# Hierarchical analysis of RNA secondary structures with pseudoknots based on sections

## TL;DR

A new method for predicting RNA pseudoknots by analyzing local sections improves computational efficiency and reveals insights into RNA folding dynamics.

## Contribution

A hierarchical approach for pseudoknot prediction that reduces computational cost and reveals RNA folding follows sequential co-transcriptional dynamics.

## Key findings

- Over 90% of pseudoknots occur in the top 3% of section pairs ranked by minimum free energy gain.
- The method achieves sensitivity >0.9 and positive predictive value >0.8 for 2-section pseudoknots.
- 3-section pseudoknots show asymmetric behavior with early-formed connections being predictable but later ones not.

## Abstract

Predicting RNA structures containing pseudoknots remains computationally challenging due to high processing costs and complexity. While standard methods for pseudoknot prediction require O(N6) time complexity, we present a hierarchical approach that significantly reduces computational cost while maintaining prediction accuracy. Our method analyzes RNA structures by dividing them into contiguous regions of unpaired bases (“sections”) derived from known secondary structures. We examine pseudoknot interactions between sections using a nearest-neighbor energy model with dynamic programming. Our algorithm scales as O(n2ℓ4), offering substantial computational advantages over existing global prediction methods. Analysis of 726 transfer messenger RNA and 454 Ribonuclease P RNA sequences reveals that biologically relevant pseudoknots are highly concentrated among section pairs with large minimum free energy (MFE) gain. Over 90% of connected section pairs appear within just the top 3% of section pairs ranked by MFE gain. For 2-clusters, our method achieves high prediction accuracy with sensitivity exceeding 0.9 and positive predictive value above 0.8. For 3-clusters, we discovered asymmetric behavior where “former” section pairs (formed early in the sequence) are predicted accurately, while “latter” section pairs do not follow local energy predictions. This asymmetry suggests that complex pseudoknot formation follows sequential co-transcriptional folding rather than global energy minimization, providing insights into RNA folding dynamics.

RNA molecules fold into structures to perform biological functions. However, predicting complex RNA structures known as “pseudoknots” is computationally expensive. Current methods often attempt to calculate the entire structure simultaneously, which requires significant computational resources. In this paper, we introduce a hierarchical approach that simplifies pseudoknot prediction. We break the RNA sequence into smaller “sections” of unpaired bases and calculate the energy required for these sections to bind locally, rather than solving for the global structure. Our analysis shows that strong local interactions are favored by biology; with over 90% of pseudoknots occurring within the top 3% of the most energetically favorable section pairs. This finding allows us to focus computational effort on the small subset of interactions that are most likely to form pseudoknots, rather than testing every possible combination. Our method achieves >90% sensitivity for simple 2-section pseudoknots. However, for complex 3-section pseudoknots, only early-forming connections are predictable. This reveals that RNA does not simply fold into the most stable structure. Instead, folding is sequential, with earlier regions establishing interactions that constrain the final structure before synthesis of the later regions.