Semiflexible polymer dynamics with a beadspring model
Abstract
We study the dynamical properties of semiflexible polymers with a recently introduced beadspring model. We focus on doublestranded DNA (dsDNA). The two parameters of the model, T^{*} and ν, are chosen to match its experimental forceextension curve. In comparison to its groundstate value, the beadspring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodes of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. At the Hessian approximation of the Hamiltonian, the polymer dynamics is linear. Using the longitudinal and transverse eigenmodes, for the linearized problem, we obtain analytical expressions of (i) the autocorrelation function of the endtoend vector, (ii) the autocorrelation function of a bond (i.e. a spring, or a tangent) vector at the middle of the chain, and (iii) the meansquare displacement of a tagged bead in the middle of the chain, as the sum over the contributions from the modes—the socalled ‘mode sums’. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlations functions (iiii) that agree very well with the analytical expressions for the linearized dynamics. This does not however mean that the nonlinearities are not present. In fact, we also study the meansquare displacement of the longitudinal component of the endtoend vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective t^{7/8} powerlaw regime in its timedependence. Nevertheless, in comparison to the full meansquare displacement of the endtoend vector the nonlinear effects remain small at all times—it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.
 Publication:

Journal of Statistical Mechanics: Theory and Experiment
 Pub Date:
 November 2014
 DOI:
 10.1088/17425468/2014/11/P11008
 arXiv:
 arXiv:1410.0139
 Bibcode:
 2014JSMTE..11..008B
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 33 pages in doublespacing format, 7 figures, to appear in JSTAT