title: RNA structures with pseudo-knots: graph-theoretical, combinatorial, and statistical properties.
abstract: The secondary structures of nucleic acids form a particularly important class of contact structures. Many important RNA molecules, however, contain pseudo-knots, a structural feature that is excluded explicitly from the conventional definition of secondary structures. We propose here a generalization of secondary structures incorporating 'non-nested' pseudo-knots, which we call bi-secondary structures, and discuss measures for the complexity of more general contact structures based on their graph-theoretical properties. Bi-secondary structures are planar trivalent graphs that are characterized by special embedding properties. We derive exact upper bounds on their number (as a function of the chain length n) implying that there are fewer different structures than sequences. Computational results show that the number of bi-secondary structures grows approximately like 2.35n. Numerical studies based on kinetic folding and a simple extension of the standard energy model show that the global features of the sequence-structure map of RNA do not change when pseudo-knots are introduced into the secondary structure picture. We find a large fraction of neutral mutations and, in particular, networks of sequences that fold into the same shape. These neutral networks percolate through the entire sequence space.
authors: Institut für Theoretische Chemie, Universität Wien, Austria. grisu@tbi.univie.ac.at
authors: C
authors: C
authors: Haslinger
authors: P F
authors: PF
authors: Stadler
mesh_terms: D001483:Base Sequence; D008956:Models, Chemical; D008957:Models, Genetic; D008958:Models, Molecular; D008969:Molecular Sequence Data; D009690:Nucleic Acid Conformation; D012313:RNA / Q000737:chemistry* / Q000235:genetics*
chemical_list: D012313:RNA