Tension dynamics in semiflexible polymers. II. Scaling solutions and applications

Abstract

In part I ͓O. Hallatschek et al., preceding paper, Phys. Rev. E 75, 031905 ͑2007͔͒ of this contribution, a systematic coarse-grained description of the dynamics of a weakly bending semiflexible polymer was developed. Here, we discuss analytical solutions of the established deterministic partial integro-differential equation for the spatiotemporal relaxation of the backbone tension. For prototypal experimental situations, such as the sudden application or release of a strong external pulling force, it is demonstrated that the tensile dynamics reflects the self-affine conformational fluctuation spectrum in a variety of intermediate asymptotic power laws. Detailed and explicit analytical predictions for the tension propagation and relaxation and corresponding results for common observables, such as the end-to-end distance, are obtained.

Dynamic structure factor of a stiff polymer in a glassy solution

“…Instead of repeating the extended discussion, we refer the reader to [11,19] for the longitudinal dynamics. For molecules that are reasonably stiff on the length scale q −1 (which is a requirement for the application of the weakly bending rod approximation on which our whole discussion is based), only the contribution due to transverse motions is measurable in practice because of the double scale separation…”

“…A key property of the WLC is its inextensibility, expressed by the arc length constraint |r (s)| = 1. This nonlinear constraint renders the dynamical equations of motion of the polymer difficult, but analytical progress can be made in the weakly bending rod limit [11], where the polymer contour is parameterized Comparison of S(q, t) to the experimentally determined dynamic structure factor of (native) F-actin at temperature T = 15…”

Glass transition and rheological redundancy in F-actin solutions

“…For more comprehensive background information on the wormlike chain, the reader is referred to ref. 42. For more specific details concerning the theory curves in Figs.…”

Torque correlation length and stochastic twist dynamics of DNA

“…Moreover, when the applied torque is large, the filament buckles [8, 34]. Following previous work [18, 20, 35, 36] (see Appendix D), we assume that the tension, F , across DNA is large ( βAF > 1), so transverse bending fluctuations are small, and the linearized equations for twist and bend are: $$2\beta \zeta {\partial }_t\theta =c_1{\partial }_s^2\theta -c_2{\partial }_s^4\theta +f\left(t\right)$$$$2\beta {\zeta }_{\perp }{\partial }_{t}R=itrue(true(c_2{\partial }_s^4\theta -c_1{\partial }_s^2\theta true){\partial }_s^{2}R+(c_2{\partial }_s^3\theta -c_1{\partial }_s\theta ){\partial }_s^{3}Rtrue)-A{\partial }_s^{4}R+\beta F{\partial }_s^{2}R+g_x\left(t\right)+i{g}_y\left(t\right)$$ where $R={\overrightarrow{r}}_{\perp }\cdot \widehat{x}+i{\overrightarrow{r}}_{\perp }\cdot \widehat{y}$, ${\zeta }_{\perp }\approx \zeta ∕\ln (2L∕d)$ [20, 37] and $\overrightarrow{g}\left(t\right)$ is bending noise. The DNA ends are clamped so that R (0) = R ( L ) = 0 and ${{\partial }_{s}R\mid }_{s=0}={{\partial }_{s}R\mid }_{s=L}=0$ [26].…”