  We have developed a novel method to evaluate the potential profile of a
molecular motor at each chemical state from only the probe's trajectory and
applied it to a rotary molecular motor F$_1$-ATPase. By using this method, we
could also obtain the information regarding the mechanochemical coupling and
energetics. We demonstrate that the position-dependent transition of the
chemical states is the key feature for the highly efficient free-energy
transduction by F$_1$-ATPase.
