This work was supported in part by DGAPA Grant IN200897.
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  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  and Voet et al.  cite a 4, 4, 2 stoichiometry [6, 7]. Several years ago Hinkle et al.  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.
According to the chemiosmotic theory, mitochondrial complexes I, III, and IV couple the redox reaction to the translocation of protons across the membrane, generating a proton electrochemical gradient (Δμ) used for the synthesis of ATP. Both Δμ and the number of ATP molecules synthesized by the ATP synthase depend on the H+/2e− stoichiometry of the respiratory complexes.
Four respiratory chain complexes are involved in the transfer of electrons from substrates to oxygen: complex I or NADH dehydrogenase , complex II or succinate dehydrogenase , complex III or cytochrome bc1 , and complex IV or cytochrome oxidase . Complexes I, III, and IV pump protons across the membrane whereas the synthesis of ATP occurs in complex V or ATP synthase [13, 14].
VECTORIAL AND CHEMICAL PROTONS
To calculate the stoichiometric relationship between the H+ pumped and the transport of electrons it is important to recognize that, in addition to the vectorial protons (pumped protons), the chemical reaction contains scalar or chemical protons. This situation can be illustrated by detergent-solubilized complex III, catalyzing the reaction,
in the absence of a membrane. It can be seen that two scalar protons are released into the medium during the chemical reaction. As we will discuss later, the presence of these chemical protons leads to paradoxical conclusions.
THE MITOCHONDRIAL COMPLEXES, THEIR REDOX REACTIONS, AND THE PUMPING OF PROTONS
Complex I pumps 4H+ across the membrane per pair of electrons, resulting in the movement of four positive charges perpendicular to the plane of the membrane. In addition, the enzyme transfers 2H+ and 2e− (two hydrogen atoms) to ubiquinone [6, 15]. The following equation describes the reaction catalyzed by complex I:
where N and P indicate the negative and positive side of the membrane.
Complex III catalyzes the reduction of two molecules of cytochrome c by ubiquinol, as shown in the following equation:
Two vectorial H+ are pumped from the matrix to the cytosolic side of the inner mitochondrial membrane, and two scalar protons are released in the intermembrane space of the mitochondrion [6, 16]. In addition, two positive charges migrate from the negative (N) side to the positive (P) side of the membrane, corresponding to the movement of two electrons from the P side to the N side of the membrane . It is worth noting that the number of H+ translocated from the matrix to the cytosol (2H+) is different from the number of protons that appears in the intermembrane space (4H+).
Complex IV receives the electrons from four molecules of cytochrome c and reduces molecular oxygen, giving two molecules of H2O, as shown in the following equation:
Four vectorial H+, corresponding to four positive charges migrating from the N to the P side of the membrane, are pumped into the intermembrane space [6, 17]. In addition, four electrons flow in the opposite direction to combine with molecular oxygen and with 4H+ coming from the mitochondrial matrix. This movement of electrons is equivalent to the flow of four positive charges from the N side to the P side of the membrane. If the movements of protons and electrons are summed up, a total of eight positive charges migrates toward the intermembrane space, four electrons are transferred to molecular oxygen, four protons are pumped across the membrane, and four scalar or chemical protons are consumed in the mitochondrial matrix during the formation of two molecules of H2O .
THE PROBLEM FOUND IN THE DEFINITION OF THE H+/2e− STOICHIOMETRY IN THE MITOCHONDRIAL RESPIRATORY COMPLEXES
Helpful insights into the definition of the H+/2e− stoichiometry in the respiratory complexes can come from a consideration of the Na+/K+ ATPase (Fig. 1). This pump catalyzes the following reaction:
The classic stoichiometry of 3Na+/ATP and 2K+/ATP can be obtained by kinetic experiments in proteoliposomes, measuring the initial rates of ATP hydrolysis and Na+ and K+ transport . It is important to mention that the same stoichiometry should be obtained if the measuring device is placed inside or outside the vesicle, tracking either the appearance of Na+ inside the vesicle or the disappearance of Na+ from the extravesicular space (Fig. 1).
This last situation does not occur in the case of complexes III and IV. The flux of positive charges from the N side of the inner membrane to the P side is 2+/2e− and 4+/2e− for complex III and IV, respectively [16, 17], and the same values are obtained whether the flow of positive charges is studied from the inside (mitochondrial matrix) or from the outside (intermembrane space). By contrast, when changes in pH are measured in the intermembrane space, complex III appears to transport 4H+/2e−, and complex IV appears to transport only 2H+/2e−, despite the fact that the redox change for the reaction catalyzed by complex IV is the larger one . If now the pH change in the mitochondrial matrix is measured, a different result is obtained, 2H+/2e− for complex III and 4H+/2e− for complex IV. In other words, the stoichiometry of “proton pumping” depends on the position of the measuring device.
The problem in the definition of the H+/2e− disappears when the number of positive charges flowing through each complex is determined. The values obtained (2+/2e− for complex III and 4+/2e− for complex IV) are the same whether we measure the flow from the mitochondrial matrix or the intermembrane space. For this reason, it seems logical to define the effective proton pumping in terms of the positive charges moving across the membrane, which in turn is related to the flow of protons and/or electrons across each complex [16, 17].
THE EFFECTIVE H+/2e− STOICHIOMETRY FOR COMPLEX I, III, AND IV IS 4, 2, AND 4, RESPECTIVELY
As mentioned, the calculation of proton pumping stoichiometry for complex III and IV is made difficult by the presence of scalar protons. However, this problem can be circumvented when the positive charge moved by each complex is related to the total number of protons disappearing from the matrix and appearing in the intermembrane space. Fig. 2 shows that 10 positive charges flow from the N side of the internal mitochondrial membrane to the P side, whereas 10 protons disappear from the matrix and appear in the intermembrane space.
Of the 10 positive charges flowing through the membrane, four are translocated by the NADH dehydrogenase, two by cytochrome bc1 and four by cytochrome oxidase. On the other hand, of the 10 protons, complex I pumps four, whereas complex III and complex IV mechanistically pump two H+ apiece. The other two H+ that appear on the cytosolic side of the inner mitochondrial membrane are scalar, and they come from the reaction catalyzed by complex III. Also, the 2H+ that disappear from the mitochondrial matrix correspond to the chemical-scalar protons used in the formation of water by cytochrome oxidase.
Next, we can correlate the flow of positive charges and the flow of protons across the membrane. One can see that four of the positive charges are related to the pumping of 4H+ by complex I (4H+/2e−). The two vectorial H+ that complex III pumps are assigned to the two positive charges that the same complex moves across the membrane (2H+/2e−). Finally, the two scalar H+ that disappear on the N side of the membrane and appear on the P side are assigned to cytochrome oxidase; in this way, the movement of positive charges (4+) in cytochrome oxidase is the same as the movement of protons (4H+), giving a stoichiometry of 4H+/2e− for this complex. In summary, the effective H+/2e− stoichiometries for complex I, III, and IV are 4, 2, and 4, respectively. As pointed out before, these values also correspond to the number of charges moved across the inner mitochondrial membrane by respiratory complexes I, III, and IV (Fig. 2).
There are several thermodynamic considerations that support a higher pumping of protons in complex I and IV. The change in redox potential for the reaction catalyzed by complex I is +0.365 V, for that catalyzed by complex III it is +0.209 V, and for the one catalyzed by complex IV it is +0.562 V . From these values one can calculate a standard free energy change of −16.8, −8.1, and −27.7 kcal/mol, respectively. In addition, it has been reported that the membrane potential across the inner mitochondrial membrane is around 150 mV with a ΔpH ranging from 0.5 to 1 unit [19, 20], resulting in a proton electrochemical gradient (Δμ) of 4.1 to 4.8 kcal/mol. It is well known that the pumping of protons across the membrane is limited by the ΔG of the reaction and the Δμ. If we assume a value of 4.4 kcal/mol for Δμ then we can calculate the maximum number of protons transported by each complex with the following equation :
where n is the number of vectorial protons pumped by the respiratory complex, Δμ the proton electrochemical gradient, and ΔG the change of free energy of the reaction. Table I summarizes the results of this analysis and shows that complex I can pump up to four protons, complex III can pump not more than two protons, and complex IV can pump up to six protons. These results agree with the stoichiometries of 4, 2, and 4 reported in 1991 by Hinkle et al. , where the term “effective” pumping of protons was recommend. According to this point of view, complex III and IV are working as if they were pumping two and four protons across the membrane, respectively.
THE STOICHIOMETRY OF THE ATP SYNTHASE
With regard to the ATP synthase, it has been shown that this enzyme can work with different stoichiometries, depending on the source of the enzyme and the environment in which the organism was grown . Most biochemistry textbooks state that three H+ are required for the synthesis of one molecule of ATP in mitochondria. However, the structure of the F0 sector of the ATP synthase , as well as experiments carried out with the ATP synthase of chloroplasts and cyanobacteria , suggest that the stoichiometry of this complex can be as high as 4H+/ATP.
Assuming a 3H+/ATP stoichiometry for mitochondrial ATP synthase and the flow of one proton for the transport of ATP, ADP, and Pi across the inner membrane, the synthesis of one ATP molecule consumes a total of 4H+. When NADH is oxidized by the respiratory chain, 10 protons are pumped into the intermembrane space, and the maximum number of ATP molecules that can be synthesized is 2.5 (10/4 = 2.5). Also, for each FADH2 that enters the respiratory chain, six protons are pumped, and the number of ATP molecules synthesized is 1.5 (6/4 = 1.5). When the stoichiometry of the ATP synthase is increased to 4H+/ATP then the yield in ATP synthesis diminishes to 2 (10/5) and 1.2 (6/5) with NADH+ and FADH2, respectively.
THE OXIDATION OF GLUCOSE AND THE PRODUCTION OF ATP
Fixing the stoichiometry of the ATP synthase at 3H+/ATP, the complete oxidation of 1 mol of glucose will produce 29 mol of ATP. This value contrasts with the value of 36 mol of ATP described in many biochemistry textbooks. The previous calculation was based on the production of 8 mol of NADH and 2 mol of FADH2 in the mitochondrial matrix, 2 mol of cytosolic NADH whose electrons are transferred to the respiratory chain via the glycerophosphate shuttle, 2 mol of cytosolic ATP produced by glycolysis, and 2 mol of GTP produced by the succinyl-CoA synthetase in the mitochondrial matrix. Later, nucleoside diphosphokinase catalyzes the transformation of GTP into ATP. Here, it is important to consider that two protons are used to transport two molecules of ATP from the matrix to the cytosol, such that the total amount of ATP synthesized during the oxidative phosphorylation diminishes in 0.5. In addition, the 2H+ (0.5 ATP) used to transport two pyruvate molecules were taken into consideration.
When cytosolic NADH is oxidized by the malate-aspartate shuttle then 4.5 mol of ATP are synthesized, because the glutamate/aspartate antiporter is coupled to the flow of one proton per glutamate  in such a way that the global yield would increase to 31 mol of ATP per mol of glucose oxidized.
SUBSTRATE-LEVEL PHOSPHORYLATION AND OXIDATIVE PHOSPHORYLATION: WHICH ONE IS MORE EFFICIENT?
To a first approximation, one may think that the efficiency of ATP synthesis is higher in mitochondrial oxidative phosphorylation than in glycolysis. However, this is not the case. To calculate the efficiency of the synthesis of ATP in each process, the following information is needed: 1) ΔGo′ for the transformation of glucose into lactate and for the oxidation of pyruvate into CO2 and H2O, and 2) ΔGo′ of hydrolysis of ATP. The ratio of these two values determines the efficiency of the reaction under standard conditions.
With regard to the first point, the transformation of 1 mol of glucose into 2 mol of lactate releases 47 kcal of free energy, whereas the complete oxidation of 2 mol of pyruvate into 6 mol of CO2 and 4 mol of water releases 566 kcal. If we assume that 7.5 kcal of free energy are needed for the synthesis of 1 mol of ATP, then the efficiency of substrate-level phosphorylation is 32% (2 × 7.5/47) whereas the efficiency of oxidative phosphorylation is 33% (25 × 7.5/566), assuming 4H+ are used for the synthesis of ATP. This value is similar to the efficiency of glycolysis, but it is an upper limit, because up to 25% of the proton electrochemical gradient is dissipated by diffusion of H+ across the membrane , decreasing the oxidative phosphorylation efficiency.
Although the two stoichiometries (4,4,2 versus 4,2,4) result in the same number of protons translocated across the inner mitochondrial membrane (10 H+), it is important to define the capacity of each complex for effective proton pumping. The analysis of chemical reactions catalyzed by each complex, as well as thermodynamic considerations, suggest a stoichiometry of 4H+/2e− for complexes I and IV and 2H+/2e− for complex III. This means that complexes III and IV behave physiologically and thermodynamically as if they were pumping two and four protons, respectively. Furthermore, these values match the number of charges moved across the inner mitochondrial membrane by respiratory complexes III and IV.
Table Table I. Thermodynamic characteristics of the reactions catalyzed by complexes I, III, and IV
The actual ΔG of the reaction was obtained with the following equation: ΔG = ΔG° + RTln([Products]/[Reactants]), where R, T and ΔG° are the universal gas constant, the absolute temperature, and the change in standard free energy of the reaction, respectively. In addition, the value of ΔG° was obtained from ΔE°, using the well known relationship ΔG° = −mFΔE°, where F is the Faraday constant, m the number of electrons participating in the reaction, and ΔE° the standard redox potential. n describes the number of vectorial protons pumped per pair of electrons. The ΔG° of the reactions catalyzed by complex I, III, and IV are as follows; − 16.8, −8.1, and −27.7 kcal/mol . The actual ΔG were calculated using mitochondrial NADH/NAD+  and Qred/Qox  ratios of 1, and intracellular pO2 of 0.015 kPa , and assuming a value of 1 for the cyt cred/cyt cox ratio.
NADH + Q + H+ => NAD+ + QH2
QH2 + 2cyt cox => Q + 2H+ + 2cyt cred
2cyt cred + 2H+ + 1/2 O2 => H2O + 2cyt cox
We thank Dr. Carolyn Slayman from Yale University for critical reading of the manuscript.