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 nonequilibrium 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.ATP | imaging technique | membrane fluctuation | RBC | spectrin A s they travel through small blood vessels and organs, RBCs undergo repeated severe deformation. The coupling and interactions between the phospholipid bilayer and the spectrin network govern the deformability of RBCs (1). The fluid-like lipid bilayer is coupled to the two-dimensional spectrin network that comprises an approximately hexagonal lattice via protein junctional complexes. The RBC membrane is remarkably soft and elastic, and thus exhibits fluctuations with amplitudes of the order of tens of nanometers. The dynamics of the RBC membrane is strongly related to the membrane structure and mechanical properties and has been explored extensively (2-6). However, experimental results available to date on RBC membrane fluctuations have provided only limited information on select regions of the cell membrane with limited spatial and/or temporal resolution (7-9). No full-field measurements of membrane fluctuations in the entire RBC arising in response to well-controlled metabolic activity have been made so far and, consequently, different techniques have led to different interpretations of the mechanistic origins of dynamic RBC membrane fluctuations with and without metabolic activity (7-9).The RBC membrane is not a static but a metabolically regulated active structure. It is known that biochemical energy controls its static and dynamic characteristics. The presence of ATP is not only crucial in maintaining the biconcave shape of the RBC membrane (10), but was also shown to increase the dynamic membrane fluctuations (7, 9). However, the regulatory mechanism of ATP in RBC membranes still remains elusive. Furthermore, these static and dynamic effects of ATP on RBC membrane fluctuations have hitherto been regarded as separate phenomena and have never been explored simultaneously.Here, we present dynamic, full-field, and quantitative measurements of ATP effects on RBC membrane morphology and fluctuations. We show that in the presence of ATP, the RBC membrane fluctuations have a non-equilibrium, metabolic component in addition to a thermal o...

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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.

The blood stage malaria parasite, the merozoite, has a small window of opportunity during which it must successfully target and invade a human erythrocyte. The process of invasion is nonetheless remarkably rapid. To date, mechanistic models of invasion have focused predominantly on the parasite actomyosin motor contribution to the energetics of entry. Here, we have conducted a numerical analysis using dimensions for an archetypal merozoite to predict the respective contributions of the host-parasite interactions to invasion, in particular the role of membrane wrapping. Our theoretical modeling demonstrates that erythrocyte membrane wrapping alone, as a function of merozoite adhesive and shape properties, is sufficient to entirely account for the first key step of the invasion process, that of merozoite reorientation to its apex and tight adhesive linkage between the two cells. Next, parasite-induced reorganization of the erythrocyte cytoskeleton and release of parasite-derived membrane can also account for a considerable energetic portion of actual invasion itself, through membrane wrapping. Thus, contrary to the prevailing dogma, wrapping by the erythrocyte combined with parasite-derived membrane release can markedly reduce the expected contributions of the merozoite actomyosin motor to invasion. We therefore propose that invasion is a balance between parasite and host cell contributions, evolved toward maximal efficient use of biophysical forces between the two cells.

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 for 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.Comment: 10 pages, 11 figure

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membranemediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.