Classification and predictions of RNA pseudoknots based on topological invariants

We propose a new topological characterization of ribonucleic acid (RNA) secondary structures with pseudoknots based on two topological invariants. Starting from the classic arc representation of RNA secondary structures, we consider a model that couples both (i) the topological genus of the graph and (ii) the number of crossing arcs of the corresponding primitive graph. We add a term proportional to these topological invariants to the standard free energy of the RNA molecule, thus obtaining a novel free-energy parametrization that takes into account the abundance of topologies of RNA pseudoknots observed in RNA databases.