Stepped versus continuous rotatory motors at the molecular scale

Nature invented molecular rotatory devices such as the flagellar motor and ATP synthase. Photoselection techniques have been frequently used to detect the rotational random walk of proteins but only rarely for the rotational drift of subunits in proteins. Pertinent theories predict an oscillatory behavior of the polarization anisotropy, r, for unidirectional rotational drift, as opposed to a monotonic relaxation of r for bidirectional random walk. The underlying assumption of an angular continuum is questionable for intersubunit rotation in proteins. We developed a theory for stepped rotatory devices. It predicts the damped oscillation of r under unidirectional drift. Damping increases with decreasing number of steps. For only three steps a quasi-monotonic relaxation of r is predicted for both random walk and drift. In photoselection experiments with active F-ATPase we observed the relaxation of r when a spectroscopic probe was attached to the central γ-subunit. This behavior is compatible with the expectation for a three-stepped rotatory device.