SU(2) Cosmological Solitons

We present a class of numerical solutions to the SU(2) nonlinear $\sigma$-model coupled to the Einstein equations with cosmological constant $\Lambda\geq 0$ in spherical symmetry. These solutions are characterized by the presence of a regular static region which includes a center of symmetry. They are parameterized by a dimensionless ``coupling constant'' $\beta$, the sign of the cosmological constant, and an integer ``excitation number'' $n$. The phenomenology we find is compared to the corresponding solutions found for the Einstein-Yang-Mills (EYM) equations with positive $\Lambda$ (EYM$\Lambda$). If we choose $\Lambda$ positive and fix $n$, we find a family of static spacetimes with a Killing horizon for $0 \leq \beta < \beta_{max}$. As a limiting solution for $\beta = \beta_{max}$ we find a {\em globally} static spacetime with $\Lambda=0$, the lowest excitation being the Einstein static universe. To interpret the physical significance of the Killing horizon in the cosmological context, we apply the concept of a trapping horizon as formulated by Hayward. For small values of $\beta$ an asymptotically de Sitter dynamic region contains the static region within a Killing horizon of cosmological type. For strong coupling the static region contains an ``eternal cosmological black hole''.Comment: 20 pages, 6 figures, Revte

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. Description: RNA FRABASE 2.0 has stored information on 1565 PDB-deposited RNA structures, including all NMR models. The RNA FRABASE 2.0 search engine algorithms operate on the database of the RNA sequences and the new library of RNA secondary structures, coded in the dot-bracket format extended to hold multi-stranded structures and to cover residues whose coordinates are missing in the PDB files. The library of RNA secondary structures (and their graphics) is made available. A high level of efficiency of the 3D search has been achieved by introducing novel tools to formulate advanced searching patterns and to screen highly populated tertiary structure elements. RNA FRABASE 2.0 also stores data and conformational parameters in order to provide "on the spot" structural filters to explore the three-dimensional RNA structures. An instant visualization of the 3D RNA structures is provided. RNA FRABASE 2.0 is freely available at http://rnafrabase.cs.put.poznan.pl webcite. Conclusions: RNA FRABASE 2.0 provides a novel database and powerful search engine which is equipped with new data and functionalities that are unavailable elsewhere. Our intention is that this advanced version of the RNA FRABASE will be of interest to all researchers working in the RNA field

RNA FRABASE version 1.0: an engine with a database to search for the three-dimensional fragments within RNA structures

The RNA FRABASE is a web-accessible engine with a relational database, which allows for the automatic search of user-defined, 3D RNA fragments within a set of RNA structures. This is a new tool to search and analyse RNA structures, directed at the 3D structure modelling. The user needs to input either RNA sequence(s) and/or secondary structure(s) given in a ‘dot-bracket’ notation. The algorithm searching for the requested 3D RNA fragments is very efficient. As of August 2007, the database contains: (i) RNA sequences and secondary structures, in the ‘dot-bracket’ notation, derived from 1065 protein data bank (PDB)-deposited RNA structures and their complexes, (ii) a collection of atom coordinates of unmodified and modified nucleotide residues occurring in RNA structures, (iii) calculated RNA torsion angles and sugar pucker parameters and (iv) information about base pairs. Advanced query involves filters sensitive to: modified residue contents, experimental method used and limits of conformational parameters. The output list of query-matching RNA fragments gives access to their coordinates in the PDB-format files, ready for direct download and visualization, conformational parameters and information about base pairs. The RNA FRABASE is automatically, monthly updated and is freely accessible at http://rnafrabase.ibch.poznan.pl (mirror at http://cerber.cs.put.poznan.pl/rnadb)

High salt solution structure of a left-handed RNA double helix

Right-handed RNA duplexes of (CG)(n) sequence undergo salt-induced helicity reversal, forming left-handed RNA double helices (Z-RNA). In contrast to the thoroughly studied Z-DNA, no Z-RNA structure of natural origin is known. Here we report the NMR structure of a half-turn, left-handed RNA helix (CGCGCG)(2) determined in 6 M NaClO(4). This is the first nucleic acid motif determined at such high salt. Sequential assignments of non-exchangeable proton resonances of the Z-form were based on the hitherto unreported NOE connectivity path [H6((n))-H5′/H5″((n))-H8((n+1))-H1′((n+1))-H6((n+2))] found for left-handed helices. Z-RNA structure shows several conformational features significantly different from Z-DNA. Intra-strand but no inter-strand base stacking was observed for both CpG and GpC steps. Helical twist angles for CpG steps have small positive values (4–7°), whereas GpC steps have large negative values (−61°). In the full-turn model of Z-RNA (12.4 bp per turn), base pairs are much closer to the helix axis than in Z-DNA, thus both the very deep, narrow minor groove with buried cytidine 2′-OH groups, and the major groove are well defined. The 2′-OH group of cytidines plays a crucial role in the Z-RNA structure and its formation; 2′-O-methylation of cytidine, but not of guanosine residues prohibits A to Z helicity reversal

New models and algorithms for RNA pseudoknot order assignment

The pseudoknot is a specific motif of the RNA structure that highly influences the overall shape and stability of a molecule. It occurs when nucleotides of two disjoint single-stranded fragments of the same chain, separated by a helical fragment, interact with each other and form base pairs. Pseudoknots are characterized by great topological diversity, and their systematic description is still a challenge. In our previous work, we have introduced the pseudoknot order: a new coefficient representing the topological complexity of the pseudoknotted RNA structure. It is defined as the minimum number of base pair set decompositions, aimed to obtain the unknotted RNA structure. We have suggested how it can be useful in the interpretation and understanding of a hierarchy of RNA folding. However, it is not trivial to unambiguously identify pseudoknots and determine their orders in an RNA structure. Therefore, since the introduction of this coefficient, we have worked on the method to reliably assign pseudoknot orders in correspondence to the mechanisms that control the biological process leading to their formation in the molecule. Here, we introduce a novel graph coloring-based model for the problem of pseudoknot order assignment. We show a specialized heuristic operating on the proposed model and an alternative integer programming algorithm. The performance of both approaches is compared with that of state-of-the-art algorithms which so far have been most efficient in solving the problem in question. We summarize the results of computational experiments that evaluate our new methods in terms of classification quality on a representative data set originating from the non-redundant RNA 3D structure repository