Related Experiment Video
Updated: Jul 6, 2026

RNA Secondary Structure Prediction Using High-throughput SHAPE
Published on: May 31, 2013
Asymptotic enumeration of RNA structures with pseudoknots
Emma Y Jin1, Christian M Reidys
1Center for Combinatorics, LPMC-TJKLC, Nankai University, Tianjin, 300071, People's Republic of China.
Abstract:
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 asymptotic expansion for the numbers of k-noncrossing RNA structures. Our results are based on the generating function for the number of k-noncrossing RNA pseudoknot structures, Sk(n), derived in Bull. Math. Biol. (2008), where k-1 denotes the maximal size of sets of mutually intersecting bonds. We prove a functional equation for the generating function Sigman>or=0 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 S3(n) approximately 10.4724.4!/n(n-1)...(n-4)(5+[sqrt]21/2)n.
Related Concept Videos
RNA Structure
Different Types of RNA Have the Same Basic Structure
There are three main types of ribonucleic acid (RNA) involved in protein synthesis: messenger RNA (mRNA), transfer RNA (tRNA), and ribosomal RNA (rRNA). All three...
RNA Structure
The basic structure of RNA consists of a five-carbon sugar and one of four nitrogenous bases. Although most RNA is single-stranded, it can form complex secondary and tertiary structures. Such structures play essential roles in the regulation of transcription and translation.
Different Types of RNA Have the Same Basic Structure
There are three main types of ribonucleic acid (RNA): messenger RNA (mRNA), transfer RNA (tRNA), and ribosomal RNA (rRNA). All three RNA types consist of a...
RNA Structure
The basic structure of RNA consists of a five-carbon sugar and one of four nitrogenous bases. Although most RNA is single-stranded, it can form complex secondary and tertiary structures. Such structures play essential roles in the regulation of transcription and translation.
Different Types of RNA Have the Same Basic Structure
There are three main types of ribonucleic acid (RNA): messenger RNA (mRNA), transfer RNA (tRNA), and ribosomal RNA (rRNA). All three RNA types consist of a...
Bacterial RNA Polymerase
In most genes, the transcription site is a single base present upstream of the coding sequence. Though RNAP is a catalytically efficient enzyme, it does not recognize...
RNA Stability
RNA Stability