Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid

Dynamics of a membrane coupled to an active fluid

The dynamics of a membrane coupled to an active fluid on top of a substrate is considered theoretically. It is assumed that the director field of the active fluid has rotational symmetry in the membrane plane. This situation is likely to be relevant for in vitro reconstructed actomyosin-membrane system. Different from a membrane coupled to a polar active fluid, this model predicts that only when the viscosity of the fluid above the membrane is sufficiently large, a contractile active fluid is able to slow down the relaxation of the membrane for perturbations with wavelength comparable to the thickness of the active fluid. Hence, our model predicts a finite-wavelength instability in the limit of strong contractility, which is different from a membrane coupled to a polar active fluid. However, a membrane coupled to an extensile active fluid is always unstable against long-wavelength perturbations due to active extensile stress enhanced membrane undulation.

Minimal Model of Cellular Symmetry Breaking

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry-breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.

Active Fingering Instability in Tissue Spreading

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

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.