Recent advances in nanotechnology have made a whole zoo of particles of different shapes available for applications, but their interaction with biological cells and their toxicity is often not well understood. Experiments have shown that particle uptake by cells is determined by an intricate interplay between physicochemical particle properties like shape, size, and surface functionalization, but also by membrane properties and particle orientation. Our work provides systematic understanding, based on a mechanical description, for membrane wrapping of nanoparticles, viruses, and bacterial forms. For rod-like particles, we find stable endocytotic states with small and high wrapping fraction; an increased aspect ratio is unfavorable for complete wrapping. For high aspect ratios and round tips, the particles enter via a submarine mode, side-first with their long edge parallel to the membrane. For small aspect ratios and flat tips, the particles enter tip-first via a rocket mode.

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5′-triphosphate (ATP) facilitates non-equilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.

Collective behavior of self-propelled particles is observed on a microscale for swimmers such as sperm and bacteria as well as for protein filaments in motility assays. The properties of such systems depend both on their dimensionality and the interactions between their particles. We introduce a model for self-propelled rods in two dimensions that interact via a separation-shifted Lennard-Jones potential. Due to the finite potential barrier, the rods are able to cross. This model allows us to efficiently simulate systems of self-propelled rods that effectively move in two dimensions but can occasionally escape to the third dimension in order to pass each other. Our quasi-two-dimensional self-propelled particles describe a class of active systems that encompasses microswimmers close to a wall and filaments propelled on a substrate. Using Monte Carlo simulations, we first determine the isotropic-nematic transition for passive rods. Using Brownian dynamics simulations, we characterize cluster formation of self-propelled rods as a function of propulsion strength, noise, and energy barrier. Contrary to rods with an infinite potential barrier, an increase of the propulsion strength does not only favor alignment but also effectively decreases the potential barrier that prevents crossing of rods. We thus find a clustering window with a maximum cluster size at medium propulsion strengths.

Membrane budding and wrapping of particles, such as viruses and nano-particles, play a key role in intracellular transport and have been studied for a variety of biological and soft matter systems. We study nano-particle wrapping by numerical minimization of bending, surface tension, and adhesion energies. We calculate deformation and adhesion energies as a function of membrane elastic parameters and adhesion strength to obtain wrapping diagrams. We predict unwrapped, partially wrapped, and completely wrapped states for prolate and oblate ellipsoids with various aspect ratios and particle sizes. In contrast to spherical particles, where partially wrapped states exist only for finite surface tensions, partially wrapped states for ellipsoids occur already for tensionless membranes. In addition, the partially wrapped states are long-lived, because of an increased energy cost for wrapping of the highly curved tips. Our results suggest a lower uptake rate of ellipsoidal particles by cells and thereby a higher virulence of tubular viruses compared with icosahedral viruses, as well as co-operative budding of ellipsoidal particles on membranes.