Cross-Linker Unbinding and Self-Similarity in Bundled Cytoskeletal Networks

The macromechanical properties of purely bundled in vitro actin networks are not only determined by the micromechanical properties of individual bundles but also by molecular unbinding events of the actin-binding protein (ABP) fascin. Under high mechanical load the network elasticity depends on the forced unbinding of individual ABPs in a rate dependent manner. Cross-linker unbinding in combination with the structural self-similarity of the network enables the introduction of a concentration-time superposition principle—broadening the mechanically accessible frequency range over 8 orders of magnitude.

Figure 1

Differential modulus $K$ normalized by its value in the linear regime as a function of strain. The nonlinear response can be tuned from hardening to weakening at a fixed strain rate $d\gamma /dt=6.25\%{\mathrm{s}}^{-1}$ by varying the fascin concentration ($R=0.02$, 0.05, 0.1, 0.2, 0.5) as shown in (a) as well as for fixed $R=0.1$ tuning the strain rate ($d\gamma /dt=0.125$, 1.25, 6.25, $12.5\%{\mathrm{s}}^{-1}$) as depicted in (b). ${\gamma }_c$ defines the onset of the nonlinear response and marks the critical deformation at which the differential modulus $K$ deviates by 5% from its value in the linear regime.

Figure 2

Differential modulus $K$ normalized by its value in the linear regime as a function of strain. A weakly bundled network ($R=0.05$) is examined at different strain rates ($d\gamma /dt=0.125$, 0.625, 1.25, 6.25, $12.5\%{\mathrm{s}}^{-1}$). The inset shows the maximum stress ${\sigma }_{\max }$ vs the strain rate.

Figure 3

Master curve for actin-fascin networks (a) in the bundle phase ($R=0.5$, 0.2, 0.1, 0.05, 0.02, 0.01) and (b) before the bundling transition ($R=0.01$, 0.005, 0.002, 0.001, 0) as described in the text. Closed symbols denote $G^{\prime }$, open symbols denote $G^{\prime \prime }$. The inset shows the dependence of $G^{\prime *}$ and $G^{\prime \prime *}$ on ${\omega }^{*}$ (full line: $\sim ({\omega }^{*}{)}^1$, dotted line: $\sim ({\omega }^{*}{)}^{1/2}$).