An optimal Mg(2+) concentration for kinetic folding of the tetrahymena ribozyme

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.

Structural, Dynamical, and Entropic Differences between SARS-CoV and SARS-CoV-2 s2m Elements Using Molecular Dynamics Simulations

The functional role of the highly conserved stem-loop II motif (s2m) in SARS-CoV and SARS-CoV-2 in the viral lifecycle remains enigmatic and an intense area of research. Structure and dynamics of the s2m are key to establishing a structure-function connection, yet a full set of atomistic resolution coordinates is not available for SARS-CoV-2 s2m. Our work constructs three-dimensional coordinates consistent with NMR solution phase data for SARS-CoV-2 s2m and provides a comparative analysis with its counterpart SARS-CoV s2m. We employed initial coordinates based on PDB ID 1XJR for SARS-CoV s2m and two models for SARS-CoV-2 s2m: one based on 1XJR in which we introduced the mutations present in SARS-CoV-2 s2m and the second based on the available SARS-CoV-2 NMR NOE data supplemented with knowledge-based methods. For each of the three systems, 3.5 μs molecular dynamics simulations were used to sample the structure and dynamics, and principal component analysis (PCA) reduced the ensembles to hierarchal conformational substates for detailed analysis. Dilute solution simulations of SARS-CoV s2m demonstrate that the GNRA-like terminal pentaloop is rigidly defined by base stacking uniquely positioned for possible kissing dimer formation. However, the SARS-CoV-2 s2m simulation did not retain the reported crystallographic SARS-CoV motifs and the terminal loop expands to a highly dynamic "nonaloop." Increased flexibility and structural disorganization are observed for the larger terminal loop, where an entropic penalty is computed to explain the experimentally observed reduction in kissing complex formation. Overall, both SARS-CoV and SARS-CoV-2 s2m elements have a similarly pronounced L-shape due to different motif interactions. Our study establishes the atomistic three-dimensional structure and uncovers dynamic differences that arise from s2m sequence changes, which sets the stage for the interrogation of different mechanistic pathways of suspected biological function.

Sub-3-Å cryo-EM structure of RNA enabled by engineered homomeric self-assembly

High-resolution structural studies are essential for understanding the folding and function of diverse RNAs. Herein, we present a nanoarchitectural engineering strategy for efficient structural determination of RNA-only structures using single-particle cryogenic electron microscopy (cryo-EM). This strategy-ROCK (RNA oligomerization-enabled cryo-EM via installing kissing loops)-involves installing kissing-loop sequences onto the functionally nonessential stems of RNAs for homomeric self-assembly into closed rings with multiplied molecular weights and mitigated structural flexibility. ROCK enables cryo-EM reconstruction of the Tetrahymena group I intron at 2.98-Å resolution overall (2.85 Å for the core), allowing de novo model building of the complete RNA, including the previously unknown peripheral domains. ROCK is further applied to two smaller RNAs-the Azoarcus group I intron and the FMN riboswitch, revealing the conformational change of the former and the bound ligand in the latter. ROCK holds promise to greatly facilitate the use of cryo-EM in RNA structural studies.

Structural dynamics of single SARS-CoV-2 pseudoknot molecules reveal topologically distinct conformers

The RNA pseudoknot that stimulates programmed ribosomal frameshifting in SARS-CoV-2 is a possible drug target. To understand how it responds to mechanical tension applied by ribosomes, thought to play a key role during frameshifting, we probe its structural dynamics using optical tweezers. We find that it forms multiple structures: two pseudoknotted conformers with different stability and barriers, and alternative stem-loop structures. The pseudoknotted conformers have distinct topologies, one threading the 5′ end through a 3-helix junction to create a knot-like fold, the other with unthreaded 5′ end, consistent with structures observed via cryo-EM and simulations. Refolding of the pseudoknotted conformers starts with stem 1, followed by stem 3 and lastly stem 2; Mg²⁺ ions are not required, but increase pseudoknot mechanical rigidity and favor formation of the knot-like conformer. These results resolve the SARS-CoV-2 frameshift signal folding mechanism and highlight its conformational heterogeneity, with important implications for structure-based drug-discovery efforts.

The RNA pseudoknot of SARS-CoV-2 promotes -1 programmed ribosomal frameshifting. Here the authors use single molecule force spectroscopy to study the folding of this pseudoknot, showing that it forms at least two different pseudoknot conformers with distinct fold topologies.

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.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Evolution of protein-coupled RNA dynamics during hierarchical assembly of ribosomal complexes

Assembly of 30S ribosomes involves the hierarchical addition of ribosomal proteins that progressively stabilize the folded 16S rRNA. Here, we use three-color single molecule FRET to show how combinations of ribosomal proteins uS4, uS17 and bS20 in the 16S 5′ domain enable the recruitment of protein bS16, the next protein to join the complex. Analysis of real-time bS16 binding events shows that bS16 binds both native and non-native forms of the rRNA. The native rRNA conformation is increasingly favored after bS16 binds, explaining how bS16 drives later steps of 30S assembly. Chemical footprinting and molecular dynamics simulations show that each ribosomal protein switches the 16S conformation and dampens fluctuations at the interface between rRNA subdomains where bS16 binds. The results suggest that specific protein-induced changes in the rRNA dynamics underlie the hierarchy of 30S assembly and simplify the search for the native ribosome structure.

Ribosomes assemble through the hierarchical addition of proteins to a ribosomal RNA scaffold. Here the authors use three-color single-molecule FRET to show how the dynamics of the rRNA dictate the order in which multiple proteins assemble on the 5′ domain of the E. coli 16S rRNA.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Molecular crowding overcomes the destabilizing effects of mutations in a bacterial ribozyme

The native structure of the Azoarcus group I ribozyme is stabilized by the cooperative formation of tertiary interactions between double helical domains. Thus, even single mutations that break this network of tertiary interactions reduce ribozyme activity in physiological Mg(2+) concentrations. Here, we report that molecular crowding comparable to that in the cell compensates for destabilizing mutations in the Azoarcus ribozyme. Small angle X-ray scattering, native polyacrylamide gel electrophoresis and activity assays were used to compare folding free energies in dilute and crowded solutions containing 18% PEG1000. Crowder molecules allowed the wild-type and mutant ribozymes to fold at similarly low Mg(2+) concentrations and stabilized the active structure of the mutant ribozymes under physiological conditions. This compensation helps explains why ribozyme mutations are often less deleterious in the cell than in the test tube. Nevertheless, crowding did not rescue the high fraction of folded but less active structures formed by double and triple mutants. We conclude that crowding broadens the fitness landscape by stabilizing compact RNA structures without improving the specificity of self-assembly.

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.

Metal-ion rescue revisited: biochemical detection of site-bound metal ions important for RNA folding

Within the three-dimensional architectures of RNA molecules, divalent metal ions populate specific locations, shedding their water molecules to form chelates. These interactions help the RNA adopt and maintain specific conformations and frequently make essential contributions to function. Defining the locations of these site-bound metal ions remains challenging despite the growing database of RNA structures. Metal-ion rescue experiments have provided a powerful approach to identify and distinguish catalytic metal ions within RNA active sites, but the ability of such experiments to identify metal ions that contribute to tertiary structure acquisition and structural stability is less developed and has been challenged. Herein, we use the well-defined P4-P6 RNA domain of the Tetrahymena group I intron to reevaluate prior evidence against the discriminatory power of metal-ion rescue experiments and to advance thermodynamic descriptions necessary for interpreting these experiments. The approach successfully identifies ligands within the RNA that occupy the inner coordination sphere of divalent metal ions and distinguishes them from ligands that occupy the outer coordination sphere. Our results underscore the importance of obtaining complete folding isotherms and establishing and evaluating thermodynamic models in order to draw conclusions from metal-ion rescue experiments. These results establish metal-ion rescue as a rigorous tool for identifying and dissecting energetically important metal-ion interactions in RNAs that are noncatalytic but critical for RNA tertiary structure.

Predicting ion-nucleic acid interactions by energy landscape-guided sampling

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Entropic origin of Mg2+-facilitated RNA folding

Mg(2+) is essential for the proper folding and function of RNA, though the effect of Mg(2+) concentration on the free energy, enthalpy, and entropy landscapes of RNA folding is unknown. This work exploits temperature-controlled single-molecule FRET methods to address the thermodynamics of RNA folding pathways by probing the intramolecular docking/undocking kinetics of the ubiquitous GAAA tetraloop-receptor tertiary interaction as a function of [Mg(2+)]. These measurements yield the barrier and standard state enthalpies, entropies, and free energies for an RNA tertiary transition, in particular, revealing the thermodynamic origin of [Mg(2+)]-facilitated folding. Surprisingly, these studies reveal that increasing [Mg(2+)] promotes tetraloop-receptor interaction by reducing the entropic barrier (-TΔS(++)(dock)) and the overall entropic penalty (-TΔS(+) (dock)) for docking, with essentially negligible effects on both the activation enthalpy (ΔH(++)(dock)) and overall exothermicity (ΔH(+)(dock)). These observations contrast with the conventional notion that increasing [Mg(2+)] facilitates folding by minimizing electrostatic repulsion of opposing RNA helices, which would incorrectly predict a decrease in ΔH(++)(dock)) and ΔH(+)(dock)) with [Mg(2+)]. Instead we propose that higher [Mg(2+)] can aid RNA folding by decreasing the entropic penalty of counterion uptake and by reducing disorder of the unfolded conformational ensemble.

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na(+) and Mg(2+)) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na(+) and Mg(2+) concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.

RNA molecules with conserved catalytic cores but variable peripheries fold along unique energetically optimized pathways

Functional and kinetic constraints must be efficiently balanced during the folding process of all biopolymers. To understand how homologous RNA molecules with different global architectures fold into a common core structure we determined, under identical conditions, the folding mechanisms of three phylogenetically divergent group I intron ribozymes. These ribozymes share a conserved functional core defined by topologically equivalent tertiary motifs but differ in their primary sequence, size, and structural complexity. Time-resolved hydroxyl radical probing of the backbone solvent accessible surface and catalytic activity measurements integrated with structural-kinetic modeling reveal that each ribozyme adopts a unique strategy to attain the conserved functional fold. The folding rates are not dictated by the size or the overall structural complexity, but rather by the strength of the constituent tertiary motifs which, in turn, govern the structure, stability, and lifetime of the folding intermediates. A fundamental general principle of RNA folding emerges from this study: The dominant folding flux always proceeds through an optimally structured kinetic intermediate that has sufficient stability to act as a nucleating scaffold while retaining enough conformational freedom to avoid kinetic trapping. Our results also suggest a potential role of naturally selected peripheral A-minor interactions in balancing RNA structural stability with folding efficiency.

Conformational heterogeneity and the determinants of tertiary stabilization in the hammerhead ribozyme from Dolichopoda cave crickets

Repetitive DNA elements in Dolichopoda cave cricket genomes contain extended hammerhead ribozymes that are functional in adult crickets, but that exhibit very low self-cleavage activity in vitro relative to other extended hammerhead ribozymes. We find that the parental ribozyme tends to misfold into alternate secondary structures in vitro, complicating analysis of contributions by specific nucleotides to activity under biologically relevant magnesium concentrations. However, minor sequence alterations that stabilize the active secondary structure, without altering candidate tertiary interacting nucleotides, boosted observed rates more than 50-fold (4.4 ± 1.7 min(-1)) and doubled the cleavage extent (>60%) in submillimolar magnesium. Productive alterations included flipping two base pairs in stem I, lengthening stem I and opening stem III to generate a trans-cleaving ribozyme. Specific peripheral nucleotides involved in tertiary stabilization were then identified through kinetic analysis for a series of sequence variants and by correlating plateau cleavage values with band intensity in native gel electrophoresis. These results demonstrate that conformational heterogeneity governs self-cleavage by the wild-type Dolichopoda hammerhead ribozyme in vitro, and they suggest a strategy for improving activity and enhancing the suitability of HHRz for intracellular and biotechnology applications.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

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.

Protein-facilitated folding of group II intron ribozymes

Multiple studies hypothesize that DEAD-box proteins facilitate folding of the ai5gamma group II intron. However, these conclusions are generally inferred from splicing kinetics, and not from direct monitoring of DEAD-box protein-facilitated folding of the intron. Using native gel electrophoresis and dimethyl sulfate structural probing, we monitored Mss-116-facilitated folding of ai5gamma intron ribozymes and a catalytically active self-splicing RNA containing full-length intron and short exons. We found that the protein directly stimulates folding of these RNAs by accelerating formation of the compact near-native state. This process occurs in an ATP-independent manner, although ATP is required for the protein turnover. As Mss 116 binds RNA nonspecifically, most binding events do not result in the formation of the compact state, and ATP is required for the protein to dissociate from such nonproductive complexes and rebind the unfolded RNA. Results obtained from experiments at different concentrations of magnesium ions suggest that Mss 116 stimulates folding of ai5gamma ribozymes by promoting the formation of unstable folding intermediates, which is then followed by a cascade of folding events resulting in the formation of the compact near-native state. Dimethyl sulfate probing results suggest that the compact state formed in the presence of the protein is identical to the near-native state formed more slowly in its absence. Our results also indicate that Mss 116 does not stabilize the native state of the ribozyme, but that such stabilization results from binding of attached exons.

Improving small-angle X-ray scattering data for structural analyses of the RNA world

Defining the shape, conformation, or assembly state of an RNA in solution often requires multiple investigative tools ranging from nucleotide analog interference mapping to X-ray crystallography. A key addition to this toolbox is small-angle X-ray scattering (SAXS). SAXS provides direct structural information regarding the size, shape, and flexibility of the particle in solution and has proven powerful for analyses of RNA structures with minimal requirements for sample concentration and volumes. In principle, SAXS can provide reliable data on small and large RNA molecules. In practice, SAXS investigations of RNA samples can show inconsistencies that suggest limitations in the SAXS experimental analyses or problems with the samples. Here, we show through investigations on the SAM-I riboswitch, the Group I intron P4-P6 domain, 30S ribosomal subunit from Sulfolobus solfataricus (30S), brome mosaic virus tRNA-like structure (BMV TLS), Thermotoga maritima asd lysine riboswitch, the recombinant tRNA(val), and yeast tRNA(phe) that many problems with SAXS experiments on RNA samples derive from heterogeneity of the folded RNA. Furthermore, we propose and test a general approach to reducing these sample limitations for accurate SAXS analyses of RNA. Together our method and results show that SAXS with synchrotron radiation has great potential to provide accurate RNA shapes, conformations, and assembly states in solution that inform RNA biological functions in fundamental ways.

Metal ion dependence of cooperative collapse transitions in RNA

Positively charged counterions drive RNA molecules into compact configurations that lead to their biologically active structures. To understand how the valence and size of the cations influences the collapse transition in RNA, small-angle X-ray scattering was used to follow the decrease in the radius of gyration (R(g)) of the Azoarcus and Tetrahymena ribozymes in different cations. Small, multivalent cations induced the collapse of both ribozymes more efficiently than did monovalent ions. Thus, the cooperativity of the collapse transition depends on the counterion charge density. Singular value decomposition of the scattering curves showed that folding of the smaller and more thermostable Azoarcus ribozyme is well described by two components, whereas collapse of the larger Tetrahymena ribozyme involves at least one intermediate. The ion-dependent persistence length, extracted from the distance distribution of the scattering vectors, shows that the Azoarcus ribozyme is less flexible at the midpoint of transition in low-charge-density ions than in high-charge-density ions. We conclude that the formation of sequence-specific tertiary interactions in the Azoarcus ribozyme overlaps with neutralization of the phosphate charge, while tertiary folding of the Tetrahymena ribozyme requires additional counterions. Thus, the stability of the RNA structure determines its sensitivity to the valence and size of the counterions.

Stabilization of three-way junctions of DNA under molecular crowding conditions

We examined the effects of molecular crowding conditions on the structures and thermodynamics of three-way junctions (TWJs) of DNA. Structural analysis utilizing gel electrophoresis and circular dichroism spectroscopy showed that the designed DNAs folded into TWJ structures in the presence of Na(+) and Mg(2+) under both dilute and molecular crowding conditions with polyethylene glycol 200 (PEG 200). From the thermodynamic parameters evaluated by UV melting techniques in the absence and presence of 5 mM Mg(2+) under dilute and molecular crowding conditions, it was clear that Mg(2+) stabilized all TWJs under the dilute condition, although the extent of stabilization depended on the stacking partners of TWJs. For example, thermodynamic stability (-DeltaG(o) (37)) of A/B-stacked TWJs (A, B, and C are the three helices of TWJ, and among these helices, A and B are stacked together) increased from 3.7 to 5.6 kcal/mol by the addition of 5 mM Mg(2+), while that of A/C-stacked TWJs (A and C are stacked together) increased only from 3.0 to 3.7 kcal/mol. Molecular crowding with PEG 200 destabilized the whole TWJ consisting of a junction point and three helical duplex arms. Crowding agents such as PEG 200 can affect the stability of DNA by modulating its hydration. To explore the crowding effects on the junction point, we evaluated the number of water molecules associated with the whole TWJ as well as the individual arms, and we found that the number of water molecules taken up by the whole TWJ was significantly smaller than the sum of the individual arms. These results show the dehydration from the junction point of the TWJ structure. Therefore, molecular crowding should be favorable for the junction point of TWJ structure and unfavorable for the duplex structure. To prove this concept, we designed truncated TWJ structures that folded into a bimolecular duplex under the dilute condition. With increasing concentrations of PEG 200 from 0 to 30 wt %, the fraction of truncated TWJ structures gradually increased, and that of the bimolecular duplex structure decreased, even in the absence of Mg(2+). We concluded that a cell-mimicking condition, in which the activity of water decreases and hydration becomes less favorable, might facilitate the formation of junction structures in comparison with duplexes.

Global stabilization of rRNA structure by ribosomal proteins S4, S17, and S20

Ribosomal proteins stabilize the folded structure of the ribosomal RNA and enable the recruitment of further proteins to the complex. Quantitative hydroxyl radical footprinting was used to measure the extent to which three different primary assembly proteins, S4, S17, and S20, stabilize the three-dimensional structure of the Escherichia coli 16S 5' domain. The stability of the complexes was perturbed by varying the concentration of MgCl(2). Each protein influences the stability of the ribosomal RNA tertiary interactions beyond its immediate binding site. S4 and S17 stabilize the entire 5' domain, while S20 has a more local effect. Multistage folding of individual helices within the 5' domain shows that each protein stabilizes a different ensemble of structural intermediates that include nonnative interactions at low Mg(2+) concentration. We propose that the combined interactions of S4, S17, and S20 with different helical junctions bias the free-energy landscape toward a few RNA conformations that are competent to add the secondary assembly protein S16 in the next step of assembly.

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.

S16 throws a conformational switch during assembly of 30S 5' domain

Rapid and accurate assembly of new ribosomal subunits is essential for cell growth. Here, we show that the ribosomal proteins make assembly more cooperative by discriminating against non-native conformations of the E. coli 16S rRNA. We used hydroxyl radical footprinting to measure how much the proteins stabilize individual rRNA tertiary interactions, revealing the free energy landscape for assembly of the 16S 5′ domain. When ribosomal proteins S4, S17, and S20 bind the 5′ domain RNA, a native and a non-native assembly intermediate are equally populated. The secondary assembly protein S16 suppresses the non-native intermediate, smoothing the path to the native complex. In the final step of 5′ domain assembly, S16 drives a conformational switch at helix 3 that stabilizes pseudoknots in the 30S decoding center. Long-range communication between the S16 binding site and the decoding center helps explain the critical role of S16 in 30S assembly.

Primitive templated catalysis of a peptide ligation by self-folding RNAs

RNA–polypeptide complexes (RNPs), which play various roles in extant biological systems, have been suggested to have been important in the early stages of the molecular evolution of life. At a certain developmental stage of ancient RNPs, their RNA and polypeptide components have been proposed to evolve in a reciprocal manner to establish highly elaborate structures and functions. We have constructed a simple model system, from which a cooperative evolution system of RNA and polypeptide components could be developed. Based on the observation that several RNAs modestly accelerated the chemical ligation of the two basic peptides. We have designed an RNA molecule possessing two peptide binding sites that capture the two peptides. This designed RNA can also accelerate the peptide ligation. The resulting ligated peptide, which has two RNA-binding sites, can in turn function as a trans-acting factor that enhances the endonuclease activity catalyzed by the designed RNA.

Reconstructing three-dimensional shape envelopes from time-resolved small-angle X-ray scattering data

Modern computing power has made it possible to reconstruct low-resolution, three-dimensional shapes from solution small-angle X-ray scattering (SAXS) data on biomolecules without a priori knowledge of the structure. In conjunction with rapid mixing techniques, SAXS has been applied to time resolve conformational changes accompanying important biological processes, such as biomolecular folding. In response to the widespread interest in SAXS reconstructions, their value in conjunction with such time-resolved data has been examined. The group I intron from Tetrahymena thermophila and its P4-P6 subdomain are ideal model systems for investigation owing to extensive previous studies, including crystal structures. The goal of this paper is to assay the quality of reconstructions from time-resolved data given the sacrifice in signal-to-noise required to obtain sharp time resolution.

Monovalent and divalent promoted GAAA tetraloop-receptor tertiary interactions from freely diffusing single-molecule studies

Proper assembly of RNA into catalytically active three-dimensional structures requires multiple tertiary binding interactions, individual characterization of which is crucial to a detailed understanding of global RNA folding. This work focuses on single-molecule fluorescence studies of freely diffusing RNA constructs that isolate the GAAA tetraloop-receptor tertiary interaction. Freely diffusing conformational dynamics are explored as a function of Mg(2+) and Na(+) concentration, both of which promote facile docking, but with 500-fold different affinities. Systematic shifts in mean fluorescence resonance energy transfer efficiency values and line widths with increasing [Na(+)] are observed for the undocked species and can be interpreted with a Debye model in terms of electrostatic relaxation and increased flexibility in the RNA. Furthermore, we identify a 34 +/- 2% fraction of freely diffusing RNA constructs remaining undocked even at saturating [Mg(2+)] levels, which agrees quantitatively with the 32 +/- 1% fraction previously reported for immobilized constructs. This verifies that the kinetic heterogeneity observed in the docking rates is not the result of surface tethering. Finally, the K(D) value and Hill coefficient for [Mg(2+)]-dependent docking decrease significantly for [Na(+)] = 25 mM vs. 125 mM, indicating Mg(2+) and Na(+) synergy in the RNA folding process.

Salt dependence of nucleic acid hairpin stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na(+) and Mg(2+) in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na(+) and Mg(2+) concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.

A kinetic intermediate that regulates proper folding of a group II intron RNA

The D135 group II intron ribozyme follows a unique folding pathway that is direct and appears to be devoid of kinetic traps. During the earliest stages of folding, D135 collapses slowly to a compact intermediate, and all subsequent assembly events are rapid. Collapse of intron domain 1 (D1) has been shown to limit the rate constant for D135 folding, although the specific substructure of the D1 kinetic intermediate has not yet been identified. Employing time-resolved nucleotide analog interference mapping, we have identified a cluster of atoms within the D1 main stem that control the rate constant for D135 collapse. Functional groups within the kappa-zeta element are particularly important for this earliest stage of folding, which is intriguing given that this same motif also serves later as the docking site for catalytic domain 5. More important, the kappa-zeta element is shown to be a divalent ion binding pocket, indicating that this region is a Mg(2+)-dependent switch that initiates the cascade of D135 folding events. By measuring the Mg(2+) dependence of the compaction rate constant, we conclude that the actual rate-limiting step in D1 compaction involves the formation of an unstable folding intermediate that is captured by the binding of Mg(2+). This carefully orchestrated folding pathway, in which formation of an active-site docking region is early and rate limiting, ensures proper folding of the intron core and faithful splicing. It may represent an important paradigm for the folding of large, multidomain RNA molecules.

Distinct contribution of electrostatics, initial conformational ensemble, and macromolecular stability in RNA folding

We distinguish the contribution of the electrostatic environment, initial conformational ensemble, and macromolecular stability on the folding mechanism of a large RNA using a combination of time-resolved "Fast Fenton" hydroxyl radical footprinting and exhaustive kinetic modeling. This integrated approach allows us to define the folding landscape of the L-21 Tetrahymena thermophila group I intron structurally and kinetically from its earliest steps with unprecedented accuracy. Distinct parallel pathways leading the RNA to its native form upon its Mg(2+)-induced folding are observed. The structures of the intermediates populating the pathways are not affected by variation of the concentration and type of background monovalent ions (electrostatic environment) but are altered by a mutation that destabilizes one domain of the ribozyme. Experiments starting from different conformational ensembles but folding under identical conditions show that whereas the electrostatic environment modulates molecular flux through different pathways, the initial conformational ensemble determines the partitioning of the flux. This study showcases a robust approach for the development of kinetic models from collections of local structural probes.

Deletion of the P5abc peripheral element accelerates early and late folding steps of the Tetrahymena group I ribozyme

The P5abc peripheral element stabilizes the Tetrahymena group I ribozyme and enhances its catalytic activity. Despite its beneficial effects on the native structure, prior studies have shown that early formation of P5abc structure during folding can slow later folding steps. Here we use a P5abc deletion variant E(deltaP5abc) to systematically probe the role of P5abc throughout tertiary folding. Time-resolved hydroxyl radical footprinting shows that E(deltaP5abc) forms its earliest stable tertiary structure on the millisecond time scale, approximately 5-fold faster than the wild-type ribozyme, and stable structure spreads throughout E(deltaP5abc) in seconds. Nevertheless, activity measurements show that the earliest detectable formation of native E(deltaP5abc) ribozyme is much slower (approximately 0.6 min(-1)), in a manner similar to that of the wild type. Also similar, only a small fraction of E(deltaP5abc) attains the native state on this time scale under standard conditions at 25 degrees C, whereas the remainder misfolds; footprinting experiments show that the misfolded conformer shares structural features with the long-lived misfolded conformer of the wild-type ribozyme. Thus, P5abc does not have a large overall effect on the rate-limiting step(s) along this pathway. However, once misfolded, E(deltaP5abc) refolds to the native state 80-fold faster than the wild-type ribozyme and is less accelerated by urea, indicating that P5abc stabilizes the misfolded structure relative to the less-ordered transition state for refolding. Together, the results suggest that, under these conditions, even the earliest tertiary folding intermediates of the wild-type ribozyme represent misfolded species and that P5abc is principally a liability during the tertiary folding process.

RNA helix stability in mixed Na+/Mg2+ solution

A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solutions, which are physiologically relevant and biologically significant, and the model was based on B-DNA helices and thus cannot directly treat RNA helices. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodynamic stability of finite length RNA helices immersed in a mixed solution of monovalent and divalent ions. Experimental comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helices. The tightly bound ion model makes quantitative predictions on how the Na+-Mg2+ competition determines helix stability and its helix length-dependence. In addition, the model gives empirical formulas for the thermodynamic parameters as functions of Na+/Mg2+ concentrations and helix length. Such formulas can be quite useful for practical applications.

Force unfolding kinetics of RNA using optical tweezers. I. Effects of experimental variables on measured results

Experimental variables of optical tweezers instrumentation that affect RNA folding/unfolding kinetics were investigated. A model RNA hairpin, P5ab, was attached to two micron-sized beads through hybrid RNA/DNA handles; one bead was trapped by dual-beam lasers and the other was held by a micropipette. Several experimental variables were changed while measuring the unfolding/refolding kinetics, including handle lengths, trap stiffness, and modes of force applied to the molecule. In constant-force mode where the tension applied to the RNA was maintained through feedback control, the measured rate coefficients varied within 40% when the handle lengths were changed by 10-fold (1.1-10.2 Kbp); they increased by two- to threefold when the trap stiffness was lowered to one-third (from 0.1 to 0.035 pN/nm). In the passive mode, without feedback control and where the force applied to the RNA varied in response to the end-to-end distance change of the tether, the RNA hopped between a high-force folded-state and a low-force unfolded-state. In this mode, the rates increased up to twofold with longer handles or softer traps. Overall, the measured rates remained with the same order-of-magnitude over the wide range of conditions studied. In the companion article on pages 3010-3021, we analyze how the measured kinetics parameters differ from the intrinsic molecular rates of the RNA, and thus how to obtain the molecular rates.

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na+ and Mg2+ play distinctive roles in helix-helix assembly. High [Na+] (>0.3 M) causes a reduced helix-helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix-helix attraction and results in a more compact and ordered helix-helix packing. Mg2+ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.

Statistical thermodynamics for chain molecules with simple RNA tertiary contacts

A statistical thermodynamic model is developed for chain molecules with simple RNA tertiary contacts. The model, which accounts for the excluded volume effect and the nonadditivity in the free energy, enables reliable predictions for the conformational entropy and partition function for simple tertiary folds. Illustrative applications are made to conformational transitions involving simple tertiary contacts. The model can predict the interplay between the secondary and the tertiary interactions in the conformational changes. Though the present form of the theory is tested and validated in a two-dimensional lattice model, the methodology, which is developed based on a general graphical representation for chain conformations, is applicable to any off-lattice chain representations. Moreover, the analytical formulation of the method makes possible the systematic development of the theory for more complex tertiary structures.

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.

Counterion charge density determines the position and plasticity of RNA folding transition states

The self-assembly of RNA structure depends on the interactions of counterions with the RNA and with each other. Comparison of various polyamines showed that the tertiary structure of the Tetrahymena ribozyme is more stable when the counterions are small and highly charged. By monitoring the folding kinetics of the ribozyme as a function of polyamine concentration, we now find that the charge density of the counterions determines the positions of the folding transition states. The transition state ensemble (TSE) between U and N moves away from the native state as the counterion valence and charge density increase, as predicted by the Hammond postulate. The TSE is broader and less structured when the RNA is refolded in polyamines rather than Mg2+. That the charge density of the counterions determines the plasticity of the TSE demonstrates the importance of interactions among condensed counterions for the self-assembly of RNA structures. We propose that the major barrier to RNA folding is dominated by entropy changes when counterion charge density is low and enthalpy differences when it is high.

Local kinetic measures of macromolecular structure reveal partitioning among multiple parallel pathways from the earliest steps in the folding of a large RNA molecule

At the heart of the RNA folding problem is the number, structures, and relationships among the intermediates that populate the folding pathways of most large RNA molecules. Unique insight into the structural dynamics of these intermediates can be gleaned from the time-dependent changes in local probes of macromolecular conformation (e.g. reports on individual nucleotide solvent accessibility offered by hydroxyl radical (()OH) footprinting). Local measures distributed around a macromolecule individually illuminate the ensemble of separate changes that constitute a folding reaction. Folding pathway reconstruction from a multitude of these individual measures is daunting due to the combinatorial explosion of possible kinetic models as the number of independent local measures increases. Fortunately, clustering of time progress curves sufficiently reduces the dimensionality of the data so as to make reconstruction computationally tractable. The most likely folding topology and intermediates can then be identified by exhaustively enumerating all possible kinetic models on a super-computer grid. The folding pathways and measures of the relative flux through them were determined for Mg(2+) and Na(+)-mediated folding of the Tetrahymena thermophila group I intron using this combined experimental and computational approach. The flux during Mg(2+)-mediated folding is divided among numerous parallel pathways. In contrast, the flux during the Na(+)-mediated reaction is predominantly restricted through three pathways, one of which is without detectable passage through intermediates. Under both conditions, the folding reaction is highly parallel with no single pathway accounting for more than 50% of the molecular flux. This suggests that RNA folding is non-sequential under a variety of different experimental conditions even at the earliest stages of folding. This study provides a template for the systematic analysis of the time-evolution of RNA structure from ensembles of local measures that will illuminate the chemical and physical characteristics of each step in the process. The applicability of this analysis approach to other macromolecules is discussed.

Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length

Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (especially multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive experimental data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helices. We quantitatively evaluate the effects of ion concentration, ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful analytical formulas for the thermodynamic parameters as functions of finite helix length, ion type, and ion concentration. We find that the helix stability is additive for high ion concentration and long helix and nonadditive for low ion concentration and short helix. All these results are tested against and supported by extensive experimental data.

Molecular beacons as probes of RNA unfolding under native conditions

Hybridization of fluorescent molecular beacons provides real-time detection of RNA secondary structure with high specificity. We used molecular beacons to measure folding and unfolding rates of the Tetrahymena group I ribozyme under native conditions. A molecular beacon targeted against 15 nt in the 5' strand of the P3 helix specifically hybridized with misfolded forms of the ribozyme, without invading the native tertiary structure. The beacon associated with the misfolded ribozyme 300 times more slowly than with an unstructured oligonucleotide containing the same target sequence, suggesting that the misfolded ribozyme core remains structured in the absence of Mg2+. The rate of beacon hybridization under native conditions revealed a linear relationship between the free energy of unfolding and Mg2+ concentration. A small fraction of the RNA population unfolded very rapidly, suggesting parallel unfolding in one step or through misfolded intermediates.

Perturbation of the hierarchical folding of a large RNA by the destabilization of its Scaffold's tertiary structure

The P4-P6 domain serves as a scaffold against which the periphery and catalytic core organize and fold during Mg2+-mediated folding of the Tetrahymena thermophila ribozyme. The most prominent structural motif of the P4-P6 domain is the tetraloop-tetraloop receptor interaction which "clamps" the distal parts of its hairpin-like structure. Destabilization of the tertiary structure of the P4-P6 domain by perturbation of the tetraloop-tetraloop receptor interaction alters the Mg2+-mediated folding pathway. The folding hierarchy of P5c approximately P4-P6 > periphery > catalytic core that is a striking attribute of the folding of the wild-type RNA is abolished. The initial steps in folding of the mutant RNA are > or =50-fold faster than those of the wild-type ribozyme with the earliest observed tertiary contacts forming around regions known to specifically bind Mg2+. The interaction between the mutant tetraloop and the tetraloop receptor appears coincidently with slowly forming catalytic core tertiary contacts. Thus, the stability conferred upon the P4-P6 domain by the tetraloop-tetraloop receptor interaction dictates the preferred folding pathway by stabilizing an early intermediate. A sub-denaturing concentration of urea diminishes the early barrier to folding the wild-type ribozyme along with complex effects on the subsequent steps of folding the wild-type and mutant RNA.

Kinetics and thermodynamics make different contributions to RNA folding in vitro and in yeast

RNAs somehow adopt specific functional structures despite the capacity to form alternative nonfunctional structures with similar stabilities. We analyzed RNA assembly during transcription in vitro and in yeast using hairpin ribozyme self-cleavage to assess partitioning between functional ribozyme structures and nonfunctional stem loops. Complementary insertions located upstream of the ribozyme inhibited ribozyme assembly more than downstream insertions during transcription in vitro, consistent with a sequential folding model in which the outcome is determined by the structure that forms first. In contrast, both upstream and downstream insertions strongly inhibited assembly of the same ribozyme variants when expressed as chimeric mRNAs in yeast, indicating that inhibitory stem loops can form even after the entire ribozyme sequence has been transcribed. Evidently, some feature unique to the intracellular environment modulates the influence of transcription polarity and enhances the contribution of thermodynamic stability to RNA folding in vivo.

Protein-independent Folding Pathway of the 16S rRNA 5′ Domain

Evolution of the ribosome from an RNA catalyst suggests that the intrinsic folding pathway of the rRNA dictates the hierarchy of ribosome assembly. To address this possibility, we probed the tertiary folding pathway of the 5' domain of the Escherichia coli 16S rRNA at 20 ms intervals using X-ray-dependent hydroxyl radical footprinting. Comparison with crystallographic structures and footprinting reactions on native 30S ribosomes showed that the RNA formed all of the predicted tertiary interactions in the absence of proteins. In 20 mM MgCl2, many tertiary interactions appeared within 20 ms. By contrast, interactions between H6, H15 and H17 near the spur of the 30S ribosome evolved over several minutes, likely due to mispairing of a central helix junction. The kinetic folding pathway of the RNA corresponded to the expected order of protein binding, suggesting that the RNA folding pathway forms the basis for early steps of ribosome assembly.

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.

Calculation of standard atomic volumes for RNA and comparison with proteins: RNA is packed more tightly

Traditionally, for biomolecular packing calculations research has focused on proteins. Besides proteins, RNA is the other large biomolecule that has tertiary structure interactions and complex packing. No one has yet quantitatively investigated RNA packing or compared its packing to that of proteins because, until recently, there were no large RNA structures. Here we address this question in detail, using Voronoi volume calculations on a set of high-resolution RNA crystal structures. We do a careful parameterization, taking into account many factors such as atomic radii, crystal packing, structural complexity, solvent, and associated protein to obtain a self-consistent, universal set of volumes that can be applied to both RNA and protein. We report this set of volumes, which we call the NucProt parameter set. Our measured values are consistent across the many different RNA structures and packing environments. When common atom types are compared between proteins and RNA, nine of 12 types show that RNA has a smaller volume and packs more tightly than protein, suggesting that close-packing may be as important for the folding of RNAs as it is for proteins. Moreover, calculated partial specific volumes show that RNA bases pack more densely than corresponding aromatic residues from proteins. Finally, we find that RNA bases have similar packing volumes to DNA bases, despite the absence of tertiary contacts in DNA. Programs, parameter sets and raw data are available online at.

Fast formation of the P3-P7 pseudoknot: a strategy for efficient folding of the catalytically active ribozyme

Formation of the P3-P7 pseudoknot structure, the core of group I ribozymes, requires long-range base pairing. Study of the Tetrahymena ribozyme appreciates the hierarchical folding of the large, multidomain RNA, in which the P3-P7 core folds significantly slower than do the other domains. Here we explored the formation of the P3-P7 pseudoknot of the Candida ribozyme that has been reported to concertedly fold to the catalytically active structure with a rate constant of 2 min(-1). We demonstrate that pseudoknot formation occurs during the rapid ribozyme compaction, coincident with formation of many tertiary interactions of the ribozyme. A low physiological concentration of magnesium (1.5 mM) is sufficient to fully support the pseudoknot formation. The presence of nonnative intermediates containing an unfolded P3-P7 region is evident. However, catalysis-based analysis shows these nonnative intermediates are stable and fail to convert to the catalytically active structure, suggesting that rapid pseudoknot formation is essential for folding of the active ribozyme. Interestingly, RNAstructure predicts no stable Alt P3 structure for the Candida ribozyme, but two stable Alt P3s for the Tetrahymena ribozyme, explaining the dramatic difference in folding of the P3-P7 core of these two ribozymes. We propose that rapid formation of the P3-P7 pseudoknot represents a folding strategy ensuring efficient production of the catalytically active structure of group I ribozymes, which sheds new light on the mechanism of effective ribozyme folding in vivo.