Oxidative phosphorylation

Oxidative phosphorylation couples respiratory redox conversion to ATP formation through chemiosmosis. ATP synthase uses inward proton flow to join ADP and inorganic phosphate.^[ref]

The intermediate electrochemical gradient explains why respiratory uncoupling can preserve oxygen consumption while reducing ATP formation. An electron ledger alone cannot determine the recovery of useful free energy.

Proton return across a coupling membrane that is not coupled to productive ATP synthase turnover. Its absolute rate, fraction of total proton return and flux control coefficient are different quantities.

The amount of ATP formed per oxygen atom reduced during coupled respiration. Oxygen molecules contain two atoms, so the ATP:${\mathrm{O}}_2$ ratio is twice the conventional phosphorylation-to-oxidation ratio for the same measurements.

Chemiosmosis couples transmembrane ion movement down an electrochemical gradient to a chemical transformation. For mitochondrial ATP synthesis, protons return from the intermembrane space to the mitochondrial matrix through ATP synthase.^[ref]

An original thermodynamic example separates the electrical and chemical contributions. At fixed temperature $T$, use ideal dilute thermodynamic activities $a$ and the electric potential $\psi$ on each side. The molar electrochemical potential difference for inward transfer of a singly charged proton isHere $R$ is the molar gas constant, $F$ the Faraday constant, and $\ln$ the natural logarithm. The sign convention is destination minus origin: a negative difference makes inward transfer favourable. Both lower proton activity and a more negative electric potential inside favour inward movement.

Stipulate $T=300\mathrm{K}$, $a_{\mathrm{matrix}}/a_{\mathrm{outside}}=0.1$, ${\psi }_{\mathrm{matrix}}-{\psi }_{\mathrm{outside}}=-0.12\mathrm{V}$, $R=8.314\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$ and $F=96485\mathrm{C}\mathrm{mo}{\mathrm{l}}^{-1}$. These illustrative inputs give approximately $-5.743$ and $-11.578\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ for the chemical and electrical terms, hence $-17.321\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ per transferred proton. For a hypothetical device coupling three inward protons per ATP to an ATP-formation cost of $45\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$,The sign follows by adding changes in the state function Gibbs free energy. It establishes thermodynamic feasibility for this chosen model, not its reaction rate. Three is a stipulated coupling count, not a universal ATP synthase stoichiometry; transport costs and leaks can also consume the available free energy.

Downhill ion transport through ATP synthase can drive ATP formation from its substrates. The electrochemical free-energy drop per transported ion combines the membrane potential and concentration term. Reverse coupling can use ATP hydrolysis to maintain the ion gradient.

Respiratory uncoupling allows proton return to bypass ATP synthase, dissipating the electrochemical gradient. Electron transport and oxygen consumption can continue while less ATP is recovered.^[ref]

In the thermodynamic example under chemiosmosis, reducing both the activity ratio to one and the electric potential difference to zero removes the driving contribution. The hypothetical ATP-forming conversion then costs $+45\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$. Continued donor oxidation would not restore coupling unless it rebuilt a usable electrochemical gradient. This distinction makes respiratory uncoupling useful conceptually: abundant oxygen consumption can coexist with poor recovery of ATP.