Dynamic depolarization of interacting fluorophores. Effect of internal rotation and energy transfer

Effects of internal rotation on the fluorescence decay functions and time-dependent anisotropies of fluorophores bound to a spherical macromolecule are theoretically investigated in the presence of the intramolecular energy transfer interaction by solving relevant rotational diffusion equations. The model system examined is one in which the energy donor is internally rotating around an axis fixed at the macromolecule and the acceptor is fixed at a definite position in the macromolecule. The effect of internal rotation in the system is described by Hill's functions with two cosine terms. The fluorescence decay function and anisotropy decay are functions of the ratio of energy-transfer probability averaged over the internal rotation angle to the rotary diffusion co-efficient. When the internal rotation is much faster than energy transfer, the decay function of the donor is predicted to be a single exponential, and the anisotropy decay is essentially described by the expression derived by Gotlieb and Wahl (1963. J. Chim. Phys. 60:849-856). However, deviation from it becomes pronounced as the rotation becomes slower. Methods of numerical analysis are presented for decay function and anisotropy decay, as well as relative quantum yield and polarization anisotropy under steady-state excitation, and examined for a simplified system under the variation of the diffusion coefficient.