Journal
BULLETIN OF MATHEMATICAL BIOLOGY
Volume 80, Issue 6, Pages 1514-1538Publisher
SPRINGER
DOI: 10.1007/s11538-018-0411-9
Keywords
Secondary structure; Rainbow; Length spectrum; Gap; Arc; Generating function; Singularity analysis
Categories
Funding
- Advanced Systems for Information Biology
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In this paper, we analyze the length spectrum of rainbows in RNA secondary structures. A rainbow in a secondary structure is a maximal arc with respect to the partial order induced by nesting. We show that there is a significant gap in this length spectrum. We shall prove that there asymptotically almost surely exists a unique longest rainbow of length at least and that with high probability any other rainbow has finite length. We show that the distribution of the length of the longest rainbow converges to a discrete limit law and that, for finite k, the distribution of rainbows of length k becomes for large n a negative binomial distribution. We then put the results of this paper into context, comparing the analytical results with those observed in RNA minimum free energy structures, biological RNA structures and relate our findings to the sparsification of folding algorithms.
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