Membrane tubulation by adhesion of spherical nanoparticles

Adhesion of spherical nanoparticles or virus-like particles to membranes can lead to membrane tubules in which linear chains of adhering particles are cooperatively wrapped by the membrane. This cooperative wrapping of spherical particles in tubules is energetically favourable compared to the individual wrapping of the particles because of a favourable interplay of bending and adhesion energies in the contact regions in which the membrane detaches from the particles, and because a particle in a tubule has two such contact regions in the membrane necks that connect the particle to the neighbouring particles, whereas an individually wrapped particle has only one contact region to the surrounding membrane. The energetic gain of cooperative wrapping strongly depends on the range of the particle-membrane adhesion potential, which determines the size of the contact regions. At sufficiently large adhesion energies for wrapping, the energy gain {Delta}E per particle is only weakly affected by the membrane tension{tau} as long as the characteristic length [Formula] of the membranes with bending rigidity{kappa} is clearly larger than the contact regions. For large particle adhesion energies at which the particles are fully wrapped, however, {Delta}E can be limited by the minimum possible radius of the membrane necks, depending on the adhesion potential range.