Determining the rotational mobility of a single molecule from a single image: a numerical study

Measurements of the orientational freedom with which a single molecule may rotate or 'wobble' about a fixed axis have provided researchers invaluable clues about the underlying behavior of a variety of biological systems. In this paper, we propose a measurement and data analysis procedure based on a widefield fluorescence microscope image for quantitatively distinguishing individual molecules that exhibit varying degrees of rotational mobility. Our proposed technique is especially applicable to cases in which the molecule undergoes rotational motions on a timescale much faster than the framerate of the camera used to record fluorescence images. Unlike currently available methods, sophisticated hardware for modulating the polarization of light illuminating the sample is not required. Additional polarization optics may be inserted in the microscope's imaging pathway to achieve superior measurement precision, but are not essential. We present a theoretical analysis, and benchmark our technique with numerical simulations using typical experimental parameters for single-molecule imaging.