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arxiv: 2606.00286 · v1 · pith:M7WDERVXnew · submitted 2026-05-29 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech· physics.bio-ph· q-bio.SC

Localization of Active Particles on Random Arrays of Parallel Filaments

Owen Santoso , Elena Koslover This is my paper

Pith reviewed 2026-06-28 19:13 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mechphysics.bio-phq-bio.SC
keywords active particlesfilament arraysquenched disorderlocalizationrandom walkenergy landscapemicrotubule polarityintermittent transport
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The pith

Active particles on random filament arrays localize at regions where filaments converge in orientation.

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

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.

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.

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.

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.

Where Pith is reading between the lines

These are 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.

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.

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.

Figures

Figures reproduced from arXiv: 2606.00286 by Elena Koslover, Owen Santoso.

Figure 1
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. 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. Figure 4: FIG. 4. Localization width, quantified by IPR [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
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] view at source ↗
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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

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

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.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 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.
axioms (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.

pith-pipeline@v0.9.1-grok · 5708 in / 1139 out tokens · 18836 ms · 2026-06-28T19:13:45.057008+00:00 · methodology

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