Nonlinear Study of Symmetry Breaking in Actin Gels: Implications for Cellular Motility

Force generation by actin polymerization is an important step in cellular motility and can induce the motion of organelles or bacteria, which move inside their host cells by trailing an actin tail behind. Biomimetic experiments on beads and droplets have identified the biochemical ingredients to induce this motion, which requires a spontaneous symmetry breaking in the absence of external fields. We find that the symmetry breaking can be captured on the basis of elasticity theory and linear flux-force relationships. Furthermore, we develop a phase-field approach to study the fully nonlinear regime and show that actin-comet formation is a robust feature, triggered by growth and mechanical stresses. We discuss the implications of symmetry breaking for self-propulsion.

Figure 1

Schematic view of a bead surrounded by an elastic gel with the Lamé coefficients $\nu$ and $\lambda$.

Figure 2

Scaled growth rates ${\overline{\omega }}^{(0)}$ and ${\overline{\omega }}^{(1)}$ depending on the perturbation mode. The parameters are $\eta =0.003$, $\sigma =0.4$, and $|\Delta {\mu }_p|/E=8.9\times {10}^{-4}$, giving rise to a steady state ${\overline{r}}_2/r_1=1.1$. The time scale is given by $r_1/(ME)$.

Figure 3

(a) Symmetry breaking of a circular gel. Shown is the evolution of the gel thickness, starting from a homogeneous thin gel with random small amplitude perturbations. The simulation time is indicated in the right top corner of each snapshot. (b) Shows the shape of the comet in the far nonlinear regime with a small surface tension added to avoid numerical instabilities. Parameters are $r_1=1.0$, $\xi =0.04$, $\Delta {\mu }_p/E=-0.00058$, $\sigma =0.4$, $\eta =0.003$, and for (b) $E/\Gamma ={10}^3$. The length scale is $r_0=1\mu \mathrm{m}$ and the time scale is $r_0^2/(M_{\Phi }E{\xi }^2)$.