(442f) Stability Analysis of Permeable Membrane Tubes Undergoing Osmotic Shocks

Lipid membranes act as the fundamental separation structure in eukaryotic cells, and play the essential biological function of regulating the chemical species that enter and leave the cell. Lipid membranes perform this gatekeeping role by being highly selective structures, regulating chemical transport by way of endo/exo-cytosis, protein channels, and an innate permeability. In particular, the cylindrical membrane geometry appears in a great number of biological structures, including: axons and dendrites, tubules within the endoplasmic reticulum, and nanotubes during cell-cell signaling. The semi-permeability of membrane tubes can give rise to large osmotic forces across the membrane, which in turn drive local shape deformations and the transport of chemical species from the surrounding bulk fluid across the membrane interface. The stability of membranes undergoing such osmotic shocks, however, remains poorly understood. One such example is the so-called “pearling instability” of axons undergoing osmotic shock, a phenomenon that resembles the Rayleigh-Plateau instability of liquid jets. Recent theoretical developments in our lab have enabled us to write constitutive laws for the flux of solute and solvent through a lipid membrane that are consistent within the framework of linear irreversible thermodynamics. In this work, we present a linear stability analysis of the permeable, cylindrical membrane to shape perturbations. Additionally, we extend the analytical explorations of the current literature by keeping our analysis general towards membranes with an intrinsic viscosity, bulk fluids with finite inertia, time-dependent solute diffusion, and non-axisymmetric modes of perturbation. The two main cases explored here are:

1. The impermeable membrane tube coupled to inner and outer bulk fluids with high viscosity contrast.
2. A semi-permeable membrane undergoing an osmotic shock.

The effects of the relative timescales between bulk viscous diffusion, solute diffusion, membrane viscous diffusion, and membrane bending on the most unstable modes will be discussed. Additionally, we will explore the appearance of multiple decaying eigenmodes for long-wavelength perturbations.