RNA secondary structure factorization in prime tangles

Abstract

Background: Due to its key role in various biological processes, RNA secondary structures have always been the focus of in-depth analyses, with great efforts from mathematicians and biologists, to find a suitable abstract representation for modelling its functional and structural properties. One contribution is due to Kauffman and Magarshak, who modelled RNA secondary structures as mathematical objects constructed in link theory: tangles of the Brauer Monoid. In this paper, we extend the tangle-based model with its minimal prime factorization, useful to analyze patterns that characterize the RNA secondary structure. Results: By leveraging the mapping between RNA and tangles, we prove that the prime factorizations of tangle-based models share some patterns with RNA folding’s features. We analyze the E. coli tRNA and provide some visual examples of interesting patterns. Conclusions: We formulate an open question on the nature of the class of equivalent factorizations and discuss some research directions in this regard. We also propose some practical applications of the tangle-based method to RNA classification and folding prediction as a useful tool for learning algorithms, even though the full factorization is not known.