A Kinetic Zipper Model with Intrachain Interactions Applied to Nucleic Acid Hairpin Folding Kinetics

Abstract

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 (ΔGnWC) and the rate at which a basepair is formed adjacent to an existing basepair (kbp+). 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 ΔGnWC ≈ −2.4 kcal/mol and kbp+ ≥ (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.