Incorporating global features of RNA motifs in predictions for an ensemble of secondary structures for encapsidated MS2 bacteriophage RNA

The secondary structure of encapsidated MS2 genomic RNA poses an interesting RNA folding challenge. Cryoelectron microscopy has demonstrated that encapsidated MS2 RNA is well-ordered. Models of MS2 assembly suggest that the RNA hairpin-protein interactions and the appropriate placement of hairpins in the MS2 RNA secondary structure can guide the formation of the correct icosahedral particle. The RNA hairpin motif that is recognized by the MS2 capsid protein dimers, however, is energetically unfavorable, and thus free energy predictions are biased against this motif. Computer programs called Crumple, Sliding Windows, and Assembly provide useful tools for prediction of viral RNA secondary structures when the traditional assumptions of RNA structure prediction by free energy minimization may not apply. These methods allow incorporation of global features of the RNA fold and motifs that are difficult to include directly in minimum free energy predictions. For example, with MS2 RNA the experimental data from SELEX experiments, crystallography, and theoretical calculations of the path for the series of hairpins can be incorporated in the RNA structure prediction, and thus the influence of free energy considerations can be modulated. This approach thoroughly explores conformational space and generates an ensemble of secondary structures. The predictions from this new approach can test hypotheses and models of viral assembly and guide construction of complete three-dimensional models of virus particles.     

Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy

We adapt here a surprising technique, the boustrophedon method, to speed up the sampling of RNA secondary structures from the Boltzmann low-energy ensemble. This technique is simple and its implementation straight-forward, as it only requires a permutation in the order of some operations already performed in the stochastic traceback stage of these algorithms. It nevertheless greatly improves their worst-case complexity from to , for n the size of the original sequence. Moreover the average-case complexity of the generation is shown to be improved from to in an Boltzmann-weighted homopolymer model based on the Nussinov–Jacobson free-energy model. These results are extended to the more realistic Turner free-energy model through experiments performed on both structured (Drosophilia melanogaster mRNA 5S) and hybrid (Staphylococcus aureus RNAIII) RNA sequences, using a boustrophedon modified version of the popular software UnaFold. This improvement allows for the sampling of greater and more significant sets of structures in a given time.      

On a seven-dimensional representation of RNA secondary structures

In this paper, we proposed a seven-dimensional (7D) representation of ribonucleic acid (RNA) secondary structures. The use of the 7D representation is illustrated by constructing structure invariants. Comparisons with the similarity/dissimilarity results based on 7D representation for a set of RNA 3 secondary structures at the 3′-terminus of different viruses, are considered to illustrate the use of our structure invariants based on the entries in derived sequence matrices restricted to a selected width of a band along the main diagonal.     

The template RNAs of RNA polymerases can have compact secondary structure, formed by long double helices with partial violations of the complementarity

A new method of contextual analysis was used to search the long non-random inverted repeats and the complementary palindromes in the genes of E. coli and T7 RNA polymerases. These genes were found to contain from 25% to 50% of all the nucleotides involved in such helices. The 5' -and 3' -ends of mRNA can be protected by neighbouring double helices from the nuclease attack. Some double helices are competing and very similar to the attenuator of E. coli trp-operon.     

New method to predict conserved RNA structures

RNA secondary structure prediction is one of the classic problems of bioinformatics. The most efficient approaches to solving this problem are based on comparative analysis. As a rule, multiple RNA sequence alignment and subsequent determination of a common secondary structure are used. A new algorithm was developed to obviate the need for preliminary multiple sequence alignment. The algorithm is based on a multilevel MEME-like iterative search for a generalized profile. The search for common blocks in RNA sequences is carried out at the first level. Then the algorithm refines the chains consisting of these blocks. Finally, the search for sets of common helices, matched with alignment blocks, is carried out. The algorithm was tested with a tRNA set containing additional junk sequences and with RFN riboswitches. The algorithm is available at http://bioinf.fbb.msu.ru/RNAAlign.     

Protein-coding structured RNAs: A computational survey of conserved RNA secondary structures overlapping coding regions in drosophilids

Functional RNA elements can be embedded also within exonic sequences coding for functional proteins. While not uncommon in viruses, only a few examples of this type have been described in some detail for eukaryotic genomes. Here we use RNAz and RNAcode, two comparative genomics methods that measure signatures of stabilizing selection acting on RNA secondary structure and peptide sequence, resp., to survey the fruit fly genomes. We estimate that there might be on the order of 1000 loci that are subject to dual selection pressure. The used genome-wide screens also expose the limitations of the currently available methods.     

Fuzzy Kernel Clustering of RNA Secondary Structure Ensemble Using a Novel Similarity Metric

Abstract

Measuring the (dis)similarity between RNA secondary structures is critical for the study of RNA secondary structures and has implications to RNA functional characterization. Although a number of methods have been developed for comparing RNA structural similarities, their applications have been limited by the complexity of the required computation. In this paper, we present a novel method for comparing the similarity of RNA secondary structures generated from the same RNA sequence, i.e., a secondary structure ensemble, using a matrix representation of the RNA structures. Relevant features of the RNA secondary structures can be easily extracted through singular value decomposition (SVD) of the representing matrices. We have mapped the feature vectors of the singular values to a kernel space, where (dis)similarities among the mapped feature vectors become more evident, making clustering of RNA secondary structures easier to handle. The pair-wise comparison of RNA structures is achieved through computing the distance between the singular value vectors in the kernel space. We have applied a fuzzy kernel clustering method, using this similarity metric, to cluster the RNA secondary structure ensembles. Our application results suggest that our fuzzy kernel clustering method is highly promising for classifications of RNA structure ensembles, because of its low computational complexity and high clustering accuracy.     

General combinatorics of RNA secondary structure

The total number of RNA secondary structures of a given length with minimal hairpin loop length m(m>0) and with minimal stack length l(l>0) is computed, under the assumption that all base pairs can occur. Asymptotics are derived from the determination of recurrence relations of decomposition properties.     

Bistable secondary structures of small RNAs and their structural probing by comparative imino proton NMR spectroscopy

We investigate 25-34 nucleotide RNA sequences, that have been rationally designed to adopt two different secondary structures that are in thermodynamic equilibrium. Experimental evidence for the co-existence of the two conformers results from the NH...N 1H NMR spectra. When compared to the NH...N 1H NMR spectra of appropriate reference sequences the equilibrium position is easily quantifiable even without the assignment of the individual NH resonances. The reference sequences represent several Watson-Crick base-paired double helical segments, each encountered in either of the two conformers of the bistable target sequence. In addition, we rationalize the influence of nucleotide mutations on the equilibrium position of one of the bistable RNA sequences. The approach further allows a detailed thermodynamic analysis and the evaluation of secondary structure predictions for multistable RNAs obtained by computational methods.     

一种新的RNA二级结构三维图形表示及其应用

本研究提出了一种新的RNA二级结构的图形表示方法,这种方法不同于以往的表示方式。根据所提出的RNA二级结构的图形表示,将对9种病毒的RNA二级结构进行图形表示,构建系统进化树,进行序列间相似性的比较和分析。根据最终结果,可以很清晰地发现,AVII与LRMV两种病毒是最为相似的,另外,较大的距离值出现在了APMV与ALMV;PDV与AVII中,这说明这几种RNA二级结构明显不相似。这一研究结果与前人相似性分析的结果是十分相似的,同时,所采取的方法更加简单易于区分观察且得到的结果又是十分可靠的,因此,这些更加证明了该方法是有效的。     

Generation of RNA pseudoknot structures with topological genus filtration

In this paper we present a sampling framework for RNA structures of fixed topological genus. We introduce a novel, linear time, uniform sampling algorithm for RNA structures of fixed topological genus g  , for arbitrary g>0$g>0$. Furthermore we develop a linear time sampling algorithm for RNA structures of fixed topological genus g   that are weighted by a simplified, loop-based energy functional. For this process the partition function of the energy functional has to be computed once, which has O(n²)$O(n^2)$ time complexity.     

A new Motzkin class for joint RNA secondary structures

In general RNA prediction problem includes genetic mapping, physical mapping and structure prediction. The ultimate goal of structure prediction is to obtain the three dimensional structure of bimolecules through computation. The key concept for solving the above mentioned problem is the appropriate representation of the biological structures. Even though, the problems that concern representations of certain biological structures like secondary structures either are characterized as NP-complete or with high complexity, few approximation algorithms and techniques had been constructed, mainly with polynomial complexity, concerning the prediction of RNA secondary structures. In this paper, a new class of Motzkin paths is introduced, the so-called semi-elevated inverse Motzkin peakless paths for the representation of two interacting RNA molecules. The basic combinatorial interpretations on single RNA secondary structures are extended via these new Motzkin paths on two RNA molecules and can be applied to the prediction methods of joint structures formed by interacting RNAs.     

Visualizing the global secondary structure of a viral RNA genome with cryo-electron microscopy

The lifecycle, and therefore the virulence, of single-stranded (ss)-RNA viruses is regulated not only by their particular protein gene products, but also by the secondary and tertiary structure of their genomes. The secondary structure of the entire genomic RNA of satellite tobacco mosaic virus (STMV) was recently determined by selective 2′-hydroxyl acylation analyzed by primer extension (SHAPE). The SHAPE analysis suggested a single highly extended secondary structure with much less branching than occurs in the ensemble of structures predicted by purely thermodynamic algorithms. Here we examine the solution-equilibrated STMV genome by direct visualization with cryo-electron microscopy (cryo-EM), using an RNA of similar length transcribed from the yeast genome as a control. The cryo-EM data reveal an ensemble of branching patterns that are collectively consistent with the SHAPE-derived secondary structure model. Thus, our results both elucidate the statistical nature of the secondary structure of large ss-RNAs and give visual support for modern RNA structure determination methods. Additionally, this work introduces cryo-EM as a means to distinguish between competing secondary structure models if the models differ significantly in terms of the number and/or length of branches. Furthermore, with the latest advances in cryo-EM technology, we suggest the possibility of developing methods that incorporate restraints from cryo-EM into the next generation of algorithms for the determination of RNA secondary and tertiary structures.     

Automated motif extraction and classification in RNA tertiary structures

We used a novel graph-based approach to extract RNA tertiary motifs. We cataloged them all and clustered them using an innovative graph similarity measure. We applied our method to three widely studied structures: Haloarcula marismortui 50S (H.m 50S), Escherichia coli 50S (E. coli 50S), and Thermus thermophilus 16S (T.th 16S) RNAs. We identified 10 known motifs without any prior knowledge of their shapes or positions. We additionally identified four putative new motifs.     

Phylogenetic hypotheses of gorgoniid octocorals according to ITS2 and their predicted RNA secondary structures

Gorgoniid octocorals taxonomy (Cnidaria; Octocorallia; Gorgoniidae) includes diagnostic characters not well defined at the generic level, and based on the family diagnosis some species could be classified in either Gorgoniidae or Plexauridae. In this study, we used sequences from the Internal Transcribed Spacer 2 (ITS2) and their predicted RNA secondary structure to both correct the alignment and reconstruct phylogenies using molecular morphometrics for 24 octocorals mostly from the Atlantic. ITS2 exhibited the six-helicoidal ring-model structure found in eukaryotes, and provided 38 parsimony-informative characters. The proposed phylogenies, though differing between sequence- and structure-base results, provided consistent support for several clades. Genera considered part of the polyphyletic genus Leptogorgia, such as Filigorgia, were distantly related to the former in all phylogenetic hypotheses. Main differences among the hypotheses consisted in the placement of Muriceopsis (previously considered from the Plexauridae family) and Filigorgia. Excluding Muriceopsis and an undescribed octocoral from Tobago, Plexaurella and Pterogorgia grouped together as a sister branch of Pinnigorgia spp. but long-branch attraction was evident for the grouping of Plexaurella nutans (another plexaurid) and Pterogorgia citrina. Unexpected results were the divergence between Caribbean genera, Gorgonia and Pseudopterogorgia, which were placed basal respect to Pacifigorgia and Leptogorgia (=Lophogorgia). ITS2 provided support to corroborate observations based on sclerite morphology: species with "capstan sclerites" (e.g., Pacifigorgia and Leptogorgia) were characterized by a long helix IV with one internal loop and a helix V with four internal loops; "scaphoid sclerites" had a predominantly long helix V if compared to helix IV; "asymmetric spiny sclerites" (Muriceopsis, Pinnigorgia and the undescribed octocoral) exhibited one or two lateral bulges in the V helix. Remarkably, Muriceopsis and Pinnigorgia were supported by a complete Compensatory Base Change (CBC) (A-U to G-C) in helix V. Filigorgia with simple "spindles" had a short helix IV and a large central ring. DNA sequences from the nuclear ITS2 region, including information from predicted RNA secondary structure, despite their reduced length, provided numerous characters and phylogenetic information among Gorgoniidae genera and species.     

Blocking of in vitro translation of Paramecium messenger RNAs is due to messenger RNA primary structure

Paramecium primaurelia mRNAs were translated in vitro in rabbit reticulocyte lysate and the products of translation were analyzed by their size. We show that the large majority of these products are of short but discrete sizes irrespective of the length of the mRNA which directs their synthesis. An illustrative example is given by the translation of mRNA of G surface antigen which directs the synthesis of a 50 kD polypeptide instead of the complete 250 kD protein. Control experiments suggest that the blocking is due to mRNA primary structure.