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BIOINF 12-003: On topological RNA interaction structures
Jing Qin and Christian M. Reidys
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Abstract
Recently a folding algorithm of topological RNA pseudoknot structures has been
presented [24]. This algorithm folds single stranded γ-structures, i.e. RNA structures
composed by distinct motifs of bounded topological genus. In this paper,
we study the two backbone analogue of
γ-structures: the RNA
γ-interaction
structures. These are RNA-RNA interaction structures that are constructed by
a finite number of building blocks over two and one backbone having genus at
most γ
. Properties of
γ-interaction structures are of practical interest since they
are the targets of topological interaction structure folding algorithms. We show
that the generating function of γ-interaction structures is algebraic, which implies
that the numbers of interaction structures can be computed recursively. We
furthermore obtain simple asymptotic formulas for 0- and 1-interaction structures.
The simplest class are the 0-interaction structures, which represent the
two backbone analogue of secondary structures.
Keywords
RNA-RNA interaction, γ-interaction structure, Shape, Symbolic enumeration, Singularity analysis, RNA secondary structure