End-monomer dynamics in semiflexible polymers

Precise experimental observations over the last few years of end-monomer dynamics in the diffusion of double-stranded DNA have given conflicting results: one study indicated an unexpected Rouse-like scaling of the mean squared displacement (MSD) $\langle r^2(t) \rangle \sim t^{1/2}$ at intermediate times, corresponding to fluctuations at length scales larger than the persistence length but smaller than the coil size; another study claimed the more conventional Zimm scaling $\langle r^2(t)\rangle \sim t^{2/3}$ in the same time range. Spurred by this experimental controversy, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations, an improved dynamic mean-field theory, and a heuristic scaling argument [1]. Both theory and simulation point to a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, $\alpha(t) = d\log\langle r^2(t) \rangle /d\log t$, drops below the Zimm value of 2/3 for sufficiently long chains. This deviation increases with chain length (though it does not reach the Rouse limit of 1/2), and is related to hydrodynamic effects in the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger scales. [1] arXiv:0809.0667v1, Macromolecules {\it in press} (2008).