Activating Membranes

We present a general dynamical theory of a membrane coupled to an actin cortex containing polymerizing filaments with active stresses and currents, and demonstrate that active membrane dynamics [S. Ramaswamy et al., Phys. Rev. Lett. 84, 3494 (2000)] and spontaneous shape oscillations emerge from this description. We also consider membrane instabilities and patterns induced by the presence of filaments with polar orientational correlations in the tangent plane of the membrane. The dynamical features we predict should be seen in a variety of cellular contexts involving the dynamics of the membrane-cytoskeleton composite and cytoskeletal extracts coupled to synthetic vesicles.

Figure 1

Schematic diagram of a membrane in an active fluid. The membrane is depicted in Monge gauge: $\mathbf{R}=\mathbf{(}x,y,h(x,y,t)\mathbf{)}$, where $h(x,y,t)$ is the height above points ($x$, $y$) on a reference plane. The signed species $\psi$ is represented by circles, with dots (crosses) denoting parallel (antiparallel) alignment with respect to the outward membrane normal $\mathbf{N}$. Dashed arrows on the membrane are the in-plane polar filaments, whose concentration is $c$, and continuous arrows denote the bulk active orientable fluid.