We make use of the physical mechanism of proton pumping in the so-called Complex I within mitochondria membranes. Our model is based on sequential charge transfer assisted by conformational changes which facilitate the indirect electron-proton coupling. The equations of motion for the proton operators are derived and solved numerically in combination with the phenomenological Langevin equation describing the periodic conformational changes. We show that with an appropriate set of parameters, protons can be transferred against an applied voltage. In addition, we demonstrate that only the joint action of the periodic energy modulation and thermal noise leads to efficient uphill proton transfer, being a manifestation of stochastic resonance.
Kaur, D., Filonenko, I., Mourokh, L., Fendler, C., and Blick, R. H. “Stochastic Resonance in a Proton Pumping Complex I of Mitochondria Membranes.” Scientific Reports 7 (2017): 12405.