  The bioactivity of nanoparticles crucially depends on their ability to cross
biomembranes. Recent simulations indicate the cooperative wrapping and
internalization of spherical nanoparticles in tubular membrane structures. In
this article, we systematically investigate the energy gain of this cooperative
wrapping by minimizing the energies of the rotationally symmetric shapes of the
membrane tubes and of membrane segments wrapping single particles. We find that
the energy gain for the cooperative wrapping of nanoparticles in membrane tubes
relative to their individual wrapping as single particles strongly depends on
the ratio of the particle radius and the range of the particle-membrane
adhesion potential. For a potential range of the order of one nanometer, the
cooperative wrapping in tubes is highly favorable for particles with a radius
of tens of nanometers and intermediate adhesion energies, but not for particles
that are significantly larger.
