The question, as amended, can be summarized as:
If there are 2–8 protons in the mitochondrial matrix (as calculated
from a pH of 8) is this sufficient for ATP synthesis, if 2–3 hydrogen
ions are required for each molecule of ATP synthesized?
The initial deficiency in the argument was that it did not consider the inter-membrane space, and my answer was:
According to the generally accepted Mitchell Hypothesis, the generation of ATP in the
mitochondrion is due to an electrochemical gradient between the
mitochondrial matrix and the inter-membrane space.
This gradient is predominantly a pH gradient — the [H+] is
higher in the inter-membrane space than in the matrix
The flow of protons down this gradient is responsible for the
production of ATP.
The H+ gradient is maintained by protons being pumped across the inner mitochondrial membrane by the flow of electrons through the electron transport chain. (i.e. The H+ concentration is kept low in the matrix and high in the inter-membrane space, even though protons are continually flowing into the matrix.
i.e. For ATP synthesis to occur there is no requirement for a high steady-state concentration of hydrogen ions in the mitochondrial matrix — quite the opposite (as is reflected by the pH 8). A relatively high concentration of hydrogen ions is only required in the inter-membrane space — as is indeed found.
The amended question assumes a pH of 6.8 for the inter-membrane space, and calculates 8.9 protons to be in this compartment.
The poster still does not state specifically what the problem is — there is still a concentration gradient of hydrogen ions, and a vast body of experimental evidence shows that it is this gradient of hydrogen ions that drives ATP synthesis.
So the implied question does not seem specific to ATP generation, but to the concept of pH in cellular compartments of small volume. There is obviously something wrong here, and the paper quoted — which addresses this question — suggests some possible explanations:
- That the pH measured is incorrect because of the methodology
- That the hydrogen ions are not free but associated with negatively charged species (possibly phosphate ions) from which they may be released, as required.
The latter point had occurred to me before reading the paper. In summary:
- The steady-state hydrogen ion concentration gradient is sufficient to drive ATP synthesis, with many hydrogen ions at any time passing through the membrane in one direction or another.
- Many of the hydrogen ions in both compartments will be buffered in a manner that allows there release
- The naive calculation is likely to be an underestimate because the pH in the inter-membrane space may be much lower.
If I were an ox-phos person I would know how many molecules of the ATP synthase complex there are per mitochondrion and the number of protons pumped into the membrane space per unit time. Such information would, presumably, bear on the problem.