A comparison of the innate flexibilities of six chains in F₁-ATPase with identical secondary and tertiary folds; 3 active enzymes and 3 structural proteins

The $\alpha$ and $\beta$ subunits comprising the hexameric assembly of F1-ATPase share a high degree of structural identity, though low primary identity. Each subunit binds nucleotide in similar pockets, yet only $\beta$ subunits are catalytically active. Why? We re-examine their internal symmetry axes and observe interesting differences. Dividing each chain into an N-terminal head region, a C-terminal foot region, and a central torso, we observe (1) that while the foot and head regions in all chains obtain high and similar mobility, the torsos obtain different mobility profiles, with the $\beta$ subunits exhibiting a higher motility compared to the $\alpha$ subunits, a trend supported by the crystallographic B-factors. The $\beta$ subunits have greater torso mobility by having fewer distributed, nonlocal packing interactions providing a spacious and soft connectivity, and offsetting the resultant softness with local stiffness elements, including an additional $\beta$ sheet. (2) A loop near the nucleotide binding-domain of the $\beta$ subunits, absent in the $\alpha$ subunits, swings to create a large variation in the occlusion of the nucleotide binding region. (3) A combination of the softest three eigenmodes significantly reduces the RMSD between the open and closed conformations of the $\beta$ subnits. (4) Comparisons of computed and observed crystallographic B-factors suggest a suppression of a particular symmetry axis in an $\alpha$ subunit. (5) Unexpectedly, the soft intra-monomer oscillations pertain to distortions that do not create inter-monomer steric clashes in the assembly, suggesting that structural optimization of the assembly evolved at all levels of complexity.