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Contact-Dependent Ion Gating Explains Directional Asymmetry in the Bacterial Flagellar Motor

T0 review · 3 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read The bacterial flagellar motor's directional torque asymmetry is caused by differential ion-release gating at the rotor–stator contact, not by mechanical coupling differences.

desk verdict A plausible and well-derived gating mechanism for the flagellar motor's CW–CCW asymmetry, but the central kinetic asymmetry is assumed rather than computed, so it should be treated as a testable hypothesis, not a closed explanation. read the letter →

arxiv 2604.00470 v2 pith:V2VKZESF submitted 2026-04-01 physics.bio-ph q-bio.BM

Jiading Zhu , Yongnan Hu , Yuhai Tu , Yuansheng Cao This is my paper · ORCID
classification physics.bio-phq-bio.BM
keywords bacterialflagellarmotortorque-speedrelationiongatingMotA-FliGcontactmechanochemicalmodelmoleculardynamicsdirectionalasymmetryrotor-statorcoupling
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

This paper argues that the two distinct torque–speed curves of the bacterial flagellar motor—concave in counterclockwise rotation and linear in clockwise rotation—arise from different ion-release rates at the rotor-stator interface, not from differences in rotor-stator mechanics. Using a stochastic mechanochemical model constrained by experimental torque-speed data and stator-rotation measurements, the authors show the motor operates under tight rotor-stator engagement, making the torque-speed relation insensitive to the interaction potential's shape. They then propose a contact-dependent gating mechanism: the MotA–FliG contact modulates the ion release rate of the proximal MotB subunit, with a tighter contact in the clockwise state slowing release and producing the linear curve, while the more open counterclockwise contact allows faster release, suppressing torque-free waits and producing the concave curve. Molecular dynamics simulations support the structural asymmetry, showing a smaller interfacial cavity and fewer hydrogen bonds in the clockwise state. If correct, this mechanism explains why both directions share the same stall torque but differ in curve shape, and it pinpoints specific interfaces for mutational tests.

What carries the argument

The central object is the contact-dependent gating rate kg for the proximal MotB subunit's ion release, embedded in a two-ion alternating stator cycle. The stator contains a MotB dimer with two channels that operate out of phase; after a power stroke, the proximal channel can release its ion early through a gating pathway when the MotA–FliG contact is open, allowing the next cycle to start immediately. When the contact is tight (CW state), this early release is suppressed, forcing the stator into a torque-free waiting phase until a slower baseline release. The tight-engagement regime is characterized by an engagement fraction γ = ⟨ωr⟩/(α⟨ωs⟩) near unity, with rotor-stator coupling depth hr i

What would settle it

A direct measurement of the ion release rates of the proximal MotB channel in the CW and CCW conformational states, either by molecular dynamics free-energy calculations of the release barrier or by single-channel electrophysiology on stator complexes with the interface held in each conformation, would settle the claim: if the release rates are similar, the proposed gating asymmetry cannot generate the observed torque-speed difference. Alternatively, a mutation that equalizes the MotA–FliG contact without changing the stator's mechanical interaction should, according to the model, make the CW

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Extended reading notes

Core claim

The central claim is that directional asymmetry in the flagellar motor's torque-speed relation is governed by contact-dependent gating of ion release: the MotA–FliG interaction modulates the ion release rate of the proximal MotB subunit, with stronger gating in the counterclockwise (CCW) state shortening torque-free waiting phases and enhancing torque, whereas weaker gating in the clockwise (CW) state yields lower torque and a linear relation. The authors establish that under physiological conditions the motor sits in a tight-engagement regime (interaction depth hr ≈ 15.4 kBT), where the torque-speed curve is independent of the rotor-stator potential's form, ruling out mechanical interaction

Load-bearing premise

The assumption that the tighter MotA–FliG contact in the clockwise state translates into a sufficiently large reduction in the ion release rate (kg,CCW ≫ kg,CW) to reproduce the observed torque-speed curvature, since the MD simulations quantify structural asymmetry but do not directly compute ion translocation kinetics or rates.

Editorial extensions

If this is right

  • Mutations that disrupt the MotA–FliG interface, such as charge-neutralizing changes at MotA Asp86/Glu94 or FliG Asp241/Asp284/Asp289, should reduce the coupling depth hr and increase stator–rotor slippage, measurably lowering stall torque under high load or high ion motive force.
  • Perturbations that alter the ion-release pathway or the MotA–FliG contact, including steric mutations at the interface, should shift the knee speed or concavity of the CCW torque-speed curve, providing a direct test of the gating mechanism.
  • The model predicts that the torque-speed curves for CCW and CW rotation remain identical at stall (same stall torque) but diverge at intermediate loads, consistent with existing measurements and offering a quantitative target for future single-stator experiments.
  • The dependence of the torque-speed curve on ion motive force is captured by scaling the stator potential and gating rate linearly with IMF, matching experimental data across a range of driving forces.
  • If the gating hypothesis holds, the same structural interface that controls directional switching also tunes the motor's load-dependent torque output, linking chemotaxis behavior to a single molecular contact.

Reading between the lines

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

  • The proposed mechanism suggests a general design principle: in rotary molecular motors, the gating of the chemical transition (ion release) can be mechanically regulated by the rotor, allowing directional control of the force-speed relationship without altering the power stroke itself; this might apply to other ion-driven rotary motors such as ATP synthase's Fo domain.
  • A testable extension beyond the paper's scope is to measure ion release rates directly using single-molecule fluorescence or electrophysiology in the two rotational states; if the rates differ by less than the model's assumed factor, the mechanism would need revision.
  • The MD-observed cavity and hydrogen-bond differences between states could be used to predict mutational effects on kg before experiments, enabling a quantitative structure-kinetics map; such predictions would clarify whether steric occlusion or electrostatic/hydration effects dominate the gating difference.
  • The model's claim that rotor-stator mechanics are irrelevant for the torque-speed shape in the tight-coupling regime could be stress-tested by engineering stators with drastically different interaction potential shapes while keeping the gating interface fixed—if the curves remain unchanged, the paper's central dichotomy is confirmed.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper presents a stochastic mechanochemical model of the bacterial flagellar motor with explicit rotor–stator coupling and two-ion stator kinetics. It first argues, from Eqs. (1)–(7) and SI analysis, that under physiological conditions the motor operates in a tight-engagement regime, so the stall torque is essentially independent of the rotor–stator interaction potential Vr. The no-gating version of the model yields a linear torque–speed curve, consistent with CW rotation. To explain the concave CCW curve, the authors introduce a contact-dependent gating mechanism: interaction between MotA and FliG modulates the ion release rate kg of the proximal MotB channel. MD simulations of the CCW and CW cryo-EM structures show a larger interfacial cavity and more hydrogen bonds in CCW, which the authors interpret as supporting faster ion release in CCW. Setting kg,CW = 0 and choosing kg,CCW values, the model reproduces the experimentally observed concave CCW torque–speed curve and its IMF dependence. The paper concludes that differential gating strength, not rotor–stator mechanics, is the origin of CW–CCW asymmetry, and proposes specific mutations to test this.

Significance. If the proposed mechanism is correct, this would be a notable advance: it connects recently resolved stator–rotor structures to the long-standing torque–speed asymmetry puzzle and offers quantitative, mutatable predictions. The paper's analytical work on the strong-coupling limit is a genuine strength: the Fokker–Planck treatment in SI Eqs. (8)–(21) gives a clean argument that the torque–speed curve is independent of Vr in the tight-engagement regime, and the derived linear relation (Eq. (10)) and gated-curve expression (SI Eq. (26)) are checkable. The mutational predictions for MotA Asp86/Glu94 and FliG Asp241/Asp284/Asp289 are concrete and falsifiable. The main weakness is that the central kinetic asymmetry kg,CCW ≫ kg,CW is assumed and fitted, not computed or measured. The MD data are structural and do not by themselves determine an ion-release rate. Thus the paper currently establishes a plausible mechanism and an internally consistent model, but not the quantitative link between molecular asymmetry and motor function claimed in the abstract.

major comments (3)
  1. [Differential contact-dependent gating explains the CW-CCW asymmetry (Fig. 5C; SI 'Torque-speed curve with gating')] The central claim that kg,CCW ≫ kg,CW is the origin of the asymmetric torque–speed curves is supported only by parameter choice, not by measurement or calculation. In Fig. 5C, kg,CW = 0 and kg,CCW is varied from 1×10^5/s to 2.5×10^5/s to generate the concave shape; in Fig. 5D and the SI, the IMF dependence is imposed through kg = 18000[(IMF/kBT)−3.65] s^−1, chosen to match the Lo et al. data. The discussion explicitly concedes: 'Our current MD simulations reveal structural asymmetry at the MotA–FliG interface but do not yet resolve the detailed ion translocation process or the corresponding kinetic rates.' The MD observables (cavity volume 915.97→508.42 Å^3; H-bonds 185→123) do not determine a rate: a smaller cavity can raise or lower a release barrier depending on where the transition state lies, and the measured cavity is at the MotA–FliG interface, not in the MotA–MotB release channel
  2. [Eqs. (10)–(11) and SI Eq. (23)–(26)] The model's 'prediction' of the CCW curve is partly a fit. The normalized gated torque–speed relation, SI Eq. (26), contains a single shape parameter σ = (γ/β)(αα0)/(α+α0)^2 that depends on kg and the gating position θg through α0 and γ. The authors state that increasing kg or decreasing θg increases concavity, and the simulation parameters in Fig. 5D are selected to match the same experimental data the model is meant to explain. Consequently, the agreement in Fig. 5D demonstrates consistency, not independent confirmation. The paper should provide a sensitivity analysis of the predicted curves to kg and θg, and ideally independent constraints on these parameters from single-stator measurements or from the MD, so that the concave shape is not merely encoded by free parameters.
  3. [SI 'Molecule Dynamics Simulation for MotA–FliG Contact Interface' and Fig. S7] The quantitative MD support for the gating asymmetry is based on a cavity-volume metric whose definition is not physically appropriate as presented. Fig. S7's caption says the cavity volume is estimated by the convex hull of interfacial Cα atoms within 5.0 Å of the opposing protein. A Cα convex hull is not a solvent-excluded or molecular-surface volume; it depends on the arbitrary 5.0 Å cutoff and residue selection, and it does not measure the hydration or steric occlusion of the ion-release pathway. In addition, the reported values 915.97 and 508.42 Å^3 and the H-bond counts 185 and 123 are given without error bars or a definition of the relevant region. Since these numbers are the only quantitative MD evidence for kg,CCW > kg,CW, the analysis should be redone with a standard cavity-definition method (e.g., solvent-excluded surface or channel-geometry analysis) and with replica-to-repli
minor comments (6)
  1. [Eq. (10)] Typo: 'with slopes ng' should be 'with slope s_ng'.
  2. [Fig. 3A] The legend lists several potential shapes (Quadratic, Linear, Cosine, U-shape), but the figure panel does not distinguish the curves. Please make the color/shape legend explicit.
  3. [Fig. 5D] The IMF values and how kg scales with IMF are not stated in the caption. The SI gives kg = 18000[(IMF/kBT)−3.65] s^−1, but this should be stated in the main text or the caption so the reader can evaluate the fit.
  4. [SI Eq. (22)] The probability densities Pg and Pd are introduced without a clear definition. Define them explicitly in terms of the gating and default pathways before using them in the boundary conditions.
  5. [SI 'Molecule Dynamics Simulation...'] The mapping of PDB entries 8UCS, 8UMD, and 8UMX to the CCW and CW states is not stated. Please specify which structures correspond to which rotational state and whether the two CW structures were merged or treated separately.
  6. [Discussion, testable predictions] The predicted effects of charge-neutralizing substitutions on the knee speed are plausible but qualitative. If the authors intend these as quantitative predictions, the model parameters that translate a changed contact probability into a changed kg should be specified.

Circularity Check

1 steps flagged · score 6.0 of 10

The gating-rate asymmetry is installed as a fitted parameter, so the quantitative match to the CCW torque–speed curve is a fit, not a prediction.

  1. fitted input called prediction [SI 'SIMULATION METHODS AND PARAMETERS' and 'TORQUE AND SPEED DEPENDENCE ON ION-MOTIVE-FORCE (IMF)'; main text Fig. 5C/D, 'DIFFERENTIAL CONTACT-DEPENDENT GATING EXPLAINS THE CW-CCW ASYMMETRY']
    "Simulation parameters were chosen to match the experimental torque-speed curves. Specifically, we used a maximum speed of 320 Hz (∼2000 rad/s), and a stall torque of 200 pN·nm, in line with measurements from [1–3]. These benchmarks were then used to tune the remaining model parameters. ... The gating rate is also IMF-dependent. For example, in Fig. 5D, we use kg = 18000[(IMF/kBT)−3.65]s−1."

    The gating rate kg is the knob that controls concavity: the SI torque-speed equation (26) depends on kg through α0 and σ, and the paper's central result is that 'stronger gating ... produces a concave torque–speed curve' while 'weaker gating ... yields ... a linear relation.' In Fig. 5C the CCW curve is produced by choosing kg values (1–2.5×10^5 s^−1), and in Fig. 5D kg is chosen as an IMF-dependent function to match the Lo et al. data. The model therefore does not predict the CCW concavity from a computed ion-release rate; it installs kg,CCW ≫ kg,CW as an input and then reports the resulting curve as the explanation. Because the authors concede that the MD structural asymmetry 'do[es] not yet resolve the detailed ion translocation process or the corresponding kinetic rates,' the quantitat

full rationale

The paper has two claims: (1) tight rotor–stator engagement makes torque–speed curves insensitive to V_r; this is supported by an independent analytical derivation and comparison with the Hosu et al. engagement fraction, so it is not circular. (2) Contact-dependent gating explains the CW–CCW torque–speed asymmetry. This second claim is only partially supported. The MD cavity/hydration asymmetry (915.97 vs 508.42 ų; 185 vs 123 H-bonds) is independent qualitative evidence that the CW interface is more constrained, and it is consistent with, but does not compute, a slower CW release rate. However, the quantitative model sets kg,CW = 0 and kg,CCW = kg by hand, and the kg values used to reproduce the experimental CCW torque–speed curves are explicitly tuned to match those curves ('These benchmarks were then used to tune the remaining model parameters'; 'we use kg = 18000[(IMF/kBT)−3.65]s−1'). Thus the central 'explanation' of the concave CCW curve is partly a fit of the very parameter that controls the shape. The discussion's caveat that ion translocation kinetics have not been resolved confirms that the magnitude of the gating asymmetry is assumed, not derived. Self-citations to earlier Tu/Cao work (refs. 28, 34, 35) provide modeling context but are not load-bearing for this derivation, so they do not independently raise the score. On balance, the circularity is partial: the qualitative mechanism has independent structural support, while the quantitative torque–speed prediction reduces by construction to the fitted gating-rate asymmetry.

Assumptions & free parameters 7 free parameters · 7 assumptions · 1 invented entities

The model depends heavily on fitted kinetic parameters (τ+, k, ξs, kg) and on assumptions about two-channel alternating operation and release-limited kinetics. The structural MD asymmetry is the main independent evidence for the key gating-rate difference, but it does not determine kg quantitatively.

free parameters (7)
  • τ+ (stator potential slope / instantaneous torque) = 39.2 pN·nm
    Set to match the experimental stall torque (~200 pN·nm) and maximum speed benchmarks in the SI.
  • k (baseline chemical jumping rate) = 1.8×10^4 s^-1
    Tuned to reproduce the maximum motor speed; also given an IMF dependence with fitted constants γ1 and c.
  • ξs (free stator load) = ~6×10^-4 pN·nm·s
    Obtained by fitting the slope of the torque-speed curve below the knee (Eq. 11).
  • hr (rotor-stator interaction depth) = 15.4±0.5 kBT
    Inferred from Hosu et al.'s rotor/stator speed ratio via Eq. 7; not measured directly.
  • kg (gating rate for proximal MotB2) = 1×10^5–2.5×10^5 s^-1 for CCW, 0 for CW
    Chosen to reproduce the concave CCW torque-speed curve; IMF-dependent form kg=18000[(IMF/kBT)-3.65] s^-1 is fit to Lo et al. data.
  • IMF scaling constants γ1, c, γ2 = γ1=2770.5 s^-1/kBT, c=3051 s^-1, γ2=1.26
    Fitted so that the model's speed and stall-torque IMF dependencies match the experimental measurements.
  • hs (stator potential well depth) = 12 kBT
    Used in the slipping analysis; consistent with τ+ and the stator geometry, and sets the strong-coupling threshold hr > hs/2.
assumptions (7)
  • domain assumption Rotational motion follows overdamped Langevin dynamics with thermal noise.
    Equations 1–2 of the main text; standard for molecular motors at low Reynolds number.
  • domain assumption Ion-driven chemical transitions are forward-only and occur at rate k(θs).
    Equation 3; justified by the authors as valid under sufficiently large ion motive force.
  • domain assumption The stator has two MotB ion channels that operate alternately and out of phase.
    Central to the gating mechanism and continuous torque generation; asserted from cryo-EM structures (refs. 17,18), not derived.
  • domain assumption Ion binding is extremely rapid; ion release is rate-limiting.
    Stated in the contact-gating section; necessary for the release-rate modulation to control the cycle.
  • domain assumption τ+ and k scale linearly with IMF.
    Adopted from experimental observations (SI, 'Torque and speed dependence on IMF'); used to compare with IMF-dependent data.
  • domain assumption The rotor-stator interaction potential Vr can be represented by simple piece-wise linear or quadratic forms.
    Adopted for tractability; the paper tests several shapes and shows insensitivity in the strong-coupling regime.
  • standard math In the stochastic-slipping regime, the 1D reduction and neglect of δ in Eq. 14 is valid because ΔVs/kBT ≈ 12.
    SI derivation of the Vr-independent CW torque-speed relation; approximation is quantified but not machine-checked.
invented entities (1)
  • Contact-dependent gating of ion release from the proximal MotB2 channel independent evidence
    purpose: To make the ion release rate direction-dependent (kg,CCW > kg,CW) and thereby produce the concave vs linear torque-speed asymmetry.
    The paper provides a falsifiable handle: mutations at MotA Asp86/Glu94 and FliG Asp241/Asp284/Asp289 are predicted to alter stall torque or knee speed. However, no direct kinetic measurement of kg is given; MD only shows interfacial geometry differences.

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Pith. "Pith review of Contact-Dependent Ion Gating Explains Directional Asymmetry in the Bacterial Flagellar Motor." pith.science (2026). https://pith.science/paper/V2VKZESF

@misc{pith2026260400470,
  author       = {Pith},
  title        = {Pith review of: Contact-Dependent Ion Gating Explains Directional Asymmetry in the Bacterial Flagellar Motor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V2VKZESF}},
  note         = {Machine review of arXiv:2604.00470}
}
read the original abstract

The bacterial flagellar motor (BFM) is a rotary molecular machine driven by the ion electrochemical potential across the cell membrane. Recent cryo-EM structures reveal a cogwheel-like architecture in which multiple stators engage a large rotor. A longstanding puzzle is the directional asymmetry of its torque-speed relation: concave in counterclockwise (CCW) rotation but nearly linear in clockwise (CW) rotation. Here, we develop a stochastic mechanochemical model that explicitly incorporates rotor-stator coupling and detailed ion translocation kinetics. By integrating physiological torque-speed data with recent measurements of rotor-stator relative motion, we show that under physiological conditions the motor operates in a tight engagement regime, rendering the torque-speed relation largely insensitive to the specific form of mechanical interactions. This finding rules out differences in rotor-stator mechanics as the origin of CW-CCW asymmetry. Guided by cryo-EM structures, we propose a contact-dependent gating mechanism in which the MotA-FliG interaction modulates the ion release rate of the MotB subunit proximal to the FliG ring. Molecular dynamics simulations indicate tighter MotA-FliG contact in the CW motor, implying a reduced ion release rate compared to CCW. Our model demonstrates that differential gating strength accounts for the observed asymmetry: stronger gating in CCW shortens torque-free waiting phases, enhances torque generation, and produces a concave torque-speed curve, whereas weaker gating in CW yields lower torque and a linear relation. This structure-based framework quantitatively links molecular asymmetry to motor function and identifies specific interfaces for targeted perturbation and mutational studies.

Figures

Figures reproduced from arXiv: 2604.00470 by the authors.

Figure 1
Figure 1. FIG. 1. Model of two coupled nano-rings. (A) Rotor-stator [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The stator-rotor slippage and the stall torque. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Torque-speed curves in the strong coupling regime. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Mechanochemical dynamics of a stator unit during one torque-generating cycle (∆ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Dynamics of instantaneous torque and the torque [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The difference of the MotA (E/F chains)–FliG (H [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.