Monte Carlo Diffusion-Enhanced Photon Inference: Distance Distributions and Conformational Dynamics in Single-Molecule FRET

Single-molecule Förster resonance energy transfer (smFRET) is utilized to study the structure and dynamics of many biomolecules, such as proteins, DNA, and their various complexes. The structural assessment is based on the well-known Förster relationship between the measured efficiency of energy transfer between a donor (D) and an acceptor (A) dye and the distance between them. Classical smFRET analysis methods called photon distribution analysis (PDA) take into account photon shot-noise, D-A distance distribution, and, more recently, interconversion between states in order to extract accurate distance information. It is known that rapid D-A distance fluctuations on the order of the D lifetime (or shorter) can increase the measured mean FRET efficiency and thus decrease the estimated D-A distance. Nonetheless, this effect has been so far neglected in smFRET experiments, potentially leading to biases in estimated distances. Here we introduce a PDA approach dubbed Monte Carlo diffusion-enhanced photon inference (MC-DEPI). MC-DEPI recolor detected photons of smFRET experiments taking into account dynamics of D-A distance fluctuations, multiple interconverting states, and photoblinking. Using this approach, we show how different underlying conditions may yield identical FRET histograms and how the additional information from fluorescence decays helps in distinguishing between the different conditions. We also introduce a machine learning fitting approach for retrieving the D-A distance distribution, decoupled from the above-mentioned effects. We show that distance interpretation of smFRET experiments of even the simplest dsDNA is nontrivial and requires decoupling the effects of rapid D-A distance fluctuations on FRET in order to avoid systematic biases in the estimation of the D-A distance distribution.