Abstract
ATP synthases are proteins that catalyse the formation of ATP through the rotatory movement of their membrane-spanning subunit. In mitochondria, ATP synthases are found to arrange as dimers at the high-curved edges of cristae. Here, a direct link is explored between the rotatory movement of ATP synthases and their preference for curved membranes. An active curvature sorting of ATP synthases in lipid nanotubes pulled from giant vesicles is found. Coarse-grained simulations confirm the curvature-seeking behaviour of rotating ATP synthases, promoting reversible and frequent protein-protein contacts. The formation of transient protein dimers relies on the membrane-mediated attractive interaction of the order of 1.5 k(B) T produced by a hydrophobic mismatch upon protein rotation. Transient dimers are sustained by a conic-like arrangement characterized by a wedge angle of θ ≈ 50°, producing a dynamic coupling between protein shape and membrane curvature. The results suggest a new role of the rotational movement of ATP synthases for their dynamic self-assembly in biological membranes.