RintC: fast and accuracy-aware decomposition of distributions of RNA secondary structures with extended logsumexp

Abstract

The analysis of secondary structures is essential to understanding the function of RNAs. Because RNA molecules thermally fluctuate, it is necessary to analyze the probability distribution of secondary structures. Existing methods, however, are not applicable to long RNAs owing to their high computational complexity. Additionally, previous research has suffered from two numerical difficulties: overflow and significant numerical error. In this research, we reduced the computational complexity in calculating the landscape of the probability distribution of secondary structures by introducing a maximum-span constraint. In addition, we resolved numerical computation problems through two techniques: extended logsumexp and accuracy-guaranteed numerical computation. We analyzed the stability of the secondary structures of 16S ribosomal RNAs at various temperatures without overflow. The results obtained are consistent with in vivo assay results reported in previous research. Furthermore, we quantitatively assessed numerical stability using our method. These results demonstrate that the proposed method is applicable to long RNAs. Source code is available on https://github.com/eukaryo/rintc.