Role of Helicity in DNA Hairpin Folding Dynamics

We study hairpin folding dynamics by means of extensive computer simulations, with particular attention paid to the influence of helicity on the folding time $\tau$. We find that the dynamical exponent $\alpha$ of the anomalous scaling $\tau \sim N^\alpha$ for a hairpin with length N changes from 1.6 ($1+\nu$) to 1.2 ($2\nu$) 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 ($\nu = 0.5$). This, to our knowledge, is the first observation of the theoretical lower bound on $\alpha$, which was predicted earlier on the basis of energy conservation for polymer translocation through a pore. 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.