  Single molecule time trajectories of biomolecules provide glimpses into
complex folding landscapes that are difficult to visualize using conventional
ensemble measurements. Recent experiments and theoretical analyses have
highlighted dynamic disorder in certain classes of biomolecules, whose dynamic
pattern of conformational transitions is affected by slower transition dynamics
of internal state hidden in a low dimensional projection. A systematic means to
analyze such data is, however, currently not well developed. Here we report a
new algorithm - Variational Bayes-double chain Markov model (VB-DCMM) - to
analyze single molecule time trajectories that display dynamic disorder. The
proposed analysis employing VB-DCMM allows us to detect the presence of dynamic
disorder, if any, in each trajectory, identify the number of internal states,
and estimate transition rates between the internal states as well as the rates
of conformational transition within each internal state. Applying VB-DCMM
algorithm to single molecule FRET data of H-DNA in 100 mM-Na$^+$ solution,
followed by data clustering, we show that at least 6 kinetic paths linking 4
distinct internal states are required to correctly interpret the duplex-triplex
transitions of H-DNA.
