Tension dynamics and viscoelasticity of extensible wormlike chains

The dynamic response of prestressed semiflexible biopolymers is characterized by the propagation and relaxation of tension, which arises due to the near inextensibility of a stiff backbone. It is coupled to the dynamics of contour length stored in thermal undulations but also to the local relaxation of elongational strain. We present a systematic theory of tension dynamics for stiff yet extensible wormlike chains. Our results show that even moderate prestress gives rise to distinct Rouse-like extensibility signatures in the high-frequency viscoelastic response.

Figure 1

(Color online) Plot of ${\widehat{J}}^{\prime },{\widehat{J}}^{″}$ (top) and ${\widehat{G}}^{\prime },{\widehat{G}}^{″}$ (bottom) from Eq. (10) for ${\varphi }_{\text{x}}=f_0/f_{\text{x}}={10}^{-2}$ and for ${\varphi }_{\text{c}}=100$ (left) and ${\varphi }_{\text{c}}=1$ (right), where ${\varphi }_{\text{c}}=f_0/f_{\text{c}}$ with $f_{\text{c}}={\ell }_{\text{p}}^2/\left({\widehat{\zeta }}^2{L}^4\right)$ and $f_{\text{x}}=k_{\text{x}}^{2/3}/{\ell }_{\text{p}}^{4/3}$. Solid lines: ${\widehat{J}}^{\prime }\left({\widehat{G}}^{\prime }\right)$ and dashed lines: ${\widehat{J}}^{″}\left({\widehat{G}}^{″}\right)$. Short lines indicate high-frequency scaling laws of Table .