The Partition Function Variant of Sankoff´s Algorithm

Many classes of functional RNA molcules are characterized by highly conserved secondary structures but little detectable sequence similarity. Reliable multiple alignments can therefore be constructed only when the shared structural features are taken into account. Sankoff's algorithm can be used to construct such structure-based alignments of RNA sequences in polynomial time. Here we extend the approach to a probabilistic one by explicitly computing the partition function of all pairwisely aligned sequences with a common set of base pairs. Stochastic backtracking can then be used to compute e.g. the probability that a prescribed sequence-structure pattern is conserved between two RNA sequences. The reliability of the alignment itself can be assessed in terms of the probabilities of each possible match

Memory efficient folding algorithms for circular RNA secondary structures

Background: A small class of RNA molecules, in particular the tiny genomes of viroids, are circular. Yet most structure prediction algorithms handle only linear RNAs. The most straightforward approach is to compute circular structures from ‘internal’ and ‘external’ substructures separated by a base pair. This is incompatible, however, with the memory-saving approach of the Vienna RNA Package which builds a linear RNA structure from shorter (internal) structures only. Result: Here we describe how circular secondary structures can be obtained without additional memory requirements as a kind of ‘post-processing’ of the linear structures

Comparative Analysis of Cyclic Sequences: Viroids and other Small Circular RNA`s

The analysis of small circular sequences requires specialized tools. While the differences between linear and circular sequences can be neglected in the case of long molecules such as bacterial genomes since in practice all analysis is performed in sequence windows, this is not true for viroids and related sequences which are usually only a few hundred basepairs long. In this contribution we present basic algorithms and corresponding software for circular RNAs. In particular, we discuss the problem of pairwise and multiple cyclic sequence alignments with affine gap costs, and an extension of a recent approach to circular RNA folding to the computation of consensus structures

Computational Chemistry with RNA Secondary Structures

The secondary structure for nucleic acids provides a level of description that is both abstract enough to allow for efficient algorithms and realistic enough to provide a good approximate to the thermodynamic and kinetics properties of RNA structure formation. The secondary structure model has furthermore been successful in explaining salient features of RNA evolution in nature and in the test tube. In this contribution we review the computational chemistry of RNA secondary structures using a simplified algorithmic approach for explanation

Alignment of RNA base pairing probability matrices

Motivation: Many classes of functional RNA molecules are characterized by highly conserved secondary structures but little detectable sequence similarity. Reliable multiple alignments can therefore be constructed only when the shared structural features are taken into account. Since multiple alignments are used as input for many subsequent methods of data analysis, structure-based alignments are an indispensable necessity in RNA bioinformatics. Results: We present here a method to compute pairwise and progressive multiple alignments from the direct comparison of base pairing probability matrices. Instead of attempting to solve the folding and the alignment problem simultaneously as in the classical Sankoff's algorithm, we use McCaskill's approach to compute base pairing probability matrices which effectively incorporate the information on the energetics of each sequences. A novel, simplified variant of Sankoff's algorithms can then be employed to extract the maximum-weight common secondary structure and an associated alignment

The RNAz web server: prediction of thermodynamically stable and evolutionarily conserved RNA structures

Many non-coding RNA genes and cis-acting regulatory elements of mRNAs contain RNA secondary structures that are critical for their function. Such functional RNAs can be predicted on the basis of thermodynamic stability and evolutionary conservation. We present a web server that uses the RNAz algorithm to detect functional RNA structures in multiple alignments of nucleotide sequences. The server provides access to a complete and fully automatic analysis pipeline that allows not only to analyze single alignments in a variety of formats, but also to conduct complex screens of large genomic regions. Results are presented on a website that is illustrated by various structure representations and can be downloaded for local view. The web server is available at: rna.tbi.univie.ac.at/RNAz

Conserved RNA secondary structures in Flaviviridae genomes

Presented here is a comprehensive computational survey of evolutionarily conserved secondary structure motifs in the genomic RNAs of the family Flaviviridae. This virus family consists of the three genera Flavivirus, Pestivirus and Hepacivirus and the group of GB virus C/hepatitis G virus with a currently uncertain taxonomic classification. Based on the control of replication and translation, two subgroups were considered separately: the genus Flavivirus, with its type I cap structure at the 5′ untranslated region (UTR) and a highly structured 3′ UTR, and the remaining three groups, which exhibit translation control by means of an internal ribosomal entry site (IRES) in the 5′ UTR and a much shorter less-structured 3′ UTR. The main findings of this survey are strong hints for the possibility of genome cyclization in hepatitis C virus and GB virus C/hepatitis G virus in addition to the flaviviruses; a surprisingly large number of conserved RNA motifs in the coding regions; and a lower level of detailed structural conservation in the IRES and 3′ UTR motifs than reported in the literature. An electronic atlas organizes the information on the more than 150 conserved, and therefore putatively functional, RNA secondary structure elements

Evolution of Metabolic Networks: A Computational Framework

Background: The metabolic architectures of extant organisms share many key pathways such as the citric acid cycle, glycolysis, or the biosynthesis of most amino acids. Several competing hypotheses for the evolutionary mechanisms that shape metabolic networks have been discussed in the literature, each of which finds support from comparative analysis of extant genomes. Alternatively, the principles of metabolic evolution can be studied by direct computer simulation. This requires, however, an explicit implementation of all pertinent components: a universe of chemical reaction upon which the metabolism is built, an explicit representation of the enzymes that implement the metabolism, of a genetic system that encodes these enzymes, and of a fitness function that can be selected for. Results: We describe here a simulation environment that implements all these components in a simplified ways so that large-scale evolutionary studies are feasible. We employ an artificial chemistry that views chemical reactions as graph rewriting operations and utilizes a toy-version of quantum chemistry to derive thermodynamic parameters. Minimalist organisms with simple string-encoded genomes produce model ribozymes whose catalytic activity is determined by an ad hoc mapping between their secondary structure and the transition state graphs that they stabilize. Fitness is computed utilizing the ideas of metabolic flux analysis. We present an implementation of the complete system and first simulation results. Conclusions: The simulation system presented here allows coherent investigations into the evolutionary mechanisms of the first steps of metabolic evolution using a self-consistent toy univers