Mechanics of Bundled Semiflexible Polymer Networks

While actin bundles are used by living cells for structural fortification, the microscopic origin of the elasticity of bundled networks is not understood. Here, we show that above a critical concentration of the actin binding protein fascin, a solution of actin filaments organizes into a pure network of bundles. While the elasticity of weakly cross-linked networks is dominated by the affine deformation of tubes, the network of bundles can be fully understood in terms of nonaffine bending undulations.

Figure 1

(a) Fluorescence micrograph of an actin-fascin network ($0.1\mathrm{mg}/\mathrm{ml}$ actin): for high fascin concentrations a purely bundled network is formed (scale bar is $10\mu \mathrm{m}$). (b) From TEM pictures (inset, scale bar is $0.2\mu \mathrm{m}$) a scaling relation for the average bundle diameter $D$ is obtained.

Figure 2

Plateau modulus $G_0$ as a function of the molar ratio $R$ of fascin with respect to actin for two different concentrations of actin: $0.4\mathrm{mg}/\mathrm{ml}$ (circles) and $0.2\mathrm{mg}/\mathrm{ml}$ (squares). The dependence of $G_0$ on $c_a$ is obtained by scaling the fits for the $0.2\mathrm{mg}/\mathrm{ml}$ actin data upon the $0.4\mathrm{mg}/\mathrm{ml}$ data points. The dashed line shows the boundary separating the two scaling regimes. The original frequency spectra for $0.4\mathrm{mg}/\mathrm{ml}$ actin at different cross-linker concentrations ($R=0,0.001,0.002,0.005,0.01,0.02,0.05,0.1,0.2,0.5$) are depicted in the inset.

Figure 3

Differential modulus $K=d\sigma /d\gamma$ plotted versus deformation $\gamma$ for fascin networks in the bundle phase ($c_a=0.4\mathrm{mg}/\mathrm{ml}$ and increasing $R$: diamonds $R=0.02$; upright triangles: $R=0.05$; circles: $R=0.1$; downright triangles: $R=0.2$; stars: $R=0.5$). The inset shows the critical strain ${\gamma }_c$ in dependence on $R$.