{"id":"322a43b6-934f-4a71-81ea-f8605ab67b4b","arxiv_id":"2411.14291","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Structural randomness in sarcomeres raises Shannon entropy, which lowers the maximum binding energy and makes the cytoskeleton easier to remodel.","lead":"This paper proposes a thermodynamic account of why nonmuscle cells have more variable sarcomere lengths than muscle cells. It uses Shannon entropy of sarcomere length distributions to estimate binding energy, arguing that disorder lowers the barrier to cytoskeletal remodeling and thus enables adaptation.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (8) is an upper bound, but Fig. 5 treats it as an equality; the claimed quantitative binding-energy ordering and Kd comparison do not follow without showing the bound is tight.","rationale":"The reader's weakest assumption concerns the identification of the Shannon entropy of the measured sarcomere length distribution with the system entropy change, and the choice of chemical potential from ATP hydrolysis. Those are real concerns, but the most load-bearing logical gap in the central claim is separate: Eq. (8) provides an inequality, yet the paper's Figure 5 and the subsequent Kd comparison treat the right-hand side as the actual binding energy. This is not a matter of parameter uncertainty; it is an internal mismatch between the derived bound and its use. The qualitative direction of the argument could survive a reframing, since a less negative upper bound can be interpreted as a lower required binding strength, but the quantitative claim that nonmuscle sarcomeres actually bind more weakly, and the comparison to measured Kd values, require the bound to be tight. The paper provides no argument that the bound is saturated, and for a genuinely nonequilibrium ATP-driven process one would generally expect strict inequality. Because the reader already returned CONDITIONAL, and this concern strengthens the need for revision without fully overturning the conceptual framework, the verdict should remain CONDITIONAL.","tokens_in":10010,"tokens_out":11077,"duration_ms":112921,"concrete_test":"Recompute the points in Fig. 5 as upper bounds rather than estimates, and overlay the actual binding free energies ΔG_bind derived from the cited Kd values (refs 49-51) for muscle and nonmuscle α-actinin, using a consistent sign convention where more negative means stronger binding. Check whether each ΔG_bind satisfies ΔG_bind ≤ ΔE_max for its cell type and whether the gap ΔE_max - ΔG_bind is approximately zero for all cell types. If the gaps are large or vary systematically between muscle and nonmuscle classes, then Fig. 5 does not estimate actual binding energies and the Kd comparison is unsupported; if the gaps are uniformly near zero, the saturation assumption would be empirically supported despite not being derived.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim rests on Eq. (8), ΔE_b ≤ ΔE_max = Δμ - (1/β)Σ P(x) ln P(x). This is an inequality derived from the second law, and because Σ P ln P < 0, the right-hand side equals Δμ + S/β, where S is the Shannon entropy. The paper, however, plots ΔE_max in Fig. 5 as \"the effective binding energy\" for each cell type and then compares these values to measured Kd values in Sec. 4 to conclude that nonmuscle sarcomere components bind more weakly than muscle ones. Mathematically, an upper bound on ΔE_b does not determine the actual ΔE_b unless the bound is saturated. In an ATP-driven nonequilibrium process, positive entropy production is expected, so σ > 0 and ΔE_b < ΔE_max strictly; the unknown gap σ/β may vary between muscle and nonmuscle cells. Therefore the ordering of the ΔE_max values does not logically imply the ordering of actual binding energies. Even if the identification of ΔS_sys with Shannon entropy and the choice Δμ = -20 kJ/mol were accepted, this inequality-to-equality step is unjustified and is load-bearing for the paper's claimed quantitative comparison.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes a nonequilibrium thermodynamics framework for sarcomere length variability. The authors model sarcomere length with an Ornstein-Uhlenbeck-type Fokker-Planck equation, obtain a Gaussian stationary distribution, equate the system entropy change with the Shannon entropy of the measured length distribution, and derive from the second law an upper bound, Eq. (8): ΔE_b ≤ ΔE_max = Δμ − (1/β) Σ P(x) ln P(x). They then use this bound to estimate effective binding energies for muscle and nonmuscle cell types and argue that higher structural randomness lowers the energy barrier for remodeling, conferring adaptive flexibility. The argument is supported by published sarcomere-length images and by a qualitative comparison with α-actinin dissociation constants.","tokens_in":10255,"tokens_out":6286,"duration_ms":59745,"significance":"If the quantitative claims were supported, the paper would offer a simple and appealing link between structural disorder and cellular adaptability. The stationary-distribution derivation and the entropy-production inequality are transparent, and the use of published images to compare sarcomere distributions is a concrete empirical step. The paper also makes a falsifiable qualitative prediction: at fixed chemical potential, higher Shannon entropy lowers the maximum binding energy. However, the central quantitative identification is not currently established, and the manuscript overinterprets an upper bound as an estimated binding energy. As it stands, the paper's contribution is best viewed as a qualitative thermodynamic bound combined with a phenomenological data comparison.","major_comments":[{"comment":"Equation (8) is an inequality, ΔE_b ≤ ΔE_max, and the second law only requires σ ≥ 0. In an ATP-driven process one expects σ > 0, so ΔE_b < ΔE_max, and the gap σ/β is unknown and may vary between cell types. The manuscript nevertheless plots ΔE_max as the effective binding energy in Fig. 5 and compares the resulting ordering with measured Kd values in §4. An ordering of upper bounds does not imply an ordering of actual binding energies, so the quantitative comparison is not logically valid unless the bound is shown to be tight or the gap is otherwise controlled.","section":"§2.3, Eq. (8); Fig. 5; §4"},{"comment":"The identification of ΔS_sys with the Shannon entropy −Σ P(x) ln P(x) omits the reference entropy of the initial or unbound state; a thermodynamic entropy change requires a defined reference state. In addition, for the continuous sarcomere-length variable, the Shannon entropy depends on the histogram bin width, and the manuscript does not report a common binning across the different published images. Without fixing these conventions, the numerical entropy values in Fig. 3b, and hence the binding-energy values derived from them, are not uniquely defined.","section":"§2.2, Eq. (5)"},{"comment":"The chemical potential Δμ is set to −20 kJ/mol on the basis of ATP hydrolysis enthalpy measurements (Refs. 36 and 37), but Δμ in Eq. (6) is the change in chemical potential as sarcomere elements transfer from the particle bath into the cytoskeletal structure. ATP hydrolysis free energy is not the same quantity, and no argument is given that the two are equal or proportional. Because Eq. (8) is linear in Δμ, the numerical binding energies and the reported proportionality in Fig. 5 are direct consequences of this unexamined assumption.","section":"§2.3"},{"comment":"The experimental validation via published Kd values is post hoc and selective. For α-actinin, the cited values support the authors' ordering, but for myosin II the cited Kd values point in the opposite direction (muscle 28.2 nM, nonmuscle 4.6 nM; Ref. 52), which contradicts the claim that muscle sarcomere components bind more stably. The authors assert that α-actinin, not myosin, drives the remodeling activity, but no independent evidence is provided that the binding energy in Eq. (8) corresponds to α-actinin rather than to the composite actin/myosin/α-actinin system described in §2.2.","section":"§4"}],"minor_comments":[{"comment":"The restoring parameter k is given in N/μm and appears directly in the drift term of the Fokker-Planck equation; for an overdamped Langevin description the drift should involve k divided by a friction coefficient, and the numerical values 10^2–10^4 N/μm are not justified. Please clarify the physical units and origin of k.","section":"§2.1, Eq. (2); Fig. 2"},{"comment":"The phrase 'variance N𝐷𝑘⁄' appears to be a typographical corruption of 'variance D/k'; the stationary solution of Eq. (2) indeed gives variance D/k, so the text should be corrected.","section":"§3.1"},{"comment":"Ref. 26 is cited in support of the Shannon-entropy expression in Eq. (5), but that reference concerns sarcomeric pattern formation; please cite a standard source for the relation between thermodynamic entropy and Shannon entropy.","section":"§2.2, Ref. 26"},{"comment":"The caption should state explicitly that the plotted quantity is ΔE_max, not ΔE_b, and should specify the units of the vertical axis.","section":"Fig. 5 caption"},{"comment":"The sentence preceding the claim that x0 does not affect the binding-energy limit is hard to parse; since the x0-independence follows directly from Eq. (8), consider simplifying the discussion of Fig. 4a.","section":"§3.2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript may fit the scope of q-bio.CB, but the quantitative overreach in Fig. 5 and §4 is the main barrier. In my reading, the defensible contribution after revision is a qualitative upper-bound statement relating structural randomness to the maximum binding energy, not an estimate of actual binding energies. The authors should be asked to either demonstrate saturation of the bound or remove the quantitative Kd comparison and clearly relabel the calculated quantity as an upper bound."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this paper has a genuinely new idea—using Shannon entropy of sarcomere-length distributions to bound effective binding energy via the second law—and the qualitative picture (nonmuscle cells are more disordered and more adaptable) is attractive. But the quantitative binding-energy estimates in Fig. 5 treat an upper bound as if it were the actual value, and that's not justified.\n\nWhat's good: The model is simple and clear. The Fokker-Planck setup with a harmonic potential gives a Gaussian distribution; Eq. (8) follows directly from nonnegative entropy production. The experimental analysis of published images across muscle and nonmuscle cell types is a real effort, and the reported entropies do separate the categories as claimed. Comparing the trend to known α-actinin Kd values is a reasonable sanity check, and the paper is honest that it is qualitative.\n\nThe soft spots: (1) The stress-test issue is on target. Eq. (8) is an upper bound: ΔE_b ≤ ΔE_max. Fig. 5 plots ΔE_max and calls it \"binding energy.\" Unless the bound is saturated (i.e., entropy production σ=0), the actual ΔE_b is smaller, and the gap could vary between cell types. So the ordering of ΔE_max doesn't logically force the ordering of actual binding energies. This is load-bearing for the quantitative conclusion. (2) The identification of ΔS_sys with the Shannon entropy of the measured length distribution (Eq. 5) drops any reference-state entropy. If that's not the thermodynamic entropy change, the numbers in kJ/mol have no physical meaning. (3) Setting Δμ = -20 kJ/mol from ATP hydrolysis for all cell types needs more justification—the chemical potential should depend on concentration and local conditions. (4) The entropy values in Fig. 3b come with no error bars, and the sample sizes are modest (n≈40–56).\n\nNone of these kills the conceptual message, but they mean the paper currently supports a qualitative hypothesis, not a quantitative estimate. A careful revision could add uncertainty quantification, test sensitivity to Δμ, and—most important—discuss when the bound might be tight, or else reframe Fig. 5 as an upper-bound comparison rather than an estimate.\n\nWho should read this: people working on cytoskeletal mechanics or nonequilibrium biology. It's a thought-provoking framework and worth a serious referee, but the referee should push on the inequality-to-equality step. I'd send it to review with major revision requested.","headline":"A genuinely new idea linking sarcomere disorder to binding-energy bounds, but the quantitative estimates over-read an upper bound as an equality.","tokens_in":10766,"tokens_out":2116,"would_cite":false,"duration_ms":19070,"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 paper derives a binding-energy ceiling from sarcomere length randomness, explaining why nonmuscle cells remodel more easily than muscle cells.","keywords":["sarcomere","Shannon entropy","nonequilibrium thermodynamics","cytoskeletal remodeling","binding energy","Fokker-Planck equation","cellular adaptation","stress fiber"],"falsifier":"An experiment that would settle the claim is to narrow a nonmuscle cell's sarcomere length distribution at constant ATP, for example by increasing crosslinking, and then measure stimulus-driven remodeling; Eq. (8) predicts remodeling must slow, and if it does not, the entropy mechanism is not controlling the behavior.","tokens_in":9755,"feed_emoji":"🧬","tokens_out":9714,"duration_ms":91475,"temperature":0.7,"pith_summary":"The paper tries to show that the structural randomness of sarcomeres—the actin–myosin contractile units of the cytoskeleton—is not mere noise but a thermodynamic resource for cellular adaptation. It derives an upper bound on how strongly sarcomere components can bind, an inequality in which the Shannon entropy of the measured sarcomere length distribution appears alongside the chemical potential supplied by ATP hydrolysis. When the authors apply the bound to published images, nonmuscle cells with broad, disordered sarcomere lengths come out with lower effective binding energies than muscle cells with narrow, ordered lengths. The payoff would be a physical explanation of why nonmuscle cytoskeletons remodel readily while muscle cytoskeletons stay stable, without invoking cell-type-specific proteins as the whole story.","feed_headline":"Disorder lowers the energy cost of cell remodeling","feed_subtitle":"Sarcomere length randomness sets a binding-energy ceiling, explaining why nonmuscle cells remodel more easily.","key_machinery":"The machinery is the inequality of Eq. (8), $\\Delta E_b^{\\max} = \\Delta\\mu - \\beta^{-1} \\sum_x P(x)\\ln P(x)$, built on a harmonic trap $U(x)=\\tfrac{1}{2}k(x-x_0)^2$ whose Fokker–Planck steady state is Gaussian with variance $D/k$. The distribution's Shannon entropy is identified with the system's entropy change; the environment contributes $-\\beta(\\Delta E-\\Delta\\mu)$; nonnegative total entropy production then converts length measurements into an energy ceiling. The model is parameterized with $D=10\\,\\mu\\mathrm{m}^2/\\mathrm{s}$, $T=310.15$ K, and $\\Delta\\mu$ around $-20$ kJ/mol from ATP hydrolysis.","core_discovery":"On the paper's own terms, the central claim is that the effective binding strength of sarcomere components can be read off from the disorder in their spacing. Using a Fokker–Planck equation for sarcomere length, the authors obtain a stationary Gaussian distribution; treating the cell as an open system that exchanges components with a grand-canonical environment and requiring nonnegative entropy production gives $\\Delta E_b \\le \\Delta E_b^{\\max} = \\Delta\\mu - \\beta^{-1}\\sum_x P(x)\\ln P(x)$. The population-level Shannon entropy therefore acts as a thermodynamic resource: the broader the measured length distribution, the lower the estimated binding energy, and the cheaper it is for the cytoskeleton to break and rebuild. Applying the formula to published images, muscle-type sarcomeres with narrow distributions have higher effective binding energies and nonmuscle-type sarcomeres with broad distributions have lower ones, which the authors take as the physical origin of adaptive flexibility.","pith_inferences":["If Eq. (8) holds, the same entropy budget should apply to other repeated cytoskeletal structures whose length distributions can be measured, such as stress-fiber periodicities in endothelial cells; the paper does not test this.","A quantitative prediction that follows from the framework but is not made in the paper is that artificially narrowing sarcomere length variance at fixed chemical potential should measurably slow stimulus-driven remodeling, a testable live-imaging experiment.","The comparison to α-actinin dissociation constants is qualitative and post hoc; a stronger test would measure binding kinetics in cells with engineered entropy levels, linking the thermodynamic ceiling to actual remodeling rates.","Because chemical potential depends on component concentration, the framework suggests that environmental ATP or nutrient fluctuations can gate whether structural disorder is expressed as flexibility, an implication the authors only touch on in the discussion."],"forward_implications":["Sarcomere randomness is a functional degree of freedom: nonmuscle cells with broader length distributions can remodel their cytoskeletons with less energetic cost per event and can therefore respond more readily to environmental cues.","Muscle-type sarcomeres, with narrow length distributions, have higher effective binding energies and are correspondingly more resistant to elongation and remodeling, matching their role in stable force generation.","The restoring contribution $k$ sets the trade-off: larger $k$ narrows the distribution and reduces the entropy term, so stiffer, more ordered cytoskeletons should adapt more slowly.","The chemical potential of the environment sets the overall scale: at high ATP, even disordered sarcomeres can form stable structures, so adaptation depends on both structural randomness and energy supply.","Cellular aging, which stiffens the cytoskeleton and reduces sarcomere variability, should lower adaptability by the same entropy mechanism."],"supporting_citations":[{"why":"Crooks' fluctuation theorem is the nonequilibrium basis for requiring nonnegative total entropy production in Eq. (7).","marker":"(30)"},{"why":"Shannon and Weaver define the entropy measure used for the system entropy change in Eq. (5).","marker":"(48)"},{"why":"Friedrich and colleagues' sarcomeric pattern-formation model is the cited precedent for expressing system entropy as Shannon entropy of the distribution.","marker":"(26)"},{"why":"ATP-hydrolysis enthalpy measurements set the chemical-potential scale of about -20 kJ/mol used in Eq. (8).","marker":"(36,37)"},{"why":"Nonmuscle α-actinin Kd values of 2.96–3.96 μM are the external comparison supporting lower nonmuscle binding.","marker":"(49)"},{"why":"Muscle α-actinin Kd of 0.4 μM is the comparison supporting higher muscle binding.","marker":"(50)"},{"why":"A second muscle α-actinin Kd of 0.59 μM corroborates the muscle-versus-nonmuscle binding difference.","marker":"(51)"},{"why":"Myosin II Kd values are used to argue that α-actinin, not myosin, dominates the remodeling difference.","marker":"(52)"}],"fun_headline_variants":["Entropy lowers energy barrier for cell flexibility","Sarcomere disorder sets remodeling energy ceiling","Entropy makes cell remodeling cheaper","Disorder lowers the cost of cellular adaptability","Sarcomere entropy explains adaptive flexibility"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the Shannon entropy computed from measured sarcomere lengths is exactly the entropy change of the sarcomere system itself, with no reference-state term, while the environment acts as a reservoir with a chemical potential set by ATP hydrolysis; if that equality fails, the computed binding energies lose their physical meaning.","fun_headline_variants_meta":{"raw":{"variants":["Entropy lowers energy barrier for cell flexibility","Sarcomere disorder sets remodeling energy ceiling","Entropy makes cell remodeling cheaper","Disorder lowers the cost of cellular adaptability","Sarcomere entropy explains adaptive flexibility"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00047,"raw_usage":{"total_tokens":2353,"prompt_tokens":972,"completion_tokens":1381,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":588,"completion_tokens_details":{"reasoning_tokens":1318}},"tokens_in":588,"tokens_out":1381,"duration_ms":10037,"temperature":1.0,"reasoning_tokens":1318,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:19:30.402171+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"An experiment that would settle the claim is to narrow a nonmuscle cell's sarcomere length distribution at constant ATP, for example by increasing crosslinking, and then measure stimulus-driven remodeling; Eq. (8) predicts remodeling must slow, and if it does not, the entropy mechanism is not controlling the behavior.","supporting_citations":[],"review_version":1}