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.     

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.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

3D maps of RNA interhelical junctions

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.     

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.     

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.     

RNAapt3D: RNA aptamer 3D-structural modeling database

RNA aptamers are oligonucleotides with high binding affinity and specificity for target molecules and are expected to be a new generation of therapeutic molecules and targeted delivery materials. The tertiary structure of RNA molecules and RNA-protein interaction sites are increasingly important as potential targets for new drugs. The pathological mechanisms of diseases must be understood in detail to guide drug design. In developing RNA aptamers as drugs, information about the interaction mechanisms and structures of RNA aptamer-target protein complexes are useful. We constructed a database, RNA aptamer 3D-structural modeling (RNAapt3D), consisting of RNA aptamer data that are potential drug candidates. The database includes RNA sequences and computationally predicted RNA tertiary structures based on secondary structures and implements methods that can be used to predict unknown structures of RNA aptamer-target molecule complexes. RNAapt3D should enable the design of RNA aptamers for target molecules and improve the efficiency and productivity of candidate drug selection. RNAapt3D can be accessed at https://rnaapt3d.medals.jp.     

RNA2D3D: A program for Generating,Viewing, and Comparing 3-Dimensional Models of RNA

Abstract

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

RNA folding on the 3D triangular lattice

Background  

Difficult problems in structural bioinformatics are often studied in simple exact models to gain insights and to derive general principles. Protein folding, for example, has long been studied in the lattice model. Recently, researchers have also begun to apply the lattice model to the study of RNA folding.     

RNA2D3D: a program for generating, viewing, and comparing 3-dimensional models of RNA

Using primary and secondary structure information of an RNA molecule, the program RNA2D3D automatically and rapidly produces a first-order approximation of a 3-dimensional conformation consistent with this information. Applicable to structures of arbitrary branching complexity and pseudoknot content, it features efficient interactive graphical editing for the removal of any overlaps introduced by the initial generating procedure and for making conformational changes favorable to targeted features and subsequent refinement. With emphasis on fast exploration of alternative 3D conformations, one may interactively add or delete base-pairs, adjacent stems can be coaxially stacked or unstacked, single strands can be shaped to accommodate special constraints, and arbitrary subsets can be defined and manipulated as rigid bodies. Compaction, whereby base stacking within stems is optimally extended into connecting single strands, is also available as a means of strategically making the structures more compact and revealing folding motifs. Subsequent refinement of the first-order approximation, of modifications, and for the imposing of tertiary constraints is assisted with standard energy refinement techniques. Previously determined coordinates for any part of the molecule are readily incorporated, and any part of the modeled structure can be output as a PDB or XYZ file. Illustrative applications in the areas of ribozymes, viral kissing loops, viral internal ribosome entry sites, and nanobiology are presented.     

Automated identification of RNA 3D modules with discriminative power in RNA structural alignments

Recent progress in predicting RNA structure is moving towards filling the ‘gap’ in 2D RNA structure prediction where, for example, predicted internal loops often form non-canonical base pairs. This is increasingly recognized with the steady increase of known RNA 3D modules. There is a general interest in matching structural modules known from one molecule to other molecules for which the 3D structure is not known yet. We have created a pipeline, metaRNAmodules, which completely automates extracting putative modules from the FR3D database and mapping of such modules to Rfam alignments to obtain comparative evidence. Subsequently, the modules, initially represented by a graph, are turned into models for the RMDetect program, which allows to test their discriminative power using real and randomized Rfam alignments. An initial extraction of 22 495 3D modules in all PDB files results in 977 internal loop and 17 hairpin modules with clear discriminatory power. Many of these modules describe only minor variants of each other. Indeed, mapping of the modules onto Rfam families results in 35 unique locations in 11 different families. The metaRNAmodules pipeline source for the internal loop modules is available at http://rth.dk/resources/mrm.     

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.     

Microstructural Reconstruction for the Testicular Cysts of Wolf Spider Using 3D Volume Rendering Technique

In insects, the alignment of neighboring spermatid in the late stages is nearly perfect, so that a transverse section of a cyst containing late spermatids transects all the spermatids at approximately the same level. However, the testicular cysts of spiders are spherical, most cysts are arranged in order of increasing maturity from the periphery to the center of the testis. For this reason, it is difficult to observe the whole spermatids within a single microscopic slide and count them. Therefore, we demonstrate microstructural reconstruction technique enabling to count exact number of sperm cells per cyst with aid of 3D volume rendering. For image processing and reconstruction, serially sectioned histologic specimens were scanned with microscopy and 3D images were reconstructed using Amira 5.3.2 software from the image stacks of the germ cells and surrounding testicular cysts subsequentially. With the information gathered by 3D reconstruction, it has finally been counted that exactly 32 (2⁵) cells of the secondary spermatocytes per cyst. This means that most cysts in P. laura contain exactly 64 (2⁶) spermatids or spermatozoa, which presumably arose from four synchronous mitotic and two meiotic divisions. In addition, the number of divisions occurring in a cyst appears to be constant for this spider because it has been known that the number of spermatids per cyst is characteristic for each species.     

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.     

RNA gradients: Shapers of 3D genome architecture

A growing body of evidence points to a role of nuclear RNAs (nucRNAs) in shaping the three-dimensional (3D) architecture of the genome within the nucleus of a eukaryotic cell. nucRNAs are non-homogeneously distributed within the nucleus where they can form global and local gradients that might contribute to instructing the formation and coordinating the function of different types of 3D genome structures. In this article, we highlight the available literature supporting a role of nucRNAs as 3D genome shapers and propose that nucRNA gradients are key mediators of genome structure and function.     

A 3D Graphical Representation of RNA Secondary Structures

Abstract

In this paper, we proposed a 3-D graphical representation of RNA secondary structures. Based on this representation, we outline an approach by constructing a 3-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with RNA secondary structure. The examination of similarities/dissimilarities among the secondary structure at the 3′-terminus of different viruses illustrates the utility of the approach.