A recently proposed chemomechanical group transfer theory of rotary biomolecular motors is applied to treat single-molecule controlled rotation experiments. In these experiments, singlemolecule fluorescence is used to measure the binding and release rate constants of nucleotides by monitoring the occupancy of binding sites. It is shown how missed events of nucleotide binding and release in these experiments can be corrected using theory, with F 1 -ATP synthase as an example. The missed events are significant when the reverse rate is very fast. Using the theory the actual rate constants in the controlled rotation experiments and the corrections are predicted from independent data, including other single-molecule rotation and ensemble biochemical experiments. The effective torsional elastic constant is found to depend on the binding/releasing nucleotide, and it is smaller for ADP than for ATP. There is a good agreement, with no adjustable parameters, between the theoretical and experimental results of controlled rotation experiments and stalling experiments, for the range of angles where the data overlap. This agreement is perhaps all the more surprising because it occurs even though the binding and release of fluorescent nucleotides is monitored at single-site occupancy concentrations, whereas the stalling and free rotation experiments have multiple-site occupancy. S ingle-molecule manipulation techniques, including stalling and controlled rotation methods or "pulling" force microscopies, have been used to augment imaging experiments in biomolecular motors (1-4). In F 1 -ATPase, for example, beyond observing the kinetics of stepping rotation resolved into ∼80°a nd ∼40°substeps (5-7), the manipulation of the rotor shaft by magnetic tweezers recently opened up the possibility of directly probing the dynamical response of the system to externally constraining the rotor angle θ. In tandem with the experimental tools of X-ray crystallography (8) and ensemble biochemical methods (9), these experiments provide added insight into the processes in chemomechanical energy transduction (7, 10-13). The kinetic pathway along which concerted substeps occur in free rotation has been established (14), whereby binding of solution ATP to an empty subunit is initiated at θ = 0°, and the release of hydrolyzed ADP from the clockwise neighboring subunit occurs simultaneously as the θ completes the ∼80°ro-tation step (Fig. 1). Using the detailed knowledge of individual substeps, stalling (3, 15) and controlled rotation (3) experiments provide an estimate of the rate constants of nucleotide binding and other processes as a function of θ. In particular, binding and release of ATP and analogs can be externally controlled to occur at angles other than 0°.In the controlled rotation experiments (1, 4) we consider here, a slow constant angular velocity rotation of the shaft was produced by magnetic tweezers. A magnetic bead was attached to the rotor shaft protruding from the stator ring with a constant magnetic dipole moment pointing in the pl...