Where does the additional 1 proton cost of oxidative phosphorylation come from?

Question

I've been quite confused by the source of the additional 1H+ cost right now. I know it costs the F1Fo-ATP synthase 3H+ to produce an ATP, and it is also stated that:

ADP3−cytoplasm + ATP4−matrix → ADP3−matrix + ATP4−cytoplasm // ADP/ATP exchange is energetically expensive: about 25% of the energy yielded from electron transfer by aerobic respiration, or one hydrogen ion, is consumed to regenerate the membrane potential that is tapped by ADP/ATP translocase.(Wikipedia/ADP/ATP Translocase)

So in some books I find out that they regard the net cost of producing an ATP as 4H+. Here is another statement:

The phosphate carrier, which works in concert with ATP-ADP translocase, mediates the electroneutral exchange of H2PO4-for OH- (or, indistinguishably, the electroneutral symport of H2PO4- and H+). The combined action of these two transporters leads to the exchange of cytosolic ADP and Pi for matrix ATP at the cost of an influx of one H+. (Berg JM, Tymoczko JL, Stryer L. Biochemistry. 5th edition. New York: W H Freeman; 2002. Section 18.5, Many Shuttles Allow Movement Across the Mitochondrial Membranes.)

And my question comes here. Why do we not consider the effect of the process of ADP + Pi → ATP on the membrane potential? It also produces a net cost of 2e-. Putting these together, this will lead to 0, i.e. no additional net cost. Or should I only consider H+ but not e-? (This might lead to another problem about H2PO4-'s breakup.)

Answer 1

The energy required for the ATP production by ATP synthase is obtained from movement of ions (H⁺ or in some cases Na⁺) downstream of their potential (proton motive force). I guess, there is no exact stoichiometric exchange as in case of ion pumps. The rotation of the motor is generated by the movement of protons through a channel. The H⁺/ATP ratio is estimated using biophysical/biochemical techniques.

Brand and Lehninger (1977) estimated this ratio to be greater than 3.

Turina et al. (2003) recalculated this ratio using constituted liposomes and their estimate is 3.9 ± 0.2.

This is an excerpt from a more recent study on chloroplast ATP synthase by Hahn et al (2018).

The symmetry mismatch between the 14-fold Fo rotor and the near-threefold F1 head means that the number of c subunits rotating past subunit a to generate one ATP is not an integer. cF1Fo requires, on average, 4.67 c subunits, or protons, to produce one ATP. The nearest integral numbers of c subunits per step would be 4, 5, and 5, equivalent to rotation angles of 103°, 129°, and 129°. Surprisingly however, the three conformations are separated by rotations of 103°, 112°, and 145°, or 4, 4.4, and 5.6 c subunits (fig. S5C). This means that the position of the c subunits relative to subunit a in the three conformations differs.

The structure and efficiency of chloroplast ATP synthase may be a little different but what I want to emphasize is that there is no exact exchange of protons and ATP.