Odd-even disparity in the population of slipped hairpins in RNA repeat sequences with implications for phase separation

Low complexity nucleotide repeat sequences, which are implicated in several neurological disorders, undergo liquid-liquid phase separation (LLPS) provided the number of repeat units, n, exceeds a critical value. Here, we establish a link between the folding landscapes of the monomers of trinucleotide repeats and their propensity to self-associate. Simulations using a coarse-grained Self-Organized Polymer (SOP) model for (CAG)n repeats in monovalent salt solutions reproduce experimentally measured melting temperatures, which are available only for small n. By extending the simulations to large n, we show that the free energy gap, {Delta}GS, between the ground state (GS) and slipped hairpin (SH) states is a predictor of aggregation propensity. The GS for even n is a perfect hairpin (PH) whereas it is a SH when n is odd. The value of {Delta}GS (zero for odd n) is larger for even n than for odd n. As a result, the rate of dimer formation is slower in (CAG)30 relative to (CAG)31, thus linking {Delta}GS to RNA-RNA association. The yield of the dimer decreases dramatically, compared to the wild type, in mutant sequences in which the population of the SH is decreases substantially. Association between RNA chains is preceded by a transition to the SH even if the GS is a PH. The finding that the excitation spectra, which depends on the exact sequence, n, and ionic conditions, is a predictor of self-association, should also hold for other RNAs (mRNA for example) that undergo LLPS.