Fluorescence depolarization Perrin equation

Fluorescence polarization cannot attain the +1 theoretical limits for maximum beam polarization owing to the nature of the absorption and emission processes, which usually correspond to electric dipole transitions. Although the excitation with linearly polarized radiation favours certain transition dipole orientations (hence certain fluorophore orientations, and the so-called photoselection process occurs), a fairly broad angular distribution is still obtained, the same happening afterwards with the angular distribution of the radiation of an electric dipole. The result being that, in the absence of fluorophore rotation and other depolarization processes, the polarization obeys the Lev shin-Perrin equation,... 

Researches on theoretical topics have not been reported very extensively. A few papers are mentioned here and some others at appropriate points later in the article. Weber has re-examined the famous Perrin equation for quantifying the rotational depolarization of fluorescence. The arguments presented in the paper are applied to the temperature dependence of the local motions of tyrosine and tryptophan residues observed in proteins. 

If the only significant process for depolarization is rotational relaxation, then the fluorescence anisotropy, for a single molecule or fluorophore, may be given by a form of the Perrin equation ... 

The relationships derived with the Perrin equation apply only to spherical fluorophores, which generally does not include fluorescent dyes [9]. If a fluorescent molecule has a planar structure, serious deviations from the Perrin equation can occur. It is therefore essential to determine which molecular motions result in the observed depolarizations and how the latter relate to the structure of the fluorescent probe. The rate of rotation of the fluorophore is an average of the inplane (Vip) and out-of-plane (Vop) rates of rotation [9]. The in-plane rotation is about an axis normal to the ring plane, whereas the out-of-plane rotation is about an axis contained in the ring plane at right angles to the absorption oscillator. There are three cases of interest in relation to the Perrin equation ... 

If the medium is highly ordered or anisotropic, the Perrin equation does not hold and microviscosity can be used only qualitatively. In this case, a fluorophore is restricted to certain motions that will occur to different extents in different dimensions. An example of such a phenomenon would be a fluorescent molecule that would align itself along the fatty acid chains of phospholipids in the phospholipid bilayer of a liposome. For fluorophores in an anisotropic medium, the time-resolved fluorescence anisotropy does not fall to zero (see Fig. 4, curve a), that is, the depolarizing rotations of the fluorophore will not attain an isotropic distribution at infinite time. The anisotropy will decay to an infinite-time anisotropy (r ) rather than to zero and will have the form... 

Fluorescence polarization is frequently expressed in terms of anisotropy (r) due to the comparatively simple equations describing rotational depolarization. The dependence of fluorescence anisotropy on molecular rotation can be described quantitatively with the well-known Perrin equation. 

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