Pith. sign in

REVIEW 4 major objections 5 minor 5 references

Adaptive flexibility of cells through nonequilibrium entropy production

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper derives a binding-energy ceiling from sarcomere length randomness, explaining why nonmuscle cells remodel more easily than muscle cells.

desk verdict A genuinely new idea linking sarcomere disorder to binding-energy bounds, but the quantitative estimates over-read an upper bound as an equality. read the letter →

arxiv 2411.14291 v2 pith:MNARJWFT submitted 2024-11-21 q-bio.CB q-bio.SC

Yuika Ueda , Shinji Deguchi This is my paper · ORCID
classification q-bio.CBq-bio.SC
keywords sarcomereShannonentropynonequilibriumthermodynamicscytoskeletalremodelingbindingenergyFokker-Planckequationcellularadaptationstressfiber
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [§2.3, Eq. (8); Fig. 5; §4] 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.
  2. [§2.2, Eq. (5)] 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.
  3. [§2.3] 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.
  4. [§4] 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.
minor comments (5)
  1. [§2.1, Eq. (2); Fig. 2] 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.
  2. [§3.1] 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.
  3. [§2.2, Ref. 26] 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.
  4. [Fig. 5 caption] The caption should state explicitly that the plotted quantity is ΔE_max, not ΔE_b, and should specify the units of the vertical axis.
  5. [§3.2] 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.

Circularity Check

1 steps flagged · score 6.0 of 10

Fig. 5's 'binding energy' is ΔE_max from Eq. (8), a linear transform of the measured Shannon entropy at fixed Δμ; the muscle/nonmuscle binding-energy ordering is therefore the measured entropy ordering restated, not an independent prediction.

  1. self definitional [Section 2.3, Eq. (8); Section 3.2; Fig. 5 caption]
    "From Eq. (7), the binding energy is defined as ΔE_b≤ΔE_max=Δμ−1/β∑P(x)lnP(x) (8). ... The effective binding energy for different types of sarcomere structures was estimated using Eq. (8) and actual measurements of the distribution (Fig. 3), showing its proportionality to the change in system entropy at a fixed chemical potential, -20 kJ/mol (Fig. 5)."

    With Δμ fixed, Eq. (8) makes the plotted quantity a linear function of the measured Shannon entropy: ΔE_max = Δμ + (1/β)H[P] because ΣP lnP = -H. Therefore the reported ordering — nonmuscle sarcomeres have lower 'binding energy' than muscle ones — is exactly the measured entropy ordering restated with a sign flip and a constant offset. It is not an independent estimate of ΔE_b: the inequality is never shown to be tight, and no measurement of actual binding energy enters the calculation. The Kd comparison in Sec. 4 is a post hoc consistency check on a quantity that was constructed from entropy alone, so the central 'prediction' reduces by construction to the input distribution and the chosen -20 kJ/mol value.

full rationale

The paper's thermodynamic derivation up to Eq. (8) is not itself circular: it combines a Fokker-Planck stationary distribution, a Shannon-entropy identification, a grand-canonical bath assumption, and the second law to obtain a bound. The circularity enters when the upper bound ΔE_max is renamed 'binding energy' and plotted in Fig. 5 as an estimate. Because Δμ is fixed at -20 kJ/mol for all cell types, Eq. (8) is a monotone linear transform of the measured Shannon entropy, so the muscle/nonmuscle ordering of the plotted quantity is forced by the input histograms and cannot fail. The subsequent comparison to α-actinin Kd values is post hoc: those values are not used to determine or validate the bound, they are just shown to point in the same direction as the already-computed ΔE_max. The paper acknowledges the proportionality but still frames the result as a demonstration that structural randomness lowers binding energy, which is the same statement as Eq. (8) with a sign convention. There is no self-citation chain; the issue is the definitional reduction of the predicted quantity to the measured entropy.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on three main inputs: a measured length distribution, a fixed chemical potential, and the identification of Shannon entropy as thermodynamic entropy. The chemical potential and the entropy identification are the least supported and are load-bearing for the quantitative binding-energy estimates.

free parameters (3)
  • chemical potential Δμ = -20 kJ/mol
    Fixed to the ATP hydrolysis energy from Refs. (36,37) and used in Eq. (8) to convert Shannon entropy into binding energy. No direct measurement of the chemical potential of sarcomere binding; the Fig. 5 estimates scale linearly with this choice.
  • diffusion coefficient D = 10 μm²/s
    Taken from literature (Refs. 31-35) for the Fokker-Planck model. Affects the model distribution in Fig. 2 but is not used in the experimental binding-energy estimates, which use measured length distributions directly.
  • restoring coefficient k = 10^2 to 10^4 N/μm (illustrative)
    Varied in Fig. 2 to show that higher k narrows the length distribution. Not fitted to the experimental data; the Fig. 5 binding-energy estimates use measured distributions directly.
assumptions (5)
  • domain assumption Sarcomere length follows a Fokker-Planck equation with harmonic potential U(x) = 0.5 k (x - x0)^2
    Sec. 2.1, Eqs. (1)-(2). The harmonic potential is justified in Supporting note 1 via equilibrium chemical potential arguments, assuming actin-myosin binding is the dominant restoring mechanism.
  • ad hoc to paper The environment is a grand canonical bath exchanging sarcomere elements and energy with chemical potential Δμ
    Sec. 2.2. Assumed to describe the forming process of the cytoskeletal structure; no experimental evidence that sarcomere assembly is grand canonical or that the chemical potential equals ATP hydrolysis energy.
  • ad hoc to paper The entropy change of the system is equal to the Shannon entropy of the sarcomere length distribution, -Σ P ln P
    Sec. 2.2, Eq. (5). Omits reference-state entropy and identifies static structural disorder with thermodynamic entropy production, a strong assumption that drives the quantitative results in Fig. 5.
  • standard math Total entropy production is nonnegative (second law)
    Sec. 2.2, Eqs. (4) and (7). Standard thermodynamics, not in question.
  • domain assumption Measured sarcomere length distributions are stationary and representative of each cell type
    Sec. 2.4. Distributions from n=40-56 sarcomeres from published images are assumed to reflect steady-state structural variability, with no test of sampling bias.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive flexibility of cells through nonequilibrium entropy production." pith.science (2026). https://pith.science/paper/MNARJWFT

@misc{pith2026241114291,
  author       = {Pith},
  title        = {Pith review of: Adaptive flexibility of cells through nonequilibrium entropy production},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MNARJWFT}},
  note         = {Machine review of arXiv:2411.14291}
}
read the original abstract

Cellular adaptation to environmental changes relies on the dynamic remodeling of subcellular structures. Among these, sarcomere structures are fundamental to the organization and function of the cytoskeletal architecture. In muscle-type cells, sarcomeres exhibit ordered structures of consistent lengths, optimized for stable force generation. By contrast, nonmuscle-type cells display a higher degree of structural variability, with sarcomeres of varying lengths that contribute not only to force generation but also to adaptive remodeling upon environmental cues. While these differences in sarcomere structures have traditionally been attributed to the unique properties of specific proteins expressed in each cell type, the functional implications of such structural variability remain unclear. Here, we present a nonequilibrium physics framework to elucidate the role of sarcomere variability in cytoskeletal adaptation. Specifically, we demonstrate that the effective binding strength of sarcomere components can be evaluated by analyzing structural randomness using Shannon entropy. The increased entropy associated with the inherent randomness of sarcomere structures in nonmuscle-type cells lowers the energy barrier for cytoskeletal remodeling, enabling flexible adaptation to environmental demands. Meanwhile, the ordered sarcomere arrangements in muscle-type cells correspond to higher binding energies and more stable cytoskeletal configurations. Although structural disorder is often regarded as unfavorable in terms of stability, our study suggests that it plays a key role in enabling adaptive responses in cellular systems.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages

  1. [1]

    Introduction Living cells adapt their internal structures in response to changes in both their internal and external environments (1,2). This adaptability is fundamental to individual cellular processes such as differentiation, proliferation, and apoptosis, as well as to higher-order processes such as tissue development and wound healing (3,4). The cytosk...

    work page

  2. [2]

    (1) where 𝑘 represents the restoring contribution of the sarcomere. Using the Fokker-Planck equation, the time evolution of 𝑃(𝑥,𝑡) is described by 𝜕𝑃(𝑥,𝑡)𝜕𝑡=−𝜕𝜕𝑥{−𝑘(𝑥−𝑥!)𝑃(𝑥,𝑡)}+𝜕

    Model 2.1 Probability distribution of sarcomere structures The sarcomere is the intracellular contractile unit with a certain periodic structure, along which actin, myosin, and α-actinin appear in a cell type-dependent probability distribution (Fig. 1). Nonmuscle-type cells tend to express sarcomeres that are more spatially irregular compared to those in ...

    work page

  3. [3]

    Results 3.1 Analysis of sarcomere length variability The probability distribution for sarcomere lengths was analyzed using our model (Eq. 3) (Fig. 2). These distributions follow a Gaussian distribution with variance N𝐷𝑘⁄, influenced by both noise and restoring contribution of sarcomeres. As 𝑘 increases, representing greater contractile force maintained wi...

    work page

  4. [4]

    Discussion In this work, we developed a nonequilibrium physical model to elucidate how the biophysical properties of sarcomeres influence cytoskeletal stability (Fig. 4). Previous studies have largely focused on self-organizing mechanisms of sarcomere patterning (21,22,25,26), but it remained unclear how sarcomere characteristics are associated with cellu...

    work page 2008

  5. [508]

    Adaptive flexibility of cytoskeletal structures through nonequilibrium entropy production

    12. Verkhovsky AB, Svitkina TM, Borisy GG. Polarity sorting of actin filaments in cytochalasin-treated fibroblasts. J Cell Sci. 1997 Aug 1;110(15):1693–704. 13. Hotulainen P, Lappalainen P. Stress fibers are generated by two distinct actin assembly mechanisms in motile cells. Journal of Cell Biology. 2006 May 8;173(3):383–94. 14. Cramer LP, Siebert M, Mit...

    work page 1997

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.