title: On topological RNA interaction structures.
abstract: Recently a folding algorithm of topological RNA pseudoknot structures was presented in Reidys et al. (2011). This algorithm folds single-stranded γ-structures, that is, RNA structures composed by distinct motifs of bounded topological genus. In this article, we set the theoretical foundations for the folding of the two backbone analogues 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 backbones having genus at most γ. Combinatorial properties of γ-interaction structures are of practical interest since they have direct implications for the folding of topological interaction structures. We compute the generating function of γ-interaction structures and show that it is algebraic, which implies that the numbers of interaction structures can be computed recursively. We obtain simple asymptotic formulas for 0- and 1-interaction structures. The simplest class of interaction structures are the 0-interaction structures, which represent the two backbone analogues of secondary structures.
authors.affiliation: Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
authors.forename: Jing
authors.initials: J
authors.lastname: Qin
authors.forename: Christian M
authors.initials: CM
authors.lastname: Reidys
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D006367:HeLa Cells; D006801:Humans; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D020537:RNA, Small Nucleolar / Q000737:chemistry* / Q000235:genetics / Q000378:metabolism*
chemical_list: D020537:RNA, Small Nucleolar