  The transport of particles across lipid-bilayer membranes is important for
biological cells to exchange information and material with their environment.
Large particles often get wrapped by membranes, a process which has been
intensively investigated in the case of hard particles. However, many particles
in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses,
macromolecular condensates, polymer-grafted nanoparticles, and microgels.
Vesicles may serve as a generic model system for deformable particles. Here, we
study non-spherical vesicles with various sizes, shapes, and elastic properties
at initially planar lipid-bilayer membranes. Using the Helfrich Hamiltonian,
triangulated membranes, and energy minimization, we predict the interplay of
vesicle shapes and wrapping states. Increasing particle softness enhances the
stability of shallow-wrapped and deep-wrapped states over non-wrapped and
complete-wrapped states. The free membrane mediates an interaction between
partial-wrapped vesicles. For the pair interaction between deep-wrapped
vesicles, we predict repulsion. For shallow-wrapped vesicles, we predict
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 medical applications, such as targeted drug
delivery.
