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REVIEW 3 major objections 4 minor 50 references

Physical Principles of Size and Frequency Scaling of Active Cytoskeletal Spirals

T0 review · 3 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Dynein-pinned microtubules rotate with a frequency that scales as the cube root of motor density, overturning the predicted 4/3 power law.

desk verdict First dynein-driven MT spiral assay with a plausible but unproven 1/3 frequency scaling; the missing tip-speed measurement and model-dependent exponent are the load-bearing weaknesses. read the letter →

arxiv 2508.10114 v1 pith:4PJHEDAD submitted 2025-08-13 cond-mat.soft physics.bio-phq-bio.BM

Aman Soni , Shivani A. Yadav , Chaitanya A. Athale This is my paper · ORCID
classification cond-mat.softphysics.bio-phq-bio.BM
keywords microtubulespiralsglidingassaydyneinscalinglawspersistencelengthactivefilamentsbucklingmotordensity
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 tries to establish a general scaling law for a cytoskeletal filament whose leading end is pinned: when dynein motors anchored on a surface push a microtubule, the filament buckles into a steady spiral whose radius shrinks with motor force density as $f^{-1/3}$, while its rotation frequency grows only as $f^{1/3}$. The frequency result contradicts a long-standing theoretical prediction of $f^{4/3}$ from models in which filament speed is proportional to motor force. The paper proposes that the frequency is set by the simple circular-motion identity $\nu \sim |V_{\mathrm{tip}}|/R$, with the gliding tip speed nearly independent of motor density and filament length. It tests this against dynein-driven microtubule spirals, simulations of an explicit motor-filament model, and scaling arguments, and additionally predicts that both radius and frequency depend on filament length through the persistence length with exponents $\pm 1/3$. The length-dependence data favor a variable persistence length over the constant value assumed in earlier work.

What carries the argument

The load-bearing identity is the kinematic relation $\omega = |V_{\mathrm{tip}}|/R$ for uniform circular motion, applied to the steady spiral's free tip. It converts the known radius scaling $R \sim (k_B T \ell_p/f)^{1/3}$, obtained by equating motor work per contour with bending energy of the near-circle spiral, into a frequency scaling; the exponent is decided by how the tip speed responds to force density. If $|V_{\mathrm{tip}}|$ is constant in $f$, the frequency scales as $f^{1/3}$; if $|V_{\mathrm{tip}}| \propto f$, the same relation yields $f^{4/3}$. A second supporting object is the variable persistence length $\ell_p(L)$ used to test length dependence.

What would settle it

Measure the instantaneous linear speed of the free tip during steady-state spiraling in a dynein gliding assay across motor densities from about 30 to 200 motors/µm$^2$ and filament lengths from 5 to 30 µm, and compare it with the straight gliding speed. If $|V_{\mathrm{tip}}|$ grows roughly linearly with motor density, the frequency exponent should approach $4/3$; if $|V_{\mathrm{tip}}|$ stays within about 10–20% of the single-motor gliding speed, the $1/3$ scaling holds. A second check: vary ATP to change motor speed without changing density and test whether $\nu R$ tracks the gliding speed.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that the rotation frequency of a pinned, motor-driven filamentous spiral is not set by the propulsive force per motor but by the ratio of a nearly constant gliding speed to the spiral radius. Starting from the previously established balance between motor work and bending energy, $R \sim (k_B T \ell_p/f)^{1/3}$, and adding the kinematic identity $\omega = |V_{\mathrm{tip}}|/R$ with $|V_{\mathrm{tip}}|$ independent of motor density and length, the paper derives $\nu \sim f^{1/3}$. Experiments on dynein-driven microtubules and simulations of explicit force-generating motors give exponents near $1/3$ rather than $4/3$, and the paper shows that if th

Load-bearing premise

The argument collapses if the speed of the free tip inside the spiral is not nearly independent of motor density and filament length, because then the frequency scaling gains an extra factor of that speed's force dependence — a linear dependence would restore the old $4/3$ law.

Editorial extensions

If this is right

  • The rotation frequency of pinned spirals should be measurable and around 0.01–0.02 Hz for dynein-driven microtubules, matching the beating frequency of clamped filaments from earlier work.
  • A density- and length-independent gliding speed determines the spiral's dynamics: motor density sets the radius and, through it, the frequency.
  • The old $f^{4/3}$ scaling is a special case of the new kinematic relation, recovered when tip velocity grows linearly with force density.
  • If microtubule persistence length varies with filament length, spiral size and frequency provide a quantitative readout of that length-dependent stiffness.
  • The same scaling argument should apply to other motor–filament systems, such as actin–myosin spirals, as long as the tip speed remains density-independent.

Reading between the lines

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

  • My inference: the measured frequency exponents (0.083 for constant persistence length, 0.369 for variable persistence length) deviate from $1/3$, and the paper attributes this to finite pivot stiffness; an equally plausible partial explanation is that the effective tip speed is weakly force-dependent in real spirals, which would push the exponent upward.
  • My inference: if actin–myosin gliding assays also show density-independent filament speed, the same $1/3$ law should replace the $4/3$ prediction there; if their speed is force-dependent, such systems should fall on the $4/3$ branch of the unified relation.
  • My inference: the spiral assay could be used as a non-invasive probe of persistence length versus filament length, avoiding thermal-fluctuation measurements of grafted microtubules.
  • My inference: a direct test on kinesin-driven microtubules, where gliding speed is also roughly density-independent, should reproduce the $f^{1/3}$ frequency scaling and would confirm that the mechanism is not specific to dynein.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. This manuscript reconstitutes dynein-driven spiraling of microtubules (MTs) in a surface gliding assay with the MT plus end pinned, and compares the measured spiral radius and rotation frequency to scaling arguments and to simulations with explicit motor force generators. The authors report that the spiral radius scales with force density as R ∼ f^{−1/3}, consistent with earlier actin-myosin results, and that the frequency scales as ν ∼ f^{1/3}, in contrast to the previously predicted ν ∼ f^{4/3}. They also propose length-scaling predictions, R ∼ ℓ_p^{1/3} and ν ∼ ℓ_p^{−1/3}, and argue that a variable-persistence-length model for MTs fits their length-dependent data better than a constant-persistence-length model. The central frequency claim rests on a kinematic relation ν = |V_tip|/R combined with the assumption that |V_tip| is independent of motor density and filament length.

Significance. If correct, the paper would establish a new experimental system—dynein-driven MT spirals—and overturn a previously proposed frequency scaling, replacing it with a much weaker dependence on motor density. The manuscript has several concrete strengths: it provides new experimental data on a cytoskeletal system other than actin-myosin; it uses explicit-motor simulations that reproduce both the spiraling morphology and the frequency range; it formulates a scaling argument that reduces to the old 4/3 law when the tip speed is force-dependent, thereby identifying the precise assumption that separates the two predictions; and it includes a data/code availability statement. However, the central frequency claim is currently supported by an unmeasured assumption about the tip speed inside the spiral, and the experimental frequency exponent is sensitive to the chosen persistence-length model. These issues must be resolved before the 1/3 scaling can be regarded as established.

major comments (3)
  1. [Theoretical scaling relation of the spiraling frequency (Eqs. 7–9); Fig. S5] The prediction ν ∼ f^{1/3} depends entirely on the statement that |V_tip| is independent of motor density and filament length. The only evidence offered is Fig. S5, which reports straight-gliding velocities in a conventional gliding assay, not the speed of the free tip in the curved, rotating spiral. In a spiral, the tip experiences elastic forces from bending and from interaction with neighboring turns, so its speed need not equal the straight-gliding speed. If |V_tip| ∼ f, Eq. (9) immediately recovers the old ν ∼ f^{4/3} scaling. Since this is exactly the point where the paper diverges from prior work, the assumption must be tested directly. The existing tracked trajectories appear to contain enough information to measure |V_tip| inside the spiral; at minimum, the authors should report this quantity for both experiments and simulations over the full density and length ranges.
  2. [Fig. 5C and the persistence-length model selection] The experimental frequency exponent is not robust: the same data give 0.083 when rescaled with constant persistence length and 0.369 when rescaled with variable persistence length. The claim that the experimental exponent is “closer to 1/3 than to 4/3” therefore holds only under the variable-persistence-length model, which is selected by RMSRE comparisons of the length-scaling data (Figs. 4F and 5F), not by a direct measurement of ℓ_p(L). In addition, the experimental scaling exponents are quoted without error bars or confidence intervals, and the sample sizes are not stated. The authors should provide these uncertainties and, ideally, an independent measurement of ℓ_p(L) or an explicit model-selection criterion that accounts for the different complexity of the two models.
  3. [Eq. (5) and the length-scaling test] The prediction ξ(L) ∼ ℓ_p^{1/3} is obtained by rearranging Eq. (4), the same radius scaling used to define ξ. The simulation test therefore confirms that the simulation obeys the input persistence-length model, and the experimental test assumes Eq. (4) in order to infer which ℓ_p model applies. This is a useful consistency check, but it is not an independent test of the predicted length exponent. The discussion should state this limitation explicitly; otherwise the length-scaling results could be overinterpreted as independent confirmation of both Eq. (4) and the variable-ℓ_p model.
minor comments (4)
  1. [Fig. 4C and Fig. 5C] The power-law fits report R² values but no confidence intervals for the exponents. Given that the key discrimination is between −1/3 and −2/3 or between 1/3 and 4/3, the authors should provide bootstrap or regression uncertainties and the number of spirals used in each fit.
  2. [Materials and methods, frequency estimation] The criterion for excluding tracks (“divergence in dominant frequency greater than 0.01 Hz”) is described only briefly. Please report how many tracks were excluded and whether the results are robust to this threshold.
  3. [Eq. (14)] The conversion from motor area density to linear force density uses a duty ratio r and MT width w. Since these enter as multiplicative constants, they do not affect the fitted exponents, but the estimated force-density values should be labeled as order-of-magnitude estimates rather than precise measurements.
  4. [General presentation] Several equations and subscripts are garbled in the text (e.g., the persistence length notation around Eq. (3) and the scaling relations in Figs. 4 and 5). A careful typesetting pass is needed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the frequency and length scaling predictions are transparent consequences of stated assumptions and are tested against simulations with known inputs.

full rationale

The paper's derivation chain is self-contained. The radius scaling (Eq. 4) follows from an energy balance equating motor work W~fRL to bending energy E_b~kTL/R^2. The frequency scaling (Eqs. 6-8) is obtained from the kinematic identity omega=V_tip/R combined with Eq. 4 and the explicitly stated assumption that |V_tip| is independent of motor density and filament length. This assumption is not fitted to the frequency data; it is supported by independent gliding-velocity measurements (Fig. S5 and refs. [33-35], including external refs. [34,35]), so the predicted 1/3 exponent is not a fit renamed as a prediction. The length-scaling predictions (Eqs. 5 and 11) are algebraic rearrangements of the same scaling laws, but they are validated against simulations in which the persistence-length input (constant or variable) is known, and the experimental comparison uses RMSRE to select between two explicit models. The main weaknesses are not circular: the constancy of |V_tip| inside the curved spiral is not directly measured, and the experimental frequency exponent is conditional on the variable-persistence-length model (0.369 vs 0.083 under constant l_p). These are correctness risks, not reductions of a prediction to its input by construction. Self-citations ([17], [33]) appear for methods and as supporting velocity references, but they are not load-bearing because external references and the paper's own simulations also support the assumption. No circular step is present.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central scaling arguments rest on a small number of physical assumptions, the most fragile being the density- and length-independence of the tip velocity. The variable persistence length formula is taken from prior literature, not fitted. No new entities are introduced.

free parameters (3)
  • pivot stiffness k_p = 10^4 to 10^5 pN/um (range explored; main sims use values in this range)
    Chosen for the pinning trap in simulations; varied in Figures S3, S4, S7 to explain deviations of the scaling exponent from the theoretical -1/3 and 1/3. The paper attributes experimental deviation to finite pivot stiffness without direct measurement.
  • duty ratio r = Not stated explicitly
    Used in the conversion from motor surface density to linear force density, f = w * r * rho_m * F_s (Eq. 14). The value is an estimate consistent with prior work [15]; it affects the absolute force density scale but not the log-log scaling exponents.
  • microtubule width w = 25 nm (standard)
    Geometric input for the band model conversion in Eq. 14; standard value from literature, not fitted.
assumptions (6)
  • domain assumption The spiral approaches a limiting circle with uniform curvature lambda = 1/R
    Used in the bending energy estimate E_b ~ kappa_b L / R^2 and the work estimate W ~ f R L to derive Eq. 4.
  • domain assumption The free tip moves at constant linear speed independent of motor density and filament length
    Used to simplify Eq. 7 to nu ~ f^{1/3} (Eq. 8). If |V_tip| ~ f, Eq. 9 recovers the prior 4/3 scaling. This is the load-bearing assumption distinguishing the new prediction.
  • domain assumption Variable persistence length model l_p(L) = l_p^0 / (1 + 441/L^2) (Eq. 3) from Pampaloni et al.
    Imported from prior literature [23]; the paper's conclusion that MT persistence length varies with length depends on this model being the correct representation.
  • domain assumption Overdamped Langevin dynamics and low Reynolds number
    Simulation model (Model section, Eqs. 1-2).
  • domain assumption Motor force-velocity and detachment kinetics (Eqs. 1-2)
    Simulation input from literature.
  • standard math Uniform circular motion relation omega = V/R
    Kinematic identity used to define spiraling frequency (Eq. 6).

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Cite this review

Pith. "Pith review of Physical Principles of Size and Frequency Scaling of Active Cytoskeletal Spirals." pith.science (2026). https://pith.science/paper/4PJHEDAD

@misc{pith2026250810114,
  author       = {Pith},
  title        = {Pith review of: Physical Principles of Size and Frequency Scaling of Active Cytoskeletal Spirals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4PJHEDAD}},
  note         = {Machine review of arXiv:2508.10114}
}
read the original abstract

Cytoskeletal filaments transported by surface immobilized molecular motors with one end pinned to the surface have been observed to spiral in a myosin-driven actin 'gliding assay'. The radius of the spiral was shown to scale with motor density with an exponent of -1/3, while the frequency was theoretically predicted to scale with an exponent of 4/3. While both the spiraling radius and frequency depend on motor density, the theory assumed independence of filament length, and remained to be tested on cytoskeletal systems other than actin-myosin. Here, we reconstitute dynein-driven microtubule spiraling and compare experiments to theory and numerical simulations. We characterize the scaling laws of spiraling MTs and find the radius dependence on force density to be consistent with previous results. Frequency on the other hand scales with force density with an exponent of ~1/3, contrary to previous predictions. We also predict that the spiral radius scales proportionally and the frequency scales inversely with filament length, both with an exponent of ~1/3. A model of variable persistence length best explains the length dependence observed in experiments. Our findings that reconcile theory, simulations, and experiments improve our understanding of the role of cytoskeletal filament elasticity, mechanics of microtubule buckling and motor transport and the physical principles of active filaments.

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    with (inset) ℓ� � for physiological MT lengths of 1 to 10 µm and (B) constant persistence length based on the results of Gittes et al. [19]. 27 ������� � ������ Figure S2: Radius analysis of spirals. (A–C) Spiraling radius as a function of motor density with MT lengths (color-...

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Reviewed August 5, 2026 · model on record in the stance chip above.