Complete Kinetic Theory of FRET

Abstract

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.

Engineering couplings for exciton transport using synthetic DNA scaffolds

“…The FRET rate is sensitive to thermal fluctuations in the orientations of the transition dipole moments and thus the ensemble FRET efficiency depends on the angular distribution that these fluctuations generate. 93 Both the timescale of the fluctuations and the shape of the distribution can influence the overall energytransfer efficiency. In the case where fluctuations are fast relative to energy-transfer time scales (dynamic limit), transition dipoles sample a large number of different configurations between energy-transfer events.…”

“…In the chromophore-DNA systems, the normal distribution is visualized as a cone centered along the transition dipole moment of the chromophore, which is at a position and orientation determined by the geometric constraints imposed by the linkers, as illustrated in Figure 5D (Section S3.5). 93,94 The cone angle of Cy5 is q Cy5 = 33 + G 2 + centered on the axis parallel to the DNA backbone. 94 The cone angle of Cy3 is centered parallel to that of Cy5 and, as discussed above, is narrower for monomeric Cy3 in duplexes than in DX tiles.…”

Integrating multiple experimental data to determine conformational ensembles of an intrinsically disordered protein

“…The flexible linkers produce a distribution of inter-dye distances, r DA , over which the FRET distance dependence must be averaged, even for a single conformation with fixed end-to-end distance r ee . The appropriate averaging over both r DA and r ee depends on the timescale of their respective motions relative to the donor excited state lifetime τ DA (τ DA ≤ τ D0 = 3.7 ns) [17,58]. To calculate the average FRET efficiency for a single conformation in the ensemble, we assume quasi-static distributions of inter-dye distances (see below).…”

“…In the limit that inter-dye dynamics are much faster than τ DA , the "transfer-rate-weighted" dynamic average limit results [17,58],…”

“…We performed Monte-Carlo simulations of the photon emission process and Brownian motion simulations of dye translational diffusion, adapting the approach in Ref. [17]. We used our measured donor-only lifetime τ D0 and Förster radius R 0 .…”