RNA substructure as a random matrix ensemble

Abstract

We obtain a closed form of generating functions of RNA substructure using hermitian matrix model with the Chebyshev polynomial of the second kind, which has the form of the hypergeometric function. To match the experimental findings of the statistical behavior, we regard the substructure as a grand canonical ensemble and find its fugacity value corresponding to the number of stems. We also suggest a hierarchical picture based on the planar structure so that the non-planar structure such as pseudoknot are included.