Analysis of single-molecule fluorescence spectroscopic data with a Markov-modulated Poisson process.

We present a photon-by-photon analysis framework for the evaluation of data from single-molecule fluorescence spectroscopy (SMFS) experiments using a Markov-modulated Poisson process (MMPP). A MMPP combines a discrete (and hidden) Markov process with an additional Poisson process reflecting the observation of individual photons. The algorithmic framework is used to automatically analyze the dynamics of the complex formation and dissociation of Cu2+ ions with the bidentate ligand 2,2'-bipyridine-4,4'dicarboxylic acid in aqueous media. The process of association and dissociation of Cu2+ ions is monitored with SMFS. The dcbpy-DNA conjugate can exist in two or more distinct states which influence the photon emission rates. The advantage of a photon-by-photon analysis is that no information is lost in preprocessing steps. Different model complexities are investigated in order to best describe the recorded data and to determine transition rates on a photon-by-photon basis. The main strength of the method is that it allows to detect intermittent phenomena which are masked by binning and that are difficult to find using correlation techniques when they are short-lived.