Structural and thermodynamic properties of a linearly perturbed matrix model for RNA folding.

The structural and thermodynamic properties of a matrix model of homo-RNA folding with linear external interaction are studied. The interaction distinguishes paired bases of the homo-RNA chain from the unpaired bases hence dividing the possible RNA structures given by the linear model into two structural regimes. The genus distribution functions show that the total number of structures for any given length of the chain are reduced for the simple linear interaction considered. The partition function of the model exhibits a scaling relation with the matrix model in which the base pairing strength parameter is re-scaled (G. Vernizzi, H. Orland, A. Zee, Phys. Rev. Lett. 94, 168103 (2005)). The thermodynamics of the model are computed for i) largely secondary structures, (with tertiary structures suppressed by a factor 10(-4)) and ii) secondary plus tertiary structures. A structural change for large even lengths is observed in the free energy and specific heat. This change with largely secondary structures appears much before (with respect to length of the chain) than when all the structures (secondary and pseudoknots) are considered. The appearance of different structures which dominate the ensemble with varying temperatures is also found as a function of the interaction parameter for different types of structures (given by different numbers of pairings).