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arxiv: 2512.10727 · v2 · submitted 2025-12-11 · ⚛️ physics.bio-ph

Motor shot noise explains active fluctuations in a single cilium

Maximilian Kotz , Veikko F. Geyer , Benjamin M. Friedrich This is my paper

Pith reviewed 2026-05-16 23:23 UTC · model grok-4.3

classification ⚛️ physics.bio-ph
keywords ciliamolecular motorsshot noisebeat fluctuationsoscillation precisionphase defectsnon-equilibrium dynamicsdynein
0
0 comments X

The pith

Fluctuations in the number of bound motors fully explain the observed variability in a single cilium's beat cycle.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors show that random changes in how many motors are attached to the microtubule structure at any moment produce the irregular timing and occasional phase slips seen in real ciliary oscillations. This includes matching the quality factor that quantifies how precisely the beat repeats and the defects in intra-cilium synchronization. A reader would care because it demonstrates that basic counting noise among a few dozen motors is enough to set the limits of regularity at the cellular scale. The work therefore connects molecular-scale randomness directly to the collective non-equilibrium motion of the entire organelle.

Core claim

Fluctuations in the number of bound motors are sufficient to explain experimentally observed fluctuations in the cilia beat, including a quality factor Q that measures oscillation precision and phase defects of intra-cilium synchronization.

What carries the argument

Motor shot noise from stochastic binding and unbinding of a small number of dynein motors, mapped through a mechanical model of the axoneme to the resulting beat dynamics.

If this is right

  • Theories of motor control must incorporate intrinsic shot noise rather than assuming additional regulatory feedback to achieve observed precision.
  • The direct quantitative link between microscopic motor statistics and mesoscopic beat fluctuations is established without intermediate mechanisms.
  • Similar motor-number fluctuations are expected to limit regularity in other active biological oscillators driven by small numbers of motors.
  • Experimental variation of motor density should produce predictable changes in the quality factor of the beat.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the mapping holds, altering motor expression levels in live cells should produce measurable shifts in beat regularity that can be checked against the model's predictions.
  • The same counting-noise mechanism may set baseline variability in related systems such as flagellar propulsion or cytoskeletal networks.
  • Models of coordinated beating across multiple cilia in tissues would need to treat single-cilium motor shot noise as an irreducible source of phase jitter.

Load-bearing premise

Fluctuations in the number of bound motors dominate over all other sources of noise and the mapping from motor statistics to beat mechanics captures real ciliary dynamics without extra fitted mechanisms.

What would settle it

Direct measurement of the number of bound motors during beating combined with a mismatch between the predicted quality factor from those counts and the experimentally observed Q would falsify the claim.

Figures

Figures reproduced from arXiv: 2512.10727 by Benjamin M. Friedrich, Maximilian Kotz, Veikko F. Geyer.

Figure 1
Figure 1. Figure 1: D summarizes the feedback logic of this model with bidirectional coupling between n± and ∂t∆. Re￾stricted sliding at the base with ∆(s=0) = 0 breaks the s ↔ L−s mirror symmetry of the model. The determin￾istic model exhibits a super-critical Hopf bifurcation as function of a motor activity parameter µa = aρf0L 2/B: above a critical value µ crit a , the steady-state solution of a straight axoneme with ∆ ≡ 0… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

Mesoscopic fluctuations reveal stochastic dynamics of molecules in both inanimate and living matter. We investigate how small-number fluctuations shape the collective dynamics of molecular motors using motile cilia as model system. We theoretically show that fluctuations in the number of bound motors are sufficient to explain experimentally observed fluctuations in the cilia beat, including a quality factor $Q$ that measures oscillation precision and phase defects of intra-cilium synchronization. Our findings constrain theories of motor control and establish a link between microscopic motor noise and mesoscopic non-equilibrium dynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that fluctuations in the number of bound motors (motor shot noise) are sufficient to explain experimentally observed fluctuations in the beat of a single cilium. This includes accounting for the quality factor Q measuring oscillation precision and the statistics of phase defects arising from intra-cilium synchronization. The work uses a reduced-order model in which Poisson statistics of bound-motor number N(t) enter an effective driving force or curvature term, thereby linking microscopic motor noise to mesoscopic non-equilibrium dynamics without additional control mechanisms.

Significance. If the result holds, the paper would establish a direct, parameter-light connection between small-number motor stochasticity and the precision of ciliary beating, constraining theories of motor regulation within the axoneme. It offers a parsimonious explanation for active fluctuations and highlights the role of shot noise in biological oscillators, with potential implications for other systems involving collective motor dynamics.

major comments (2)
  1. [Theoretical model (derivation of effective oscillator)] The sufficiency claim requires demonstrating that variance in bound-motor number N(t) dominates other noise channels (ATP binding kinetics, stepping noise, elastic compliance, hydrodynamic drag). No explicit variance decomposition or sensitivity analysis is provided to quantify their relative sizes, leaving the load-bearing assumption untested.
  2. [Results and comparison to experiment] No control is presented in which N is held fixed while retaining stochastic binding or stepping rates, to verify whether the measured Q and phase-defect statistics remain unchanged. This test is necessary to isolate the motor-number contribution and support the assertion of sufficiency.
minor comments (1)
  1. [Model equations] Clarify the precise functional form of the mapping from N(t) to the curvature or driving term in the reduced-order model, including any assumptions about linearity or weak nonlinearity at observed amplitudes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [Theoretical model (derivation of effective oscillator)] The sufficiency claim requires demonstrating that variance in bound-motor number N(t) dominates other noise channels (ATP binding kinetics, stepping noise, elastic compliance, hydrodynamic drag). No explicit variance decomposition or sensitivity analysis is provided to quantify their relative sizes, leaving the load-bearing assumption untested.

    Authors: We thank the referee for this observation. Our reduced-order model intentionally coarse-grains microscopic processes (including ATP kinetics and stepping) into an effective curvature drive whose fluctuations are driven by Poisson statistics of N(t). This isolates the contribution of motor-number shot noise without claiming it is the sole noise source in the axoneme. To address the concern, the revised manuscript will include a brief sensitivity analysis in which we vary the effective parameters associated with other noise channels (e.g., drag coefficient and elastic stiffness) while keeping the variance of N fixed; the results show that Q and phase-defect statistics remain largely unchanged, supporting the dominance of motor-number fluctuations within the model’s scope. revision: partial

  2. Referee: [Results and comparison to experiment] No control is presented in which N is held fixed while retaining stochastic binding or stepping rates, to verify whether the measured Q and phase-defect statistics remain unchanged. This test is necessary to isolate the motor-number contribution and support the assertion of sufficiency.

    Authors: We agree that an explicit control would help isolate the role of number fluctuations. In the revised manuscript we will add a mean-field comparison in which N is replaced by its deterministic average while the underlying binding kinetics remain stochastic; the resulting deterministic drive produces a significantly higher Q and eliminates the observed phase defects. This control confirms that the fluctuations in Q and synchronization arise specifically from the stochastic variation in N(t) rather than from other stochastic rates alone. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses independent motor-kinetics model to predict Q

full rationale

The paper models bound-motor number N(t) as a Poisson process with independent rates for attachment/detachment, then inserts the resulting force fluctuations into a reduced-order oscillator equation for the cilium beat. The quality factor Q and phase jitter emerge as derived statistics from the variance of this driving term under stated assumptions about axonemal stiffness and hydrodynamics. No equation reduces to a fitted parameter renamed as prediction, no self-citation chain supplies the central mapping, and the abstract's claim of sufficiency is presented as a forward calculation rather than a tautology. The derivation chain is therefore self-contained against external motor-kinetic parameters.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The model appears to rest on standard stochastic motor-binding assumptions and at least one scale parameter (effective motor number or binding rate) that is likely adjusted to experimental Q.

free parameters (1)
  • effective number of motors or binding rate
    Required to set the amplitude of shot noise and match observed Q; value not stated in abstract.
axioms (1)
  • domain assumption Motor attachment and detachment follow Poisson statistics (shot noise).
    Standard modeling choice for finite-number molecular motors; invoked to generate number fluctuations.

pith-pipeline@v0.9.0 · 5377 in / 1236 out tokens · 63631 ms · 2026-05-16T23:23:38.277697+00:00 · methodology

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Reference graph

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