1999/05/01 by Christian Haslinger · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #RNA and protein synthesis mechanisms #RNA Research and Splicing #Genomics and Chromatin Dynamics #Protein secondary structure #Embedding #Mathematics #Pseudoknot #Sequence (biology) #Nucleic acid secondary structure #Generalization #Combinatorics #Folding (DSP implementation) #Simple (philosophy) #RNA #Discrete mathematics #Computer science #Physics #Biology #Mathematical analysis
paper · pdf · doi:10.1006/bulm.1998.0085
openalex publication_date 1999/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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.