Local similarity in RNA secondary structures

Abstract

We present a systematic treatment of alignment distance and local similarity algorithms on trees and forests. We build upon the tree alignment algorithm for ordered trees given by Jiang et. al (1995) and extend it to calculate local forest alignments, which is essential for finding local similar regions in RNA secondary structures. The time complexity of our algorithm is Motivation IntroductionRNA is a chain molecule, mathematically a string over a four letter alphabet. It is built from nucleotides containing the bases A(denine), C(ytosine), G(uanine), and U(racil). By folding back onto itself, an RNA molecule forms structure, stabilized by the forces of hydrogen bonds between certain pairs of bases (A-U, C-G, G-U), and dense stacking of neighbouring base pairs.The investigation of RNA secondary structures is a challenging task in molecular biology. RNA molecules have a large variety of functions in the cell which often depend on special structural properties. String edit distance [25] clearly is the most successful model in sequence comparison. It is used in document processing, file comparison, molecular sequence analysis, and numerous other applications of approximate string matching. The basic model is that one string is "edited" into another string by a sequence of edit operations, such as single character replacement (R), deletion (D) or insertion (I). The weights associated with the edit operations sum up to an overall score, and the edit sequence giving the minimal score defines the edit distance of the two strings. Equivalently, the editing process, ignoring the order of edit operations, can be represented as an alignment. This equivalence does not generalize to trees, as already mentioned in [1]. For each tree alignment one can construct a corresponding sequence of edit operations, but not vice versa. One can understand editing as finding a largest common sub-structure, while aligning means finding the smallest common superstructure (In fact, this depends on the scoring scheme.). Which model is favourable depends on the problem. Previous workThe first generalization of the edit model from strings to rooted ordered trees is due to [23], algorithmically improved in [31] and implemented and applied to computa-

Prediction of consensus RNA secondary structures including pseudoknots

“…With automatically produced sequence alignments the accuracy is notably lower. Despite recent progress [13,37,21,42,22], it remains an important problem to efficiently produce structurally correct sequence alignments.…”

Computational methods in noncoding RNA research

“…If we describe each local secondary structure as a separate tree, the problem of aligning two structures is then translated into the problem of aligning a forest of trees. This is the approach used by RNAForester [57]. The advantage of the forest approach is that alignments now have a "local" flavor, permitting the program to find similar sub-structures when the global structures are divergent, and therefore detected conserved motifs in two RNA structures.…”

A common core of secondary structure of the internal transcribed spacer 2 (ITS2) throughout the Eukaryota

“…If the correct structure is given, an alignment of even extremely divergent sequences can be performed automatically using, for example, RNAforester (Höchsmann et al 2003) or MARNA (Siebert and Backofen 2003). This was exemplified by the alignment of the ITS2 from Beroe ovata (Ctenophora, Metazoa), and Pandorina morum (Chlorophyta, Viridiplantae) ( Fig.1), accumulating additional evidence for the global conservation of the ITS2 structure.…”