Topological Classification of RNA Structures via Intersection Graph

We introduce a new algebraic representation of RNA secondary structures as a composition of hairpins, considered as basic loops. Starting from it, we define an abstract algebraic representation and we propose a novel methodology to classify RNA structures based on two topological invariants, the genus and the crossing number. It takes advantage of the abstract representation to easily obtain two intersection graphs: one of the RNA molecule and another one of the relative shape. The edges cardinality of the former corresponds to the number of interactions among hairpins, whereas the edges cardinality of the latter is the crossing number of the shape associated to the molecule. The aforementioned crossing number together with the genus permits to define a more precise energy function than the standard one which is based on the genus only. Our methodology is validated over a subset of RNA structures extracted from Pseudobase++ database, and we classify them according to the two topological invariants.