Photon-by-Photon Hidden Markov Model Analysis for Microsecond Single-Molecule FRET Kinetics

The function of biological macromolecules involves large-scale conformational dynamics spanning multiple time scales, from microseconds to seconds. Such conformational motions, which may involve whole domains or subunits of a protein, play a key role in allosteric regulation. There is an urgent need for experimental methods to probe the fastest of these motions. Single-molecule fluorescence experiments can in principle be used for observing such dynamics, but there is a lack of analysis methods that can extract the maximum amount of information from the data, down to the microsecond time scale. To address this issue, we introduce H²MM, a maximum likelihood estimation algorithm for photon-by-photon analysis of single-molecule fluorescence resonance energy transfer (FRET) experiments. H²MM is based on analytical estimators for model parameters, derived using the Baum-Welch algorithm. An efficient and effective method for the calculation of these estimators is introduced. H²MM is shown to accurately retrieve the reaction times from ∼1 s to ∼10 μs and even faster when applied to simulations of freely diffusing molecules. We further apply this algorithm to single-molecule FRET data collected from Holliday junction molecules and show that at low magnesium concentrations their kinetics are as fast as ∼10⁴ s^-1. The new algorithm is particularly suitable for experiments on freely diffusing individual molecules and is readily incorporated into existing analysis packages. It paves the way for the broad application of single-molecule fluorescence to study ultrafast functional dynamics of biomolecules.