{"id":"88e473de-b6c4-4496-9369-412bc8397458","arxiv_id":"2508.10114","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Dynein-driven microtubule spirals rotate with frequency scaling as force density to the one-third power, not four-thirds, and their length scaling supports a variable persistence length model.","lead":"Pinned microtubules pushed by dynein motors form spirals whose radius shrinks with motor density as the known minus one-third power, but whose rotation frequency grows only as the one-third power of force density, not the previously predicted four-thirds. The results suggest microtubule persistence length depends on filament length, which shifts how spiral radius and frequency scale with size.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Claimed 1/3 frequency scaling hinges on unmeasured constancy of spiral tip speed; experiments also depend on persistence-length model.","rationale":"The reader's weakest_assumption identifies exactly the load-bearing step: the derivation of ν ∼ f^{1/3} assumes |V_tip| is independent of motor density and length, and this is only supported by straight-gliding measurements and simulations, not by direct measurement inside spirals. I checked the manuscript for a direct tip-speed measurement and found none: Fig. S5 is explicitly labeled as an in silico gliding assay, and the experimental frequency analysis uses FFT of tracked tip positions without reporting tip speeds as a function of f or L. The kinematic relation ω = V/R is plausible for a steadily rotating spiral, but it transfers the burden to V_tip, and that burden is not met. I also note the additional model dependence of the experimental exponent (0.083 vs 0.369 in Fig. 5C), which reinforces the conditionality of the claim: the 1/3 result only appears after adopting the variable-persistence-length rescaling, which is selected by RMSRE comparisons without statistical testing. My proposed test directly measures the missing quantity and would settle whether the frequency claim is an independent discovery or a consequence of an auxiliary model choice. Since the reader already issued a CONDITIONAL verdict, my read does not change that verdict; it sharpens the condition.","tokens_in":16191,"tokens_out":6536,"duration_ms":77016,"concrete_test":"From the existing MTrackJ trajectories used for the FFT frequency analysis, compute the mean instantaneous tip speed |V_tip| in steady-state spirals (e.g., from cubic-spline derivatives of the tracked X-Y positions after the 350 s equilibration). Plot log|V_tip| vs log f at fixed MT length and vs log L at fixed motor density, for both experiment and simulation. Fit the slope: if it is within ~0.1 of zero, the constant-|V_tip| assumption behind Eq. 8 is internally consistent with the claimed 1/3 scaling; if it is near 1, the frequency data support Eq. 9 and the old 4/3 scaling. In the same pass, also recompute the experimental ν(f) exponent without the variable-ℓ_p rescaling and with an independently measured ℓ_p(L) from thermal-fluctuation shape analysis of the same MT preparation; if the exponent moves far from 1/3, the central claim is model-dependent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central frequency claim rests entirely on Eq. 8, which obtains ν ∼ f^{1/3} only after asserting that |V_tip| is independent of motor density and filament length; if |V_tip| ∼ f, Eq. 9 recovers the old ν ∼ f^{4/3}. The only support offered for constant |V_tip| is Fig. S5, which reports straight-gliding velocity in an in silico gliding assay, not the speed of the free tip in the curved, rotating spiral. In a buckled spiral the tip experiences elastic and normal forces from adjacent turns, so its speed need not equal the straight-gliding speed; the kinematic bridge ν ≈ |V_tip|/R from the measured R(f) to the claimed ν(f) is therefore unvalidated. This is not a peripheral detail—it is the exact place where the new 1/3 prediction diverges from the previous 4/3 prediction. Additionally, the experimental frequency exponent is not robust to the persistence-length model: the same data give 0.083 under constant ℓ_p and 0.369 under variable ℓ_p (Fig. 5C), so the '~1/3' claim is already conditional on the variable-ℓ_p model selected by RMSRE rather than by a direct measurement of ℓ_p(L). Both missing measurements can be obtained from the existing tracked trajectories and MT samples.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16525,"tokens_out":4277,"duration_ms":53458,"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":[{"comment":"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.","section":"Theoretical scaling relation of the spiraling frequency (Eqs. 7–9); Fig. S5"},{"comment":"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.","section":"Fig. 5C and the persistence-length model selection"},{"comment":"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.","section":"Eq. (5) and the length-scaling test"}],"minor_comments":[{"comment":"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.","section":"Fig. 4C and Fig. 5C"},{"comment":"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.","section":"Materials and methods, frequency estimation"},{"comment":"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.","section":"Eq. (14)"},{"comment":"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.","section":"General presentation"}],"recommendation":"major_revision","confidential_remarks":"The paper is a good candidate for the journal if the authors can supply the missing direct measurement of tip speed in spirals and make the experimental frequency exponent robust to model choice. The first issue is not merely a technicality; it is the precise assumption that separates the new 1/3 scaling from the old 4/3 scaling. I would encourage the editor to request a revision rather than reject, because the experimental system and simulation framework are valuable and the requested analysis appears feasible from the data already in hand."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe thing to know: this paper reports the first dynein-driven microtubule spiraling assay, and it claims the spiral frequency scales with force density as f^(1/3), not the f^(4/3) predicted earlier. The new experiment is real, and the radius scaling they measure (exponent -0.37) is consistent with the long-standing -1/3. The simulations reproduce the spiraling patterns and roughly match the measured frequency exponent. That is a solid core.\n\nWhere the paper is genuinely innovative is in using length-dependent scaling of radius and frequency as a probe of the persistence-length model. The variable persistence-length model from Pampaloni et al. fits their data better than the constant one. That is an interesting, falsifiable way to address a contested property.\n\nNow the soft spots, in order of severity. The frequency scaling argument hinges on the assumption that the free tip speed in the spiral is independent of motor density and filament length. They justify this with straight-gliding velocities from simulations and prior work, but they never measure the tip speed inside the curved, buckled spiral. If that speed grows with force density, their own Eq. 9 recovers the old 4/3. The stress-test note is right: this is exactly where the 1/3 result lives or dies.\n\nSecond, the experimental frequency exponent is not robust. The same data give 0.083 under constant persistence length and 0.369 under variable persistence length (Fig. 5C). So the \"~1/3\" claim is contingent on choosing the variable model, and that choice is made by RMSRE without confidence intervals or a statistical test. That is load-bearing selection.\n\nThird, practical reproducibility: experimental exponents have no error bars, and the number of spirals analyzed is not stated. The GitHub repository link in the Methods is a placeholder. These are easy fixes.\n\nSo: is the paper worth a serious referee? Yes. The system is new, the question matters, and the scaling argument is clear enough to test. But the current manuscript should not be accepted as is. The authors need to measure or otherwise bound the tip speed in the spiral, report uncertainty on the exponents, and address the model-dependence of the frequency result directly. I would send it to review with the expectation of major revision.","headline":"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.","tokens_in":17016,"tokens_out":2348,"would_cite":true,"duration_ms":25429,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Dynein-pinned microtubules rotate with a frequency that scales as the cube root of motor density, overturning the predicted 4/3 power law.","keywords":["microtubule spirals","gliding assay","dynein","scaling laws","persistence length","active filaments","buckling","motor density"],"falsifier":"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.","tokens_in":16097,"feed_emoji":"🌀","tokens_out":4667,"duration_ms":49727,"temperature":0.7,"pith_summary":"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.","feed_headline":"Spiral frequency climbs only with cube root of motor force","feed_subtitle":"Dynein-driven microtubule experiments overturn a predicted 4/3 scaling law.","key_machinery":"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.","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the original scaling argument for spiral radius $R \\sim f^{-1/3}$ and the $4/3$ frequency prediction that this paper tests and modifies.","marker":"[15]"},{"why":"Provides numerical simulations of buckling instabilities and spatio-temporal dynamics of active elastic filaments, including the $4/3$ frequency scaling benchmark.","marker":"[18]"},{"why":"Provides the standard constant flexural rigidity and persistence length of microtubules used in the constant-$\\ell_p$ model.","marker":"[19]"},{"why":"Supplies the variable persistence length formula $\\ell_p(L)$ used to predict and fit the length-dependent radius and frequency scaling.","marker":"[23]"},{"why":"Provides the prior clamped-microtubule wave-oscillation experiments and the assay methodology that the spiral experiments extend.","marker":"[17]"},{"why":"Supplies single-molecule gliding assay evidence that filament speed is independent of motor density, underpinning the assumption that $|V_{\\mathrm{tip}}|$ is constant.","marker":"[35]"},{"why":"Provides the dynein-based collective transport measurements and motor-density calibration used to convert surface density to linear force density.","marker":"[33]"},{"why":"Supplies single-molecule dynein processivity and stepping parameters used as simulation inputs for motor velocity and stall force.","marker":"[12]"}],"fun_headline_variants":["Motor spiral frequency scales as force^(1/3), not 4/3","Cube-root law governs spiral frequency in actin and microtubules","New experiments overturn predicted 4/3 spiral frequency scaling","Spiral frequency ties to force cube root in dynein-driven microtubules"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Motor spiral frequency scales as force^(1/3), not 4/3","Cube-root law governs spiral frequency in actin and microtubules","New experiments overturn predicted 4/3 spiral frequency scaling","Spiral frequency ties to force cube root in dynein-driven microtubules"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00016,"raw_usage":{"total_tokens":1088,"prompt_tokens":782,"completion_tokens":306,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":526,"completion_tokens_details":{"reasoning_tokens":229}},"tokens_in":526,"tokens_out":306,"duration_ms":4558,"temperature":1.0,"reasoning_tokens":229,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T20:53:49.330410+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Bourdieu, T","cited_arxiv_id":null,"evidence_quote":"Supplies the original scaling argument for spiral radius $R \\sim f^{-1/3}$ and the $4/3$ frequency prediction that this paper tests and modifies."},{"cited_title":"Buckling instabilities and spatio-temporal dynamics of active elastic filaments","cited_arxiv_id":null,"evidence_quote":"Provides numerical simulations of buckling instabilities and spatio-temporal dynamics of active elastic filaments, including the $4/3$ frequency scaling benchmark."},{"cited_title":"Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape","cited_arxiv_id":null,"evidence_quote":"Provides the standard constant flexural rigidity and persistence length of microtubules used in the constant-$\\ell_p$ model."},{"cited_title":"Thermal fluctuations of grafted microtubules provide evi- dence of a length-dependent persistence length","cited_arxiv_id":null,"evidence_quote":"Supplies the variable persistence length formula $\\ell_p(L)$ used to predict and fit the length-dependent radius and frequency scaling."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the prior clamped-microtubule wave-oscillation experiments and the assay methodology that the spiral experiments extend."},{"cited_title":"Movement of microtubules by single kinesin molecules","cited_arxiv_id":null,"evidence_quote":"Supplies single-molecule gliding assay evidence that filament speed is independent of motor density, underpinning the assumption that $|V_{\\mathrm{tip}}|$ is constant."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the dynein-based collective transport measurements and motor-density calibration used to convert surface density to linear force density."},{"cited_title":"Single- molecule analysis of dynein processivity and stepping behavior","cited_arxiv_id":null,"evidence_quote":"Supplies single-molecule dynein processivity and stepping parameters used as simulation inputs for motor velocity and stall force."}],"review_version":1}