Single-Molecule FRET: Theory and Analysis of Photon Sequences

Abstract

Single-molecule FRET measurements contain information on conformational dynamics because the rate of energy transfer depends on the distance between donor and acceptor labels attached to a molecule. The output of such measurements is a sequence of photons of different colors separated by apparently random time intervals. In addition, the delay time between laser pulse and photon arrival can be recorded. To extract information from such raw data, it is necessary to understand in detail all the complex microscopic processes involved. We consider various quantitative methods to analyze sequences of photons emitted by a molecule with interchanging conformational states. Photon sequences with recorded interphoton times can be analyzed by maximizing the appropriate likelihood functions with respect to the parameters of a model of the conformational dynamics. The consistency of the model with the data can be checked by recoloring the photons trajectory and comparing the predicted and observed FRET efficiency histograms. These photon-by-photon methods are rigorous for both immobilized and diffusing molecules. Binned photon sequences, in which only the numbers of donor and acceptor photons in consecutive time intervals are recorded, can be analyzed by constructing FRET efficiency histograms or, alternatively, by analyzing the whole sequence of photon counts using likelihood-based methods. For the FRET efficiency histograms, we derive accurate multi-Gaussian approximations without any adjustable parameters when the molecule has multiple conformational states. For the whole sequence analysis, we provide approximate likelihood functions for the binned photon sequences. It is shown how these methods can be extended to include information from photon delay times.