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If the proton concentration in the mitochondrial matrix (based on its pH) is multiplied by its volume, the total number of protons in somewhere in between 2 and 8.

My question is whether this is sufficient for ATP synthesis, if 2–3 hydrogen ions are required for each molecule of ATP synthesized.

My calculation is as follows:

pH = –log[H+]

The pH of the mitochondrial matrix is ca. 8. Thus, [H+] = 10-8 M (moles per litre).

If the mitochondrial volume is 0.2 μm3 this is equivalent to 2x10-10 μl = 2x10-16 litre

Using Avagadro’s number as 6x1023 it follows that:

Total number of protons in the matrix of a mitochondrion = 10-8 x 2x10-16 x 6x1023

= 1.2 (although other figures may give a value as high as 8).

If a pH of 6.8 is considered for the inter-membrane space along with a 0.1 fl volume, the number is 6.7 protons.

I found a paper where the question is adressed. First, the definition of pH at very low volumes is challenged, along with its measuring techniques. Second, it proposes novel mechanisms for proton availability in such situations. (http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0045832)

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    $\begingroup$ Can you please explain how you got to the numbers 2 and 8? For the moment, the question is unclear as we have no idea what calculation you've made and what you misunderstanding is. Also, the number of protons in a piece of matter is not the same thing as the number of free protons. $\endgroup$
    – Remi.b
    Aug 11 '18 at 21:52
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    $\begingroup$ You should edit your post to include that calculation. While you're at it, try rewording it so that it's a clear question, instead of just a statement. It's an interesting point, though $\endgroup$
    – De Novo
    Aug 11 '18 at 23:00
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    $\begingroup$ This is a chemistry question. Not really a biology question. I think Chemistry.SE would be a better fit for your question. $\endgroup$
    – Remi.b
    Aug 11 '18 at 23:05
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    $\begingroup$ @Remi.b I'm guessing the chemists would say it's a biology question, since it's about mitochondria. But, again, it needs to be a question before we can say for sure what it's about :) $\endgroup$
    – De Novo
    Aug 11 '18 at 23:12
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    $\begingroup$ I have edited the question so that it is clearer. It should also make the unexpressed assumptions — addressed in my answer — more obvious. If I have changed your meaning, do say so, but try to keep things clear. $\endgroup$
    – David
    Aug 13 '18 at 22:22
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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.

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  • $\begingroup$ Thank you for clarifying the question. Electrochemical gradient, as you mentioned it, relies on the CONCENTRATION gradient. The formula du=RTln(C1/C2)+zFdV, allows you to know if the transport is energetically favorable.and gives you a number for that energy change. The actual pumping however relies on the quantity, not on concentration. It is true that protons are pumped frome the inter-membrane space to the matrix, and that the concentration is higher there (about an order of magnitude). $\endgroup$ Aug 13 '18 at 16:11
  • $\begingroup$ My guess is that the volume of the intermembrane space will be smaller as well. But I will search the number to give you an actual quantity, to avoid subjective definitions, such as "small". $\endgroup$ Aug 13 '18 at 16:11
  • $\begingroup$ I´ve just find a paper that adresses this question, I leave it here in case anyone is interested:The Final Frontier of pH and the Undiscovered Country Beyond Wojciech Bal1 *, Ewa Kurowska1 , Wolfgang Maret2 1 Institute of Biochemistry and Biophysics, Polish Academy of Sciences, Warsaw, Poland, 2 King’s College London, Diabetes and Nutritional Sciences Division, London, United Kingdom $\endgroup$ Aug 13 '18 at 17:16
  • $\begingroup$ @RosaliaMoretta — Your enthusiasm for a numerical approach to biology is admirable, but it is perhaps expressed in a manner other than expected on this list. As a poster your first obligation is to express your problem clearly. Your question still has an (unhelpful) title that appears at odds with your question, which is still not clearly explained. I will edit it slightly, but you need to correct the focus on the matrix alone, and present information on the pH of the intermembrane space. If the paper you mention is relevant you should summarize it and provide a journal reference. $\endgroup$
    – David
    Aug 13 '18 at 21:46
  • $\begingroup$ @RosaliaMoretta I enjoyed your question, and this answer is excellent. Since you're new, let me point out what you should do when someone answers. Choose the best answer by clicking the little gray checkmark next to it (which turns it green). You should also upvote any useful answer when you have the upvote privilege. This answer should get both (an upvote and a checkmark). $\endgroup$
    – De Novo
    Aug 14 '18 at 16:58

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