The orientational freedom of molecular probes. The orientation factor in intramolecular energy transfer

The measurement of the efficiency of Förster long-range resonance energy transfer between donor (D) and acceptor (A) luminophores attached to the same macromolecular substrate can be used to estimate the D-A separation, R. If the D and A transition dipoles sample all orientations with respect to the substrate (the isotropic condition) in a time short compared with the transfer time (the dynamic averaging condition), the average orientation factor less than K2 greater than is 2/3. If the isotropic condition is not satisfied but the dynamic averaging condition is, upper and lower bounds for less than K2 greater than, and thus R, may be obtained from observed D and A depolarizations, and these limits may be further narrowed if the transfer depolarization is also known. This paper offers experimental protocols for obtaining this reorientational information and presents contour plots of less than K2 greater than min and less than K2 greater than max as functions of generally observable depolarizations. This permits an uncertainty to be assigned to the determined value of R. The details of the D and A reoreintational process need not be known, but the orientational distributions are assumed to have at least approximate axial symmetry with respect to a stationary substrate. Average depolarization factors are derived for various orientational distribution functions that demonstrate the effects of various mechanisms for reorientation of the luminophores. It is shown that in general the static averaging regime does not lend itself to determinations of R.