Abstract
The bacterial flagellar motor is an ion-driven rotary machine in the cell envelope of bacteria. Using a gold nanoparticle as a probe, we observed the precession of flagella during rotation. Since the mechanism of flagella precession was unknown, we investigated it using a combination of full simulations, theory, and experiments. The results show that the mechanism can be well explained by fluid mechanics. The validity of our theory was confirmed by our full simulation, which was utilized to predict both the filament tilt angle and motor torque from experimental flagellar precession data. The knowledge obtained is important in understanding mechanical properties of the bacterial motor and hook.
Highlights
The bacterial flagellar motor is an ion-driven rotary machine in the cell envelope of bacteria
The flagellar motor of swimming bacteria, such as Escherichia coli (E. coli) and Serratia marcescens (S. marcescens), is a rotary molecular machine that is powered by an ion flux; the diameter of the motor is ~45 nm
The torque generated by the motor is transmitted to a helical flagellar filament through a hook, which allows the filament to rotate as a screw propeller so that the bacteria can swim in fluid[1]
Summary
We assumed that the cell body was stuck to a wall surface, as shown in Fig. 1a, similar to the set-up used in previous experimental studies[2,3,4,5]; this allowed for a better comparison between the numerical and experimental results. In this configuration, the flagellar filament exhibits torque-induced precession with angular velocity Ωf and tilt angle θ, the angle between the principal axis of the filament and the normal axis. From the angular velocity Ωf obtained by the full simulation, we calculated the spin angular velocity Ωspin and revolution angular velocity Ωrev for the E. coli model, as shown in Fig. 5a; the time-averaged values are shown in intervals of ∆t = 10, to smooth high-frequency noise, which corresponds to ~0.03 sec in actual time under the conditions of a motor torque Tm = 103 pN∙nm and fluid viscosity μ = 10−3 Pa∙s. Our simple theory agreed well with the full BEM simulations, allowing the filament tilt angle and applied motor torque to be predicted, based on experimental flagellar precession data. The knowledge obtained is important in understanding mechanical properties of the bacterial motor and hook
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