Coupling between switching regulation and torque generation in bacterial flagellar motor

The bacterial flagellar motor plays a crucial role in both bacterial locomotion and chemotaxis. Recent experiments reveal that the switching dynamics of the motor depends on the motor rotation speed, and thus the motor torque, non-monotonically. Here we present a unified mathematical model which models motor torque generation based on experimental torque-speed curves and torque-dependent switching based on the conformational spread model. The model successfully reproduces the observed switching rate as a function of the rotation speed, and provides a generic physical explanation independent of most details. A stator affects the switching dynamics through two mechanisms: accelerating the conformation flipping rates of individual rotor switching units, which favours slower motor speed and thus increasing torque; and affecting more switching units within unit time, which favours faster speed. Consequently, the switching rate shows a maximum at intermediate speed. Our model predicts that a motor switches more often with more stators. The load-switching relation may serve as a mechanism for sensing the physical environment, similar to the chemotaxis system for sensing the chemical environment. It may also coordinate the switch dynamics of motors within a cell.