Is the Formation of the Correct Nucleating Loop the Rate-Limiting Step in Hairpin Formation in ss-Polynucleotides?

Abstract

Numerous kinetics measurements on the formation of single-stranded (ss) DNA and RNA hairpin structures with ∼4-20 nucleotides (nt) in the loop and ∼5-8 base-pairs in the stem, indicate that the time required to form hairpins is ∼10-500 microseconds. If ss-polynucleotide chain is treated as an ideal semiflexible polymer with a statistical segment length of ∼4 nt, the theoretical estimate for the end-to-end contact time for an ∼10-nt long chain is expected to be tens-of-nanoseconds. To explain this discrepancy in time-scale, we proposed that the formation of the nucleating loop, prior to the zipping step, is slowed down as a result of transient trapping in misfolded conformations, with mis-paired base-pairs, non-native hydrogen bonding, or intrastrand stacking interactions in the unfolded state. Experimental measurements of end-to-end contact formation indicate that loop closure times for 4-nt poly(dT) loops are ∼400 ns, and for 4-nt poly(dA) loops are ∼8 microseconds, thus confirming that intrachain interactions slow down the configurational diffusion of the chain (Wang and Nau, J. Am. Chem. Soc. 2004, 126, 808). Interestingly, despite this evidence for intrachain interactions slowing down diffusion, the hairpin closing times for both ssDNA and RNA hairpins are found to scale with the length of the loop as L2.2-2.6, in reasonable agreement with the scaling behavior expected for loop-closure of a semiflexible polymer.Here, we present a kinetic zipper model that explicitly includes all misfolded microstates with non-native contacts, to describe the hairpin relaxation rates. The temperature and loop-size dependence for the relaxation rates is described in terms of two free parameters, the configurational diffusion coefficient that is relevant for the single-strand chain dynamics, and one parameter that characterizes the strength of non-native interactions prior to the formation of the nucleating loop.