RNA substructure as a random matrix ensemble.

Abstract

Combinatorial analysis of a certain abstraction of RNA structures has been studied to investigate their statistics. Our approach regards the backbone of secondary structures as an alternate sequence of paired and unpaired sets of nucleotides, which can be described by a random matrix model. We obtain the generating function of the structures using the Hermitian matrix model with the Chebyshev polynomial of the second kind and analyze the statistics with respect to the number of stems. To match the experimental findings of the statistical behavior, we consider the structures in a grand canonical ensemble and find a fugacity value corresponding to an appropriate number of stems.