAMoS: Self-propelled Agent-based Models with SAMoS, https://github.com/sknepneklab/SAMoS, 2024, Accessed: 2024-04-29

    R. Sknepnek, SAMoS: Self-propelled Agent-based Models with SAMoS, https://github.com/sknepneklab/SAMoS, 2024, Accessed: 2024-04-29

    2024

  36. [44]

    Leimkuhler and C

    B. Leimkuhler and C. Matthews, Molecular Dynamics: With Deterministic and Stochastic Numerical Methods , Springer International Publishing, 2015

    2015

  37. [45]

    S. G. Krantz, Handbook of Complex Variables , Birkh¨ auser Boston, MA, 1st edn., 1999

    1999

  38. [46]

    Supplementary Material

  39. [47]

    Mitchison and M

    T. Mitchison and M. Kirschner, Nature, 1984, 312, 237– 242

    1984

  40. [48]

    Howard and A

    J. Howard and A. A. Hyman, Nature, 2003, 422, 753– 758

    2003

  41. [49]

    Wegner, Journal of Molecular Biology , 1976, 108, 139–150

    A. Wegner, Journal of Molecular Biology , 1976, 108, 139–150

    1976

  42. [50]

    T. D. Pollard and G. G. Borisy, Cell, 2003, 112, 453–465

    2003

  43. [51]

    Hansen and I

    J.-P. Hansen and I. R. McDonald, Theory of Simple Liq- uids, Academic Press, London, 2nd edn., 1986

    1986

  44. [52]

    Helfferich, J

    J. Helfferich, J. Brisch, H. Meyer, O. Benzerara, F. Ziebert, J. Farago and J. Baschnagel, European Phys- ical Journal E , 2018, 41, 71

    2018

Pith tools

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