Fractional Brownian motion and the critical dynamics of zipping polymers

TL;DR

This study models the critical dynamics of zipping and unzipping DNA-like polymers, revealing anomalous behavior characterized by fractional Brownian motion with specific scaling laws at the transition temperature.

Contribution

It demonstrates that the critical zipping dynamics follow fractional Brownian motion, providing new insights into polymer translocation and DNA hairpin formation at equilibrium.

Findings

Dynamics scale as τ ∼ L^{2.26}, exceeding Rouse time.

Probability distributions match fractional Brownian motion with H=0.44.

Identifies anomalous diffusion behavior at the critical point.

Abstract

We consider two complementary polymer strands of length $L$ attached by a common end monomer. The two strands bind through complementary monomers and at low temperatures form a double stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature $T=T_c$ using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as $\tau \sim L^{2.26(2)}$, exceeding the Rouse time $\sim L^{2.18}$. We investigate the probability distribution function, the velocity autocorrelation function, the survival probability and boundary behaviour of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent $H=0.44(1)$. We discuss similarities and differences with unbiased polymer translocation.