We
have developed a hidden Markov model and optimization procedure
for photon-based single-molecule FRET data, which takes into account
the trace-dependent background intensities. This analysis technique
reveals an unprecedented amount of detail in the folding kinetics
of the Diels–Alderase ribozyme. We find a multitude of extended
(low-FRET) and compact (high-FRET) states. Five states were consistently
and independently identified in two FRET constructs and at three Mg2+ concentrations. Structures generally tend to become more
compact upon addition of Mg2+. Some compact structures
are observed to significantly depend on Mg2+ concentration,
suggesting a tertiary fold stabilized by Mg2+ ions. One
compact structure was observed to be Mg2+-independent,
consistent with stabilization by tertiary Watson–Crick base
pairing found in the folded Diels–Alderase structure. A hierarchy
of time scales was discovered, including dynamics of 10 ms or faster,
likely due to tertiary structure fluctuations, and slow dynamics on
the seconds time scale, presumably associated with significant changes
in secondary structure. The folding pathways proceed through a series
of intermediate secondary structures. There exist both compact pathways
and more complex ones, which display tertiary unfolding, then secondary
refolding, and, subsequently, again tertiary refolding.