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.

MOTIVATION: G-quadruplexes (G4s) are non-canonical nucleic acid structures formed in guanine-rich regions that modulate gene regulation and genomic stability. The thermodynamic stability of G4s directly influences their biological functions and potential as therapeutic targets. However, current quantitative frameworks for predicting G4 stability rely on predetermined structural features, limiting their effectiveness for diverse G4 topologies, and fail to account for environmental factors such as ion concentration and pH that significantly modulate G4 stability in cellular contexts. RESULTS: We present G4STAB, a multi-input deep learning neural network that accurately predicts DNA G4 melting temperatures based on sequence features, salt concentration, and pH. Trained on 2382 diverse DNA G4 sequences, our model achieves high accuracy (R 2=0.8) without relying on predetermined G4 structural features. G4STAB successfully captures established G4 stability determinants and proposes previously unobserved sequence-stability relationships. Analysis of 391 502 experimentally validated G4s reveals that cancer-like ionic environments alter G4 stability profiles, with a 13.5-fold increase in the number of structures exhibiting physiological melting temperatures (36-42°C). These findings suggest systematic genomic patterns in G4 stability responses across chromosomes and gene types. AVAILABILITY AND IMPLEMENTATION: G4STAB is available at https://github.com/donn-liew/G4STAB; G4STAB web database interface is available at https://donn-liew.github.io/g4stab-web-database/.