Folding of RNA involves parallel pathways

Watching ion-driven kinetics of ribozyme folding and misfolding caused by energetic and topological frustration one molecule at a time

Folding of ribozymes into well-defined tertiary structures usually requires divalent cations. How Mg2+ ions direct the folding kinetics has been a long-standing unsolved problem because experiments cannot detect the positions and dynamics of ions. To address this problem, we used molecular simulations to dissect the folding kinetics of the Azoarcus ribozyme by monitoring the path each molecule takes to reach the folded state. We quantitatively establish that Mg2+ binding to specific sites, coupled with counter-ion release of monovalent cations, stimulate the formation of secondary and tertiary structures, leading to diverse pathways that include direct rapid folding and trapping in misfolded structures. In some molecules, key tertiary structural elements form when Mg2+ ions bind to specific RNA sites at the earliest stages of the folding, leading to specific collapse and rapid folding. In others, the formation of non-native base pairs, whose rearrangement is needed to reach the folded state, is the rate-limiting step. Escape from energetic traps, driven by thermal fluctuations, occurs readily. In contrast, the transition to the native state from long-lived topologically trapped native-like metastable states is extremely slow. Specific collapse and formation of energetically or topologically frustrated states occur early in the assembly process.

Enhancement of the thermal stability of G-quadruplex structures by urea

The solute urea has been used extensively as a denaturant in protein folding studies; double-stranded nucleic acid structures are also destabilized by urea, but comparatively less than proteins. In previous research, the solute has been shown to strongly destabilize folded G-quadruplex DNA structures. This contribution demonstrates the stabilizing effect of urea on the G-quadruplex formed by the oligodeoxyribonucleotide (ODN), G3T (d[5'-GGGTGGGTGGGTGGG-3']), and related sequences in the presence of sodium or potassium cations. Stabilization is observed up to 7 M urea, which was the highest concentration we investigated. The folded structure of G3T has three G-tetrads and three loops that consist of single thymine residues. ODNs related to G3T, in which the thymine residues in the loop are substituted by adenosine residues, also exhibit enhanced stability in the presence of molar concentrations of urea. The circular dichroism (CD) spectra of these ODNs in the presence of urea are consistent with that of a G-quadruplex. As the urea concentration increases, the spectral intensities of the peaks and troughs change, while their positions change very little. The heat-induced transition from the folded to unfolded state, T_m, was measured by monitoring the change in the UV absorption as a function of temperature. G-quadruplex structures with loops containing single bases exhibited large increases in T_m with increasing urea concentrations. These data imply that the loop region play a significant role in the thermal stability of tetra-helical DNA structures in the presence of the solute urea.

A study of the interaction between TMAO and urea in water using NMR spectroscopy

Trimethylamine N-oxide (TMAO) and urea are small organic biological molecules. While TMAO is known as a protective osmolyte that promotes the native form of biomolecules, urea is a denaturant. An understanding of the impact of TMAO and urea on water structure may aid in uncovering the molecular mechanisms that underlie this activity. Here we investigate binary solutions of TMAO-water, urea-water and ternary solutions of TMAO-urea-water using NMR spectroscopy at 300 K. An enhancement of the total hydrogen bonding in water was found upon the addition of TMAO and this effect was neutralised by a mole ratio of 1-part TMAO to 4-parts urea. Urea was found to have little effect on the strength of water's hydrogen bonding network and the dynamics of water molecules. Evidence was found for a weak interaction between TMAO and urea. Taken together, these results suggest that TMAO's function as a protective osmolyte, and its counteraction of urea, may be driven by the strength of its hydrogen bond interactions with water, and by a secondary reinforcement of water's own hydrogen bond network. They also suggest that the TMAO-urea complex forms through the donation of a hydrogen bond by urea.

RAFFT: Efficient prediction of RNA folding pathways using the fast Fourier transform

We propose a novel heuristic to predict RNA secondary structure formation pathways that has two components: (i) a folding algorithm and (ii) a kinetic ansatz. This heuristic is inspired by the kinetic partitioning mechanism, by which molecules follow alternative folding pathways to their native structure, some much faster than others. Similarly, our algorithm RAFFT starts by generating an ensemble of concurrent folding pathways ending in multiple metastable structures, which is in contrast with traditional thermodynamic approaches that find single structures with minimal free energies. When we constrained the algorithm to predict only 50 structures per sequence, near-native structures were found for RNA molecules of length ≤ 200 nucleotides. Our heuristic has been tested on the coronavirus frameshifting stimulation element (CFSE): an ensemble of 68 distinct structures allowed us to produce complete folding kinetic trajectories, whereas known methods require evaluating millions of sub-optimal structures to achieve this result. Thanks to the fast Fourier transform on which RAFFT (RNA folding Algorithm wih Fast Fourier Transform) is based, these computations are efficient, with complexity O ( L 2logL ).

Thoughts on how to think (and talk) about RNA structure

Recent events have pushed RNA research into the spotlight. Continued discoveries of RNA with unexpected diverse functions in healthy and diseased cells, such as the role of RNA as both the source and countermeasure to a severe acute respiratory syndrome coronavirus 2 infection, are igniting a new passion for understanding this functionally and structurally versatile molecule. Although RNA structure is key to function, many foundational characteristics of RNA structure are misunderstood, and the default state of RNA is often thought of and depicted as a single floppy strand. The purpose of this perspective is to help adjust mental models, equipping the community to better use the fundamental aspects of RNA structural information in new mechanistic models, enhance experimental design to test these models, and refine data interpretation. We discuss six core observations focused on the inherent nature of RNA structure and how to incorporate these characteristics to better understand RNA structure. We also offer some ideas for future efforts to make validated RNA structural information available and readily used by all researchers.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

Metal ions and sugar puckering balance single-molecule kinetic heterogeneity in RNA and DNA tertiary contacts

The fidelity of group II intron self-splicing and retrohoming relies on long-range tertiary interactions between the intron and its flanking exons. By single-molecule FRET, we explore the binding kinetics of the most important, structurally conserved contact, the exon and intron binding site 1 (EBS1/IBS1). A comparison of RNA-RNA and RNA-DNA hybrid contacts identifies transient metal ion binding as a major source of kinetic heterogeneity which typically appears in the form of degenerate FRET states. Molecular dynamics simulations suggest a structural link between heterogeneity and the sugar conformation at the exon-intron binding interface. While Mg2+ ions lock the exon in place and give rise to long dwell times in the exon bound FRET state, sugar puckering alleviates this structural rigidity and likely promotes exon release. The interplay of sugar puckering and metal ion coordination may be an important mechanism to balance binding affinities of RNA and DNA interactions in general.

Iterative annealing mechanism explains the functions of the GroEL and RNA chaperones

Molecular chaperones are ATP-consuming machines, which facilitate the folding of proteins and RNA molecules that are kinetically trapped in misfolded states. Unassisted folding occurs by the kinetic partitioning mechanism according to which folding to the native state, with low probability as well as misfolding to one of the many metastable states, with high probability, occur rapidly. GroEL is an all-purpose stochastic machine that assists misfolded substrate proteins to fold. The RNA chaperones such as CYT-19, which are ATP-consuming enzymes, help the folding of ribozymes that get trapped in metastable states for long times. GroEL does not interact with the folded proteins but CYT-19 disrupts both the folded and misfolded ribozymes. The structures of GroEL and RNA chaperones are strikingly different. Despite these differences, the iterative annealing mechanism (IAM) quantitatively explains all the available experimental data for assisted folding of proteins and ribozymes. Driven by ATP binding and hydrolysis and GroES binding, GroEL undergoes a catalytic cycle during which it samples three allosteric states, T (apo), R (ATP bound), and R^″ (ADP bound). Analyses of the experimental data show that the efficiency of the GroEL-GroES machinery and mutants is determined by the resetting rate k _{R ″  → T} , which is largest for the wild-type (WT) GroEL. Generalized IAM accurately predicts the folding kinetics of Tetrahymena ribozyme and its variants. Chaperones maximize the product of the folding rate and the steady-state native state fold by driving the substrates out of equilibrium. Neither the absolute yield nor the folding rate is optimized.

Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover

We investigated frictional effects on the folding rates of a human telomerase hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV PK) using simulations of the Three Interaction Site (TIS) model for RNA. The heat capacity from TIS model simulations, calculated using temperature replica exchange simulations, reproduces nearly quantitatively the available experimental data for the hTR HP. The corresponding results for BWYV PK serve as predictions. We calculated the folding rates ( k_F) from more than 100 folding trajectories for each value of the solvent viscosity (η) at a fixed salt concentration of 200 mM. By using the theoretical estimate (∝ √N where N is the number of nucleotides) for folding free energy barrier, k_F data for both the RNAs are quantitatively fit using one-dimensional Kramers's theory with two parameters specifying the curvatures in the unfolded basin and the barrier top. In the high-friction regime (η ≳ 10^-5 Pa·s), for both HP and PK, k_F values decrease as 1/η, whereas in the low friction regime, k_F values increase as η increases, leading to a maximum folding rate at a moderate viscosity (∼10^-6 Pa·s), which is the Kramers turnover. From the fits, we find that the speed limit to RNA folding at water viscosity is between 1 and 4 μs, which is in accord with our previous theoretical prediction as well as results from several single molecule experiments. Both the RNA constructs fold by parallel pathways. Surprisingly, we find that the flux through the pathways could be altered by changing solvent viscosity, a prediction that is more easily testable in RNA than in proteins.

Monovalent ions modulate the flux through multiple folding pathways of an RNA pseudoknot

The assembly mechanism of RNA, vital to describing its functions, depends on both the sequence and the metal ion concentration. How the latter influences the folding trajectories remains an important unsolved problem. Here, we examine the folding pathways of an RNA pseudoknot (PK) with key functional roles in transcription and translation, using a combination of experiments and simulations. We demonstrate that the PK, consisting of two hairpins with differing stabilities, folds by parallel pathways. Surprisingly, the flux between them is modulated by monovalent salt concentration. Our work shows that the order of assembly of PKs is determined by the relative stability of the hairpins, implying that the folding landscape can be controlled by sequence and ion concentration.

The functions of RNA pseudoknots (PKs), which are minimal tertiary structural motifs and an integral part of several ribozymes and ribonucleoprotein complexes, are determined by their structure, stability, and dynamics. Therefore, it is important to elucidate the general principles governing their thermodynamics/folding mechanisms. Here, we combine laser temperature-jump experiments and coarse-grained simulations to determine the folding/unfolding pathways of VPK, a variant of the mouse mammary tumor virus (MMTV) PK involved in ribosomal frameshifting. Fluorescent nucleotide analogs (2-aminopurine and pyrrolocytidine) placed at different stem/loop positions in the PK serve as local probes allowing us to monitor the order of assembly of VPK that has two constituent hairpins with different intrinsic stabilities. We show that at 50 mM KCl, the dominant folding pathway populates only the more stable hairpin intermediate; as the salt concentration is increased, a parallel folding pathway emerges involving the less stable hairpin as an alternate intermediate. Notably, the flux between the pathways is modulated by the ionic strength. Our findings support the principle that the order of PK structure formation is determined by the relative stabilities of the hairpins, which can be altered by sequence variations or salt concentrations. The experimental results of salt effects on the partitioning between the two folding pathways are in remarkable agreement with simulations that were performed with no adjustable parameters. Our study not only unambiguously demonstrates that VPK folds by parallel pathways but also showcases the power of combining experiments and simulations for a more enriched description of RNA self-assembly.

Molecular chaperones maximize the native state yield on biological times by driving substrates out of equilibrium

Molecular chaperones facilitate the folding of proteins and RNA in vivo. Under physiological conditions, the in vitro folding of Tetrahymena ribozyme by the RNA chaperone CYT-19 behaves paradoxically; increasing the chaperone concentration reduces the yield of native ribozymes. In contrast, the protein chaperone GroEL works as expected; the yield of the native substrate increases with chaperone concentration. The discrepant chaperone-assisted ribozyme folding thus contradicts the expectation that it operates as an efficient annealing machine. To resolve this paradox, we propose a minimal stochastic model based on the Iterative Annealing Mechanism (IAM) that offers a unified description of chaperone-mediated folding of both proteins and RNA. Our theory provides a general relation that quantitatively predicts how the yield of native states depends on chaperone concentration. Although the absolute yield of native states decreases in the Tetrahymena ribozyme, the product of the folding rate and the steady-state native yield increases in both cases. By using energy from ATP hydrolysis, both CYT-19 and GroEL drive their substrate concentrations far out of equilibrium, thus maximizing the native yield in a short time. This also holds when the substrate concentration exceeds that of GroEL. Our findings satisfy the expectation that proteins and RNA be folded by chaperones on biologically relevant time scales, even if the final yield is lower than what equilibrium thermodynamics would dictate. The theory predicts that the quantity of chaperones in vivo has evolved to optimize native state production of the folded states of RNA and proteins in a given time.

Equilibrium Denaturation and Preferential Interactions of an RNA Tetraloop with Urea

Urea is an important organic cosolute with implications in maintaining osmotic stress in cells and differentially stabilizing ensembles of folded biomolecules. We report an equilibrium study of urea-induced denaturation of a hyperstable RNA tetraloop through unbiased replica exchange molecular dynamics. We find that, in addition to destabilizing the folded state, urea smooths the RNA free energy landscape by destabilizing specific configurations, and forming favorable interactions with RNA nucleobases. A linear concentration-dependence of the free energy (m-value) is observed, in agreement with the results of other RNA hairpins and proteins. Additionally, analysis of the hydrogen-bonding and stacking interactions within RNA primarily show temperature-dependence, while interactions between RNA and urea primarily show concentration-dependence. Our findings provide valuable insight into the effects of urea on RNA folding and describe the thermodynamics of a basic RNA hairpin as a function of solution chemistry.

Optimizing RNA structures by sequence extensions using RNAcop

A key aspect of RNA secondary structure prediction is the identification of novel functional elements. This is a challenging task because these elements typically are embedded in longer transcripts where the borders between the element and flanking regions have to be defined. The flanking sequences impact the folding of the functional elements both at the level of computational analyses and when the element is extracted as a transcript for experimental analysis. Here, we analyze how different flanking region lengths impact folding into a constrained structure by computing probabilities of folding for different sizes of flanking regions. Our method, RNAcop (RNA context optimization by probability), is tested on known and de novo predicted structures. In vitro experiments support the computational analysis and suggest that for a number of structures, choosing proper lengths of flanking regions is critical. RNAcop is available as web server and stand-alone software via http://rth.dk/resources/rnacop.

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

Kinetic and thermodynamic origins of osmolyte-influenced nucleic acid folding

The influential role of monovalent and divalent metal cations in facilitating conformational transitions in both RNA and DNA has been a target of intense biophysical research efforts. However, organic neutrally charged cosolutes can also significantly alter nucleic acid conformational transitions. For example, highly soluble small molecules such as trimethylamine N-oxide (TMAO) and urea are occasionally utilized by organisms to regulate cellular osmotic pressure. Ensemble studies have revealed that these so-called osmolytes can substantially influence the thermodynamics of nucleic acid conformational transitions. In the present work, we exploit single-molecule FRET (smFRET) techniques to measure, for first time, the kinetic origins of these osmolyte-induced changes to the folding free energy. In particular, we focus on smFRET RNA and DNA constructs designed as model systems for secondary and tertiary structure formation. These findings reveal that TMAO preferentially stabilizes both secondary and tertiary interactions by increasing kfold and decreasing kunfold, whereas urea destabilizes both conformational transitions, resulting in the exact opposite shift in kinetic rate constants (i.e., decreasing kfold and increasing kunfold). Complementary temperature-dependent smFRET experiments highlight a thermodynamic distinction between the two different mechanisms responsible for TMAO-facilitated conformational transitions, while only a single mechanism is seen for the destabilizing osmolyte urea. Finally, these results are interpreted in the context of preferential interactions between osmolytes, and the solvent accessible surface area (SASA) associated with the (i) nucleobase, (ii) sugar, and (iii) phosphate groups of nucleic acids in order to map out structural changes that occur during the conformational transitions.

Generalized iterative annealing model for the action of RNA chaperones

As a consequence of the rugged landscape of RNA molecules their folding is described by the kinetic partitioning mechanism according to which only a small fraction (φF) reaches the folded state while the remaining fraction of molecules is kinetically trapped in misfolded intermediates. The transition from the misfolded states to the native state can far exceed biologically relevant time. Thus, RNA folding in vivo is often aided by protein cofactors, called RNA chaperones, that can rescue RNAs from a multitude of misfolded structures. We consider two models, based on chemical kinetics and chemical master equation, for describing assisted folding. In the passive model, applicable for class I substrates, transient interactions of misfolded structures with RNA chaperones alone are sufficient to destabilize the misfolded structures, thus entropically lowering the barrier to folding. For this mechanism to be efficient the intermediate ribonucleoprotein complex between collapsed RNA and protein cofactor should have optimal stability. We also introduce an active model (suitable for stringent substrates with small φF), which accounts for the recent experimental findings on the action of CYT-19 on the group I intron ribozyme, showing that RNA chaperones do not discriminate between the misfolded and the native states. In the active model, the RNA chaperone system utilizes chemical energy of adenosine triphosphate hydrolysis to repeatedly bind and release misfolded and folded RNAs, resulting in substantial increase of yield of the native state. The theory outlined here shows, in accord with experiments, that in the steady state the native state does not form with unit probability.

Folding pathways of the Tetrahymena ribozyme

Like many structured RNAs, the Tetrahymena group I intron ribozyme folds through multiple pathways and intermediates. Under standard conditions in vitro, a small fraction reaches the native state (N) with kobs ≈ 0.6 min(-1), while the remainder forms a long-lived misfolded conformation (M) thought to differ in topology. These alternative outcomes reflect a pathway that branches late in folding, after disruption of a trapped intermediate (Itrap). Here we use catalytic activity to probe the folding transitions from Itrap to the native and misfolded states. We show that mutations predicted to weaken the core helix P3 do not increase the rate of folding from Itrap but they increase the fraction that reaches the native state rather than forming the misfolded state. Thus, P3 is disrupted during folding to the native state but not to the misfolded state, and P3 disruption occurs after the rate-limiting step. Interestingly, P3-strengthening mutants also increase native folding. Additional experiments show that these mutants are rapidly committed to folding to the native state, although they reach the native state with approximately the same rate constant as the wild-type ribozyme (~1 min(-1)). Thus, the P3-strengthening mutants populate a distinct pathway that includes at least one intermediate but avoids the M state, most likely because P3 and the correct topology are formed early. Our results highlight multiple pathways in RNA folding and illustrate how kinetic competitions between rapid events can have long-lasting effects because the "choice" is enforced by energy barriers that grow larger as folding progresses.

Single-molecule studies of riboswitch folding

The folding dynamics of riboswitches are central to their ability to modulate gene expression in response to environmental cues. In most cases, a structural competition between the formation of a ligand-binding aptamer and an expression platform (or some other competing off-state) determines the regulatory outcome. Here, we review single-molecule studies of riboswitch folding and function, predominantly carried out using single-molecule FRET or optical trapping approaches. Recent results have supplied new insights into riboswitch folding energy landscapes, the mechanisms of ligand binding, the roles played by divalent ions, the applicability of hierarchical folding models, and kinetic vs. thermodynamic control schemes. We anticipate that future work, based on improved data sets and potentially combining multiple experimental techniques, will enable the development of more complete models for complex RNA folding processes. This article is part of a Special Issue entitled: Riboswitches.

Ribosome assembly factors Pwp1 and Nop12 are important for folding of 5.8S rRNA during ribosome biogenesis in Saccharomyces cerevisiae

Previous work from our lab suggests that a group of interdependent assembly factors (A(3) factors) is necessary to create early, stable preribosomes. Many of these proteins bind at or near internal transcribed spacer 2 (ITS2), but in their absence, ITS1 is not removed from rRNA, suggesting long-range communication between these two spacers. By comparing the nonessential assembly factors Nop12 and Pwp1, we show that misfolding of rRNA is sufficient to perturb early steps of biogenesis, but it is the lack of A(3) factors that results in turnover of early preribosomes. Deletion of NOP12 significantly inhibits 27SA(3) pre-rRNA processing, even though the A(3) factors are present in preribosomes. Furthermore, pre-rRNAs are stable, indicating that the block in processing is not sufficient to trigger turnover. This is in contrast to the absence of Pwp1, in which the A(3) factors are not present and pre-rRNAs are unstable. In vivo RNA structure probing revealed that the pre-rRNA processing defects are due to misfolding of 5.8S rRNA. In the absence of Nop12 and Pwp1, rRNA helix 5 is not stably formed. Interestingly, the absence of Nop12 results in the formation of an alternative yet unproductive helix 5 when cells are grown at low temperatures.

Complex RNA folding kinetics revealed by single-molecule FRET and hidden Markov models

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.

Urea-induced denaturation of preQ1-riboswitch

Urea, a polar molecule with a large dipole moment, not only destabilizes folded RNA structures but can also enhance the folding rates of large ribozymes. Unlike the mechanism of urea-induced unfolding of proteins, which is well understood, the action of urea on RNA has barely been explored. We performed extensive all-atom molecular dynamics simulations to determine the molecular underpinnings of urea-induced RNA denaturation. Urea displays its denaturing power in both secondary and tertiary motifs of the riboswitch structure. Our simulations reveal that the denaturation of RNA structures is mainly driven by the hydrogen-bonding and stacking interactions of urea with the bases. Through detailed studies of the simulation trajectories, we found that geminate pairs between urea and bases due to hydrogen bonds and stacks persist only ~0.1-1 ns, which suggests that the urea-base interaction is highly dynamic. Most importantly, the early stage of base-pair disruption is triggered by penetration of water molecules into the hydrophobic domain between the RNA bases. The infiltration of water into the narrow space between base pairs is critical in increasing the accessibility of urea to transiently disrupted bases, thus allowing urea to displace inter-base hydrogen bonds. This mechanism--water-induced disruption of base pairs resulting in the formation of a "wet" destabilized RNA followed by solvation by urea--is the exact opposite of the two-stage denaturation of proteins by urea. In the latter case, initial urea penetration creates a dry globule, which is subsequently solvated by water, leading to global protein unfolding. Our work shows that the ability to interact with both water and polar or nonpolar components of nucleotides makes urea a powerful chemical denaturant for nucleic acids.

The long-range P3 helix of the Tetrahymena ribozyme is disrupted during folding between the native and misfolded conformations

RNAs are prone to misfolding, but how misfolded structures are formed and resolved remains incompletely understood. The Tetrahymena group I intron ribozyme folds in vitro to a long-lived misfolded conformation (M) that includes extensive native structure but is proposed to differ in topology from the native state (N). A leading model predicts that exchange of the topologies requires unwinding of the long-range, core helix P3, despite the presence of P3 in both conformations. To test this model, we constructed 16 mutations to strengthen or weaken P3. Catalytic activity and in-line probing showed that nearly all of the mutants form the M state before folding to N. The P3-weakening mutations accelerated refolding from M (3- to 30-fold) and the P3-strengthening mutations slowed refolding (6- to 1400-fold), suggesting that P3 indeed unwinds transiently. Upon depletion of Mg(2+), the mutations had analogous effects on unfolding from N to intermediates that subsequently fold to M. The magnitudes for the P3-weakening mutations were larger than in refolding from M, and small-angle X-ray scattering showed that the ribozyme expands rapidly to intermediates from which P3 is disrupted subsequently. These results are consistent with previous results indicating unfolding of native peripheral structure during refolding from M, which probably permits rearrangement of the core. Together, our results demonstrate that exchange of the native and misfolded conformations requires loss of a core helix in addition to peripheral structure. Further, the results strongly suggest that misfolding arises from a topological error within the ribozyme core, and a specific topology is proposed.

Understanding the role of three-dimensional topology in determining the folding intermediates of group I introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg(2+)-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (∙OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ∙OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.

RNA under tension: Folding Landscapes, Kinetic partitioning Mechanism, and Molecular Tensegrity

Non-coding RNA sequences play a great role in controlling a number of cellular functions, thus raising the need to understand their complex conformational dynamics in quantitative detail. In this perspective, we first show that single molecule pulling when combined with with theory and simulations can be used to quantitatively explore the folding landscape of nucleic acid hairpins, and riboswitches with tertiary interactions. Applications to riboswitches, which are non-coding RNA elements that control gene expression by undergoing dynamical conformational changes in response to binding of metabolites, lead to an organization principle that assembly of RNA is determined by the stability of isolated helices. We also point out the limitations of single molecule pulling experiments, with molecular extension as the only accessible parameter, in extracting key parameters of the folding landscapes of RNA molecules.

Quantitation of ten 30S ribosomal assembly intermediates using fluorescence triple correlation spectroscopy

The self-assembly of bacterial 30S ribosomes involves a large number of RNA folding and RNA-protein binding steps. The sequence of steps determines the overall assembly mechanism and the structure of the mechanism has ramifications for the robustness of biogenesis and resilience against kinetic traps. Thermodynamic interdependencies of protein binding inferred from omission-reconstitution experiments are thought to preclude certain assembly pathways and thus enforce ordered assembly, but this concept is at odds with kinetic data suggesting a more parallel assembly landscape. A major challenge is deconvolution of the statistical distribution of intermediates that are populated during assembly at high concentrations approaching in vivo assembly conditions. To specifically resolve the intermediates formed by binding of three ribosomal proteins to the full length 16S rRNA, we introduce Fluorescence Triple-Correlation Spectroscopy (F3CS). F3CS identifies specific ternary complexes by detecting coincident fluctuations in three-color fluorescence data. Triple correlation integrals quantify concentrations and diffusion kinetics of triply labeled species, and F3CS data can be fit alongside auto-correlation and cross-correlation data to quantify the populations of 10 specific ribosome assembly intermediates. The distribution of intermediates generated by binding three ribosomal proteins to the entire native 16S rRNA included significant populations of species that were not previously thought to be thermodynamically accessible, questioning the current interpretation of the classic omission-reconstitution experiments. F3CS is a general approach for analyzing assembly and function of macromolecular complexes, especially those too large for traditional biophysical methods.

Allosteric tertiary interactions preorganize the c-di-GMP riboswitch and accelerate ligand binding

Cyclic diguanylate (c-di-GMP) is a bacterial second messenger important for physiologic adaptation and virulence. Class-I c-di-GMP riboswitches are phylogenetically widespread and thought to mediate pleiotropic genetic responses to the second messenger. Previous studies suggest that the RNA aptamer domain switches from an extended free state to a compact, c-di-GMP-bound conformation in which two helical stacks dock side-by-side. Single molecule fluorescence resonance energy transfer (smFRET) experiments now reveal that the free RNA exists in four distinct populations that differ in dynamics in the extended and docked conformations. In the presence of c-di-GMP and Mg(2+), a stably docked population (>30 min) becomes predominant. smFRET mutant analysis demonstrates that tertiary interactions distal to the c-di-GMP binding site strongly modulate the RNA population structure, even in the absence of c-di-GMP. These allosteric interactions accelerate ligand recognition by preorganizing the RNA, favoring rapid c-di-GMP binding.

Computational prediction of efficient splice sites for trans-splicing ribozymes

Group I introns have been engineered into trans-splicing ribozymes capable of replacing the 3'-terminal portion of an external mRNA with their own 3'-exon. Although this design makes trans-splicing ribozymes potentially useful for therapeutic application, their trans-splicing efficiency is usually too low for medical use. One factor that strongly influences trans-splicing efficiency is the position of the target splice site on the mRNA substrate. Viable splice sites are currently determined using a biochemical trans-tagging assay. Here, we propose a rapid and inexpensive alternative approach to identify efficient splice sites. This approach involves the computation of the binding free energies between ribozyme and mRNA substrate. We found that the computed binding free energies correlate well with the trans-splicing efficiency experimentally determined at 18 different splice sites on the mRNA of chloramphenicol acetyl transferase. In contrast, our results from the trans-tagging assay correlate less well with measured trans-splicing efficiency. The computed free energy components suggest that splice site efficiency depends on the following secondary structure rearrangements: hybridization of the ribozyme's internal guide sequence (IGS) with mRNA substrate (most important), unfolding of substrate proximal to the splice site, and release of the IGS from the 3'-exon (least important). The proposed computational approach can also be extended to fulfill additional design requirements of efficient trans-splicing ribozymes, such as the optimization of 3'-exon and extended guide sequences.

Chain length determines the folding rates of RNA

We show that the folding rates (k(F)s) of RNA are determined by N, the number of nucleotides. By assuming that the distribution of free-energy barriers separating the folded and the unfolded states is Gaussian, which follows from central limit theorem arguments and polymer physics concepts, we show that k(F)≈k(0)exp(-αN(0.5)). Remarkably, the theory fits experimental rates spanning over 7 orders of magnitude with k(0)~1.0(μs)(-1). Our finding suggests that the speed limit of RNA folding is ~ 1 μs, [corrected] just as it is in the folding of globular proteins.

RNA folding pathways and the self-assembly of ribosomes

Many RNAs do not directly code proteins but are nonetheless indispensable to cellular function. These strands fold into intricate three-dimensional shapes that are essential structures in protein synthesis, splicing, and many other processes of gene regulation and expression. A variety of biophysical and biochemical methods are now showing, in real time, how ribosomal subunits and other ribonucleoprotein complexes assemble from their molecular components. Footprinting methods are particularly useful for studying the folding of long RNAs: they provide quantitative information about the conformational state of each residue and require little material. Data from footprinting complement the global information available from small-angle X-ray scattering or cryo-electron microscopy, as well as the dynamic information derived from single-molecule Förster resonance energy transfer (FRET) and NMR methods. In this Account, I discuss how we have used hydroxyl radical footprinting and other experimental methods to study pathways of RNA folding and 30S ribosome assembly. Hydroxyl radical footprinting probes the solvent accessibility of the RNA backbone at each residue in as little as 10 ms, providing detailed views of RNA folding pathways in real time. In conjunction with other methods such as solution scattering and single-molecule FRET, time-resolved footprinting of ribozymes showed that stable domains of RNA tertiary structure fold in less than 1 s. However, the free energy landscapes for RNA folding are rugged, and individual molecules kinetically partition into folding pathways that lead through metastable intermediates, stalling the folding or assembly process. Time-resolved footprinting was used to follow the formation of tertiary structure and protein interactions in the 16S ribosomal RNA (rRNA) during the assembly of 30S ribosomes. As previously observed in much simpler ribozymes, assembly occurs in stages, with individual molecules taking different routes to the final complex. Interactions occur concurrently in all domains of the 16S rRNA, and multistage protection of binding sites of individual proteins suggests that initial encounter complexes between the rRNA and ribosomal proteins are remodeled during assembly. Equilibrium footprinting experiments showed that one primary binding protein was sufficient to stabilize the tertiary structure of the entire 16S 5'-domain. The rich detail available from the footprinting data showed that the secondary assembly protein S16 suppresses non-native structures in the 16S 5'-domain. In doing so, S16 enables a conformational switch distant from its own binding site, which may play a role in establishing interactions with other domains of the 30S subunit. Together, the footprinting results show how protein-induced changes in RNA structure are communicated over long distances, ensuring cooperative assembly of even very large RNA-protein complexes such as the ribosome.

Fast folding of RNA pseudoknots initiated by laser temperature-jump

RNA pseudoknots are examples of minimal structural motifs in RNA with tertiary interactions that stabilize the structures of many ribozymes. They also play an essential role in a variety of biological functions that are modulated by their structure, stability, and dynamics. Therefore, understanding the global principles that determine the thermodynamics and folding pathways of RNA pseudoknots is an important problem in biology, both for elucidating the folding mechanisms of larger ribozymes as well as addressing issues of possible kinetic control of the biological functions of pseudoknots. We report on the folding/unfolding kinetics of a hairpin-type pseudoknot obtained with microsecond time-resolution in response to a laser temperature-jump perturbation. The kinetics are monitored using UV absorbance as well as fluorescence of extrinsically attached labels as spectroscopic probes of the transiently populated RNA conformations. We measure folding times of 1-6 ms at 37 °C, which are at least 100-fold faster than previous observations of very slow folding pseudoknots that were trapped in misfolded conformations. The measured relaxation times are remarkably similar to predictions of a computational study by Thirumalai and co-workers (Cho, S. S.; Pincus, D.L.; Thirumalai, D. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 17349-17354). Thus, these studies provide the first observation of a fast-folding pseudoknot and present a benchmark against which computational models can be refined.

The Azoarcus group I intron ribozyme misfolds and is accelerated for refolding by ATP-dependent RNA chaperone proteins

Structured RNAs traverse complex energy landscapes that include valleys representing misfolded intermediates. In Neurospora crassa and Saccharomyces cerevisiae, efficient splicing of mitochondrial group I and II introns requires the DEAD box proteins CYT-19 and Mss116p, respectively, which promote folding transitions and function as general RNA chaperones. To test the generality of RNA misfolding and the activities of DEAD box proteins in vitro, here we measure native folding of a small group I intron ribozyme from the bacterium Azoarcus by monitoring its catalytic activity. To develop this assay, we first measure cleavage of an oligonucleotide substrate by the prefolded ribozyme. Substrate cleavage is rate-limited by binding and is readily reversible, with an internal equilibrium near unity, such that the amount of product observed is less than the amount of native ribozyme. We use this assay to show that approximately half of the ribozyme folds readily to the native state, whereas the other half forms an intermediate that transitions slowly to the native state. This folding transition is accelerated by urea and increased temperature and slowed by increased Mg(2+) concentration, suggesting that the intermediate is misfolded and must undergo transient unfolding during refolding to the native state. CYT-19 and Mss116p accelerate refolding in an ATP-dependent manner, presumably by disrupting structure in the intermediate. These results highlight the tendency of RNAs to misfold, underscore the roles of CYT-19 and Mss116p as general RNA chaperones, and identify a refolding transition for further dissection of the roles of DEAD box proteins in RNA folding.

RNA folding in living cells

RNA folding is the most essential process underlying RNA function. While significant progress has been made in understanding the forces driving RNA folding in vitro, exploring the rules governing intracellular RNA structure formation is still in its infancy. The cellular environment hosts a great diversity of factors that potentially influence RNA folding in vivo. For example, the nature of transcription and translation is known to shape the folding landscape of RNA molecules. Trans-acting factors such as proteins, RNAs and metabolites, among others, are also able to modulate the structure and thus the fate of an RNA. Here we summarize the ongoing efforts to uncover how RNA folds in living cells.

Taming free energy landscapes with RNA chaperones

Many non-coding RNAs fold into complex three-dimensional structures, yet the self-assembly of RNA structure is hampered by mispairing, weak tertiary interactions, electrostatic barriers, and the frequent requirement that the 5' and 3' ends of the transcript interact. This rugged free energy landscape for RNA folding means that some RNA molecules in a population rapidly form their native structure, while many others become kinetically trapped in misfolded conformations. Transient binding of RNA chaperone proteins destabilize misfolded intermediates and lower the transition states between conformations, producing a smoother landscape that increases the rate of folding and the probability that a molecule will find the native structure. DEAD-box proteins couple the chemical potential of ATP hydrolysis with repetitive cycles of RNA binding and release, expanding the range of conditions under which they can refold RNA structures.

Multistage collapse of a bacterial ribozyme observed by time-resolved small-angle X-ray scattering

Ribozymes must fold into compact, native structures to function properly in the cell. The first step in forming the RNA tertiary structure is the neutralization of the phosphate charge by cations, followed by collapse of the unfolded molecules into more compact structures. The specificity of the collapse transition determines the structures of the folding intermediates and the folding time to the native state. However, the forces that enable specific collapse in RNA are not understood. Using time-resolved SAXS, we report that upon addition of 5 mM Mg(2+) to the Azoarcus group I ribozyme up to 80% of chains form compact structures in less than 1 ms. In 1 mM Mg(2+), the collapse transition produces extended structures that slowly approach the folded state, while > or = 1.5 mM Mg(2+) leads to an ensemble of random coils that fold with multistage kinetics. Increased flexibility of molecules in the intermediate ensemble correlates with a Mg(2+)-dependent increase in the fast folding population and a previously unobserved crossover in the collapse kinetics. Partial denaturation of the unfolded RNA with urea also increases the fraction of chains following the fast-folding pathway. These results demonstrate that the preferred collapse mechanism depends on the extent of Mg(2+)-dependent charge neutralization and that non-native interactions within the unfolded ensemble contribute to the heterogeneity of the ribozyme folding pathways at the very earliest stages of tertiary structure formation.

Computational approaches to 3D modeling of RNA

Many exciting discoveries have recently revealed the versatility of RNA and its importance in a variety of functions within the cell. Since the structural features of RNA are of major importance to their biological function, there is much interest in predicting RNA structure, either in free form or in interaction with various ligands, including proteins, metabolites and other molecules. In recent years, an increasing number of researchers have developed novel RNA algorithms for predicting RNA secondary and tertiary structures. In this review, we describe current experimental and computational advances and discuss recent ideas that are transforming the traditional view of RNA folding. To evaluate the performance of the most recent RNA 3D folding algorithms, we provide a comparative study in order to test the performance of available 3D structure prediction algorithms for an RNA data set of 43 structures of various lengths and motifs. We find that the algorithms vary widely in terms of prediction quality across different RNA lengths and topologies; most predictions have very large root mean square deviations from the experimental structure. We conclude by outlining some suggestions for future RNA folding research.

Compact intermediates in RNA folding

Large noncoding RNAs fold into their biologically functional structures via compact yet disordered intermediates, which couple the stable secondary structure of the RNA with the emerging tertiary fold. The specificity of the collapse transition, which coincides with the assembly of helical domains, depends on RNA sequence and counterions. It determines the specificity of the folding pathways and the magnitude of the free energy barriers to the ensuing search for the native conformation. By coupling helix assembly with nascent tertiary interactions, compact folding intermediates in RNA also play a crucial role in ligand binding and RNA-protein recognition.

Multiple unfolding events during native folding of the Tetrahymena group I ribozyme

Despite the ubiquitous nature of misfolded intermediates in RNA folding, little is known about their physical properties or the folding transitions that allow them to continue folding productively. Folding of the Tetrahymena group I ribozyme includes sequential accumulation of two intermediates, termed I(trap) and misfolded (M). Here, we probe the structure and folding transition of I(trap) and compare them to those of M. Hydroxyl radical and dimethyl sulfate footprinting show that both I(trap) and M are extensively structured and crudely resemble the native RNA. However, regions of the core P3-P8 domain are more exposed to solvent in I(trap) than in M. I(trap) rearranges to continue folding nearly 1000-fold faster than M, and urea accelerates folding of I(trap) much less than M. Thus, the rate-limiting transition from I(trap) requires a smaller increase in exposed surface. Mutations that disrupt peripheral tertiary contacts give large and nearly uniform increases in re-folding of M, whereas the same mutations give at most modest increases in folding from I(trap). Intriguingly, mutations within the peripheral element P5abc give 5- to 10-fold accelerations in escape from I(trap), whereas ablation of P13, which lies on the opposite surface in the native structure, near the P3-P8 domain, has no effect. Thus, the unfolding required from I(trap) appears to be local, whereas the unfolding of M appears to be global. Further, the modest effects from several mutations suggest that there are multiple pathways for escape from I(trap) and that escape is aided by loosening nearby native structural constraints, presumably to facilitate local movements of nucleotides or segments that have not formed native contacts. Overall, these and prior results suggest a model in which the global architecture and peripheral interactions of the RNA are achieved relatively early in folding. Multiple folding and re-folding events occur on the predominant pathway to the native state, with increasing native core interactions and cooperativity as folding progresses.

Multiple native states reveal persistent ruggedness of an RNA folding landscape

According to the “thermodynamic hypothesis”, the sequence of a biological macromolecule defines its folded, active structure as a global energy minimum on the folding landscape.1,2 But the enormous complexity of folding landscapes of large macromolecules raises a question: Is there indeed a unique global energy minimum corresponding to a unique native conformation, or are there deep local minima corresponding to alternative active conformations?3 Folding of many proteins is well described by two-state models, leading to highly simplified representations of protein folding landscapes with a single native conformation.4,5 Nevertheless, accumulating experimental evidence suggests a more complex topology of folding landscapes with multiple active conformations that can take seconds or longer to interconvert.6,7,8 Here we employ single molecule experiments to demonstrate that an RNA enzyme folds into multiple distinct native states that interconvert much slower than the time scale of catalysis. These data demonstrate that the severe ruggedness of RNA folding landscapes extends into conformational space occupied by native conformations.

Kinetic cooperativity in Escherichia coli 30S ribosomal subunit reconstitution reveals additional complexity in the assembly landscape

The Escherichia coli 30S ribosomal subunit self-assembles in vitro in a hierarchical manner, with the RNA binding by proteins enabled by the prior binding of others under equilibrium conditions. Early 16S rRNA binding proteins also bind faster than late-binding proteins, but the specific causes for the slow binding of late proteins remain unclear. Previously, a pulse-chase monitored by quantitative mass spectrometry method was developed for monitoring 30S subunit assembly kinetics, and here a modified experimental scheme was used to probe kinetic cooperativity by including a step where subsets of ribosomal proteins bind and initiate assembly prior to the pulse-chase kinetics. In this work, 30S ribosomal subunit kinetic reconstitution experiments revealed that thermodynamic dependency does not always correlate with kinetic cooperativity. Some folding transitions that cause subsequent protein binding to be more energetically favorable do not result in faster protein binding. Although 3(') domain primary protein S7 is required for RNA binding by both proteins S9 and S19, prior binding of S7 accelerates the binding of S9, but not S19, indicating there is an additional mechanistic step required for S19 to bind. Such data on kinetic cooperativity and the presence of multiphasic assembly kinetics reveal complexity in the assembly landscape that was previously hidden.

Urea destabilizes RNA by forming stacking interactions and multiple hydrogen bonds with nucleic acid bases

Urea titration of RNA by urea is an effective approach to investigate the forces stabilizing this biologically important molecule. We used all atom molecular dynamics simulations using two urea force fields and two RNA constructs to elucidate in atomic detail the destabilization mechanism of folded RNA in aqueous urea solutions. Urea denatures RNA by forming multiple hydrogen bonds with the RNA bases and has little influence on the phosphodiester backbone. Most significantly we discovered that urea engages in stacking interactions with the bases. We also estimate, for the first time, the m-value for RNA, which is a measure of the strength of urea-RNA interactions. Our work provides a conceptual understanding of the mechanism by which urea enhances RNA folding rates.

Assembly mechanisms of RNA pseudoknots are determined by the stabilities of constituent secondary structures

Understanding how RNA molecules navigate their rugged folding landscapes holds the key to describing their roles in a variety of cellular functions. To dissect RNA folding at the molecular level, we performed simulations of three pseudoknots (MMTV and SRV-1 from viral genomes and the hTR pseudoknot from human telomerase) using coarse-grained models. The melting temperatures from the specific heat profiles are in good agreement with the available experimental data for MMTV and hTR. The equilibrium free energy profiles, which predict the structural transitions that occur at each melting temperature, are used to propose that the relative stabilities of the isolated helices control their folding mechanisms. Kinetic simulations, which corroborate the inferences drawn from the free energy profiles, show that MMTV folds by a hierarchical mechanism with parallel paths, i.e., formation of one of the helices nucleates the assembly of the rest of the structure. The SRV-1 pseudoknot, which folds in a highly cooperative manner, assembles in a single step in which the preformed helices coalesce nearly simultaneously to form the tertiary structure. Folding occurs by multiple pathways in the hTR pseudoknot, the isolated structural elements of which have similar stabilities. In one of the paths, tertiary interactions are established before the formation of the secondary structures. Our work shows that there are significant sequence-dependent variations in the folding landscapes of RNA molecules with similar fold. We also establish that assembly mechanisms can be predicted using the stabilities of the isolated secondary structures.

A complex assembly landscape for the 30S ribosomal subunit

The ribosome is a complex macromolecular machine responsible for protein synthesis in the cell. It consists of two subunits, each of which contains both RNA and protein components. Ribosome assembly is subject to intricate regulatory control and is aided by a multitude of assembly factors in vivo, but can also be carried out in vitro. The details of the assembly process remain unknown even in the face of atomic structures of the entire ribosome and after more than three decades of research. Some of the earliest research on ribosome assembly produced the Nomura assembly map of the small subunit, revealing a hierarchy of protein binding dependencies for the 20 proteins involved and suggesting the possibility of a single intermediate. Recent work using a combination of RNA footprinting and pulse-chase quantitative mass spectrometry paints a picture of small subunit assembly as a dynamic and varied landscape, with sequential and hierarchical RNA folding and protein binding events finally converging on complete subunits. Proteins generally lock tightly into place in a 5' to 3' direction along the ribosomal RNA, stabilizing transient RNA conformations, while RNA folding and the early stages of protein binding are initiated from multiple locations along the length of the RNA.

Single-Molecule Fluorescence Studies of RNA: A Decade's Progress

Over the past decade, single-molecule fluorescence studies have elucidated the structure-function relationship of RNA molecules. The real-time observation of individual RNAs by single-molecule fluorescence has unveiled the dynamic behavior of complex RNA systems in unprecedented detail, revealing the presence of transient intermediate states and their kinetic pathways. This review provides an overview of how single-molecule fluorescence has been used to explore the dynamics of RNA folding and catalysis.

Exhaustive Enumeration of Kinetic Model Topologies for the Analysis of Time-Resolved RNA Folding

Unlike protein folding, the process by which a large RNA molecule adopts a functionally active conformation remains poorly understood. Chemical mapping techniques, such as Hydroxyl Radical (·OH) footprinting report on local structural changes in an RNA as it folds with single nucleotide resolution. The analysis and interpretation of this kinetic data requires the identification and subsequent optimization of a kinetic model and its parameters. We detail our approach to this problem, specifically focusing on a novel strategy to overcome a factorial explosion in the number of possible models that need to be tested to identify the best fitting model. Previously, smaller systems (less than three intermediates) were computationally tractable using a distributed computing approach. However, for larger systems with three or more intermediates, the problem became computationally intractable. With our new enumeration strategy, we are able to significantly reduce the number of models that need to be tested using non-linear least squares optimization, allowing us to study systems with up to five intermediates. Furthermore, two intermediate systems can now be analyzed on a desktop computer, which eliminates the need for a distributed computing solution for most medium-sized data sets. Our new approach also allows us to study potential degeneracy in kinetic model selection, elucidating the limits of the method when working with large systems. This work establishes clear criteria for determining if experimental ·OH data is sufficient to determine the underlying kinetic model, or if other experimental modalities are required to resolve any degeneracy.