Abstract
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.
Highlights
Recent technological advances in single molecule experiments on biomolecules have provided an unprecedented chance to investigate dynamics of proteins and nucleic acids at single molecule (SM) level, which has previously been elusive in conventional experiments [1,2,3,4,5,6,7]
While the notion of dynamical heterogeneity or broken ergodicity seems better recognized in the research field of nucleic acids [81] than in proteins, which likely arises from more homopolymer-like nature of building block of nucleotides [82], biomolecules in general can have a rugged folding landscape with many local basins of attraction and kinetic barriers with varying heights [83]
Conformational dynamics of biomolecules on rugged landscapes can be heterogeneous, which gives rise to static or dynamic disorder depending on the time scale of observation or the height distribution of kinetic barrier
Summary
Recent technological advances in single molecule experiments on biomolecules have provided an unprecedented chance to investigate dynamics of proteins and nucleic acids at single molecule (SM) level, which has previously been elusive in conventional experiments [1,2,3,4,5,6,7]. Unfolding pathways gleaned from individual SM trajectories indicate rugged folding landscapes inherent to biomolecules [4, 8, 9]. Long time trajectories from SM measurements, which can be extended more than hundreds seconds, allow us to address how a rugged conformational landscape is sampled over time [7, 10, 11]. One of the striking findings from these measurements is that even under the same folding condition, conformational dynamics of individual molecules differ substantially from one another while still maintaining their biological functions. Cofactor-induced conformational transitions of T. ribozymes [12], Holliday junctions [13], TPP-riboswitch [14], and preQ1-riboswitch [15] are the recent seminal examples that exhibit molecular heterogeneity at equilibrium.
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