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Rotation of a single bacterial flagellar motor is powered by multiple statorstethered to the cell wall. In a "power-stroke" model the observed independenceof the speed at low load on the number of stators is explained by atorque-dependent stepping mechanism independent of the strength of the statortethering spring. On the other hand, in models that depend solely on the statorspring to explain the observed behavior, exceedingly small stator springconstants are required. To study the dynamics of the motor driven by externalforces (such as those exerted by an optical tweezer), back-stepping isintroduced when stators are driven far out of equilibrium. Our model withback-stepping reproduces the observed absence of a barrier to backwardrotation, as well the behaviors in the high-speed negative-torque regime.Recently measured temperature dependence of the motor speed near zero load(Yuan & Berg 2010 Biophys J) is explained quantitatively by the thermallyactivated stepping rates in our model. Finally, we suggest that the generalmechanical properties of all molecular motors (linear and rotary),characterized by their force(torque)-speed curve, can be determined by theirpower-stroke potentials and the dependence of the stepping rates on themechanical state of the motor (force or speed). The torque-speed curve for theclockwise rotating flagellar motor has been observed for the first timerecently (Yuan et al. 2010 PNAS). Its quasi-linear behavior is quantitativelyreproduced by our model. In particular, we show that concave and convex shapesof the torque-speed curve can be achieved by changing the interaction potentialfrom linear to quadratic form. We also show that reversing the stepping ratedependence on force (torque) can lead to non-monotonicity in the speed-loaddependency.

The Effects of Stator Compliance, Backs Steps, Temperature, and Clockwise Rotation on the Torque-Speed Curve of Bacterial Flagellar Motor