Single-molecule transition-state analysis of RNA folding

High-throughput determination of RNA tertiary contact thermodynamics by quantitative DMS chemical mapping

Structured RNAs often contain long-range tertiary contacts that are critical to their function. Despite the importance of tertiary contacts, methods to measure their thermodynamics are low throughput or require specialized instruments. Here, we introduce a new quantitative chemical mapping method (qMaPseq) to measure Mg2+-induced formation of tertiary contact thermodynamics in a high-throughput manner using standard biochemistry equipment. With qMaPseq, we measured the ΔG of 98 unique tetraloop/tetraloop receptor (TL/TLR) variants in a one-pot reaction. These results agree well with measurements from specialized instruments (R2= 0.64). Furthermore, the DMS reactivity of the TL directly correlates to the stability of the contact (R2= 0.68), the first direct evidence that a single DMS reactivity measurement reports on thermodynamics. Combined with structure prediction, DMS reactivity allowed the development of experimentally accurate 3D models of TLR mutants. These results demonstrate that qMaPseq is broadly accessible, high-throughput and directly links DMS reactivity to thermodynamics.

Effects of mRNA conformational switching on translational noise in gene circuits

Intragenic translational heterogeneity describes the variation in translation at the level of transcripts for an individual gene. A factor that contributes to this source of variation is the mRNA structure. Both the composition of the thermodynamic ensemble, i.e., the stationary distribution of mRNA structures, and the switching dynamics between those play a role. The effect of the switching dynamics on intragenic translational heterogeneity remains poorly understood. We present a stochastic translation model that accounts for mRNA structure switching and is derived from a Markov model via approximate stochastic filtering. We assess the approximation on various timescales and provide a method to quantify how mRNA structure dynamics contributes to translational heterogeneity. With our approach, we allow quantitative information on mRNA switching from biophysical experiments or coarse-grain molecular dynamics simulations of mRNA structures to be included in gene regulatory chemical reaction network models without an increase in the number of species. Thereby, our model bridges a gap between mRNA structure kinetics and gene expression models, which we hope will further improve our understanding of gene regulatory networks and facilitate genetic circuit design.

Single-molecule FRET observes opposing effects of urea and TMAO on structurally similar meso- and thermophilic riboswitch RNAs

Bacteria live in a broad range of environmental temperatures that require adaptations of their RNA sequences to maintain function. Riboswitches are regulatory RNAs that change conformation upon typically binding metabolite ligands to control bacterial gene expression. The paradigmatic small class-I preQ1 riboswitches from the mesophile Bacillus subtilis (Bsu) and the thermophile Thermoanaerobacter tengcongensis (Tte) adopt similar pseudoknot structures when bound to preQ1. Here, we use UV-melting analysis combined with single-molecule detected chemical denaturation by urea to compare the thermodynamic and kinetic folding properties of the two riboswitches, and the urea-countering effects of trimethylamine N-oxide (TMAO). Our results show that, first, the Tte riboswitch is more thermotolerant than the Bsu riboswitch, despite only subtle sequence differences. Second, using single-molecule FRET, we find that urea destabilizes the folded pseudoknot structure of both riboswitches, yet has a lower impact on the unfolding kinetics of the thermodynamically less stable Bsu riboswitch. Third, our analysis shows that TMAO counteracts urea denaturation and promotes folding of both the riboswitches, albeit with a smaller effect on the more stable Tte riboswitch. Together, these findings elucidate how subtle sequence adaptations in a thermophilic bacterium can stabilize a common RNA structure when a new ecological niche is conquered.

Elucidating the Self-cleavage Dynamics of Hairpin Ribozyme by Mode-decomposed Infrared Spectroscopy

While catalytic reactions of biomolecular processes play an indispensable role in life, extracting the underlying molecular picture often remains challenging. Based on ab initio simulations of the self-cleavage reaction of hairpin ribozyme, mode-decomposed infrared spectra, and cosine similarity analysis to correlate the product with reactant IR spectra, we demonstrate a strategy to extract molecular details from characteristic spectral changes. Our results are in almost quantitative agreement with the experimental IR band library of nucleic acids and suggest that the spectral range of 800-1200 cm-1 is particularly valuable to monitor self-cleavage. Importantly, the cosine similarities also disclose that IR peaks subject to slight shifts due to self-cleavage might be unrelated, while strongly shifting resonances can correspond to the same structural dynamics. This framework of correlating complex IR spectra at the molecular level along biocatalytic reaction pathways is broadly applicable.

An anionic ligand snap-locks a long-range interaction in a magnesium-folded riboswitch

The archetypical transcriptional crcB fluoride riboswitch from Bacillus cereus is an intricately structured non-coding RNA element enhancing gene expression in response to toxic levels of fluoride. Here, we used single molecule FRET to uncover three dynamically interconverting conformations appearing along the transcription process: two distinct undocked states and one pseudoknotted docked state. We find that the fluoride anion specifically snap-locks the magnesium-induced, dynamically docked state. The long-range, nesting, single base pair A40-U48 acts as the main linchpin, rather than the multiple base pairs comprising the pseudoknot. We observe that the proximally paused RNA polymerase further fine-tunes the free energy to promote riboswitch docking. Finally, we show that fluoride binding at short transcript lengths is an early step toward partitioning folding into the docked conformation. These results reveal how the anionic fluoride ion cooperates with the magnesium-associated RNA to govern regulation of downstream genes needed for fluoride detoxification of the cell.

Single-Molecular Förster Resonance Energy Transfer Measurement on Structures and Interactions of Biomolecules

Single-molecule Förster resonance energy transfer (smFRET) inherits the strategy of measurement from the effective "spectroscopic ruler" FRET and can be utilized to observe molecular behaviors with relatively high throughput at nanometer scale. The simplicity in principle and configuration of smFRET make it easy to apply and couple with other technologies to comprehensively understand single-molecule dynamics in various application scenarios. Despite its widespread application, smFRET is continuously developing and novel studies based on the advanced platforms have been done. Here, we summarize some representative examples of smFRET research of recent years to exhibit the versatility and note typical strategies to further improve the performance of smFRET measurement on different biomolecules.

Mg2+ Sensing by an RNA Fragment: Role of Mg2+-Coordinated Water Molecules

RNA molecules selectively bind to specific metal ions to populate their functional active states, making it important to understand their source of ion selectivity. In large RNA systems, metal ions interact with the RNA at multiple locations, making it difficult to decipher the precise role of ions in folding. To overcome this complexity, we studied the role of different metal ions (Mg²⁺, Ca²⁺, and K⁺) in the folding of a small RNA hairpin motif (5'-ucCAAAga-3') using unbiased all-atom molecular dynamics simulations. The advantage of studying this system is that it requires specific binding of a single metal ion to fold to its native state. We find that even for this small RNA, the folding free energy surface (FES) is multidimensional as different metal ions present in the solution can simultaneously facilitate folding. The FES shows that specific binding of a metal ion is indispensable for its folding. We further show that in addition to the negatively charged phosphate groups, the spatial organization of electronegative nucleobase atoms drives the site-specific binding of the metal ions. Even though the binding site cannot discriminate between different metal ions, RNA folds efficiently only in a Mg²⁺ solution. We show that the rigid network of Mg²⁺-coordinated water molecules facilitates the formation of important interactions in the transition state. The other metal ions such as K⁺ and Ca²⁺ cannot facilitate the formation of such interactions. These results allow us to hypothesize possible metal-sensing mechanisms in large metalloriboswitches and also provide useful insights into the design of appropriate collective variables for studying large RNA molecules using enhanced sampling methods.

Site-Selective RNA Functionalization via DNA-Induced Structure

Methods for RNA functionalization at specific sites are in high demand but remain a challenge, particularly for RNAs produced by transcription rather than by total synthesis. Recent studies have described acylimidazole reagents that react in high yields at 2'-OH groups stochastically at nonbase-paired regions, covering much of the RNA in scattered acyl esters. Localized reactions, if possible, could prove useful in many applications, providing functional handles at specific sites and sequences of the biopolymer. Here, we describe a DNA-directed strategy for in vitro functionalization of RNA at site-localized 2'-OH groups. The method, RNA Acylation at Induced Loops (RAIL), utilizes complementary helper DNA oligonucleotides that expose gaps or loops at selected positions while protecting the remainder in DNA-RNA duplexes. Reaction with an acylimidazole reagent is then carried out, providing high yields of 2'-OH conjugation at predetermined sites. Experiments reveal optimal helper oligodeoxynucleotide designs and conditions for the reaction, and tests of the approach are carried out to control localized ribozyme activities and to label RNAs with dual-color fluorescent dyes. The RAIL approach offers a simple and novel strategy for site-selective labeling and control of RNAs, potentially of any length and origin.

Salt effect on thermodynamics and kinetics of a single RNA base pair

Due to the polyanionic nature of RNAs, the structural folding of RNAs are sensitive to solution salt conditions, while there is still lack of a deep understanding of the salt effect on the thermodynamics and kinetics of RNAs at a single base-pair level. In this work, the thermodynamic and the kinetic parameters for the base-pair AU closing/opening at different salt concentrations were calculated by 3-µsec all-atom molecular dynamics (MD) simulations at different temperatures. It was found that for the base-pair formation, the enthalpy change [Formula: see text] is nearly independent of salt concentration, while the entropy change [Formula: see text] exhibits a linear dependence on the logarithm of salt concentration, verifying the empirical assumption based on thermodynamic experiments. Our analyses revealed that such salt concentration dependence of the entropy change mainly results from the dependence of ion translational entropy change for the base pair closing/opening on salt concentration. Furthermore, the closing rate increases with the increasing of salt concentration, while the opening rate is nearly independent of salt concentration. Additionally, our analyses revealed that the free energy surface for describing the base-pair opening and closing dynamics becomes more rugged with the decrease of salt concentration.

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.

Mechanistic role of nucleobases in self-cleavage catalysis of hairpin ribozyme at ambient versus high-pressure conditions

Ribozymes catalyze the site-specific self-cleavage of intramolecular phosphodiester bonds. Initially thought to act as metalloenzymes, they are now known to be functional even in the absence of divalent metal ions and specific nucleobases directly participate in the self-cleavage reaction. Here, we use extensive replica exchange molecular dynamics simulations to probe the precise mechanistic role of nucleobases by simulating precatalytic reactant and active precursor states of a hairpin ribozyme along its reaction path at ambient as well as high-pressure conditions. The results provide novel key insights into the self-cleavage of ribozymes. We find that deprotonation of the hydroxyl group is crucial and might be the penultimate step to the self-cleavage. The G8 nucleobase is found to stabilize the activated precursor into inline arrangement for facile nucleophilic attack of the scissile phosphate only after deprotonation of the hydroxyl group. The protonated A38 nucleobase, in contrast, mainly acts a proton donor to the O5'-oxygen leaving group that eventually leads to the self-cleavage. Indeed, systematic high-pressure simulations of catalytically relevant states confirm these findings and, moreover, provide support to the role of ribozymes as piezophilic biocatalysts with regard to their relevance in early life under extreme conditions in the realm of RNA world hypothesis.

Detection of Mg2+-dependent, coaxial stacking rearrangements in a bulged three-way DNA junction by single-molecule FRET

Three-way helical junctions (3WJs) arise in genetic processing, and they have architectural and functional roles in structured nucleic acids. An internal bulge at the junction core allows the helical domains to become oriented into two possible, coaxially stacked conformers. Here, the helical stacking arrangements for a series of bulged, DNA 3WJs were examined using ensemble fluorescence resonance energy transfer (FRET) and single-molecule FRET (smFRET) approaches. The 3WJs varied according to the GC content and sequence of the junction core as well as the pyrimidine content of the internal bulge. Mg²⁺ titration experiments by ensemble FRET show that both stacking conformations have similar Mg²⁺ requirements for folding. Strikingly, smFRET experiments reveal that a specific junction sequence can populate both conformers and that this junction undergoes continual interconversion between the two stacked conformers. These findings will support the development of folding principles for the rational design of functional DNA nanostructures.

Sequence-Dependent Effects of Monovalent Cations on the Structural Dynamics of Trinucleotide-Repeat DNA Hairpins

Repetitive trinucleotide DNA sequences at specific genetic loci are associated with numerous hereditary, neurodegenerative diseases. The propensity of single-stranded domains containing these sequences to form secondary structure via extensive self-complementarity disrupts normal DNA processing to create genetic instabilities. To investigate these intrastrand structural dynamics, a DNA hairpin system was devised for single-molecule fluorescence study of the folding kinetics and energetics for secondary structure formation between two interacting, repetitive domains with specific numbers of the same trinucleotide motif (CXG), where X = T or A. Single-molecule fluorescence resonance energy transfer (smFRET) data show discrete conformational transitions between unstructured and closed hairpin states. The lifetimes of the closed hairpin states correlate with the number of repeats, with (CTG) _N/(CTG) _N domains maintaining longer-lived, closed states than equivalent-sized (CAG) _N/(CAG) _N domains. NaCl promotes similar degree of stabilization for the closed hairpin states of both repeat sequences. Temperature-based, smFRET experiments reveal that NaCl favors hairpin closing for (CAG) _N/(CAG) _N by preordering single-stranded repeat domains to accelerate the closing transition. In contrast, NaCl slows the opening transition of CTG hairpins; however, it promotes misfolded conformations that require unfolding. Energy diagrams illustrate the distinct folding pathways of (CTG) _N and (CAG) _N repeat domains and identify features that may contribute to their gene-destabilizing effects.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding

The real-time search for native RNA structure is essential for the operation of regulatory RNAs. We previously reported that a fraction of the Azoarcus ribozyme achieves a compact structure in less than a millisecond. To scrutinize the forces that drive initial folding steps, we used time-resolved SAXS to compare the folding dynamics of this ribozyme in thermodynamically isostable concentrations of different counterions. The results show that the size of the fast-folding population increases with the number of available counterions and correlates with the flexibility of initial RNA structures. Within 1 ms of folding, Mg²⁺ exhibits a smaller preferential interaction coefficient per charge, ΔΓ₊/ Z, than Na⁺ or [Co(NH₃)₆]³⁺. The lower ΔΓ₊/ Z corresponds to a smaller yield of folded RNA, although Mg²⁺ stabilizes native RNA more efficiently than other ions at equilibrium. These results suggest that strong Mg²⁺-RNA interactions impede the search for globally native structure during early folding stages.

Single-Molecule Fluorescence Reveals Commonalities and Distinctions among Natural and in Vitro-Selected RNA Tertiary Motifs in a Multistep Folding Pathway

Decades of study of the RNA folding problem have revealed that diverse and complex structured RNAs are built from a common set of recurring structural motifs, leading to the perspective that a generalizable model of RNA folding may be developed from understanding of the folding properties of individual structural motifs. We used single-molecule fluorescence to dissect the kinetic and thermodynamic properties of a set of variants of a common tertiary structural motif, the tetraloop/tetraloop-receptor (TL/TLR). Our results revealed a multistep TL/TLR folding pathway in which preorganization of the ubiquitous AA-platform submotif precedes the formation of the docking transition state and tertiary A-minor hydrogen bond interactions form after the docking transition state. Differences in ion dependences between TL/TLR variants indicated the occurrence of sequence-dependent conformational rearrangements prior to and after the formation of the docking transition state. Nevertheless, varying the junction connecting the TL/TLR produced a common kinetic and ionic effect for all variants, suggesting that the global conformational search and compaction electrostatics are energetically independent from the formation of the tertiary motif contacts. We also found that in vitro-selected variants, despite their similar stability at high Mg²⁺ concentrations, are considerably less stable than natural variants under near-physiological ionic conditions, and the occurrence of the TL/TLR sequence variants in Nature correlates with their thermodynamic stability in isolation. Overall, our findings are consistent with modular but complex energetic properties of RNA structural motifs and will aid in the eventual quantitative description of RNA folding from its secondary and tertiary structural elements.

Biophysical Insights from Temperature-Dependent Single-Molecule Förster Resonance Energy Transfer

Single-molecule fluorescence microscopy techniques can be used in combination with micrometer length-scale temperature control and Förster resonance energy transfer (FRET) in order to gain detailed information about fundamental biophysical phenomena. In particular, this combination of techniques has helped foster the development of remarkable quantitative tools for studying both time- and temperature-dependent structural kinetics of biopolymers. Over the past decade, multiple research efforts have successfully incorporated precise spatial and temporal control of temperature into single-molecule FRET (smFRET)-based experiments, which have uncovered critical thermodynamic information on a wide range of biological systems such as conformational dynamics of nucleic acids. This review provides an overview of various temperature-dependent smFRET approaches from our laboratory and others, highlighting efforts in which such methods have been successfully applied to studies of single-molecule nucleic acid folding.

Soft Interactions with Model Crowders and Non-canonical Interactions with Cellular Proteins Stabilize RNA Folding

Living cells contain diverse biopolymers, creating a heterogeneous crowding environment, the impact of which on RNA folding is poorly understood. Here, we have used single-molecule fluorescence resonance energy transfer to monitor tertiary structure formation of the hairpin ribozyme as a model to probe the effects of polyethylene glycol and yeast cell extract as crowding agents. As expected, polyethylene glycol stabilizes the docked, catalytically active state of the ribozyme, in part through excluded volume effects; unexpectedly, we found evidence that it additionally displays soft, non-specific interactions with the ribozyme. Yeast extract has a profound effect on folding at protein concentrations 1000-fold lower than found intracellularly, suggesting the dominance of specific interactions over volume exclusion. Gel shift assays and affinity pull-down followed by mass spectrometry identified numerous non-canonical RNA-binding proteins that stabilize ribozyme folding; the apparent chaperoning activity of these ubiquitous proteins significantly compensates for the low-counterion environment of the cell.

Thermodynamics and kinetics of RNA tertiary structure formation in the junctionless hairpin ribozyme

The hairpin ribozyme consists of two RNA internal loops that interact to form the catalytically active structure. This docking transition is a rare example of intermolecular formation of RNA tertiary structure without coupling to helix annealing. We have used temperature-dependent surface plasmon resonance (SPR) to characterize the thermodynamics and kinetics of RNA tertiary structure formation for the junctionless form of the ribozyme, in which loops A and B reside on separate molecules. We find docking to be strongly enthalpy-driven and to be accompanied by substantial activation barriers for association and dissociation, consistent with the structural reorganization of both internal loops upon complex formation. Comparisons with the parallel analysis of a ribozyme variant carrying a 2'-O-methyl modification at the self-cleavage site and with published data in other systems reveal a surprising diversity of thermodynamic signatures, emphasizing the delicate balance of contributions to the free energy of formation of RNA tertiary structure.

Metals induce transient folding and activation of the twister ribozyme

Twister is a small ribozyme present in almost all kingdoms of life that rapidly self-cleaves in variety of divalent metal ions. We used activity assays, bulk FRET and single-molecule FRET (smFRET) to understand how different metal ions promote folding and self-cleavage of the Oryza sativa Twister ribozyme. Although most ribozymes require additional Mg²⁺ for catalysis, Twister inverts this expectation, requiring 20–30 times less Mg²⁺ to self-cleave than to fold. Transition metals such as Co²⁺, Ni²⁺ and Zn²⁺ activate Twister more efficiently than Mg²⁺ ions. Although Twister is fully active in ≤ 0.5 mM MgCl₂, smFRET experiments showed that the ribozyme visits the folded state infrequently under these conditions. Comparison of folding and self-cleavage rates indicates that most folding events lead to catalysis, which correlates with metal bond strength. Thus, the robust activity of Twister reports on transient metal ion binding under physiological conditions.

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces.

Pressure modulates the self-cleavage step of the hairpin ribozyme

The ability of certain RNAs, denoted as ribozymes, to not only store genetic information but also catalyse chemical reactions gave support to the RNA world hypothesis as a putative step in the development of early life on Earth. This, however, might have evolved under extreme environmental conditions, including the deep sea with pressures in the kbar regime. Here we study pressure-induced effects on the self-cleavage of hairpin ribozyme by following structural changes in real-time. Our results suggest that compression of the ribozyme leads to an accelerated transesterification reaction, being the self-cleavage step, although the overall process is retarded in the high-pressure regime. The results reveal that favourable interactions between the reaction site and neighbouring nucleobases are strengthened under pressure, resulting therefore in an accelerated self-cleavage step upon compression. These results suggest that properly engineered ribozymes may also act as piezophilic biocatalysts in addition to their hitherto known properties.

Intrinsic Base-Pair Rearrangement in the Hairpin Ribozyme Directs RNA Conformational Sampling and Tertiary Interface Formation

Dynamic fluctuations in RNA structure enable conformational changes that are required for catalysis and recognition. In the hairpin ribozyme, the catalytically active structure is formed as an intricate tertiary interface between two RNA internal loops. Substantial alterations in the structure of each loop are observed upon interface formation, or docking. The very slow on-rate for this relatively tight interaction has led us to hypothesize a double conformational capture mechanism for RNA-RNA recognition. We used extensive molecular dynamics simulations to assess conformational sampling in the undocked form of the loop domain containing the scissile phosphate (loop A). We observed several major accessible conformations with distinctive patterns of hydrogen bonding and base stacking interactions in the active-site internal loop. Several important conformational features characteristic of the docked state were observed in well-populated substates, consistent with the kinetic sampling of docking-competent states by isolated loop A. Our observations suggest a hybrid or multistage binding mechanism, in which initial conformational selection of a docking-competent state is followed by induced-fit adjustment to an in-line, chemically reactive state only after formation of the initial complex with loop B.

Amino Acid Specific Effects on RNA Tertiary Interactions: Single-Molecule Kinetic and Thermodynamic Studies

In light of the current models for an early RNA-based universe, the potential influence of simple amino acids on tertiary folding of ribozymal RNA into biochemically competent structures is speculated to be of significant evolutionary importance. In the present work, the folding-unfolding kinetics of a ubiquitous tertiary interaction motif, the GAAA tetraloop-tetraloop receptor (TL-TLR), is investigated by single-molecule fluorescence resonance energy transfer spectroscopy in the presence of natural amino acids both with (e.g., lysine, arginine) and without (e.g., glycine) protonated side chain residues. By way of control, we also investigate the effects of a special amino acid (e.g., proline) and amino acid mimetic (e.g., betaine) that contain secondary or quaternary amine groups rather than a primary amine group. This combination permits systematic study of amino acid induced (or amino acid like) RNA folding dynamics as a function of side chain complexity, pK_a, charge state, and amine group content. Most importantly, each of the naturally occurring amino acids is found to destabilize the TL-TLR tertiary folding equilibrium, the kinetic origin of which is dominated by a decrease in the folding rate constant (k_dock), also affected by a strongly amino acid selective increase in the unfolding rate constant (k_undock). To further elucidate the underlying thermodynamics, single-molecule equilibrium constants (K_eq) for TL-TLR folding have been probed as a function of temperature, which reveal an amino acid dependent decrease in both overall exothermicity (ΔΔH° > 0) and entropic cost (-TΔΔS° < 0) for the overall folding process. Temperature-dependent studies on the folding/unfolding kinetic rate constants reveal analogous amino acid specific changes in both enthalpy (ΔΔH^⧧) and entropy (ΔΔS^⧧) for accessing the transition state barrier. The maximum destabilization of the TL-TLR tertiary interaction is observed for arginine, which is consistent with early studies of arginine and guanidine ion-inhibited self-splicing kinetics for the full Tetrahymena ribozyme [ Yarus , M. ; Christian , E. L. Nature 1989 , 342 , 349 - 350 ; Yarus , M. Science 1988 , 240 , 1751 - 1758 ].

Single-Molecule FRET Reveals Three Conformations for the TLS Domain of Brome Mosaic Virus Genome

Metabolite-dependent conformational switching in RNA riboswitches is now widely accepted as a critical regulatory mechanism for gene expression in bacterial systems. More recently, similar gene regulation mechanisms have been found to be important for viral systems as well. One of the most abundant and best-studied systems is the tRNA-like structure (TLS) domain, which has been found to occur in many plant viruses spread across numerous genera. In this work, folding dynamics for the TLS domain of Brome Mosaic Virus have been investigated using single-molecule fluorescence resonance energy transfer techniques. In particular, burst fluorescence methods are exploited to observe metal-ion ([M(n+)])-induced folding in freely diffusing RNA constructs resembling the minimal TLS element of brome mosaic virus RNA3. The results of these experiments reveal a complex equilibrium of at least three distinct populations. A stepwise, or consecutive, thermodynamic model for TLS folding is developed, which is in good agreement with the [M(n+)]-dependent evolution of conformational populations and existing structural information in the literature. Specifically, this folding pathway explains the metal-ion dependent formation of a functional TLS domain from unfolded RNAs via two consecutive steps: 1) hybridization of a long-range stem interaction, followed by 2) formation of a 3'-terminal pseudoknot. These two conformational transitions are well described by stepwise dissociation constants for [Mg(2+)] (K1 = 328 ± 30 μM and K2 = 1092 ± 183 μM) and [Na(+)] (K1 = 74 ± 6 mM and K2 = 243 ± 52 mM)-induced folding. The proposed thermodynamic model is further supported by inhibition studies of the long-range stem interaction using a complementary DNA oligomer, which effectively shifts the dynamic equilibrium toward the unfolded conformation. Implications of this multistep conformational folding mechanism are discussed with regard to regulation of virus replication.

Mg(2+) shifts ligand-mediated folding of a riboswitch from induced-fit to conformational selection

Bacterial riboswitches couple small-molecule ligand binding to RNA conformational changes that widely regulate gene expression, rendering them potential targets for antibiotic intervention. Despite structural insights, the ligand-mediated folding mechanisms of riboswitches are still poorly understood. Using single-molecule fluorescence resonance energy transfer (smFRET), we have investigated the folding mechanism of an H-type pseudoknotted preQ1 riboswitch in dependence of Mg(2+) and three ligands of distinct affinities. We show that, in the absence of Mg(2+), both weakly and strongly bound ligands promote pseudoknot docking through an induced-fit mechanism. By contrast, addition of as low as 10 μM Mg(2+) generally shifts docking toward conformational selection by stabilizing a folded-like conformation prior to ligand binding. Supporting evidence from transition-state analysis further highlights the particular importance of stacking interactions during induced-fit and of specific hydrogen bonds during conformational selection. Our mechanistic dissection provides unprecedented insights into the intricate synergy between ligand- and Mg(2+)-mediated RNA folding.

Using sm-FRET and denaturants to reveal folding landscapes

RNA folding studies aim to clarify the relationship among sequence, tridimensional structure, and biological function. In the last decade, the application of single-molecule fluorescence resonance energy transfer (sm-FRET) techniques to investigate RNA structure and folding has revealed the details of conformational changes and timescale of the process leading to the formation of biologically active RNA structures with subnanometer resolution on millisecond timescales. In this review, we initially summarize the first wave of single-molecule FRET-based RNA techniques that focused on analyzing the influence of mono- and divalent metal ions on RNA function, and how these studies have provided very valuable information about folding pathways and the presence of intermediate and low-populated states. Next, we describe a second generation of single-molecule techniques that combine sm-FRET with the use of chemical denaturants as an emerging powerful approach to reveal information about the dynamics and energetics of RNA folding that remains hidden using conventional sm-FRET approaches. The main advantages of using the competing interplay between folding agents such as metal ions and denaturants to observe and manipulate the dynamics of RNA folding and RNA-ligand interactions is discussed in the context of the adenine riboswitch aptamer.

Native purification and labeling of RNA for single molecule fluorescence studies

The recent discovery that non-coding RNAs are considerably more abundant and serve a much wider range of critical cellular functions than recognized over previous decades of research into molecular biology has sparked a renewed interest in the study of structure-function relationships of RNA. To perform their functions in the cell, RNAs must dominantly adopt their native conformations, avoiding deep, non-productive kinetic traps that may exist along a frustrated (rugged) folding free energy landscape. Intracellularly, RNAs are synthesized by RNA polymerase and fold co-transcriptionally starting from the 5' end, sometimes with the aid of protein chaperones. By contrast, in the laboratory RNAs are commonly generated by in vitro transcription or chemical synthesis, followed by purification in a manner that includes the use of high concentrations of urea, heat and UV light (for detection), resulting in the denaturation and subsequent refolding of the entire RNA. Recent studies into the nature of heterogeneous RNA populations resulting from this process have underscored the need for non-denaturing (native) purification methods that maintain the co-transcriptional fold of an RNA. Here, we present protocols for the native purification of an RNA after its in vitro transcription and for fluorophore and biotin labeling methods designed to preserve its native conformation for use in single molecule fluorescence resonance energy transfer (smFRET) inquiries into its structure and function. Finally, we present methods for taking smFRET data and for analyzing them, as well as a description of plausible overall preparation schemes for the plethora of non-coding RNAs.

Paradigms of ribosome synthesis: Lessons learned from ribosomal proteins

The proteome in all cells is manufactured via the intricate process of translation by multimolecular factories called ribosomes. Nevertheless, these ribonucleoprotein particles, the largest of their kind, also have an elaborate assembly line of their own. Groundbreaking discoveries that bacterial ribosomal subunits can be self-assembled in vitro jumpstarted studies on how ribosomes are constructed. Until recently, ribosome assembly has been investigated almost entirely in vitro with bacterial small subunits under equilibrium conditions. In light of high-resolution ribosome structures and a more sophisticated toolkit, the past decade has been defined by a burst of kinetic studies in vitro and, importantly, also a shift to examining ribosome maturation in living cells, especially in eukaryotes. In this review, we summarize the principles governing ribosome assembly that emerged from studies focusing on ribosomal proteins and their interactions with rRNA. Understanding these paradigms has taken center stage, given the linkage between anomalous ribosome biogenesis and proliferative disorders.

Molecular crowding accelerates ribozyme docking and catalysis

All biological processes take place in highly crowded cellular environments. However, the effect that molecular crowding agents have on the folding and catalytic properties of RNA molecules remains largely unknown. Here, we have combined single-molecule fluorescence resonance energy transfer (smFRET) and bulk cleavage assays to determine the effect of a molecular crowding agents on the folding and catalysis of a model RNA enzyme, the hairpin ribozyme. Our single-molecule data reveal that PEG favors the formation of the docked (active) structure by increasing the docking rate constant with increasing PEG concentrations. Furthermore, Mg²⁺ ion-induced folding in the presence of PEG occurs at concentrations ∼7-fold lower than in the absence of PEG, near the physiological range (∼1 mM). Lastly, bulk cleavage assays in the presence of the crowding agent show that the ribozyme’s activity increases while the heterogeneity decreases. Our data is consistent with the idea that molecular crowding plays an important role in the stabilization of ribozyme active conformations in vivo.

Single-molecule tools for enzymology, structural biology, systems biology and nanotechnology: an update

Toxicology is the highly interdisciplinary field studying the adverse effects of chemicals on living organisms. It requires sensitive tools to detect such effects. After their initial implementation during the 1990s, single-molecule fluorescence detection tools were quickly recognized for their potential to contribute greatly to many different areas of scientific inquiry. In the intervening time, technical advances in the field have generated ever-improving spatial and temporal resolution and have enabled the application of single-molecule fluorescence to increasingly complex systems, such as live cells. In this review, we give an overview of the optical components necessary to implement the most common versions of single-molecule fluorescence detection. We then discuss current applications to enzymology and structural studies, systems biology, and nanotechnology, presenting the technical considerations that are unique to each area of study, along with noteworthy recent results. We also highlight future directions that have the potential to revolutionize these areas of study by further exploiting the capabilities of single-molecule fluorescence microscopy.

Probing protein multidimensional conformational fluctuations by single-molecule multiparameter photon stamping spectroscopy

Conformational motions of proteins are highly dynamic and intrinsically complex. To capture the temporal and spatial complexity of conformational motions and further to understand their roles in protein functions, an attempt is made to probe multidimensional conformational dynamics of proteins besides the typical one-dimensional FRET coordinate or the projected conformational motions on the one-dimensional FRET coordinate. T4 lysozyme hinge-bending motions between two domains along α-helix have been probed by single-molecule FRET. Nevertheless, the domain motions of T4 lysozyme are rather complex involving multiple coupled nuclear coordinates and most likely contain motions besides hinge-bending. It is highly likely that the multiple dimensional protein conformational motions beyond the typical enzymatic hinged-bending motions have profound impact on overall enzymatic functions. In this report, we have developed a single-molecule multiparameter photon stamping spectroscopy integrating fluorescence anisotropy, FRET, and fluorescence lifetime. This spectroscopic approach enables simultaneous observations of both FRET-related site-to-site conformational dynamics and molecular rotational (or orientational) motions of individual Cy3-Cy5 labeled T4 lysozyme molecules. We have further observed wide-distributed rotational flexibility along orientation coordinates by recording fluorescence anisotropy and simultaneously identified multiple intermediate conformational states along FRET coordinate by monitoring time-dependent donor lifetime, presenting a whole picture of multidimensional conformational dynamics in the process of T4 lysozyme open-close hinge-bending enzymatic turnover motions under enzymatic reaction conditions. By analyzing the autocorrelation functions of both lifetime and anisotropy trajectories, we have also observed the dynamic and static inhomogeneity of T4 lysozyme multidimensional conformational fluctuation dynamics, providing a fundamental understanding of the enzymatic reaction turnover dynamics associated with overall enzyme as well as the specific active-site conformational fluctuations that are not identifiable and resolvable in the conventional ensemble-averaged experiment.

Different fluorophore labeling strategies and designs affect millisecond kinetics of DNA hairpins

Changes in molecular conformations are one of the major driving forces of complex biological processes. Many studies based on single-molecule techniques have shed light on conformational dynamics and contributed to a better understanding of living matter. In particular, single-molecule FRET experiments have revealed unprecedented information at various time scales varying from milliseconds to seconds. The choice and the attachment of fluorophores is a pivotal requirement for single-molecule FRET experiments. One particularly well-studied millisecond conformational change is the opening and closing of DNA hairpin structures. In this study, we addressed the influence of base- and terminal-labeled fluorophores as well as the fluorophore DNA interactions on the extracted kinetic information of the DNA hairpin. Gibbs free energies varied from ∆G⁰ = −3.6 kJ/mol to ∆G⁰ = −0.2 kJ/mol for the identical DNA hairpin modifying only the labeling scheme and design of the DNA sample. In general, the base-labeled DNA hairpin is significantly destabilized compared to the terminal-labeled DNA hairpin and fluorophore DNA interactions additionally stabilize the closed state of the DNA hairpin. Careful controls and variations of fluorophore attachment chemistry are essential for a mostly undisturbed measurement of the underlying energy landscape of biomolecules.

Fluorescence tools to investigate riboswitch structural dynamics

Riboswitches are novel regulatory elements that respond to cellular metabolites to control gene expression. They are constituted of highly conserved domains that have evolved to recognize specific metabolites. Such domains, so-called aptamers, are folded into intricate structures to enable metabolite recognition. Over the years, the development of ensemble and single-molecule fluorescence techniques has allowed to probe most of the mechanistic aspects of aptamer folding and ligand binding. In this review, we summarize the current fluorescence toolkit available to study riboswitch structural dynamics. We fist describe those methods based on fluorescent nucleotide analogues, mostly 2-aminopurine (2AP), to investigate short-range conformational changes, including some key steady-state and time-resolved examples that exemplify the versatility of fluorescent analogues as structural probes. The study of long-range structural changes by Förster resonance energy transfer (FRET) is mostly discussed in the context of single-molecule studies, including some recent developments based on the combination of single-molecule FRET techniques with controlled chemical denaturation methods. This article is part of a Special Issue entitled: Riboswitches.

A hierarchical model for assembly of eukaryotic 60S ribosomal subunit domains

Despite having structures for eukaryotic large ribosomal subunits, it has been unclear how these ribonucleoprotein complexes are constructed in living cells. Here, Gamalinda et al. used proteomics to assay changes in the levels of ribosomal protein and assembly factors in preribosomes upon depletion of ribosomal proteins that function in 60S assembly. The results show that the eukaryotic 60S ribosomal subunits are assembled in a hierarchical fashion. This study further reveals striking differences and similarities between bacterial and eukaryotic large ribosomal subunits, providing insights into the evolution of RNA–protein particles.

Despite having high-resolution structures for eukaryotic large ribosomal subunits, it remained unclear how these ribonucleoprotein complexes are constructed in living cells. Nevertheless, knowing where ribosomal proteins interact with ribosomal RNA (rRNA) provides a strategic platform to investigate the connection between spatial and temporal aspects of 60S subunit biogenesis. We previously found that the function of individual yeast large subunit ribosomal proteins (RPLs) in precursor rRNA (pre-rRNA) processing correlates with their location in the structure of mature 60S subunits. This observation suggested that there is an order by which 60S subunits are formed. To test this model, we used proteomic approaches to assay changes in the levels of ribosomal proteins and assembly factors in preribosomes when RPLs functioning in early, middle, and late steps of pre-60S assembly are depleted. Our results demonstrate that structural domains of eukaryotic 60S ribosomal subunits are formed in a hierarchical fashion. Assembly begins at the convex solvent side, followed by the polypeptide exit tunnel, the intersubunit side, and finally the central protuberance. This model provides an initial paradigm for the sequential assembly of eukaryotic 60S subunits. Our results reveal striking differences and similarities between assembly of bacterial and eukaryotic large ribosomal subunits, providing insights into how these RNA–protein particles evolved.

BOBA FRET: bootstrap-based analysis of single-molecule FRET data

Time-binned single-molecule Förster resonance energy transfer (smFRET) experiments with surface-tethered nucleic acids or proteins permit to follow folding and catalysis of single molecules in real-time. Due to the intrinsically low signal-to-noise ratio (SNR) in smFRET time traces, research over the past years has focused on the development of new methods to extract discrete states (conformations) from noisy data. However, limited observation time typically leads to pronounced cross-sample variability, i.e., single molecules display differences in the relative population of states and the corresponding conversion rates. Quantification of cross-sample variability is necessary to perform statistical testing in order to assess whether changes observed in response to an experimental parameter (metal ion concentration, the presence of a ligand, etc.) are significant. However, such hypothesis testing has been disregarded to date, precluding robust biological interpretation. Here, we address this problem by a bootstrap-based approach to estimate the experimental variability. Simulated time traces are presented to assess the robustness of the algorithm in conjunction with approaches commonly used in thermodynamic and kinetic analysis of time-binned smFRET data. Furthermore, a pair of functionally important sequences derived from the self-cleaving group II intron Sc.ai5γ (d3'EBS1*/IBS1*) is used as a model system. Through statistical hypothesis testing, divalent metal ions are shown to have a statistically significant effect on both thermodynamic and kinetic aspects of their interaction. The Matlab source code used for analysis (bootstrap-based analysis of smFRET data, BOBA FRET), as well as a graphical user interface, is available via http://www.aci.uzh.ch/rna/.

An RNA folding motif: GNRA tetraloop-receptor interactions

Nearly two decades after Westhof and Michel first proposed that RNA tetraloops may interact with distal helices, tetraloop–receptor interactions have been recognized as ubiquitous elements of RNA tertiary structure. The unique architecture of GNRA tetraloops (N=any nucleotide, R=purine) enables interaction with a variety of receptors, e.g., helical minor grooves and asymmetric internal loops. The most common example of the latter is the GAAA tetraloop–11 nt tetraloop receptor motif. Biophysical characterization of this motif provided evidence for the modularity of RNA structure, with applications spanning improved crystallization methods to RNA tectonics. In this review, we identify and compare types of GNRA tetraloop–receptor interactions. Then we explore the abundance of structural, kinetic, and thermodynamic information on the frequently occurring and most widely studied GAAA tetraloop–11 nt receptor motif. Studies of this interaction have revealed powerful paradigms for structural assembly of RNA, as well as providing new insights into the roles of cations, transition states and protein chaperones in RNA folding pathways. However, further research will clearly be necessary to characterize other tetraloop–receptor and long-range tertiary binding interactions in detail – an important milestone in the quantitative prediction of free energy landscapes for RNA folding.

Single-molecule chemical denaturation of riboswitches

To date, single-molecule RNA science has been developed almost exclusively around the effect of metal ions as folding promoters and stabilizers of the RNA structure. Here, we introduce a novel strategy that combines single-molecule Förster resonance energy transfer (FRET) and chemical denaturation to observe and manipulate RNA dynamics. We demonstrate that the competing interplay between metal ions and denaturant agents provides a platform to extract information that otherwise will remain hidden with current methods. Using the adenine-sensing riboswitch aptamer as a model, we provide strong evidence for a rate-limiting folding step of the aptamer domain being modulated through ligand binding, a feature that is important for regulation of the controlled gene. In the absence of ligand, the rate-determining step is dominated by the formation of long-range key tertiary contacts between peripheral stem-loop elements. In contrast, when the adenine ligand interacts with partially folded messenger RNAs, the aptamer requires specifically bound Mg²⁺ ions, as those observed in the crystal structure, to progress further towards the native form. Moreover, despite that the ligand-free and ligand-bound states are indistinguishable by FRET, their different stability against urea-induced denaturation allowed us to discriminate them, even when they coexist within a single FRET trajectory; a feature not accessible by existing methods.

Intermolecular domain docking in the hairpin ribozyme: metal dependence, binding kinetics and catalysis

The hairpin ribozyme is a prototype small, self-cleaving RNA motif. It exists naturally as a four-way RNA junction containing two internal loops on adjoining arms. These two loops interact in a cation-driven docking step prior to chemical catalysis to form a tightly integrated structure, with dramatic changes occurring in the conformation of each loop upon docking. We investigate the thermodynamics and kinetics of the docking process using constructs in which loop A and loop B reside on separate molecules. Using a novel CD difference assay to isolate the effects of metal ions linked to domain docking, we find the intermolecular docking process to be driven by sub-millimolar concentrations of the exchange-inert Co(NH₃)₆³⁺. RNA self-cleavage requires binding of lower-affinity ions with greater apparent cooperativity than the docking process itself, implying that, even in the absence of direct coordination to RNA, metal ions play a catalytic role in hairpin ribozyme function beyond simply driving loop-loop docking. Surface plasmon resonance assays reveal remarkably slow molecular association, given the relatively tight loop-loop interaction. This observation is consistent with a “double conformational capture” model in which only collisions between loop A and loop B molecules that are simultaneously in minor, docking-competent conformations are productive for binding.

General acid-base catalysis mediated by nucleobases in the hairpin ribozyme

The catalytic mechanism by which the hairpin ribozyme accelerates cleavage or ligation of the phosphodiester backbone of RNA has been incompletely understood. There is experimental evidence for an important role for an adenine (A38) and a guanine (G8), and it has been proposed that these act in general acid-base catalysis. In this work we show that a large reduction in cleavage rate on substitution of A38 by purine (A38P) can be reversed by replacement of the 5'-oxygen atom at the scissile phosphate by sulfur (5'-PS), which is a much better leaving group. This is consistent with A38 acting as the general acid in the unmodified ribozyme. The rate of cleavage of the 5'-PS substrate by the A38P ribozyme increases with pH log-linearly, indicative of a requirement for a deprotonated base with a relatively high pK(a). On substitution of G8 by diaminopurine, the 5'-PS substrate cleavage rate at first increases with pH and then remains at a plateau, exhibiting an apparent pK(a) consistent with this nucleotide acting in general base catalysis. Alternative explanations for the pH dependence of hairpin ribozyme reactivity are discussed, from which we conclude that general acid-base catalysis by A38 and G8 is the simplest and most probable explanation consistent with all the experimental data.

Kinetic mechanism of conformational switch between bistable RNA hairpins

Transitions between the different conformational states play a critical role in many RNA catalytic and regulatory functions. In this study, we use the Kinetic Monte Carlo method to investigate the kinetic mechanism for the conformational switches between bistable RNA hairpins. We find three types of conformational switch pathways for RNA hairpins: refolding after complete unfolding, folding through basepair-exchange pathways and through pseudoknot-assisted pathways, respectively. The result of the competition between the three types of pathways depends mainly on the location of the rate-limiting base stacks (such as the GC base stacks) in the structures. Depending on the structural relationships between the two bistable hairpins, the conformational switch can follow single or multiple dominant pathways. The predicted folding pathways are supported by the activation energy results derived from the Arrhenius plot as well as the NMR spectroscopy data.

The role of counterion valence and size in GAAA tetraloop-receptor docking/undocking kinetics

For RNA to fold into compact, ordered structures, it must overcome electrostatic repulsion between negatively charged phosphate groups by counterion recruitment. A physical understanding of the counterion-assisted folding process requires addressing how cations kinetically and thermodynamically control the folding equilibrium for each tertiary interaction in a full-length RNA. In this work, single-molecule FRET (fluorescence resonance energy transfer) techniques are exploited to isolate and explore the cation-concentration-dependent kinetics for formation of a ubiquitous RNA tertiary interaction, that is, the docking/undocking of a GAAA tetraloop with its 11-nt receptor. Rate constants for docking (k(dock)) and undocking (k(undock)) are obtained as a function of cation concentration, size, and valence, specifically for the series Na(+), K(+), Mg(2+), Ca(2+), Co(NH(3))(6)(3+), and spermidine(3+). Increasing cation concentration acceleratesk(dock)dramatically but achieves only a slight decrease in k(undock). These results can be kinetically modeled using parallel cation-dependent and cation-independent docking pathways, which allows for isolation of the folding kinetics from the interaction energetics of the cations with the undocked and docked states, respectively. This analysis reveals a preferential interaction of the cations with the transition state and docked state as compared to the undocked RNA, with the ion-RNA interaction strength growing with cation valence. However, the corresponding number of cations that are taken up by the RNA upon folding decreases with charge density of the cation. The only exception to these behaviors is spermidine(3+), whose weaker influence on the docking equilibria with respect to Co(NH(3))(6)(3+) can be ascribed to steric effects preventing complete neutralization of the RNA phosphate groups.

Cooperative tertiary interaction network guides RNA folding

Noncoding RNAs form unique 3D structures, which perform many regulatory functions. To understand how RNAs fold uniquely despite a small number of tertiary interaction motifs, we mutated the major tertiary interactions in a group I ribozyme by single-base substitutions. The resulting perturbations to the folding energy landscape were measured using SAXS, ribozyme activity, hydroxyl radical footprinting, and native PAGE. Double- and triple-mutant cycles show that most tertiary interactions have a small effect on the stability of the native state. Instead, the formation of core and peripheral structural motifs is cooperatively linked in near-native folding intermediates, and this cooperativity depends on the native helix orientation. The emergence of a cooperative interaction network at an early stage of folding suppresses nonnative structures and guides the search for the native state. We suggest that cooperativity in noncoding RNAs arose from natural selection of architectures conducive to forming a unique, stable fold.

Folding path of P5abc RNA involves direct coupling of secondary and tertiary structures

Folding mechanisms in which secondary structures are stabilized through the formation of tertiary interactions are well documented in protein folding but challenge the folding hierarchy normally assumed for RNA. However, it is increasingly clear that RNA could fold by a similar mechanism. P5abc, a small independently folding tertiary domain of the Tetrahymena thermophila group I ribozyme, is known to fold by a secondary structure rearrangement involving helix P5c. However, the extent of this rearrangement and the precise stage of folding that triggers it are unknown. We use experiments and simulations to show that the P5c helix switches to the native secondary structure late in the folding pathway and is directly coupled to the formation of tertiary interactions in the A-rich bulge. P5c mutations show that the switch in P5c is not rate-determining and suggest that non-native interactions in P5c aid folding rather than impede it. Our study illustrates that despite significant differences in the building blocks of proteins and RNA, there may be common ways in which they self-assemble.

Thermodynamic origins of monovalent facilitated RNA folding

Cations have long been associated with formation of native RNA structure and are commonly thought to stabilize the formation of tertiary contacts by favorably interacting with the electrostatic potential of the RNA, giving rise to an "ion atmosphere". A significant amount of information regarding the thermodynamics of structural transitions in the presence of an ion atmosphere has accumulated and suggests stabilization is dominated by entropic terms. This work provides an analysis of how RNA-cation interactions affect the entropy and enthalpy associated with an RNA tertiary transition. Specifically, temperature-dependent single-molecule fluorescence resonance energy transfer studies have been exploited to determine the free energy (ΔG°), enthalpy (ΔH°), and entropy (ΔS°) of folding for an isolated tetraloop-receptor tertiary interaction as a function of Na(+) concentration. Somewhat unexpectedly, increasing the Na(+) concentration changes the folding enthalpy from a strongly exothermic process [e.g., ΔH° = -26(2) kcal/mol at 180 mM] to a weakly exothermic process [e.g., ΔH° = -4(1) kcal/mol at 630 mM]. As a direct corollary, it is the strong increase in folding entropy [Δ(ΔS°) > 0] that compensates for this loss of exothermicity for the achievement of more favorable folding [Δ(ΔG°) < 0] at higher Na(+) concentrations. In conjunction with corresponding measurements of the thermodynamics of the transition state barrier, these data provide a detailed description of the folding pathway associated with the GAAA tetraloop-receptor interaction as a function of Na(+) concentration. The results support a potentially universal mechanism for monovalent facilitated RNA folding, whereby an increasing monovalent concentration stabilizes tertiary structure by reducing the entropic penalty for folding.

Electrostatics of nucleic acid folding under conformational constraint

RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.