The ends of a large RNA molecule are necessarily close

Abstract

We show on general theoretical grounds that the two ends of single-stranded (ss) RNA molecules (consisting of roughly equal proportions of A, C, G and U) are necessarily close together, largely independent of their length and sequence. This is demonstrated to be a direct consequence of two generic properties of the equilibrium secondary structures, namely that the average proportion of bases in pairs is ∼60% and that the average duplex length is ∼4. Based on mfold and Vienna computations on large numbers of ssRNAs of various lengths (1000–10 000 nt) and sequences (both random and biological), we find that the 5′–3′ distance—defined as the sum of H-bond and covalent (ss) links separating the ends of the RNA chain—is small, averaging 15–20 for each set of viral sequences tested. For random sequences this distance is ∼12, consistent with the theory. We discuss the relevance of these results to evolved sequence complementarity and specific protein binding effects that are known to be important for keeping the two ends of viral and messenger RNAs in close proximity. Finally we speculate on how our conclusions imply indistinguishability in size and shape of equilibrated forms of linear and covalently circularized ssRNA molecules.

Combinatorial Insights into RNA Secondary Structure

“…We also showed that the expected 5 0 -3 0 distance is bounded by a constant that does not depend on the sequence length. As already mentioned, this phenomenon was proved by Clote for the homopolymer model and for structures with stickiness p [19], and it has been experimentally observed for the thermodynamic model [98].…”

The end-to-end distance of RNA as a randomly self-paired polymer

“…In the RSPP of f¼0.6 (or f eff ¼0.27), the expected end-to-end distance, /XS % 12:0,14:4, and 24:9, for N¼500, 1000, and 10 000. Yoffe et al (2011) have also shown that for tymovirus, with a viral RNA of N ¼6300 and an unusually low pairing fraction of f¼0.45, the end-to-end distance is considerably higher at 26 7 5. The prediction of RSPP that /XS increases as f decreases agrees qualitatively with that findings.…”

“…The RSPP is a very simple and extremely approximate model to explain the end-to-end proximity of RNA molecules. Yoffe et al (2011) have demonstrated that the end-toend distance of RNAs approaches an asymptotic value of 12 7 5 for RNA of N Z 500. In the RSPP of f¼0.6 (or f eff ¼0.27), the expected end-to-end distance, /XS % 12:0,14:4, and 24:9, for N¼500, 1000, and 10 000.…”

“…As demonstrated in the recent work of Yoffe et al (2011), this proximity of the two ends of a RNA molecule is a general property, remarkably independent of its length or sequence. Yoffe et al have provided a systematic computational check of this result for a wide range of lengths and sequences (both biological and random), and have presented a statistical mechanical theory for random sequences of arbitrary lengths.…”

RNA structure in splicing: An evolutionary perspective

“…62,63 Although the mutation rate of microsatellites (i.e., AC repeats) in fish corresponds to that in mammals, the mutation in fish often causes gain or loss of multiple repeats whereas it rarely does in mammals. 62,64,65 Given this bias toward creating short blocks of AC or GT repeats, it is possible to see how a hairpin that bridges introns could arise or be destroyed by a single mutational event. However, we have shown that the bridging efficiency plateaus at 6 repeats, which may explain how its function is preserved even with high mutation rates.…”