Complete Kinetic Theory of FRET

Förster resonance energy transfer (FRET) can be used to measure distances and infer structures at the molecular level. However, the flexible linkers with which the fluorophores are attached to a macromolecule introduce a lack of knowledge. Both the dye's geometry and kinetics give rise to uncertainties. Whereas the impact of the geometry is already well understood, the real extent of the kinetics has not been investigated thoroughly. Here, we present a single-molecule (sm)FRET theory that defines the kinetics of dye movements in a complete form. We introduce a formal nomenclature and provide a recipe for the calculation of the corresponding FRET efficiency. We further analyze experimental data in order to obtain parameters characterizing the geometry and kinetics of the FRET dyes and use them to resimulate the FRET efficiencies by diffusion of fluorophore and linker movement. We show in a real case scenario of dye molecules attached to dsDNA that when making geometrical and kinetic assumptions commonly used in the FRET community one obtains results differing from the experimental data. In contrast, our stochastic simulations taking kinetic parameters from experiments into account reproduce the correct FRET efficiencies. Furthermore, we present a method enabling us to classify the kinetics of the dyes by investigating single realizations of the simulated transfer process. The results support our notion that the common kinetic assumptions are not appropriate over the whole range of distances inferred by FRET even for the simple situation of dyes attached to DNA where few interactions occur.