Frustrated shapes of solid domains in fluid membrane vesicles: From rolls and folds to crumples and wrinkles

Abstract

Fluid-solid composite vesicles, comprising 2D solid domains integrated into a topologically-closed fluid bilayer membrane, exhibit complex morphologies arising from the geometric frustration between spherical closure of the membrane and 2D solid elasticity. This scenario is distinct from the better studied case of multi-fluid domain vesicles. Here, we study the elastic energies and shape equilibria of a closed vesicle membrane containing a single, flexible circular solid domain using discrete finite-element (Surface Evolver) simulations, determining the key physical and mechanical parameters to govern shape selection. While we find that the 2D solid (shear) elasticity has minimal impact on the highly-under inflated morphologies, the geometrically non-linear resistance of the solid to Gaussian curvature substantially impacts the shape and elastic patterns form for inflated vesicles, by an amount that it grows with ratio of vesicle size to the elastic thickness of solid. For sufficiently large (thin) vesicles we characterize a generic sequence of ground state patterns of solid shape with increasing inflation: from cylindrical rolls and isometric folds to spatially complex patterns of crumples and wrinkles and ultimately to smooth caps. This sequence of non-isometric patterns at high-inflation is shown to be governed by the same far-from-threshold mechanics used to describe similar shape transitions in microscopic sheets on curved liquid interfaces, establishing that inflated shapes are governed by two basic mechanical scales of membrane tension. We find our predictions for highly-anisotropic shape equilibria of fluid-solid composite vesicles closely match experimentally observed shapes of giant unilamellar vesicles of phase-separated DPPC and DOPC.