Viscous-Fingering-Like Instability of Cell Fragments

We present a novel flow instability that can arise in thin films of cytoskeletal fluids if the friction with the substrate on which the film lies is sufficiently strong. We consider a two-dimensional, membrane-bound fragment containing actin filaments that polymerize at the edge and depolymerize in the fragment. Performing a linear stability analysis of the initial state due to perturbations of the fragment boundary, we find, in the limit of large friction, that the perturbed actin velocity and pressure fields obey the same laws governing the viscous fingering instability of an interface between immiscible fluids in a Hele-Shaw cell. A remarkable feature of this instability is that it is independent of the strength of the interaction between actin filaments and myosin motors.

Figure 1

Schematic drawing of actin cytoskeleton in the unperturbed, radial state of the fragment. The direction of average actin polarization is radial, and is indicated by $\mathbf{p}=\widehat{\mathbf{r}}$.

Figure 2

Critical value of friction, ${\xi }_c$, in units of $\eta /R_0^2$, versus $|\zeta |\Delta \mu /\eta k_d$ for $m=2$ (solid line), $m=3$ (long dashed line), and $m=4$ (short dashed line). Surface tension, $\gamma /\eta k_d{R}_0$, is taken to be zero.