Pseudoknot RNA Structures with Arc-Length ≥ 3

2007/08/23 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.0708.3134

18 pages, 4 figures

arxiv created 2007/08/23 · openalex publication_date 2007/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study k-noncrossing RNA structures with arc-length ≥ 3, i.e. RNA molecules in which for any i, the nucleotides labeled i and i+j (j=1,2) cannot form a bond and in which there are at most k-1 mutually crossing arcs. Let \sf S_k,3(n) denote their number. Based on a novel functional equation for the generating function ∑_{n≥ 0}\sf S_k,3(n)zⁿ, we derive for arbitrary k≥ 3 exponential growth factors and for k=3 the subexponential factor. Our main result is the derivation of the formula \sf S_3,3(n) ∼ (6.11170⋅ 4!)/(n(n-1)...(n-4)) 4.54920ⁿ.

Related

• Pseudoknot RNA structures with arc-length ≥ 4
• k-noncrossing RNA structures with arc-length ≥ 3
• Canonical RNA pseudoknot structures
• Asymptotic Enumeration of RNA Structures with Pseudoknots
• Central and Local Limit Theorems for RNA Structures