Single-molecule FRET with diffusion and conformational dynamics

Under relatively mild conditions, we show how one can extract information about conformational dynamics from F?rster resonance energy transfer (FRET) experiments on diffusing molecules without modeling diffusion. Starting from a rigorous theory that does treat diffusion, we first examine when the single-molecule FRET efficiency distribution can be decomposed into the measured distribution of the total number of photons and the efficiency distribution of an immobilized molecule in the absence of shot noise. If the conformation does not change during the time the molecule spends in the laser spot, this is possible when (I) the efficiency is independent of the location in the laser spot and (II) the total number of photons does not depend on conformation. This decomposition is approximate when the conformation changes during the diffusion time. However, it does provide a simple framework for analyzing data. This is illustrated for a two-state system where the FRET efficiency distribution can be found analytically for all values of the interconversion rates. If the arrival time of each donor and acceptor photon can be monitored, we introduce an alternative procedure that allows one to rigorously extract the rates of conformational changes when the above two conditions hold. In this case, the pattern of colors in the photon trajectory depends solely on conformational dynamics. This can be exploited in the framework of statistical inference because the likelihood function, which must be optimized with respect to the model rate parameters, depends only on how the conformation changes during the interval between photons with specified colors.