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 .
Combinatorial analysis of a certain abstract 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 random matrix model. We obtain the generating function of the structures using Hermitian matrix model with 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 .
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We obtain a closed form of generating functions of RNA substructure using hermitian
Combinatorial analysis of a certain abstract 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 random matrix model. We obtain the generating function of the structures using Hermitian
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, which has the form of the hypergeometric function
and analyze the statistics with respect to the number of stems
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regard the substructure as
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