Role of helicity in DNA hairping folding dynamics

TL;DR

This study uses computer simulations to explore how helicity influences DNA hairpin folding times, revealing a change in the scaling exponent and proposing a new theoretical framework for understanding the dynamics.

Contribution

It demonstrates the impact of helicity on folding dynamics and introduces a scaling argument linking duplex relaxation to folding times.

Findings

Scaling exponent decreases from 1.6 to 1.2 when helicity is removed.

First observation of the theoretical lower bound on the anomalous scaling exponent.

Folding dynamics are governed by duplex relaxation in helical chains.

Abstract

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.