To make it more clear, polarization (p) and anisotropy (r) are defined in terms of the intensities of light parallel I
par and perpendicular I
per to the excitation light's polarization:
[tex]p = \frac{I_{par} - I_{per}}{I_{par}+ I_{per}}[/tex]
[tex]r = \frac{I_{par} - I_{per}}{I_{par}+2I_{per}}[/tex]
These two values are related by:
[tex]r = \frac{2p}{3-p}[/tex]
The polarization value should be fairly straightforward to understand: as the sample goes from completely polarized (I
per = 0) to completely depolarized (I
per = I
par), p goes from 1 to 0.
Now, consider we have a mixture of two populations of molecules, 1 and 2. If the proportion of molecules are f
1 and f
2 and these molecules have polarizations p
1 and p
2, the overall polarization of the solution, p, is given by:
[tex]\left(\frac{1}{p} - \frac{1}{3}\right)^{-1} = f_1 \left(\frac{1}{p_1} - \frac{1}{3}\right)^{-1} + f_2 \left(\frac{1}{p_2} - \frac{1}{3}\right)^{-1}[/tex]
(for a derviation see
Weber 1952 Biochem J. 51:145)
This equation is obviously not so easy to work with. However, if we use the anisotropy measurement as defined above, the overall anisotropy of the mixture, r, is easy to calculate:
[tex]r = f_1r_1 + f_2r_2[/tex]
This is the main reason for why we have that strange definition for anisotropy.
In case you find it useful, here is a good practical guide for analyzing FP data:
http://labs.fhcrc.org/hahn/Methods/biochem_meth/beacon_fluorescence_guide.pdf