Membrane tethers are long, slender membrane tubes that transport biological cargo (proteins and viruses) and engineered materials (particles and drugs) in organelles, vesicles, and cells. Nanoparticles with enhanced bioavailability and reduced toxicity are attracting great attention in nanomedicine for their ability to target membrane tethers, particularly tunneling nanotubes, which share similar structures and functions with membrane tethers. Nevertheless, the molecular mechanisms that control the cooperative wrapping of nanoparticles within and on membrane tethers are not well understood. Our study aims to map the wrapping behavior and the associated membrane deformation for spherical nanoparticles entering and exiting membrane tethers (modeling both out-to-in and in-to-out wrapping). By integrating continuum membrane models and finite-element analysis, we systematically quantify how the equilibrium shapes, obtained via energy minimization, are governed by membrane spontaneous curvature, nanoparticle size, and interparticle distance. For out-to-in wrapping, the discontinuous binding-envelopment transitions between the nonwrapped and the complete-wrapped states are facilitated by long interparticle distances and small particle sizes, for which both the adhesion strengths and the energy barriers are low. For negative spontaneous curvature, however, the adhesion strengths are low while the energy barriers are high. The deformations of the contact lines that separate the membrane into the bound and unbound segments are larger for the shortest or the longest interparticle distances. For in-to-out wrapping, the stable partial-wrapped states are identified. In particular, the short interparticle distances lead to the discontinuous transitions between the shallow-wrapped and the deep-wrapped states. Negative spontaneous curvature, short interparticle distances, and large particle sizes favor the stable partial-wrapped states. Instead of aggregating into compact linear chains along the membrane tethers, the nanoparticles remain separated at well-defined lowest-energy positions. The deformations of the contact lines are slightly larger than those for out-to-in wrapping. The competition between the local curvature and the spontaneous curvature of the membrane gives rise to rich wrapping diagrams, and our numerically determined adhesion strengths are in agreement with the theoretical predictions. Our findings provide important insights into tether-nanoparticle interactions and offer guidelines for the design of functional nanomedicines.

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• Analog computation
• Physics of computation