Cooperative wrapping of nanoparticles by membrane tubes

Abstract

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 ρ/R of the particle radius R and the range ρ 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.

Cooperative wrapping of nanoparticles of various sizes and shapes by lipid membranes

“…43,44 Theoretical analysis shows that the energy gain for cooperative wrapping of NPs in membrane tubes is larger than individual wrapping of NPs. 45,46 However, cooperative wrapping of NPs is still far from being fully understood. [43][44][45][46][47][48][49] The present theoretical analysis only obtains the system energy of different wrapping phases and lacks the dynamic process of cooperative wrapping.…”

“…45,46 However, cooperative wrapping of NPs is still far from being fully understood. [43][44][45][46][47][48][49] The present theoretical analysis only obtains the system energy of different wrapping phases and lacks the dynamic process of cooperative wrapping. 50 In particular, it cannot capture the membrane structure transition when the number of NPs gradually increases.…”

Particle-based membrane model for mesoscopic simulation of cellular dynamics

“…7 shows snapshots of the simulation performed for a spherical nanoparticle of 100 nm radius interacting with a 1 µm membrane patch, with u A catenoidal membrane segment, which corresponds to zero bending energy, is expected in the unbound neck region, when the interaction range ρ approaches zero 105 . Yet, for non-zero interaction range, the catenary is still a good approximation for this region 105 . The good fit to the catenary curve is an indication that the particlebased model very well captures the zero-energy regions and assumes corresponding minimal surface geometries.…”

“…As a final test of the usefulness of our membrane model to handle substantial deformations and model biologically relevant membrane remodeling processes, we simulate the interaction of spherical nanoparticles with the membrane, as a well-known benchmark system [105][106][107][108][109] . This simple system mimics the endocytosis of nanoparticles or viral capsids by cell membranes.…”

“…The nanoparticle interacts with the membrane through a Morse-type surface adhesion energy density of U p exp [− (r − R) /ρ], where r is the radial distance between the center of the nanoparticle and the membrane surface. For this type of nanoparticle-membrane interaction, and with a continuum membrane model, semi-analytical studies 105 have been carried out on the degree to which the surface of the nanoparticle is covered by the membrane, as a function of the dimensionless adhesion energy u = U p R 2 /κ as well as the potential range, ρ. The parameter u is the ratio between the nanoparticle-membrane adhesion energy and the energy needed to bend the membrane to a spherical shape.…”