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.
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