The proton pumping mechanism of the bc₁ complex

The bc₁ complex is a proton pump of the mitochondrial electron transport chain which transfers electrons from ubiquinol to cytochrome c. It operates via the modified Q cycle in which the two electrons from oxidation of ubiquinol at the Q_o center are bifurcated such that the first electron is passed to Cytc via an iron sulfur center and c₁ whereas the second electron is passed across the membrane by b_L and b_H to reduce ubiquinone at the Q_i center. Proton pumping occurs because oxidation of ubiquinol at the Q_o center releases protons to the P-side and reduction of ubiquinone at the Q_i center takes up protons from the N-side. However, the mechanisms which prevent the thermodynamically more favorable short circuit reactions and so ensure precise bifurcation and proton pumping are not known. Here we use statistical thermodynamics to show that reaction steps that originate from high energy states cannot support high flux even when they have large rate constants. We show how the chemistry of ubiquinol oxidation and the structure of the Q_o site can result in free energy profiles that naturally suppress flux through the short circuit pathways while allowing high rates of bifurcation. These predictions are confirmed through in-silico simulations using a Markov state model.