  The bacterial flagellar motor drives the rotation of flagellar filaments and
enables many species of bacteria to swim. Torque is generated by interaction of
stator units, anchored to the peptidoglycan cell wall, with the rotor. Recent
experiments [Yuan, J. & Berg, H. C. (2008) PNAS 105, 1182-1185] show that near
zero load the speed of the motor is independent of the number of stators. Here,
we introduce a mathematical model of the motor dynamics that explains this
behavior based on a general assumption that the stepping rate of a stator
depends on the torque exerted by the stator on the rotor. We find that the
motor dynamics can be characterized by two time scales: the moving-time
interval for the mechanical rotation of the rotor and the waiting-time interval
determined by the chemical transitions of the stators. We show that these two
time scales depend differently on the load, and that their crossover provides
the microscopic explanation for the existence of two regimes in the
torque-speed curves observed experimentally. We also analyze the speed
fluctuation for a single motor using our model. We show that the motion is
smoothed by having more stator units. However, the mechanism for such
fluctuation reduction is different depending on the load. We predict that the
speed fluctuation is determined by the number of steps per revolution only at
low load and is controlled by external noise for high load. Our model can be
generalized to study other molecular motor systems with multiple
power-generating units.
