A Genus Comparison in the Topological Analysis of RNA Structures

While RNA folding prediction remains challenging, even with machine and deep learning methods, it can also be approached from a topological mathematics perspective. The purpose of the present paper is to elucidate this problem for students and researchers in both the mathematical physics and biology fields, fostering interest in developing novel theoretical and applied solutions that could propel RNA research forward. With this intention, the mathematical method, based on matrix field theory, to compute the topological classification of RNA structures is reviewed. Similarly, McGenus, a computational software that exploits matrix field theory for topological and folding predictions, is examined. To further illustrate the outcomes of this mathematical approach, two types of analyses are performed: the prediction results from McGenus are compared with topological information extracted from experimentally-determined RNA structures, and the topology of RNA structures is investigated for biological significance, both in evolutionary and functional terms. Lastly, we advocate for more research efforts to be conducted at the intersection between physics, mathematics and biology, with a particular focus on the potential contributions that topology can make to the study of RNA folding and structure.