Linear stability of cylindrical, multicomponent vesicles

Abstract

Vesicles are important surrogate structures made up of multiple phospholipids and cholesterol distributed in the form of a lipid bilayer. Tubular vesicles can undergo pearling i.e., formation of beads on the liquid thread akin to the Rayleigh-Plateau instability. Previous studies have inspected the effects of surface tension on the pearling instabilities of single-component vesicles. In this study, we perform a linear stability analysis on a multicomponent cylindrical vesicle. We solve the Stokes equations along with the Cahn-Hilliard equations to develop the linearized dynamic equations governing the vesicle shape and surface concentration fields. This helps us show that multicomponent vesicles can undergo pearling, buckling, and wrinkling even in the absence of surface tension, which is a significantly different result from studies on single-component vesicles. This behaviour arises due to the competition between the free energies of phase separation, line tension, and bending for this multi-phospholipid system. We determine the conditions under which axisymmetric and non-axisymmetric modes are dominant, and supplement our results with an energy analysis that shows the sources for these instabilities. We further show that these trends qualitatively match recent experiments.

Figures (15)

• Figure 1: Problem setup. We examine the stability of a cylindrical vesicle with Newtonian fluid inside and outside with viscosities $\lambda \mu$ and $\mu$ respectively. The membrane has multiple lipids and is characterized by an order parameter $q$ representing different phase-separated domains, a bending modulus $\kappa_c$ depending on $q$, a line tension parameter $\gamma$, and surface tension $\sigma$.
• Figure 2: Snapshots of $(a)$ pearling $(n=0)$$(b)$ buckling $(n=1)$$(c)$ wrinkling $(n=2)$ modes for single-component vesicles.
• Figure 3: Growth rate vs. wavenumber for an equiviscous ($\lambda = 1$), single-component vesicle at $\Gamma=0$ and $\Gamma=5$ for (a) pearling mode ($n=0$), and (b) buckling mode ($n=1$). Results are validated against published results boedec_jaeger_leonetti_2014
• Figure 4: Most unstable growth rates with respect to the isotropic membrane tension $\Gamma$ for single-component vesicles. The red circles represent $n=0$ pearling modes, black circles represent $n=1$ buckling modes, and blue circles represent $n=2$ wrinkling modes. In the plot, $\lambda =1$.
• Figure 5: Different unstable modes for multicomponent vesicle: $(a)$ pearling $(n=0)$$(b)$ buckling $(n=1)$$(c)$ wrinkling $(n=2)$, and $(d)$ wrinkling $(n=3)$.