A kinetic zipper model with intrachain interactions applied to nucleic acid hairpin folding kinetics

Single-stranded DNA and RNA hairpin structures with 4-10 nucleotides (nt) in the loop and 5-8 basepairs (bp) in the stem fold on 10-100 μs timescale. In contrast, theoretical estimate of first contact time of two ends of an ideal semiflexible polymer of similar lengths (with persistence length ~2-nt) is 10-100 ns. We propose that this three-orders-of-magnitude difference between these two timescales is a result of roughness in the folding free energy surface arising from intrachain interactions. We present a statistical mechanical model that explicitly includes all misfolded microstates with nonnative Watson-Crick (WC) and non-WC contacts. Rates of interconversion between different microstates are described in terms of two adjustable parameters: the strength of the non-WC interactions (ΔG(nWC)) and the rate at which a basepair is formed adjacent to an existing basepair (k(bp)(+)). The model accurately reproduces the temperature and loop-length dependence of the measured relaxation rates in temperature-jump studies of a 7-bp stem, single-stranded DNA hairpin with 4-20-nt-long poly(dT) loops, with ΔG(nWC) ≈ -2.4 kcal/mol and k(bp)(+) ≥ (1 ns)(-1), in 100 mM NaCl. Thus, our model provides a microscopic interpretation of the slow hairpin folding times as well as an estimate of the strength of intrachain interactions.