Analysis of orientational dynamics of single fluorophore trajectories from three-angle polarization experiments

An algorithm of single fluorophore orientation reconstruction based on a recently proposed method [J. T. Fourkas, Opt. Lett. 26, 211 (2001)] is studied, which converts three measured intensities {I(0),I(45),I(90)} to the dipole orientation {I(T),theta,phi}. Fluctuations in the detected signals {deltaI(0),deltaI(45),deltaI(90)} caused by the shot noise results in different profiles in deltatheta and deltaphi, causing the originally equivalent coordinates (X,Y,Z) to separate into in-plane (X,Y) and out-of-plane (Z) components. The overall fluctuation in deltatheta turns out to be higher than deltaphi, and thus noise has a greater effect on the Z component of the signal than on the X and Y components. Therefore, care should be taken not to interpret differences in the in-plane and out-of-plane dynamics as being evidence of nonisotropic rotational motion. For some molecular orientations around Theta=pi2, the total signal intensity cannot be inverted directly to angular coordinates. An optimization method is proposed that calculates the corrected angular coordinates for the points in the trajectory. To test the effects of this recovery scheme, the covariance/correlation functions for reconstructed angular trajectories were calculated for the case of isotropic rotational diffusion. Rotational correlation functions of rank [script-l] were found to deviate from the ideal single exponential decay as a result of the noise. This effect becomes more significant for large [script-l] cases. The correlation functions were fitted to a stretch exponential to characterize their deviation from the true single exponential decay. Correlation functions of Z have larger deviations from the true correlation function due to the larger noise in the Z component. The trends and the distributions of stretched exponential parameters {tau(F)} and {beta(F)} fitted from trajectories of a given size T also exhibit the influences from noise. Again, large [script-l] cases show a greater effect from the noise which eliminates the benefit of calculating higher rank correlation functions because of the smaller time constants. Due to the errors in estimating the correlation functions, significant differences between correlation functions of different orders can result from the statistics rather than being an indication of a nondiffusive behavior.