Role of Helicity in DNA Hairpin Folding Dynamics

We study hairpin folding dynamics by means of extensive molecular dynamics simulations, with particular attention paid to the influence of helicity on the folding time. We find that the dynamical exponent a in the anomalous scaling n(t) similar to t(1/alpha) of the hairpin length n with time changes from 1.6 (similar or equal to 1 + nu, where nu is the Flory exponent) to 1.2 (similar or equal to 2 nu) in three dimensions, when duplex helicity is removed. The relation alpha = 2 nu in rotationless hairpin folding is further verified in two dimensions (nu = 0.75) and for a ghost chain (nu = 0.5). Our findings suggest that the folding dynamics in long helical chains is governed by the duplex dynamics, contrasting the earlier understanding based on the stem-flower picture of unpaired segments. We propose a scaling argument for alpha = 1 + nu in helical chains, assuming that duplex relaxation required for orientational positioning of the next pair of bases is the rate-limiting process.