Abstract
The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps. Here we propose a simple physical model, based on the storage of energy in protein springs, that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. We also predict a sublinear speed versus torque relationship for fixed load at low torque, and a peak in rotor diffusion as a function of torque. Our model provides a comprehensive framework for understanding and analyzing stepping behavior in the bacterial flagellar motor and proposes novel, testable predictions. More broadly, the storage of energy in protein springs by the flagellar motor may provide useful general insights into the design of highly efficient molecular machines.
Highlights
Bacteria swim by virtue of tiny rotary motors that drive rotation of helical flagella
What is the origin of motor steps and how can these steps be reconciled with the near perfect efficiency of the motor observed at low speeds [2]? We argue that steps, including backward steps, are an inevitable consequence of the physical structure of the motor—a stator driving a ‘‘bumpy’’ rotor through a viscous medium
Forward steps are more likely to occur than backward steps, so that on average the motor moves forward
Summary
Bacteria swim by virtue of tiny rotary motors that drive rotation of helical flagella. These motors are powered by a transmembrane proton (or Naz) flux which is converted into torque. A new result has provided direct insight into motor operation [1]: at low speeds, the bacterial flagellar motor proceeds by steps. This stepping is stochastic in nature, as manifested by the occurrence of occasional backward steps even for motors locked in one rotation direction. What is the origin of motor steps and how can these steps be reconciled with the near perfect efficiency of the motor observed at low speeds [2]? We argue that steps, including backward steps, are an inevitable consequence of the physical structure of the motor—a stator driving a ‘‘bumpy’’ rotor through a viscous medium
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