Coupling between Flagellar Motor Rotation and Proton Flux in Bacteria

The bacterial flagellar motor is driven by a flow of proton according to the electrochemical potential gradient across the membrane. For understanding efficient and smooth transformation of both electric and chemical potential energies of proton into a mechanical work, loose coupling has been assumed between the flow of protons and the rotation of the motor. In the mechanism proposed, two kinds of protein molecules arranged on a disc and on a ring surrounding the disc repeat fast and reversible reactions regulated by the binding of protons. Based on this mechanism, the relations of the torque generated in the motor and the flux of protons to the speed of rotation of the motor have been derived. The results of numerical calculations show reasonable agreement with most of the experimental results. Particular attention has been paid to the possibility of reverse transformation of free energy. It is expected that by rotating the motor in the reverse direction by an external force, the flux of protons is decreased and finally reversed; that is, protons may be pumped out against the potential gradient.