  Rotation of a single bacterial flagellar motor is powered by multiple stators
tethered to the cell wall. In a "power-stroke" model the observed independence
of the speed at low load on the number of stators is explained by a
torque-dependent stepping mechanism independent of the strength of the stator
tethering spring. On the other hand, in models that depend solely on the stator
spring to explain the observed behavior, exceedingly small stator spring
constants are required. To study the dynamics of the motor driven by external
forces (such as those exerted by an optical tweezer), back-stepping is
introduced when stators are driven far out of equilibrium. Our model with
back-stepping reproduces the observed absence of a barrier to backward
rotation, 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 thermally
activated stepping rates in our model. Finally, we suggest that the general
mechanical properties of all molecular motors (linear and rotary),
characterized by their force(torque)-speed curve, can be determined by their
power-stroke potentials and the dependence of the stepping rates on the
mechanical state of the motor (force or speed). The torque-speed curve for the
clockwise rotating flagellar motor has been observed for the first time
recently (Yuan et al. 2010 PNAS). Its quasi-linear behavior is quantitatively
reproduced by our model. In particular, we show that concave and convex shapes
of the torque-speed curve can be achieved by changing the interaction potential
from linear to quadratic form. We also show that reversing the stepping rate
dependence on force (torque) can lead to non-monotonicity in the speed-load
dependency.
