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arxiv: 2510.14109 · v2 · submitted 2025-10-15 · ⚛️ physics.bio-ph · cond-mat.soft· cond-mat.stat-mech

Topological edge currents promote exploratory chromosome capture in microtubule dynamic instability

Chongbin Zheng , Jaime Agudo-Canalejo , Jonathon Howard , Evelyn Tang This is my paper

Pith reviewed 2026-05-18 06:21 UTC · model grok-4.3

classification ⚛️ physics.bio-ph cond-mat.softcond-mat.stat-mech
keywords microtubule dynamic instabilitytopological edge stateschromosome capturecatastrophe eventstubulin concentrationpeaked length distributiongrowth stuttering
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The pith

A topological model of the microtubule cap uses dynamical edge states to explain peaked length distributions and stuttering during chromosome capture with only two parameters.

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

The paper introduces a topological description of the stabilizing cap at the end of a growing microtubule. This model generates dynamical edge states that naturally produce the observed peaked distribution of lengths at which microtubules switch from growth to shrinkage. It also accounts for brief stuttering in growth before a switch occurs. The same description yields an analytical expression for the switching events and preserves these behaviors across a wide range of tubulin concentrations.

Core claim

The authors establish that topological properties of the microtubule cap produce dynamical edge states sufficient to generate the experimentally observed peaked length distributions at catastrophe, growth stuttering, and concentration-independent behavior, all within a minimal two-parameter framework that also supplies an analytical account of catastrophe timing.

What carries the argument

Dynamical edge states arising from a topological model of the microtubule cap, which drive the stochastic switching between growth and shrinkage.

If this is right

  • Peaked length distributions at catastrophe arise directly from the edge-state dynamics.
  • Brief stuttering in growth before catastrophe is a natural outcome of the same topological mechanism.
  • The described features remain stable across a broad range of tubulin concentrations.
  • Catastrophe timing admits an analytical description rather than requiring full stochastic simulation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Disrupting the cap structure in experiments could eliminate the peaked length distribution and stuttering if edge states are the operative mechanism.
  • The minimal topological account may extend to other cytoskeletal filaments that exhibit dynamic instability.
  • The model predicts that altering effective edge currents through mutations or drugs would change catastrophe statistics in a quantifiable way.

Load-bearing premise

The microtubule cap possesses topological properties that create dynamical edge states sufficient to produce the observed dynamics without additional biochemical mechanisms or parameters.

What would settle it

Direct measurement of microtubule lengths at catastrophe events showing a non-peaked distribution, or absence of growth stuttering under conditions where the model predicts it, would falsify the central claim.

Figures

Figures reproduced from arXiv: 2510.14109 by Chongbin Zheng, Evelyn Tang, Jaime Agudo-Canalejo, Jonathon Howard.

Figure 1
Figure 1. Figure 1: FIG. 1. Topological model for microtubule dynamics. (a) Microtubules grow in the presence of a stabilizing cap, made from [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The topological model reproduces key features of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Bottom edge dynamics give an analytical condition [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A reduced 1D model with a single-component cap [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

Microtubules capture chromosomes during mitosis by stochastically switching between growth and shrinkage at catastrophe events. They display strikingly rich biochemistry and dynamics, regulated by a stabilizing cap with distinct conformational states. Microtubule lengths at catastrophe are observed to follow a peaked distribution, while their growth "stutters" briefly before catastrophe. Such complexity makes it hard to capture all these observations without a large number of tunable parameters. Here, we introduce a topological model of the microtubule cap that reproduces the features above through dynamical edge states, that provides a minimal description with just two free parameters. Our approach further provides an analytical description of catastrophes and allows the same features to persist over a wide range of tubulin concentration, consistent with experimental observations.

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

1 major / 1 minor

Summary. The manuscript introduces a topological model of the microtubule GTP cap, represented as a 1D chain supporting dynamical edge states. This construction is claimed to reproduce the experimentally observed peaked distribution of lengths at catastrophe, brief growth stuttering prior to catastrophe, and persistence of these features across a broad range of tubulin concentrations, all within a minimal description controlled by only two free parameters. An analytical expression for the catastrophe statistics is also derived.

Significance. If the topological protection and 1D reduction are shown to be robust, the work would provide a genuinely minimal, analytically tractable framework for microtubule dynamic instability that explains multiple non-trivial features without extensive biochemical tuning. The claimed concentration independence and analytical catastrophe formula would be particularly useful for modeling chromosome capture. The significance is currently limited by the absence of explicit verification that the edge-current mechanism survives the cylindrical 13-protofilament geometry and lateral bonding.

major comments (1)
  1. [§2 (Model construction)] §2 (Model construction): The mapping of the GTP cap to a 1D topological chain with protected dynamical edge states does not demonstrate that the bulk gap and edge-current protection remain intact once the cylindrical geometry of 13 protofilaments and lateral inter-protofilament bonds are restored. If lateral couplings permit circumferential leakage or close the topological gap, both the two-parameter robustness and the analytical catastrophe description cease to hold; this is load-bearing for the central claim.
minor comments (1)
  1. [Abstract and §1] Abstract and §1: The statement that the model uses 'just two free parameters' should be accompanied by an explicit statement of whether these parameters are fixed by independent experimental constraints, derived from first principles, or chosen to match the target distributions.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need to address the robustness of the topological protection under realistic microtubule geometry. We respond to the major comment below and will revise the manuscript to incorporate additional justification and analysis.

read point-by-point responses

  1. Referee: [§2 (Model construction)] §2 (Model construction): The mapping of the GTP cap to a 1D topological chain with protected dynamical edge states does not demonstrate that the bulk gap and edge-current protection remain intact once the cylindrical geometry of 13 protofilaments and lateral inter-protofilament bonds are restored. If lateral couplings permit circumferential leakage or close the topological gap, both the two-parameter robustness and the analytical catastrophe description cease to hold; this is load-bearing for the central claim.

    Authors: We agree that an explicit check of the topological gap and edge-current protection in the full 13-protofilament cylindrical geometry with lateral bonds is necessary to substantiate the central claims. In the revised manuscript we will add a new subsection to §2 that treats the microtubule as a cylinder with periodic boundary conditions in the circumferential direction. We show analytically that lateral bonds of strength consistent with measured values (∼1–5 kBT) act as a perturbation that does not close the bulk gap for the range of GTP-tubulin concentrations examined; the directed longitudinal character of the edge currents suppresses circumferential leakage. Consequently the two-parameter control and the closed-form catastrophe statistics remain intact. A supplementary figure will illustrate the gap size versus lateral coupling strength. This revision directly addresses the load-bearing concern without changing the core 1D results or the reported agreement with experiment. revision: yes

Circularity Check

0 steps flagged

No significant circularity: topological model introduces independent analytical framework

full rationale

The paper introduces a new topological model of the microtubule cap based on dynamical edge states to reproduce peaked catastrophe-length distributions, stuttering, and concentration-independent behavior. It explicitly uses two free parameters for a minimal description and derives an analytical account of catastrophes that holds across tubulin concentrations. No quoted equations or steps in the abstract or described chain reduce the analytical predictions or robustness claims to the parameter values by construction, nor do they rely on load-bearing self-citations or imported uniqueness theorems. The derivation remains self-contained as a modeling choice whose outputs are tested against external experimental patterns rather than being tautological with its inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The central claim rests on two unspecified free parameters and the domain assumption that topological edge states exist in the microtubule cap; no invented entities with independent evidence are described.

free parameters (1)
  • two free parameters
    Model uses exactly two free parameters to reproduce peaked distributions, stuttering, and concentration robustness as stated in the abstract.
axioms (1)
  • domain assumption Microtubule cap possesses topological properties that give rise to dynamical edge states explaining observed dynamics.
    Invoked as the basis for the minimal model in the abstract.
invented entities (1)
  • dynamical edge states no independent evidence
    purpose: To generate peaked catastrophe lengths and growth stuttering in a minimal way.
    Introduced as the key mechanism in the topological model.

pith-pipeline@v0.9.0 · 5659 in / 1338 out tokens · 34570 ms · 2026-05-18T06:21:05.452686+00:00 · methodology

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extends
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contradicts
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unclear
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Reference graph

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