Fractional Brownian motion and the critical dynamics of zipping polymers

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 similar to L-2.26(2), exceeding the Rouse time similar to L-2.18. We investigate the probability distribution function, velocity autocorrelation function, survival probability, and boundary behavior 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 to and differences from unbiased polymer translocation.