Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures

2026-02-22

AI Summary

This study addresses the long-standing lack of rigorous asymptotic analysis for the joint statistical properties of hairpin loops and base pairs in RNA secondary structures. By integrating analytic combinatorics and probabilistic methods—specifically generating functions, singularity analysis, and the multivariate central limit theorem—the authors establish, for the first time, that the joint distribution of these two quantities converges asymptotically to a bivariate normal distribution. They derive exact asymptotic expressions for the means, variances, covariance, and correlation coefficient, with the latter precisely quantified as 0.2123. This work provides a foundational theoretical framework for stochastic modeling and statistical inference of RNA structural features, offering precise asymptotic characterizations of key combinatorial parameters.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Lexical Semantics and Morphology

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs in RNA secondary structures, and give convincing evidence that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation $\sqrt{5 \sqrt{5} -11}/2= 0.2123322205\dots$

Problem

• RNA secondary structures
• hairpins
• basepairs
• asymptotic statistics
• bivariate normal distribution

Innovation

• RNA secondary structure
• asymptotic analysis
• bivariate normal distribution
• hairpin
• basepair