Regime-Changing Hidden Markov Modeling and Statistical Analysis for Complex Single-Molecule Time Series

Single-molecule Forster Resonance Energy Transfer (smFRET) experiments provide time-series data offering insight into biomolecular structure and dynamics. Extracting insight and dissecting mechanism, however, are not trivial, particularly when smFRET is extended to complex systems involving multiple molecular components or FRET pairs. Hidden Markov models (HMMs) provide a powerful and extendable framework to address molecular function and structure. Here, we demonstrate an extension of HMM-based inference called ‘Regime-Changing HMM’ exploiting alternating laser excitation (ALEx) spectroscopy, and we test its limitations using simulated data and previously reported switchable FRET data involving complex stoichiometries. We further compare regime-changing HMM to previously described statistical analysis methods and demonstrate the method's superiority in inferring correct HMM topology and kinetic parameters. We then apply the method to DNA polymerase binding and replication to identify binding of multiple polymerases to a DNA overhang construct and to extract binding, dissociation, and polymerization kinetics. The presented statistical algorithm provides objective quantification of single-molecule trajectories and successfully identifies, segments, and analyses photophysical, dynamical, and stoichiometric ‘regimes’ within these trajectories. Our work illuminates important mechanisms in DNA replication and paves the way for experimental extension to studies of large complexes and molecular machines and to the field of single-molecule enzymology.