Figure 3. Influence of crosslinking on actin network dynamics.

Contractile actin networks are generated by encapsulating Xenopus extract supplemented with different concentrations of the actin crosslinker α-Actinin. The inward contractile flow and actin network density were measured (as in Fig. 1). (a) The steady-state network behavior is shown for a sample supplemented with 10 μM α-Actinin (see Movie 4). A spinning disk confocal fluorescence image of the equatorial cross section of the network labeled with GFP-Lifeact (left) is shown, together with graphs depicting the inward radial network flow and network density as a function of distance from the contraction center (middle) and the net actin turnover as a function of network density (right). The thin grey lines depict data from individual droplets, and the thick line is the average over different droplets. The dashed lines show the results for the control unsupplemented sample. The network contracts in a non-homogeneous manner, reflected by the non-linear dependence of the radial network flow on the distance from the contraction center. (b,c) The concentration-dependent effect of α-Actinin on network density and flow. The network density (b) and radial flow (c) are plotted as a function of distance from the contraction center. For each α-Actinin concentration, the mean (line) and std (shaded region) over different droplets are depicted. The position of the network density peak moves towards the inner boundary with increasing α-Actinin concentrations, and the radial velocity becomes a non-linear function of the distance from the contraction center. (d) The derivative of the radial velocity, $-\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^{2}V\right)$, is plotted as a function of distance from the contraction center. This function becomes position-dependent for α-Actinin concentrations ≥ 4μM. According to the model, this derivative should be approximately equal to the ratio between the active stress and the effective network viscosities, $\frac{{\sigma }_A\left(r\right)}{2\mu \left(r\right)+\lambda \left(r\right)}$. (e) The derivative of the radial velocity, $-\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^{2}V\right)$, is plotted as a function of network density. According to the model, this derivative should be approximately equal to the ratio between the active stress and the effective network viscosities, $\frac{{\sigma }_A\left(\rho \right)}{2\mu \left(\rho \right)+\lambda \left(\rho \right)}$. For α-Actinin concentrations ≥4μM this ratio becomes density-dependent, indicating that the scaling relation between the active stress and the effective viscosity no longer holds.