Coupling of vectorial proton flow to a biochemical reaction by local electric interactions

For a transmembrane redox enzyme and a (passive) protonophore, the complete set of rate equations is given. Turnover causes cyclic variation of their electric polarization. This is responsible not only for effects of the electric field on the rate constants but also for the generation of an electric field felt by neighboring molecules. It is calculated that, when the systems are close together at a fixed distance, cycling of the two systems becomes coupled enabling the protonophore to pump protons against their electrochemical gradient. If the electrochemical gradient for protons approaches the input force of the redox reaction, slip (incomplete coupling between the chemical and proton-transport reactions) results. By using different sets of parameters, both kinetically reversible and kinetically irreversible proton pumps can be simulated.