Representation, searching and discovery of patterns of bases in complex RNA structures

Graph Theoretical Methods and Workflows for Searching and Annotation of RNA Tertiary Base Motifs and Substructures

The increasing number and complexity of structures containing RNA chains in the Protein Data Bank (PDB) have led to the need for automated structure annotation methods to replace or complement expert visual curation. This is especially true when searching for tertiary base motifs and substructures. Such base arrangements and motifs have diverse roles that range from contributions to structural stability to more direct involvement in the molecule's functions, such as the sites for ligand binding and catalytic activity. We review the utility of computational approaches in annotating RNA tertiary base motifs in a dataset of PDB structures, particularly the use of graph theoretical algorithms that can search for such base motifs and annotate them or find and annotate clusters of hydrogen-bond-connected bases. We also demonstrate how such graph theoretical algorithms can be integrated into a workflow that allows for functional analysis and comparisons of base arrangements and sub-structures, such as those involved in ligand binding. The capacity to carry out such automatic curations has led to the discovery of novel motifs and can give new context to known motifs as well as enable the rapid compilation of RNA 3D motifs into a database.

Finding recurrent RNA structural networks with fast maximal common subgraphs of edge-colored graphs

RNA tertiary structure is crucial to its many non-coding molecular functions. RNA architecture is shaped by its secondary structure composed of stems, stacked canonical base pairs, enclosing loops. While stems are precisely captured by free-energy models, loops composed of non-canonical base pairs are not. Nor are distant interactions linking together those secondary structure elements (SSEs). Databases of conserved 3D geometries (a.k.a. modules) not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local elements, loops. Representing the RNA structure as a graph has recently allowed to expend this work to pairs of SSEs, uncovering a hierarchical organization of these 3D modules, at great computational cost. Systematically capturing recurrent patterns on a large scale is a main challenge in the study of RNA structures. In this paper, we present an efficient algorithm to compute maximal isomorphisms in edge colored graphs. We extend this algorithm to a framework well suited to identify RNA modules, and fast enough to considerably generalize previous approaches. To exhibit the versatility of our framework, we first reproduce results identifying all common modules spanning more than 2 SSEs, in a few hours instead of weeks. The efficiency of our new algorithm is demonstrated by computing the maximal modules between any pair of entire RNA in the non-redundant corpus of known RNA 3D structures. We observe that the biggest modules our method uncovers compose large shared sub-structure spanning hundreds of nucleotides and base pairs between the ribosomes of Thermus thermophilus, Escherichia Coli, and Pseudomonas aeruginosa.

Ribonucleic Acids (RNAs) are performing a broad range of essential molecular functions in cells, many of which rely on intricate folding properties of the molecule. Watson-Crick and Wobble base pairs form early, stack onto each other to create stems connected by loops, which are themselves stabilized by more sophisticated base interaction patterns. These networks are essential to shape RNA 3D structures but unfortunately still poorly understood. Here, we undertake the task to build a catalog of base interaction networks occurring in multiple structures. However, a pairwise comparison of all RNA structures is computationally heavy. Therefore, we devise an algorithm leveraging intrinsic properties of RNA base interaction networks that enables us to quickly mine full databases of 3D structures. Compared to previous methods, our techniques bring the total running time of the analysis from months to hours while performing more general searches. The data collected though this work will benefit molecular evolution studies and serve in structure prediction tools.

A unified dinucleotide alphabet describing both RNA and DNA structures

By analyzing almost 120 000 dinucleotides in over 2000 nonredundant nucleic acid crystal structures, we define 96+1 diNucleotide Conformers, NtCs, which describe the geometry of RNA and DNA dinucleotides. NtC classes are grouped into 15 codes of the structural alphabet CANA (Conformational Alphabet of Nucleic Acids) to simplify symbolic annotation of the prominent structural features of NAs and their intuitive graphical display. The search for nontrivial patterns of NtCs resulted in the identification of several types of RNA loops, some of them observed for the first time. Over 30% of the nearly six million dinucleotides in the PDB cannot be assigned to any NtC class but we demonstrate that up to a half of them can be re-refined with the help of proper refinement targets. A statistical analysis of the preferences of NtCs and CANA codes for the 16 dinucleotide sequences showed that neither the NtC class AA00, which forms the scaffold of RNA structures, nor BB00, the DNA most populated class, are sequence neutral but their distributions are significantly biased. The reported automated assignment of the NtC classes and CANA codes available at dnatco.org provides a powerful tool for unbiased analysis of nucleic acid structures by structural and molecular biologists.

Mining for recurrent long-range interactions in RNA structures reveals embedded hierarchies in network families

The wealth of the combinatorics of nucleotide base pairs enables RNA molecules to assemble into sophisticated interaction networks, which are used to create complex 3D substructures. These interaction networks are essential to shape the 3D architecture of the molecule, and also to provide the key elements to carry molecular functions such as protein or ligand binding. They are made of organised sets of long-range tertiary interactions which connect distinct secondary structure elements in 3D structures. Here, we present a de novo data-driven approach to extract automatically from large data sets of full RNA 3D structures the recurrent interaction networks (RINs). Our methodology enables us for the first time to detect the interaction networks connecting distinct components of the RNA structure, highlighting their diversity and conservation through non-related functional RNAs. We use a graphical model to perform pairwise comparisons of all RNA structures available and to extract RINs and modules. Our analysis yields a complete catalog of RNA 3D structures available in the Protein Data Bank and reveals the intricate hierarchical organization of the RNA interaction networks and modules. We assembled our results in an online database (http://carnaval.lri.fr) which will be regularly updated. Within the site, a tool allows users with a novel RNA structure to detect automatically whether the novel structure contains previously observed RINs.

Going beyond base-pairs: topology-based characterization of base-multiplets in RNA

Identification and characterization of base-multiplets, which are essentially mediated by base-pairing interactions, can provide insights into the diversity in the structure and dynamics of complex functional RNAs, and thus facilitate hypothesis driven biological research. The necessary nomenclature scheme, an extension of the geometric classification scheme for base-pairs by Leontis and Westhof, is however available only for base-triplets. In the absence of information on topology, this scheme is not applicable to quartets and higher order multiplets. Here we propose a topology-based classification scheme which, in conjunction with a graph-based algorithm, can be used for the automated identification and characterization of higher order base-multiplets in RNA structures. Here, the RNA structure is represented as a graph, where nodes represent nucleotides and edges represent base-pairing connectivity. Sets of connected components (of n nodes) within these graphs constitute subgraphs representing multiplets of "n" nucleotides. The different topological variants of the RNA multiplets thus correspond to different nonisomorphic forms of these subgraphs. To annotate RNA base-multiplets unambiguously, we propose a set of topology-based nomenclature rules for quartets, which are extendable to higher multiplets. We also demonstrate the utility of our approach toward the identification and annotation of higher order RNA multiplets, by investigating the occurrence contexts of selected examples in order to gain insights regarding their probable functional roles.

De novo discovery of structural motifs in RNA 3D structures through clustering

As functional components in three-dimensional (3D) conformation of an RNA, the RNA structural motifs provide an easy way to associate the molecular architectures with their biological mechanisms. In the past years, many computational tools have been developed to search motif instances by using the existing knowledge of well-studied families. Recently, with the rapidly increasing number of resolved RNA 3D structures, there is an urgent need to discover novel motifs with the newly presented information. In this work, we classify all the loops in non-redundant RNA 3D structures to detect plausible RNA structural motif families by using a clustering pipeline. Compared with other clustering approaches, our method has two benefits: first, the underlying alignment algorithm is tolerant to the variations in 3D structures. Second, sophisticated downstream analysis has been performed to ensure the clusters are valid and easily applied to further research. The final clustering results contain many interesting new variants of known motif families, such as GNAA tetraloop, kink-turn, sarcin-ricin and T-loop. We have also discovered potential novel functional motifs conserved in ribosomal RNA, sgRNA, SRP RNA, riboswitch and ribozyme.

Chemoinformatics at the University of Sheffield 2002-2014

This paper summarises work in chemoinformatics carried out in the Information School of the University of Sheffield during the period 2002-2014. Research studies are described on fingerprint-based similarity searching, data fusion, applications of reduced graphs and pharmacophore mapping, and on the School's teaching in chemoinformatics.

Chemoinformatics Research at the University of Sheffield: A History and Citation Analysis

This paper reviews the work of the Chemoinformatics Research Group in the Department of Information Studies at the University of Sheffield, focusing particularly on the work carried out in the period 1985-2002. Four major research areas are discussed, these involving the development of methods for: substructure searching in databases of three-dimensional structures, including both rigid and flexible molecules; the representation and searching of the Markush structures that occur in chemical patents; similarity searching in databases of both two-dimensional and three-dimensional structures; and compound selection and the design of combinatorial libraries. An analysis of citations to 321 publications from the Group shows that it attracted a total of 3725 residual citations during the period 1980-2002. These citations appeared in 411 different journals, and involved 910 different citing organizations from 54 different countries, thus demonstrating the widespread impact of the Group's work.

InterRNA: a database of base interactions in RNA structures

A major component of RNA structure stabilization are the hydrogen bonded interactions between the base residues. The importance and biological relevance for large clusters of base interactions can be much more easily investigated when their occurrences have been systematically detected, catalogued and compared. In this paper, we describe the database InterRNA (INTERactions in RNA structures database—http://mfrlab.org/interrna/) that contains records of known RNA 3D motifs as well as records for clusters of bases that are interconnected by hydrogen bonds. The contents of the database were compiled from RNA structural annotations carried out by the NASSAM (http://mfrlab.org/grafss/nassam) and COGNAC (http://mfrlab.org/grafss/cognac) computer programs. An analysis of the database content and comparisons with the existing corpus of knowledge regarding RNA 3D motifs clearly show that InterRNA is able to provide an extension of the annotations for known motifs as well as able to provide novel interactions for further investigations.

RNAMotifScanX: a graph alignment approach for RNA structural motif identification

RNA structural motifs are recurrent three-dimensional (3D) components found in the RNA architecture. These RNA structural motifs play important structural or functional roles and usually exhibit highly conserved 3D geometries and base-interaction patterns. Analysis of the RNA 3D structures and elucidation of their molecular functions heavily rely on efficient and accurate identification of these motifs. However, efficient RNA structural motif search tools are lacking due to the high complexity of these motifs. In this work, we present RNAMotifScanX, a motif search tool based on a base-interaction graph alignment algorithm. This novel algorithm enables automatic identification of both partially and fully matched motif instances. RNAMotifScanX considers noncanonical base-pairing interactions, base-stacking interactions, and sequence conservation of the motifs, which leads to significantly improved sensitivity and specificity as compared with other state-of-the-art search tools. RNAMotifScanX also adopts a carefully designed branch-and-bound technique, which enables ultra-fast search of large kink-turn motifs against a 23S rRNA. The software package RNAMotifScanX is implemented using GNU C++, and is freely available from http://genome.ucf.edu/RNAMotifScanX.

RASS: a web server for RNA alignment in the joint sequence-structure space

Comparison of ribonucleic acid (RNA) molecules is important for revealing their evolutionary relationships, predicting their functions and predicting their structures. Many methods have been developed for comparing RNAs using either sequence or three-dimensional (3D) structure (backbone geometry) information. Sequences and 3D structures contain non-overlapping sets of information that both determine RNA functions. When comparing RNA 3D structures, both types of information need to be taken into account. However, few methods compare RNA structures using both sequence and 3D structure information. Recently, we have developed a new method based on elastic shape analysis (ESA) that compares RNA molecules by combining both sequence and 3D structure information. ESA treats RNA structures as 3D curves with sequence information encoded on additional coordinates so that the alignment can be performed in the joint sequence-structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. In this study, we implement a web server for the method, called RASS, to make it publicly available to research community. The web server is located at http://cloud.stat.fsu.edu/RASS/.

RNA structural motif recognition based on least-squares distance

RNA structural motifs are recurrent structural elements occurring in RNA molecules. RNA structural motif recognition aims to find RNA substructures that are similar to a query motif, and it is important for RNA structure analysis and RNA function prediction. In view of this, we propose a new method known as RNA Structural Motif Recognition based on Least-Squares distance (LS-RSMR) to effectively recognize RNA structural motifs. A test set consisting of five types of RNA structural motifs occurring in Escherichia coli ribosomal RNA is compiled by us. Experiments are conducted for recognizing these five types of motifs. The experimental results fully reveal the superiority of the proposed LS-RSMR compared with four other state-of-the-art methods.

RNA global alignment in the joint sequence-structure space using elastic shape analysis

The functions of RNAs, like proteins, are determined by their structures, which, in turn, are determined by their sequences. Comparison/alignment of RNA molecules provides an effective means to predict their functions and understand their evolutionary relationships. For RNA sequence alignment, most methods developed for protein and DNA sequence alignment can be directly applied. RNA 3-dimensional structure alignment, on the other hand, tends to be more difficult than protein structure alignment due to the lack of regular secondary structures as observed in proteins. Most of the existing RNA 3D structure alignment methods use only the backbone geometry and ignore the sequence information. Using both the sequence and backbone geometry information in RNA alignment may not only produce more accurate classification, but also deepen our understanding of the sequence-structure-function relationship of RNA molecules. In this study, we developed a new RNA alignment method based on elastic shape analysis (ESA). ESA treats RNA structures as three dimensional curves with sequence information encoded on additional dimensions so that the alignment can be performed in the joint sequence-structure space. The similarity between two RNA molecules is quantified by a formal distance, geodesic distance. Based on ESA, a rigorous mathematical framework can be built for RNA structure comparison. Means and covariances of full structures can be defined and computed, and probability distributions on spaces of such structures can be constructed for a group of RNAs. Our method was further applied to predict functions of RNA molecules and showed superior performance compared with previous methods when tested on benchmark datasets. The programs are available at http://stat.fsu.edu/ ∼jinfeng/ESA.html.

NASSAM: a server to search for and annotate tertiary interactions and motifs in three-dimensional structures of complex RNA molecules

Similarities in the 3D patterns of RNA base interactions or arrangements can provide insights into their functions and roles in stabilization of the RNA 3D structure. Nucleic Acids Search for Substructures and Motifs (NASSAM) is a graph theoretical program that can search for 3D patterns of base arrangements by representing the bases as pseudo-atoms. The geometric relationship of the pseudo-atoms to each other as a pattern can be represented as a labeled graph where the pseudo-atoms are the graph’s nodes while the edges are the inter-pseudo-atomic distances. The input files for NASSAM are PDB formatted 3D coordinates. This web server can be used to identify matches of base arrangement patterns in a query structure to annotated patterns that have been reported in the literature or that have possible functional and structural stabilization implications. The NASSAM program is freely accessible without any login requirement at http://mfrlab.org/grafss/nassam/.

Novel base triples in RNA structures revealed by graph theoretical searching methods

Background

Highly hydrogen bonded base interactions play a major part in stabilizing the tertiary structures of complex RNA molecules, such as transfer-RNAs, ribozymes and ribosomal RNAs.

Results

We describe the graph theoretical identification and searching of highly hydrogen bonded base triples, where each base is involved in at least two hydrogen bonds with the other bases. Our approach correlates theoretically predicted base triples with literature-based compilations and other actual occurrences in crystal structures. The use of ‘fuzzy’ search tolerances has enabled us to discover a number of triple interaction types that have not been previously recorded nor predicted theoretically.

Conclusions

Comparative analyses of different ribosomal RNA structures reveal several conserved base triple motifs in 50S rRNA structures, indicating an important role in structural stabilization and ultimately RNA function.

Clustering RNA structural motifs in ribosomal RNAs using secondary structural alignment

RNA structural motifs are the building blocks of the complex RNA architecture. Identification of non-coding RNA structural motifs is a critical step towards understanding of their structures and functionalities. In this article, we present a clustering approach for de novo RNA structural motif identification. We applied our approach on a data set containing 5S, 16S and 23S rRNAs and rediscovered many known motifs including GNRA tetraloop, kink-turn, C-loop, sarcin–ricin, reverse kink-turn, hook-turn, E-loop and tandem-sheared motifs, with higher accuracy than the state-of-the-art clustering method. We also identified a number of potential novel instances of GNRA tetraloop, kink-turn, sarcin–ricin and tandem-sheared motifs. More importantly, several novel structural motif families have been revealed by our clustering analysis. We identified a highly asymmetric bulge loop motif that resembles the rope sling. We also found an internal loop motif that can significantly increase the twist of the helix. Finally, we discovered a subfamily of hexaloop motif, which has significantly different geometry comparing to the currently known hexaloop motif. Our discoveries presented in this article have largely increased current knowledge of RNA structural motifs.

Feature-based 3D motif filtering for ribosomal RNA

MOTIVATION

RNA 3D motifs are recurrent substructures in an RNA subunit and are building blocks of the RNA architecture. They play an important role in binding proteins and consolidating RNA tertiary structures. RNA 3D motif searching consists of two steps: candidate generation and candidate filtering. We proposed a novel method, known as Feature-based RNA Motif Filtering (FRMF), for identifying motifs based on a set of moment invariants and the Earth Mover's Distance in the second step.

RESULTS

A positive set of RNA motifs belonging to six characteristic types, with eight subtypes occurring in HM 50S, is compiled by us. The proposed method is validated on this representative set. FRMF successfully finds most of the positive fragments. Besides the proposed new method and the compiled positive set, we also recognize some new motifs, in particular a π-turn and some non-standard A-minor motifs are found. These newly discovered motifs provide more information about RNA structure conformation.

AVAILABILITY

Matlab code can be downloaded from www.cs.cityu.edu.hk/~yingshen/FRMF.html

CONTACT

cshswong@cityu.edu.hk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

RNAMotifScan: automatic identification of RNA structural motifs using secondary structural alignment

Recent studies have shown that RNA structural motifs play essential roles in RNA folding and interaction with other molecules. Computational identification and analysis of RNA structural motifs remains a challenging task. Existing motif identification methods based on 3D structure may not properly compare motifs with high structural variations. Other structural motif identification methods consider only nested canonical base-pairing structures and cannot be used to identify complex RNA structural motifs that often consist of various non-canonical base pairs due to uncommon hydrogen bond interactions. In this article, we present a novel RNA structural alignment method for RNA structural motif identification, RNAMotifScan, which takes into consideration the isosteric (both canonical and non-canonical) base pairs and multi-pairings in RNA structural motifs. The utility and accuracy of RNAMotifScan is demonstrated by searching for kink-turn, C-loop, sarcin-ricin, reverse kink-turn and E-loop motifs against a 23S rRNA (PDBid: 1S72), which is well characterized for the occurrences of these motifs. Finally, we search these motifs against the RNA structures in the entire Protein Data Bank and the abundances of them are estimated. RNAMotifScan is freely available at our supplementary website (http://genome.ucf.edu/RNAMotifScan).

FRASS: the web-server for RNA structural comparison

Background

The impressive increase of novel RNA structures, during the past few years, demands automated methods for structure comparison. While many algorithms handle only small motifs, few techniques, developed in recent years, (ARTS, DIAL, SARA, SARSA, and LaJolla) are available for the structural comparison of large and intact RNA molecules.

Results

The FRASS web-server represents a RNA chain with its Gauss integrals and allows one to compare structures of RNA chains and to find similar entries in a database derived from the Protein Data Bank. We observed that FRASS scores correlate well with the ARTS and LaJolla similarity scores. Moreover, the-web server can also reproduce satisfactorily the DARTS classification of RNA 3D structures and the classification of the SCOR functions that was obtained by the SARA method.

Conclusions

The FRASS web-server can be easily used to detect relationships among RNA molecules and to scan efficiently the rapidly enlarging structural databases.

The RNA backbone plays a crucial role in mediating the intrinsic stability of the GpU dinucleotide platform and the GpUpA/GpA miniduplex

The side-by-side interactions of nucleobases contribute to the organization of RNA, forming the planar building blocks of helices and mediating chain folding. Dinucleotide platforms, formed by side-by-side pairing of adjacent bases, frequently anchor helices against loops. Surprisingly, GpU steps account for over half of the dinucleotide platforms observed in RNA-containing structures. Why GpU should stand out from other dinucleotides in this respect is not clear from the single well-characterized H-bond found between the guanine N2 and the uracil O4 groups. Here, we describe how an RNA-specific H-bond between O2′(G) and O2P(U) adds to the stability of the GpU platform. Moreover, we show how this pair of oxygen atoms forms an out-of-plane backbone ‘edge’ that is specifically recognized by a non-adjacent guanine in over 90% of the cases, leading to the formation of an asymmetric miniduplex consisting of ‘complementary’ GpUpA and GpA subunits. Together, these five nucleotides constitute the conserved core of the well-known loop-E motif. The backbone-mediated intrinsic stabilities of the GpU dinucleotide platform and the GpUpA/GpA miniduplex plausibly underlie observed evolutionary constraints on base identity. We propose that they may also provide a reason for the extreme conservation of GpU observed at most 5′-splice sites.

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.

Finding 3D motifs in ribosomal RNA structures

The identification of small structural motifs and their organization into larger subassemblies is of fundamental interest in the analysis, prediction and design of 3D structures of large RNAs. This problem has been studied only sparsely, as most of the existing work is limited to the characterization and discovery of motifs in RNA secondary structures. We present a novel geometric method for the characterization and identification of structural motifs in 3D rRNA molecules. This method enables the efficient recognition of known 3D motifs, such as tetraloops, E-loops, kink-turns and others. Furthermore, it provides a new way of characterizing complex 3D motifs, notably junctions, that have been defined and identified in the secondary structure but have not been analyzed and classified in three dimensions. We demonstrate the relevance and utility of our approach by applying it to the Haloarcula marismortui large ribosomal unit. Pending the implementation of a dedicated web server, the code accompanying this article, written in JAVA, is available upon request from the contact author.

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.

Analysis and classification of RNA tertiary structures

There is a fast growing interest in noncoding RNA transcripts. These transcripts are not translated into proteins, but play essential roles in many cellular and pathological processes. Recent efforts toward comprehension of their function has led to a substantial increase in both the number and the size of solved RNA structures. With the aim of addressing questions relating to RNA structural diversity, we examined RNA conservation at three structural levels: primary, secondary, and tertiary structure. Additionally, we developed an automated method for classifying RNA structures based on spatial (three-dimensional [3D]) similarity. Applying the method to all solved RNA structures resulted in a classified database of RNA tertiary structures (DARTS). DARTS embodies 1333 solved RNA structures classified into 94 clusters. The classification is hierarchical, reflecting the structural relationship between and within clusters. We also developed an application for searching DARTS with a new structure. The search is fast and its performance was successfully tested on all solved RNA structures since the creation of DARTS. A user-friendly interface for both the database and the search application is available online. We show intracluster and intercluster similarities in DARTS and demonstrate the usefulness of the search application. The analysis reveals the current structural repertoire of RNA and exposes common global folds and local tertiary motifs. Further study of these conserved substructures may suggest possible RNA domains and building blocks. This should be beneficial for structure prediction and for gaining insights into structure-function relationships.

Pseudoknot structures with conserved base triples in telomerase RNAs of ciliates

Telomerase maintains the integrity of telomeres, the ends of linear chromosomes, by adding G-rich repeats to their 3′-ends. Telomerase RNA is an integral component of telomerase. It contains a template for the synthesis of the telomeric repeats by the telomerase reverse transcriptase. Although telomerase RNAs of different organisms are very diverse in their sequences, a functional non-template element, a pseudoknot, was predicted in all of them. Pseudoknot elements in human and the budding yeast Kluyveromyces lactis telomerase RNAs contain unusual triple-helical segments with AUU base triples, which are critical for telomerase function. Such base triples in ciliates have not been previously reported. We analyzed the pseudoknot sequences in 28 ciliate species and classified them in six different groups based on the lengths of the stems and loops composing the pseudoknot. Using miniCarlo, a helical parameter-based modeling program, we calculated 3D models for a representative of each morphological group. In all cases, the predicted structure contains at least one AUU base triple in stem 2, except for that of Colpidium colpoda, which contains unconventional GCG and AUA triples. These results suggest that base triples in a pseudoknot element are a conserved feature of all telomerases.

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.

The ARTS web server for aligning RNA tertiary structures

RNA molecules with common structural features may share similar functional properties. Structural comparison of RNAs and detection of common substructures is, thus, a highly important task. Nevertheless, the current available tools in the RNA community provide only a partial solution, since they either work at the 2D level or are suitable for detecting predefined or local contiguous tertiary motifs only. Here, we describe a web server built around ARTS, a method for aligning tertiary structures of nucleic acids (both RNA and DNA). ARTS receives a pair of 3D nucleic acid structures and searches for a priori unknown common substructures. The search is truly 3D and irrespective of the order of the nucleotides on the chain. The identified common substructures can be large global folds with hundreds and even thousands of nucleotides as well as small local motifs with at least two successive base pairs. The method is highly efficient and has been used to conduct an all-against-all comparison of all the RNA structures in the Protein Data Bank. The web server together with a software package for download are freely accessible at http://bioinfo3d.cs.tau.ac.il/ARTS.

The building blocks and motifs of RNA architecture

RNA motifs can be defined broadly as recurrent structural elements containing multiple intramolecular RNA-RNA interactions, as observed in atomic-resolution RNA structures. They constitute the modular building blocks of RNA architecture, which is organized hierarchically. Recent work has focused on analyzing RNA backbone conformations to identify, define and search for new instances of recurrent motifs in X-ray structures. One current view asserts that recurrent RNA strand segments with characteristic backbone configurations qualify as independent motifs. Other considerations indicate that, to characterize modular motifs, one must take into account the larger structural context of such strand segments. This follows the biologically relevant motivation, which is to identify RNA structural characteristics that are subject to sequence constraints and that thus relate RNA architectures to sequences.

The application of cluster analysis in the intercomparison of loop structures in RNA

We have developed a computational approach for the comparison and classification of RNA loop structures. Hairpin or interior loops identified in atomic resolution RNA structures were intercompared by conformational matching. The root-mean-square deviation (RMSD) values between all pairs of RNA fragments of interest, even if from different molecules, are calculated. Subsequently, cluster analysis is performed on the resulting matrix of RMSD distances using the unweighted pair group method with arithmetic mean (UPGMA). The cluster analysis objectively reveals groups of folds that resemble one another. To demonstrate the utility of the approach, a comprehensive analysis of all the terminal hairpin tetraloops that have been observed in 15 RNA structures that have been determined by X-ray crystallography was undertaken. The method found major clusters corresponding to the well-known GNRA and UNCG types. In addition, two tetraloops with the unusual primary sequence UMAC (M is A or C) were successfully assigned to the GNRA cluster. Larger loop structures were also examined and the clustering results confirmed the occurrence of variations of the GNRA and UNCG tetraloops in these loops and provided a systematic means for locating them. Nineteen examples of larger loops that closely resemble either the GNRA or UNCG tetraloop were found in the large ribosomal RNAs. When the clustering approach was extended to include all structures in the SCOR database, novel relationships were detected including one between the ANYA motif and a less common folding of the GAAA tetraloop sequence.