Relaxation time asymmetry in stator dynamics of the bacterial flagellar motor

Abstract

The bacterial flagellar motor is the membrane-embedded rotary motor, which turns the flagellum that provides thrust to many bacteria. This large multimeric complex, composed of a few dozen constituent proteins, is a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels that dynamically bind to the peptidoglycan at the rotor periphery and apply torque. Their dynamic exchange is a function of the viscous load on the flagellum, allowing the bacterium to adapt to its local environment, although the molecular mechanisms of mechanosensitivity remain unknown. Here, by actively perturbing the steady-state stator stoichiometry of individual motors, we reveal a stoichiometry-dependent asymmetry in stator remodeling kinetics. We interrogate the potential effect of next-neighbor interactions and local stator unit depletion and find that neither can explain the observed asymmetry. We then simulate and fit two mechanistically diverse models that recapitulate the asymmetry, finding assembly dynamics to be particularly well described by a two-state catch-bond mechanism.

Fig. 1.. Experimental measurements.

(A) Single measurement of a 300-nm bead, showing motor torque and stator number as a function of time. The experimental protocol for single-motor measurements was the following: unperturbed steady-state measurement (orange), motor stall via magnetic tweezers (10 min), release from stall and relaxation back to steady state (light blue), introduction of ionophore (8 min), removal of ionophore, and motor resurrection to steady state (purple). (B) A schematic of the torque-speed plane for the example in (A), where colors correspond to the experimental steps. Solid arrows represent observed transitions, and open arrows represent nonobserved transitions. Bottom inset shows the experimental assay. (C) Individual traces of motor torque versus time and (D) stator number versus time for the steady state (orange), release from stall (light blue), and resurrection (purple) measurements. Black lines show the average behavior of all motors. In (D), the black lines represent 〈N〉(t). Subplots from top to bottom show 1300-, 500-, and 300-nm beads (27, 33, and 31 measurements, respectively).

Fig. 2.. Stator unit stoichiometry, rates, and characteristic times for release from stall and resurrection experiments.

(A) Evolution of stator stoichiometry for release from stall (light blue) and resurrection (purple). Viscous loads, from the top to bottom are γ₁₃₀₀, γ₅₀₀, and γ₃₀₀. Light blue and purple lines show the average of multiple traces, i.e., 〈N〉(t), shading shows SD, and the orange line shows 〈N〉(t) of steady-state measurements. The black line shows the best fit of the Hill-Langmuir model (Eq. 2) to each time series (with the exception of release from stall for γ₁₃₀₀). (B) The rates (top) and characteristic times (bottom) as a function of single stator torque at steady state, τ_ss. Error bars on τ_ss are the SD of all measurements. Error bars on rates and t_c represent the 90% high-density interval from ABC inference.

Fig. 3.. Comparison of different mechanistic models with the experimental dataset.

(A) Steady state trajectories (yellow), stall (green), and resurrection (purple), where shaded zones show SD from the mean. The mechanistic models shown are the speed-rate model (blue) of Wadhwa et al. (6) (Eq. 1 using the rates of Eq. 5). The two-state catch-bond model (eq. S8) (red) and Hill-Langmuir model with constant rates for each γ (black). (B) Schematics of the speed-rate and two-state catch-bond models, showing transitions between the unbound (u) and bound (b) states in the first case and the weakly (w) and strongly bound (s) states in the second. (C) Bayes factors for different models normalized to the speed-rate model. Blue and red bars show the speed-rate and two-state catch-bond models from (B). (D) Energetic contribution β(ε(τ) − μ_r) as a function of τ_ss (torque per stator unit) for the speed-rate model. Error bars show high-density region. (E) Rates of the speed-rate model as a function of motor speed over the range of observed speeds. Shading shows high-density region of 1/t_c. (F) Rates of the two-state catch-bond as a function of τ_ss. Triangles mark maximum a priori values, shading shows the high-density region. (G) Schematic of energy landscape and transitions for the rates in (F) following the same color scheme. The distance along the reaction coordinate is unknown.