As stated already, there is no DIRECT connection between the elcetron transport process and the ATP synthesis process. Rather, these are coupled indirectly through the generation of a H+ gradient across the inner mitchondrial membrane.
The electron transfer from NADH to CoQ is inextricably linked to H+ transport across the membrane. One does not happen without the other. We can calculate the ΔG°' for the this redox reaction:
|Standard reduction potentials for the two "half reactions"|
|1||NAD+ + 2e-||→||NADH||-0.34V|
|2||CoQ + 2e-||→||CoQH2||0.04V|
invert (1) change it's sign and then add
|NADH||→||NAD+ + 2e-||0.34V|
|CoQ + 2e-||→||CoQH2||0.04V|
|NADH + CoQ → NAD+ + CoQH2||ΔE°' = 0.38V|
To put this in terms of ΔG°':
ΔG°' = -nF(ΔE°')
ΔG°'= -2 * 96.5 * 0.38
ΔG°'= -73 kJ/Mole
The STANDARD Free energy of electron transfer through complex I = -73 kJ/M. A rather large favorable energy toward reducing CoQ to CoQH2. This is an energy obtained under standard conditions. This means, of course that as conditions change so can the OBSERVED free energy. The observed free energy can changes because electron transfer is linked to H+ gradient formation. As the gradient builds it places "pressure" on the standard free energy.
The energy of the proton gradient, too, can be written in terms of a ΔG'.
ΔG' = RT(ΔpH + F*ΔΨ)
so for the system (electron transfer AND H+ gradient)
ΔG = ΔG°'ET + ΔG'H+g
The proton gradient free energy can be any value up to but CANNOT exceed the free energy of electron transfer!
If you blow a tire on your car... you open the trunk and you get out a jack to raise the car to change the tire.... The jack has a load capacity (amount it can lift) which is similar to the free energy of electron transfer. The chances are good that you can raise your car sufficently high to change the tire. The mass of your car is analagous to the free energy of the proton gradient. If you tried to raise a vehicle that is heavier than the load capacity (an 18 wheel semi-truck for instance) there is a VERY HIGH probability that the truck will not be raised, but rather the jack will cease to function instead.
Complex V will use the free energy stored in the proton gradient to synthesize ATP from ADP and phosphate. ... I hear you... Isn't this the reverse of a hydrolysis reaction??? "But you told us that the ΔG°' of ALL hydrolysis reactions favors the products (ADP and Phosphate). and in water is for all practical purposes not reversible
Yes that is true. In this case, however, there are TWO things to consider. The free energy of the hydrolysis reaction AND the free energy of the proton gradient. In complex V (so long as the membrane is intact) these are linked. Complex V provides the "only" way for protons to back down the gradient AND the only way to go through complex V is to rotate the γ subunit (and thus do work to synthesize ATP). Furthermore, the ATP synthesis actually occurs in an anzyme active site that excludes water to facilitate the condensation.
Of course the energy of the H+ gradient and the energy of ATP synthesis are also linked (so ling as the inner mitochiondrial membrane is in tact). The ΔG' of the H+ gradient must be sufficiently high to overcome the energy of ATP hydrolysis.
ΔGtotal = ΔGH+g + ΔGATP synthesis < 0 (must be negative)
The actual at any one time ΔGH+g will vary substantially depending on the physiological state and current energy demands. There will usually be just enough proton gradient to ensure that the ΔGtotal is near zero but negative.
So let's put that jack to use...SAY... you found a walnut and you are hungry. It takes a lot of energy to crack a walnut. So what do you do? You use the jack to raise your car (or any weight up to the load capacity of the jack). Then you can place the walnut under the tire and let the car back down again to crack the walnut (OK so this is a ridiculous scenario).... But the analogies are:
In order to talk about free energies, the reactions must be reversible. This is the case here as well. In fact The whole system can be reversed. Experimentally one can have sufficiently high [ATP] (and low [ADP]) that The H+ gradient can be built up (by reversing the complex V reaction) to the point that (as an example) CoQH2 can reduce NAD+ via complex I.