Criteria for the rapid diffusion limit of fluorescence energy transfer

Excitation energy transfer in a system where the spatial relationship between the donor and acceptor is not fixed generally leads to a nonexponential decay of donor fluorescence. A single-exponential decay, however, is expected as a limiting form when the diffusion of the donors and/or acceptors is sufficiently rapid. The exponential character at the rapid diffusion limit will greatly facilitate the analysis of experimental data. In this paper a theoretical framework is presented that allows the calculation of the criterion for the rapid diffusion limit. Explicit criteria are given for various donor-acceptor geometries, all for the case of energy transfer via the resonance interaction of the Förster type. The criteria, except for the cases of densely distributed acceptors under a wide surface, have a common form Dτ_Da⁴/R₀≫λ, where τ_D is the lifetime of donor fluorescence in the absence of acceptors, D is the sum of diffusion coefficients of the donor and acceptor, a is the distance of closest approach between the donor and acceptor, R ₀ is the critical distance for energy transfer, and λ is a geometrical constant with a value less than one. Exponential decays are not easily obtained when acceptors are densely distributed under a wide surface. The results are compared with the criterion given earlier by Thomas et al. [D. D. Thomas, W. F. Carlsen, and L. Stryer, Proc. Natl. Acad. Sci. U.S.A. 75, 5746 (1978)]. Experimental aspects, such as the effect of heterogeneity in a sample, are also discussed.