Fluid membranes can drive linear aggregation of adsorbed spherical nanoparticles

Curvature variation controls particle aggregation on fluid vesicles

Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the direction of largest curvature. Multiple particles form arcs, or, at large enough numbers, a complete ring surrounding the vesicle in its equatorial plane. The resulting vesicle shape resembles a snowman. Our results indicate that these physical interactions on membranes with anisotropic shapes can be exploited by cells to drive macromolecules to preferred regions of cellular or intracellular membranes, and utilized to initiate dynamic processes such as cell division. The same principle could be used to find the midplane of an artificial vesicle, as a first step towards dividing it into two equal parts.

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

Understanding the interaction between nanoparticles (NPs) and cell membranes is crucial for the design of NP-based drug delivery systems and for the assessment of the risks exerted by the NPs. Recent experimental and theoretical studies have shown that cell membranes can mediate attraction between NPs and form tubular structures to wrap multiple NPs. However, the cooperative wrapping process is still not well understood, and the shape effect of NPs is not considered. In this article, we use large-scale coarse-grained molecular dynamics (CGMD) simulations to study the cooperative wrapping of NPs when a varying number of NPs adhered to the membrane. Spherical, prolate and oblate NPs of different sizes are considered in this study. We find that, in addition to tubular structures, the membrane can form a pocket-like and a handle-like structure to wrap multiple NPs depending on the size and shape of the NPs. Furthermore, we find that NPs can mediate membrane hemifusion or fusion during this process. Our findings provide new insights into the interaction of NPs with the cell membrane.

Membrane structure formation induced by two types of banana-shaped proteins

The assembly of banana-shaped rodlike proteins on membranes and the associated membrane shape transformations are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between the assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number of inclusions of two types, corresponding to the curved rods of opposite curvatures, both for flat membranes and vesicles. Rods of the same type aggregate into linear assemblies perpendicular to the rod axis, leading to membrane tubulation. However, rods of the other type, those of opposite curvature, are attracted to the lateral sides of these assemblies, and stabilize a straight bump structure that prevents tubulation. When the two types of rods have almost opposite curvatures, the bumps attract one another, forming a striped structure. Positive surface tension is found to stabilize stripe formation. The simulation results agree well with the theoretical predictions provided the point-like curvatures of the model are scaled-down to account for the effective flexibility of the simulated rods.

Counterintuitive cooperative endocytosis of like-charged nanoparticles in cellular internalization: computer simulation and experiment

The nanoparticles (NPs) functionalized with charged ligands are of particular significance due to their potential drug/gene delivery and biomedical applications. However, the molecular mechanism of endocytosis of the charged NPs by cells, especially the effect of the NP-NP and NP-biomembrane interactions on the internalization pathways is still poorly understood. In this work, we systematically investigate the internalization behaviors of the positively charged NPs by combining experiment technology and dissipative particle dynamics (DPD) simulation. We experimentally find an interesting but highly counterintuitive phenomenon, i.e. the multiple positively charged NPs prefer to enter cells cooperatively although the like-charged NPs have obvious electrostatic repulsion. Furthermore, we adopt the DPD simulation to confirm the experimental findings, and reveal that the mechanism of the cooperative endocytosis between like-charged NPs is definitely caused by the interplay of particle size, the charged ligand density on particle surface and local concentration of NPs. Importantly, we not only observe the normal cooperative endocytosis of like-charged NPs in cell biomembrane like neutral NP case, but also predict the 'bud' cooperative endocytosis of like-charged NPs which is absence in the neutral NP case. The results indicate that electrostatic repulsion between the positively charged nanoparticles plays an important role in the 'bud' cooperative endocytosis of like-charged NPs.

Curvature-Driven Migration of Colloids on Tense Lipid Bilayers

Inspired by proteins that generate membrane curvature, sense the underlying membrane geometry, and migrate driven by curvature gradients, we explore the question: Can colloids, adhered to lipid bilayers, also sense and respond to membrane geometry? We report the migration of Janus microparticles adhered to giant unilamellar vesicles elongated to present spatially varying curvatures. In our experiments, colloids migrate only when the membranes are tense, suggesting that they migrate to minimize membrane area. By determining the energy dissipated along a trajectory, the energy field is inferred to depend on the local deviatoric curvature, like curvature driven capillary migration on interfaces between immiscible fluids. In this latter system, energy gradients are larger, so colloids move deterministically, whereas the paths traced by colloids on vesicles have significant fluctuations. By addressing the role of Brownian motion, we show that the observed migration is analogous to curvature driven capillary migration, with membrane tension playing the role of interfacial tension. Since this motion is mediated by membrane shape, it can be turned on and off by dynamically deforming the vesicle. While particle-particle interactions on lipid membranes have been considered in many contributions, we report here an exciting and previously unexplored modality to actively direct the migration of colloids to desired locations on lipid bilayers.

Membrane-mediated aggregation of anisotropically curved nanoparticles

Using systematic numerical simulations, we study the self-assembly of elongated curved nanoparticles on lipid vesicles. Our simulations are based on molecular dynamics of a coarse-grained implicit-solvent model of self-assembled lipid membranes with a Langevin thermostat. Here we consider only the case wherein the nanoparticle-nanoparticle interaction is repulsive, only the concave surface of the nanoparticle interacts attractively with the lipid head groups and only the outer surface of the vesicle is exposed to the nanoparticles. Upon their adhesion on the vesicle, the curved nanoparticles generate local curvature on the membrane. The resulting nanoparticle-generated membrane curvature leads in turn to nanoparticle self-assembly into two main types of aggregates corresponding to chain aggregates at low adhesion strengths and aster aggregates at high adhesion strength. The chain-like aggregates are due to the fact that at low values of adhesion strength, the nanoparticles prefer to lie parallel to each other. As the adhesion strength is increased, a splay angle between the nanoparticles is induced with a magnitude that increases with increasing adhesion strength. The origin of the splay angles between the nanoparticles is shown to be saddle-like membrane deformations induced by a tilt of the lipids around the nanoparticles. This phenomenon of membrane mediated self-assembly of anisotropically curved nanoparticles is explored for systems with varying nanoparticle number densities, adhesion strength, and nanoparticle intrinsic curvature.

Incorporation of Soft Particles into Lipid Vesicles: Effects of Particle Size and Elasticity

The interaction between particles and lipid biomembranes plays an essential role in many fields such as endocytosis, drug delivery, and intracellular traffic. Here we conduct a theoretical study on the incorporation of elastic particles of different sizes and rigidities into a lipid vesicle through adhesive wrapping. It is shown that while the incorporation of relatively small particles involves smooth shape evolution, the vesicle wrapping of large particles exhibits a discontinuous shape transition, followed by a protrusion of the vesicle membrane at infinitesimal cost of elastic deformation energy. Moreover, softer particles require stronger adhesion energy to achieve successful internalization and delay the onset of discontinuous shape transition to a higher wrapping degree. Depending on the adhesion energy, particle-vesicle size, and rigidity ratios, and the spontaneous curvature of the vesicle, a rich variety of wrapping phase diagrams consisting of stable and metastable states of no-wrapping, partial-wrapping, and full-wrapping are established. The underlying mechanism of the discontinuous shape transformation of the vesicle and the relation between the uptake proneness and uptake efficiency are discussed. These results shed further light on the elasticity effects in cellular uptake of elastic particles and may provide rational design guidelines for controlled endocytosis and diagnostics delivery.

Multipole analysis of the strain-mediated coupling between proteins adsorbed at tubular lipid membrane surface

The tubular lipid membranes (TLMs) pulled out from vesicles are often used in in vitro studies of the interactions between curvature-inducing proteins and highly curved membranes. The protein molecules adsorbed at the membrane surface deform the TLM and couple with each other due to the induced strain. Here we propose an approach which models the single curvature-inducing protein action on the lipid bilayer by the multipole, the superposition of the point forces applied to the membrane in the region of the protein adsorption. We show that to be localized in the area of the protein size at the TLM surface, the force multipoles satisfying the mechanical equilibrium conditions should be composed of three or more point forces. The protein coupling energy mediated by the membrane strain is studied in detail. In the region of the tubular membrane stability the maximal distance between two neighboring interacting protein-induced force multipoles is estimated to be of the order of the TLM cross section perimeter. In the vicinity of the TLM instability in the region of the vanishing stretching force applied to the TLM, the interaction radius increases drastically. The high affinity of the single curvature-inducing protein molecule to the regions in the vicinity of the TLM ends is explained and related to the boundary conditions in the experimental set-ups. The reasons for the aggregate formation on the membrane surface are also discussed.

How curvature-generating proteins build scaffolds on membrane nanotubes

Bin/Amphiphysin/Rvs (BAR) domain proteins control the curvature of lipid membranes in endocytosis, trafficking, cell motility, the formation of complex subcellular structures, and many other cellular phenomena. They form 3D assemblies that act as molecular scaffolds to reshape the membrane and alter its mechanical properties. It is unknown, however, how a protein scaffold forms and how BAR domains interact in these assemblies at protein densities relevant for a cell. In this work, we use various experimental, theoretical, and simulation approaches to explore how BAR proteins organize to form a scaffold on a membrane nanotube. By combining quantitative microscopy with analytical modeling, we demonstrate that a highly curving BAR protein endophilin nucleates its scaffolds at the ends of a membrane tube, contrary to a weaker curving protein centaurin, which binds evenly along the tube's length. Our work implies that the nature of local protein-membrane interactions can affect the specific localization of proteins on membrane-remodeling sites. Furthermore, we show that amphipathic helices are dispensable in forming protein scaffolds. Finally, we explore a possible molecular structure of a BAR-domain scaffold using coarse-grained molecular dynamics simulations. Together with fluorescence microscopy, the simulations show that proteins need only to cover 30-40% of a tube's surface to form a rigid assembly. Our work provides mechanical and structural insights into the way BAR proteins may sculpt the membrane as a high-order cooperative assembly in important biological processes.

Melting transition in lipid vesicles functionalised by mobile DNA linkers

We study phase behaviour of lipid-bilayer vesicles functionalised by ligand-receptor complexes made of synthetic DNA by introducing a modelling framework and a dedicated experimental platform. In particular, we perform Monte Carlo simulations that combine a coarse grained description of the lipid bilayer with state of art analytical models for multivalent ligand-receptor interactions. Using density of state calculations, we derive the partition function in pairs of vesicles and compute the number of ligand-receptor bonds as a function of temperature. Numerical results are compared to microscopy and fluorimetry experiments on large unilamellar vesicles decorated by DNA linkers carrying complementary overhangs. We find that vesicle aggregation is suppressed when the total number of linkers falls below a threshold value. Within the model proposed here, this is due to the higher configurational costs required to form inter-vesicle bridges as compared to intra-vesicle loops, which are in turn related to membrane deformability. Our findings and our numerical/experimental methodologies are applicable to the rational design of liposomes used as functional materials and drug delivery applications, as well as to study inter-membrane interactions in living systems, such as cell adhesion.

Lipid membrane-mediated attraction between curvature inducing objects

The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.

Hydrophilic nanoparticles stabilising mesophase curvature at low concentration but disrupting mesophase order at higher concentrations

Using high pressure small angle X-ray scattering (HP-SAXS), we have studied monoolein (MO) mesophases at 18 wt% hydration in the presence of 10 nm silica nanoparticles (NPs) at NP-lipid number ratios (ν) of 1 × 10(-6), 1 × 10(-5) and 1 × 10(-4) over the pressure range 1-2700 bar and temperature range 20-60 °C. In the absence of the silica NPs, the pressure-temperature (p-T) phase diagram of monoolein exhibited inverse bicontinuous cubic gyroid (Q), lamellar alpha (Lα), and lamellar crystalline (Lc) phases. The addition of the NPs significantly altered the p-T phase diagram, changing the pressure (p) and the temperature (T) at which the transitions between these mesophases occurred. In particular, a strong NP concentration effect on the mesophase behaviour was observed. At low NP concentration, the p-T region pervaded by the Q phase and the Lα-Q mixture increased, and we attribute this behaviour to the NPs forming clusters at the mesophase domain boundaries, encouraging transition to the mesophase with a higher curvature. At high NP concentrations, the Q phase was no longer observed in the p-T phase diagram. Instead, it was dominated by the lamellar (L) phases until the transition to a fluid isotropic (FI) phase at 60 °C at low pressure. We speculate that NPs formed aggregates with a "chain of pearls" structure at the mesophase domain boundaries, hindering transitions to the mesophases with higher curvatures. These observations were supported by small angle neutron scattering (SANS) and scanning electron microscopy (SEM). Our results have implications to nanocomposite materials and nanoparticle cellular entry where the interactions between NPs and organised lipid structures are an important consideration.

Long-range attraction of particles adhered to lipid vesicles

Many biological systems fold thin sheets of lipid membrane into complex three-dimensional structures. This microscopic origami is often mediated by the adsorption and self-assembly of proteins on a membrane. As a model system to study adsorption-mediated interactions, we study the collective behavior of micrometric particles adhered to a lipid vesicle. We estimate the colloidal interactions using a maximum likelihood analysis of particle trajectories. When the particles are highly wrapped by a tense membrane, we observe strong long-range attractions with a typical binding energy of 150k_{B}T and significant forces extending a few microns.

Shape deformation of lipid membranes by banana-shaped protein rods: Comparison with isotropic inclusions and membrane rupture

The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However, the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on the region of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membrane edge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradual change in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced by the rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesicle curvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles as well as formation of a high-genus vesicle.

Gold nanoparticles in model biological membranes: A computational perspective

The electronic, optical, catalytic, and magnetic properties of metal nanoparticles (NPs) make them extremely interesting for biomedical applications. In this rapidly moving field, monolayer-protected gold nanoparticles emerge both as a reference system and as promising candidates for drug and gene delivery, photothermal treatment, and imaging applications. Despite the technological relevance, there is still poor understanding of the molecular processes driving the interactions of metal nanoparticles with cells, and with cell membranes in particular. In this paper we review molecular-level computational studies of the interaction between monolayer-protected gold NPs and model lipid membranes. Our review comprises a brief description of the most relevant experimental results in this field and of the questions they raised, followed by a description of the computational achievements reported so far. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Rigidity of transmembrane proteins determines their cluster shape

Protein aggregation in cell membrane is vital for the majority of biological functions. Recent experimental results suggest that transmembrane domains of proteins such as α-helices and β-sheets have different structural rigidities. We use molecular dynamics simulation of a coarse-grained model of protein-embedded lipid membranes to investigate the mechanisms of protein clustering. For a variety of protein concentrations, our simulations under thermal equilibrium conditions reveal that the structural rigidity of transmembrane domains dramatically affects interactions and changes the shape of the cluster. We have observed stable large aggregates even in the absence of hydrophobic mismatch, which has been previously proposed as the mechanism of protein aggregation. According to our results, semiflexible proteins aggregate to form two-dimensional clusters, while rigid proteins, by contrast, form one-dimensional string-like structures. By assuming two probable scenarios for the formation of a two-dimensional triangular structure, we calculate the lipid density around protein clusters and find that the difference in lipid distribution around rigid and semiflexible proteins determines the one- or two-dimensional nature of aggregates. It is found that lipids move faster around semiflexible proteins than rigid ones. The aggregation mechanism suggested in this paper can be tested by current state-of-the-art experimental facilities.

Membrane tubule formation by banana-shaped proteins with or without transient network structure

In living cells, membrane morphology is regulated by various proteins. Many membrane reshaping proteins contain a Bin/Amphiphysin/Rvs (BAR) domain, which consists of a banana-shaped rod. The BAR domain bends the biomembrane along the rod axis and the features of this anisotropic bending have recently been studied. Here, we report on the role of the BAR protein rods in inducing membrane tubulation, using large-scale coarse-grained simulations. We reveal that a small spontaneous side curvature perpendicular to the rod can drastically alter the tubulation dynamics at high protein density, whereas no significant difference is obtained at low density. A percolated network is intermediately formed depending on the side curvature. This network suppresses tubule protrusion, leading to the slow formation of fewer tubules. Thus, the side curvature, which is generated by protein–protein and membrane–protein interactions, plays a significant role in tubulation dynamics. We also find that positive surface tensions and the vesicle membrane curvature can stabilize this network structure by suppressing the tubulation.

Partial wrapping and spontaneous endocytosis of spherical nanoparticles by tensionless lipid membranes

Computer simulations of an implicit-solvent particle-based model are performed to investigate the interactions between small spherical nanoparticles and tensionless lipid bilayers. We found that nanoparticles are either unbound, wrapped by the bilayer, or endocytosed. The degree of wrapping increases with increasing the adhesion strength. The transition adhesion strength between the unbound and partially wrapped states decreases as the nanoparticle diameter is increased. We also observed that the transition adhesion strength between the wrapped states and endocytosis state decreases with increasing the nanoparticle diameter. The partial wrapping of the nanoparticles by the tensionless bilayer is explained by an elastic theory which accounts for the fact that the interaction between the nanoparticle and the bilayer extends beyond the contact region. The theory predicts that for small nanoparticles, the wrapping angle increases continuously with increasing the adhesion strength. However, for relatively large nanoparticles, the wrapping angle exhibits a discontinuity between weakly and strongly wrapped states. The size of the gap in the wrapping angle between the weakly wrapped and strongly wrapped states increases with decreasing the range of nanoparticle-bilayer interaction.

When Physics Takes Over: BAR Proteins and Membrane Curvature

Cell membranes become highly curved during membrane trafficking, cytokinesis, infection, immune response, or cell motion. Bin/amphiphysin/Rvs (BAR) domain proteins with their intrinsically curved and anisotropic shape are involved in many of these processes, but with a large spectrum of modes of action. In vitro experiments and multiscale computer simulations have contributed in identifying a minimal set of physical parameters, namely protein density on the membrane, membrane tension, and membrane shape, that control how bound BAR domain proteins behave on the membrane. In this review, we summarize the multifaceted coupling of BAR proteins to membrane mechanics and propose a simple phase diagram that recapitulates the effects of these parameters.

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.

Aggregation of nanoparticles on one and two-component bilayer membranes

Using dissipative particle dynamics simulations the aggregation of nanoparticles on single and two-component bilayers is investigated. For a uniform bilayer the aggregation of nanoparticles depends strongly on the location of the particles in the bilayer; particles residing on the bilayer exterior cluster strongly under the influence of bilayer-mediated interactions, whereas the interaction between the particles in the bilayer interior is significantly weaker leading to more loosely bound, dynamic aggregates. The aggregation of nanoparticles on two-component bilayers composed of immiscible components changes due to competition between nanoparticle clustering and their adsorption on the boundary between the bilayer components. This reduces the size of the nanoparticle clusters formed on the bilayer exterior, with the clusters adhering onto the boundary between the bilayer components. Due to their weaker attraction nanoparticles in the interior of a mixed bilayer no longer aggregate and instead form strings along the boundary between the two bilayer components. Nanoparticles with an affinity to one bilayer component nucleate small domains of their favoured component around themselves. For asymmetric mixtures this leads to a notable change in the aggregation behaviour of the nanoparticles.

Membrane tension controls the assembly of curvature-generating proteins

Proteins containing a Bin/Amphiphysin/Rvs (BAR) domain regulate membrane curvature in the cell. Recent simulations have revealed that BAR proteins assemble into linear aggregates, strongly affecting membrane curvature and its in-plane stress profile. Here, we explore the opposite question: do mechanical properties of the membrane impact protein association? By using coarse-grained molecular dynamics simulations, we show that increased surface tension significantly impacts the dynamics of protein assembly. While tensionless membranes promote a rapid formation of long-living linear aggregates of N-BAR proteins, increase in tension alters the geometry of protein association. At high tension, protein interactions are strongly inhibited. Increasing surface density of proteins leads to a wider range of protein association geometries, promoting the formation of meshes, which can be broken apart with membrane tension. Our work indicates that surface tension may play a key role in recruiting proteins to membrane-remodelling sites in the cell.

BAR domain proteins are known to reshape cell membranes. Using coarse-grained molecular dynamics simulations, Simunovic and Voth demonstrate that membrane tension strongly affects the association of BAR proteins, in turn controlling their recruitment to membrane-remodelling sites.

Transport of spherical colloids in layered phases of binary mixtures with rod-like particles

The transport properties of colloids in anisotropic media constitute a general problem of fundamental interest in experimental sciences, with a broad range of technological applications. This work investigates the transport of soft spherical colloids in binary mixtures with rod-like particles by means of Monte Carlo and Brownian Dynamics simulations. Layered phases are considered, that range from smectic phases to lamellar phases, depending on the molar fraction of the spherical particles. The investigation serves to characterize the distinct features of transport within layers versus those of transport across neighboring layers, both of which are neatly differentiated. The insertion of particles into layers and the diffusion across them occur at a smaller rate than the intralayer diffusion modulated by the formation of transitory cages in its initial stages. Collective events, in which two or more colloids diffuse across layers in a concerted way, are described as a non-negligible process in these fluids.

Intake of silica nanoparticles by giant lipid vesicles: influence of particle size and thermodynamic membrane state

The uptake of nanoparticles into cells often involves their engulfment by the plasma membrane and a fission of the latter. Understanding the physical mechanisms underlying these uptake processes may be achieved by the investigation of simple model systems that can be compared to theoretical models. Here, we present experiments on a massive uptake of silica nanoparticles by giant unilamellar lipid vesicles (GUVs). We find that this uptake process depends on the size of the particles as well as on the thermodynamic state of the lipid membrane. Our findings are discussed in the light of several theoretical models and indicate that these models have to be extended in order to capture the interaction between nanomaterials and biological membranes correctly.

How hydrophobic nanoparticles aggregate in the interior of membranes: A computer simulation

Lipid-based dispersion of hydrophobic nanoparticles (NPs) not only gives fundamental insight into how nanomaterials distribute in live cells and organisms, but also provides a quite general route to designing nanocarrier agents in triggered drug delivery and medical imaging. It is not clearly understood how hydrophobic NPs arrange in the interior of a membrane. In this paper, with computer simulation techniques, we demonstrate that hydrophobic NPs having a diameter compared to the hydrophobic thickness of the membrane are capable of clustering in the hydrophobic interior of a cell membrane. Except from the isotropic aggregation, an unexpected linear arrangement of spherical NPs, which is still not found from experiments, is identified here. The free-energy costs associated with linear and isotropic aggregations are computed explicitly to interpret aggregation behavior and the obtained phase diagrams give us a comprehensive understanding of where linear aggregation is expected. In this work we also shows that NP size and membrane tension play key roles in determining the NP aggregate, while the effects of NP concentration and membrane curvature seem to be relatively weak.

Binding to semiflexible polymers: a novel method to control the structures of small numbers of building blocks

Through the molecular dynamics simulation method, we demonstrate that long semi-flexible polymer chains can serve as an effective soft elastic medium for manipulating the ordered structures of small numbers of building blocks, which can be easily controlled by the chain bending stiffness. For two spherical particles in a polymer-particle mixture, three types of local organization are identified: monomer level tight particle bridging, direct contact aggregation, and dispersion. For small numbers of spherical particles in a polymer-particle mixture, the ordered structures of particles, such as spherical and linear particle aggregations, depend mainly on chain bending stiffness. For non-spherical building blocks, the relative orientations of neighboring building blocks are also strongly affected by chain bending stiffness. These results can help us to understand the complexity of the self-assembly of small numbers of building blocks in polymer-particle mixtures and the gene activity in living cells, as well as to construct novel materials in the nanotechnology field.

Wrapping of nanoparticles by membranes

How nanoparticles interact with biomembranes is central for understanding their bioactivity. Biomembranes wrap around nanoparticles if the adhesive interaction between the nanoparticles and membranes is sufficiently strong to compensate for the cost of membrane bending. In this article, we review recent results from theory and simulations that provide new insights on the interplay of bending and adhesion energies during the wrapping of nanoparticles by membranes. These results indicate that the interplay of bending and adhesion during wrapping is strongly affected by the interaction range of the particle-membrane adhesion potential, by the shape of the nanoparticles, and by shape changes of membrane vesicles during wrapping. The interaction range of the particle-membrane adhesion potential is crucial both for the wrapping process of single nanoparticles and the cooperative wrapping of nanoparticles by membrane tubules.

Protein-mediated transformation of lipid vesicles into tubular networks

Key cellular processes are frequently accompanied by protein-facilitated shape changes in the plasma membrane. N-BAR-domain protein modules generate curvature by means of complex interactions with the membrane surface. The way they assemble and the mechanism by which they operate are largely dependent on their binding density. Although the mechanism at lower densities has recently begun to emerge, how membrane scaffolds form at high densities remains unclear. By combining electron microscopy and multiscale simulations, we show that N-BAR proteins at high densities can transform a lipid vesicle into a 3D tubular network. We show that this process is a consequence of excess adhesive energy combined with the local stiffening of the membrane, which occurs in a narrow range of mechanical properties of both the membrane and the protein. We show that lipid diffusion is significantly reduced by protein binding at this density regime and even more in areas of high Gaussian curvature, indicating a potential effect on molecular transport in cells. Finally, we reveal that the breaking of the bilayer topology is accompanied by the nematic arrangement of the protein on the surface, a structural motif that likely drives the formation of reticular structures in living cells.

A universal law for cell uptake of one-dimensional nanomaterials

Understanding cell interaction with one-dimensional nanomaterials, including nanotubes, nanowires, nanofibers, filamentous bacteria, and certain nanoparticle chains, has fundamental importance to many applications such as biomedical diagnostics, therapeutics, and nanotoxicity. Here we show that cell uptake of one-dimensional nanomaterials via receptor-mediated endocytosis is dominated by a single dimensionless parameter that scales with the membrane tension and radius of the nanomaterial and inversely with the membrane bending stiffness. It is shown that as cell membrane internalizes one-dimensional nanomaterials the uptake follows a near-perpendicular entry mode at small membrane tension but it switches to a near-parallel interaction mode at large membrane tension.

Linear aggregation of proteins on the membrane as a prelude to membrane remodeling

Adhesion and insertion of curvature-mediating proteins can induce dramatic structural changes in cell membranes, allowing them to participate in several key cellular tasks. The way proteins interact to generate curvature remains largely unclear, especially at early stages of membrane remodeling. Using a coarse-grained model of Bin/amphiphysin/Rvs domain with an N-terminal helix (N-BAR) interacting with flat membranes and vesicles, we demonstrate that at low protein surface densities, binding of N-BAR domain proteins to the membrane is followed by a linear aggregation and the formation of meshes on the surface. In this process, the proteins assemble at the base of emerging membrane buds. Our work shows that beyond a more straightforward scaffolding mechanism at high bound densities, the interplay of anisotropic interactions and the local stress imposed by the N-BAR proteins results in deep invaginations and endocytic vesicular bud-like deformations, an order of magnitude larger than the size of the individual protein. Our results imply that by virtue of this mechanism, cell membranes may achieve rapid local increases in protein concentration.

An unusual pathway for the membrane wrapping of rodlike nanoparticles and the orientation- and membrane wrapping-dependent nanoparticle interaction

Although rapid progress has been made in understanding the interaction of nanoparticles (NPs) with lipid membrane, little is known about the interaction between neighboring NPs on the membrane. With the aid of computer simulation techniques, in this work we systematically investigate the membrane mediated interaction between anisotropic NPs with at least one dimension with the size of several nanometers, and find that the interaction between neighboring NPs is orientation- and membrane wrapping-dependent. For rodlike NPs with a weak NP-membrane adhesion strength that the membrane wrapping of NPs occurs at a slow rate and has a limited extent, the orientation-dependent interaction between two neighboring anisotropic NPs arises purely as a result of non-homogeneous distribution of membrane curvature induced by anisotropic NP adsorption. While for rodlike NPs with a strong NP-membrane adhesion, the rapid wrapping rate and extensive wrapping cause the different responses of upper and lower leaflets of the membrane to the NP adsorption, which force the NPs to enter the hydrophobic part of the membrane and lead to the formation of inverted micelles surrounding the NPs. The unusual asymmetrical wrapping also induces orientation-dependent NP interaction, which shows a short-range repulsion, intermediate-range attraction and long-range repulsion for rodlike NPs.

Dynamics of self-assembly of model viral capsids in the presence of a fluctuating membrane

A coarse-grained computational model is used to investigate the effect of a fluctuating fluid membrane on the dynamics of patchy-particle assembly into virus capsid-like cores. Results from simulations for a broad range of parameters are presented, showing the effect of varying interaction strength, membrane stiffness, and membrane viscosity. Furthermore, the effect of hydrodynamic interactions is investigated. Attraction to a membrane may promote assembly, including for subunit interaction strengths for which it does not occur in the bulk, and may also decrease single-core assembly time. The membrane budding rate is strongly increased by hydrodynamic interactions. The membrane deformation rate is important in determining the finite-time yield. Higher rates may decrease the entropic penalty for assembly and help guide subunits toward each other but may also block partial cores from being completed. For increasing subunit interaction strength, three regimes with different effects of the membrane are identified.

Self-assembly of binary nanoparticles on soft elastic shells

The self-assembly behaviors and phase transitions of binary nanoparticles (NPs) adsorbed on a soft elastic shell are investigated through molecular dynamics simulation. The conformations of adsorbed binary NPs depend on the bending energy K(b) of elastic shell and the binding energy D0 between the NPs and the elastic shell. The ordered structures of binary NPs are observed at the moderate adhesive strength and bending energy, in which the small NPs are located near the vertices of regular pentagons as well as the large NPs are distributed along the sides of the regular pentagons. The shape of soft elastic shell can be adjusted by adding the adsorbed binary NPs, and this investigation can provide an effective way to regulate and reshape surfaces or membranes with the sizes in the micrometer range or smaller.

Nanoparticle-induced permeability of lipid membranes

Monte Carlo simulations using the bond fluctuation method with explicit solvent reveal the mechanism of enhanced permeability of lipid bilayers induced by the adsorption of nanoparticles with controlled hydrophobicity. Simulation results indicate an adsorption transition of nanoparticles on the bilayer in a certain range of relative degree of hydrophobicity. In this range the nanoparticles can translocate through the bilayer, reversibly destabilizing the structure of the bilayer and inducing enhanced permeability for water and small solutes. This transition is broader for amphiphilic nanoparticles.

Exact Relation between Potential of Mean Force and Free-Energy Profile

We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobian scale factor and Leibnizian contributions must also be considered, as well a Fixman term with correct mass dependence. Our newly derived relations are verified with new non-trivial benchmark numerical examples for which exact results can be computed, and compared with relations available in the literature that turn out to exhibit significant deviations from the exact values.

Mechanism of membrane tube formation induced by adhesive nanocomponents

We report numerical simulations of membrane tubulation driven by large colloidal particles. Using Monte Carlo simulations we study how the process depends on particle size and binding strength, and present accurate free energy calculations to sort out how tube formation compares with the competing budding process. We find that tube formation is a result of the collective behavior of the particles adhering on the surface, and it occurs for binding strengths that are smaller than those required for budding. We also find that long linear aggregates of particles forming on the membrane surface act as nucleation seeds for tubulation by lowering the free energy barrier associated to the process.

Tubulation and aggregation of spherical nanoparticles adsorbed on vesicles

How nanoparticles interact with biomembranes is central for understanding their bioactivity. In this Letter, we report novel tubular membrane structures induced by adsorbed spherical nanoparticles, which we obtain from energy minimization. The membrane tubules enclose linear aggregates of particles and protrude into the vesicles. The high stability of the particle-filled tubules implies strongly attractive, membrane-mediated interactions between the particles. The tubular structures may provide a new route to encapsulate nanoparticles reversibly in vesicles.

Influence of fluctuating membranes on self-assembly of patchy colloids

A coarse-grained computational model is used to investigate the effect of a fluid membrane on patchy-particle assembly into biologically relevant structures motivated by viral cores and clathrin. For cores, we demonstrate a nonmonotonic dependence of the promotion of assembly on membrane stiffness. If the membrane is significantly deformable, cores are enveloped in buds, although this effect is suppressed for very flexible membranes. In the less deformable regime, we observe no marked enhancement for cores, even for strong adhesion to the surface. For clathrinlike particles, we again observe the formation of buds, whose morphology depends on membrane flexibility.