On the rotational brownian motion of a bacterial idle motor. I. Theory of time-dependent fluorescence depolarization.

A rotational diffusion equation and its Green's function for a spheroidal particle such as a bacterial body, to which an actively driving but idle motor is attached, are presented. As an application of the theory, general expressions for the time-dependent fluorescence depolarization caused by such a particle have been obtained. Measurement of such depolarizalion should provide a useful tool for determination of the rate of revolution of the rotating motor attached to cell bodies such as bacteria under various solution conditions, if a fluorescent (or phosphorescent) label is attached to the motor shaft.