Physical Models of Proton-Pumping Complexes of Mitochondria Membranes

The models are proposed for all three proton-pumping complexes. The model for Complex IV includes the electron source, electron drain, and three electron sites in between, as well as proton source, proton drain and three proton sites in between. Electon transport occurs along the inner mitochondria membrane and the protons are transferred across the membrane. The chemical potential of the electron source is larger than that of the electron drain, while the protons are pumped to the higher potential.. The middle electron and proton sites are in the close proximity, so their electrostatic interaction facilitates the energy transfer. We suggest that in Complex I the energy exchange is mediated by the conformational changes. In both cases, we use the methods of condensed matter and statistical physics to derive quantum equations of motion for the electron and proton operators in the presence of protein environment and to calculate the electron and proton currents. In the model of the Complex III, we couple the equations of motion to phenological Langevin equation describing electron and proton transport by quinons.