Sidewall contact regulating the nanorod packing inside vesicles with relative volumes

Intracellular packing of one-dimensional and rodlike materials plays an important role in many biological processes such as cell mimicking, microtubule protrusion, cell division, frustrated phagocytosis, and pathogenicity. To understand the mechanical interplay between cells/intracellular membranous organelles and encapsulated rodlike materials, we perform theoretical analyses to investigate how the morphologies and mechanical behaviors of lipid vesicles of given relative volumes are regulated by encapsulated rigid nanorods of finite diameters and selected geometries, including a cylindrical nanorod, a nanorod with one widened end, and a cone-shaped nanorod. The contact between the vesicle protrusion and the sidewall of the rod, neglected in most theoretical studies, is shown to play an important role in regulating vesicle tubulation, membrane tension, and axial contact force on the nanorod. As the nanorod length increases, the confining vesicle evolves from a prolate into different shapes, such as a lemon, a conga drum, a cherry, and a bowling pin, depending on the radical size of the nanorod and the relative vesicle volume. The corresponding morphological phase diagrams are determined. Moreover, phase diagrams of the buckling of the encapsulated nanorods are determined based on the classical Euler buckling theory. It is shown that there exists an optimal filament number at which the encapsulated weakly cross-linked filament bundle maintains the largest length in a mechanically stable state. Similarities and differences between the nanorod packing in vesicles at a given pressure difference and a relative volume are discussed. Our results provide valuable insight into the biophysics underlying cell interactions with one-dimensional and rodlike materials.