Structures and mechanical behaviors of soft nanotubes confining adhesive single or multiple elastic nanoparticles

The mechanical interaction between soft membrane nanotubes and confined nanoparticles plays essential roles in numerous cellular activities such as inter- and intracellular transport and signaling, membrane tubulation and pearling transformation driven by adsorbed nanocomponents, and cooperative cell uptake. The aim of this work is to theoretically analyze how structures and mechanical behaviors of particle-in-tube complexes are regulated by the particle elasticity, covering the cases of a single particle and multiple particles of spatial periodicity. Depending on the interplay of membrane tension, adhesion energy, nanoparticle size, and the rigidity ratio between the nanoparticles and soft tubes, characteristic interaction states in terms of wrapping degrees of the confined particles have been identified, and the corresponding wrapping phase diagrams are determined. As the particles become softer, the adhesion energy required for the partial-wrapping state becomes lower but that for full-wrapping is larger, and a rich variety of characteristic system configurations are observed including the bulged or undulated cylinders, necklaces of spheres or prolates, and sausage-string shapes. Moreover, two fundamental modes of interaction between multiple nanoparticles and the soft nanotube are revealed, the cooperative wrapping and individual wrapping. Based on perturbation analysis at small tube deformation and configurational assumptions of catenoid, torus, and one-sheeted hyperboloid at more general tube deformation, we have also obtained analytical solutions on the wrapping of rigid spherical nanoparticles in soft tubes. Comparison between wrapping of elastic particles by a flat membrane and by a soft membrane tube is discussed. This study enriches our knowledge on the diversity of membrane tubules in morphologies and structures.