RNA Structures with Pseudo-knots: Graph-theoretical, Combinatorial, and Statistical Properties
✍ Scribed by C Haslinger; P.F Stadler
- Publisher
- Springer
- Year
- 1999
- Tongue
- English
- Weight
- 461 KB
- Volume
- 61
- Category
- Article
- ISSN
- 1522-9602
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✦ Synopsis
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.