3 H+ are required to synthesis one ATP. Depending on the organism, there can be from 10 to 14 c-subunits in the c-ring of ATP synthase. For practicality/consistency's sake, let's assume 10.
Every c-subunit is protonated (from the cytoplasmic side of the mitochondrion) and rotated almost 360 degrees within the lipid membrane before it is ultimately deprotonated, which releases a proton into the matrix. Thus, since the c-ring is 10 subunits big (in this case), 10 protons are being introduced to the matrix every 360 degree turn, which mean that1 proton = a 36 degree turn.
These protons allow for the gamma-subunit to be turned at the inside of the hexamer (of 3 alpha-subunits and 3 catalytic beta-subunits) found below the rotor. The b-subunits are thus located 120 degrees apart.Every 120 degrees precisely, that beta-subunit changes shape,dictated by the rotation of the gamma-subunit, and enters one of the three states that ultimately catalyze one ATP from ADP and inorganic phosphate (sinceonly one of the three states actually forms ATP). Since the gamma-subunit catalyses the formation of 1 ATP every 120 degrees, afull 360 degree rotation would yield 3 ATPs.
This is where things go awry in my mind. Within 360 degrees, 10 protons and 3 ATPs are made. Thus, that makes (10/3) protons per ATP, or 3.33 protons/ATP. When the gamma-subunit receives a proton, it rotates 36 degrees, butATP formation only happens at precisely 120 degrees, and the only common interval between 36 and 120 is 360 (when 3 as opposed to 1 ATPs are made)!