 Solution

ATP synthase couples a membrane-embedded rotary motor to a soluble catalytic head. Its membrane sector contains a rotating ring of c subunits and a stationary a subunit providing offset proton-access pathways. Its catalytic sector contains an ${\alpha }_3{\beta }_3$ head with catalytic sites primarily on the $\beta$ subunits, a central rotating shaft, and a peripheral stator that prevents the head simply co-rotating.

A proton-motive force, combining a membrane potential and a proton chemical potential difference, drives directional proton passage and ring rotation. Rotation of the central shaft changes the conformations and binding affinities of successive catalytic sites, allowing ADP and inorganic phosphate to bind, form ATP, and release it in a coordinated cycle. The ATP synthase rotary mechanism therefore couples ion transport, torque, and chemical work rather than requiring a proton to react directly at every catalytic site.

The motor is reversible: sufficiently favorable ATP hydrolysis can drive proton pumping against its electrochemical potential gradient. In mitochondria, the respiratory chain establishes the gradient used for oxidative ATP production; analogous coupling operates in bacterial membranes and in chloroplast photophosphorylation. The number of protons per revolution depends on the c-ring stoichiometry, whereas a full catalytic rotation normally produces three ATP molecules. It is therefore inappropriate to assign one universal integer proton-to-ATP ratio to all organisms. Transport and leakage can increase the whole-cell energetic cost beyond the motor's ideal ratio.