Spark: Sparsified Hierarchical Energy Minimization of RNA Pseudoknots

Motivation. Determining RNA structure is essential for understanding RNA function and interaction networks. Although experimental techniques yield high-accuracy structures, they are costly and time-consuming; thus, computational approaches – especially minimum-free-energy (MFE) prediction algorithms – are indispensable. Accurately predicting pseudoknots, however, remains challenging because their inclusion usually leads to prohibitive computational complexity. Recent work demonstrated that sparsification can improve the efficiency of complex pseudoknot prediction algorithms such as Knotty. This finding suggests similar gains are possible for already efficient algorithms like HFold, which targets a complementary class of hierarchically constrained pseudoknots. Results. We introduce Spark, an exact, fully sparsified algorithm for predicting pseudoknotted RNA structures. Like its non-sparsified predecessor HFold, Spark searches for the minimum-energy structure under the HotKots 2.0 energy model, a pseudoknot extension of the Turner model. Because the sparsification is non-heuristic, Spark preserves the asymptotic time- and space-complexity guarantees of HFold while greatly reducing the constant factors. We benchmarked the performance of Spark against HFold and, as a pseudoknot-free baseline, RNAfold. Compared with HFold, Spark substantially lowers both run time and memory usage, while achieving run-time figures close to those of RNAfold. Across all tested sequence lengths, Spark used the least memory and consistently ran faster than HFold. Conclusion. By extending non-heuristic sparsification to hierarchical pseudoknot prediction, Spark delivers an exceptionally fast and memory-efficient tool accurate prediction of pseudoknotted RNA structures, enabling routine analysis of long sequences. The algorithm broadens the practical scope of computational RNA biology and provides a solid foundation for future advances in structure-based functional annotation. Availability. Spark’s implementation and detailed results are available at https://github.com/TheCOBRALab/Spark.