Structural and combinatorial constraints on base pairing in large nucleotide sequences

In this paper we discuss the constraints and combinatorial problems of folding long RNA and single stranded DNA molecules into base paired structures. A computer code FOLD-A was designed to perform base pairing foldings of very long sequence chains and search for low energy configurations. The logic of the FOLD-A algorithm is described in some detail. The applications of FOLD-A to the A-protein gene of MS2 and the whole genome of the phi X 174 phage with over 5300 bases are discussed in the accompanying paper.     

A continuous analog for RNA folding

A linear segment in which a number of pairs of intervals of equal length are identified as potential stems is the subject of a folding problem analogous to inference of RNA secondary structure. A quantity of free energy (or equivalently, energy per unit length) is associated with each stem, and the various types of loops are assigned energy costs as a function of their lengths. Inference of stable structures can then be carried out in the same way as in RNA folding. More important, perturbation of stem lengths and energy densities (modelling various mutational processes affecting nucleotide sequences) allows the delineation of domains of stability of various foldings, through the explicit calculation of their boundaries, in a low-dimensional parameter space.     

Unique Optimal Foldings of Proteins on a Triangular Lattice

Background: A problem for unique protein folding was raised in 1998: are there proteins having unique optimal foldings for all lengths in the hydrophobic-hydrophilic (hydrophobic-polar; HP) model? To such a question, it was proved that on a square lattice there are (i) closed chains of monomers having unique optimal foldings for all even lengths and (ii) open monomer chains having unique optimal foldings for all lengths divisible by four. In this article, we aim to extend the previous work on a square lattice to the optimal foldings of proteins on a triangular lattice by examining the uniqueness property or stability of HP chain folding. Method: We consider this protein folding problem on a triangular lattice using graph theory. For an HP chain with length n > 13, generally it is very time-consuming to enumerate all of its possible folding conformations. Hence, one can hardly know whether or not it has a unique optimal folding. A natural problem is to determine for what value of n there is an n-node HP chain that has a unique optimal folding on a triangular lattice. Results and conclusion: Using graph theory, this article proves that there are both closed and open chains having unique optimal foldings for all lengths >19 in a triangular lattice. This result is not only general from the theoretical viewpoint, but also can be expected to apply to areas of protein structure prediction and protein design because of their close relationship with the concept of energy state and designability.     

Analysis of RNA motifs

RNA motifs are directed and ordered stacked arrays of non-Watson-Crick base pairs forming distinctive foldings of the phosphodiester backbones of the interacting RNA strands. They correspond to the 'loops' - hairpin, internal and junction - that intersperse the Watson-Crick two-dimensional helices as seen in two-dimensional representations of RNA structure. RNA motifs mediate the specific interactions that induce the compact folding of complex RNAs. RNA motifs also constitute specific protein or ligand binding sites. A given motif is characterized by all the sequences that fold into essentially identical three-dimensional structures with the same ordered array of isosteric non-Watson-Crick base pairs. It is therefore crucial, when analyzing a three-dimensional RNA structure in order to identify and compare motifs, to first classify its non-Watson-Crick base pairs geometrically.     

Practicality and time complexity of a sparsified RNA folding algorithm

Commonly used RNA folding programs compute the minimum free energy structure of a sequence under the pseudoknot exclusion constraint. They are based on Zuker's algorithm which runs in time O(n(3)). Recently, it has been claimed that RNA folding can be achieved in average time O(n(2)) using a sparsification technique. A proof of quadratic time complexity was based on the assumption that computational RNA folding obeys the "polymer-zeta property". Several variants of sparse RNA folding algorithms were later developed. Here, we present our own version, which is readily applicable to existing RNA folding programs, as it is extremely simple and does not require any new data structure. We applied it to the widely used Vienna RNAfold program, to create sibRNAfold, the first public sparsified version of a standard RNA folding program. To gain a better understanding of the time complexity of sparsified RNA folding in general, we carried out a thorough run time analysis with synthetic random sequences, both in the context of energy minimization and base pairing maximization. Contrary to previous claims, the asymptotic time complexity of a sparsified RNA folding algorithm using standard energy parameters remains O(n(3)) under a wide variety of conditions. Consistent with our run-time analysis, we found that RNA folding does not obey the "polymer-zeta property" as claimed previously. Yet, a basic version of a sparsified RNA folding algorithm provides 15- to 50-fold speed gain. Surprisingly, the same sparsification technique has a different effect when applied to base pairing optimization. There, its asymptotic running time complexity appears to be either quadratic or cubic depending on the base composition. The code used in this work is available at: .     

Removal of covalent heterogeneity reveals simple folding behavior for P4-P6 RNA

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior.     

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 comparison of thermodynamic foldings with comparatively derived structures of 16S and 16S-like rRNAs.

To increase our understanding of the dynamics and complexities of the RNA folding process, and therewith to improve our ability to predict RNA secondary structure by computational means, we have examined the foldings of a large number of phylogenetically and structurally diverse 16S and 16S-like rRNAs and compared these results with their comparatively derived secondary structures. Our initial goals are to establish the range of prediction success for this class of rRNAs, and to begin comparing and contrasting the foldings of these RNAs. We focus here on structural features that are predicted with confidence as well as those that are poorly predicted. Whereas the large set of Archaeal and (eu)Bacterial 16S rRNAs all fold well (69% and 55% respectively), some as high as 80%, many Eucarya and mitochondrial 16S rRNAs are poorly predicted (approximately 30%), with a few of these predicted as low as 10-20%. In general, base pairs interacting over a short distance and, in particular, those closing hairpin loops, are predicted significantly better than long-range base pairs and those closing multistem loops and bulges. The prediction success of hairpin loops varies, however, with their size and context. Analysis of some of the RNAs that do not fold well suggests that the composition of some hairpin loops (e.g., tetraloops) and the higher frequency of noncanonical pairs in their comparatively derived structures might contribute to these lower success rates. Eucarya and mitochondrial rRNAs reveal further novel tetraloop motifs, URRG/A and CRRG, that interchange with known stable tetraloop in the procaryotes.     

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.     

Structural characterization of naturally occurring RNA single mismatches

RNA is known to be involved in several cellular processes; however, it is only active when it is folded into its correct 3D conformation. The folding, bending and twisting of an RNA molecule is dependent upon the multitude of canonical and non-canonical secondary structure motifs. These motifs contribute to the structural complexity of RNA but also serve important integral biological functions, such as serving as recognition and binding sites for other biomolecules or small ligands. One of the most prevalent types of RNA secondary structure motifs are single mismatches, which occur when two canonical pairs are separated by a single non-canonical pair. To determine sequence–structure relationships and to identify structural patterns, we have systematically located, annotated and compared all available occurrences of the 30 most frequently occurring single mismatch-nearest neighbor sequence combinations found in experimentally determined 3D structures of RNA-containing molecules deposited into the Protein Data Bank. Hydrogen bonding, stacking and interaction of nucleotide edges for the mismatched and nearest neighbor base pairs are described and compared, allowing for the identification of several structural patterns. Such a database and comparison will allow researchers to gain insight into the structural features of unstudied sequences and to quickly look-up studied sequences.     

Complete probabilistic analysis of RNA shapes

Background  

Soon after the first algorithms for RNA folding became available, it was recognised that the prediction of only one energetically optimal structure is insufficient to achieve reliable results. An in-depth analysis of the folding space as a whole appeared necessary to deduce the structural properties of a given RNA molecule reliably. Folding space analysis comprises various methods such as suboptimal folding, computation of base pair probabilities, sampling procedures and abstract shape analysis. Common to many approaches is the idea of partitioning the folding space into classes of structures, for which certain properties can be derived.     

Immobilized small deoxyribozyme to distinguish RNA secondary structures

The RNA folding variation due to one or more mutations leads to different RNA splicing, RNA processing, and translational controls as a result of differences in the primary and higher-ordered structures that interact with other cellular molecules. Thus, distinguishing RNA folding is one of the guides to detect the gene functions related to disease and drug responses. We found, previously, a small Ca(2+)-dependent deoxyribozyme with its site-specific RNA cleavage [Sugimoto, N., Okumoto, Y., and Ohmichi, T. (1999) J. Chem. Soc., Perkin Trans. 2, 1382-1388]. In this study, we report the potential of this deoxyribozyme as a useful tool to distinguish RNA foldings. It is found that the immobilized deoxyribozyme using avidin-biotin interaction cleaves the target site within only single-stranded RNAs. The systematic design for the target RNA hairpin loops shows that the immobilized deoxyribozyme is able to cleave them with a > or =17 nucleotide loop size at only one site under single-turnover conditions. Furthermore, an RNA cleavage reaction is detected using the immobilized deoxyribozyme on a surface plasmon resonance (SPR) sensor chip. These results show that the immobilized deoxyribozymes on a column and on an SPR sensor chip become a novel and useful tool to distinguish the RNA foldings.     

Integrated multi-level quality control for proteomic profiling studies using mass spectrometry

Background

Evolutionary conservation of RNA secondary structure is a typical feature of many functional non-coding RNAs. Since almost all of the available methods used for prediction and annotation of non-coding RNA genes rely on this evolutionary signature, accurate measures for structural conservation are essential.

Results

We systematically assessed the ability of various measures to detect conserved RNA structures in multiple sequence alignments. We tested three existing and eight novel strategies that are based on metrics of folding energies, metrics of single optimal structure predictions, and metrics of structure ensembles. We find that the folding energy based SCI score used in the RNAz program and a simple base-pair distance metric are by far the most accurate. The use of more complex metrics like for example tree editing does not improve performance. A variant of the SCI performed particularly well on highly conserved alignments and is thus a viable alternative when only little evolutionary information is available. Surprisingly, ensemble based methods that, in principle, could benefit from the additional information contained in sub-optimal structures, perform particularly poorly. As a general trend, we observed that methods that include a consensus structure prediction outperformed equivalent methods that only consider pairwise comparisons.

Conclusion

Structural conservation can be measured accurately with relatively simple and intuitive metrics. They have the potential to form the basis of future RNA gene finders, that face new challenges like finding lineage specific structures or detecting mis-aligned sequences.     

An efficient and economic site-specific deuteration strategy for NMR studies of homologous oligonucleotide repeat sequences.

We describe herein the use of a 2H-labeling strategy to achieve specific assignments of considerably overlapped cross peaks in the 1H-NMR spectrum of a DNA trinucleotide repeat sequence. Our strategy focuses on site-specific 2H-labeling of base moieties to simplify the NMR spectral regions which contain the major portion of the structural information. To achieve efficient preparation of 2H8- or 2H6-labeled DNA and RNA nucleosides and nucleotides, the existing synthetic and purification procedures were significantly improved. Our experiments demonstrate that pyrimidine H6 deuteration reactions may be carried out using non-deuterated base reagents with DMSO-d6 as a 2H donor. These reactions are simple and economic to perform and produce base deuterated nucleosides and nucleotides in high yield. The 2H-labeled residues have been incorporated into oligonucleotides with minor modifications of the existing reaction conditions. Using the homologous CGG repeat sequence, d(CGG)5, as an example, the effectiveness of the site-specific base deuteration strategy is demonstrated. In the otherwise extensively overlapped spectra of d(CGG)5, 2H-labeling has permitted unambiguous identification of a sequential connectivity at a central CG step and confirmation of several other NOE assignments. This information is critical for elucidation of the structure and the folding of the CGG repeat sequences and will contribute to the intensive effort to understand the mechanisms of triplet expansion, which has been implicated in the development of a number of hereditary neurodegenerative diseases. In addition to the two dimensional spectral simplification in a key spectral region using site-specific 2H8/2H6-labeling, the potential applications of the prescribed strategy in homonuclear three dimensional experiments are also discussed.