Maximum likelihood trajectories from single molecule fluorescence resonance energy transfer experiments

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Abstract
Single molecule fluorescence resonance energy transfer (FRET) experiments are a powerful and versatile tool for studying conformationalmotions of single biomolecules. However, the small number of recorded photons typically limits the achieved time resolution. We develop a maximum likelihood theory that uses the full information of the recorded photon arrival times to reconstruct nanometer distance trajectories. In contrast to the conventional, intensity-based approach, our maximum likelihood approach does not suffer from biased a priori distance distributions. Furthermore, by providing probability distributions for the distance, the theory also yields rigorous error bounds. Applied to a burst of 230 photons obtained from a FRET dye pair site-specifically linked to the neural fusion protein syntaxin-1a, the theory enables one to distinguish time-resolved details of millisecond fluctuations from shot noise. From cross validation, an effective diffusion coefficient is also determined from the FRET data.