title: On RNA-RNA interaction structures of fixed topological genus.
abstract: Interacting RNA complexes are studied via bicellular maps using a filtration via their topological genus. Our main result is a new bijection for RNA-RNA interaction structures and a linear time uniform sampling algorithm for RNA complexes of fixed topological genus. The bijection allows to either reduce the topological genus of a bicellular map directly, or to lose connectivity by decomposing the complex into a pair of single stranded RNA structures. Our main result is proved bijectively. It provides an explicit algorithm of how to rewire the corresponding complexes and an unambiguous decomposition grammar. Using the concept of genus induction, we construct bicellular maps of fixed topological genus g uniformly in linear time. We present various statistics on these topological RNA complexes and compare our findings with biological complexes. Furthermore we show how to construct loop-energy based complexes using our decomposition grammar.
authors: Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Electronic address: benjaminfmm@imada.sdu.dk.
authors: Benjamin M M
authors: BM
authors: Fu
authors: Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Electronic address: hillary@imada.sdu.dk.
authors: Hillary S W
authors: HS
authors: Han
authors: Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. Electronic address: duck@santafe.edu.
authors: Christian M
authors: CM
authors: Reidys
mesh_terms: D000465:Algorithms; D055641:Mathematical Concepts; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D012313:RNA / Q000737:chemistry*
chemical_list: D012313:RNA
keywords: Bicellular map; Decomposition; Non-uniform sampling; RNA–RNA interaction structure; Topological genus; Uniform generation