Combinatorics of saturated secondary structures of RNA.

Following Zuker (1986), a saturated secondary structure for a given RNA sequence is a secondary structure such that no base pair can be added without violating the definition of secondary structure, e.g., without introducing a pseudoknot. In the Nussinov-Jacobson energy model (Nussinov and Jacobson, 1980), where the energy of a secondary structure is -1 times the number of base pairs, saturated secondary structures are local minima in the energy landscape, hence form kinetic traps during the folding process. Here we present recurrence relations and closed form asymptotic limits for combinatorial problems related to the number of saturated secondary structures. In addition, Python source code to compute the number of saturated secondary structures having k base pairs can be found at the web servers link of bioinformatics.bc.edu/clotelab/.     

3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar-phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.     

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.     

SwS: a solvation web service for nucleic acids

SwS, based on a statistical analysis of crystallographic structures deposited in the NDB, is designed to provide an exhaustive overview of the solvation of nucleic acid structural elements through the generation of 3D solvent density maps. A first version (v1.0) of this web service focuses on the interaction of DNA, RNA and hybrid base pairs linked by two or three hydrogen bonds with water, cations and/or anions. Data provided by SwS are updated on a weekly basis and can be used by: (i) those involved in molecular dynamics simulation studies for validation purposes; (ii) crystallographers for help in the interpretation of solvent density maps; and all those involved in (iii) drug design and, more generally, in (iv) nucleic acid structural studies. SwS provides also statistical data related to the frequency of occurrence of different types of base pairs in crystallographic structures and the conformation of the involved nucleotides. This web service has been designed to allow a maximum of flexibility in terms of queries and has also been developed with didactic considerations in mind. AVAILABILITY: http://www-ibmc.u-strasbg.fr/arn/sws.html     

Ligand Depot: a data warehouse for ligands bound to macromolecules

Ligand Depot is an integrated data resource for finding information about small molecules bound to proteins and nucleic acids. The initial release (version 1.0, November, 2003) focuses on providing chemical and structural information for small molecules found as part of the structures deposited in the Protein Data Bank. Ligand Depot accepts keyword-based queries and also provides a graphical interface for performing chemical substructure searches. A wide variety of web resources that contain information on small molecules may also be accessed through Ligand Depot. AVAILABILITY: Ligand Depot is available at http://ligand-depot.rutgers.edu/. Version 1.0 supports multiple operating systems including Windows, Unix, Linux and the Macintosh operating system. The current drawing tool works in Internet Explorer, Netscape and Mozilla on Windows, Unix and Linux.     

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.     

Visualizing RNA base-pairing probabilities with RNAbow diagrams

There are many effective ways to represent a minimum free energy RNA secondary structure that make it easy to locate its helices and loops. It is a greater challenge to visualize the thermal average probabilities of all folds in a partition function sum; dot plot representations are often puzzling. Therefore, we introduce the RNAbows visualization tool for RNA base pair probabilities. RNAbows represent base pair probabilities with line thickness and shading, yielding intuitive diagrams. RNAbows aid in disentangling incompatible structures, allow comparisons between clusters of folds, highlight differences between wild-type and mutant folds, and are also rather beautiful.     

GSDS: 基因结构显示系统

构建了一个用于绘制基因结构示意图的网站系统(http://gsds.cbi.pku.edu.cn/)。用户可提交核酸序列、NCBI核酸序列号或基因外显子位置信息, 得到基因结构示意图; 并可指定在基因结构图上标注某些特定区域。系统允许用户同时输入多个基因, 并指定输出次序和标注区域。结果可用位图和矢量图两种图形格式显示。点击位图格式结果, 可以查看相应序列。系统提供中英文两种用户界面。     

Topological classification of RNA structures

We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non-planar diagrams correspond to pseudoknotted structures and have higher genus. The topological genus allows for the definition of topological folding motifs, similar in spirit to those introduced and commonly used in protein folding. We analyze real RNA structures from the databases Worldwide Protein Data Bank and Pseudobase and classify them according to their topological genus. For simplicity, we limit our analysis by considering only Watson-Crick complementary base pairs and G-U wobble base pairs. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.     

Computing the partition function and sampling for saturated secondary structures of RNA, with respect to the Turner energy model.

An RNA secondary structure is saturated if no base pairs can be added without violating the definition of secondary structure. Here we describe a new algorithm, RNAsat, which for a given RNA sequence a, an integral temperature 0 相似文献   

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

Background  

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

Database of non-canonical base pairs found in known RNA structures

Atomic resolution RNA structures are being published at an increasing rate. It is common to find a modest number of non-canonical base pairs in these structures in addition to the usual Watson-Crick pairs. This database summarizes the occurrence of these rare base pairs in accordance with standard nomenclature. The database, http://prion.bchs.uh.edu/, contains information such as sequence context, sugar pucker conformation, anti / syn base conformations, chemical shift, p K (a)values, melting temperature and free energy. Of the 29 anticipated pairs with two or more hydrogen bonds, 20 have been encountered to date. In addition, four unexpected pairs with two hydrogen bonds have been reported bringing the total to 24. Single hydrogen bond versions of five of the expected geometries have been encountered among the single hydrogen bond interactions. In addition, 18 different types of base triplets have been encountered, each of which involves three to six hydrogen bonds. The vast majority of the rare base pairs are antiparallel with the bases in the anti configuration relative to the ribose. The most common are the GU wobble, the Sheared GA pair, the Reverse Hoogsteen pair and the GA imino pair.     

Vfold: A Web Server for RNA Structure and Folding Thermodynamics Prediction

Background

The ever increasing discovery of non-coding RNAs leads to unprecedented demand for the accurate modeling of RNA folding, including the predictions of two-dimensional (base pair) and three-dimensional all-atom structures and folding stabilities. Accurate modeling of RNA structure and stability has far-reaching impact on our understanding of RNA functions in human health and our ability to design RNA-based therapeutic strategies.

Results

The Vfold server offers a web interface to predict (a) RNA two-dimensional structure from the nucleotide sequence, (b) three-dimensional structure from the two-dimensional structure and the sequence, and (c) folding thermodynamics (heat capacity melting curve) from the sequence. To predict the two-dimensional structure (base pairs), the server generates an ensemble of structures, including loop structures with the different intra-loop mismatches, and evaluates the free energies using the experimental parameters for the base stacks and the loop entropy parameters given by a coarse-grained RNA folding model (the Vfold model) for the loops. To predict the three-dimensional structure, the server assembles the motif scaffolds using structure templates extracted from the known PDB structures and refines the structure using all-atom energy minimization.

Conclusions

The Vfold-based web server provides a user friendly tool for the prediction of RNA structure and stability. The web server and the source codes are freely accessible for public use at “http://rna.physics.missouri.edu”.     

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.     

Non-canonical base pairs and higher order structures in nucleic acids: crystal structure database analysis

Non-canonical base pairs, mostly present in the RNA, often play a prominent role towards maintaining their structural diversity. Higher order structures like base triples are also important in defining and stabilizing the tertiary folded structure of RNA. We have developed a new program BPFIND to analyze different types of canonical and non-canonical base pairs and base triples involving at least two direct hydrogen bonds formed between polar atoms of the bases or sugar O2' only. We considered 104 possible types of base pairs, out of which examples of 87 base pair types are found to occur in the available RNA crystal structures. Analysis indicates that approximately 32.7% base pairs in the functional RNA structures are non-canonical, which include different types of GA and GU Wobble base pairs apart from a wide range of base pair possibilities. We further noticed that more than 10.4% of these base pairs are involved in triplet formation, most of which play important role in maintaining long-range tertiary contacts in the three-dimensional folded structure of RNA. Apart from detection, the program also gives a quantitative estimate of the conformational deformation of detected base pairs in comparison to an ideal planar base pair. This helps us to gain insight into the extent of their structural variations and thus assists in understanding their specific role towards structural and functional diversity.