Time-Heterogeneity of the Förster Radius from Dipole Orientational Dynamics Explains Observed Dynamic Shift

Förster resonance energy transfer (FRET) is a quantum mechanical phenomenoninvolving the non-radiative transfer of energy between coupled electricdipoles. Due to the strong dependence of FRET on the distance between thedipoles, it is frequently used as a “molecular ruler" in biology, chemistry,and physics. This is done by placing dipolar molecules called dyes on moleculesof interest. In time-resolved confocal single-molecule FRET (smFRET)experiments, the joint distribution of the FRET efficiency and the donorfluorescence lifetime can reveal underlying molecular conformational dynamicsvia deviation from their theoretical Förster relationship. This deviation isreferred to as a dynamic shift. Quantifying the dynamic shift caused by themotion of the fluorescent dyes is essential to decoupling the dynamics of thestudied molecules and the dyes. We develop novel Langevin models for the dyelinker dynamics, including rotational dynamics, based on first physicsprinciples and proper dye linker chemistry to match accessible volumespredicted by molecular dynamics simulations. By simulating the dyes' stochastictranslational and rotational dynamics, we show that the observed dynamic shiftcan largely be attributed to the mutual orientational dynamics of the electricdipole moments associated with the dyes, not their accessible volume.