Up to my knowledge, there are two different things: delta pH and delta Psi, corresponding to:
delta pH: difference between proton concentrations, but no charge, all protons have counterions.
delta Psi: electrical potential at the inner membrane, involving charge, like in a capacitor.
(Both seems to play a role in mitochondria: Having no charge,
but pH differences, can still drive the ATP synthetase)
In general, the protons do not need any other compound in their role as potential energy keeping agents,
not OH- or NAD+ or any redox carrier.
It is just protons being pumped outside the matrix, and just protons,
which's inflow to the matrix drives ATP synthetase.
There is an electrical potential driven ADP/ATP exchanger though, so
the ratio between ADP which is 3- and ATP which is 4-, may also play a role...
In conclusion, in both cases proton gradients represent order (instead of entropy),
meaning that the very mixing of matrix and intermembrane space leads to "liberation" of free enthalpy,
rising the temperature.
Hope I used the right words, hope it helps :-)
Best, Matthias
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