Converting conformational changes to electrostatic energy in molecular motors: The energetics of ATP synthase

F-1-ATPase is the catalytic component of the ATP synthase molecular machine responsible for most of the uphill synthesis of ATP in living systems. The enormous advances in biochemical and structural studies of this machine provide an opportunity for detailed understanding of the nature of its rotary mechanism. However, further quantitative progress in this direction requires development of reliable ways of translating the observed structural changes to the corresponding energies. This requirement is particularly challenging because we are dealing with a large system that couples major structural changes with a chemical process. The present work provides such a structure-function correlation by using the linear response approximation to describe the rotary mechanism. This approach allows one to evaluate the energy of transitions between different conformational states by considering only the changes in the corresponding electrostatic energies of the ligands. The relevant energetics are also obtained by calculating the linear response approximation-based free energies of transferring the ligands from water to the different sites of F-1-ATPase in their different conformational states. We also use the empirical valence bond approach to evaluate the actual free-energy profile for the ATP synthesis in the different conformational states of the system. Integrating the information from the different approaches provides a semiquantitative structure-function correlation for F-1-ATPase. It is found that the conformational changes are converted to changes in the electrostatic interaction between the protein and its ligands, which drives the ATP synthesis.