Local similarity in RNA secondary structures

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 O(/F/sub 1///spl middot//F/sub 2//)/spl middot/deg(F/sub 1/)/spl middot/deg(F/sub 2/)/spl middot/(deg(F/sub 1/)+deg(F/sub 2/)) where /Fi/ is the number of nodes in forest Fi and deg(Fi) is the degree of Fi. We provide carefully engineered dynamic programming implementations using dense, two-dimensional tables which considerably reduces the space requirement. We suggest a new representation of RNA secondary structures as forests that allow reasonable scoring of edit operations on RNA secondary structures. The comparison of RNA secondary structures is facilitated by a new visualization technique for RNA secondary structure alignments. Finally, we show how potential regulatory motifs can be discovered solely by their structural preservation, and independent of their sequence conservation and position.

1. Motivation

RNA 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.