Thermodynamics of a model for RNA folding

Abstract: We analyze the thermodynamic properties of a simplified model for folded RNA molecules recently studied by G. Vernizzi, H. Orland, A. Zee (in Phys. Rev. Lett. 94 (2005) 168103). The model consists of a chain of one-flavor base molecules with a flexible backbone and all possible pairing interactions equally allowed. The spatial pseudoknot structure of the model can be effi- ciently studied by introducing a N × N hermitian random matrix model at each chain site, and associating Feynman diagrams of these models to spatial configurations of the molecules. We obtain an exact expression for the topo- logical expansion of the partition function of the system. We calculate exact and asymptotic expressions for the free energy, specific heat, entanglement and chemical potential and study their behavior as a function of temperature. Our results are consistent with the interpretation of 1/N as being a measure of the concentration of Mg++ in solution