End-Monomer Dynamics in Semiflexible Polymers

Abstract

Spurred by an experimental controversy in the literature, we investigate the end-monomer dynamics of semiflexible polymers through Brownian hydrodynamic simulations and dynamic mean-field theory. 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) 〈r 2 (t)〉 ~ 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 〈r 2 (t)〉 ~ t 2/3 in the same time range. Using hydrodynamic simulations, analytical and scaling theories, we find a novel intermediate dynamical regime where the effective local exponent of the end-monomer MSD, α(t) = d log〈r 2 (t)〉/d log t, drops below the Zimm value of 2/3 for sufficiently long chains. The deviation from the Zimm prediction increases with chain length, though it does not reach the Rouse limit of 1/2. The qualitative features of this intermediate regime, found in simulations and in an improved mean-field theory for semiflexible polymers, in particular the variation of α(t) with chain and persistence lengths, can be reproduced through a heuristic scaling argument. Anomalously low values of the effective exponent α are explained by hydrodynamic effects related to the slow crossover from dynamics on length scales smaller than the persistence length to dynamics on larger length scales.

Unusual swelling of a polymer in a bacterial bath

“…In equilibrium, in the absence of hydrodynamic interactions, the mean square displacement of the end-monomer behaves as [70] (∆r N )…”

Communication: Self-assembly of semiflexible-flexible block copolymers

“…Explicitly, H B penalizes noncollinear orientation of the bond vectors through a bending rigidity term. 16,17 Motion of a system of such chains are simulated using a Langevin equation involving forces arising from the harmonic springs, and in the case of B monomers, the bending potentials. Additionally, the beads are acted upon by a force F P which represents the influence of the potential fields arising out of the SCFT framework.…”

Anisotropic Hydrodynamic Mean-Field Theory for Semiflexible Polymers under Tension

“…In fact, the solvent-mediated coupling between all points on the polymer is not an incidental element in the method, but a key to its success: the long-range interactions make the mean-field approach more realistic. This has already been demonstrated for F = 0, where an earlier, isotropic MFT [19,20] was able to model precisely the dynamics of an end-monomer in DNA strands observed through fluorescence correlation spectroscopy (FCS) [21]; the experimental validation is reviewed in Sec. II below.…”

“…We begin by reviewing the isotropic MFT approach to semiflexible polymers at F = 0 [19,20,[25][26][27] and F = 0 [22][23][24]. The starting point is the WLC Hamiltonian,…”

“…To extract dynamics, one can adopt a Zimm-like hydrodynamic pre-averaging approach [19,20,27], described in more detail below in the context of the anisotropic MFT. Within this approach, the chain contour obeys a Langevin equation that can be solved through normal mode decomposition.…”