Bacterial flagellar motor

An ion-powered rotary machine driving bacterial flagellar motion. Its energy source and conformational switch are separable: inward ion flux can power either rotational direction.

A minimal bacterial flagellar motor model combines angular velocity $\omega >0$ with bound and detached probabilities $P_A+P_B=1$. With detachment rate $k_0$ in the first half-turn and attachment rate $k_0$ in the second, the periodic stationary bound probability is $P_A=\alpha e^{-\beta \theta }$ on $0\le \theta \le \pi$, where $\alpha =(1+e^{-\pi \beta }{)}^{-1}$, and $P_A(\theta +\pi )=1-P_A(\theta )$. The one-way switching windows describe externally driven kinetics rather than detailed balance with a passive heat bath.

For the driven two-state rotary motor with a triangular bound potential of height $U_0$, the torque scale is $T_0=U_0/\pi$. Differentiating the phase-averaged torque gives ${\overline{T}}^{\prime }(s)=T_0[2P_A(s)-1]/\pi$. The decreasing crossing of $P_A=1/2$ therefore gives $s_{\max }=\ln (2\alpha )/\beta$ and ${\overline{T}}_{\max }=T_0\ln \cosh (\pi \beta /2)/(\pi \beta )$. The slow-speed limit is $T_0/2$; the fast-speed limit vanishes as $T_0\pi k_0/(8\omega )$.

A switch-complex component participating in organization of the bacterial flagellar rotor's cytoplasmic ring.

Its location in the C ring connects assembly of the cytoplasmic rotor structure to the larger switching machinery. Structural assembly, directional switching and ion-driven torque generation involve interacting but distinct components. ^[ref]

A switch-complex protein involved in reception of phosphorylated CheY and control of rotational bias.

Binding of phosphorylated CheY changes the switch’s rotational bias. A change in bias alters the balance of swimming behaviours without requiring the motor to sense external attractant directly. ^[ref]

A rotor protein involved in stator contact and torque generation. Changes in its organization contribute to directional switching without reversal of ion flow.

A stator-associated protein contributing proton-coupling machinery and anchorage to the cell envelope in the familiar proton-driven motor.

A stator protein contributing to ion-coupled force generation in proton-driven bacterial flagellar motors.

Together with its stator partners, it couples ion movement to mechanical interaction with the rotor. The surrounding membrane supplies an electrochemical energy source; the flagellar filament is the load rather than the source of that energy. ^[ref]