Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by Vernizzi et al. in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (on the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytical expression for T_c. The regime studied for this model exhibits analogies with the dense polymer systems studied by de Gennes.