Membrane tubulation by spherical nanoparticles: effect of lateral tension

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 membrane bending and particle adhesion energies in the membrane necks that connect the particles to the neighbouring particles in the tubule. In this article, we investigate how the energy gain for the cooperative wrapping of spherical nanoparticles in tubules is affected by lateral membrane tension as well as by the membrane thickness, which limits the radius of the membrane necks between the particles. We find that membrane tension tends to stabilize weakly undulated tubule shapes at intermediate particle adhesion energies, but only moderately affects the energy gain of cooperative wrapping at larger adhesion energies. For tight membrane necks limited by the membrane thickness, however, the energy gain of cooperative wrapping can vanish if the range of the particle adhesion potential is too small to still lead to a favourable interplay of bending and adhesion energies in these necks.