= Solution
The central prediction of the <ATP synthase> <ATP synthase rotary mechanism> is relative motion of the central shaft and catalytic head, not simply a change in bulk <ATP> <concentration>. In the foundational single-molecule experiment, a visible marker coupled to the central gamma shaft reported its angular position relative to the immobilized catalytic head. Sustained directional rotations during <ATP hydrolysis> demonstrated rotary motion directly. The catalytic head contains three beta sites within an alpha-three beta-three assembly; their changing nucleotide affinities motivate the <binding-change mechanism>. <Direct observation of the rotation of F1-ATPase by Hiroyuki Noji and others>[1997 primary study, direct shaft-marker rotation]{ref}
An angular trajectory gives more information than an average rotational speed. At low <ATP>, pauses before roughly 120-degree advances become longer as <ATP> falls, supporting an ATP-binding-limited wait. Reducing marker drag and improving temporal resolution reveals substeps and ATP-independent catalytic dwells. The early high-speed study resolved approximately 90-degree and 30-degree substeps, with more than one slow event during the catalytic dwell. Numerical angles vary with preparation and operational definition, so these observations should not be imposed as exact universal geometric increments.<Resolution of distinct rotational substeps by submillisecond kinetic analysis of F1-ATPase by Ryohei Yasuda and others>[2001 primary abstract and Figures 4–8]{ref}
The dwell-time model in <2/b> tests serial <chemical kinetics>; the angle histogram tests preferred positions. Comparing probe loads checks whether viscous drag limits the observed speed. Measuring <torque> and <angular displacement> estimates mechanical <work>, while a separate <hydrolysis> readout tests chemical coupling. With one <ATP> per 120-degree step, the chemical budget per revolution is three <ATP>, but rotation alone does not count every chemical event or establish unity efficiency.
A probe can perturb the very process it reports, and inhibited pauses or unresolved reversals can bias averages. Isolated F1 observed during <hydrolysis> also does not demonstrate proton-driven <ATP> synthesis by intact membrane F0F1. Testing reverse synthesis requires evidence for chemical <gene expression> under the corresponding driving conditions; a rotation movie by itself is insufficient. These distinctions connect the single-molecule motion to the free-energy balance without overinterpreting it.
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