An algebraic representation for tree alignment of RNA pseudoknotted structures

The methods proposed in the literature for RNA comparison focus mainly on pseudoknot free structures. The comparison of pseudoknotted structures is still a challenge. In this work, we propose a new algebraic representation of RNA secondary structures based on relations among hairpins in terms of nesting, crossing, and concatenation. Such algebraic representation is obtained from a defined multiple context-free grammar, which maps any kind of RNA secondary structures into extended trees, i.e., ordered trees where internal nodes are labeled with algebraic operators and leaves are labeled with loops. These extended trees permit the definition of the RNA secondary structure comparison as a tree alignment problem.