RNA three-dimensional structure drives the sequence organization of potato spindle tuber viroid quasispecies

RNA viruses and viroids exist and evolve as quasispecies due to error-prone replication. Quasispecies consist of a few dominant master sequences alongside numerous variants that contribute to genetic diversity. Upon environmental changes, certain variants within quasispecies have the potential to become the dominant sequences, leading to the emergence of novel infectious strains. However, the emergence of new infectious variants remains unpredictable. Using mutant pools prepared by saturation mutagenesis of selected stem and loop regions, our study of potato spindle tuber viroid (PSTVd) demonstrates that mutants forming local three-dimensional (3D) structures similar to the wild type (WT) are more likely to accumulate in PSTVd quasispecies. The selection mechanisms underlying this biased accumulation are likely associated with cell-to-cell movement and long-distance trafficking. Moreover, certain trafficking-defective PSTVd mutants can be spread by functional sister genomes in the quasispecies. Our study reveals that the RNA 3D structure of stems and loops constrains the evolution of viroid quasispecies. Mutants with a structure similar to WT have a higher likelihood of being maintained within the quasispecies and can potentially give rise to novel infectious variants. These findings emphasize the potential of targeting RNA 3D structure as a more robust approach to defend against viroid infections.

Anionic G•U pairs in bacterial ribosomal rRNAs

Wobble GU pairs (or G•U) occur frequently within double-stranded RNA helices interspersed between standard G=C and A-U Watson-Crick pairs. Another type of G•U pair interacting via their Watson-Crick edges has been observed in the A site of ribosome structures between a modified U34 in the tRNA anticodon triplet and G + 3 in the mRNA. In such pairs, the electronic structure of the U is changed with a negative charge on N3(U), resulting in two H-bonds between N1(G)…O4(U) and N2(G)…N3(U). Here, we report that such pairs occur in other highly conserved positions in ribosomal RNAs of bacteria in the absence of U modification. An anionic cis Watson-Crick G•G pair is also observed and well conserved in the small subunit. These pairs are observed in tightly folded regions.

Seriation Using Tree-penalized Path Length

Given a sample of n data points and an n by n dissimilarity matrix, data seriation methods produce a linear ordering of the objects, putting similar objects nearby in the ordering. One may visualize the reordered dissimilarity matrix with a heat map and thus understand the structure of the data, while still displaying the full matrix of dissimilarities. Good orderings produce heat maps that are easy to read and allow for clear interpretation. We consider two popular seriation methods, minimizing path length by solving the Traveling Salesman Problem (TSP), and Optimal Leaf Ordering (OLO), which minimizes path length among all orderings consistent with a given tree structure. Learning from the strengths and weaknesses of the two methods, we introduce a new hybrid seriation method, tree-penalized Path Length (tpPL). The objective is a linear combination of path length and the extent of violations of the tree structure, with a parameter that transitions the optimal paths smoothly from TSP to OLO. We present a detailed study over 44 synthetic datasets which are designed to bring out the strengths and weaknesses of the three methods, finding that the hybrid nature of tpPL enables it to overcome the weaknesses of TSP and OLO.

Lone Pair…π Contacts and Structure Signatures of r(UNCG) Tetraloops, Z-Turns, and Z-Steps: A WebFR3D Survey

Z-DNA and Z-RNA have long appeared as oddities to nucleic acid scientists. However, their Z-step constituents are recurrently observed in all types of nucleic acid systems including ribosomes. Z-steps are NpN steps that are isostructural to Z-DNA CpG steps. Among their structural features, Z-steps are characterized by the presence of a lone pair…π contact that involves the stacking of the ribose O4′ atom of the first nucleotide with the 3′-face of the second nucleotide. Recently, it has been documented that the CpG step of the ubiquitous r(UNCG) tetraloops is a Z-step. Accordingly, such r(UNCG) conformations were called Z-turns. It has also been recognized that an r(GAAA) tetraloop in appropriate conditions can shapeshift to an unusual Z-turn conformation embedding an ApA Z-step. In this report, we explore the multiplicity of RNA motifs based on Z-steps by using the WebFR3D tool to which we added functionalities to be able to retrieve motifs containing lone pair…π contacts. Many examples that underscore the diversity and universality of these motifs are provided as well as tutorial guidance on using WebFR3D. In addition, this study provides an extensive survey of crystallographic, cryo-EM, NMR, and molecular dynamics studies on r(UNCG) tetraloops with a critical view on how to conduct database searches and exploit their results.

Neocles B. Leontis (1955 - 2020)

None.

Functional analysis reveals G/U pairs critical for replication and trafficking of an infectious non-coding viroid RNA

While G/U pairs are present in many RNAs, the lack of molecular studies to characterize the roles of multiple G/U pairs within a single RNA limits our understanding of their biological significance. From known RNA 3D structures, we observed that the probability a G/U will form a Watson-Crick (WC) base pair depends on sequence context. We analyzed 17 G/U pairs in the 359-nucleotide genome of Potato spindle tuber viroid (PSTVd), a circular non-coding RNA that replicates and spreads systemically in host plants. Most putative G/U base pairs were experimentally supported by selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE). Deep sequencing PSTVd genomes from plants inoculated with a cloned master sequence revealed naturally occurring variants, and showed that G/U pairs are maintained to the same extent as canonical WC base pairs. Comprehensive mutational analysis demonstrated that nearly all G/U pairs are critical for replication and/or systemic spread. Two selected G/U pairs were found to be required for PSTVd entry into, but not for exit from, the host vascular system. This study identifies critical roles for G/U pairs in the survival of an infectious RNA, and increases understanding of structure-based regulation of replication and trafficking of pathogen and cellular RNAs.

A three-dimensional RNA motif mediates directional trafficking of Potato spindle tuber viroid from epidermal to palisade mesophyll cells in Nicotiana benthamiana

Potato spindle tuber viroid (PSTVd) is a circular non-coding RNA of 359 nucleotides that replicates and spreads systemically in host plants, thus all functions required to establish an infection are mediated by sequence and structural elements in the genome. The PSTVd secondary structure contains 26 Watson-Crick base-paired stems and 27 loops. Most of the loops are believed to form three-dimensional (3D) structural motifs through non-Watson-Crick base pairing, base stacking, and other local interactions. Homology-based prediction using the JAR3D online program revealed that loop 27 (nucleotides 177-182) most likely forms a 3D structure similar to the loop of a conserved hairpin located in the 3' untranslated region of histone mRNAs in animal cells. This stem-loop, which is involved in 3'-end maturation, is not found in polyadenylated plant histone mRNAs. Mutagenesis showed that PSTVd genomes containing base substitutions in loop 27 predicted by JAR3D to disrupt the 3D structure were unable to replicate in Nicotiana benthamiana leaves following mechanical rub inoculation, with one exception: a U178G/U179G double mutant was replication-competent and able to spread within the upper epidermis of inoculated leaves, but was confined to this cell layer. Remarkably, direct delivery of the U178G/U179G mutant into the vascular system by needle puncture inoculation allowed it to spread systemically and enter mesophyll cells and epidermal cells of upper leaves. These findings highlight the importance of RNA 3D structure for PSTVd replication and intercellular trafficking and indicate that loop 27 is required for epidermal exit, but not epidermal entry or transit between other cell types. Thus, requirements for RNA trafficking between epidermal and underlying palisade mesophyll cells are unique and directional. Our findings further suggest that 3D structure and RNA-protein interactions constrain RNA sequence evolution, and validate JAR3D as a tool to predict RNA 3D structure.

How to fold and protect mitochondrial ribosomal RNA with fewer guanines

Mammalian mitochondrial ribosomes evolved from bacterial ribosomes by reduction of ribosomal RNAs, increase of ribosomal protein content, and loss of guanine nucleotides. Guanine is the base most sensitive to oxidative damage. By systematically comparing high-quality, small ribosomal subunit RNA sequence alignments and solved 3D ribosome structures from mammalian mitochondria and bacteria, we deduce rules for folding a complex RNA with the remaining guanines shielded from solvent. Almost all conserved guanines in both bacterial and mammalian mitochondrial ribosomal RNA form guanine-specific, local or long-range, RNA–RNA or RNA–protein interactions. Many solvent-exposed guanines conserved in bacteria are replaced in mammalian mitochondria by bases less sensitive to oxidation. New guanines, conserved only in the mitochondrial alignment, are strategically positioned at solvent inaccessible sites to stabilize the ribosomal RNA structure. New mitochondrial proteins substitute for truncated RNA helices, maintain mutual spatial orientations of helices, compensate for lost RNA–RNA interactions, reduce solvent accessibility of bases, and replace guanines conserved in bacteria by forming specific amino acid–RNA interactions.

Lagrangian observations of homogeneous random environments

This article deals with the distribution of the view of a random environment as seen by an observer whose location at each moment is determined by the environment. The main application is in statistical fluid mechanics, where the environment consists of a random velocity field and the observer is a particle moving in the velocity field, possibly subject to molecular diffusion. Several results on such Lagrangian observations of the environment have appeared in the literature, beginning with the 1957 dissertation of J. L. Lumley. This article unites these results into a simple unified framework and rounds out the theory with new results in several directions. When the environment is homogeneous, the problem can be re-cast in terms of certain random mappings on the physical space that are based on the random location of the observer. If these mappings preserve the invariant measure on the physical space, then the view from the random location has the same distribution as the view from the origin. If these mappings satisfy the flow property and the environment is stationary, then the succession of Lagrangian observations over time forms a strictly stationary process. In particular, for motion in a homogeneous, stationary, and nondivergent velocity field, the Lagrangian velocity (the velocity of the particle) is strictly stationary, which was first observed by Lumley. In the compressible case, the distribution of a Lagrangian observation has a density with respect to the distribution of the view from the origin, and in some cases convergence in distribution of the Lagrangian observations as time tends to infinity can be shown.

Dispersion of particle systems in Brownian flows

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

DETECTING CONFORMATIONAL DIFFERENCES BETWEEN RNA 3D STRUCTURES

A method is described for detecting local conformational differences between two 3D structures of the same RNA molecule. These could be distinct 3D structures of the same molecule from the same organism, or homologous molecules from different organisms. In this approach, we detect the variability that exists among the relative translation and rotation operations that are needed to superimpose local neighborhoods after an initial rigid-body global superposition. Each translation and rotation is represented by a three dimensional vector. Thus, we investigate the variability within sets of multivariate data. We demonstrate that the method is able to identify both small- and large-scale conformational changes. Matlab/Octave programs to read RNA 3D structure files and compare structures have been developed and are freely accessible at: https://github.com/BGSU-RNA/ConformationalChange.

JAR3D Webserver: Scoring and aligning RNA loop sequences to known 3D motifs

Many non-coding RNAs have been identified and may function by forming 2D and 3D structures. RNA hairpin and internal loops are often represented as unstructured on secondary structure diagrams, but RNA 3D structures show that most such loops are structured by non-Watson-Crick basepairs and base stacking. Moreover, different RNA sequences can form the same RNA 3D motif. JAR3D finds possible 3D geometries for hairpin and internal loops by matching loop sequences to motif groups from the RNA 3D Motif Atlas, by exact sequence match when possible, and by probabilistic scoring and edit distance for novel sequences. The scoring gauges the ability of the sequences to form the same pattern of interactions observed in 3D structures of the motif. The JAR3D webserver at http://rna.bgsu.edu/jar3d/ takes one or many sequences of a single loop as input, or else one or many sequences of longer RNAs with multiple loops. Each sequence is scored against all current motif groups. The output shows the ten best-matching motif groups. Users can align input sequences to each of the motif groups found by JAR3D. JAR3D will be updated with every release of the RNA 3D Motif Atlas, and so its performance is expected to improve over time.

The RNA 3D Motif Atlas: Computational methods for extraction, organization and evaluation of RNA motifs

RNA 3D motifs occupy places in structured RNA molecules that correspond to the hairpin, internal and multi-helix junction "loops" of their secondary structure representations. As many as 40% of the nucleotides of an RNA molecule can belong to these structural elements, which are distinct from the regular double helical regions formed by contiguous AU, GC, and GU Watson-Crick basepairs. With the large number of atomic- or near atomic-resolution 3D structures appearing in a steady stream in the PDB/NDB structure databases, the automated identification, extraction, comparison, clustering and visualization of these structural elements presents an opportunity to enhance RNA science. Three broad applications are: (1) identification of modular, autonomous structural units for RNA nanotechnology, nanobiology and synthetic biology applications; (2) bioinformatic analysis to improve RNA 3D structure prediction from sequence; and (3) creation of searchable databases for exploring the binding specificities, structural flexibility, and dynamics of these RNA elements. In this contribution, we review methods developed for computational extraction of hairpin and internal loop motifs from a non-redundant set of high-quality RNA 3D structures. We provide a statistical summary of the extracted hairpin and internal loop motifs in the most recent version of the RNA 3D Motif Atlas. We also explore the reliability and accuracy of the extraction process by examining its performance in clustering recurrent motifs from homologous ribosomal RNA (rRNA) structures. We conclude with a summary of remaining challenges, especially with regard to extraction of multi-helix junction motifs.

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.

R3D-2-MSA: the RNA 3D structure-to-multiple sequence alignment server

The RNA 3D Structure-to-Multiple Sequence Alignment Server (R3D-2-MSA) is a new web service that seamlessly links RNA three-dimensional (3D) structures to high-quality RNA multiple sequence alignments (MSAs) from diverse biological sources. In this first release, R3D-2-MSA provides manual and programmatic access to curated, representative ribosomal RNA sequence alignments from bacterial, archaeal, eukaryal and organellar ribosomes, using nucleotide numbers from representative atomic-resolution 3D structures. A web-based front end is available for manual entry and an Application Program Interface for programmatic access. Users can specify up to five ranges of nucleotides and 50 nucleotide positions per range. The R3D-2-MSA server maps these ranges to the appropriate columns of the corresponding MSA and returns the contents of the columns, either for display in a web browser or in JSON format for subsequent programmatic use. The browser output page provides a 3D interactive display of the query, a full list of sequence variants with taxonomic information and a statistical summary of distinct sequence variants found. The output can be filtered and sorted in the browser. Previous user queries can be viewed at any time by resubmitting the output URL, which encodes the search and re-generates the results. The service is freely available with no login requirement at http://rna.bgsu.edu/r3d-2-msa.

Isosteric and nonisosteric base pairs in RNA motifs: molecular dynamics and bioinformatics study of the sarcin-ricin internal loop

The sarcin-ricin RNA motif (SR motif) is one of the most prominent recurrent RNA building blocks that occurs in many different RNA contexts and folds autonomously, that is, in a context-independent manner. In this study, we combined bioinformatics analysis with explicit-solvent molecular dynamics (MD) simulations to better understand the relation between the RNA sequence and the evolutionary patterns of the SR motif. A SHAPE probing experiment was also performed to confirm the fidelity of the MD simulations. We identified 57 instances of the SR motif in a nonredundant subset of the RNA X-ray structure database and analyzed their base pairing, base-phosphate, and backbone-backbone interactions. We extracted sequences aligned to these instances from large rRNA alignments to determine the frequency of occurrence for different sequence variants. We then used a simple scoring scheme based on isostericity to suggest 10 sequence variants with a highly variable expected degree of compatibility with the SR motif 3D structure. We carried out MD simulations of SR motifs with these base substitutions. Nonisosteric base substitutions led to unstable structures, but so did isosteric substitutions which were unable to make key base-phosphate interactions. The MD technique explains why some potentially isosteric SR motifs are not realized during evolution. We also found that the inability to form stable cWW geometry is an important factor in the case of the first base pair of the flexible region of the SR motif. A comparison of structural, bioinformatics, SHAPE probing, and MD simulation data reveals that explicit solvent MD simulations neatly reflect the viability of different sequence variants of the SR motif. Thus, MD simulations can efficiently complement bioinformatics tools in studies of conservation patterns of RNA motifs and provide atomistic insight into the role of their different signature interactions.

The Nucleic Acid Database: new features and capabilities

The Nucleic Acid Database (NDB) (http://ndbserver.rutgers.edu) is a web portal providing access to information about 3D nucleic acid structures and their complexes. In addition to primary data, the NDB contains derived geometric data, classifications of structures and motifs, standards for describing nucleic acid features, as well as tools and software for the analysis of nucleic acids. A variety of search capabilities are available, as are many different types of reports. This article describes the recent redesign of the NDB Web site with special emphasis on new RNA-derived data and annotations and their implementation and integration into the search capabilities.

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.

R3D Align web server for global nucleotide to nucleotide alignments of RNA 3D structures

The R3D Align web server provides online access to ‘RNA 3D Align’ (R3D Align), a method for producing accurate nucleotide-level structural alignments of RNA 3D structures. The web server provides a streamlined and intuitive interface, input data validation and output that is more extensive and easier to read and interpret than related servers. The R3D Align web server offers a unique Gallery of Featured Alignments, providing immediate access to pre-computed alignments of large RNA 3D structures, including all ribosomal RNAs, as well as guidance on effective use of the server and interpretation of the output. By accessing the non-redundant lists of RNA 3D structures provided by the Bowling Green State University RNA group, R3D Align connects users to structure files in the same equivalence class and the best-modeled representative structure from each group. The R3D Align web server is freely accessible at http://rna.bgsu.edu/r3dalign/.

Comprehensive survey and geometric classification of base triples in RNA structures

Base triples are recurrent clusters of three RNA nucleobases interacting edge-to-edge by hydrogen bonding. We find that the central base in almost all triples forms base pairs with the other two bases of the triple, providing a natural way to geometrically classify base triples. Given 12 geometric base pair families defined by the Leontis-Westhof nomenclature, combinatoric enumeration predicts 108 potential geometric base triple families. We searched representative atomic-resolution RNA 3D structures and found instances of 68 of the 108 predicted base triple families. Model building suggests that some of the remaining 40 families may be unlikely to form for steric reasons. We developed an on-line resource that provides exemplars of all base triples observed in the structure database and models for unobserved, predicted triples, grouped by triple family, as well as by three-base combination (http://rna.bgsu.edu/Triples). The classification helps to identify recurrent triple motifs that can substitute for each other while conserving RNA 3D structure, with applications in RNA 3D structure prediction and analysis of RNA sequence evolution.

Noncanonical hydrogen bonding in nucleic acids. Benchmark evaluation of key base-phosphate interactions in folded RNA molecules using quantum-chemical calculations and molecular dynamics simulations

RNA molecules are stabilized by a wide range of noncanonical interactions that are not present in DNA. Among them, the recently classified base-phosphate (BPh) interactions belong to the most important ones. Twelve percent of nucleotides in the ribosomal crystal structures are involved in BPh interactions. BPh interactions are highly conserved and provide major constraints on RNA sequence evolution. Here we provide assessment of the energetics of BPh interactions using MP2 computations extrapolated to the complete basis set of atomic orbitals and corrected for higher-order electron correlation effects. The reference computations are compared with DFT-D and DFT-D3 approaches, the SAPT method, and the molecular mechanics force field. The computations, besides providing the basic benchmark for the BPh interactions, allow some refinements of the original classification, including identification of some potential doubly bonded BPh patterns. The reference computations are followed by analysis of some larger RNA fragments that consider the context of the BPh interactions. The computations demonstrate the complexity of interaction patterns utilizing the BPh interactions in real RNA structures. The BPh interactions are often involved in intricate interaction networks. We studied BPh interactions of protonated adenine that can contribute to catalysis of hairpin ribozyme, the key BPh interaction in the S-turn motif of the sarcin-ricin loop, which may predetermine the S-turn topology and complex BPh patterns from the glmS riboswitch. Finally, the structural stability of BPh interactions in explicit solvent molecular dynamics simulations is assessed. The simulations well preserve key BPh interactions and allow dissection of structurally/functionally important water-meditated BPh bridges, which could not be considered in earlier bioinformatics classification of BPh interactions.

Sharing and archiving nucleic acid structure mapping data

Nucleic acids are particularly amenable to structural characterization using chemical and enzymatic probes. Each individual structure mapping experiment reveals specific information about the structure and/or dynamics of the nucleic acid. Currently, there is no simple approach for making these data publically available in a standardized format. We therefore developed a standard for reporting the results of single nucleotide resolution nucleic acid structure mapping experiments, or SNRNASMs. We propose a schema for sharing nucleic acid chemical probing data that uses generic public servers for storing, retrieving, and searching the data. We have also developed a consistent nomenclature (ontology) within the Ontology of Biomedical Investigations (OBI), which provides unique identifiers (termed persistent URLs, or PURLs) for classifying the data. Links to standardized data sets shared using our proposed format along with a tutorial and links to templates can be found at http://snrnasm.bio.unc.edu.

WebFR3D--a server for finding, aligning and analyzing recurrent RNA 3D motifs

WebFR3D is the on-line version of ‘Find RNA 3D’ (FR3D), a program for annotating atomic-resolution RNA 3D structure files and searching them efficiently to locate and compare RNA 3D structural motifs. WebFR3D provides on-line access to the central features of FR3D, including geometric and symbolic search modes, without need for installing programs or downloading and maintaining 3D structure data locally. In geometric search mode, WebFR3D finds all motifs similar to a user-specified query structure. In symbolic search mode, WebFR3D finds all sets of nucleotides making user-specified interactions. In both modes, users can specify sequence, sequence–continuity, base pairing, base-stacking and other constraints on nucleotides and their interactions. WebFR3D can be used to locate hairpin, internal or junction loops, list all base pairs or other interactions, or find instances of recurrent RNA 3D motifs (such as sarcin–ricin and kink-turn internal loops or T- and GNRA hairpin loops) in any PDB file or across a whole set of 3D structure files. The output page provides facilities for comparing the instances returned by the search by superposition of the 3D structures and the alignment of their sequences annotated with pairwise interactions. WebFR3D is available at http://rna.bgsu.edu/webfr3d.

R3D Align: global pairwise alignment of RNA 3D structures using local superpositions

MOTIVATION

Comparing 3D structures of homologous RNA molecules yields information about sequence and structural variability. To compare large RNA 3D structures, accurate automatic comparison tools are needed. In this article, we introduce a new algorithm and web server to align large homologous RNA structures nucleotide by nucleotide using local superpositions that accommodate the flexibility of RNA molecules. Local alignments are merged to form a global alignment by employing a maximum clique algorithm on a specially defined graph that we call the 'local alignment' graph.

RESULTS

The algorithm is implemented in a program suite and web server called 'R3D Align'. The R3D Align alignment of homologous 3D structures of 5S, 16S and 23S rRNA was compared to a high-quality hand alignment. A full comparison of the 16S alignment with the other state-of-the-art methods is also provided. The R3D Align program suite includes new diagnostic tools for the structural evaluation of RNA alignments. The R3D Align alignments were compared to those produced by other programs and were found to be the most accurate, in comparison with a high quality hand-crafted alignment and in conjunction with a series of other diagnostics presented. The number of aligned base pairs as well as measures of geometric similarity are used to evaluate the accuracy of the alignments.

AVAILABILITY

R3D Align is freely available through a web server http://rna.bgsu.edu/R3DAlign. The MATLAB source code of the program suite is also freely available for download at that location.

Classification and energetics of the base-phosphate interactions in RNA

Structured RNA molecules form complex 3D architectures stabilized by multiple interactions involving the nucleotide base, sugar and phosphate moieties. A significant percentage of the bases in structured RNA molecules in the Protein Data Bank (PDB) hydrogen-bond with phosphates of other nucleotides. By extracting and superimposing base-phosphate (BPh) interactions from a reduced-redundancy subset of 3D structures from the PDB, we identified recurrent phosphate-binding sites on the RNA bases. Quantum chemical calculations were carried out on model systems representing each BPh interaction. The calculations show that the centers of each cluster obtained from the structure superpositions correspond to energy minima on the potential energy hypersurface. The calculations also show that the most stable phosphate-binding sites occur on the Watson-Crick edge of guanine and the Hoogsteen edge of cytosine. We modified the 'Find RNA 3D' (FR3D) software suite to automatically find and classify BPh interactions. Comparison of the 3D structures of the 16S and 23S rRNAs of Escherichia coli and Thermus thermophilus revealed that most BPh interactions are phylogenetically conserved and they occur primarily in hairpin, internal or junction loops or as part of tertiary interactions. Bases that form BPh interactions, which are conserved in the rRNA 3D structures are also conserved in homologous rRNA sequence alignments.

Frequency and isostericity of RNA base pairs

Most of the hairpin, internal and junction loops that appear single-stranded in standard RNA secondary structures form recurrent 3D motifs, where non-Watson-Crick base pairs play a central role. Non-Watson-Crick base pairs also play crucial roles in tertiary contacts in structured RNA molecules. We previously classified RNA base pairs geometrically so as to group together those base pairs that are structurally similar (isosteric) and therefore able to substitute for each other by mutation without disrupting the 3D structure. Here, we introduce a quantitative measure of base pair isostericity, the IsoDiscrepancy Index (IDI), to more accurately determine which base pair substitutions can potentially occur in conserved motifs. We extract and classify base pairs from a reduced-redundancy set of RNA 3D structures from the Protein Data Bank (PDB) and calculate centroids (exemplars) for each base combination and geometric base pair type (family). We use the exemplars and IDI values to update our online Basepair Catalog and the Isostericity Matrices (IM) for each base pair family. From the database of base pairs observed in 3D structures we derive base pair occurrence frequencies for each of the 12 geometric base pair families. In order to improve the statistics from the 3D structures, we also derive base pair occurrence frequencies from rRNA sequence alignments.

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.