Diagrammatic Theory of RNA Structures and Ensembles with Trinucleotide Repeats

Abstract

Trinucleotide repeat expansion disorders (TRED) are associated with the overexpansion of (CNG) repeats on the genome. mRNA transcripts of sequences with greater than 60 to 100 (CNG) tandem units have been implicated in TRED pathogenesis. In this paper, we develop a diagrammatic theory to study the structural diversity of these (CNG)n RNA sequences. Representing structural elements on the chains conformation by a set of graphs and employing elementary diagrammatic methods, we have formulated a renormalization procedure to resum these graphs and arrive at a closed-form expression for the ensemble partition function. With a simple approximation for the renormalization and applied to extended (CNG)n sequences, this theory can comprehensively capture an infinite set of conformations with any number and any combination of duplexes, hairpins and 2-way junctions. To quantify the diversity of different (CNG)n ensembles, the analytical equations derived from the diagrammatic theory were solved numerically to derive equilibrium estimates for the secondary structural contents of the chains. The results suggest that the structural ensembles of (CNG)n repeat sequence with n ~ 60 are surprisingly diverse, and they are dominated largely by open segments, with only a small fraction of the nucleotides forming base pairs. At the same time, the variance in the secondary-structural contents on the chains is also quite large, indicating that their structures can undergo strong equilibrium fluctuations and are expected to be rather suspectable to perturbations. STATEMENT OF SIGNIFICANCETrinucleotide repeat expansion disorders (TRED) are associated with the overexpansion of (CNG) repeats on the genome. mRNA transcripts of sequences with critical length greater than 60 to 100 (CNG) tandem units have been implicated in TRED pathogenesis, though their structures remain poorly characterized. Conventional view has tacitly assumed that conformations with maximal C:G base pairing dominate at equilibrium, but here we demonstrate that (CNG) repeat sequences are characterized by diverse ensembles of structurally heterogeneous folds and with a large variance of secondary structural contents. These ensembles of structures also undergo strong equilibrium fluctuations, rendering them rather susceptible to perturbations. These results were based on a novel diagrammatic approach to the ensemble partition function.