ATP synthase converts the electrochemical potential at the inner mitochondrial membrane into chemical energy, producing the ATP that powers the cell. Using electron cryo-tomography we show that the ATP synthase of mammalian mitochondria is arranged in long approximately 1-microm rows of dimeric supercomplexes, located at the apex of cristae membranes. The dimer ribbons enforce a strong local curvature on the membrane with a 17-nm outer radius. Calculations of the electrostatic field strength indicate a significant increase in charge density, and thus in the local pH gradient of approximately 0.5 units in regions of high membrane curvature. We conclude that the mitochondrial cristae act as proton traps, and that the proton sink of the ATP synthase at the apex of the compartment favours effective ATP synthesis under proton-limited conditions. We propose that the mitochondrial ATP synthase organises itself into dimer ribbons to optimise its own performance.