The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.     

Does water play a structural role in the folding of small nucleic acids?

Nucleic acid structure and dynamics are known to be closely coupled to local environmental conditions and, in particular, to the ionic character of the solvent. Here we consider what role the discrete properties of water and ions play in the collapse and folding of small nucleic acids. We study the folding of an experimentally well-characterized RNA hairpin-loop motif (sequence 5'-GGGC[GCAA]GCCU-3') via ensemble molecular dynamics simulation and, with nearly 500 micros of aggregate simulation time using an explicit representation of the ionic solvent, report successful ensemble folding simulations with a predicted folding time of 8.8(+/-2.0) micros, in agreement with experimental measurements of approximately 10 micros. Comparing our results to previous folding simulations using the GB/SA continuum solvent model shows that accounting for water-mediated interactions is necessary to accurately characterize the free energy surface and stochastic nature of folding. The formation of the secondary structure appears to be more rapid than the fastest ionic degrees of freedom, and counterions do not participate discretely in observed folding events. We find that hydrophobic collapse follows a predominantly expulsive mechanism in which a diffusion-search of early structural compaction is followed by the final formation of native structure that occurs in tandem with solvent evacuation.     

Tris-borate is a poor counterion for RNA: a cautionary tale for RNA folding studies

Native polyacrylamide gel electrophoresis is a powerful approach for visualizing RNA folding states and folding intermediates. Tris-borate has a high-buffering capacity and is therefore widely used in electrophoresis-based investigations of RNA structure and folding. However, the effectiveness of Tris-borate as a counterion for RNA has not been systematically investigated. In a recirculated Hepes/KCl buffer, the catalytic core of the bI5 group I intron RNA undergoes a conformational collapse characterized by a bulk transition midpoint, or Mg_1/2, of ~3 mM, consistent with extensive independent biochemical experiments. In contrast, in Tris-borate, RNA collapse has a much smaller apparent Mg_1/2, equal to 0.1 mM, because in this buffer the RNA undergoes a different, large amplitude, folding transition at low Mg²⁺ concentrations. Analysis of structural neighbors using a short-lived, RNA-tethered, photocrosslinker indicates that the global RNA structure eventually converges in the two buffer systems, as the divalent ion concentration approaches ~1 mM Mg²⁺. The weak capacity of Tris-borate to stabilize RNA folding may reflect relatively unfavorable interactions between the bulky Tris-borate ion and RNA or partial coordination of RNA functional groups by borate. Under some conditions, Tris-borate is a poor counterion for RNA and its use merits careful evaluation in RNA folding studies.     

Structural transitions of confined model proteins: molecular dynamics simulation and experimental validation

Proteins fold in a confined space not only in vivo, i.e., folding assisted by molecular chaperons and chaperonins in a crowded cellular medium, but also in vitro as in production of recombinant proteins. Despite extensive work on protein folding in bulk, little is known about how and to what extent the thermodynamics and kinetics of protein folding are altered by confinement. In this work, we use a Gō-like off-lattice model to investigate the folding and stability of an all beta-sheet protein in spherical cages of different sizes and surface hydrophobicity. We find whereas extreme confinement inhibits correct folding, a hydrophilic cage stabilizes the protein due to restriction of the unfolded configurations. In a hydrophobic cage, however, strong attraction from the cage surface destabilizes the confined protein because of competition between self-aggregation and adsorption of hydrophobic residues. We show that the kinetics of protein collapse and folding is strongly correlated with both the cage size and the surface hydrophobicity. It is demonstrated that a cage of moderate size and hydrophobicity optimizes both the folding yield and kinetics of structural transitions. To support the simulation results, we have also investigated the refolding of hen-egg lysozyme in the presence of cetyltrimethylammoniumbromide (CTAB) surfactants that provide an effective confinement of the proteins by micellization. The influence of the surfactant hydrophobicity on the structural and biological activity of the protein is determined with circular dichroism spectrum, fluorescence emission spectrum, and biological activity assay. It is shown that, as predicted by coarse-grained simulations, CTAB micelles facilitate the collapse of denatured lysozyme, whereas the addition of beta-cyclodextrin-grafted-PNIPAAm, a weakly hydrophobic stripper, dissociates CTAB micelles and promotes the conformational rearrangement and thereby gives an improved recovery of lysozyme activity.     

Thermodynamics and Kinetics of Single-Chain Monellin Folding with Structural Insights into Specific Collapse in the Denatured State Ensemble

Proteins, which behave as random coils in high denaturant concentrations undergo collapse transition similar to polymers on denaturant dilution. We study collapse in the denatured ensemble of single-chain monellin (MNEI) using a coarse-grained protein model and molecular dynamics simulations. The model is validated by quantitatively comparing the computed guanidinium chloride and pH-dependent thermodynamic properties of MNEI folding with the experiments. The computed properties such as the fraction of the protein in the folded state and radius of gyration (R_g) as function of [GuHCl] are in good agreement with the experiments. The folded state of MNEI is destabilized with an increase in pH due to the deprotonation of the residues Glu24 and Cys42. On decreasing [GuHCl], the protein in the unfolded ensemble showed specific compaction. The R_g of the protein decreased steadily with [GuHCl] dilution due to increase in the number of native contacts in all the secondary structural elements present in the protein. MNEI folding kinetics is complex with multiple folding pathways and transiently stable intermediates are populated in these pathways. In strong stabilizing conditions, the protein in the unfolded ensemble showed transition to a more compact unfolded state where R_g decreased by ≈ 17% due to the formation of specific native contacts in the protein. The intermediate populated in the dominant MNEI folding pathway satisfies the structural features of the dry molten globule inferred from experiments.     

RNA and protein folding: common themes and variations

Visualizing the navigation of an ensemble of unfolded molecules through the bumpy energy landscape in search of the native state gives a pictorial view of biomolecular folding. This picture, when combined with concepts in polymer theory, provides a unified theory of RNA and protein folding. Just as for proteins, the major folding free energy barrier for RNA scales sublinearly with the number of nucleotides, which allows us to extract the elusive prefactor for RNA folding. Several folding scenarios can be anticipated by considering variations in the energy landscape that depend on sequence, native topology, and external conditions. RNA and protein folding mechanism can be described by the kinetic partitioning mechanism (KPM) according to which a fraction (Phi) of molecules reaches the native state directly, whereas the remaining fraction gets kinetically trapped in metastable conformations. For two-state folders Phi approximately 1. Molecular chaperones are recruited to assist protein folding whenever Phi is small. We show that the iterative annealing mechanism, introduced to describe chaperonin-mediated folding, can be generalized to understand protein-assisted RNA folding. The major differences between the folding of proteins and RNA arise in the early stages of folding. For RNA, folding can only begin after the polyelectrolyte problem is solved, whereas protein collapse requires burial of hydrophobic residues. Cross-fertilization of ideas between the two fields should lead to an understanding of how RNA and proteins solve their folding problems.     

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 Mg²⁺) 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 Mg²⁺ concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.     

Kinetic traps in the folding of beta alpha-repeat proteins: CheY initially misfolds before accessing the native conformation

The βα-repeat class of proteins, represented by the (βα)₈ barrel and the α/β/α sandwich, are among the most common structural platforms in biology. Previous studies on the folding mechanisms of these motifs have revealed or suggested that the initial event involves the submillisecond formation of a kinetically trapped species that must at least partially unfold before productive folding to the respective native conformation can occur. To test the generality of these observations, CheY, a bacterial response regulator, was subjected to an extensive analysis of its folding reactions. Although earlier studies had proposed the formation of an off-pathway intermediate, the data available were not sufficient to rule out an alternative on-pathway mechanism. A global analysis of single- and double-jump kinetic data, combined with equilibrium unfolding data, was used to show that CheY folds and unfolds through two parallel channels defined by the state of isomerization of a prolyl peptide bond in the active site. Each channel involves a stable, highly structured folding intermediate whose kinetic properties are better described as the properties of an off-pathway species. Both intermediates subsequently flow through the unfolded state ensemble and adopt the native cis-prolyl isomer prior to forming the native state. Initial collapse to off-pathway folding intermediates is a common feature of the folding mechanisms of βα-repeat proteins, perhaps reflecting the favored partitioning to locally determined substructures that cannot directly access the native conformation. Productive folding requires the dissipation of these prematurely folded substructures as a prelude to forming the larger-scale transition state that leads to the native conformation. Results from Gō-modeling studies in the accompanying paper elaborate on the topological frustration in the folding free-energy landscape of CheY.     

Protein folding in the landscape perspective: Chevron plots and non-arrhenius kinetics

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have “chevron plot” dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponental behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process. Proteins 30:2–33, 1998. © 1998 Wiley-Liss, Inc.     

Understanding the Role of Three-Dimensional Topology in Determining the?Folding Intermediates of Group I Introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg²⁺-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (⋅OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ⋅OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.     

Folding of the Tetrahymena ribozyme by polyamines: importance of counterion valence and size

Polyamines are abundant metabolites that directly influence gene expression. Although the role of polyamines in DNA condensation is well known, their role in RNA folding is less understood. Non-denaturing gel electrophoresis was used to monitor the equilibrium folding transitions of the Tetrahymena ribozyme in the presence of polyamines. All of the polyamines tested induce near-native structures that readily convert to the native conformation in Mg(2+). The stability of the folded structure increases with the charge of the polyamine and decreases with the size of the polyamine. When the counterion excluded volume becomes large, the transition to the native state does not go to completion even under favorable folding conditions. Brownian dynamics simulations of a model polyelectrolyte suggest that the kinetics of counterion-mediated collapse and the dimensions of the collapsed RNA chains depend on the structure of the counterion. The results are consistent with delocalized condensation of polyamines around the RNA. However, the effective charge of the counterions is lowered by their excluded volume. The stability of the folded RNA is enhanced when the spacing between amino groups matches the distance between adjacent phosphate groups. These results show how changes in intracellular polyamine concentrations could alter RNA folding pathways.     

An obligate intermediate along the slow folding pathway of a group II intron ribozyme

Most RNA molecules collapse rapidly and reach the native state through a pathway that contains numerous traps and unproductive intermediates. The D135 group II intron ribozyme is unusual in that it can fold slowly and directly to the native state, despite its large size and structural complexity. Here we use hydroxyl radical footprinting and native gel analysis to monitor the timescale of tertiary structure collapse and to detect the presence of obligate intermediates along the folding pathway of D135. We find that structural collapse and native folding of Domain 1 precede assembly of the entire ribozyme, indicating that D1 contains an on-pathway intermediate to folding of the D135 ribozyme. Subsequent docking of Domains 3 and 5, for which D1 provides a preorganized scaffold, appears to be very fast and independent of one another. In contrast to other RNAs, the D135 ribozyme undergoes slow tertiary collapse to a compacted state, with a rate constant that is also limited by the formation D1. These findings provide a new paradigm for RNA folding and they underscore the diversity of RNA biophysical behaviors.     

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.     

Imaging of single hairpin ribozymes in solution by atomic force microscopy.

The hairpin ribozyme is a short endonucleolytic RNA motif isolated from a family of related plant virus satellite RNAs. It consists of two independently folding domains, each comprising two Watson-Crick helices flanking a conserved internal loop. The domains need to physically interact (dock) for catalysis of site-specific cleavage and ligation reactions. Using tapping-mode atomic force microscopy in aqueous buffer solution, we were able to produce high quality images of individual hairpin ribozyme molecules with extended terminal helices. Three RNA constructs with either the essential cleavage site guanosine or a detrimental adenosine substitution and with or without a 6-nt insertion to confer flexibility to the interdomain hinge show structural differences that correlate with their ability to form the active docked conformation. The observed contour lengths and shapes are consistent with previous bulk-solution measurements of the transient electric dichroism decays for the same RNA constructs. The active docked construct appears as an asymmetrically docked conformation that might be an indication of a more complicated docking event than a simple collapse around the interdomain hinge.     

Thermodynamics and kinetics of the hairpin ribozyme from atomistic folding/unfolding simulations

We report a set of atomistic folding/unfolding simulations for the hairpin ribozyme using a Monte Carlo algorithm. The hairpin ribozyme folds in solution and catalyzes self-cleavage or ligation via a specific two-domain structure. The minimal active ribozyme has been studied extensively, showing stabilization of the active structure by cations and dynamic motion of the active structure. Here, we introduce a simple model of tertiary-structure formation that leads to a phase diagram for the RNA as a function of temperature and tertiary-structure strength. We then employ this model to capture many folding/unfolding events and to examine the transition-state ensemble (TSE) of the RNA during folding to its active “docked” conformation. The TSE is compact but with few tertiary interactions formed, in agreement with single-molecule dynamics experiments. To compare with experimental kinetic parameters, we introduce a novel method to benchmark Monte Carlo kinetic parameters to docking/undocking rates collected over many single molecular trajectories. We find that topology alone, as encoded in a biased potential that discriminates between secondary and tertiary interactions, is sufficient to predict the thermodynamic behavior and kinetic folding pathway of the hairpin ribozyme. This method should be useful in predicting folding transition states for many natural or man-made RNA tertiary structures.     

Predicting Ion Binding Properties for RNA Tertiary Structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg²⁺ 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 Mg²⁺ 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 Mg²⁺/Na⁺ ion-binding to various RNA and DNA structures over a wide range of Mg²⁺ and Na⁺ concentrations.     

A folding control element for tertiary collapse of a group II intron ribozyme

Ribozymes derived from the group II intron ai5gamma collapse to a compact intermediate, folding to the native state through a slow, direct pathway that is unperturbed by kinetic traps. Molecular collapse of ribozyme D135 requires high magnesium concentrations and is thought to involve a structural element in domain 1 (D1). We used nucleotide analog interference mapping, in combination with nondenaturing gel electrophoresis, to identify RNA substructures and functional groups that are essential for D135 tertiary collapse. This revealed that the most crucial atoms for compaction are located within a small section of D1 that includes the kappa and zeta elements. This small substructure controls specific collapse of the molecule and, in later steps of the folding pathway, it forms the docking site for catalytic D5. In this way, the stage is set for proper active site formation during the earliest steps of ribozyme folding.     

Entropy-driven folding of an RNA helical junction: an isothermal titration calorimetric analysis of the hammerhead ribozyme

Helical junctions are extremely common motifs in naturally occurring RNAs, but little is known about the thermodynamics that drive their folding. Studies of junction folding face several challenges: non-two-state folding behavior, superposition of secondary and tertiary structural energetics, and drastically opposing enthalpic and entropic contributions to folding. Here we describe a thermodynamic dissection of the folding of the hammerhead ribozyme, a three-way RNA helical junction, by using isothermal titration calorimetry of bimolecular RNA constructs. By using this method, we show that tertiary folding of the hammerhead core occurs with a highly unfavorable enthalpy change, and is therefore entropically driven. Furthermore, the enthalpies and heat capacities of core folding are the same whether supported by monovalent or divalent ions. These properties appear to be general to the core sequence of bimolecular hammerhead constructs. We present a model for the ion-induced folding of the hammerhead core that is similar to those advanced for the folding of much larger RNAs, involving ion-induced collapse to a structured, non-native state accompanied by rearrangement of core residues to produce the native fold. In agreement with previous enzymological and structural studies, our thermodynamic data suggest that the hammerhead structure is stabilized in vitro predominantly by diffusely bound ions. Our approach addresses several significant challenges that accompany the study of junction folding, and should prove useful in defining the thermodynamic determinants of stability in these important RNA motifs.