Complex RNA Folding Kinetics Revealed by Single-Molecule FRET and Hidden Markov Models

[Image: see text] 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 Mg(2+) concentrations. Structures generally tend to become more compact upon addition of Mg(2+). Some compact structures are observed to significantly depend on Mg(2+) concentration, suggesting a tertiary fold stabilized by Mg(2+) ions. One compact structure was observed to be Mg(2+)-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.