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.)