Formation of spatial structure of RNA molecules

In this review we consider several experimental and theoretical approaches for investigation of RNA folding and determination of nucleotides that play an important role upon folding of such molecules as tRNA and several classes of ribozymes. It has been shown that nucleotides in the D- and T-loop regions are the last to be involved in tRNA structure or they are not included in the folding nucleus of tRNA. Using the specially elaborated method SHAPE it has been demonstrated that the model of hierarchical folding which was recognized for a long time is not correct for tRNA folding. In the second part of the given review the algorithms and programs used for the prediction of secondary structures of RNA as well as for modeling of RNA folding are considered.     

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.     

Formation of RNA spatial structures

The review considers different experimental and theoretical approaches to the investigation of RNA folding and identification of nucleotides that critically affect the folding of molecules, such as tRNA, and several classes of ribozymes. For instance, it has been shown that nucleotides of the D- and T-loop regions are the last to be involved in the tRNA structure, or, rather, they are not included in the tRNA folding nucleus. A specially developed SHAPE method was used to show that the long-recognized hierarchical folding model does not hold true for tRNA folding. In the second part of the review, algorithms and programs used for the prediction of RNA secondary structures, as well as for modeling RNA folding, are considered.     

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg²⁺ ion concentrations are low, K⁺ concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo–like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg²⁺ (0.5–2 mM) and K⁺ (140 mM) if the solution is supplemented with physiological amounts (∼20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution.     

Structure of a folding intermediate reveals the interplay between core and peripheral elements in RNA folding

Though the molecular architecture of many native RNA structures has been characterized, the structures of folding intermediates are poorly defined. Here, we present a nucleotide-level model of a highly structured equilibrium folding intermediate of the specificity domain of the Bacillus subtilis RNase P RNA, obtained using chemical and nuclease mapping, circular dichroism spectroscopy, small-angle X-ray scattering and molecular modeling. The crystal structure indicates that the 154 nucleotide specificity domain is composed of several secondary and tertiary structural modules. The structure of the intermediate contains modules composed of secondary structures and short-range tertiary interactions, implying a sequential order of tertiary structure formation during folding. The intermediate lacks the native core and several long-range interactions among peripheral regions, such as a GAAA tetraloop and its receptor. Folding to the native structure requires the local rearrangement of a T-loop in the core in concert with the formation of the GAAA tetraloop-receptor interaction. The interplay of core and peripheral structure formation rationalizes the high degree of cooperativity observed in the folding transition leading to the native structure.     

Comparing multiple RNA secondary structures using tree comparisons

In a previous paper, an algorithm was presented for analyzingmultiple RNA secondary structures utilizing a multiple stringalignment algorithm. In this paper we present another approachto the problem of comparing many secondary structures by utilizinga very efficient tree-matching algorithm that will compare twotrees in O(|T₁|x|T₂|x L₁ x L₂) in the worst case and very closeto O(|T₁|x|T₂|) for average trees representing secondary structures.The result of the pairwise comparison algorithm is then usedwith acluster algorithm to produce a multiple structure clusteringwhich can be displayed in ataxonomy tree to show related structures. Received on September 15, 1989; accepted on June 12, 1990     

iFoldRNA: three-dimensional RNA structure prediction and folding

Three-dimensional RNA structure prediction and folding is of significant interest in the biological research community. Here, we present iFoldRNA, a novel web-based methodology for RNA structure prediction with near atomic resolution accuracy and analysis of RNA folding thermodynamics. iFoldRNA rapidly explores RNA conformations using discrete molecular dynamics simulations of input RNA sequences. Starting from simplified linear-chain conformations, RNA molecules (<50 nt) fold to native-like structures within half an hour of simulation, facilitating rapid RNA structure prediction. All-atom reconstruction of energetically stable conformations generates iFoldRNA predicted RNA structures. The predicted RNA structures are within 2-5 A root mean squre deviations (RMSDs) from corresponding experimentally derived structures. RNA folding parameters including specific heat, contact maps, simulation trajectories, gyration radii, RMSDs from native state, fraction of native-like contacts are accessible from iFoldRNA. We expect iFoldRNA will serve as a useful resource for RNA structure prediction and folding thermodynamic analyses. AVAILABILITY: http://iFoldRNA.dokhlab.org.     

Three-dimensional models of the tRNA-like 3' termini of some plant viral RNAs.

Various plant viral RNAs possess a 3'' terminus with tRNA-like properties. These viral RNAs are charged with an amino acid upon incubation with the cognate aminoacyl-tRNA synthetase and ATP. We have studied the structure of end-labelled 3''-terminal fragments of turnip yellow mosaic virus RNA and brome mosaic virus RNA 2 with chemical modifications of the adenosine and cytidine residues and with enzymatic digestions using RNase T1, nuclease S1 and the double-strand-specific ribonuclease from cobra venom. The data indicate that the 3'' termini of these plant viral RNAs lack a cloverleaf structure as found in classical tRNA. The three-dimensional folding, however, reveals a striking resemblance with classical tRNA. The models proposed are supported by phylogenetic data. Apparently distinct three-dimensional solutions have evolved to meet the requirements for faithful recognition by tRNA-specific enzymes. The way in which the aminoacyl acceptor arms of these tRNA-like structures are constructed reveal novel features in RNA folding which may have a bearing on the secondary and tertiary structures of RNA in general. The dynamic behaviour of brome mosaic virus RNA 2 in solution presumably is illustrative of conformational transitions, which RNAs generally undergo on changing the ionic conditions.     

Interspecific variation in mitochondrial serine transfer RNA (UCN) in Euptychiina butterflies (Lepidoptera: Satyrinae): structure and alignment

The nucleotide variation and structural patterns of mitochondrial RNA molecule have been proposed as useful tools in molecular systematics; however, their usefulness is always subject to a proper assessment of homology in the sequence alignment. The present study describes the secondary structure of mitochondrial tRNA for the amino acid serine (UCN) on 13 Euptychiina species and the evaluation of its potential use for evolutionary studies in this group of butterflies. The secondary structure of tRNAs showed variation among the included species except between Hermeuptychia sp1 and sp2. Variation was concentrated in the ribotimidina-pseudouridine-cystosine (TψC), dihydrouridine (DHU) and variable loops and in the DHU and TψC arms. These results suggest this region as a potential marker useful for taxonomic differentiation of species in this group and also confirm the importance of including information from the secondary structure of tRNA to optimize the alignments.     

The computer simulation of RNA folding involving pseudoknot formation.

The algorithm and the program for the prediction of RNA secondary structure with pseudoknot formation have been proposed. The algorithm simulates stepwise folding by generating random structures using Monte Carlo method, followed by the selection of helices to final structure on the basis of both their probabilities of occurrence in a random structure and free energy parameters. The program versions have been tested on ribosomal RNA structures and on RNAs with pseudoknots evidenced by experimental data. It is shown that the simulation of folding during RNA synthesis improves the results. The introduction of pseudoknot formation permits to predict the pseudoknotted structures and to improve the prediction of long-range interactions. The computer program is rather fast and allows to predict the structures for long RNAs without using large memory volumes in usual personal computer.     

Prediction of alternative RNA secondary structures based on fluctuating thermodynamic parameters.

In this paper we present a new method for predicting a set of RNA secondary structures that are thermodynamically favored in RNA folding simulations. This method uses a large number of 'simulated energy rules' (SER) generated by perturbing the free energy parameters derived experimentally within the range of the experimental errors. The structure with the lowest free energy is computed for each SER. Structural comparisons are used to avoid multiple generation of similar structures. Computed structures are evaluated using the energy distribution of the lowest free energy structures derived in the simulation. Predicted be graphically displayed with their occurring frequencies in the simulation by dot-plot representations. On average, about 90% of phylogenetic helixes in the known models of tRNA, Group I self-splicing intron, and Escherichia coli 16 S rRNA, were predicted using the method.     

An improved secondary structure computation method and its application to intervening sequences in the human alpha-like globin mRNA precursors

Current secondary structure prediction computations have a seriousdrawback. The calculated thermodynamically most stable structureoften differs from that observed in solution or in crystal form.In this paper we suggest a way to partially overcome some ofthese limitations by simulating the RNA folding process andcalculating the frequencies of occurrence of the various substructuresobtained. The frequently recurring substructures are then selectedto construct the secondary structure of the whole RNA. 142 tRNAmolecules and an E. coli 16S rRNA molecule have been examinedby this method. The percentages of successful prediction ofthe correct helices are significantly higher than those calculatedpreviously. The secondary structures of intervening sequences(IVSs) excised from human -like globin pre-mRNAs are also computed.Thus, in this method the secondary structures obtained are composedof the statistically more significant substructures. This hasalso been demonstrated by using randomly shuffled sequences.The secondary structures of each of the randomized sequencesare computed and their mean and standard deviations are usedin evaluating the significance of the substructures obtainedin the folding of the biological sequence. Some potentiallyappealing structural features aligning adjacent exons for ligationhave been found. Received on April 3, 1987; accepted on October 18, 1987     

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA''s allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA''s helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA''s different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.     

The tRNA-like structure of turnip yellow mosaic virus RNA: structural organization of the last 159 nucleotides from the 3' OH terminus

The secondary structure of the isolated tRNA-like sequence (n=159) present at the 3' OH terminus of turnip yellow mosaic virus RNA has been established from partial nuclease digestion with S1 nuclease and T1, CL₃, and Naja oxiana RNases. The fragment folds into a 6-armed structure with two main domains. The first domain, of loose structure and nearest the 5' OH terminus, is composed of one large arm which extends into the coat protein cistron. The second, more compact domain, is composed of the five other arms and most probably contains the structure recognized by valyl-tRNA synthetase. In this domain three successive arms strikingly resemble the T[unk], anticodon, and D arms found in tRNA. Near the amino-acid accepting terminus, however, there is a new stem and loop region not found in standard tRNA. This secondary structure is compatible with a L-shaped three-dimensional organization in which the corner of the L and the anticodon-containing limb are similar to, and the amino-acid accepting region different from, that in tRNA. Ethylnitrosourea accessibility studies have shown similar tertiary structure features in the T[unk] loop of tRNA^Val and in the homologous region of the viral RNA.     

An efficient algorithm to compute the landscape of locally optimal RNA secondary structures with respect to the Nussinov-Jacobson energy model.

We make a novel contribution to the theory of biopolymer folding, by developing an efficient algorithm to compute the number of locally optimal secondary structures of an RNA molecule, with respect to the Nussinov-Jacobson energy model. Additionally, we apply our algorithm to analyze the folding landscape of selenocysteine insertion sequence (SECIS) elements from A. Bock (personal communication), hammerhead ribozymes from Rfam (Griffiths-Jones et al., 2003), and tRNAs from Sprinzl's database (Sprinzl et al., 1998). It had previously been reported that tRNA has lower minimum free energy than random RNA of the same compositional frequency (Clote et al., 2003; Rivas and Eddy, 2000), although the situation is less clear for mRNA (Seffens and Digby, 1999; Workman and Krogh, 1999; Cohen and Skienna, 2002),(1) which plays no structural role. Applications of our algorithm extend knowledge of the energy landscape differences between naturally occurring and random RNA. Given an RNA molecule a(1), ... , a(n) and an integer k > or = 0, a k-locally optimal secondary structure S is a secondary structure on a(1), ... , a(n) which has k fewer base pairs than the maximum possible number, yet for which no basepairs can be added without violation of the definition of secondary structure (e.g., introducing a pseudoknot). Despite the fact that the number numStr(k) of k-locally optimal structures for a given RNA molecule in general is exponential in n, we present an algorithm running in time O(n (4)) and space O(n (3)), which computes numStr(k) for each k. Structurally important RNA, such as SECIS elements, hammerhead ribozymes, and tRNA, all have a markedly smaller number of k-locally optimal structures than that of random RNA of the same dinucleotide frequency, for small and moderate values of k. This suggests a potential future role of our algorithm as a tool to detect noncoding RNA genes.     

Common structures of the 5' non-coding RNA in enteroviruses and rhinoviruses. Thermodynamical stability and statistical significance

A total of 4051 suboptimal secondary structures are predicted by folding the 5' non-coding region of ten polioviruses, five human rhinoviruses and three coxsackieviruses using our new suboptimal folding algorithm for the prediction of both optimal and suboptimal RNA secondary structures. A comparative analysis of these RNA secondary structures reveals the conservation of common secondary structure that can be supported by phylogenetic data. The thermodynamic stability and statistical significance of these predicted, conserved helical elements are assessed and significant structure motifs in the 5' non-coding region are proposed. The possible roles of these structure motifs in the virus life cycle are discussed.     

Stochastic context-free grammars for tRNA modeling.

Stochastic context-free grammars (SCFGs) are applied to the problems of folding, aligning and modeling families of tRNA sequences. SCFGs capture the sequences' common primary and secondary structure and generalize the hidden Markov models (HMMs) used in related work on protein and DNA. Results show that after having been trained on as few as 20 tRNA sequences from only two tRNA subfamilies (mitochondrial and cytoplasmic), the model can discern general tRNA from similar-length RNA sequences of other kinds, can find secondary structure of new tRNA sequences, and can produce multiple alignments of large sets of tRNA sequences. Our results suggest potential improvements in the alignments of the D- and T-domains in some mitochondrial tRNAs that cannot be fit into the canonical secondary structure.