Relaxation Dynamics of Semiflexible Polymers

We study the relaxation dynamics of a semiflexible chain by introducing a time-dependent tension. The chain has one of its ends attached to a large bead, and the other end is fixed. We focus on the initial relaxation of the chain that is initially strongly stretched. Using a tension that is self-consistently determined, we obtain the evolution of the end-to-end distance with no free parameters. Our results are in good agreement with single molecule experiments on double stranded DNA.

Figure 1

DNA extension plotted vs time. (a) DNA length $L=14.5\mu \mathrm{m}$, bead radius $b=0.5\mu \mathrm{m}$, and initial extension $z(0)=0.825L$; (b) $L=20.1\mu \mathrm{m}$, $b=1.4\mu \mathrm{m}$, and $z(0)=0.848L$. The solution of Eqs. (11, 14) (solid line) and the experimental data points are shown. The computational error in the solid line is about $4\%$ at the longest times shown and diminishes at shorter times. For comparison, the solution of Eq. (13) (dashed line) is also shown.

Figure 2

Theoretical extension, computed from Eqs. (11, 14), vs the scaled time $t/t_o$, where $t_o=6\pi \eta L_{p}Lb/k_{B}T$, for three different bead radii: $b=0.25\mu \mathrm{m}$ (full line), $b=0.5\mu \mathrm{m}$ (dashed line), and $b=1\mu \mathrm{m}$ (dotted line). $L=14.5\mu \mathrm{m}$ and $z(0)/L=0.825$. Inset: Same as above but against the time (unscaled).

Figure 3

Experimental results for DNA relaxation. The time axis is divided by $t_o$. Circles are for $b=1.4\mu \mathrm{m}$ [same system as for Fig. 1b], plusses are for $b=0.5\mu \mathrm{m}$ [same system as for Fig. 1a], and triangles are for a system with $b=1\mu \mathrm{m}$, $z(0)/L=0.84$, and $L=17.7\mu \mathrm{m}$.