Wrapping anisotropic microgel particles in lipid membranes: Effects of particle shape and membrane rigidity.

Cellular engulfment and uptake of macromolecular assemblies or nanoparticles via endocytosis can be associated to both healthy and disease-related biological processes as well as delivery of drug nanoparticles and potential nanotoxicity of pollutants. Depending on the physical and chemical properties of the system, the adsorbed particles may remain at the membrane surface, become wrapped by the membrane, or translocate across the membrane through an endocytosis-like process. In this paper, we address the question of how the wrapping of colloidal particles by lipid membranes can be controlled by the shape of the particles, the particle-membrane adhesion energy, the membrane phase behavior, and the membrane-bending rigidity. We use a model system composed of soft core-shell microgel particles with spherical and ellipsoidal shapes, together with phospholipid membranes with varying composition. Confocal microscopy data clearly demonstrate how tuning of these basic properties of particles and membranes can be used to direct wrapping and membrane deformation and the organization of the particles at the membrane. The deep-wrapped states are more favorable for ellipsoidal than for spherical microgel particles of similar volume. Theoretical calculations for fixed adhesion strength predict the opposite behavior-wrapping becomes more difficult with increasing aspect ratio. The comparison with the experiments implies that the microgel adhesion strength must increase with increasing particle stretching. Considering the versatility offered by microgels systems to be synthesized with different shapes, functionalizations, and mechanical properties, the present findings further inspire future studies involving nanoparticle-membrane interactions relevant for the design of novel biomaterials and therapeutic applications.

Membrane-Mediated Interactions Between Nonspherical Elastic Particles.

The transport of particles across lipid-bilayer membranes is important for biological cells to exchange information and material with their environment. Large particles often get wrapped by membranes, a process which has been intensively investigated in the case of hard particles. However, many particles in vivo and in vitro are deformable, e.g., vesicles, filamentous viruses, macromolecular condensates, polymer-grafted nanoparticles, and microgels. Vesicles may serve as a generic model system for deformable particles. Here, we study nonspherical vesicles with various sizes, shapes, and elastic properties at initially planar lipid-bilayer membranes. Using the Helfrich Hamiltonian, triangulated membranes, and energy minimization, we predict the interplay of vesicle shapes and wrapping states. Increasing particle softness enhances the stability of shallow-wrapped and deep-wrapped states over nonwrapped and complete-wrapped states. The free membrane mediates an interaction between partial-wrapped vesicles. For the pair interaction between deep-wrapped vesicles, we predict repulsion. For shallow-wrapped vesicles, we predict attraction for tip-to-tip orientation and repulsion for side-by-side orientation. Our predictions may guide the design and fabrication of deformable particles for efficient use in medical applications, such as targeted drug delivery.

Active particles induce large shape deformations in giant lipid vesicles.

Biological cells generate intricate structures by sculpting their membrane from within to actively sense and respond to external stimuli or to explore their environment1-4. Several pathogenic bacteria also provide examples of how localized forces strongly deform cell membranes from inside, leading to the invasion of neighbouring healthy mammalian cells5. Giant unilamellar vesicles have been successfully used as a minimal model system with which to mimic biological cells6-11, but the realization of a minimal system with localized active internal forces that can strongly deform lipid membranes from within and lead to dramatic shape changes remains challenging. Here we present a combined experimental and simulation study that demonstrates how self-propelled particles enclosed in giant unilamellar vesicles can induce a plethora of non-equilibrium shapes and active membrane fluctuations. Using confocal microscopy, in the experiments we explore the membrane response to local forces exerted by self-phoretic Janus microswimmers. To quantify dynamic membrane changes, we perform Langevin dynamics simulations of active Brownian particles enclosed in thin membrane shells modelled by dynamically triangulated surfaces. The most pronounced shape changes are observed at low and moderate particle loadings, with the formation of tether-like protrusions and highly branched, dendritic structures, whereas at high volume fractions globally deformed vesicle shapes are observed. The resulting state diagram predicts the conditions under which local internal forces generate various membrane shapes. A controlled realization of such distorted vesicle morphologies could improve the design of artificial systems such as small-scale soft robots and synthetic cells.

Filamentous active matter: Band formation, bending, buckling, and defects.

Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

Osmotic Concentration-Controlled Particle Uptake and Wrapping-Induced Lysis of Cells and Vesicles.

In vivo, high protein and ion concentrations determine the preferred volumes of cells, organelles, and vesicles. Deformations of their lipid-bilayer membranes by nanoparticle wrapping reduce the interior volumes available to solutes and thus induce large osmotic pressure differences. Osmotic concentration can therefore be an important control parameter for wrapping of nanoparticles. We employ a curvature-elasticity model of the membrane and contact interaction with spherical particles to study their wrapping at initially spherical vesicles. Although the continuous particle-binding transition is independent of the presence of solutes, the discontinuous envelopment transition shifts to higher adhesion strengths and the corresponding energy barrier increases with increasing osmotic concentration. High osmotic concentrations stabilize partial-wrapped, membrane-bound states for both, particle attachment to the inside and the outside. In this regime, wrapping of particles controls membrane tension, with power-law dependencies on osmotic concentration and adhesion strength. For high adhesion strengths, particle wrapping can lead to the opening of mechanosensitive channels in cell membranes and to lysis. Membrane tension-induced stabilization of partial-wrapped states as well as wrapping-induced lysis play important roles not only for desired mechano-bacteriocidal effects of engineered nanomaterials but may also determine viral burst sizes of bacteria and control endocytosis for mammalian cells.

Chronology of motor-mediated microtubule streaming.

We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.

Collective behavior of self-propelled rods with quorum sensing.

Active agents-like phoretic particles, bacteria, sperm, and cytoskeletal filaments in motility assays-show a large variety of motility-induced collective behaviors, such as aggregation, clustering, and phase separation. The behavior of dense suspensions of engineered phoretic particles and of bacteria during biofilm formation is determined by two qualitatively different physical mechanisms: (i) volume exclusion (short-range steric repulsion) and (ii) quorum sensing (longer-range reduced propulsion due to alteration of the local chemical environment). To systematically characterize such systems, we study semi-penetrable self-propelled rods in two dimensions, with a propulsion force that decreases with increasing local rod density, by employing Brownian dynamics simulations. Volume exclusion and quorum sensing both lead to phase separation; however, the structure of the systems and the rod dynamics vastly differ. Quorum sensing enhances the polarity of the clusters, induces perpendicularity of rods at the cluster borders, and enhances cluster formation. For systems where the rods essentially become passive at high densities, formation of asters and stripes is observed. Systems of rods with larger aspect ratios show more ordered structures compared to those with smaller aspect ratios, due to their stronger alignment, with almost circular asters for strongly density-dependent propulsion force. With increasing range of the quorum-sensing interaction, the local density decreases, asters become less stable, and polar hedgehog clusters and clusters with domains appear.

Nanomaterial interactions with biomembranes: Bridging the gap between soft matter models and biological context.

Synthetic polymers, nanoparticles, and carbon-based materials have great potential in applications including drug delivery, gene transfection, in vitro and in vivo imaging, and the alteration of biological function. Nature and humans use different design strategies to create nanomaterials: biological objects have emerged from billions of years of evolution and from adaptation to their environment resulting in high levels of structural complexity; in contrast, synthetic nanomaterials result from minimalistic but controlled design options limited by the authors' current understanding of the biological world. This conceptual mismatch makes it challenging to create synthetic nanomaterials that possess desired functions in biological media. In many biologically relevant applications, nanomaterials must enter the cell interior to perform their functions. An essential transport barrier is the cell-protecting plasma membrane and hence the understanding of its interaction with nanomaterials is a fundamental task in biotechnology. The authors present open questions in the field of nanomaterial interactions with biological membranes, including: how physical mechanisms and molecular forces acting at the nanoscale restrict or inspire design options; which levels of complexity to include next in computational and experimental models to describe how nanomaterials cross barriers via passive or active processes; and how the biological media and protein corona interfere with nanomaterial functionality. In this Perspective, the authors address these questions with the aim of offering guidelines for the development of next-generation nanomaterials that function in biological media.

Nanoparticle wrapping at small non-spherical vesicles: curvatures at play.

Nanoparticles in biological systems encounter lipid-bilayer membranes as barriers. They interact with plasma membranes, membranous organelles, such as the endoplasmic reticulum and the Golgi apparatus, the nucleus, and intracellular and extracellular vesicles, such as autophagosomes, lysosomes, and exosomes. Extracellular vesicles have recently attracted particular attention, as they are involved in the transmission of biological signals and as regulators for biological processes. For example, exosomes, small vesicles containing proteins, mRNA, and miRNA, that are released by cells into the extracellular environment, have been suggested to participate in tumor metastasis. Furthermore, vesicles can be applied as targeted-drug-delivery systems. We systematically characterize wrapping of spherical nanoparticles that enter and exit vesicles, depending on particle size, vesicle size, vesicle reduced volume, and membrane spontaneous curvature. We predict the complex wrapping behavior, in particular for large particle-to-vesicle size ratios, where the shape changes of the free membrane contribute significantly to the deformation energy and where nanoparticle wrapping transitions and vesicle shape transitions are coupled. Partial-wrapped membrane-bound particles impose boundary conditions on the membrane that stabilise oblates and stomatocytes for particle entry, and prolates and stomatocytes for particle exit. Our results suggest that nanoparticles may stimulate autophagocytic engulfment, which would facilitate transport of the nanoparticles into lysosomes and would lead to subsequent degradation of nanoparticle-attached proteins.

Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors.

Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.

Complex self-propelled rings: a minimal model for cell motility.

Collective behavior of active matter is observed for self-propelled particles, such as vibrated disks and active Brownian particles, as well as for cytoskeletal filaments in motile cells. Here, a system of quasi two-dimensional penetrable self-propelled rods inside rigid rings is used to construct a complex self-propelled particle. The rods interact sterically with each other and with a stationary or mobile ring via a separation-shifted Lennard-Jones potential. They either have a sliding attachment to the inside of the ring at one of their ends, or can move freely within the ring confinement. We study the inner structure and dynamics of the mobile self-propelled rings. We find that these complex particles cannot only be characterized as active Brownian particles, but can also exhibit cell-like motility: random walks, persistent motion, circling, and run-and-circle motion.

Capillary assembly of microscale ellipsoidal, cuboidal, and spherical particles at interfaces.

Micron-sized anisotropic particles with homogeneous surface properties at a fluid interface can deform the interface due to their shape. The particles thereby create excess interfacial area and interact in order to minimize this area, which lowers the total interfacial energy. We present a systematic investigation of the interface deformations around single ellipsoidal particles and cuboidal particles with rounded edges in the near field for various contact angles and particle aspect ratios. The correlation of these deformations with capillary bond energies-the interaction energies of two particles at contact-quantifies the relation between the interactions and the near-field deformations. We characterize the interactions using effective power laws and investigate how anisotropic particles self-assemble by capillary forces. Interface deformations and particle interactions for cuboidal particles are weaker compared with those for ellipsoidal particles with the same aspect ratios. For both particle shapes, the bound state in side-by-side orientation is most stable, while the interaction in tip-to-side orientation is repulsive. Furthermore, we find capillary attraction between spherical and ellipsoidal particles. Our calculations therefore suggest cluster formation of spherical and ellipsoidal particles, which elucidates the role of spherical particles as stoppers for the growth of worm-like chains of ellipsoidal particles. The interaction between spherical and ellipsoidal particles might also explain the suppression of the "coffee-ring effect" that has been observed for evaporating droplets with mixtures of spherical and ellipsoidal particles. In general, our calculations of the near-field interactions complement previous calculations in the far field and help to predict colloidal assembly and rheological properties of particle-laden interfaces.

Membrane-wrapping contributions to malaria parasite invasion of the human erythrocyte.

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.

Interfacing electrogenic cells with 3D nanoelectrodes: position, shape, and size matter.

An in-depth understanding of the interface between cells and nanostructures is one of the key challenges for coupling electrically excitable cells and electronic devices. Recently, various 3D nanostructures have been introduced to stimulate and record electrical signals emanating from inside of the cell. Even though such approaches are highly sensitive and scalable, it remains an open question how cells couple to 3D structures, in particular how the engulfment-like processes of nanostructures work. Here, we present a profound study of the cell interface with two widely used nanostructure types, cylindrical pillars with and without a cap. While basic functionality was shown for these approaches before, a systematic investigation linking experimental data with membrane properties was not presented so far. The combination of electron microscopy investigations with a theoretical membrane deformation model allows us to predict the optimal shape and dimensions of 3D nanostructures for cell-chip coupling.

Shape and orientation matter for the cellular uptake of nonspherical particles.

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.

Fluctuation pressure of biomembranes in planar confinement.

The fluctuation pressure of a lipid-bilayer membrane is important for the stability of lamellar phases and the adhesion of membranes to surfaces. In contrast to many theoretical studies, which predict a decrease of the pressure with the cubed inverse distance between the membranes, Freund suggested very recently a linear inverse distance dependence [Proc. Natl. Acad. Sci. USA 110, 2047 (2013)]. We address this discrepancy by performing Monte Carlo simulations for a membrane model discretized on a square lattice and employ the wall theorem to evaluate the pressure for a single membrane between parallel walls. For distances that are small compared with the lattice constant, the pressure indeed depends on the inverse distance as predicted by Freund. For intermediate distances, the pressure depends on the cubed inverse distance as predicted by Helfrich [Z. Naturforsch. A 33, 305 (1978)]. Here, the crossover length between the two regimes is a molecular length scale. Finally, for distances large compared with the mean squared fluctuations of the membrane, the entire membrane acts as a soft particle and the pressure on the walls again depends linearly on the inverse distance.

Confinement effects in block copolymer modified bicontinuous microemulsions.

It has been established that the addition of amphiphilic diblock copolymers has a boosting effect in bicontinuous microemulsions by decreasing the minimum amount of surfactant needed to solubilize equal volumes of oil and water. The strength of the polymer effect was found to be about twice larger than the theoretical prediction. This discrepancy is explained by confinement. Previous experimental studies always considered large oil and water domains of size d compared to the typical polymer end-to-end radius, R(ee). The ratio of these two parameters R(ee)/d defines the confinement parameter. We investigated the sensitivity of the polymer influence extending the range of confinement. We combined macroscopic observations of the phase behavior with microscopic measurements of the structure by small-angle neutron scattering (SANS). Both results were compared with computer simulations on the basis of the theoretical concept of Helfrich. The simulations predict an enhanced sensitivity of the polymer at medium confinement and a reversed behavior at larger confinement. The higher sensitivity at medium confinement is only slightly visible experimentally, whereas the reversed behavior (antiboosting) is clearly present. Finally, a comparison with homopolymer addition showed a common high confinement behavior for diblock copolymers and for homopolymers.

Collective behavior of penetrable self-propelled rods in two dimensions.

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.

Curling and local shape changes of red blood cell membranes driven by cytoskeletal reorganization.

Human red blood cells (RBCs) lack the actin-myosin-microtubule cytoskeleton that is responsible for shape changes in other cells. Nevertheless, they can display highly dynamic local deformations in response to external perturbations, such as those that occur during the process of apical alignment preceding merozoite invasion in malaria. Moreover, after lysis in divalent cation-free media, the isolated membranes of ruptured ghosts show spontaneous inside-out curling motions at the free edges of the lytic hole, leading to inside-out vesiculation. The molecular mechanisms that drive these rapid shape changes are unknown. Here, we propose a molecular model in which the spectrin filaments of the RBC cortical cytoskeleton control the sign and dynamics of membrane curvature depending on whether the ends of the filaments are free or anchored to the bilayer. Computer simulations of the model reveal that curling, as experimentally observed, can be obtained either by an overall excess of weakly-bound filaments throughout the cell, or by the flux of such filaments toward the curling edges. Divalent cations have been shown to arrest the curling process, and Ca2+ ions have also been implicated in local membrane deformations during merozoite invasion. These effects can be replicated in our model by attributing the divalent cation effects to increased filament-membrane binding. This process converts the curl-inducing loose filaments into fully bound filaments that arrest curling. The same basic mechanism can be shown to account for Ca2+-induced local and dynamic membrane deformations in intact RBCs. The implications of these results in terms of RBC membrane dynamics under physiological, pathological, and experimental conditions is discussed.

Metabolic remodeling of the human red blood cell membrane.

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.