Melting of branched RNA molecules.

In this Letter we show that the melting thermodynamics of RNA molecules is very sensitive to the branching geometry. We find that, when pairing interactions are described by a Gō model, unbranched RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents while RNA molecules with the branching geometry of a Cayley tree, with coordination number three, have a free energy that shows no thermodynamic singularity within numerical precision. Nevertheless, we provide an analytical proof that the free energy does have a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge but only on the high-temperature side of this singularity.