I. THE MODEL OF THE BACTERIAL FLAGELLAR MOTOR A. Stator-Rotor interaction

The model for the stator-rotor interaction is discussed in the sections The stator-rotor interaction and The rotor switching dynamics of the main text. The model is based on the model Oster and Blair and coworkers [1, 2] and Meacci and Tu [3], but extended to include the conformational transitions of the rotor protein complex. Here, we discuss aspects of the model that are not discussed in the main text. But, for completeness, we also give the main equations already presented in the main text. In our model, each stator-rotor interaction is described by 4 energy surfaces, U r sj , with the subscript sj = 0, 1 denoting the conformational state of stator protein j and the supersript r = 0, 1 denoting the conformational state of the rotor (clockwise or counterclockwise). The stator-rotor interaction potentials are periodic saw-tooth potentials. The 2 surfaces corresponding to the two conformatinal states of the stator protein are equal except for a shift of half a period, while the 2 surfaces corresponding to the conformatinal states of the rotor are each other’s mirror image plus a shift. We assume that the stator proteins are fixed by the peptidoglycan layer and that only the rotor complex moves. The equation-of-motion of the rotor is then given by