Steps in the bacterial flagellar motor

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 [Sowa et al. (2005) Nature 437, 916–919]. Here we propose a simple physical model 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. Our model also predicts a sublinear torque-speed relationship at low torque, and a peak in rotor diffusion as a function of torque.

💡 Research Summary

The paper addresses the puzzling observation that bacterial flagellar motors, which are generally regarded as smooth rotary engines, exhibit discrete stepping behavior when operating at low rotational speeds. Building on the experimental findings of Sowa et al. (2005), the authors propose a minimalist yet physically grounded model in which the rotor experiences a “tilted corrugated potential.” This potential combines a constant torque τ that tilts the energy landscape and a periodic contact interaction V(θ)=V₀ cos(Nθ) arising from structural features of the motor (e.g., stator‑rotor interactions). The total energy is therefore U(θ)=−τθ+V₀ cos(Nθ).

In this landscape the rotor is trapped in local minima separated by energy barriers. Thermal fluctuations (kBT) enable stochastic transitions over these barriers, which the authors treat as a one‑dimensional random walk governed by the overdamped Langevin equation or, equivalently, by the Fokker‑Planck description. Transition rates are obtained from Kramers theory:

k₊(θ₀)=k₀ exp