Buckling modes and collapsed morphologies of pressurized vesicles

Lipid bilayers are ubiquitous in cellular biology, forming the membranes which surround most cells and many subcellular structures such as the nucleus and mitochondria. Understanding the mechanisms behind membrane deformation is thus crucial for illuminating the steady-state morphologies of these structures, as well as dynamic cellular processes such as endocytosis. We examine the stability of these materials under external forces, building on the numerical framework of Zhu et al., which simulates an evolving Stokes film by means of a variational integrator based on Onsager's principle of least energy dissipation for out-of-equilibrium processes. We simulate the collapse of pressurized vesicles and compare our results to the predictions of linear stability analysis, using spherical harmonic decomposition to examine dominant modes and growth rates. To better understand the steady-state morphologies of membranes after buckling under pressure, repulsion must be enforced to prevent self-intersection of the geometry. We incorporate a tangent point energy into our functional to penalize material points in close proximity while accounting for the connectivity of the surface. We study the steady shapes which arise from continued pressurization after the collapse of membrane vesicles and discuss their characteristic geometrical features. In many cases these steady shapes are bowl-like structures reminiscent of stomatocyte cells.