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The adsorption of particles onto fluid membranes can lead to membrane-mediated interactions between particles that promote their self-assembly and lead to changes in membrane morphology. However, in contrast with rigid particles, relatively little is known about deformable particles, which introduce additional complexities due to the mutual deformability of the particles and the membrane. Here, we use Monte Carlo simulations and umbrella sampling to investigate the equilibrium properties of hinge-like particles adsorbed on membrane vesicles by means of anisotropic, attractive interactions. We vary the hinge stiffness, adhesive area fraction, patterning of adhesive regions, and number of adsorbed particles. Depending on their properties, isolated particles can conform to the vesicle, induce invaginations of the membrane, or exhibit multistable behavior in which they sample distinct classes of configurations due to the interplay of particle and membrane deformations. With two adsorbed particles, the properties of the particles can be used to promote aggregation, bias the particles to different parts of the vesicle, or stabilize the coexistence of both cases. With multiple adsorbed particles, the number and type control their organization and collective impact on the vesicle, which can adopt shapes ranging from roughly spherical to dumbbell-like and multi-lobed. Our results highlight how modifying the mechanical properties and patterned adhesion of deformable particles, which is possible with DNA nanotechnology, influences their self-assembly and the resulting shapes of both the particles and vesicles. 

Nanoparticles adsorbed on a membrane can induce deformations of the membrane that give rise to effective interactions between the particles. Previous studies have focused primarily on rigid nanoparticles with fixed shapes. However, DNA origami technology has enabled the creation of deformable nanostructures with controllable shapes and mechanical properties, presenting new opportunities to modulate interactions between particles adsorbed on deformable surfaces. Here we use coarse-grained molecular dynamics simulations to investigate deformable, hinge-like nanostructures anchored to lipid membranes via cholesterol anchors. We characterize deformations of the particles and membrane as a function of the hinge stiffness. Flexible particles adopt open configurations to conform to a flat membrane, whereas stiffer particles induce deformations of the membrane. We further show that particles spontaneously aggregate and that cooperative effects lead to changes in their shape when they are close together. Using umbrella sampling methods, we quantify the effective interaction between two particles and show that stiffer hinge-like particles experience stronger and longer-ranged attraction. Our results demonstrate that interactions between deformable, membrane-anchored nanoparticles can be controlled by modifying mechanical properties of the particles, suggesting new ways to modulate the self-assembly of particles on deformable surfaces.