Topological constraints: using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.     

Helix Capping in RNA Structure

Helices are an essential element in defining the three-dimensional architecture of structured RNAs. While internal basepairs in a canonical helix stack on both sides, the ends of the helix stack on only one side and are exposed to the loop side, thus susceptible to fraying unless they are protected. While coaxial stacking has long been known to stabilize helix ends by directly stacking two canonical helices coaxially, based on analysis of helix-loop junctions in RNA crystal structures, herein we describe helix capping, topological stacking of a helix end with a basepair or an unpaired nucleotide from the loop side, which in turn protects helix ends. Beyond the topological protection of helix ends against fraying, helix capping should confer greater stability onto the resulting composite helices. Our analysis also reveals that this general motif is associated with the formation of tertiary structure interactions. Greater knowledge about the dynamics at the helix-junctions in the secondary structure should enhance the prediction of RNA secondary structure with a richer set of energetic rules and help better understand the folding of a secondary structure into its three-dimensional structure. These together suggest that helix capping likely play a fundamental role in driving RNA folding.     

New insights into the fundamental role of topological constraints as a determinant of two-way junction conformation

Recent studies have shown that topological constraints encoded at the RNA secondary structure level involving basic steric and stereochemical forces can significantly restrict the orientations sampled by helices across two-way RNA junctions. Here, we formulate these topological constraints in greater quantitative detail and use this topological framework to rationalize long-standing but poorly understood observations regarding the basic behavior of RNA two-way junctions. Notably, we show that the asymmetric nature of the A-form helix and the finite length of a bulge provide a physical basis for the experimentally observed directionality and bulge-length amplitude dependence of bulge induced inter-helical bends. We also find that the topologically allowed space can be modulated by variations in sequence, particularly with the addition of non-canonical GU base pairs at the junction, and, surprisingly, by the length of the 5' and 3' helices. A survey of two-way RNA junctions in the protein data bank confirms that junction residues have a strong preference to adopt looped-in, non-canonically base-paired conformations, providing a route for extending our bulge-directed framework to internal loop motifs and implying a simplified link between secondary and tertiary structure. Finally, our results uncover a new simple mechanism for coupling junction-induced topological constraints with tertiary interactions.     

How RNA folds.

We describe the RNA folding problem and contrast it with the much more difficult protein folding problem. RNA has four similar monomer units, whereas proteins have 20 very different residues. The folding of RNA is hierarchical in that secondary structure is much more stable than tertiary folding. In RNA the two levels of folding (secondary and tertiary) can be experimentally separated by the presence or absence of Mg2+. Secondary structure can be predicted successfully from experimental thermodynamic data on secondary structure elements: helices, loops, and bulges. Tertiary interactions can then be added without much distortion of the secondary structure. These observations suggest a folding algorithm to predict the structure of an RNA from its sequence. However, to solve the RNA folding problem one needs thermodynamic data on tertiary structure interactions, and identification and characterization of metal-ion binding sites. These data, together with force versus extension measurements on single RNA molecules, should provide the information necessary to test and refine the proposed algorithm.     

Quantifying the energetic interplay of RNA tertiary and secondary structure interactions

To understand the RNA-folding problem, we must know the extent to which RNA structure formation is hierarchical (tertiary folding of preformed secondary structure). Recently, nuclear magnetic resonance (NMR) spectroscopy was used to show that Mg2+-dependent tertiary interactions force secondary structure rearrangement in the 56-nt tP5abc RNA, a truncated subdomain of the Tetrahymena group I intron. Here we combine mutagenesis with folding computations, nondenaturing gel electrophoresis, high-resolution NMR spectroscopy, and chemical-modification experiments to probe further the energetic interplay of tertiary and secondary interactions in tP5abc. Point mutations predicted to destabilize the secondary structure of folded tP5abc greatly disrupt its Mg2+-dependent folding, as monitored by nondenaturing gels. Imino proton assignments and sequential NOE walks of the two-dimensional NMR spectrum of one of the tP5abc mutants confirm the predicted secondary structure, which does not change in the presence of Mg2+. In contrast to these data on tP5abc, the same point mutations in the context of the P4-P6 domain (of which P5abc is a subdomain) shift the Mg2+ dependence of P4-P6 folding only moderately, and dimethyl sulfate (DMS) modification experiments demonstrate that Mg2+ does cause secondary structure rearrangement of the P4-P6 mutants' P5abc subdomains. Our data provide experimental support for two simple conclusions: (1) Even single point mutations at bases involved only in secondary structure can be enough to tip the balance between RNA tertiary and secondary interactions. (2) Domain context must be considered in evaluating the relative importance of tertiary and secondary contributions. This tertiary/secondary interplay is likely relevant to the folding of many large RNA and to bimolecular snRNA-snRNA and snRNA-intron RNA interactions.     

Conformational changes in transfer RNA. I. Equilibrium theory

We report the results of semi-empirical calculations describing thermodynamic properties of transfer RNA conformations. The most important new features of the procedure are: (1) the use of parameters obtained from model oligoribonucleotides to evaluate the free energy of helical regions and small hairpin loops, and (2) the use of a model which is somewhat more realistic than the freely jointed chain for evaluating internal loops and intermediate size hairpin loops. The new parameters lead to important quantitative and qualitative differences from predictions which would have been made in the past and lead to a priori predictions of tRNA melting temperatures which are within about 6°C of the experimental values. The results suggest the following conclusions: (1) The early melting transition observed in several tRNA's is partly the result of tertiary unfolding, and partly the result of the loss of some secondary structure. (2) The part of the secondary structure which melts during the early transition is different for different tRNA's. For fMet and Tyr from E. coli, the calculations predict that the dihydrouradiene arm melts out early. For yeast Phe the acceptor stem and anticodon helix melt first. (3) The results also suggest the possibility that tertiary unfolding and early secondary structural melting do not occur independently but are coupled, so that the two types of structure are probably mutually stabilizing.     

Helical junctions as determinants for RNA folding: origin of tertiary structure stability of the hairpin ribozyme

Helical junctions are ubiquitous structural elements that govern the folding and tertiary structure of RNAs. The tobacco ringspot virus hairpin ribozyme consists of two helix-loop-helix elements that lie on adjacent arms of a four-way junction. In the active form of the hairpin ribozyme, the loops are in proximity. The nature of the helical junction determines the stability of the hairpin ribozyme tertiary structure [Walter, N. G., Burke, J. M., and Millar, D. P. (1999) Nat. Struct. Biol. 6, 544-549] and thus its catalytic activity. We used two-, three-, and four-way junction hairpin ribozymes as model systems to investigate the thermodynamic basis for the different tertiary structure stabilities. The equilibrium between docked and extended conformers was analyzed as a function of temperature using time-resolved fluorescence resonance energy transfer (trFRET). As the secondary and tertiary structure transitions overlap, information from UV melting curves and trFRET had to be combined to gain insight into the thermodynamics of both structural transitions. It turned out that the higher tertiary structure stability observed in the context of a four-way junction is the result of a lower entropic cost for the docking process. In the two- and three-way junction ribozymes, a high entropic cost counteracts the favorable enthalpic term, rendering the docked conformer only marginally stable. Thus, two- and three-way junction tertiary structures are more sensitive toward regulation by ligands, whereas four-way junctions provide a stable scaffold. Altogether, RNA folding and stability appear to be governed by principles similar to those for the folding of proteins.     

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.     

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

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

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.     

The GAAA tetraloop-receptor interaction contributes differentially to folding thermodynamics and kinetics for the P4-P6 RNA domain

Tetraloops with the generic sequence GNRA are commonly found in RNA secondary structure, and interactions of such tetraloops with "receptors" elsewhere in RNA play important roles in RNA structure and folding. However, the contributions of tetraloop-receptor interactions specifically to the kinetics of RNA tertiary folding, rather than the thermodynamics of maintaining tertiary structure once folded, have not been reported. Here we investigate the role of the key GAAA tetraloop-receptor motif in folding of the P4-P6 domain of the Tetrahymena group I intron RNA. Insertions of one or more nucleotides into the tetraloop significantly disrupt the thermodynamics of tertiary folding; single-nucleotide insertions shift the folding free energy by 2-4 kcal/mol (DeltaDeltaG(o)'). The folding kinetics of several modified P4-P6 domains were determined by stopped-flow fluorescence spectroscopy, using an internally incorporated pyrene residue as the chromophore. In contrast to the thermodynamic results, the kinetics of Mg(2+)-induced folding were barely affected by the tetraloop modifications, with a DeltaDeltaG(++) of 0.2-0.4 kcal/mol and a Phi value (ratio of the kinetic and thermodynamic contributions) of <0.1. These data indicate an early transition state for folding of P4-P6 with respect to forming the tetraloop-receptor contact, consistent with previous results for modifications elsewhere in P4-P6. We conclude that the GAAA tetraloop-receptor motif contributes little to the stabilization of the transition state for Mg(2+)-induced P4-P6 folding. Rather, the tetraloop-receptor motif acts to clamp the RNA once folding has occurred. This is the first report to correlate the kinetic and thermodynamic contributions of an important RNA tertiary motif, the GNRA tetraloop-receptor. The results are related to possible models for the Mg(2+)-induced folding of the P4-P6 RNA, including a model invoking rapid nonspecific electrostatic collapse.     

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.     

Differential chemical probing of a group II self-splicing intron identifies bases involved in tertiary interactions and supports an alternative secondary structure model of domain V.

Dimethyl sulfate modification was used to probe for tertiary structural elements in the group II intron PI.LSU/2 from the mitochondrial pre-ribosomal RNA of the brown alga Pylaiella littoralis. Modification of the lariat form of the intron under conditions that allow both native folding and conformational homogeneity is found to be generally consistent with secondary and tertiary structural features identified previously for group II ribozymes. A comparison of chemical probing at temperatures just below and above the first melting transition illustrates the cooperative unfolding of tertiary structure and identifies novel candidates for tertiary interactions in addition to defining elements of secondary structure. Substitution of the GAAA terminal loop of domain V is shown to be compatible with retention of conformational homogeneity (despite the loss of an important tertiary interaction), but produces a concise methylation footprint in domain I at the site previously shown to harbor the receptor for that loop. The analysis also identified two nucleotide positions in domain V with novel secondary and potential tertiary structural roles. The proposed refinement of domain V secondary structure is supported by an expanded comparative analysis of group II sequences and bears increased resemblance to U2:U6 snRNA pairing in the spliceosome.     

Energetics and cooperativity of tertiary hydrogen bonds in RNA structure.

Tertiary interactions that allow RNA to fold into intricate three-dimensional structures are being identified, but little is known about the thermodynamics of individual interactions. Here we quantify the tertiary structure contributions of individual hydrogen bonds in a "ribose zipper" motif of the recently crystallized Tetrahymena group I intron P4-P6 domain. The 2'-hydroxyls of P4-P6 nucleotides C109/A184 and A183/G110 participate in forming the "teeth" of the zipper. These four nucleotides were substituted in all combinations with their 2'-deoxy and (separately) 2'-methoxy analogues, and thermodynamic effects on the tertiary folding DeltaG degrees ' were assayed by the Mg2+ dependence of electrophoretic mobility in nondenaturing gels. The 2'-deoxy series showed a consistent trend with an average contribution to the tertiary folding DeltaG degrees' of -0.4 to -0.5 kcal/mol per hydrogen bond. Contributions were approximately additive, reflecting no cooperativity among the hydrogen bonds. Each "tooth" of the ribose zipper (comprising two hydrogen bonds) thus contributes about -1.0 kcal/mol to the tertiary folding DeltaG degrees'. Single 2'-methoxy substitutions destabilized folding by approximately 1 kcal/mol, but the trend reversed with multiple 2'-methoxy substitutions; the folding DeltaG degrees' for the quadruple 2'-methoxy derivative was approximately unchanged relative to wild-type. On the basis of these data and on temperature-gradient gel results, we conclude that entropically favorable hydrophobic interactions balance enthalpically unfavorable hydrogen bond deletions and steric clashes for multiple 2'-methoxy substitutions. Because many of the 2'-deoxy derivatives no longer have the characteristic hydrogen-bond patterns of the ribose zipper motif but simply have individual long-range ribose-base or ribose-ribose hydrogen bonds, we speculate that the energetic value of -0.4 to -0.5 kcal/mol per tertiary hydrogen bond may be more generally applicable to RNA folding.     

A simple molecular model for thermophilic adaptation of functional nucleic acids

RNA molecules have numerous functions including catalysis and small molecule recognition, which typically arise from a tertiary structure. There is increasing interest in mechanisms for the thermostability of functional RNA molecules. Sosnick, Pan, and co-workers introduced the notion of "functional stability" as the free energy of the tertiary (functional) state relative to the next most stable (nonfunctional) state. We investigated the extent to which secondary structure stability influences the functional stability of nucleic acids. Intramolecularly folding DNA triplexes containing alternating T*AT and C+*GC base triples were used as a three-state model for the folding of nucleic acids with functional tertiary structures. A four-base-pair tunable region was included adjacent to the triplex-forming portion of the helix to allow secondary structure strength to be modulated. The degree of folding cooperativity was controlled by pH, with high cooperativity maintained by lower pH (5.5), and no cooperativity by higher pH (7.0). We find a linear relationship between functional free energy and the free energy of the secondary structure element adjacent to tertiary interactions, but only when folding is cooperative. We translate the definition of functional stability into equations and perform simulations of the thermodynamic data, which lend support to this model. The ability to increase the melting temperature of tertiary structure by strengthening base-pairing interactions separate from tertiary interactions provides a simple means for evolving thermostability in functional RNAs.     

Analysis of Four-Way Junctions in RNA Structures

RNA secondary structures can be divided into helical regions composed of canonical Watson-Crick and related base pairs, as well as single-stranded regions such as hairpin loops, internal loops, and junctions. These elements function as building blocks in the design of diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze existing RNA four-way junctions in terms of base-pair interactions and 3D configurations. Specifically, we identify nine broad junction families according to coaxial stacking patterns and helical configurations. We find that helices within junctions tend to arrange in roughly parallel and perpendicular patterns and stabilize their conformations using common tertiary motifs such as coaxial stacking, loop-helix interaction, and helix packing interaction. Our analysis also reveals a number of highly conserved base-pair interaction patterns and novel tertiary motifs such as A-minor-coaxial stacking combinations and sarcin/ricin motif variants. Such analyses of RNA building blocks can ultimately help in the difficult task of RNA 3D structure prediction.     

Promoting RNA helical stacking via A-minor junctions

RNA molecules take advantage of prevalent structural motifs to fold and assemble into well-defined 3D architectures. The A-minor junction is a class of RNA motifs that specifically controls coaxial stacking of helices in natural RNAs. A sensitive self-assembling supra-molecular system was used as an assay to compare several natural and previously unidentified A-minor junctions by native polyacrylamide gel electrophoresis and atomic force microscopy. This class of modular motifs follows a topological rule that can accommodate a variety of interchangeable A-minor interactions with distinct local structural motifs. Overall, two different types of A-minor junctions can be distinguished based on their functional self-assembling behavior: one group makes use of triloops or GNRA and GNRA-like loops assembling with helices, while the other takes advantage of more complex tertiary receptors specific for the loop to gain higher stability. This study demonstrates how different structural motifs of RNA can contribute to the formation of topologically equivalent helical stacks. It also exemplifies the need of classifying RNA motifs based on their tertiary structural features rather than secondary structural features. The A-minor junction rule can be used to facilitate tertiary structure prediction of RNAs and rational design of RNA parts for nanobiotechnology and synthetic biology.