In aerobic eukaryotic respiration, oxidative phosphorylation couples oxidation of NADH and FADH$_2$ to ATP synthesis across the inner mitochondrial membrane.

It combines two machines already conceptually distinct:

1. a respiratory electron-transport chain builds a proton-motive force;
2. ATP synthase uses proton return to drive ATP formation.

Electron flow through the mitochondrial chain

NADH donates electrons to Complex I. Electrons derived from FADH$_2$ can enter through Complex II. Both routes feed ubiquinone (Q), a small lipid-soluble redox carrier that moves within the inner membrane.

Q transfers electrons to Complex III, which passes them to cytochrome c, a small mobile protein electron carrier on the outer face of the inner membrane. Cytochrome c then transfers electrons to Complex IV.

A simplified path is

NADH → I ┐
          ├→ Q → III → cytochrome c → IV → O2
FADH2 → II┘

Complex IV transfers electrons ultimately to molecular oxygen, reducing it to water.

Thus oxygen is consumed at the end of the chain; glycolysis and the citric-acid cycle do not themselves use O$_2$ directly.

Electron transfer drives proton pumping

Complexes I, III and IV couple favorable electron transfer to movement of protons from the mitochondrial matrix to the intermembrane space. Complex II transfers electrons into the chain but does not pump protons in the same way.

The inner mitochondrial membrane therefore develops a proton-motive force with higher proton electrochemical potential on the intermembrane-space side and lower proton electrochemical potential on the matrix side.

ATP synthase closes the energy-conversion loop

Protons return toward the matrix through ATP synthase. Their downhill electrochemical movement drives

$$\mathrm{ADP+P_i\rightarrow ATP+H_2O}.$$

The overall architecture is

NADH/FADH2 oxidation
        ↓
electron transport to O2
        ↓
proton pumping
        ↓
proton-motive force
        ↓
ATP synthase
        ↓
ATP

The ETC therefore does not phosphorylate ADP directly, and ATP synthase does not oxidize NADH directly. The proton gradient couples the two subsystems.

NADH and FADH2 do not yield identical ATP amounts

Electrons entering from NADH pass through more proton-pumping machinery than electrons entering through Complex II from FADH$_2$. Consequently, NADH generally supports more ATP synthesis per electron pair.

Frequently used approximate mitochondrial values are about

$$2.5\ \mathrm{ATP/NADH}$$

and

$$1.5\ \mathrm{ATP/FADH_2},$$

but these are not exact universal stoichiometric constants. Effective ATP yield depends on proton/ATP coupling, metabolite transport, membrane leak and how reducing equivalents generated outside the mitochondrial matrix are transferred into the respiratory system.

Oxidative phosphorylation is therefore a chemiosmotic coupling process: redox free energy is first converted into a transmembrane proton electrochemical gradient and only then into ATP.