Interface-packing analysis of F1-ATPase using integral equation theory and manifold learning

It has been shown that the translational entropy of water plays a key role in biological processes such as protein folding and ligand binding. Under the physiological condition, tightly packed protein conformations like native structures are achieved so that the translational entropy of water is maximized. In this study, we investigate the rotation mechanism of a rotary protein motor, F₁-ATPase, by analyzing the packing at the interfaces between the subunits. The packing at the interface between a subunit pair is analyzed using the change in the solvent entropy upon forming subunit pair, $∆S$. It is found that as the γ subunit rotates, the $∆S$ value of a α-β subunit pair decrease because the interface packing becomes loose. However, because the interface packing of another α-β subunit pair becomes tighter upon the rotation, $∆S$ of this α-β subunit pair increases, leading to a compensation of the decrease in $∆S$. Such compensation would be necessary to maximize the solvent entropy of F₁-ATPase. In this study, packing at the interfaces between the subunits is also analyzed using a manifold-learning technique, and it is suggested a possibility that a qualitative estimation of the $∆S$ values of some α-β subunit pairs can be predicted using a manifold-learning technique.