{"id":"7e9914b9-047b-4391-89c2-37967387b97c","arxiv_id":"1908.07570","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":17,"one_line_summary":"A two-state kinetic model predicts that kinesin's randomness parameter has a non-monotonic ATP dependence if ATP binds with both heads attached, but a monotonic decrease if the trailing head detaches first.","lead":"This paper models two competing possibilities for how the kinesin motor waits for ATP and shows that the randomness parameter should behave differently in each case. Measuring this parameter as a function of ATP concentration and force could settle a standing experimental controversy.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The monotonic-vs-minimum randomness contrast is not robust to the model's two-state compression: adding one slow ATP-independent state can make the 1HB prediction non-monotonic.","rationale":"I agree with the reader that the load-independence of the 2HB->1HB transition (stated after Fig. 1) is a real and testable assumption, and the reader's suggested check is worthwhile. However, I find a more fundamental problem in the same area of the argument: the qualitative prediction is derived from a deliberately two-state model, and the paper's own words concede that this compression is severe enough to force r >= 0.5, whereas the cited experiments report r values below 0.5. The Discussion attempts to reassure the reader that adding ATP-independent states will not change the qualitative [T]-dependence, but the mathematics of summed dwell times shows otherwise. A single slow ATP-independent state can move the randomness minimum into the experimentally accessible [T] range for the 1HB model, turning the predicted monotonic decrease into a non-monotonic curve. This undermines the central claim that randomness measurements will unambiguously discriminate the waiting states, because the predicted contrast may be an artifact of the collapsed state count rather than a robust property of the two waiting-state scenarios. The paper's other contributions are not affected: the dwell-time comparison in Fig. 3 is a genuine emergent check, and the analytical expressions for P(n) and P(v) are valuable. The right outcome remains CONDITIONAL as the reader recommended: the paper should be accepted only if the claims are softened from 'unambiguous' to 'within the minimal two-state model', and ideally the SI should include the three-state sensitivity test. The reader's concern about load-dependent k is compatible with mine and is partially the same family of assumption-sensitivity issue, but the state-compression issue is more load-bearing because it threatens the [T]-dependence even at zero load.","tokens_in":26579,"tokens_out":15564,"duration_ms":346640,"concrete_test":"Append one ATP-independent exponential state with rate c in the range 5-100 s^-1 to the fitted 1HB model (Table 2) and to the 2HB model (Table 1), choosing c so that the total randomness at saturating [T] matches the sub-0.5 values in Visscher et al. (13) or Verbrugge et al. (47). Compute rC([T]) exactly as (sum of inverse rate squares)/(sum of inverse rates)^2. If the 1HB rC develops a minimum at any such c, or the 2HB minimum disappears, the predicted qualitative contrast is not robust. Separately, allow the 2HB->1HB rate k to carry a Bell load factor k(F) = k0 exp(+-beta F d_k) with |d_k| <= 2 nm and recheck whether the 1HB monotonic versus 2HB minimum distinction survives for F up to 7 pN.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weakness is not a single rate but the reduction to exactly two states, on which the qualitative contrast rests. The paper acknowledges (Discussion: 'the calculated randomness parameters cannot be below 0.5' and 'we compressed many potentially relevant states into one internal state') that the two-state model is a simplification, then argues that adding ATP-independent states will not change the qualitative [T]-dependence. That argument is not generally correct. For a dwell time that is a sum of an ATP-dependent exponential with rate k_ATP([T]) and an ATP-independent exponential with rate c, the chemical randomness is r = (k_ATP^-2 + c^-2)/(k_ATP^-1 + c^-1)^2, which has a minimum at k_ATP = c, regardless of the bare rates in the two-state model. In the fitted 1HB model (Table 2), k = 538 s^-1 and the ATP-dependent sum x = k+ + k- + gamma reaches only about 188 s^-1, so the two-state rC decreases monotonically. But if a single slow internal state with c ≈ 20 s^-1 is added, the minimum moves to x ≈ 20 s^-1, which is reached at a finite [T]; the 1HB rC then becomes non-monotonic. Thus the claimed 'monotonic in 1HB, minimum in 2HB' signature is an artifact of the collapsed state count, and the paper's robustness claim ('we argue ... should be observable') is unsupported by the manuscript.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper develops a two-state kinetic model for kinesin-1 stepping in which the ATP-waiting state is either one-head-bound (1HB) or two-heads-bound (2HB) to the microtubule. For each scenario the authors derive closed-form expressions for the run-length distribution, the velocity distribution, and the chemical and mechanical randomness parameters as functions of ATP concentration [T] and resistive load F. The parameters are fitted to published run-length, velocity, and force-velocity data, while the dwell-time data of the two conflicting single-molecule experiments (Mickolajczyk et al. and Isojima et al.) are deliberately not used in the fit; the model reproduces those dwell times well. The central prediction is that the randomness parameter as a function of [T] and F is qualitatively different in the two models: the 2HB model shows a clear minimum in the randomness parameter as [T] is varied, whereas the 1HB model shows a monotonic decrease that is almost flat with increasing force. The paper proposes that measuring the randomness parameter would discriminate between the two waiting states and resolve the controversy.","tokens_in":26999,"tokens_out":7864,"duration_ms":72015,"significance":"If the central prediction were robust, the paper would give experimentalists a straightforward, low-bias observable with which to resolve the long-standing disagreement about kinesin's ATP-waiting state. The work has real strengths: the analytical derivations in the SI are internally consistent; the comparison of the predicted 1HB and 2HB dwell times to the two conflicting experiments is a genuine not-fitted check; the prediction that P(n) is [T]-independent is consistent with existing experiments; and the authors test a variant of the 1HB model with a [T]-independent backward-step rate, showing that some qualitative features survive that modification. However, the central claim rests on the two-state compression of the kinetic cycle, and the manuscript does not establish that the qualitative monotonic-versus-minimum randomness signature survives the inclusion of additional ATP-independent internal states. The significance must therefore be considered conditional on that robustness.","major_comments":[{"comment":"The robustness argument against the two-state compression is not generally correct. For a dwell time that is the sum of an ATP-dependent exponential with rate x([T]) and an ATP-independent exponential with rate c, the chemical randomness is r = (c^{-2}+x^{-2})/(c^{-1}+x^{-1})^2, which has a minimum at x = c. In the fitted 1HB model (Table 2), k = 538 s^{-1} and the maximal ATP-dependent sum x_max = k_+^0 + k_-^0 + γ^0 ≈ 188 s^{-1}, so the two-state r_C decreases monotonically with [T]. If a single slow internal state with c ≈ 20 s^{-1} is added, the minimum occurs at a finite [T] (roughly 2.5 µM), making the 1HB r_C non-monotonic. Thus the claimed 'monotonic in 1HB, minimum in 2HB' signature is demonstrably an artifact of the collapsed state count, and the assertion that the qualitative difference 'should be amenable to experimental verification' is unsupported by the manuscript as written.","section":"Discussion, 'Randomness parameters are dramatically different between the two waiting states'"},{"comment":"The comparison of the predicted randomness parameters to the experimental data of Verbrugge et al. (47) and Visscher et al. (13) is only qualitative, and the two-state model has a hard lower bound r ≥ 0.5. In Fig. 5(a) several reported experimental values appear to fall below 0.5, which the model cannot reproduce. The paper acknowledges this and proposes an ad hoc vertical rescaling, but the rescaling is not derived from the model. Since the paper proposes the randomness parameter as the key discriminator between waiting states, the model must at least reproduce the experimental magnitudes in the region of the predicted minimum before the qualitative prediction can be considered quantitatively testable.","section":"Fig. 5 and accompanying text"},{"comment":"The assumption that the 2HB→1HB transition rate k is independent of load is used to generate the force dependence of the randomness parameters that the paper contrasts between the two models. If k itself is load-dependent (e.g., k(F) = k_0 exp(δF/k_B T)), the predicted near-flatness of the 1HB r_C as a function of F could be altered, and the qualitative contrast with the 2HB model might change. The paper states the assumption but gives no physical justification or sensitivity analysis. Because the force dependence is part of the central predictive claim, this missing analysis is a load-bearing gap.","section":"Main text after Fig. 1"}],"minor_comments":[{"comment":"The symbol kT is used for the total rate k + k_+ + k_- + γ, which is easily confused with k_B T used elsewhere in the same paragraph; please use a distinct symbol such as K_T or k_tot.","section":"Eq. (2)"},{"comment":"The definition of d± is garbled in the sentence 'd±= d±‖F‖/F and the load Fd = (|F|kBT)/(F⊥dγ)'; the notation for the parallel and perpendicular components of the load should be rewritten clearly.","section":"Main text, parameter definitions"},{"comment":"The name 'Micolajczky et al.' is misspelled; it should be 'Mickolajczyk et al.'.","section":"Introduction"},{"comment":"The phrase 'observables quantities' should be 'observable quantities'.","section":"Abstract"},{"comment":"The caption labels panels (a) and (b) as 2HB and 1HB, but the text above says the upper panel is for the 2HB model and the lower panel is for the 1HB model; the caption and text are inconsistent.","section":"Fig. 3 caption"},{"comment":"The main text says 'we found analytical expressions for rC and rM', but rM is actually computed numerically by truncating the sums in Eq. (S31)-(S32) at a finite time t = 0.5 s. Please clarify that only rC is obtained in closed form and describe the numerical convergence of rM.","section":"SI Sections III.B and VI"}],"recommendation":"major_revision","confidential_remarks":"The paper is a modest extension of the authors' earlier model (Vu et al. 2016), with the main new element being the [T]-dependence of the randomness parameters. The analytical machinery is sound and the not-fitted dwell-time comparison is a genuine strength. My main concern is that the central discriminating prediction is not robust to the two-state compression, and the Discussion's robustness argument is demonstrably incorrect for a simple counterexample. The authors should be asked either to prove robustness in a more general setting or to soften the central claim accordingly. The fit to the journal's scope is fine; the manuscript is suitable for a molecular-biophysics audience."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The paper's genuinely new product is a pair of two-state kinetic schemes for kinesin's ATP waiting state, solved analytically for run length, velocity, and randomness as functions of [T] and load. The headline prediction is that the randomness parameter rC or rM has a minimum in the 2HB model but decreases monotonically in the 1HB model, offering a clean experimental discriminator. That contrast is the reason to read the paper. The second thing: the contrast is not robust to the model's own compression of internal states. The stress-test calculation is correct: add a single slow ATP-independent state with rate c ≈ 20 s^-1 to the 1HB scheme, and the randomness parameter develops a minimum at finite [T], just like the 2HB model. The paper's argument that ATP-independent states cannot change the qualitative [T]-dependence is wrong because a slow state sets a second timescale; rC has a minimum when the ATP-dependent rate crosses c. With the fitted parameters in Table 2, the 1HB two-state rC is monotonic only because the mean ATP-dependent rate stays below k = 538 s^-1; a slow internal state reverses that. The paper itself notes it 'compressed many potentially relevant states into one internal state,' but dismisses the consequence too quickly.\n\nWhat is good: the analytic derivations in the SI are careful and transparent; the run-length expression is explicitly identified as equivalent to earlier work, which is honest; and the dwell-time comparison in Fig. 3 against the two conflicting experiments is a genuine, not-fitted check that works well. The SI variant where k- is [T]-independent shows the randomness predictions are robust to that particular modeling choice. That is real work.\n\nSoft spots, in proportion: the load-independence assumption for k (stated after Fig. 1) is unexamined, and if load changes k the force-dependent contrast could shift. Existing randomness data (Visscher, Verbrugge) agree only qualitatively, and the paper admits two-state randomness cannot go below 0.5. Those are minor to moderate. The slow-state issue is load-bearing. The 'unambiguously' framing in the abstract and conclusion is stronger than the evidence.\n\nBottom line: this is a useful analytic model for a field that needs testable discriminators, and the authors are honest about most limitations. But the central claim that randomness measurements can unambiguously settle the waiting state is not supported, because the monotonic-versus-minimum signature is an artifact of collapsing all ATP-independent steps into one fast rate. A referee should ask for a sensitivity analysis with an added slow internal state, and for softened language. I would send this to peer review; a good referee can sharpen it into a valuable contribution.","headline":"Solid two-state kinesin model and a clever randomness discriminator, but the monotonic-vs-minimum signature evaporates if a slow ATP-independent state is added; needs a robustness check before the 'unambiguous' claim stands.","tokens_in":27513,"tokens_out":5401,"would_cite":true,"duration_ms":47933,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The randomness parameter of kinesin's stepping has opposite ATP- and force-dependence depending on whether the motor waits for ATP with both heads bound or with one head detached, and measuring it can settle which waiting state is real.","keywords":["kinesin","molecular motor","ATP waiting state","randomness parameter","two-state kinetic model","load dependence","hand-over-hand mechanism","single-molecule biophysics"],"falsifier":"Measure the randomness parameter of kinesin-1 at zero load across ATP concentrations from about 10 µM to 1 mM using a high-resolution dark-field or iSCAT assay: a clear minimum near 100 µM would support the both-heads-bound waiting state, whereas a monotonic decrease would support the one-head-bound state. Repeating the measurement at 4–6 pN of resistive load would test the predicted near-flat versus force-dependent behavior.","tokens_in":26381,"feed_emoji":"🧬","tokens_out":9189,"duration_ms":80708,"temperature":0.7,"pith_summary":"Dimeric kinesin walks along microtubules by hydrolyzing one ATP per step, but it is still debated whether the motor waits for ATP with both heads attached to the track or with the trailing head already detached. This paper constructs two minimal kinetic models—one for each waiting state—and solves them analytically for the run-length distribution, the velocity distribution, and the randomness parameter (the normalized variance of dwell times) as functions of ATP concentration and resistive load. The central prediction is that the randomness parameter is qualitatively different between the two scenarios: it develops a minimum near 100 µM ATP when both heads wait bound, and decreases monotonically while staying almost flat with force when one head is detached. Because the randomness parameter can be extracted directly from stepping trajectories, the authors argue that measuring it at a few ATP concentrations and loads could resolve the controversy.","feed_headline":"Kinesin's ATP wait leaves a fingerprint in step randomness","feed_subtitle":"A measurable randomness pattern could end the debate over whether kinesin waits with one or two heads attached.","key_machinery":"The central object is a two-state chemical-kinetic scheme in which the motor alternates between a state with both heads bound to the microtubule (2HB) and a state with one head bound (1HB); forward stepping, backward stepping, and detachment occur from the 1HB state. ATP dependence enters either the 2HB→1HB transition (2HB model) or the stepping and detachment rates (1HB model), with Michaelis-Menten kinetics, and load dependence enters through Bell-model exponentials on the load-bearing rates. The analytical solution yields closed forms for the stationary fluxes, the run-length distribution $P(n)$, the velocity distribution $P(v)$ (involving modified Bessel functions), and the chemical randomness parameter $r_C = (k^2 + (k_+ + k_- + \\gamma)^2)/(k + k_+ + k_- + \\gamma)^2$, where $k$ is the 2HB→1HB rate and $k_+$, $k_-$, $\\gamma$ are the forward, backward, and detachment rates. The qualitative difference between models arises from which rate changes with [T] and load, producing or suppressing a crossover in the rate-limiting step.","core_discovery":"On the authors' own terms, the discovery is that the waiting state of kinesin for ATP is encoded in the [T]- and F-dependence of the randomness parameter. In the 2HB model, where ATP binds to the leading head while both heads are on the microtubule, the randomness parameter is non-monotonic in ATP concentration with a minimum near [T] = 100 µM at all forces studied; in the 1HB model, where ATP binds only after the trailing head has detached, it decreases monotonically and is nearly flat as force increases. The difference arises because in the 2HB model the rate-limiting step switches from ATP binding at low [T] to the stepping transition at high [T], while in the 1HB model the stepping transition is always rate-limiting and is only slowed further by load. Run-length distributions, by contrast, are predicted to be insensitive to the waiting state, and velocity distributions are bimodal under load in both models, differing only quantitatively at low ATP.","pith_inferences":["An extension the authors do not spell out: the same two-state discrimination could be tried on other processive motors, such as myosin V or dynein, where a non-monotonic versus monotonic randomness parameter would likewise reveal when ATP binds relative to partner-head detachment.","A direct test of the model's load-bearing assumption would be to measure the lifetime of the both-heads-bound state as a function of load; if that lifetime changes with force, the predicted force contrast between the waiting states would need revision.","Because the model compresses many ATP-independent internal states into one, it likely overestimates the absolute level of the randomness parameter; the most decisive experimental comparison is therefore the shape of r([T]) and r(F) curves, not their absolute values."],"forward_implications":["A measurement of the randomness parameter over ATP concentrations from roughly 10 µM to 1 mM at zero load can discriminate the waiting states: a minimum near 100 µM supports the both-heads-bound model, a monotonic decrease supports the one-head-bound model.","The predicted bimodality of the velocity distribution under load is present in both models at both low and high ATP, so this signature can be tested without first resolving the waiting-state question.","The run-length distribution is predicted to be independent of ATP concentration in both models, consistent with existing data above about 10 µM, so run lengths cannot serve as the discriminating observable.","Because the 1HB model keeps the randomness parameter close to one and nearly flat with force, while the 2HB model produces a force-dependent dip, repeating the measurement at 4–6 pN would provide a second, independent discriminator."],"supporting_citations":[{"why":"The iSCAT experiment concluding kinesin waits for ATP with both heads bound; its 2HB dwell-time data are compared with the model.","marker":"(1)"},{"why":"The dark-field experiment concluding ATP binds only after the trailing head detaches; its 1HB dwell-time data anchor the alternative model.","marker":"(2)"},{"why":"Supplies the zero-load run-length and velocity distributions used to fit the model's rate parameters.","marker":"(12)"},{"why":"The earlier stepping model predicting bimodal velocity distributions that this work extends to ATP-concentration dependence.","marker":"(15)"},{"why":"Provides load- and ATP-dependent velocity data and forward/backward step ratios used to fit load-sensitive parameters.","marker":"(41)"},{"why":"Optical-trapping randomness-parameter measurements under load used to compare with the model's force predictions.","marker":"(13)"},{"why":"Fluorescence-based randomness-parameter measurements at zero load used to compare with the model's zero-force predictions.","marker":"(47)"}],"fun_headline_variants":["Randomness parameter settles kinesin ATP-wait debate","Kinesin's wait state encoded in randomness pattern","One randomness measurement could end kinesin wait debate","Step randomness reveals how kinesin waits for ATP","Randomness pattern could pick kinesin waiting-state model"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions rest on the assumption that the rate of the both-heads-bound to one-head-bound transition is independent of external load; if load changes that rate, the predicted force contrast between the two waiting states would be altered.","fun_headline_variants_meta":{"raw":{"variants":["Randomness parameter settles kinesin ATP-wait debate","Kinesin's wait state encoded in randomness pattern","One randomness measurement could end kinesin wait debate","Step randomness reveals how kinesin waits for ATP","Randomness pattern could pick kinesin waiting-state model"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000804,"raw_usage":{"total_tokens":3490,"prompt_tokens":863,"completion_tokens":2627,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":479,"completion_tokens_details":{"reasoning_tokens":2549}},"tokens_in":479,"tokens_out":2627,"duration_ms":21778,"temperature":1.0,"reasoning_tokens":2549,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T12:12:57.360235+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the randomness parameter of kinesin-1 at zero load across ATP concentrations from about 10 µM to 1 mM using a high-resolution dark-field or iSCAT assay: a clear minimum near 100 µM would support the both-heads-bound waiting state, whereas a monotonic decrease would support the one-head-bound state. Repeating the measurement at 4–6 pN of resistive load would test the predicted near-flat versus force-dependent behavior.","supporting_citations":[],"review_version":1}