2007/06/21 by Emma Yu Jin, Emma Y. Jin, Jin, Emma Y. +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #05A16 #Biomolecules (q-bio.BM) #Combinatorics (math.CO) #DNA and Nucleic Acid Chemistry #FOS: Biological sciences #FOS: Mathematics #RNA Research and Splicing #RNA and protein synthesis mechanisms #math.CO #msc:05A16 #q-bio.BM
paper · pdf · doi:10.48550/arxiv.0706.3137
22 pages, 7 figures
arxiv created 2007/06/21 · openalex publication_date 2007/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present the asymptotic enumeration of RNA structures with pseudoknots. We develop a general framework for the computation of exponential growth rate and the sub exponential factors for k-noncrossing RNA structures. Our results are based on the generating function for the number of k-noncrossing RNA pseudoknot structures, \sf Sk(n), derived in \citeReidys:07pseu, where k-1 denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function ∑n≥ 0\sf Sk(n)zn and obtain for k=2 and k=3 the analytic continuation and singular expansions, respectively. It is implicit in our results that for arbitrary k singular expansions exist and via transfer theorems of analytic combinatorics we obtain asymptotic expression for the coefficients. We explicitly derive the asymptotic expressions for 2- and 3-noncrossing RNA structures. Our main result is the derivation of the formula \sf S3(n) ∼ (10.4724⋅ 4!)/(n(n-1)...(n-4)) ((5+√(21))/(2))n.