Origins of Elasticity in Intermediate Filament Networks

Intermediate filaments are common structural elements found in abundance in all metazoan cells, where they form networks that contribute to the elasticity. Here, we report measurements of the linear and nonlinear viscoelasticity of networks of two distinct intermediate filaments, vimentin and neurofilaments. Both exhibit predominantly elastic behavior with strong nonlinear strain stiffening. We demonstrate that divalent ions behave as effective cross-linkers for both networks, and that the elasticity of these networks is consistent with the theory for that of semiflexible polymers.

Figure 1

(a) $G^{\prime }$ (solid symbols) and $G^{\prime \prime }$ (open symbols) as a function of frequency in the linear regime. (b) $G^{\prime }$ (solid symbols) and $G^{\prime \prime }$ (open symbols) as a function of strain, $\gamma$. Samples of vimentin (squares) and neurofilaments (circles) are probed at a $2\mathrm{mg}/\mathrm{ml}$ filament concentration and a 5 mM ${\mathrm{Mg}}^{2+}$.

Figure 2

(a) $G_0$ as a function of $c_{\mathrm{IF}}$ holding $R$ constant, where $R=1000$ for neurofilaments (circles) and $R=215$ for vimentin (squares). Solid line is obtained using a regression fit and depicts $G_0\sim c_{\mathrm{NF}}^{2.5}$ for neurofilaments, while dashed line depicts $G_0\sim c_V^2$. (b) $G_0$ as a function of $c_{\mathrm{Mg}}$ holding $c_{\mathrm{IF}}$ constant, where $c_{\mathrm{IF}}=1\mathrm{mg}/\mathrm{ml}$ for neurofilaments (circles) and $c_{\mathrm{IF}}=2\mathrm{mg}/\mathrm{ml}$ for vimentin (squares).

Figure 3

$K^{\prime }$ at $0.6\mathrm{rad}/\sec $ as a function of $\sigma$ for vimentin and neurofilament networks: [$c_{\mathrm{Mg}}=2\mathrm{mM}$ (open symbols), $c_{\mathrm{Mg}}=8\mathrm{mM}$ (solid symbols) and $c_{\mathrm{IF}}=2\mathrm{mg}/\mathrm{ml}$ (all symbols)]. The solid line shows a $3/2$ power law. The inset shows the data sets rescaled by ${\sigma }_c$ and $G_0$ depicting the universal form of the stiffening response; the rescaled theory is indicated by the dashed red line, while the solid black line depicts the deviation due to enthalpic backbone stretching.

Figure 4

The dependence of $c_{\mathrm{IF}}^{1/2}{G}_0$ on ${\sigma }_c$. Vimentin data points are obtained with ${\mathrm{Mg}}^{2+}$, while NF data points are obtained with ${\mathrm{Mg}}^{2+}$ (closed circles), ${\mathrm{Ca}}^{2+}$ (open circles), and ${\mathrm{Zn}}^{2+}$ (crossed circles). The solid lines reflect regression fits. The affine thermal model predicts a power law of $3/2$, shown for reference.

Figure 5

(a) The dependence of $l_c$ on $c_{\mathrm{IF}}$ at fixed $R$, where $R=1000$ for NFs (circles) and $R=215$ for vimentin (squares). A power law of $-0.4$ is shown for reference. (b) The dependence of $l_c$ on $c_{\mathrm{Mg}}$, holding $c_{\mathrm{IF}}$ constant. A regression fit results in a power law of $-0.23$ for both vimentin and neurofilament networks.