  Respiration in bacteria involves a sequence of energetically-coupled electron
and proton transfers creating an electrochemical gradient of protons (a
proton-motive force) across the inner bacterial membrane. With a simple kinetic
model we analyze a redox loop mechanism of proton-motive force generation
mediated by a molecular shuttle diffusing inside the membrane. This model,
which includes six electron-binding and two proton-binding sites, reflects the
main features of nitrate respiration in E. coli bacteria. We describe the time
evolution of the proton translocation process. We find that the electron-proton
electrostatic coupling on the shuttle plays a significant role in the process
of energy conversion between electron and proton components. We determine the
conditions where the redox loop mechanism is able to translocate protons
against the transmembrane voltage gradient above 200 mV with a thermodynamic
efficiency of about 37%, in the physiologically important range of temperatures
from 250 to 350 K.
