The size of RNA as an ideal branched polymer

Because of the branching arising from partial self-complementarity, long single-stranded (ss) RNA molecules are significantly more compact than linear arrangements (e.g., denatured states) of the same sequence of monomers. To elucidate the dependence of compactness on the nature and extent of branching, we represent ssRNA secondary structures as tree graphs which we treat as ideal branched polymers, and use a theorem of Kramers for evaluating their root-mean-square radius of gyration, R̂g=√〈R_g2〈. We consider two sets of sequences-random and viral-with nucleotide sequence lengths (N) ranging from 100 to 10 000. The RNAs of icosahedral viruses are shown to be more compact (i.e., to have smaller R̂_g) than the random RNAs. For the random sequences we find that R̂_g varies as N^1/3. These results are contrasted with the scaling of R̂_g for ideal randomly branched polymers (N^1/4), and with that from recent modeling of (relatively short, N ≤ 161) RNA tertiary structures (N^2/5).