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What's the source of hydrogen in the reduction of oxygen to water in metabolism?

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Is this implying that half the hydrogen comes from NADH and the other half from lone protons?

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I don't think they're implying that; they've just combined the two half reactions. NADH doesn't interact directly with oxygen (it is oxidized at complex I). I think that the protons used in the conversion of oxygen to water are, ultimately, free in solution. – canadianer Jun 18 '14 at 15:27

The equation you've shown is similar to other cellular respiration equations that I've seen, in that, it is trying to simplify a pretty complex process.

My guess is that you're doing first year cell biology like I am, so you probably know that there is a difference between the pH of the mitochondrial matrix (7.8 - making it alkaline) and the inter membrane space (roughly that of the cytosol - usually about 7). The lower the pH of a solution, the greater the concentration of H+. My point is that the solutions on either side of the inner mitochondrial membrane both have a concentration of H+.

So even though, when NADH is oxidised, it loses a H+ to solution, thereby contributing to the pH of the mitochondrial matrix, what is the likelihood that that particular H+ will be the H+ that is part of the molecule that takes the electrons at the end of the electron transport chain? I think low.

Indirectly, NADH does contribute H+ to the overall pH of the mitochondrial matrix but it doesn't directly give the H+ to "half an oxygen gas molecule".

Check the video below which is from the publisher of the textbook my course uses.

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So the proton source is water? Also I'm not doing first-year bio. If I showed you the rest of the slide you'd be scared ;). – Dissenter Jun 19 '14 at 0:10
So what are you doing? :) Proton source is not water its the solution in the mitochondrial matrix. – melburnianlaura Jun 19 '14 at 0:27
What do you mean the proton source is the solution? – Dissenter Jun 19 '14 at 0:32
I'm not sure I can explain it any better than I did in my first answer. Sorry I can't help. – melburnianlaura Jun 19 '14 at 0:38
It's okay; the problem is that the proton is not found alone in water; it's hydrated. If you are suggesting that the proton source is in the solution, then the most likely source is water, and not hydronium ion or any hydrated derivatives of the protons because heteroytic bond clevage is less costly when it only has to be performed twice - i.e. on water - rather than thrice - i.e. with hydronium ion. – Dissenter Jun 19 '14 at 0:41

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