  We study a simplified model of the RNA molecule proposed by G. Vernizzi, H.
Orland and A. Zee 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 (of 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 analytic
expression for T_c. The regime studied for this model exhibits analogies with
that for the dense polymer systems studied by de Gennes
