%0 Journal Article %1 Haslinger-Stadler-1999 %A Haslinger, Christian %A Stadler, Peter F. %D 1999 %J Bulletin of Mathematical Biology %K combinatorics, graph, pseudoknot, rna, statistics %N 3 %P 437--467 %R 10.1006/bulm.1998.0085 %T RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties %U http://dx.doi.org/10.1006/bulm.1998.0085 %V 61 %X 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.

@article{Haslinger-Stadler-1999, abstract = {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.}, added-at = {2009-05-19T18:00:18.000+0200}, author = {Haslinger, Christian and Stadler, Peter F.}, biburl = {https://www.bibsonomy.org/bibtex/2dc9aac25c9eb0811b4227107dc85c32c/earthfare}, citeulike-article-id = {4544547}, description = {CiteULike: Everyone's library}, doi = {10.1006/bulm.1998.0085}, interhash = {26ca9de20da4d68817c130a8597f1943}, intrahash = {dc9aac25c9eb0811b4227107dc85c32c}, journal = {Bulletin of Mathematical Biology}, keywords = {combinatorics, graph, pseudoknot, rna, statistics}, month = May, number = 3, pages = {437--467}, posted-at = {2009-05-19 09:17:33}, priority = {2}, timestamp = {2009-05-19T18:03:27.000+0200}, title = {RNA structures with pseudo-knots: Graph-theoretical, combinatorial, and statistical properties}, url = {http://dx.doi.org/10.1006/bulm.1998.0085}, volume = 61, year = 1999 }