Pith. sign in

REVIEW 2 major objections 2 minor 40 references

Localization of Active Particles on Random Arrays of Parallel Filaments

T0 review · 2 major / 2 minor · reviewed 2026-06-28 · grok-4.3

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

Pith's one-line read Active particles on random filament arrays localize at regions where filaments converge in orientation.

desk verdict The paper reduces intermittent transport on random parallel filaments to a 1D random-walk landscape and finds peak localization at intermediate run lengths. read the letter →

arxiv 2606.00286 v1 pith:M7WDERVX submitted 2026-05-29 cond-mat.dis-nn cond-mat.stat-mechphysics.bio-phq-bio.SC

Owen Santoso , Elena Koslover This is my paper · ORCID
classification cond-mat.dis-nncond-mat.stat-mechphysics.bio-phq-bio.SC
keywords activeparticlesfilamentarraysquencheddisorderlocalizationrandomwalkenergylandscapemicrotubulepolarityintermittenttransport
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 examines particles that switch between diffusive motion and directed transport along parallel filaments arranged with random polarities. It establishes that these particles accumulate at sites of convergent filament orientation because the quenched disorder creates effective traps. In the limit of rapid attachment and detachment, the full system reduces to motion on a noisy one-dimensional energy landscape whose wells are set by a random-walk structure. Localization reaches a maximum at intermediate run lengths, long enough for particles to detect polarity bias but short enough to prevent easy escape from traps. This shows how active transport combined with fixed environmental disorder produces spontaneous spatial organization without any additional guiding cues.

What carries the argument

A noisy one-dimensional effective energy landscape approximated by a random walk, obtained by averaging over fast attachment-detachment kinetics on quenched filament polarities.

What would settle it

Numerical trajectories or experimental particle distributions on a known random filament array that show no density peaks at sites of convergent orientation.

Watch

Extended reading notes

Core claim

In the rapid attachment-detachment limit, disordered arrays of parallel filaments map onto a noisy one-dimensional effective energy landscape whose structure is approximated by a random walk. Particle density therefore peaks at locations of convergent filament orientation, with the depth and width of the resulting wells determined by the transport kinetics and the geometric arrangement of the filaments. Localization is strongest for intermediate run lengths, where directed motion persists long enough to sense the quenched polarity disorder yet remains short enough that particles remain trapped in local wells.

Load-bearing premise

Attachment and detachment occur rapidly enough that the three-dimensional particle motion collapses to an effective one-dimensional energy landscape governed by the random filament orientations.

Editorial extensions

If this is right

  • Density maxima form specifically at convergent filament orientations rather than at random locations.
  • Well depth and width on the effective landscape scale directly with run length and attachment rate.
  • Localization strength exhibits a non-monotonic dependence on run length and reaches a maximum at intermediate values.
  • The same mapping applies to any intermittently processive particle on a fixed, disordered filament network.

Reading between the lines

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

  • The same random-walk landscape construction could be used to predict localization in mixed-polarity microtubule bundles inside axons or other cellular compartments.
  • Adding weak filament bending or slow polarity flips would turn the static wells into slowly evolving traps whose escape statistics could be measured.
  • In a two-dimensional sheet of filaments the effective landscape would become a two-dimensional random potential whose percolation properties might allow long-range particle spreading despite local trapping.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper examines transport of intermittently switching active particles on quenched random arrays of parallel filaments, motivated by mixed-polarity microtubule bundles in dendrites. It claims that such arrays produce localization at sites of convergent filament polarity. In the rapid attachment-detachment limit the 2D dynamics reduce to motion in a noisy 1D effective energy landscape whose wells are approximated by a random walk; well depth and width are expressed in terms of run length, attachment-detachment rates and geometry. Localization strength is maximal at intermediate run lengths.

Significance. If the mapping to the random-walk landscape is rigorously derived and validated, the work supplies a concrete mechanism by which quenched filament disorder generates robust spatial organization in active transport, with direct relevance to intracellular trafficking. The explicit dependence of well statistics on kinetics and geometry is a positive feature.

major comments (2)
  1. [model reduction paragraph] Model-reduction paragraph (following the abstract): the claim that successive filament segments produce uncorrelated steps in the effective landscape is load-bearing for the random-walk approximation. The text must derive the condition under which residual transverse excursions at finite run length do not induce spatial correlations between adjacent wells; without this, the predicted localization at intermediate run lengths rests on an unverified assumption.
  2. [results on localization vs run length] Results section on localization strength versus run length: the statement that localization peaks at intermediate run lengths requires quantitative comparison (e.g., mean-squared displacement or occupation probability) between the effective 1D landscape and the original 2D intermittent dynamics. If the comparison is only qualitative or performed after fitting, the central claim that the random-walk landscape captures the non-monotonic behavior is not yet demonstrated.
minor comments (2)
  1. [abstract] Abstract: the phrase 'whose structure is approximated by a random walk' should be accompanied by a brief statement of the approximation error or the regime of validity.
  2. [model section] Notation: define the effective potential V_eff and the noise strength explicitly when first introduced, rather than leaving them implicit in the landscape description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major point below and will revise the manuscript accordingly to strengthen the presentation of the model reduction and the validation of the localization results.

read point-by-point responses

  1. Referee: [model reduction paragraph] Model-reduction paragraph (following the abstract): the claim that successive filament segments produce uncorrelated steps in the effective landscape is load-bearing for the random-walk approximation. The text must derive the condition under which residual transverse excursions at finite run length do not induce spatial correlations between adjacent wells; without this, the predicted localization at intermediate run lengths rests on an unverified assumption.

    Authors: We agree that an explicit derivation of the decorrelation condition is required to place the random-walk approximation on firmer ground. In the revised manuscript we will insert a dedicated paragraph immediately after the model-reduction statement. This paragraph will derive the condition that transverse excursions remain uncorrelated between adjacent wells when the mean run length is smaller than the typical filament segment length by a factor set by the attachment-detachment rates and the filament spacing; the derivation follows from a perturbative expansion of the transverse diffusion time scale relative to the longitudinal run time. revision: yes

  2. Referee: [results on localization vs run length] Results section on localization strength versus run length: the statement that localization peaks at intermediate run lengths requires quantitative comparison (e.g., mean-squared displacement or occupation probability) between the effective 1D landscape and the original 2D intermittent dynamics. If the comparison is only qualitative or performed after fitting, the central claim that the random-walk landscape captures the non-monotonic behavior is not yet demonstrated.

    Authors: We acknowledge that the present comparison between the 2D dynamics and the effective 1D landscape is primarily qualitative. In the revision we will add a new figure (or panel set) that overlays quantitative measures—specifically the run-length dependence of the long-time mean-squared displacement and the steady-state occupation probability density—obtained from direct 2D Monte Carlo simulations against the same quantities computed from the 1D random-walk landscape. No additional fitting parameters will be introduced; the landscape parameters are taken directly from the analytic expressions already given in the text. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; effective landscape derived from kinetics and geometry

full rationale

The paper derives the noisy 1D effective energy landscape in the rapid attachment-detachment limit directly from the underlying transport kinetics and filament geometry, with well depths and widths expressed explicitly as functions of those inputs. The random-walk approximation for the landscape structure follows from the quenched random orientations of the filaments, which is an input assumption rather than a fitted output. No equations reduce predictions to fitted parameters by construction, no self-citation chains bear the central claim, and the mapping is presented as a standard model reduction without renaming known results or smuggling ansatzes. The derivation remains self-contained against the stated assumptions.

Assumptions & free parameters 1 free parameters · 1 assumptions · 0 invented entities

Based on abstract only; the central claim rests on the rapid attachment-detachment limit and the random-walk approximation of the effective landscape.

free parameters (1)
  • run length
    Localization strength depends on intermediate values of run length; no explicit fitted value given.
assumptions (1)
  • domain assumption rapid attachment-detachment limit allows reduction to noisy 1D effective energy landscape approximated by random walk
    Invoked to obtain the landscape description from transport kinetics and filament geometry.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Localization of Active Particles on Random Arrays of Parallel Filaments." pith.science (2026). https://pith.science/paper/M7WDERVX

@misc{pith2026260600286,
  author       = {Pith},
  title        = {Pith review of: Localization of Active Particles on Random Arrays of Parallel Filaments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M7WDERVX}},
  note         = {Machine review of arXiv:2606.00286}
}
read the original abstract

Quenched disorder in the environment can fundamentally alter transport dynamics in both active and passive systems. We explore how disordered arrays of filaments govern the distribution of intermittently moving particles which switch between diffusive and processive transport. Motivated by the mixed-polarity arrangements of parallel microtubules observed in mammalian dendrites, we show that such arrays tend to result in localization of particles at regions of convergent filament orientation. In the rapid attachment-detachment limit, the disordered system can be described by a noisy one-dimensional effective energy landscape, whose structure is approximated by a random walk. The depth and width of wells on this landscape are expressed as a function of the transport kinetics and system geometry. Localization is shown to be strongest at intermediate run-lengths, where biased transport persists long enough to sense the quenched filament polarity but not so long as to facilitate escape from local traps. These results demonstrate robust localization of particles moving on random filament networks, highlighting the emergent spatial organization that arises from an interplay of active transport and quenched disorder.

Figures

Figures reproduced from arXiv: 2606.00286 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Simulation snapshot of biased particles (orange) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Steady-state localization width (IPR [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Localization width, quantified by IPR [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: FIG. 3. Depth of energy landscape collapses to a universal [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references

  1. [1]

    Oxford University Press, 1996

    Barry D Hughes.Random walks and random environ- ments. Oxford University Press, 1996

    1996

  2. [2]

    Supercooled liquids and the glass transition.Nature, 410(6825):259– 267, 2001

    Pablo G Debenedetti and Frank H Stillinger. Supercooled liquids and the glass transition.Nature, 410(6825):259– 267, 2001

    2001

  3. [3]

    Anoma- lous diffusion in disordered media: statistical mecha- nisms, models and physical applications.Phys Rep, 195(4-5):127–293, 1990

    Jean-Philippe Bouchaud and Antoine Georges. Anoma- lous diffusion in disordered media: statistical mecha- nisms, models and physical applications.Phys Rep, 195(4-5):127–293, 1990

    1990

  4. [4]

    Cytoplasmic crowding acts as a porous medium re- ducing macromolecule diffusion.P Natl Acad Sci, 123(4):e2519599123, 2026

    Olivier Destrian, Nicolas Moisan, Ren´ e-Marc M` ege, Benoit Ladoux, Benoit Goyeau, and Morgan Chabanon. Cytoplasmic crowding acts as a porous medium re- ducing macromolecule diffusion.P Natl Acad Sci, 123(4):e2519599123, 2026

    2026

  5. [5]

    Search and localization dynamics of the crispr- cas9 system.Phys Rev Lett, 127(20):208102, 2021

    Qiao Lu, Deepak Bhat, Darya Stepanenko, and Simone Pigolotti. Search and localization dynamics of the crispr- cas9 system.Phys Rev Lett, 127(20):208102, 2021

    2021

  6. [6]

    Diffusion, subdiffusion, and trapping of active particles in hetero- geneous media.Phys

    Oleksandr Chepizhko and Fernando Peruani. Diffusion, subdiffusion, and trapping of active particles in hetero- geneous media.Phys. Rev. Lett., 111:160604, Oct 2013

    2013

  7. [7]

    The limiting behavior of a one-dimensional random walk in a random medium.Theory of Probability & Its Applications, 27(2):256–268, 1983

    Ya G Sinai. The limiting behavior of a one-dimensional random walk in a random medium.Theory of Probability & Its Applications, 27(2):256–268, 1983. 6

    1983

  8. [8]

    Localization and spread- ing of diseases in complex networks.Phys Rev Lett, 109(12):128702, 2012

    Alexander V Goltsev, Sergey N Dorogovtsev, Joao G Oliveira, and Jose FF Mendes. Localization and spread- ing of diseases in complex networks.Phys Rev Lett, 109(12):128702, 2012

    2012

Show all 40 references
  1. [9]

    A diversity of localized timescales in network ac- tivity.elife, 3:e01239, 2014

    Rishidev Chaudhuri, Alberto Bernacchia, and Xiao-Jing Wang. A diversity of localized timescales in network ac- tivity.elife, 3:e01239, 2014

    2014

  2. [10]

    Suppression of epileptic seizures via anderson localization.J Roy Soc Interface, 14(127), 2017

    Benjamin J Zhang, Maysamreza Chamanzar, and Mohammad-Reza Alam. Suppression of epileptic seizures via anderson localization.J Roy Soc Interface, 14(127), 2017

    2017

  3. [11]

    Non-hermitian localization and population biology.Phys Rev E, 58(2):1383, 1998

    David R Nelson and Nadav M Shnerb. Non-hermitian localization and population biology.Phys Rev E, 58(2):1383, 1998

    1998

  4. [12]

    Susceptible- infected-susceptible model on networks with eigenvector localization.Phys Rev E, 101(4):042310, 2020

    Zong-Wen Wei and Bing-Hong Wang. Susceptible- infected-susceptible model on networks with eigenvector localization.Phys Rev E, 101(4):042310, 2020

    2020

  5. [13]

    Right time, right place: probing the functions of organelle positioning.Trends Cell Biol, 26(2):121–134, 2016

    Petra van Bergeijk, Casper C Hoogenraad, and Lukas C Kapitein. Right time, right place: probing the functions of organelle positioning.Trends Cell Biol, 26(2):121–134, 2016

    2016

  6. [14]

    Mitostasis in neurons: maintaining mitochondria in an extended cel- lular architecture.Neuron, 96(3):651–666, 2017

    Thomas Misgeld and Thomas L Schwarz. Mitostasis in neurons: maintaining mitochondria in an extended cel- lular architecture.Neuron, 96(3):651–666, 2017

    2017

  7. [15]

    Cellular logistics: unraveling the interplay between microtubule organiza- tion and intracellular transport.Annu Rev Cell Dev Bi, 35:29–54, 2019

    Mithila Burute and Lukas C Kapitein. Cellular logistics: unraveling the interplay between microtubule organiza- tion and intracellular transport.Annu Rev Cell Dev Bi, 35:29–54, 2019

    2019

  8. [16]

    Which way to go? cytoskeletal organization and polarized transport in neurons.Mol Cell Neurosci, 46(1):9–20, 2011

    Lukas C Kapitein and Casper C Hoogenraad. Which way to go? cytoskeletal organization and polarized transport in neurons.Mol Cell Neurosci, 46(1):9–20, 2011

    2011

  9. [17]

    Searching through cellular landscapes

    Elena F Koslover. Searching through cellular landscapes. InTarget Search Problems, pages 541–577. Springer, 2024

    2024

  10. [18]

    An intrinsic compartmentalization code for pe- ripheral membrane proteins in photoreceptor neurons.J Cell Biol, 218(11):3753–3772, 2019

    Nycole A Maza, William E Schiesser, and Peter D Calvert. An intrinsic compartmentalization code for pe- ripheral membrane proteins in photoreceptor neurons.J Cell Biol, 218(11):3753–3772, 2019

    2019

  11. [19]

    Patterning and polarization of cells by intra- cellular flows.Curr Opin Cell Biol, 62:123–134, 2020

    Rukshala Illukkumbura, Tom Bland, and Nathan W Goehring. Patterning and polarization of cells by intra- cellular flows.Curr Opin Cell Biol, 62:123–134, 2020

    2020

  12. [20]

    Spatial regulation of endosomes in growing dendrites.Dev Biol, 486:5–14, 2022

    Chan Choo Yap and Bettina Winckler. Spatial regulation of endosomes in growing dendrites.Dev Biol, 486:5–14, 2022

    2022

  13. [21]

    Memoryless self-reinforcing directionality in endosomal active trans- port within living cells.Nat Mater, 14(6):589–593, 2015

    Kejia Chen, Bo Wang, and Steve Granick. Memoryless self-reinforcing directionality in endosomal active trans- port within living cells.Nat Mater, 14(6):589–593, 2015

    2015

  14. [22]

    Activity-dependent trafficking of lysosomes in dendrites and dendritic spines

    Marisa S Goo, Laura Sancho, Natalia Slepak, Daniela Boassa, Thomas J Deerinck, Mark H Ellisman, Brenda L Bloodgood, and Gentry N Patrick. Activity-dependent trafficking of lysosomes in dendrites and dendritic spines. J Cell Biol, 216(8):2499–2513, 2017

    2017

  15. [23]

    Correlative live- cell and superresolution microscopy reveals cargo trans- port dynamics at microtubule intersections.P Natl Acad Sci, 110(9):3375–3380, 2013

    ˇStefan B´ alint, Ione Verdeny Vilanova, ´Angel San- doval ´Alvarez, and Melike Lakadamyali. Correlative live- cell and superresolution microscopy reveals cargo trans- port dynamics at microtubule intersections.P Natl Acad Sci, 110(9):3375–3380, 2013

    2013

  16. [24]

    Microtubule organization de- termines axonal transport dynamics.Neuron, 92(2):449– 460, 2016

    Shaul Yogev, Roshni Cooper, Richard Fetter, Mark Horowitz, and Kang Shen. Microtubule organization de- termines axonal transport dynamics.Neuron, 92(2):449– 460, 2016

    2016

  17. [25]

    Active cargo positioning in antiparallel transport networks.P Natl Acad Sci, 116(30):14835– 14842, 2019

    Mathieu Richard, Carles Blanch-Mercader, Hajer Enno- mani, Wenxiang Cao, Enrique M De La Cruz, Jean- Fran¸ cois Joanny, Frank J¨ ulicher, Laurent Blanchoin, and Pascal Martin. Active cargo positioning in antiparallel transport networks.P Natl Acad Sci, 116(30):14835– 14842, 2019

    2019

  18. [26]

    Cycling state that can lead to glassy dynamics in intracellular transport.Phys Rev X, 6(1):011037, 2016

    Monika Scholz, Stanislav Burov, Kimberly L Weirich, Bj¨ orn J Scholz, SM Ali Tabei, Margaret L Gardel, and Aaron R Dinner. Cycling state that can lead to glassy dynamics in intracellular transport.Phys Rev X, 6(1):011037, 2016

    2016

  19. [27]

    Tunable intracellular transport on con- verging microtubule morphologies.Biophysical Reports, 4(3), 2024

    Niranjan Sarpangala, Brooke Randell, Ajay Gopinathan, and Oleg Kogan. Tunable intracellular transport on con- verging microtubule morphologies.Biophysical Reports, 4(3), 2024

    2024

  20. [28]

    Cytoskeletal network morphology regulates intracellular transport dynamics.Biophys J, 109(8):1574–1582, 2015

    David Ando, Nickolay Korabel, Kerwyn Casey Huang, and Ajay Gopinathan. Cytoskeletal network morphology regulates intracellular transport dynamics.Biophys J, 109(8):1574–1582, 2015

    2015

  21. [29]

    First passage of molecular motors on networks of cytoskeletal filaments

    Paul J Mlynarczyk and Steven M Abel. First passage of molecular motors on networks of cytoskeletal filaments. Phys Rev E, 99(2):022406, 2019

    2019

  22. [30]

    Encounter times of intermittently running par- ticles.Phys Biol, 2026

    Lizzy Teryoshin, Mario Hidalgo-Soria, and Elena F Koslover. Encounter times of intermittently running par- ticles.Phys Biol, 2026

    2026

  23. [31]

    Mixed microtubules steer dynein-driven cargo transport into dendrites.Curr Biol, 20(4):290–299, 2010

    Lukas C Kapitein, Max A Schlager, Marijn Kuijpers, Phebe S Wulf, Myrrhe van Spronsen, Frederick C MacK- intosh, and Casper C Hoogenraad. Mixed microtubules steer dynein-driven cargo transport into dendrites.Curr Biol, 20(4):290–299, 2010

    2010

  24. [32]

    Quantitative mapping of dense microtubule arrays in mammalian neurons.elife, 10:e67925, 2021

    Eugene A Katrukha, Daphne Jurriens, Desiree M Salas Pastene, and Lukas C Kapitein. Quantitative mapping of dense microtubule arrays in mammalian neurons.elife, 10:e67925, 2021

    2021

  25. [33]

    Stability properties of neuronal mi- crotubules.Cytoskeleton, 73(9):442–460, 2016

    Peter W Baas, Anand N Rao, Andrew J Matamoros, and Lanfranco Leo. Stability properties of neuronal mi- crotubules.Cytoskeleton, 73(9):442–460, 2016

    2016

  26. [34]

    Localization of random walks in one- dimensional random environments.Commun Math Phys, 92(4):491–506, 1984

    AO Golosov. Localization of random walks in one- dimensional random environments.Commun Math Phys, 92(4):491–506, 1984

    1984

  27. [35]

    See Supplemental Material for derivations and model de- tails

  28. [36]

    Nonreciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems.Phys Rev B, 110(15):155116, 2024

    Aleksandra Nelson and Evelyn Tang. Nonreciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems.Phys Rev B, 110(15):155116, 2024

    2024

  29. [37]

    Diffusion in a rough potential.P Natl Acad Sci, 85(7):2029–2030, 1988

    Robert Zwanzig. Diffusion in a rough potential.P Natl Acad Sci, 85(7):2029–2030, 1988

  30. [38]

    Cargo navigation across 3d microtubule intersections.P Natl Acad Sci, 115(3):537–542, 2018

    Jared P Bergman, Matthew J Bovyn, Florence F Doval, Abhimanyu Sharma, Manasa V Gudheti, Steven P Gross, Jun F Allard, and Michael D Vershinin. Cargo navigation across 3d microtubule intersections.P Natl Acad Sci, 115(3):537–542, 2018

    2018

  31. [39]

    Formation of microtubule-based traps controls the sorting and concentration of vesicles to restricted sites of regenerating neurons after axotomy.J Cell Biol, 176(4):497–507, 2007

    Hadas Erez, Guy Malkinson, Masha Prager-Khoutorsky, Chris I De Zeeuw, Casper C Hoogenraad, and Micha E Spira. Formation of microtubule-based traps controls the sorting and concentration of vesicles to restricted sites of regenerating neurons after axotomy.J Cell Biol, 176(4):4...

    2007

  32. [40]

    Bidirectional cargo transport: mov- ing beyond tug of war.Nat Rev Mol Cell Biol, 15(9):615, 2014

    William O Hancock. Bidirectional cargo transport: mov- ing beyond tug of war.Nat Rev Mol Cell Biol, 15(9):615, 2014

    2014

Pith tools

Reviewed June 28, 2026 · model on record in the stance chip above.