Abstract
BackgroundRNA secondary structure comparison is a fundamental task for several studies, among which are RNA structure prediction and evolution. The comparison can currently be done efficiently only for pseudoknot-free structures due to their inherent tree representation.ResultsIn this work, we introduce an algebraic language to represent RNA secondary structures with arbitrary pseudoknots. Each structure is associated with a unique algebraic RNA tree that is derived from a tree grammar having concatenation, nesting and crossing as operators. From an algebraic RNA tree, an abstraction is defined in which the primary structure is neglected. The resulting structural RNA tree allows us to define a new measure of similarity calculated exploiting classical tree alignment.ConclusionsThe tree grammar with its operators permit to uniquely represent any RNA secondary structure as a tree. Structural RNA trees allow us to perform comparison of RNA secondary structures with arbitrary pseudoknots without taking into account the primary structure.
Highlights
RNA secondary structure comparison is a fundamental task for several studies, among which are RNA structure prediction and evolution
Hairpin is the basic one, consisting of only one weak interaction closing a sequence of unpaired nucleotides
Inspired by the Waterman’s result, our first objective is to define a set of algebraic operators able to represent any kind of RNA secondary structure, including the pseudoknotted ones, as a combination of simple hairpin loops
Summary
RNA secondary structure comparison is a fundamental task for several studies, among which are RNA structure prediction and evolution. The comparison can currently be done efficiently only for pseudoknot-free structures due to their inherent tree representation. An internal loop (A), Guanine (G), Cytosine (C) and Uracil (U) - linked (Fig. 1b) is defined by two weak bonds alternating with together by phosphodiester bonds, referred to as strong two non-empty sequences of nucleotides linked by strong bonds. A bulge (Fig. 1c) is a special case of internal loop in tree-dimensional shapes known as secondary and tertiary which one of the two sequences of nucleotides is empty. During the folding process each nucleotide A helix (Fig. 1d) is a special case of internal loop can interact with another one by establishing a hydrogen in which both sequences are empty. A multi-loop bond, referred to as weak bond, mainly forming Watson- (Fig. 1e) consists of more than two weak bonds separated
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