A model for the dynamics of extensible semiflexible polymers

TL;DR

This paper introduces a Hamiltonian model for semiflexible polymers that bridges the gap between Rouse and worm-like chain models, matching experimental DNA data and analyzing mode decay times.

Contribution

It develops a unified Hamiltonian framework for semiflexible polymers, interpolating between existing models and matching experimental force-extension curves.

Findings

Eigenvalues scale as (p/N)^2 and p^2(p-1)^2/N^4 for different modes.

Decay times scale as (N/p)^4 and are limited by the orientational time scale.

The model can replicate DNA force-extension behavior.

Abstract

We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental force-extension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4 respectively for small p. We also show that the associated decay times tau_p ~ (N/p)^4 will not be observed if they exceed the orientational time scale tau_r ~ N^3 for an equally-long rigid rod, as the driven decay is then washed out by diffusive motion.