Hierarchical analysis of RNA secondary structures with pseudoknots based on sections

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 [Formula: see text], 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.