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

Abstract

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.

Analyzing Single-Molecule Protein Transportation Experiments via Hierarchical Hidden Markov Models

“…Though the consistency of BIC for Gaussian HMMs has not been completely established (Cappe et al, 2005; Finesso, 1990; Ryden, 1995), it has been shown through simulations that BIC empirically tends to select the correct model when the sample size is large but could give highly variable results when the sample size is small or moderate (Celeux and Durand, 2008; Ryden, 1995; MacKAY, 2002; Watkins and Yang, 2005; Frühwirth-Schnatter, 2006; Keribin, 2000). In the context of FRET trajectories, the variability of BIC for HMMs has also been observed (van de Meent et al, 2014; Blanco and Walter, 2010; Keller et al, 2014). The general recommendation in the statistics literature and in the FRET literature for the state-selection of HMM is to use BIC as a first step of preliminary analysis and then assess the selection result based on scientific and experimental insight (McKinney et al, 2006; Greenfeld et al, 2012; Bulla et al, 2010; Keller et al, 2014; Celeux and Durand, 2008).…”

“…In the context of FRET trajectories, the variability of BIC for HMMs has also been observed (van de Meent et al, 2014; Blanco and Walter, 2010; Keller et al, 2014). The general recommendation in the statistics literature and in the FRET literature for the state-selection of HMM is to use BIC as a first step of preliminary analysis and then assess the selection result based on scientific and experimental insight (McKinney et al, 2006; Greenfeld et al, 2012; Bulla et al, 2010; Keller et al, 2014; Celeux and Durand, 2008). We adopt this recommendation.…”

Markov state models of biomolecular conformational dynamics

“…Optical force spectroscopy experiments of calmodulin extrapolated to zero force also yielded a multistate MSM describing exchange among on- and off-pathway intermediates [76]. The complex MSM obtained from single-molecule FRET studies of the Diels-Alderase ribozyme permitted the use of transition path theory and transition matrix eigenvector analysis for describing the Mg 2+ -dependent folding pathway [77]. …”

Single Molecule Cluster Analysis dissects splicing pathway conformational dynamics

“…For example, it has been demonstrated that in certain favorable cases interstate dynamics can be extracted from histograms through an analysis of photon arrival times and lifetimes 17 . In addition, state-to-state transition kinetics have been extracted utilizing clustering algorithms to identify distinct kinetic behaviors 18,19 . All of these approaches have focused on small datasets with 2–3 FRET states and limited dynamics.…”