Automated 3D structure composition for large RNAs

Understanding the numerous functions that RNAs play in living cells depends critically on knowledge of their three-dimensional structure. Due to the difficulties in experimentally assessing structures of large RNAs, there is currently great demand for new high-resolution structure prediction methods. We present the novel method for the fully automated prediction of RNA 3D structures from a user-defined secondary structure. The concept is founded on the machine translation system. The translation engine operates on the RNA FRABASE database tailored to the dictionary relating the RNA secondary structure and tertiary structure elements. The translation algorithm is very fast. Initial 3D structure is composed in a range of seconds on a single processor. The method assures the prediction of large RNA 3D structures of high quality. Our approach needs neither structural templates nor RNA sequence alignment, required for comparative methods. This enables the building of unresolved yet native and artificial RNA structures. The method is implemented in a publicly available, user-friendly server RNAComposer. It works in an interactive mode and a batch mode. The batch mode is designed for large-scale modelling and accepts atomic distance restraints. Presently, the server is set to build RNA structures of up to 500 residues.     

Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library

BackgroundWe re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications.MethodsClustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into ‘existing’ or hypothetical, and the latter into, ‘RNA-like’ or ‘non RNA-like’ topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups.ResultsThe unsupervised PAM and K-means clustering approaches correctly classify 72–77% of all existing graph topologies and 75–82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%.ConclusionsUsing linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach.General significanceOur updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.     

Entanglements of structure elements revealed in RNA 3D models

Computational methods to predict RNA 3D structure have more and more practical applications in molecular biology and medicine. Therefore, it is crucial to intensify efforts to improve the accuracy and quality of predicted three-dimensional structures. A significant role in this is played by the RNA-Puzzles initiative that collects, evaluates, and shares RNAs built computationally within currently nearly 30 challenges. RNA-Puzzles datasets, subjected to multi-criteria analysis, allow revealing the strengths and weaknesses of computer prediction methods. Here, we study the issue of entangled RNA fragments in the predicted RNA 3D structure models. By entanglement, we mean an arrangement of two structural elements such that one of them passes through the other. We propose the classification of entanglements driven by their topology and components. It distinguishes two general classes, interlaces and lassos, and subclasses characterized by element types—loops, dinucleotide steps, open single-stranded fragments—and puncture multiplicity. Our computational pipeline for entanglement detection, applied for 1,017 non-redundant models from RNA-Puzzles, has shown the frequency of different entanglements and allowed identifying 138 structures with intersected assemblies.     

RNA 3D Modules in Genome-Wide Predictions of RNA 2D Structure

Recent experimental and computational progress has revealed a large potential for RNA structure in the genome. This has been driven by computational strategies that exploit multiple genomes of related organisms to identify common sequences and secondary structures. However, these computational approaches have two main challenges: they are computationally expensive and they have a relatively high false discovery rate (FDR). Simultaneously, RNA 3D structure analysis has revealed modules composed of non-canonical base pairs which occur in non-homologous positions, apparently by independent evolution. These modules can, for example, occur inside structural elements which in RNA 2D predictions appear as internal loops. Hence one question is if the use of such RNA 3D information can improve the prediction accuracy of RNA secondary structure at a genome-wide level. Here, we use RNAz in combination with 3D module prediction tools and apply them on a 13-way vertebrate sequence-based alignment. We find that RNA 3D modules predicted by metaRNAmodules and JAR3D are significantly enriched in the screened windows compared to their shuffled counterparts. The initially estimated FDR of 47.0% is lowered to below 25% when certain 3D module predictions are present in the window of the 2D prediction. We discuss the implications and prospects for further development of computational strategies for detection of RNA 2D structure in genomic sequence.     

Automated classification of RNA 3D motifs and the RNA 3D Motif Atlas

The analysis of atomic-resolution RNA three-dimensional (3D) structures reveals that many internal and hairpin loops are modular, recurrent, and structured by conserved non-Watson–Crick base pairs. Structurally similar loops define RNA 3D motifs that are conserved in homologous RNA molecules, but can also occur at nonhomologous sites in diverse RNAs, and which often vary in sequence. To further our understanding of RNA motif structure and sequence variability and to provide a useful resource for structure modeling and prediction, we present a new method for automated classification of internal and hairpin loop RNA 3D motifs and a new online database called the RNA 3D Motif Atlas. To classify the motif instances, a representative set of internal and hairpin loops is automatically extracted from a nonredundant list of RNA-containing PDB files. Their structures are compared geometrically, all-against-all, using the FR3D program suite. The loops are clustered into motif groups, taking into account geometric similarity and structural annotations and making allowance for a variable number of bulged bases. The automated procedure that we have implemented identifies all hairpin and internal loop motifs previously described in the literature. All motif instances and motif groups are assigned unique and stable identifiers and are made available in the RNA 3D Motif Atlas (http://rna.bgsu.edu/motifs), which is automatically updated every four weeks. The RNA 3D Motif Atlas provides an interactive user interface for exploring motif diversity and tools for programmatic data access.     

RNAMotif, an RNA secondary structure definition and search algorithm

RNA molecules fold into characteristic secondary and tertiary structures that account for their diverse functional activities. Many of these RNA structures are assembled from a collection of RNA structural motifs. These basic building blocks are used repeatedly, and in various combinations, to form different RNA types and define their unique structural and functional properties. Identification of recurring RNA structural motifs will therefore enhance our understanding of RNA structure and help associate elements of RNA structure with functional and regulatory elements. Our goal was to develop a computer program that can describe an RNA structural element of any complexity and then search any nucleotide sequence database, including the complete prokaryotic and eukaryotic genomes, for these structural elements. Here we describe in detail a new computational motif search algorithm, RNAMotif, and demonstrate its utility with some motif search examples. RNAMotif differs from other motif search tools in two important aspects: first, the structure definition language is more flexible and can specify any type of base–base interaction; second, RNAMotif provides a user controlled scoring section that can be used to add capabilities that patterns alone cannot provide.     

STAR3D: a stack-based RNA 3D structural alignment tool

The various roles of versatile non-coding RNAs typically require the attainment of complex high-order structures. Therefore, comparing the 3D structures of RNA molecules can yield in-depth understanding of their functional conservation and evolutionary history. Recently, many powerful tools have been developed to align RNA 3D structures. Although some methods rely on both backbone conformations and base pairing interactions, none of them consider the entire hierarchical formation of the RNA secondary structure. One of the major issues is that directly applying the algorithms of matching 2D structures to the 3D coordinates is particularly time-consuming. In this article, we propose a novel RNA 3D structural alignment tool, STAR3D, to take into full account the 2D relations between stacks without the complicated comparison of secondary structures. First, the 3D conserved stacks in the inputs are identified and then combined into a tree-like consensus. Afterward, the loop regions are compared one-to-one in accordance with their relative positions in the consensus tree. The experimental results show that the prediction of STAR3D is more accurate for both non-homologous and homologous RNAs than other state-of-the-art tools with shorter running time.     

LB3D: a protein three-dimensional substructure search program based on the lower bound of a root mean square deviation value

Searching for protein structure-function relationships using three-dimensional (3D) structural coordinates represents a fundamental approach for determining the function of proteins with unknown functions. Since protein structure databases are rapidly growing in size, the development of a fast search method to find similar protein substructures by comparison of protein 3D structures is essential. In this article, we present a novel protein 3D structure search method to find all substructures with root mean square deviations (RMSDs) to the query structure that are lower than a given threshold value. Our new algorithm runs in O(m + N/m(0.5)) time, after O(N log N) preprocessing, where N is the database size and m is the query length. The new method is 1.8-41.6 times faster than the practically best known O(N) algorithm, according to computational experiments using a huge database (i.e., >20,000,000 C-alpha coordinates).     

Secondary structure of the 3'-noncoding region of flavivirus genomes: comparative analysis of base pairing probabilities.

The prediction of the complete matrix of base pairing probabilities was applied to the 3'' noncoding region (NCR) of flavivirus genomes. This approach identifies not only well-defined secondary structure elements, but also regions of high structural flexibility. Flaviviruses, many of which are important human pathogens, have a common genomic organization, but exhibit a significant degree of RNA sequence diversity in the functionally important 3''-NCR. We demonstrate the presence of secondary structures shared by all flaviviruses, as well as structural features that are characteristic for groups of viruses within the genus reflecting the established classification scheme. The significance of most of the predicted structures is corroborated by compensatory mutations. The availability of infectious clones for several flaviviruses will allow the assessment of these structural elements in processes of the viral life cycle, such as replication and assembly.     

PROMALS3D: a tool for multiple protein sequence and structure alignments

Although multiple sequence alignments (MSAs) are essential for a wide range of applications from structure modeling to prediction of functional sites, construction of accurate MSAs for distantly related proteins remains a largely unsolved problem. The rapidly increasing database of spatial structures is a valuable source to improve alignment quality. We explore the use of 3D structural information to guide sequence alignments constructed by our MSA program PROMALS. The resulting tool, PROMALS3D, automatically identifies homologs with known 3D structures for the input sequences, derives structural constraints through structure-based alignments and combines them with sequence constraints to construct consistency-based multiple sequence alignments. The output is a consensus alignment that brings together sequence and structural information about input proteins and their homologs. PROMALS3D can also align sequences of multiple input structures, with the output representing a multiple structure-based alignment refined in combination with sequence constraints. The advantage of PROMALS3D is that it gives researchers an easy way to produce high-quality alignments consistent with both sequences and structures of proteins. PROMALS3D outperforms a number of existing methods for constructing multiple sequence or structural alignments using both reference-dependent and reference-independent evaluation methods.     

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner''s energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner''s model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner''s rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.     

In silico selection of RNA aptamers

In vitro selection of RNA aptamers that bind to a specific ligand usually begins with a random pool of RNA sequences. We propose a computational approach for designing a starting pool of RNA sequences for the selection of RNA aptamers for specific analyte binding. Our approach consists of three steps: (i) selection of RNA sequences based on their secondary structure, (ii) generating a library of three-dimensional (3D) structures of RNA molecules and (iii) high-throughput virtual screening of this library to select aptamers with binding affinity to a desired small molecule. We developed a set of criteria that allows one to select a sequence with potential binding affinity from a pool of random sequences and developed a protocol for RNA 3D structure prediction. As verification, we tested the performance of in silico selection on a set of six known aptamer–ligand complexes. The structures of the native sequences for the ligands in the testing set were among the top 5% of the selected structures. The proposed approach reduces the RNA sequences search space by four to five orders of magnitude—significantly accelerating the experimental screening and selection of high-affinity aptamers.     

Arrangement of 3D structural motifs in ribosomal RNA

Structural 3D motifs in RNA play an important role in the RNA stability and function. Previous studies have focused on the characterization and discovery of 3D motifs in RNA secondary and tertiary structures. However, statistical analyses of the distribution of 3D motifs along the RNA appear to be lacking. Herein, we present a novel strategy for evaluating the distribution of 3D motifs along the RNA chain and those motifs whose distributions are significantly non-random are identified. By applying it to the X-ray structure of the large ribosomal subunit from Haloarcula marismortui, helical motifs were found to cluster together along the chain and in the 3D structure, whereas the known tetraloops tend to be sequentially and spatially dispersed. That the distribution of key structural motifs such as tetraloops differ significantly from a random one suggests that our method could also be used to detect novel 3D motifs of any size in sufficiently long/large RNA structures. The motif distribution type can help in the prediction and design of 3D structures of large RNA molecules.     

RAG: RNA-As-Graphs database--concepts, analysis, and features

MOTIVATION: Understanding RNA's structural diversity is vital for identifying novel RNA structures and pursuing RNA genomics initiatives. By classifying RNA secondary motifs based on correlations between conserved RNA secondary structures and functional properties, we offer an avenue for predicting novel motifs. Although several RNA databases exist, no comprehensive schemes are available for cataloguing the range and diversity of RNA's structural repertoire. RESULTS: Our RNA-As-Graphs (RAG) database describes and ranks all mathematically possible (including existing and candidate) RNA secondary motifs on the basis of graphical enumeration techniques. We represent RNA secondary structures as two-dimensional graphs (networks), specifying the connectivity between RNA secondary structural elements, such as loops, bulges, stems and junctions. We archive RNA tree motifs as 'tree graphs' and other RNAs, including pseudoknots, as general 'dual graphs'. All RNA motifs are catalogued by graph vertex number (a measure of sequence length) and ranked by topological complexity. The RAG inventory immediately suggests candidates for novel RNA motifs, either naturally occurring or synthetic, and thereby might stimulate the prediction and design of novel RNA motifs. AVAILABILITY: The database is accessible on the web at http://monod.biomath.nyu.edu/rna     

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     

Identifying novel sequence variants of RNA 3D motifs

Predicting RNA 3D structure from sequence is a major challenge in biophysics. An important sub-goal is accurately identifying recurrent 3D motifs from RNA internal and hairpin loop sequences extracted from secondary structure (2D) diagrams. We have developed and validated new probabilistic models for 3D motif sequences based on hybrid Stochastic Context-Free Grammars and Markov Random Fields (SCFG/MRF). The SCFG/MRF models are constructed using atomic-resolution RNA 3D structures. To parameterize each model, we use all instances of each motif found in the RNA 3D Motif Atlas and annotations of pairwise nucleotide interactions generated by the FR3D software. Isostericity relations between non-Watson–Crick basepairs are used in scoring sequence variants. SCFG techniques model nested pairs and insertions, while MRF ideas handle crossing interactions and base triples. We use test sets of randomly-generated sequences to set acceptance and rejection thresholds for each motif group and thus control the false positive rate. Validation was carried out by comparing results for four motif groups to RMDetect. The software developed for sequence scoring (JAR3D) is structured to automatically incorporate new motifs as they accumulate in the RNA 3D Motif Atlas when new structures are solved and is available free for download.     

FR3D: finding local and composite recurrent structural motifs in RNA 3D structures

New methods are described for finding recurrent three-dimensional (3D) motifs in RNA atomic-resolution structures. Recurrent RNA 3D motifs are sets of RNA nucleotides with similar spatial arrangements. They can be local or composite. Local motifs comprise nucleotides that occur in the same hairpin or internal loop. Composite motifs comprise nucleotides belonging to three or more different RNA strand segments or molecules. We use a base-centered approach to construct efficient, yet exhaustive search procedures using geometric, symbolic, or mixed representations of RNA structure that we implement in a suite of MATLAB programs, “Find RNA 3D” (FR3D). The first modules of FR3D preprocess structure files to classify base-pair and -stacking interactions. Each base is represented geometrically by the position of its glycosidic nitrogen in 3D space and by the rotation matrix that describes its orientation with respect to a common frame. Base-pairing and base-stacking interactions are calculated from the base geometries and are represented symbolically according to the Leontis/Westhof basepairing classification, extended to include base-stacking. These data are stored and used to organize motif searches. For geometric searches, the user supplies the 3D structure of a query motif which FR3D uses to find and score geometrically similar candidate motifs, without regard to the sequential position of their nucleotides in the RNA chain or the identity of their bases. To score and rank candidate motifs, FR3D calculates a geometric discrepancy by rigidly rotating candidates to align optimally with the query motif and then comparing the relative orientations of the corresponding bases in the query and candidate motifs. Given the growing size of the RNA structure database, it is impossible to explicitly compute the discrepancy for all conceivable candidate motifs, even for motifs with less than ten nucleotides. The screening algorithm that we describe finds all candidate motifs whose geometric discrepancy with respect to the query motif falls below a user-specified cutoff discrepancy. This technique can be applied to RMSD searches. Candidate motifs identified geometrically may be further screened symbolically to identify those that contain particular basepair types or base-stacking arrangements or that conform to sequence continuity or nucleotide identity constraints. Purely symbolic searches for motifs containing user-defined sequence, continuity and interaction constraints have also been implemented. We demonstrate that FR3D finds all occurrences, both local and composite and with nucleotide substitutions, of sarcin/ricin and kink-turn motifs in the 23S and 5S ribosomal RNA 3D structures of the H. marismortui 50S ribosomal subunit and assigns the lowest discrepancy scores to bona fide examples of these motifs. The search algorithms have been optimized for speed to allow users to search the non-redundant RNA 3D structure database on a personal computer in a matter of minutes.     

RNA FRABASE 2.0: an advanced web-accessible database with the capacity to search the three-dimensional fragments within RNA structures

Background  

Recent discoveries concerning novel functions of RNA, such as RNA interference, have contributed towards the growing importance of the field. In this respect, a deeper knowledge of complex three-dimensional RNA structures is essential to understand their new biological functions. A number of bioinformatic tools have been proposed to explore two major structural databases (PDB, NDB) in order to analyze various aspects of RNA tertiary structures. One of these tools is RNA FRABASE 1.0, the first web-accessible database with an engine for automatic search of 3D fragments within PDB-derived RNA structures. This search is based upon the user-defined RNA secondary structure pattern. In this paper, we present and discuss RNA FRABASE 2.0. This second version of the system represents a major extension of this tool in terms of providing new data and a wide spectrum of novel functionalities. An intuitionally operated web server platform enables very fast user-tailored search of three-dimensional RNA fragments, their multi-parameter conformational analysis and visualization.     

Viral IRES Prediction System - a Web Server for Prediction of the IRES Secondary Structure In Silico

The internal ribosomal entry site (IRES) functions as cap-independent translation initiation sites in eukaryotic cells. IRES elements have been applied as useful tools for bi-cistronic expression vectors. Current RNA structure prediction programs are unable to predict precisely the potential IRES element. We have designed a viral IRES prediction system (VIPS) to perform the IRES secondary structure prediction. In order to obtain better results for the IRES prediction, the VIPS can evaluate and predict for all four different groups of IRESs with a higher accuracy. RNA secondary structure prediction, comparison, and pseudoknot prediction programs were implemented to form the three-stage procedure for the VIPS. The backbone of VIPS includes: the RNAL fold program, aimed to predict local RNA secondary structures by minimum free energy method; the RNA Align program, intended to compare predicted structures; and pknotsRG program, used to calculate the pseudoknot structure. VIPS was evaluated by using UTR database, IRES database and Virus database, and the accuracy rate of VIPS was assessed as 98.53%, 90.80%, 82.36% and 80.41% for IRES groups 1, 2, 3, and 4, respectively. This advance useful search approach for IRES structures will facilitate IRES related studies. The VIPS on-line website service is available at http://140.135.61.250/vips/.