  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.
