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.