Method to extract multiple states in F1-ATPase rotation experiments from jump distributions

A method is proposed for analyzing fast (10 mu s) single-molecule rotation trajectories in F-1 adenosinetriphosphatase (F-1-ATPase). This method is based on the distribution of jumps in the rotation angle that occur in the transitions during the steps between subsequent catalytic dwells. The method is complementary to the stalling technique devised by H. Noji et al. [Biophys. Rev. 9, 103-118, 2017], and can reveal multiple states not directly detectable as steps. A bimodal distribution of jumps is observed at certain angles, due to the system being in either of 2 states at the same rotation angle. In this method, a multistate theory is used that takes into account a viscoelastic fluctuation of the imaging probe. Using an established sequence of 3 specific states, a theoretical profile of angular jumps is predicted, without adjustable parameters, that agrees with experiment for most of the angular range. Agreement can be achieved at all angles by assuming a fourth state with an similar to 10 mu s lifetime and a dwell angle about 40 degrees after the adenosine 5'-triphosphate (ATP) binding dwell. The latter result suggests that the ATP binding in one beta subunit and the adenosine 5'-diphosphate (ADP) release from another beta subunit occur via a transient whose lifetime is similar to 10 mu s and is about 6 orders of magnitude smaller than the lifetime for ADP release from a singly occupied F-1-ATPase. An internal consistency test is given by comparing 2 independent ways of obtaining the relaxation time of the probe. They agree and are similar to 15 mu s.