Dynamics of the bacterial flagellar motor with multiple stators

TL;DR

This paper presents a mathematical model explaining how bacterial flagellar motors operate with multiple stators, revealing load-dependent dynamics and fluctuations, and providing insights into their torque-speed behavior.

Contribution

The model introduces a new understanding of bacterial flagellar motor dynamics with multiple stators, explaining load-dependent regimes and fluctuation mechanisms.

Findings

Motor speed is independent of stator number at near zero load.

Two distinct time scales govern motor dynamics, explaining torque-speed regimes.

Speed fluctuations depend on load and number of steps per revolution.

Abstract

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.