On the H⁺/2e^- stoichiometry of the respiratory chain

To calculate the number of ATP molecules synthesized during oxidative phosphorylation, and to understand the yield and efficiency of this process, it is necessary to know the H⁺/2e^- stoichiometry of the respiratory complexes, as well as the H⁺/ATP ratio for the ATP synthase. However, in most biochemistry textbooks, this topic is treated poorly. For example, several books simply mention that mitochondrial respiratory complexes pump protons across the membrane, without any reference to the number of protons translocated per pair of electrons [1-4]. Stryer's textbook [5] mentions a 4H⁺/2e^-, 2H⁺/2e^-, 4H ⁺/2e^- stoichiometry for complex I, III, and IV, respectively, but most recent editions of the biochemistry textbooks of Nelson and Cox [6] and Voet et al. [7] cite a 4, 4, 2 stoichiometry [6, 7]. Several years ago Hinkle et al. [8] proposed a 4, 2, 4 stoichiometry for the "effective" pumping of protons across the membrane; interestingly, these values are identical to the number of charges moved across the inner mitochondrial membrane by respiratory complexes I, III, and IV. The present work describes several arguments in favor of the stoichiometry of 4, 2, 4 for complex I, III, and IV, respectively.