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Does Native State Topology Determine the RNA Folding Mechanism? doi:10.1016/j.jmb.2004.02.024 J. Mol. Biol. (2004) 337, 789–797 Does Native State Topology Determine the RNA Folding Mechanism? Eric J. Sorin1, Bradley J. Nakatani1, Young Min Rhee1 Guha Jayachandran2, V Vishal1 and Vijay S. Pande1,3,4,5* 1Department of Chemistry Recent studies in protein folding suggest that native state topology plays a Stanford University, Stanford dominant role in determining the folding mechanism, yet an analogous CA 94305-5080, USA statement has not been made for RNA, most likely due to the strong coupling between the ionic environment and conformational energetics 2Department of Computer that make RNA folding more complex than protein folding. Applying a Science, Stanford University distributed computing architecture to sample nearly 5000 complete tRNA Stanford, CA 94305-5080 folding events using a minimalist, atomistic model, we have characterized USA the role of native topology in tRNA folding dynamics: the simulated bulk 3Department of Biophysics folding behavior predicts well the experimentally observed folding Stanford University, Stanford mechanism. In contrast, single-molecule folding events display multiple CA 94305-5080, USA discrete folding transitions and compose a largely diverse, heterogeneous 4 dynamic ensemble. This both supports an emerging view of hetero- Department of Structural geneous folding dynamics at the microscopic level and highlights the Biology, Stanford University need for single-molecule experiments and both single-molecule and bulk Stanford, CA 94305-5080 simulations in interpreting bulk experimental measurements. USA q 2004 Elsevier Ltd. All rights reserved. 5Stanford Synchrotron Radiation Laboratory Stanford University Stanford, CA 94305-5080 USA Keywords: RNA folding; bulk kinetics; mechanism; distributed computing; *Corresponding author biasing potential Introduction pathways have been made.6,7 Ferrara and Caflisch studied the folding of peptides forming beta struc- The study of biological self-assembly is at the ture and concluded that the folding free energy forefront of modern biophysics, with many labora- landscape is determined by the topology of the tories around the world focused on answering the native state, whereas specific atomic interactions question “How do biopolymers adopt biologically determine the pathway(s) followed,8 and our active native folds?” In recent years, protein recent comparison between protein and RNA hair- folding studies have put forth a new “topology- pin structures supports this line of reasoning.9 driven” view of folding by recognizing correlations This is not surprising when one considers that between folding mechanism and topology of the the folding transition states for proteins of similar native state.1 For instance, the laboratories of shape were shown to be insensitive to significant Goddard and Plaxco have put forth several reports sequence mutations.10 – 12 connecting the folding rates of small proteins with Here, we attempt to directly characterize the the topological character of those proteins,2–5 and contribution of native state topology to the RNA comparisons between topology and unfolding folding mechanism at both the single-molecule and bulk levels. Because bulk experiments inher- Abbreviations used: RMSD, root-mean-squared ently include ensemble-averaged observables, deviations; LJ, Lennard–Jones. with distributions around those averages expected E-mail address of the corresponding author: within a given system, single-molecule studies [email protected] complement bulk studies by allowing observation 0022-2836/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. 790 Bulk tRNA Folding Simulations of dynamics that are masked by such ensemble- at best, the simplified biasing potential used here averaging.13 – 15 Yet differences between single- presents an ideal methodology to probe the molecule and bulk folding behaviors can be relationship between topology and folding mecha- profound, as detailed herein. nism: the folding potential is built on information In the past, the ability of simulation to predict from the native tRNA fold. If the relationship bulk system dynamical properties has been hin- between topology and folding mechanism is negli- dered by the limited number of events that one gible, our results should show significant disagree- could simulate. Using a distributed computing ment with experimental observations. If, on the architecture16 to overcome this barrier, we have other hand, this relationship is significant, the collected nearly 5000 complete folding events for agreement with experiment should also be the 76 nucleotide tRNA topology, which is signifi- significant. cantly more complex than the small, fast-folding Indeed, we show below that the bulk folding systems commonly examined in folding behavior predicted by this simple, atomistic, simulations.9,17,18 This degree of sampling repre- minimalist model predicts well the experimentally sents ,500 CPU years of work conducted on observed bulk folding mechanism, suggesting that ,10,000 CPUs within our global computing topology does in fact contribute to the bulk folding network†. mechanism. Furthermore, massive sampling has, Interestingly, topological considerations have for the first time, allowed direct comparison of only been applied to the smallest of RNAs,9 likely simulated ensemble kinetics to single-molecule because the folding of functional RNAs is known folding simulations, illustrating a tremendous to be more complex than that of small proteins heterogeneity inherent to individual folding events due to the coupling of RNA conformational ener- that collectively contribute to a topologically dri- getics with the predominantly ionic environment.19 ven bulk folding mechanism. We discuss below For instance, it has been demonstrated that the the general results seen in single-molecule folding identity and concentration of ions present can trajectories, followed by analysis of kinetic and alter the folding and unfolding dynamics exhibited mechanistic observations from an ensemble- by the tRNA topology,20 – 22 further complicating averaged perspective, as well as the role of poly- our understanding of RNA folding. meric entropy in folding. Caveats of the model are To directly assess the relationship between then discussed in Methods. native topology and RNA folding mechanism, we employ a minimalist model similar to the Go¯-like models previously used to study protein Results folding.15,23 – 28 We improve upon these models by developing a folding potential that: (i) treats the Diverse pathways in tRNA folding polymer in atomic detail; (ii) introduces attractive non-native interaction energies; and (iii) includes The native fold of tRNA can be described in ion-dependent effects on the folding dynamics. terms of nine “substructures” (Figure 1(a)). The These features allow for a much more accurate well-defined secondary structure is composed of approximation of the true energetics than the four helix-stem regions (S1,S2,S3,S4), while the coarse-grained models commonly used to study tertiary structure consists of a set of five regions of 28 the dynamics of large biomolecules, while inher- long-range contact (T12,T13,T14,T23,T24), where ently maintaining the polymeric entropy expected the dual subscripts denote the two helix-stems in from atomistic models, thereby allowing a causal contact for a given tertiary region. Formation of relationship to be inferred between changes in these substructures in simulated single-molecule the energetics of the model and changes in the folding events occur as a series of numerous, dis- resulting dynamics. crete transitions in the fraction of native contacts, Striving for simplicity, we consider the most Q. To quantitatively characterize the observed elementary model of the ionic effect in RNA fold- pathways, the relative folding times for these ing, which assumes that monovalent and divalent nine substructures were calculated. In many cases, cations stabilize secondary and tertiary structure, multiple substructures folded in the same time respectively. We propose that such a simple model range. To unambiguously determine the sub- is adequate to capture the essential folding structural folding order in a given trajectory, the dynamics observed in experiments under varying variance in the fraction of native contacts within ionic conditions: our model employs two para- each substructure throughout that trajectory, meters, 12 and 13, which specify the energetic bene- VarðQÞ; was calculated, and the relative folding fit of native secondary and tertiary interactions, time of each substructure was defined as the tem- respectively, coupled only in their simultaneous poral point at which VarðQÞ was a maximum (i.e. use in thermal calibrations of the model. the point at which Q was increasing most rapidly). We note that while the use of Go¯-like potentials Pearson correlations (defined as the covariance to extract precise folding dynamics is questionable of two sets divided by the product of their stan- dard deviations) between folding times for each pair of substructures within the ensemble of fold- † Folding@Home, http://folding.stanford.edu ing events were then evaluated, and the resulting Bulk tRNA Folding Simulations 791 Table 1. Weighting of tRNA folding pathways Class Weight (%) Pathway I 36.3 S4 [S2,T12]S3 [T13,T23][T14,T24]S1 10.6 S4 S3 [S2,T12][T13,T23][T14,T24]S1 4.5 [S2,T12]S4 S3 [T13,T23][T14,T24]S1 1.7 S4 [S2,T12]S3 T24 [T13,T23]T14 S1 II 13.0 S4 [S2,T12]S3 S1 [T13,T23][T14,T24] 3.4 S4 S3 [S2,T12]S1 [T13,T23][T14,T24] 2.2 S4 [S2,T12]S3 S1 T14 [T13,T23]T24 1.5 S4 [S2,T12]S1 S3 [T13,T23][T14,T24] 1.4 [S2,T12]S4 S3 S1 [T13,T23][T14,T24] III 8.1 S4 [S2,T12]S3 [T13,T23]S1 [T14,T24] 2.4 S4 S3 [S2,T12][T13,T23]S1 [T14,T24] 2.4 S4 S3 [S2,T12][T13,T23]S1 [T14,T24] 1.6 S4 [S2,T12]S3 [T13,T23]T14 S1 T24 stages of folding exhibited a much larger variation. For this reason, the ordering of the substructural folding events within phase 2 was used to classify folding trajectories. The observed statistical weighting of folding pathways is detailed for each folding class in Table 1.
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