1. Department of Applied Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
2. The Clarendon Laboratory, Department of Physics, Oxford University, Parks Road, Oxford OX1 3PU, UK
3. Division of Biological Science, Graduate School of Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan
4. PRESTO, Japan Science and Technology Corporation (JST) 4-1-8, Honmachi, Kawagoe, Saitama 332-0012, Japan
5. *These authors contributed equally to this work

Correspondence to: Richard M. Berry² Correspondence and requests for materials should be addressed to R.M.B. (Email: r.berry1@physics.ox.ac.uk).

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria^{1, 2}. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane³; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor^{4, 5}. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H⁺-driven and Na⁺-driven motors, respectively. Here we demonstrate a stepping motion of a Na⁺-driven chimaeric flagellar motor in Escherichia coli ⁶ at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor^{7, 8}. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.

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