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Transport of engineered particles across lipid-bilayer membranes is important to exchange infor-
mation and material with the environment. Large particles often get wrapped by membranes, a
process which has been intensively investigated in the case of hard particles [1]. However, many
particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecu-
lar condensates, polymer-grafted nanoparticles, and microgels. Vesicles may serve as a generic
model system for deformable particles [2]. Here, we study the interaction of non-spherical vesicles
of various sizes, shapes, and elastic properties with planar lipid-bilayer membranes. Using the
Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the inter-
play of vesicle shapes and wrapping states. We show that increasing particle softness stabilizes
partial-wrapped over non-wrapped and complete-wrapped states. During the wrapping process,
a shape change of the vesicles from prolate to oblate is observed. Furthermore, we calculate the
membrane-mediated pair interaction between two partial-wrapped, prolate vesicles. We predict
purely repulsive interaction between the vesicles in deep-wrapped states. For shallow-wrapped
states the interaction potential depends on the orientation of the vesicles, with attraction for
tip-to-tip orientation, and repulsion for side-by-side orientation. Our predictions may guide the
design and fabrication of deformable particles for efficient use in diagnostics and therapeutics. |