Information content of fluorescence polarization and anisotropy

The equality of information content in fluorescence polarization and emission anisotropy is a common assumption and the two quantities are used according to practical considerations. However, an information-theoretic analysis presented here reveals that their information content is substantially different. A scaling relation exists between polarization and anisotropy, and normalization allows their direct comparison. Various measures of information such as the absolute, relative, differential, and potential entropies all appear larger for anisotropy over part or all of its normalized overlap with the polarization function. The larger information content coincides with the signal range where the emitted light is polarized mostly in the parallel direction. Polarization takes on larger absolute entropy only when the emission is about perpendicular to the incident light and when the differential entropy is considered over the entire physical domain. The additional information locally afforded by polarization appears to be related to its larger signal range whereas the extra information in anisotropy may be attributed to a second perpendicular emission plane in its definition, which is oriented along the axis of propagation of light and takes the contribution of all degrees of rotational freedom into account. Thus anisotropy may be considered as a more accurate and more informative representation of the underlying physical phenomena. Some practical aspects relevant to studies of protein-ligand interactions are also discussed.