No evidence that mRNAs have lower folding free energies than random sequences with the same dinucleotide distribution

This work investigates whether mRNA has a lower estimated folding free energy than random sequences. The free energy estimates are calculated by the mfold program for prediction of RNA secondary structures. For a set of 46 mRNAs it is shown that the predicted free energy is not significantly different from random sequences with the same dinucleotide distribution. For random sequences with the same mononucleotide distribution it has previously been shown that the native mRNA sequences have a lower predicted free energy, which indicates a more stable structure than random sequences. However, dinucleotide content is important when assessing the significance of predicted free energy as the physical stability of RNA secondary structure is known to depend on dinucleotide base stacking energies. Even known RNA secondary structures, like tRNAs, can be shown to have predicted free energies indistinguishable from randomized sequences. This suggests that the predicted free energy is not always a good determinant for RNA folding.     

Conservation of secondary structure in 5 S ribosomal RNA: a uniform model for eukaryotic, eubacterial, archaebacterial and organelle sequences is energetically favourable

The most commonly accepted secondary structure models for 5S RNA differ for molecules of eubacterial origin, where the four-helix model of Fox and Woese is generally cited, and those of eukaryotic origin, where a fifth helix is assumed to exist. We have carefully aligned all available sequences from eukaryotes, eubacteria, chloroplasts, archaebacteria and plant mitochondria. We could thus derive a unified secondary structure model applicable to all 5S RNA sequences known to-date. It contains the five helices already present in the eukaryotic model, extended by additional segments that were not previously assumed to be universally present. One of the helices can be written in two equilibrium forms, which could reflect the existence of a flexible, dynamic structure. For the derivation of the model and the estimation of the free energies we followed a set of rules optimized to predict the tRNA cloverleaf. The stability of the unified model is higher than that of nearly all previously proposed sequence-specific and general models.     

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.     

Identifying constraints on the higher-order structure of RNA: continued development and application of comparative sequence analysis methods.

Comparative sequence analysis addresses the problem of RNA folding and RNA structural diversity, and is responsible for determining the folding of many RNA molecules, including 5S, 16S, and 23S rRNAs, tRNA, RNAse P RNA, and Group I and II introns. Initially this method was utilized to fold these sequences into their secondary structures. More recently, this method has revealed numerous tertiary correlations, elucidating novel RNA structural motifs, several of which have been experimentally tested and verified, substantiating the general application of this approach. As successful as the comparative methods have been in elucidating higher-order structure, it is clear that additional structure constraints remain to be found. Deciphering such constraints requires more sensitive and rigorous protocols, in addition to RNA sequence datasets that contain additional phylogenetic diversity and an overall increase in the number of sequences. Various RNA databases, including the tRNA and rRNA sequence datasets, continue to grow in number as well as diversity. Described herein is the development of more rigorous comparative analysis protocols. Our initial development and applications on different RNA datasets have been very encouraging. Such analyses on tRNA, 16S and 23S rRNA are substantiating previously proposed associations and are now beginning to reveal additional constraints on these molecules. A subset of these involve several positions that correlate simultaneously with one another, implying units larger than a basepair can be under a phylogenetic constraint.     

A contact-waiting-time metric and RNA folding rates

Metrics for indirectly predicting the folding rates of RNA sequences are of interest. In this letter, we introduce a simple metric of RNA structural complexity, which accounts for differences in the energetic contributions of RNA base contacts toward RNA structure formation. We apply the metric to RNA sequences whose folding rates were previously determined experimentally. We find that the metric has good correlation (correlation coefficient: −0.95, p?0.01) with the logarithmically transformed folding rates of those RNA sequences. This suggests that the metric can be useful for predicting RNA folding rates. We use the metric to predict the folding rates of bacterial and eukaryotic group II introns. Future applications of the metric (e.g., to predict structural RNAs) could prove fruitful.     

A correlation between N2-dimethylguanosine presence and alternate tRNA conformers.

Even though the evolutionary conservation of the cloverleaf model is strongly suggestive of powerful constraints on the secondary structure of functional tRNAs, some mitochondrial tRNAs cannot be folded into this form. From the optimal base pairing pattern of these recalcitrant tRNAs, structural correlations between the length of the anticodon stem and the lengths of connector regions between the two helical domains, formed by the coaxial stacking of the anticodon and D-stems and the acceptor and T-stems, have been derived and used to scan the tRNA and tRNA gene database. We show here that some cytosolic tRNA gene sequences that are compatible with the cloverleaf model can also be folded into patterns proposed for the unusual mitochondrial tRNAs. Furthermore, the ability to be folded into these atypical structures correlates in the mature RNA sequences with the presence of dimethylguanosine, whose role may be to prevent the unusual mitochondrial tRNA pattern folding.     

Identifying complete RNA structural ensembles including pseudoknots

The close relationship between RNA structure and function underlines the significance of accurately predicting RNA structures from sequence information. Structural topologies such as pseudoknots are of particular interest due to their ubiquity and direct involvement in RNA function, but identifying pseudoknots is a computationally challenging problem and existing heuristic approaches usually perform poorly for RNA sequences of even a few hundred bases. We survey the performance of pseudoknot prediction methods on a data set of full-length RNA sequences representing varied sequence lengths, and biological RNA classes such as RNase P RNA, Group I Intron, tmRNA and tRNA. Pseudoknot prediction methods are compared with minimum free energy and suboptimal secondary structure prediction methods in terms of correct base-pairs, stems and pseudoknots and we find that the ensemble of suboptimal structure predictions succeeds in identifying correct structural elements in RNA that are usually missed in MFE and pseudoknot predictions. We propose a strategy to identify a comprehensive set of non-redundant stems in the suboptimal structure space of a RNA molecule by applying heuristics that reduce the structural redundancy of the predicted suboptimal structures by merging slightly varying stems that are predicted to form in local sequence regions. This reduced-redundancy set of structural elements consistently outperforms more specialized approaches.in data sets. Thus, the suboptimal folding space can be used to represent the structural diversity of an RNA molecule more comprehensively than optimal structure prediction approaches alone.     

Recognition of the folding consensus in RNA secondary structures by the topological-filtering method.

Functionally homologous RNA sequences can substantially diverge in their primary sequences but it can be reasonably assumed that they are related in their higher-degree structures. The problem to find such structures and simultaneously satisfy as far as possible the free-energy-minimization criterion, is considered here in two aspects. Firstly a quantitative measure of the folding consensus among secondary structures is defined, translating each structure into a linear representation and using the correlation theorem to compare them. Secondly an algorithm for the parallel search for secondary structures according to the free-energy-minimization criterion, but with a filtering action on the basis of the folding consensus measure is presented. The method is tested on groups of RNA sequences different in origin and in functions, for which proposals of homologous secondary structures based on experimental data exist. A comparison of the results with a blank consisting of a search on the basis of the free energy minimization alone is always performed. In these tests the method shows its ability in obtaining, from different sequences, secondary structures characterized by a high-folding consensus measure also when lower free energy but not homologous structures are possible. Two applications are also shown. The first demonstrates the transfer of experimental data available for one sequence, to a functionally related and therefore homologous one. The second application is the possibility of using a topological probe in the search for precise structural motifs.     

RNA sequence analysis using covariance models.

We describe a general approach to several RNA sequence analysis problems using probabilistic models that flexibly describe the secondary structure and primary sequence consensus of an RNA sequence family. We call these models 'covariance models'. A covariance model of tRNA sequences is an extremely sensitive and discriminative tool for searching for additional tRNAs and tRNA-related sequences in sequence databases. A model can be built automatically from an existing sequence alignment. We also describe an algorithm for learning a model and hence a consensus secondary structure from initially unaligned example sequences and no prior structural information. Models trained on unaligned tRNA examples correctly predict tRNA secondary structure and produce high-quality multiple alignments. The approach may be applied to any family of small RNA sequences.     

Common evolutionary trends for SINE RNA structures

Short interspersed elements (SINEs) and long interspersed elements (LINEs) are transposable elements in eukaryotic genomes that mobilize through an RNA intermediate. Understanding their evolution is important because of their impact on the host genome. Most eukaryotic SINEs are ancestrally related to tRNA genes, although the typical tRNA cloverleaf structure is not apparent for most SINE consensus RNAs. Using a cladistic method where RNA structural components were coded as polarized and ordered multistate characters, we showed that related structural motifs are present in most SINE RNAs from mammals, fishes and plants, suggesting common selective constraints imposed at the SINE RNA structural level. Based on these results, we propose a general multistep model for the evolution of tRNA-related SINEs in eukaryotes.     

Prediction of common secondary structures of RNAs: a genetic algorithm approach

In this study we apply a genetic algorithm to a set of RNA sequences to find common RNA secondary structures. Our method is a three-step procedure. At the first stage of the procedure for each sequence, a genetic algorithm is used to optimize the structures in a population to a certain degree of stability. In this step, the free energy of a structure is the fitness criterion for the algorithm. Next, for each structure, we define a measure of structural conservation with respect to those in other sequences. We use this measure in a genetic algorithm to improve the structural similarity among sequences for the structures in the population of a sequence. Finally, we select those structures satisfying certain conditions of structural stability and similarity as predicted common structures for a set of RNA sequences. We have obtained satisfactory results from a set of tRNA, 5S rRNA, rev response elements (RRE) of HIV-1 and RRE of HIV-2/SIV, respectively.     

A Test and Refinement of Folding Free Energy Nearest Neighbor Parameters for RNA Including N6-Methyladenosine

RNA folding free energy change parameters are widely used to predict RNA secondary structure and to design RNA sequences. These parameters include terms for the folding free energies of helices and loops. Although the full set of parameters has only been traditionally available for the four common bases and backbone, it is well known that covalent modifications of nucleotides are widespread in natural RNAs. Covalent modifications are also widely used in engineered sequences. We recently derived a full set of nearest neighbor terms for RNA that includes N⁶-methyladenosine (m⁶A). In this work, we test the model using 98 optical melting experiments, matching duplexes with or without N⁶-methylation of A. Most experiments place RRACH, the consensus site of N⁶-methylation, in a variety of contexts, including helices, bulge loops, internal loops, dangling ends, and terminal mismatches. For matched sets of experiments that include either A or m⁶A in the same context, we find that the parameters for m⁶A are as accurate as those for A. Across all experiments, the root mean squared deviation between estimated and experimental free energy changes is 0.67 kcal/mol. We used the new experimental data to refine the set of nearest neighbor parameter terms for m⁶A. These parameters enable prediction of RNA secondary structures including m⁶A, which can be used to model how N⁶-methylation of A affects RNA structure.     

Maximizing RNA folding rates: a balancing act

Large ribozymes typically require very long times to refold into their active conformation in vitro, because the RNA is easily trapped in metastable misfolded structures. Theoretical models show that the probability of misfolding is reduced when local and long-range interactions in the RNA are balanced. Using the folding kinetics of the Tetrahymena ribozyme as an example, we propose that folding rates are maximized when the free energies of forming independent domains are similar to each other. A prediction is that the folding pathway of the ribozyme can be reversed by inverting the relative stability of the tertiary domains. This result suggests strategies for optimizing ribozyme sequences for therapeutics and structural studies.     

Evidence that microRNA precursors, unlike other non-coding RNAs, have lower folding free energies than random sequences

MOTIVATION: Most non-coding RNAs are characterized by a specific secondary and tertiary structure that determines their function. Here, we investigate the folding energy of the secondary structure of non-coding RNA sequences, such as microRNA precursors, transfer RNAs and ribosomal RNAs in several eukaryotic taxa. Statistical biases are assessed by a randomization test, in which the predicted minimum free energy of folding is compared with values obtained for structures inferred from randomly shuffling the original sequences. RESULTS: In contrast with transfer RNAs and ribosomal RNAs, the majority of the microRNA sequences clearly exhibit a folding free energy that is considerably lower than that for shuffled sequences, indicating a high tendency in the sequence towards a stable secondary structure. A possible usage of this statistical test in the framework of the detection of genuine miRNA sequences is discussed.     

Predicting the secondary structures and tertiary interactions of 211 group I introns in IE subgroup

The large number of currently available group I intron sequences in the public databases provides opportunity for studying this large family of structurally complex catalytic RNA by large-scale comparative sequence analysis. In this study, the detailed secondary structures of 211 group I introns in the IE subgroup were manually predicted. The secondary structure-favored alignments showed that IE introns contain 14 conserved stems. The P13 stem formed by long-range base-pairing between P2.1 and P9.1 is conserved among IE introns. Sequence variations in the conserved core divide IE introns into three distinct minor subgroups, namely IE1, IE2 and IE3. Co-variation of the peripheral structural motifs with core sequences supports that the peripheral elements function in assisting the core structure folding. Interestingly, host-specific structural motifs were found in IE2 introns inserted at S516 position. Competitive base-pairing is found to be conserved at the junctions of all long-range paired regions, suggesting a possible mechanism of establishing long-range base-pairing during large RNA folding. These findings extend our knowledge of IE introns, indicating that comparative analysis can be a very good complement for deepening our understanding of RNA structure and function in the genomic era.     

The evolution of 5S RNA secondary structures

We have applied the Pipas-McMahon algorithm based on free energy calculations to the search for a 5S RNA base-pair structure common to all known sequences. We find that a 'Y' shaped model is consistently among the structures having the lowest free energy using 5S RNA sequences from either eukaryotic or prokaryotic sources. Compaison of this 'Y' structure with models which have recently been proposed show these models to be remarkably similar, and the minor differences are explicable based on the technique used to obtain the model. That prokaryotic and eukaryotic 5S RNA can adopt a similar secondary structure is strong support for its resistance to change during evolution.     

Small mobile sequences in bacteria display diverse structure/function motifs

Small repeat sequences in bacterial genomes, which represent non-autonomous mobile elements, have close similarities to archaeon and eukaryotic miniature inverted repeat transposable elements. These repeat elements are found in both intergenic and intragenic chromosomal regions, and contain an array of diverse motifs. These can include DNA sequences containing an integration host factor binding site and a proposed DNA methyltransferase recognition site, transcribed RNA secondary structural motifs, which are involved in mRNA regulation, and translated open reading frames found fused to other open reading frames. Some bacterial mobile element fusions are in evolutionarily conserved protein and RNA genes. Others might represent or lead to creation of new protein genes. Here we review the remarkable properties of these small bacterial mobile elements in the context of possible beneficial roles resulting from random insertions into the genome.