Lipid membrane-mediated attraction between curvature inducing objects

Nonadditivity in Many-Body Interactions between Membrane-Deforming Spheres Increases Disorder

Membrane-induced interactions play an important role in organizing membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their nonadditive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The confined colloidal particles cause a large deformation of the membrane while not being physicochemically attached to it and interact through it. Two particles attract with a maximum force of 0.2 pN. For three particles, compact equilateral triangles were preferred over linear arrangements. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, at the same time, diffusivity of the particles increases. Our experiments show that the nonadditive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

Shape equilibria of vesicles with rigid planar inclusions

Motivated by recent studies of two-phase lipid vesicles possessing 2D solid domains integrated within a fluid bilayer phase, we study the shape equilibria of closed vesicles possessing a single planar, circular inclusion. While 2D solid elasticity tends to expel Gaussian curvature, topology requires closed vesicles to maintain an average, non-zero Gaussian curvature leading to an elementary mechanism of shape frustration that increases with inclusion size. We study elastic ground states of the Helfrich model of the fluid-planar composite vesicles, analytically and computationally, as a function of planar fraction and reduced volume. Notably, we show that incorporation of a planar inclusion of only a few percent dramatically shifts the ground state shapes of vesicles from predominantly prolate to oblate, and moreover, shifts the optimal surface-to-volume ratio far from spherical shapes. We show that for sufficiently small planar inclusions, the elastic ground states break symmetry via a complex variety of asymmetric oblate, prolate, and triaxial shapes, while inclusion sizes above about 8% drive composite vesicles to adopt axisymmetric oblate shapes. These predictions cast useful light on the emergent shape and mechanical responses of fluid-solid composite vesicles.

Highly Ordered Nanoassemblies of Janus Spherocylindrical Nanoparticles Adhering to Lipid Vesicles

In recent years, there has been a heightened interest in the self-assembly of nanoparticles (NPs) that is mediated by their adsorption onto lipid membranes. The interplay between the adhesive energy of NPs on a lipid membrane and the membrane's curvature energy causes it to wrap around the NPs. This results in an interesting membrane curvature-mediated interaction, which can lead to the self-assembly of NPs on lipid membranes. Recent studies have demonstrated that Janus spherical NPs, which adhere to lipid vesicles, can self-assemble into well-ordered nanoclusters with various geometries, including a few Platonic solids. The present study explores the additional effect of geometric anisotropy on the self-assembly of Janus NPs on lipid vesicles. Specifically, the current study utilized extensive molecular dynamics simulations to investigate the arrangement of Janus spherocylindrical NPs on lipid vesicles. We found that the additional geometric anisotropy significantly expands the range of NPs' self-assemblies on lipid vesicles. The specific geometries of the resulting nanoclusters depend on several factors, including the number of Janus spherocylindrical NPs adhering to the vesicle and their aspect ratio. The lipid membrane-mediated self-assembly of NPs, demonstrated by this work, provides an alternative cost-effective route for fabricating highly engineered nanoclusters in three dimensions. Such structures, with the current wide range of material choices, have great potential for advanced applications, including biosensing, bioimaging, drug delivery, nanomechanics, and nanophotonics.

Role of Shape in Particle-Lipid Membrane Interactions: From Surfing to Full Engulfment

Understanding and manipulating the interactions between foreign bodies and cell membranes during endo- and phagocytosis is of paramount importance, not only for the fate of living cells but also for numerous biomedical applications. This study aims to elucidate the role of variables such as anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength in this essential process using a minimal experimental biomimetic system comprising giant unilamellar vesicles and rod-like particles with different curvatures and aspect ratios. We find that the particle wrapping process is dictated by the balance between the elastic free energy penalty and adhesion free energy gain, leading to two distinct engulfment pathways, tip-first and side-first, emphasizing the significance of the particle orientation in determining the pathway. Moreover, our experimental results are consistent with theoretical predictions in a state diagram, showcasing how to control the wrapping pathway from surfing to partial to complete wrapping by the interplay between membrane tension and adhesive strength. At moderate particle concentrations, we observed the formation of rod clusters, which exhibited cooperative and sequential wrapping. Our study contributes to a comprehensive understanding of the mechanistic intricacies of endocytosis by highlighting how the interplay between the anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength can influence the engulfment pathway.

Non-close-packed hexagonal self-assembly of Janus nanoparticles on planar membranes

The adhesion modes of an ensemble of spherical Janus nanoparticles on planar membranes are investigated through large-scale molecular dynamics simulations of a coarse-grained implicit-solvent model. We found that the Janus nanoparticles adhering to planar membranes exhibit a rich phase behavior that depends on their adhesion energy density and areal number density. In particular, effective repulsive membrane-curvature-mediated interactions between the Janus nanoparticles lead to their self-assembly into an ordered hexagonal superlattice at intermediate densities and intermediate to high adhesion energy density, with a lattice constant determined by their areal density. The melting behavior of the hexagonal superlattice proceeds through a two-stage melting scenario in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young classical theory of two-dimensional melting.

Lipid vesicles induced ordered nanoassemblies of Janus nanoparticles

Since many advanced applications require specific assemblies of nanoparticles (NPs), considerable efforts have been made to fabricate nanoassemblies with specific geometries. Although nanoassemblies can be fabricated through top-down approaches, recent advances show that intricate nanoassemblies can also be obtained through self-assembly, mediated for example by DNA strands. Here, we show, through extensive molecular dynamics simulations, that highly ordered self-assemblies of NPs can be mediated by their adhesion to lipid vesicles (LVs). Specifically, Janus NPs are considered so that the amount by which they are wrapped by the LV is controlled. The specific geometry of the nanoassembly is the result of effective curvature-mediated repulsion between the NPs and the number of NPs adhering to the LV. The NPs are arranged on the LV into polyhedra which satisfy the upper limit of Euler's polyhedral formula, including several deltahedra and three Platonic solids, corresponding to the tetrahedron, octahedron, and icosahedron.

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.

Thermal fluctuations of the lipid membrane determine particle uptake into Giant Unilamellar Vesicles

Phagocytic particle uptake is crucial for the fate of both living cells and pathogens. Invading particles have to overcome fluctuating lipid membranes as the first physical barrier. However, the energy and the role of the fluctuation-based particle-membrane interactions during particle uptake are not understood. We tackle this problem by indenting the membrane of differently composed Giant Unilamellar Vesicles (GUVs) with optically trapped particles until particle uptake. By continuous 1 MHz tracking and autocorrelating the particle's positions within 30µs delays for different indentations, the fluctuations' amplitude, the damping, the mean forces, and the energy profiles were obtained. Remarkably, the uptake energy into a GUV becomes predictable since it increases for smaller fluctuation amplitudes and longer relaxation time. Our observations could be explained by a mathematical model based on continuous suppression of fluctuation modes. Hence, the reduced particle uptake energy for protein-ligand interactions LecA-Gb3 or Biotin-Streptavidin results also from pronounced, low-friction membrane fluctuations.

Endocytosis of Coacervates into Liposomes

Recent studies have shown that the interactions between condensates and biological membranes are of functional importance. Here, we study how the interaction between complex coacervates and liposomes as model systems can lead to wetting, membrane deformation, and endocytosis. Depending on the interaction strength between coacervates and liposomes, the wetting behavior ranged from nonwetting to engulfment (endocytosis) and complete wetting. Endocytosis of coacervates was found to be a general phenomenon: coacervates made from a wide range of components could be taken up by liposomes. A simple theory taking into account surface energies and coacervate sizes can explain the observed morphologies. Our findings can help to better understand condensate-membrane interactions in cellular systems and provide new avenues for intracellular delivery using coacervates.

Modes of adhesion of two Janus nanoparticles on the outer or inner side of lipid vesicles

Using molecular dynamics simulations of a coarse-grained model, in conjunction with the weighted histogram analysis method, the adhesion modes of two spherical Janus nanoparticles (NPs) on the outer or inner side of lipid vesicles are explored. In particular, the effects of the area fraction, J, of the NPs that interact attractively with lipid head groups, the adhesion strength and the size of the NPs on their adhesion modes are investigated. The NPs are found to exhibit two main modes of adhesion when adhered to the outer side of the vesicle. In the first mode, which occurs at relatively low values of J, the NPs are apart from each other. In the second mode, which occurs at higher values of J, the NPs form an in-plane dimer. Janus NPs, which adhere to the inner side of the vesicle, are always found to be apart from each other, regardless of the value of J and their diameter.

Field-mediated interactions of passive and conformation-active particles: multibody and retardation effects

Particles in soft matter interact through the deformation field they create, as in the "cheerios" effect or the curvature-mediated interactions of membrane proteins. Using a simple model for field-mediated interactions between passive particles, or active particles that switch conformation randomly or synchronously, we derive generic results concerning multibody interactions, activity driven patterns, and retardation effects.

Phase diagram of SALR fluids on spherical surfaces

We investigate the phase diagram of a fluid of hard-core disks confined to the surface of a sphere and whose interaction potential contains a short-range attraction followed by a long-range repulsive tail (SALR). Based on previous work in the bulk we derive a stability criterion for the homogeneous phase of the fluid, and locate a region of instability linked to the presence of a negative minimum in the spherical harmonics expansion of the interaction potential. The inhomogeneous phases contained within this region are characterized using a mean-field density functional theory. We find several inhomogeneous patterns that can be separated into three broad classes: cluster crystals, stripes, and bubble crystals, each containing topological defects. Interestingly, while the periodicity of inhomogeneous phases at large densities is mainly determined by the position of the negative minimum of the potential expansion, the finite size of the system induces a richer behavior at smaller densities.

Curvature-Mediated Pair Interactions of Soft Nanoparticles Adhered to a Cell Membrane

The curvature-mediated interactions by cell membranes are crucial in many biological processes. We systematically studied the curvature-mediated wrapping of soft nanoparticles (NPs) by a tensionless membrane and the underlying pair interactions between NPs in determining it. We found that there are three types of wrapping pathways, namely, independence, cooperation, and tubulation. The particle size, adhesion strength, and softness are found to be strongly related with the wrapping mechanism. Reducing the adhesion strength transforms the wrapping pathway from cooperation to independence, while enhancing the NP softness requires a stronger adhesion to achieve the cooperative wrapping. This transformation of the wrapping pathway is controlled by the curvature-mediated interactions between NPs. For either soft or rigid NPs, the pair interactions are repulsive at short-ranged distances between NPs, while at long-ranged distances, a larger adhesion between NPs and a membrane is needed to generate attraction between NPs. Moreover, an enhancement of NP softness weakens the repulsion between NPs. These distinct behaviors of soft NPs are ascribed to the gentler deformation of the membrane at the face-to-face region between NPs due to the flattening and spreading of soft NPs along the membrane, requiring a reduced energy cost for soft NPs to approach each other. Our results provide a mechanistic understanding in detail about the membrane-mediated interactions between NPs and their interactions with cell membranes, which is helpful to understand the curvature-mediated assemblies of adhesive proteins or NPs on membranes, and offer novel possibilities for designing an effective NP-based vehicle for controlled drug delivery.

Avidity and surface mobility in multivalent ligand-receptor binding

Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand-receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy-or avidity-is a strongly nonlinear function of the ligand-receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand-receptor affinity in determining the binding and transport of small particles attached to membranes.

Triggered interactions between nanoparticles and lipid membranes: design principles for gel formation or disruption-and-release

Lipid bilayer vesicles offer exciting possibilities for stimulated response, taking advantage of the membrane's flexibility and impermeability. We show how synergistic interactions between vesicles and polymer-based nanoparticles can be triggered at the nanoscale using UV light. This interaction leads either to adhesion and a membrane-based gel, or to nanoscale wrapping of the particles by the membrane and then vesicle destruction. To map the response, we varied the particle-membrane interactions via their surface charge densities. We found a crossover from adhesion to destruction at a well-defined region in parameter space. We modeled these results by accounting for the electrostatic attraction and the energy of membrane bending. We then synthesized amphiphilic polymers containing a UV-responsive nitrobenzyl moiety that switches its charge, and showed how a trigger predictably led to either a vesicle gel or disruption and release. The results pave the way to a new triggering mechanism and new response modes in soft materials.

Spatial arrangements of spherical nanoparticles on lipid vesicles

We report results of a numerical investigation of the modes of adhesion of two spherical nanoparticles (NPs) on lipid vesicles based on molecular dynamics simulations, in conjunction with the weighted histogram analysis method, of an implicit-solvent model of self-assembled membranes. Our investigation shows that the NPs exhibit a sequence of three modes of adhesion. For low adhesive interactions, the adhering NPs are apart from each other. As the adhesive interaction is increased, the NPs dimerize into in-plane dimers. As the adhesive interaction is further increased for relatively large vesicles, the NPs dimerize into tubular dimers. However, for small vesicles, the tubular dimer state is not observed. For higher values of the adhesive interaction, four endocytosis modes are observed, depending on the initial locations of the NPs on the vesicle and the relative size of the NPs with respect to that of the vesicle. For relatively large vesicles, the NPs are endocytosed individually or as a dimer. For relatively small vesicles, only one NP is endocytosed if the initial distance between the NPs is large, while the second NP remains adhered to the outer leaflet of the vesicle. However, if the initial distance between the NPs is small, one NP is endocytosed, while the other is internalized in the vesicle through a pore.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

Particle engulfment by strongly asymmetric membranes with area reservoirs

Biological cells are capable of undergoing extensive shape transformations thanks to the existence of membrane area reservoirs from which they can pull out membrane when required. A particularly relevant example of such membrane remodelling is given by endocytic and phagocytic processes, during which the cell membrane engulfs nano- and micrometer sized particles. Recently, it was shown that cell-like membrane reservoirs can be mimicked in giant vesicles with nanotubes stabilized by strong bilayer asymmetry, as quantified by the membrane's spontaneous curvature. Here, we theoretically investigate particle engulfment by such strongly-asymmetric membranes. We find that, depending on the sign of the spontaneous curvature, the engulfment transition may be continuous or discontinuous. Moreover, we find that, in the case of particle engulfment, the presence of asymmetry-stabilized reservoirs is not well captured by the constant-tension model typically used to describe cell-membrane deformations. This highlights the need for a better understanding of the nature of cellular membrane reservoirs, in order to accurately describe membrane remodelling processes.

Antibacterial Action of Nanoparticles by Lethal Stretching of Bacterial Cell Membranes

It is commonly accepted that nanoparticles (NPs) can kill bacteria; however, the mechanism of antimicrobial action remains obscure for large NPs that cannot translocate the bacterial cell wall. It is demonstrated that the increase in membrane tension caused by the adsorption of NPs is responsible for mechanical deformation, leading to cell rupture and death. A biophysical model of the NP-membrane interactions is presented which suggests that adsorbed NPs cause membrane stretching and squeezing. This general phenomenon is demonstrated experimentally using both model membranes and Pseudomonas aeruginosa and Staphylococcus aureus, representing Gram-positive and Gram-negative bacteria. Hydrophilic and hydrophobic quasi-spherical and star-shaped gold (Au)NPs are synthesized to explore the antibacterial mechanism of non-translocating AuNPs. Direct observation of nanoparticle-induced membrane tension and squeezing is demonstrated using a custom-designed microfluidic device, which relieves contraction of the model membrane surface area and eventual lipid bilayer collapse. Quasi-spherical nanoparticles exhibit a greater bactericidal action due to a higher interactive affinity, resulting in greater membrane stretching and rupturing, corroborating the theoretical model. Electron microscopy techniques are used to characterize the NP-bacterial-membrane interactions. This combination of experimental and theoretical results confirm the proposed mechanism of membrane-tension-induced (mechanical) killing of bacterial cells by non-translocating NPs.

Biological lipid nanotubes and their potential role in evolution

The membrane of cells and organelles are highly deformable fluid interfaces, and can take on a multitude of shapes. One distinctive and particularly interesting property of biological membranes is their ability to from long and uniform nanotubes. These nanoconduits are surprisingly omnipresent in all domains of life, from archaea, bacteria, to plants and mammals. Some of these tubes have been known for a century, while others were only recently discovered. Their designations are different in different branches of biology, e.g. they are called stromule in plants and tunneling nanotubes in mammals. The mechanical transformation of flat membranes to tubes involves typically a combination of membrane anchoring and external forces, leading to a pulling action that results in very rapid membrane nanotube formation - micrometer long tubes can form in a matter of seconds. Their radius is set by a mechanical balance of tension and bending forces. There also exists a large class of membrane nanotubes that form due to curvature inducing molecules. It seems plausible that nanotube formation and functionality in plants and animals may have been inherited from their bacterial ancestors during endosymbiotic evolution. Here we attempt to connect observations of nanotubes in different branches of biology, and outline their similarities and differences with the aim of providing a perspective on their joint functions and evolutionary origin.

Precipitation of Calcium Carbonate Inside Giant Unilamellar Vesicles Composed of Fluid-Phase Lipids

Biomineralization of CaCO₃ commonly involves the formation of amorphous CaCO₃ precursor particles that are produced in a confined space surrounded by a lipid bilayer. While the influence of confinement itself has been investigated with different model systems, the impact of an enclosing continuous lipid bilayer on CaCO₃ formation in a confined space is still poorly understood as appropriate model systems are rare. Here, we present a new versatile method based on droplet-based microfluidics to produce fluid-phase giant unilamellar vesicles (GUVs) in the presence of high CaCl₂ concentrations. These GUVs can be readily investigated by means of confocal laser scanning microscopy in combination with bright-field microscopy, demonstrating that the formed CaCO₃ particles are in conformal contact with the fluid-phase lipid bilayer and thus suggesting a strong interaction between the particle and the membrane. Atomic force microscopy adhesion studies with membrane-coated spheres on different CaCO₃ crystals corroborated this notion of a strong interaction between the lipids and CaCO₃.

Wrapping of Microparticles by Floppy Lipid Vesicles

Lipid membranes, the barrier defining living cells and many of their subcompartments, bind to a wide variety of nano- and micrometer sized objects. In the presence of strong adhesive forces, membranes can strongly deform and wrap the particles, an essential step in crossing the membrane for a variety of healthy and disease-related processes. A large body of theoretical and numerical work has focused on identifying the physical properties that underly wrapping. Using a model system of micron-sized colloidal particles and giant unilamellar lipid vesicles with tunable adhesive forces, we measure a wrapping phase diagram and make quantitative comparisons to theoretical models. Our data are consistent with a model of membrane-particle interactions accounting for the adhesive energy per unit area, membrane bending rigidity, particle size, and vesicle radius.

Adhesion and Aggregation of Spherical Nanoparticles on Lipid Membranes

We present a review of recent results on the adhesion, wrapping and aggregation of spherical nanoparticles (NPs) on lipid membranes via molecular dynamics simulations of an implicit solvent model. We show that the degree of wrapping of small NPs, by tensionless planar membranes, can increase continuously with the adhesion strength. However, the degree of wrapping exhibits a discontinuity for large NPs or short interaction range. The adhesion of NPs to small vesicles, without volume constraint, also exhibits a discontinuity between weakly wrapped states and fully endocytosed states. Multiple spherical NPs, bound to tensionless planar membranes are either in a gas state, at weak adhesion strength, or aggregate, at relatively high adhesion strength, into a multitude of structures, corresponding to in-plane chains, out-of-plane tubes and rings, and out-of-plane single-chain tubes. Annealing scans and free energy calculations show that the gas and tube phases are the predominantly stable phases. In-plane chains are only stable for small aggregates and the out-of-plane bitubes are long-lived metastable states.

Interactions of particulate matter and pulmonary surfactant: Implications for human health

Particulate matter (PM), which is the primary contributor to air pollution, has become a pervasive global health threat. When PM enters into a respiratory tract, the first body tissues to be directly exposed are the cells of respiratory tissues and pulmonary surfactant. Pulmonary surfactant is a pivotal component to modulate surface tension of alveoli during respiration. Many studies have proved that PM would interact with pulmonary surfactant to affect the alveolar activity, and meanwhile, pulmonary surfactant would be adsorbed to the surface of PM to change the toxic effect of PM. This review focuses on recent studies of the interactions between micro/nanoparticles (synthesized and environmental particles) and pulmonary surfactant (natural surfactant and its models), as well as the health effects caused by PM through a few significant aspects, such as surface properties of PM, including size, surface charge, hydrophobicity, shape, chemical nature, etc. Moreover, in vitro and in vivo studies have shown that PM leads to oxidative stress, inflammatory response, fibrosis, and cancerization in living bodies. By providing a comprehensive picture of PM-surfactant interaction, this review will benefit both researchers for further studies and policy-makers for setting up more appropriate regulations to reduce the adverse effects of PM on public health.

Size-dependent aggregation of hydrophobic nanoparticles in lipid membranes

The aggregation of nanoparticles affects their reactivity, transport across biological membranes, uptake into cells, toxicity, and fate in the environment. In the case of membrane-embedded, hydrophobic nanoparticles the relationship between size and aggregation pattern is not well understood. Here, we explore this relationship for the case of spherically symmetrical nanoparticles using the MARTINI coarse-grained force field. We find that the free energy of dimerization depends strongly on nanoparticle size: the smallest molecules (mimicking C60 fullerene) aggregate only weakly, the largest ones form large three-dimensional aggregates causing major deformations in the host membrane, and the intermediate-sized particles show a tendency to form linear aggregates. Suppressing membrane undulations reduces very significantly aggregation, and substantially abolishes linear aggregation, suggesting a relationship between membrane curvature and aggregation geometry. At low concentration, when placed on membranes of variable curvature, the intermediate size nanoparticles move rapidly to high curvature regions - suggesting that they can sense membrane curvature. At high concentration, the same nanoparticles induce massive membrane deformations, without affecting the mechanical stability of the membrane - suggesting that they can generate membrane curvature.

Binding of a Brownian nanoparticle to a thermally fluctuating membrane surface

We investigate the Brownian dynamics of a nanoparticle bound to a thermally undulating elastic membrane. The ligand-functionalized nanoparticle is assumed to interact monovalently with the receptor expressed on the membrane. In order to resolve the nanoparticle transient motion subject to the instantaneous membrane configuration in a consistent manner, we employ a set of coupled Langevin equations that simultaneously incorporate the hydrodynamic effects, ligand-receptor binding interaction, intramembrane elastic forces, and thermal fluctuations. We show that the presence of a deformable, elastic fluid membrane not only affects the dynamics of a bound nanoparticle but also alters the effective binding potential felt by the nanoparticle. In contrast to a nanoparticle bound to a flat surface, the oscillatory characteristics of the nanoparticle velocity autocorrelation function are suppressed and transition to an anticorrelated long-time tail. Moreover, the nanoparticle position fluctuation becomes more coherent with that of the membrane binding site, and the width of the distribution of the nanoparticle distance from the membrane decreases with increasing membrane bending rigidity. By introducing a locally harmonic, bistable potential as an effective potential for the ligand-receptor pair, the rate of nanoparticle transitioning between two bound states is facilitated by membrane undulations as a result of stronger positional variations associated with the nanoparticle.

Probing Nanoparticle/Membrane Interactions by Combining Amphiphilic Diblock Copolymer Assembly and Plasmonics

Understanding the interactions between nanoparticles (NPs) and boundaries of cells is crucial both for their toxicity and therapeutic applications. Besides specific receptor-mediated endocytosis of surface-functionalized NPs, passive internalization is prompted by relatively unspecific parameters, such as particle size and charge. Based on theoretical treatments, adhesion to and bending of the cell membrane can induce NP wrapping. Experimentally, powerful tools are needed to selectively probe possible membrane-NP motifs at very dilute conditions and avoid dye labeling. In this work, we employ surface resonance-enhanced dynamic light scattering, surface plasmon resonance, electron microscopy, and simulations for sensing interactions between plasmonic AuNPs and polymersomes. We distinguish three different interaction scenarios at nanomolar concentrations by tuning the surface charge of AuNPs and rationalize these events by balancing vesicle bending and electrostatic/van der Waals AuNP and vesicle adhesion. The clarification of the physical conditions under which nanoparticles passively translocate across membranes can aid in the rational design of drugs that cannot exploit specific modes of cellular uptake and also elucidates physical properties that render nanoparticles in the environment particularly toxic.

Spatial organization of active particles with field-mediated interactions

We consider a system of independent pointlike particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the boundaries of the phase and pattern diagram in the stationary state.

Saffman-Delbrück and beyond: A pointlike approach

We show that a very good analytical approximation of Saffman-Delbrück's (SD) law (mobility of a bio-membrane inclusion) can be obtained easily from the velocity field produced by a pointlike force in a 2D fluid embedded in a solvent, by using a small wavelength cutoff of the order of the particle's radius a . With this method, we obtain analytical generalizations of the SD law that take into account the bilayer nature of the membrane and the intermonolayer friction b . We also derive, in a calculation that consistently couples the quasi-planar two-dimensional (2D) membrane flow with the 3D solvent flow, the correction to the SD law arising when the inclusion creates a local spontaneous curvature. For an inclusion spanning a flat bilayer, the SD law is found to hold simply upon replacing the 2D viscosity [Formula: see text] of the membrane by the sum of the monolayer viscosities, without influence of b as long as b is above a threshold in practice well below known experimental values. For an inclusion located in only one of the two monolayers (or adhering to one monolayer), the SD law is influenced by b when b < [Formula: see text]/(4a²) . In this case, the mobility can be increased by up to a factor of two, as the opposite monolayer is not fully dragged by the inclusion. For an inclusion creating a local spontaneous curvature, we show that the total friction is the sum of the SD friction and that due to the pull-back created by the membrane deformation, a point that was assumed without demonstration in the literature.

Protein Recruitment through Indirect Mechanochemical Interactions

Some of the key proteins essential for important cellular processes are capable of recruiting other proteins from the cytosol to phospholipid membranes. The physical basis for this cooperativity of binding is, surprisingly, still unclear. Here, we suggest a general feedback mechanism that explains cooperativity through mechanochemical coupling mediated by the mechanical properties of phospholipid membranes. Our theory predicts that protein recruitment, and therefore also protein pattern formation, involves membrane deformation and is strongly affected by membrane composition.

Nanoparticles binding to lipid membranes: from vesicle-based gels to vesicle tubulation and destruction

While cells offer numerous inspiring examples in which membrane morphology and function are controlled by interactions with viruses or proteins, we still lack design principles for controlling membrane morphology in synthetic systems. With experiments and simulations, we show that spherical nanoparticles binding to lipid-bilayer membrane vesicles results in a remarkably rich set of collective morphologies that are controllable via the particle binding energy. We separately study cationic and anionic particles, where the adhesion is tuned by addition of oppositely charged lipids to the vesicles. When the binding energy is weak relative to a characteristic membrane-bending energy, vesicles adhere to one another and form a soft solid gel, a novel and useful platform for controlled release. With larger binding energy, a transition from partial to complete wrapping of the nanoparticles causes a remarkable vesicle destruction process culminating in rupture, nanoparticle-membrane tubules, and an apparent inversion of the vesicles. These findings help unify the diverse phenomena observed previously. They also open the door to a new class of vesicle-based, closed-cell gels that are more than 99% water and can encapsulate and release on demand, and show how to drive intentional membrane remodeling for shape-responsive systems.

A Multi-Scale Approach to Membrane Remodeling Processes

We present a multi-scale simulation procedure to describe membrane-related biological processes that span over a wide range of length scales. At macroscopic length-scale, a membrane is described as a flexible thin film modeled by a dynamic triangulated surface with its spatial conformations governed by an elastic energy containing only a few model parameters. An implicit protein model allows us to include complex effects of membrane-protein interactions in the macroscopic description. The gist of this multi-scale approach is a scheme to calibrate the implicit protein model using finer scale simulation techniques e.g., all atom and coarse grain molecular dynamics. We previously used this approach and properly described the formation of membrane tubular invaginations upon binding of B-subunit of Shiga toxin. Here, we provide a perspective of our multi-scale approach, summarizing its main features and sketching possible routes for future development.

Single-Nanometer Changes in Nanopore Geometry Influence Curvature, Local Properties, and Protein Localization in Membrane Simulations

Nanoporous surfaces are used in many applications in intracellular sensing and drug delivery. However, the effects of such nanostructures on cell membrane properties are still far from understood. Here, we use coarse-grained molecular dynamics simulations to show that nanoporous substrates can stimulate membrane-curvature effects and that this curvature-sensing effect is much more sensitive than previously thought. We define a series of design parameters for inducing a nanoscale membrane curvature and show that nanopore taper plays a key role in membrane deformation, elucidating a previously unexplored fabrication parameter applicable to many nanostructured biomaterials. We report significant changes in the membrane area per lipid and thickness at regions of curvature. Finally, we demonstrate that regions of the nanopore-induced membrane curvature act as local hotspots for an increased bioactivity. We show spontaneous binding and localization of the epsin N-terminal homology (ENTH) domain to the regions of curvature. Understanding this interplay between the membrane curvature and nanoporosity at the biointerface helps both explain recent biological results and suggests a pathway for developing the next generation of cell-active substrates.

Unusual Organization of I-BAR Proteins on Tubular and Vesicular Membranes

Protein-mediated membrane remodeling is a ubiquitous and critical process for proper cellular function. Inverse Bin/Amphiphysin/Rvs (I-BAR) domains drive local membrane deformation as a precursor to large-scale membrane remodeling. We employ a multiscale approach to provide the molecular mechanism of unusual I-BAR domain-driven membrane remodeling at a low protein surface concentration with near-atomistic detail. We generate a bottom-up coarse-grained model that demonstrates similar membrane-bound I-BAR domain aggregation behavior as our recent Mesoscopic Membrane with Explicit Proteins model. Together, these models bridge several length scales and reveal an aggregation behavior of I-BAR domains. We find that at low surface coverage (i.e., low bound protein density), I-BAR domains form transient, tip-to-tip strings on periodic flat membrane sheets. Inside of lipid bilayer tubules, we find linear aggregates parallel to the axis of the tubule. Finally, we find that I-BAR domains form tip-to-tip aggregates around the edges of membrane domes. These results are supported by in vitro experiments showing low curvature bulges surrounded by I-BAR domains on giant unilamellar vesicles. Overall, our models reveal new I-BAR domain aggregation behavior in membrane tubules and on the surface of vesicles at low surface concentration that add insight into how I-BAR domain proteins may contribute to certain aspects of membrane remodeling in cells.

Assembling responsive microgels at responsive lipid membranes

Directed colloidal self-assembly at fluid interfaces can have a large impact in the fields of nanotechnology, materials, and biomedical sciences. The ability to control interfacial self-assembly relies on the fine interplay between bulk and surface interactions. Here, we investigate the interfacial assembly of thermoresponsive microgels and lipogels at the surface of giant unilamellar vesicles (GUVs) consisting of phospholipids bilayers with different compositions. By altering the properties of the lipid membrane and the microgel particles, it is possible to control the adsorption/desorption processes as well as the organization and dynamics of the colloids at the vesicle surface. No translocation of the microgels and lipogels through the membrane was observed for any of the membrane compositions and temperatures investigated. The lipid membranes with fluid chains provide highly dynamic interfaces that can host and mediate long-range ordering into 2D hexagonal crystals. This is in clear contrast to the conditions when the membranes are composed of lipids with solid chains, where there is no crystalline arrangement, and most of the particles desorb from the membrane. Likewise, we show that in segregated membranes, the soft microgel colloids form closely packed 2D crystals on the fluid bilayer domains, while hardly any particles adhere to the more solid bilayer domains. These findings thus present an approach for selective and controlled colloidal assembly at lipid membranes, opening routes toward the development of tunable soft materials.

Poly(Ionic Liquid) Nanoparticles Selectively Disrupt Biomembranes

Polymer-based nanoparticles have an increasing presence in research due to their attractive properties, such as flexible surface functionality design and the ability to scale up production. Poly(ionic liquid) (PIL) nanoparticles of size below 50 nm are very unique in terms of their high charge density and internal onion-like morphology. The interaction between PIL nanoparticles and giant unilamellar vesicles (GUVs) of various surface charge densities is investigated. GUVs represent a convenient model system as they mimic the size and curvature of plasma membranes, while simultaneously offering direct visualization of the membrane response under the microscope. Incubating PIL nanoparticles with GUVs results in poration of the lipid membrane in a concentration- and charge-dependent manner. A critical poration concentration of PILs is located and the interactions are found to be analogous to those of antimicrobial peptides. Microbial mimetic membranes are already affected at submicromolar PIL concentrations where contrast loss is observed due to sugar exchange across the membrane, while at high concentrations the collapse of vesicles is observed. Finally, a confocal microscopy-based approach assessing the particle permeation through the membrane is reported and a mechanism based on bilayer frustration and pore stabilization via particle integration in the membrane is proposed.

Colloid supported lipid bilayers for self-assembly

The use of colloid supported lipid bilayers (CSLBs) has recently been extended to create colloidal joints, that enable the assembly of structures with internal degrees of flexibility, and to study lipid membranes on curved and closed geometries. These novel applications of CSLBs rely on previously unappreciated properties: the simultaneous fluidity of the bilayer, lateral mobility of inserted (linker) molecules and colloidal stability. Here we characterize every step in the manufacturing of CSLBs in view of these requirements using confocal microscopy and fluorescence recovery after photobleaching (FRAP). Specifically, we have studied the influence of different particle properties (roughness, surface charge, chemical composition, polymer coating) on the quality and mobility of the supported bilayer. We find that the insertion of lipopolymers in the bilayer can affect its homogeneity and fluidity. We improve the colloidal stability by inserting lipopolymers or double-stranded inert DNA into the bilayer. We include surface-mobile DNA linkers and use FRAP to characterize their lateral mobility both in their freely diffusive and bonded state. Finally, we demonstrate the self-assembly of flexibly linked structures from the CSLBs modified with surface-mobile DNA linkers. Our work offers a collection of experimental tools for working with CSLBs in applications ranging from controlled bottom-up self-assembly to model membrane studies.

Capillarity-driven migration of small objects: A critical review

The phenomena on the capillarity-driven migration of small objects are full of interest for both scientific and engineering communities, and a critical review is thereby presented. The small objects mentioned here deal with the non-deformable objects, such as particles, rods, disks and metal sheets; and besides them, the soft objects are considered, such as droplets and bubbles. Two types of interfaces are analyzed, i.e., the solid-fluid interface and the fluid-fluid interface. Due to the easily deformable properties of the soft objects and distorted interfacial shapes induced by small objects, a more convenient way to obtain the driving force is through the potential energy of the system. The asymmetric factors causing the object migration include the asymmetric configuration of the interface, and the difference between the interfacial tensions. Finally, a simple outlook on the potential applications of small object migration is made. These behaviors may cast new light on the design of microfluidics and new devices, environment cleaning, oil and gas displacement and mineral industries.

Aggregation of nanoparticles regulated by mechanical properties of nanoparticle-membrane system

The aggregation of nanoparticles (NPs) on the cell membrane is crucial for the cellular uptake process and has important biological implications in protein-membrane interactions. In this paper, we systematically investigate how the aggregation is regulated by the mechanical properties of the NP-membrane system, including the membrane tension, and the size and shape of the NPs. Results show that when NPs aggregate parallel to the cell membrane, increasing the membrane tension will modulate the membrane-mediated interaction between the NPs from attractive to attractive-repulsive and finally to purely repulsive. In contrast, the membrane-mediated interaction is attractive and independent of the membrane tension when the NPs aggregate to a tubular configuration. For the aggregation of NPs of different sizes, the large-size NP is wrapped to a greater extent than the small-size NP. For the aggregation of nonspherical NPs, low aspect ratio and weak NP-membrane adhesion strength lead to the side-to-side configuration, whereas a system with a high aspect ratio and strong NP-membrane adhesion strength prefers the tip-to-tip configuration. Importantly, NPs of different sizes and anisotropic shapes are found to facilitate the aggregation process by reducing the energy barrier that should be overcome during the aggregation. The results reveal the mechanism of the aggregation of NPs on the cell membrane and provide guidelines to the design of NP-based drug delivery systems.

The 2018 biomembrane curvature and remodeling roadmap

The importance of curvature as a structural feature of biological membranes has been recognized for many years and has fascinated scientists from a wide range of different backgrounds. On the one hand, changes in membrane morphology are involved in a plethora of phenomena involving the plasma membrane of eukaryotic cells, including endo- and exocytosis, phagocytosis and filopodia formation. On the other hand, a multitude of intracellular processes at the level of organelles rely on generation, modulation, and maintenance of membrane curvature to maintain the organelle shape and functionality. The contribution of biophysicists and biologists is essential for shedding light on the mechanistic understanding and quantification of these processes. Given the vast complexity of phenomena and mechanisms involved in the coupling between membrane shape and function, it is not always clear in what direction to advance to eventually arrive at an exhaustive understanding of this important research area. The 2018 Biomembrane Curvature and Remodeling Roadmap of Journal of Physics D: Applied Physics addresses this need for clarity and is intended to provide guidance both for students who have just entered the field as well as established scientists who would like to improve their orientation within this fascinating area.

Field-Embedded Particles Driven by Active Flips

Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite of the surrounding one. Our approach combines Monte Carlo simulations with analytical methods based on dynamical density functional approaches.

Stability of membrane-induced self-assemblies of spherical nanoparticles

The self-assembly of spherical nanoparticles, resulting from their adhesion on tensionless lipid membranes, is investigated through molecular dynamics simulations of a coarse-grained implicit-solvent model. Our simulations indicate that, with increasing adhesion strength, while reshaping the membrane, the nanoparticles aggregate into a sequence of self-assemblies corresponding to in-plane chains, two-row tubular (bitube) chains, annular (ring) chains, and single-row tubular (tube) chains. Annealing scans, with respect to adhesion strength, show that the transitions between the various phases are highly first-order with significant hystereses. Free energy calculations indicate that the gas and single-row tubular chains are stable over wide ranges of adhesion strength. In contrast, the in-plane chains are only stable for small aggregates of NPs, and the bitube and ring chains are long-lived metastable states over a wide range of adhesion strength.

Robust nonequilibrium pathways to microcompartment assembly

Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet and the extent and topography of an elastic shell. The resulting metastable microcompartment structures closely resemble those of carboxysomes, with a narrow size distribution and faceted shells. The essence of their assembly dynamics can be understood from a simpler mathematical model that combines elements of classical nucleation theory with continuum elasticity. These results highlight important control variables for achieving nanoscale encapsulation in general and for modulating the size and shape of carboxysomes in particular.

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.

Micrometer-sized TPM emulsion droplets with surface-mobile binding groups

Colloids coated with lipid membranes have been widely employed for fundamental studies of lipid membrane processes, biotechnological applications such as drug delivery and biosensing, and more recently, for self-assembly. The latter has been made possible by inserting DNA oligomers with covalently linked hydrophobic anchors into the membrane. The lateral mobility of the DNA linkers on micrometer-sized droplets and solid particles has opened the door to creating structures with unprecedented structural flexibility. Here, we investigate micro-emulsions of TPM (3-(trimethoxysilyl)propyl methacrylate) as a platform for lipid monolayers and further functionalization with proteins and DNA oligonucleotides. TPM droplets can be produced with a narrow size distribution and are polymerizable, thus providing supports for model lipid membranes with controlled size and curvature. With fluorescence recovery after photobleaching, we observed that droplet-attached lipids, NeutrAvidin proteins, as well as DNA oligonucleotides all show mobility on the surface. We explored the assembly of micron-sized particles on TPM-droplets by exploiting either avidin-biotin interactions or double-stranded DNA with complementary single-stranded end groups. While the single molecules are mobile, the particles that are attached to them are not. We propose that this is caused by the heterogeneous nature of emulsified TPM, which forms an oligomer network that limits the collective motion of linkers, but allows the surface mobility of individual molecules.

Clustering on Membranes: Fluctuations and More

Clustering of extracellular ligands and proteins on the plasma membrane is required to perform specific cellular functions, such as signaling and endocytosis. Attractive forces that originate in perturbations of the membrane's physical properties contribute to this clustering, in addition to direct protein-protein interactions. However, these membrane-mediated forces have not all been equally considered, despite their importance. In this review, we describe how line tension, lipid depletion, and membrane curvature contribute to membrane-mediated clustering. Additional attractive forces that arise from protein-induced perturbation of a membrane's fluctuations are also described. This review aims to provide a survey of the current understanding of membrane-mediated clustering and how this supports precise biological functions.

Membrane-Mediated Cooperativity of Proteins

Besides direct protein-protein interactions, indirect interactions mediated by membranes play an important role for the assembly and cooperative function of proteins in membrane shaping and adhesion. The intricate shapes of biological membranes are generated by proteins that locally induce membrane curvature. Indirect curvature-mediated interactions between these proteins arise because the proteins jointly affect the bending energy of the membranes. These curvature-mediated interactions are attractive for crescent-shaped proteins and are a driving force in the assembly of the proteins during membrane tubulation. Membrane adhesion results from the binding of receptor and ligand proteins that are anchored in the apposing membranes. The binding of these proteins strongly depends on nanoscale shape fluctuations of the membranes, leading to a fluctuation-mediated binding cooperativity. A length mismatch between receptor-ligand complexes in membrane adhesion zones causes repulsive curvature-mediated interactions that are a driving force for the length-based segregation of proteins during membrane adhesion.