Using angle-dependent velocity to detect fast states in rotary motors

A data-driven modeling method of the molecular machine F1-ATPase is presented. On the one hand, our theory is built to treat a variety of different type of single-molecule and ensemble experiments used to probe the F1-ATPase. On the other hand, the model is applied to different F-ATPase species, like the Thermophilic Bacillus and Paracoccus Denitrificans, since their α₃β₃ ring structure is highly conserved and hence the mechano-chemistry is presumably similar, even though their stepping kinetics vary. An elastic molecular transfer theory provides a framework for a multi-state model which includes the probe used in single-molecule imaging and magnetic manipulation. When applied to unconstrained rotation of single F1-ATPase, the model is able to enhance the resolution of the single-molecule imaging. In the rotation of the F1-ATPase, the use of the angle-dependent velocity provides a tool for the detection of fast states of microsecond life time which are hidden by the fluctuations of the imaging probe. Ultimately, the motivation is to gain biological/physiological insight: our model-based method was used to predict the life time of the intermediate during the correlated behaviour in F-ATPase. The release of nucleotides would be a bottleneck process, but the binding of another nucleotide to another site acts to accelerate the release by 5-6 orders of magnitude. The correlated behavior is captured in our model via the angle-dependent rate constants of the individual substeps. We propose that the allosteric mechanism is universally found in all F-ATPase species and may be present in other members of the AAA+ ring proteins.