Linear stability of cylindrical multicomponent vesicles

Vesicles are important surrogate structures used to understand the mechanical behavior of cell membranes and other organelles. They are made up of multiple phospholipids and cholesterol distributed in the form of a lipid bilayer. These vesicles are often found as tubular shaped structures. Tubular vesicles can undergo pearling – formation of beads on the liquid threads akin to the Rayleigh Plateau instability. Previous studies have inspected the effects of surface tension on the pearling instabilities of vesicles. However, not much has been discussed about the pearling instabilities in multicomponent vesicles which involve an additional factor, phase separation and domain line tension. We perform a linear stability analysis on a cylindrical vesicle with multiple phospholipids on the surface undergoing phase separation and diffusion. We solve the Stokes equations along with the Cahn-Hilliard equations to develop the linearized dynamic equations governing the shape and concentration fields. We delineate the effects of phase separation on pearling and vice-versa. We provide estimates of critical dimensionless numbers that would aid an experimentalist in exploring such phenomena.