The effect of Brownian motion of fluorescent probes on measuring nanoscale distances by Förster resonance energy transfer.

Förster resonance energy transfer (FRET) is a powerful optical technique to determine intra-molecular distances. However, the dye rotational motion and the linker flexibility complicate the relationship between the measured energy transfer efficiency and the distance between the anchoring points of the dyes. In this study, we present a simple model that describes the linker and dye dynamics as diffusion on a sphere. Single-pair energy transfer was treated in the weak excitation limit, photon statistics and scaffold flexibility were ignored, and different time-averaging regimes were considered. Despite the approximations, our model provides new insights for experimental designs and results interpretation in single-molecule FRET. Monte Carlo simulations produced distributions of the inter-dye distance, the dipole orientation factor, κ(2), and the transfer efficiency, E, which were in perfect agreement with independently derived theoretical functions. Contrary to common perceptions, our data show that longer linkers will actually restrict the motion of dye dipoles and hence worsen the isotropic 2∕3 approximation of κ(2). It is also found that the thermal motions of the dye-linker system cause fast and large efficiency fluctuations, as shown by the simulated FRET time-trajectories binned on a microsecond time scale. A fundamental resolution limit of single-molecule FRET measurements emerges around 1-10 μs, which should be considered for the interpretation of data recorded on such fast time scales.