F0-F1 coupling and symmetry mismatch in ATP synthase resolved in every F0 rotation step

The F0F1 ATP synthase, essential for cellular energy production, is composed of the F0 and F1 rotary motors. While both F0 and F1 have pseudo-symmetric structures, their symmetries do not match. How the symmetry mismatch is solved remains elusive due to missing intermediate structures of rotational steps. Here, for ATP synthases with 3- and 10-fold symmetries in F1 and F0, respectively, we uncovered the mechanical couplings between F0 and F1 at every 36{degrees} rotation step via molecular dynamics simulations and comparison of cryo-electron microscopy structures from three species. We found that the frustration is shared by several elements. The F1 stator partially rotates relative to the F0 stator via elastic distortion of the b-subunits. The rotor can be distorted. The c-ring rotary angles can be deviated from symmetric ones. Additionally, the F1 motor may take non-canonical structures relieving stronger frustration. Together, we provide comprehensive understanding to solve the symmetry mismatch.