Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer

TL;DR

This paper develops a 2D hydrodynamic model for a fluid membrane coupled with an active polar fluid layer, revealing instabilities and size-dependent diffusion, extending previous work to biological membrane systems.

Contribution

It introduces a coupled hydrodynamic theory for membrane and active fluid layers, highlighting instabilities and size-dependent diffusion effects.

Findings

System exhibits generic instabilities due to active drive and membrane fluctuations.

Diffusion coefficients depend strongly on system size, unlike in equilibrium.

Model extends previous theories to biological membrane and cortical actin layers.

Abstract

We construct a coarse-grained effective two-dimensional (2d) hydrodynamic theory as a theoretical model for a coupled system of a fluid membrane and a thin layer of a polar active fluid in its ordered state that is anchored to the membrane. We show that such a system is prone to generic instabilities through the interplay of nonequilibrium drive, polar order and membrane fluctuation. We use our model equations to calculate diffusion coefficients of an inclusion in the membrane and show that their values depend strongly on the system size, in contrast to their equilibrium values. Our work extends the work of S. Sankararaman and S. Ramaswamy [Phys. Rev. Lett., 102, 118107 (2009)] to a coupled system of a fluid membrane and an ordered active fluid layer. Our model is broadly inspired by and should be useful as a starting point for theoretical descriptions of the coupled dynamics of a cell membrane and a cortical actin layer anchored to it.