The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.
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