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In the matrix model of RNA [G Vernizzi, H Orland and A Zee, Phys. Rev. Lett. 94, 168103 (2005)] we introduce external interactions on n bases in the action of the partition function where n ≤ L and L is the length of the polymer chain. The RNA structures found in the model can be separated into two regimes: (i) 0 ≤ α ≤ 1, n < L and 0 ≤ α < 1, n = L where unpaired and paired base structures exist and (ii) α = 1, n = L with only completely paired base structures. Figures for the genus distribution functions show differences at small lengths. We consider the situation when the strength of external perturbation is different on different bases in the polymer chain.

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).

We study a matrix model of RNA in which an external perturbation on n nucleotides is introduced in the action of the partition function of the polymer chain. The effect of the perturbation appears in the exponential generating function of the partition function as a factor exp(1-nalpha/L) (where alpha is the ratio of strengths of the original to the perturbed term and L is the length of the chain). The asymptotic behavior of the genus distribution functions as a function of length for the matrix model with interaction is analyzed numerically for all n