Energetics of association of two ATP synthase dimers driven by the membrane. (A) Deformation of the membrane induced by two ATP synthase dimers for different values of the dimer-to-dimer distance. The deformation is quantified by the position-dependent curvature of the membrane (Materials and methods) along the two directions defining the membrane plane. (B) Potential of mean force as a function of the distance between the two dimers, calculated using umbrella-sampling molecular dynamics simulations, totaling 15 μs (Materials and methods). The sampling error is indicated with a gray band along the free-energy profile. (C) Distribution of dimer-to-dimer distances deduced from analysis of published cryo-EM tomograms of fragmented mitochondrial cristae. Inset figure adapted from Davies et al. (2012).