Spontaneous curvature of bilayer membranes from molecular simulations: Asymmetric lipid densities and asymmetric adsorption

Measuring the mechanical properties of asymmetric membranes in computer simulations - new methods and insights

We present Monte Carlo simulations of an ultra coarse-grained lipid bilayer with different numbers of lipids on both leaflets. In the simulations, we employ a new method for measuring the elastic parameters of the membrane, including the area per lipid, area elasticity modulus, and bending rigidity. The method also allows measurement of the spontaneous curvature and non-local bending modulus, which are not accessible by standard computer simulations with periodic boundary conditions. For membranes with lipid densities much smaller than the liquid to gel transition density, ρg, we find a very good agreement between the simulation results and the theory expressing the bilayer elastic free energy as the sum of quadratic free energies in the strains associated with the area density and the local curvature of the monolayers. The theory fails when the lipid area density (in the symmetric reference case) is only slightly smaller than ρg. Increasing the degree of asymmetry and changing the density of the condensed leaflet to a value larger than ρg, causes the layer to phase separate between regions with distinct densities which, in turn, may also induce density variations in the dilated liquid layer. Moreover, the phase separation may also trigger local curvature variations along the membrane, which can be attributed to the disparity between the values of the elastic parameters of the coexisting bilayer segments that are mechanically coupled. This mechanism leading to density-curvature variations and instabilities may play a role in cellular processes occurring in liquid-ordered raft domains that are surrounded by the disordered liquid matrix of the cell.

The many faces of membrane tension for biomembranes and vesicles

Membrane tension is generated by external forces and constraints that affect the membrane's surface area. Many studies have been pursued to elucidate this intuitive concept. Here, we focus on biomimetic model systems, for which the notion of membrane tension can be elaborated in a quantitative manner. Bottom-up, these membrane systems are planar bilayers, unilamellar nanovesicles, and giant unilamellar vesicles (GUVs). For planar bilayers and nanovesicles, we need to distinguish the mechanical bilayer tension within the whole bilayer from the mechanical leaflet tensions within the individual bilayer leaflets. In addition, the fluctuation spectrum of the bilayer defines the bilayer's fluctuation tension. These different tensions can be determined by molecular dynamics simulations. On the micron-scale, GUV membranes as observed by light microscopy, experience both a mechanical and a curvature-elastic tension, as follows from the theory of curvature elasticity. The curvature-elastic tension represents a material parameter, whereas the mechanical tension is a kind of hidden variable that depends on the size and shape of the membrane as demonstrated for multispherical shapes of GUVs. Furthermore, the excess membrane area stored in the shape fluctuations is again governed by a fluctuation tension. Many membrane systems exhibit characteristic tension thresholds. Examples include, the shapes of tubular membranes and the morphological responses of vesicle membranes to condensate droplets.

Toward the Evolutionary Optimisation of Small Molecules Within Coarse-Grained Simulations: Training Molecules to Hide Behind Lipid Head Groups

Exploring the vast chemical space of small molecules poses a significant challenge. We develop a new strategy to efficiently explore this space using coarse-grained toy-like molecules utilizing the Martini3 force field and graph representations. This yields initial proof-of-concept results for the approach enabling the identification of optimal molecules with specific properties targeting lipid bilayers. By leveraging genetic algorithms and coarse-grained molecular dynamics simulations, we demonstrate the potential of our method in designing simple, linear molecules. Our findings show a good convergence toward molecules with weak amphiphilic properties, resembling known (general anesthetic) molecules. While this study demonstrates the feasibility of our method, further refinement is needed to fully realize its potential and explore more complex molecular topologies. Nevertheless, these encouraging results suggest a new path for future research in small molecule discovery and design without relying on extensive data sets.

Asymmetrical calcium ions induced stress and remodeling in lipid bilayer membranes

Ca2+ ions play crucial roles in regulating many chemical and biological processes, but their impact on lipid bilayer membranes remains elusive, especially when the impacts on the two leaflets are asymmetrical. Using a recently developed multisite Ca2+ model, we performed molecular dynamics simulations to study the impact of Ca2+ on the properties of membranes composed of POPC and POPS and observed that both the structure and fluidity of the membranes were significantly affected. In particular, we examined the influence of asymmetrically distributed Ca2+ on asymmetric lipid bilayers and found that imbalanced stress in the two leaflets was generated, with the negatively charged leaflet on the Ca2+-rich side becoming more condensed, which in turn induced membrane curvature that bent the membrane away from the Ca2+-rich side. We employed continuum mechanics to study the large-scale deformations of a spherical vesicle and found that the vesicle can go through vesiculation to form a multi-spherical shape in which a number of spheres are connected with infinitesimal necks, depending on the specific Ca2+ distributions. These results provide new insights into the underlying mechanisms of many biological phenomena involving Ca2+-membrane interactions and may lead to new methods for manipulating the membrane curvature of vesicles in chemical, biological, and nanosystems.

Budding of Asymmetric Lipid Bilayers: Effects of Cholesterol, Anionic Lipid, and Electric Field

Membrane budding is vital for various cellular processes such as synaptic activity regulation, vesicle transport and release, and endocytosis/exocytosis. Although protein-mediated membrane budding has been extensively investigated, the effects of the lipid asymmetry of the two leaflets and the asymmetrically electrical environments of the cellular membrane on membrane budding remain elusive. In this work, using coarse-grained molecular dynamics simulations, we systematically investigate the impacts of lipid bilayer asymmetry and external electric fields mimicking the asymmetric membrane potential on the membrane budding. The results show that the differential stress induced by the asymmetric distribution of lipids in the two leaflets is a crucial factor for the membrane budding. The unidirectional flip of cholesterol induced by the membrane curvature and the asymmetric ion adsorption induced by the anionic lipids promote the budding process. Furthermore, the external electric field applied perpendicularly to the bilayer plane increases the transmembrane potential and produces an additional differential stress across the leaflets by imposing an asymmetric torque on the lipid headgroups in the two leaflets, facilitating the membrane budding. These findings offer insights into how the structural and the environmental asymmetry in natural cellular membranes influence membrane budding in cellular processes.

Effects of Normal and Lateral Electric Fields on Membrane Mechanical Properties

As a core component of biological and synthetic membranes, lipid bilayers are key to compartmentalizing chemical processes. Bilayer morphology and mechanical properties are heavily influenced by electric fields, such as those caused by biological ion concentration gradients. We present atomistic simulations exploring the effects of electric fields applied normally and laterally to lipid bilayers. We find that normal fields decrease membrane tension, while lateral fields increase it. Free energy perturbation calculations indicate the importance of dipole-dipole interactions to these tension changes, especially for lateral fields. We additionally show that membrane area compressibilities can be related to their cohesive energies, allowing us to estimate changes in membrane bending rigidity under applied fields. We find that normal and lateral fields decrease and increase bending rigidity, respectively. These results point to the use of directed electric fields to locally control membrane stiffness, thereby modulating associated cellular processes.

Molecular Dynamics Simulations Show That Short Peptides Can Drive Synthetic Cell Division by Binding to the Inner Membrane Leaflet

An important functionality of lifelike "synthetic cells" is to mimic cell division. Currently, specialized proteins that induce membrane fission in living cells are the primary candidates for dividing synthetic cells. However, interactions between lipid membranes and proteins that are not found in living cells may also be suitable. Here, we discuss the potential of short membrane-anchored peptides to induce cell division. Specifically, we used the coarse-grained MARTINI model to investigate the interaction between short membrane-anchored peptides and a lipid bilayer patch. The simulation revealed that the anchored peptide induces significant spontaneous curvature and suggests that the lipid-peptide complex can be considered as a conically shaped "bulky headgroup" lipid. By systematically increasing the electrostatic charge of the peptide, we find that membrane-anchored peptides may generate sufficiently large constriction forces even at dilute coverages. Finally, we show that when the peptide has an opposite charge to the membrane, the peptide may induce division by binding the inner membrane leaflet of a synthetic cell, that is, cell division from within.

The diffuse interface description of fluid lipid membranes captures key features of the hemifusion pathway and lateral stress profile

Topological transitions of lipid membranes are ubiquitous in key biological processes for cell life, like neurotransmission, fertilization, morphogenesis, and viral infections. Despite this, they are not well understood due to their multiscale nature, which limits the use of molecular models and calls for a mesoscopic approach such as the celebrated Canham-Helfrich one. Unfortunately, such a model cannot handle topological transitions, hiding the crucial involved forces and the appearance of the experimentally observed hemifused intermediates. In this work, we describe the membrane as a diffuse interface preserving the Canham-Helfrich elasticity. We show that pivotal features of the hemifusion pathway are captured by this mesoscopic approach, e.g. a (meta)stable hemifusion state and the fusogenic behavior of negative monolayer spontaneous curvatures. The membrane lateral stress profile is calculated as a function of the elastic rigidities, yielding a coarse-grained version of molecular models findings. Insights into the fusogenic mechanism are reported and discussed.

Methyl-β-cyclodextrin asymmetrically extracts phospholipid from bilayers, granting tunable control over differential stress in lipid vesicles

Lipid asymmetry - that is, a nonuniform lipid distribution between the leaflets of a bilayer - is a ubiquitous feature of biomembranes and is implicated in several cellular phenomena. Differential tension - that is, unequal lateral monolayer tensions comparing the leaflets of a bilayer- is closely associated with lipid asymmetry underlying these varied roles. Because differential tension is not directly measurable in combination with the fact that common methods to adjust this quantity grant only semi-quantitative control over it, a detailed understanding of lipid asymmetry and differential tension are impeded. To overcome these challenges, we leveraged reversible complexation of phospholipid by methyl-β-cyclodextrin (mbCD) to tune the direction and magnitude of lipid asymmetry in synthetic vesicles. Lipid asymmetry generated in our study induced (i) vesicle shape changes and (ii) gel-liquid phase coexistence in 1-component vesicles. By applying mass-action considerations to interpret our findings, we discuss how this approach provides access to phospholipid thermodynamic potentials in bilayers containing lipid asymmetry (which are coupled to the differential tension of a bilayer). Because lipid asymmetry yielded by our approach is (i) tunable and (ii) maintained over minute to hour timescales, we anticipate that this approach will be a valuable addition to the experimental toolbox for systematic investigation into the biophysical role(s) of lipid asymmetry (and differential tension).

Multiscale remodeling of biomembranes and vesicles

Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.

Curvature-induced clustering of cell adhesion proteins

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such a curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670).

Spontaneous curvature generation by peptides in asymmetric bilayers

Peptides and proteins play crucial roles in membrane remodeling by inducing spontaneous curvature. However, extracting spontaneous curvatures from simulations of asymmetric bilayers is challenging because differential stress (i.e., the difference of the leaflet surface tensions) arising from leaflet area strains can vary substantially among initial conditions. This study investigates peptide-induced spontaneous curvatureδc 0 p in asymmetric bilayers consisting of a single lipid type and a peptide confined to one leaflet;δc 0 p is calculated from the Helfrich equation using the first moment of the lateral pressure tensor and an alternative expression using the differential stress. It is shown that differential stress introduced during initial system generation is effectively relaxed by equilibrating using P21 periodic boundary conditions, which allows lipids to switch leaflets across cell boundaries and equalize their chemical potentials across leaflets. This procedure leads to robust estimates ofδc 0 p for the systems simulated, and is recommended when equality of chemical potentials between the leaflets is a primary consideration.

Particle Deformability Enables Control of Interactions between Membrane-Anchored Nanoparticles

Nanoparticles adsorbed on a membrane can induce deformations of the membrane that give rise to effective interactions between the particles. Previous studies have focused primarily on rigid nanoparticles with fixed shapes. However, DNA origami technology has enabled the creation of deformable nanostructures with controllable shapes and mechanical properties, presenting new opportunities to modulate interactions between particles adsorbed on deformable surfaces. Here we use coarse-grained molecular dynamics simulations to investigate deformable, hinge-like nanostructures anchored to lipid membranes via cholesterol anchors. We characterize deformations of the particles and membrane as a function of the hinge stiffness. Flexible particles adopt open configurations to conform to a flat membrane, whereas stiffer particles induce deformations of the membrane. We further show that particles spontaneously aggregate and that cooperative effects lead to changes in their shape when they are close together. Using umbrella sampling methods, we quantify the effective interaction between two particles and show that stiffer hinge-like particles experience stronger and longer-ranged attraction. Our results demonstrate that interactions between deformable, membrane-anchored nanoparticles can be controlled by modifying mechanical properties of the particles, suggesting new ways to modulate the self-assembly of particles on deformable surfaces.

Molecular mechanisms and energetics of lipid droplet formation and directional budding

The formation and budding of lipid droplets (LDs) are known to be governed by the LD size and by membrane tensions in the endoplasmic reticulum (ER) bilayer and LD-monolayers. Using coarse-grained simulations of an LD model, we first show that ER-embedded LDs of different sizes can form through a continuous transition from wide LD lenses to spherical LDs at a fixed LD size. The ER tendency to relax its bilayer modulates the transition via a subtle interplay between the ER and LD lipid densities. By calculating the energetic landscape of the LD transition, we demonstrate that this size-independent transition is regulated by the mechanical force balance of ER and LD-tensions, independent from membrane bending and line tension whose energetic contributions are negligible according to our calculations. Our findings explain experimental observation of stable LDs of various shapes. We then propose a novel mechanism for directional LD budding where the required membrane asymmetry is provided by the exchange of lipids between the LD-monolayers. Remarkably, we demonstrate that this budding process is energetically neutral. Consequently, LD budding can proceed by a modest energy input from proteins or other driving agents. We obtain equal lipid densities and membrane tensions in LD-monolayers throughout budding. Our findings indicate that unlike LD formation, LD budding by inter-monolayer lipid exchange is a tension-independent process.

RE, Mocskos EE, Facelli JC, Pickholz M, Ferraro MB. Molecular dynamics study of the mechanical properties of drug loaded model systems: A comparison of a polymersome with a bilayer

In this work we implement a new methodology to study structural and mechanical properties of systems having spherical and planar symmetries throughout Molecular Dynamics simulations. This methodology is applied here to a drug delivery system based in polymersomes, as an example. The chosen model drug was the local anesthetic prilocaine due to previous parameterization within the used coarse grain scheme. In our approach, mass density profiles (MDPs) are used to obtain key structural parameters of the systems, and pressure profiles are used to estimate the curvature elastic parameters. The calculation of pressure profiles and radial MPDs required the development of specific methods, which were implemented in an in-house built version of the GROMACS 2018 code. The methodology presented in this work is applied to characterize poly(ethylene oxide)-poly(butadiene) polymersomes and bilayers loaded with the model drug prilocaine. Our results show that structural properties of the polymersome membrane could be obtained from bilayer simulations, with significantly lower computational cost compared to whole polymersome simulations, but the bilayer simulations are insufficient to get insights on their mechanical aspects, since the elastic parameters are canceled out for the complete bilayer (as consequence of the symmetry). The simulations of entire polymersomes, although more complex, offer a complementary approach to get insights on the mechanical behavior of the systems.

Probing the elastic response of lipid bilayers and nanovesicles to leaflet tensions via volume per lipid

Biological and biomimetic membranes are based on lipid bilayers, consisting of two monolayers or leaflets. One important but challenging physical parameter of these membranes is their tension. For a long time, this tension was explicitly or implicitly taken to be the bilayer tension, acting on the whole bilayer membrane. More recently, it has been realized that it is useful to decompose the bilayer tension into two leaflet tensions and that these tensions are accessible to molecular dynamics simulations. To divide the bilayer up into two leaflets, it is necessary to introduce a midsurface that defines the spatial extent of the two leaflets. In previous studies, this midsurface was obtained from the density profiles across the bilayer and was then used to compute the molecular area per lipid. Here, we develop an alternative approach based on three-dimensional Voronoi tessellation and molecular volume per lipid. Using this volume-based approach, we determine the reference states with tensionless leaflets as well as the optimal volumes and areas per lipid. The optimal lipid volumes have practically the same value in both leaflets, irrespective of the size and curvature of the nanovesicles, whereas the optimal lipid areas are different for the two leaflets and depend on the vesicle size. In addition, we introduce lateral volume compressibilities to describe the elastic response of the lipid volume to the leaflet tensions. We show that the outer leaflet of a nanovesicle is more densely packed and less compressible than the inner leaflet and that this difference becomes more pronounced for smaller vesicles.

Leaflet Tensions Control the Spatio-Temporal Remodeling of Lipid Bilayers and Nanovesicles

Biological and biomimetic membranes are based on lipid bilayers, which consist of two monolayers or leaflets. To avoid bilayer edges, which form when the hydrophobic core of such a bilayer is exposed to the surrounding aqueous solution, a single bilayer closes up into a unilamellar vesicle, thereby separating an interior from an exterior aqueous compartment. Synthetic nanovesicles with a size below 100 nanometers, traditionally called small unilamellar vesicles, have emerged as potent platforms for the delivery of drugs and vaccines. Cellular nanovesicles of a similar size are released from almost every type of living cell. The nanovesicle morphology has been studied by electron microscopy methods but these methods are limited to a single snapshot of each vesicle. Here, we review recent results of molecular dynamics simulations, by which one can monitor and elucidate the spatio-temporal remodeling of individual bilayers and nanovesicles. We emphasize the new concept of leaflet tensions, which control the bilayers' stability and instability, the transition rates of lipid flip-flops between the two leaflets, the shape transformations of nanovesicles, the engulfment and endocytosis of condensate droplets and rigid nanoparticles, as well as nanovesicle adhesion and fusion. To actually compute the leaflet tensions, one has to determine the bilayer's midsurface, which represents the average position of the interface between the two leaflets. Two particularly useful methods to determine this midsurface are based on the density profile of the hydrophobic lipid chains and on the molecular volumes.

Bacterial lipids drive compartmentalization on the nanoscale

The design of cellular functions in synthetic systems, inspired by the internal partitioning of living cells, is a constantly growing research field that is paving the way to a large number of new remarkable applications. Several hierarchies of internal compartments like polymersomes, liposomes, and membranes are used to control the transport, release, and chemistry of encapsulated species. However, the experimental characterization and the comprehension of glycolipid mesostructures are far from being fully addressed. Lipid A is indeed a glycolipid and the endotoxic part of Gram-negative bacterial lipopolysaccharide; it is the moiety that is recognized by the eukaryotic receptors giving rise to the modulation of innate immunity. Herein we propose, for the first time, a combined approach based on hybrid Particle-Field (hPF) Molecular Dynamics (MD) simulations and Small Angle X-Ray Scattering (SAXS) experiments to gain a molecular picture of the complex supramolecular structures of lipopolysaccharide (LPS) and lipid A at low hydration levels. The mutual support of data from simulations and experiments allowed the unprecedented discovery of the presence of a nano-compartmentalized phase composed of liposomes of variable size and shape which can be used in synthetic biological applications.

Membrane curvature sensing by model biomolecular condensates

Biomolecular condensates (BCs) are fluid droplets that form in biological cells by liquid-liquid phase separation. Their major components are intrinsically disordered proteins. Vast attention has been given in recent years to BCs inside the cytosol and nucleus. BCs at the cell membrane have not been studied to the same extent so far. However, recent studies provide increasingly more examples of interfaces between BCs and membranes which function as platforms for diverse biomolecular processes. Galectin-3, for example, is known to mediate clathrin-independent endocytosis and has been recently shown to undergo liquid-liquid phase separation, but the function of BCs of galectin-3 in endocytic pit formation is unknown. Here, we use dissipative particle dynamics simulations to study a generic coarse-grained model for BCs interacting with lipid membranes. In analogy to galectin-3, we consider polymers comprising two segments - one of them mediates multivalent attractive interactions between the polymers, and the other one has affinity for association with specific lipid head groups. When these polymers are brought into contact with a multi-component membrane, they spontaneously assemble into droplets and, simultaneously, induce lateral separation of lipids within the membrane. Interestingly, we find that if the membrane is bent, the polymer droplets localize at membrane regions curved inward. Although the polymers have no particular shape or intrinsic curvature, they appear to sense membrane curvature when clustered at the membrane. Our results indicate toward a generic mechanism of membrane curvature sensing by BCs involved in such processes as endocytosis.

Effects of Shape on Interaction Dynamics of Tetrahedral Nanoplastics and the Cell Membrane

Cellular uptake of nanoplastics is instrumental in their environmental accumulation and transfer to humans through the food chain. Despite extensive studies using spherical plastic nanoparticles, the influence of the morphological characteristics of environmentally released nanoplastics is understudied. Using dissipative particle dynamics simulations, we modeled the interactions between a cell membrane and hydrophobic nanotetrahedra, which feature high shape anisotropy and large surface curvature seen for environmental nanoplastics. We observe robust uptake of nanotetrahedra with sharp vertices and edges by the lipid membrane. Two local energy minimum configurations of nanotetrahedra embedded in the membrane bilayer were identified for particles of large sizes. Further analysis of particle dynamics within the membrane shows that the two interaction states exhibit distinct translational and rotational dynamics in the directions normal and parallel to the plane of the membrane. The membrane confinement significantly arrests the out-of-plane motion, resulting in caged translation and subdiffusive rotation. While the in-plane diffusion remains Brownian, we find that the translational and rotational modes decouple from each other as the particle size increases. The rotational diffusion decreases by a greater extent compared to the translational diffusion, deviating from the continuum theory predictions. These results provide fundamental insights into the shape effect on the nanoparticle dynamics in crowded lipid membranes.

Remodeling of Biomembranes and Vesicles by Adhesion of Condensate Droplets

Condensate droplets are formed in aqueous solutions of macromolecules that undergo phase separation into two liquid phases. A well-studied example are solutions of the two polymers PEG and dextran which have been used for a long time in biochemical analysis and biotechnology. More recently, phase separation has also been observed in living cells where it leads to membrane-less or droplet-like organelles. In the latter case, the condensate droplets are enriched in certain types of proteins. Generic features of condensate droplets can be studied in simple binary mixtures, using molecular dynamics simulations. In this review, I address the interactions of condensate droplets with biomimetic and biological membranes. When a condensate droplet adheres to such a membrane, the membrane forms a contact line with the droplet and acquires a very high curvature close to this line. The contact angles along the contact line can be observed via light microscopy, lead to a classification of the possible adhesion morphologies, and determine the affinity contrast between the two coexisting liquid phases and the membrane. The remodeling processes generated by condensate droplets include wetting transitions, formation of membrane nanotubes as well as complete engulfment and endocytosis of the droplets by the membranes.

Determination of elastic parameters of lipid membranes from simulation under varied external pressure

Many cellular processes such as endocytosis, exocytosis, and vesicle trafficking involve membrane deformations, which can be analyzed in the framework of the elastic theories of lipid membranes. These models operate with phenomenological elastic parameters. A connection between these parameters and the internal structure of lipid membranes can be provided by three-dimensional (3D) elastic theories. Considering a membrane as a 3D layer, Campelo et al. [F. Campelo et al., Adv. Colloid Interface Sci. 208, 25 (2014)10.1016/j.cis.2014.01.018] developed a theoretical basis for the calculation of elastic parameters. In this work we generalize and improve this approach by considering a more general condition of global incompressibility instead of local incompressibility. Crucially, we find an important correction to the theory of Campelo et al., which if not taken into account leads to a significant miscalculation of elastic parameters. With the total volume conservation taken into account, we derive an expression for the local Poisson's ratio, which determines how the local volume changes upon stretching and permits a more precise determination of elastic parameters. Also, we substantially simplify the procedure by calculating the derivatives of the moments of the local tension with respect to stretching instead of calculating the local stretching modulus. We obtain a relation between the Gaussian curvature modulus as a function of stretching and the bending modulus, showing that these two elastic parameters are not independent, as was previously assumed. The proposed algorithm is applied to membranes composed of pure dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and their mixture. The following elastic parameters of these systems are obtained: the monolayer bending and stretching moduli, spontaneous curvature, neutral surface position, and local Poisson's ratio. It is shown that the bending modulus of the DPPC/DOPC mixture follows a more complex trend than predicted by the classical Reuss averaging, which is often employed in theoretical frameworks.

Low-THz Vibrations of Biological Membranes

A growing body of work has linked key biological activities to the mechanical properties of cellular membranes, and as a means of identification. Here, we present a computational approach to simulate and compare the vibrational spectra in the low-THz region for mammalian and bacterial membranes, investigating the effect of membrane asymmetry and composition, as well as the conserved frequencies of a specific cell. We find that asymmetry does not impact the vibrational spectra, and the impact of sterols depends on the mobility of the components of the membrane. We demonstrate that vibrational spectra can be used to distinguish between membranes and, therefore, could be used in identification of different organisms. The method presented, here, can be immediately extended to other biological structures (e.g., amyloid fibers, polysaccharides, and protein-ligand structures) in order to fingerprint and understand vibrations of numerous biologically-relevant nanoscale structures.

Intercellular Receptor-ligand Binding: Effect of Protein-membrane Interaction

Gaining insights into the intercellular receptor-ligand binding is of great importance for understanding numerous physiological and pathological processes, and stimulating new strategies in drug design and discovery. In contrast to the in vitro protein interaction in solution, the anchored receptor and ligand molecules interact with membrane in situ, which affects the intercellular receptor-ligand binding. Here, we review theoretical, simulation and experimental works regarding the regulatory effects of protein-membrane interactions on intercellular receptor-ligand binding mainly from the following aspects: membrane fluctuations, membrane curvature, glycocalyx, and lipid raft. In addition, we discuss biomedical significances and possible research directions to advance the field and highlight the importance of understanding of coupling effects of these factors in pharmaceutical development.

Effect of Local Stress on Accurate Modeling of Bacterial Outer Membranes Using All-Atom Molecular Dynamics

Biological membranes are fundamental components of living organisms that play an undeniable role in their survival. Molecular dynamics (MD) serves as an essential computational tool for studying biomembranes on molecular and atomistic scales. The status quo of MD simulations of biomembranes studies a nanometer-sized membrane patch periodically extended under periodic boundary conditions (PBCs). In nature, membranes are usually composed of different lipids in their two layers (referred to as leaflets). This compositional asymmetry imposes a fixed ratio of lipid numbers between the two leaflets in a periodically constrained membrane, which needs to be set appropriately. The widely adopted methods of defining a leaflet lipid ratio suffer from the lack of control over the mechanical tension of each leaflet, which could significantly influence research findings. In this study, we investigate the role of membrane-building protocol and the resulting initial stress state on the interaction between small molecules and asymmetric membranes. We model the outer membrane of Pseudomonas aeruginosa bacteria using two different building protocols and probe their interactions with the Pseudomonas quinolone signal (PQS). Our results show that differential stress could shift the position of free energy minimum for the PQS molecule between the two leaflets of the asymmetric membrane. This work provides critical insights into the relationship between the initial per-leaflet tension and the spontaneous intercalation of PQS.

Determination of Elastic Parameters of Lipid Membranes with Molecular Dynamics: A Review of Approaches and Theoretical Aspects

Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the development of molecular dynamics (MD), a variety of in silico methods have been proposed for the determination of elastic parameters of simulated lipid membranes. These MD methods allow for the consideration of details unattainable in experimental techniques and represent a distinct scientific field, which is rapidly developing. This work provides a review of these MD approaches with a focus on theoretical aspects. Two main challenges are identified: (i) the ambiguity in the transition from the continuum description of elastic theories to the discrete representation of MD simulations, and (ii) the determination of intrinsic elastic parameters of lipid mixtures, which is complicated due to the composition-curvature coupling effect.

Compartmentalizing and sculpting nanovesicles by phase-separated aqueous nanodroplets

Phase-separated liquid droplets inside giant vesicles have been intensely studied as biomimetic model systems to understand cellular microcompartmentation and molecular crowding and sorting. On the nanoscale, however, how aqueous nanodroplets interact with and shape nanovesicles is poorly understood. We perform coarse-grained molecular simulations to explore the architecture of compartmentalized nanovesicles by phase-separated aqueous nanodroplets, and their morphological evolution under osmotic deflation. We show that phase separation of a biphasic liquid mixture can form both stable two-compartment and meta-stable multi-compartment nanovesicles. We identify morphological transitions of stable two-compartment nanovesicles between tube, sheet and cup morphologies, characterized by membrane asymmetry and phase-separation propensity between the aqueous phases. We demonstrate that the formation of local sheets and in turn cup-shaped nanovesicles is promoted by negative line tensions resulting from large separation propensities, an exclusive nanoscale phenomenon which is not expected for larger vesicles where energetic contributions of the line tensions are dominated by those of the membrane tensions. Despite their instability, we observe long-lived multi-compartment nanovesicles, such as nanotubules and branched tubules, whose prolonged lifetime is attributed to interfacial tensions and membrane asymmetry. Aqueous nanodroplets can thus form novel membrane nanostructures, crucial for cellular processes and forming cellular organelles on the nanoscale.

Polymyxins induce lipid scrambling and disrupt the homeostasis of Gram-negative bacteria membrane

Polymyxins are increasingly used as the last-line therapeutic option for the treatment of infections caused by multidrug-resistant Gram-negative bacteria. However, efforts to address the resistance in superbugs are compromised by a poor understanding of the bactericidal modes because high-resolution detection of the cell structure is still lacking. By performing molecular dynamics simulations at a coarse-grained level, here we show that polymyxin B (PmB) disrupts Gram-negative bacterial membranes by altering lipid homeostasis and asymmetry. We found that the binding of PmBs onto the asymmetric outer membrane (OM) loosens the packing of lipopolysaccharides (LPS) and induces unbalanced bending torque between the inner and outer leaflets, which in turn triggers phospholipids to flip from the inner leaflet to the outer leaflet to compensate for the stress deformation. Meanwhile, some LPSs may be detained on the inner membrane (IM). Then, the lipid-scrambled OM undergoes phase separation. Defects are created at the boundaries between LPS-rich domains and phospholipid-rich domains, which consequently facilitate the uptake of PmB across the OM. Finally, PmBs target LPSs detained on the IM and similarly perturb the IM. This lipid Scramble, membrane phase Separation, and peptide Translocation model depicts a novel mechanism by which polymyxins kill bacteria and sheds light on developing a new generation of polymyxins or antibiotic adjuvants with improved killing activities and higher therapeutic indices.

Large stress asymmetries of lipid bilayers and nanovesicles generate lipid flip-flops and bilayer instabilities

Much effort has been devoted to lipid bilayers and nanovesicles with a compositional asymmetry between the two leaflets of the bilayer membranes. Here, we address another fundamental asymmetry related to lipid densities and membrane tensions. To avoid membrane rupture, the osmotic conditions must be adjusted in such a way that the bilayer membranes are subject to a relatively low bilayer tension. However, even for vanishing bilayer tension, the individual leaflets can still experience significant leaflet tensions if one leaflet is stretched whereas the other leaflet is compressed. Such a stress asymmetry between the two leaflets can be directly controlled in molecular dynamics simulations by the initial assembly of the lipid bilayers. This stress asymmetry is varied here over a wide range to determine the stability and instability regimes of the asymmetric bilayers. The stability regime shrinks with decreasing size and increasing membrane curvature of the nanovesicle. In the instability regimes, the lipids undergo stress-induced flip-flops with a flip-flop rate that increases with increasing stress asymmetry. The onset of flip-flops can be characterized by a cumulative distribution function that is well-fitted by an exponential function for planar bilayers but has a sigmoidal shape for nanovesicles. In addition, the bilayer membranes form transient non-bilayer structures that relax back towards ordered bilayers with a reduced stress asymmetry. Our study reveals intrinsic limits for the possible magnitude of the transbilayer stress asymmetry and shows that the leaflet tensions represent key parameters for the flip-flop rates.

Self-Assembly of Lipid Mixtures in Solutions: Structures, Dynamics Processes and Mechanical Properties

The self-assembly of lipid mixtures in aqueous solution was investigated by dissipative particle dynamics simulation. Two types of lipid molecules were modelled, where three mixed structures, i.e., the membrane, perforated membrane and vesicle, were determined in the self-assembly processes. Phase behaviour was investigated by using the phase diagrams based on the tail chain lengths for the two types of lipids. Several parameters, such as chain number and average radius of gyration, were employed to explore the structural formations of the membrane and perforated membrane in the dynamic processes. Interface tension was used to demonstrate the mechanical properties of the membrane and perforated membrane in the equilibrium state and dynamics processes. Results help us to understand the self-assembly mechanism of the biomolecule mixtures, which has a potential application for designing the lipid molecule-based bio-membranes in solutions.

Multispherical shapes of vesicles highlight the curvature elasticity of biomembranes

Giant lipid vesicles form unusual multispherical or "multi-balloon" shapes consisting of several spheres that are connected by membrane necks. Such multispherical shapes have been recently observed when the two sides of the membranes were exposed to different sugar solutions. This sugar asymmetry induced a spontaneous curvature, the sign of which could be reversed by swapping the interior with the exterior solution. Here, previous studies of multispherical shapes are reviewed and extended to develop a comprehensive theory for these shapes. Each multisphere consists of large and small spheres, characterized by two radii, the large-sphere radius, R_l, and the small-sphere radius, R_s. For positive spontaneous curvature, the multisphere can be built up from variable numbers N_l and N_s of large and small spheres. In addition, multispheres consisting of N_*=N_l+N_s equally sized spheres are also possible and provide examples for constant-mean-curvature surfaces. For negative spontaneous curvature, all multispheres consist of one large sphere that encloses a variable number N_s of small spheres. These general features of multispheres arise from two basic properties of curvature elasticity: the local shape equation for spherical membrane segments and the stability conditions for closed membrane necks. In addition, the (N_l+N_s)-multispheres can form several (N_l+N_s)-patterns that differ in the way, in which the spheres are mutually connected. These patterns may involve multispherical junctions consisting of individual spheres that are connected to more than two neighboring spheres. The geometry of the multispheres is governed by two polynomial equations which imply that (N_l+N_s)-multispheres can only be formed within a certain restricted range of vesicle volumes. Each (N_l+N_s)-pattern can be characterized by a certain stability regime that depends both on the stability of the closed necks and on the multispherical geometry. Interesting and challenging topics for future studies include the response of multispheres to locally applied external forces, membrane fusion between spheres to create multispherical shapes of higher-genus topology, and the enlarged morphological complexity of multispheres arising from lipid phase separation and intramembrane domains.

Stability and Deformation of Vesicles in a Cylindrical Flow

In this work, we used dissipative particle dynamics to study the stability, deformation, and rupture of polymer vesicles confined in cylindrical channels under the flow field. The morphological evolution, elongation, and rupture of vesicles and the corresponding mechanisms were intensively investigated. Bullet-like vesicles, leaking vesicles, spherical micelles, hamburger-like micelles, and bilayers were observed by changing the degree of confinement and dimensionless shear rate. We found that increasing the dimensionless shear rate and the degree of confinement can cause the deformation or rupture of polymeric vesicles. The asphericity parameter was utilized to describe the degree of elongation of vesicles deviating from the sphere in the direction of the flow. The results show that the aggregates are more likely to be spherical when the confinement is weak, while they become elongated bullet-like shapes when the confinement is strong. The investigation of dynamics reveals that the degree of confinement and the dimensionless shear rate can affect the chain stretching and reorganization during the process of vesicle elongation. Furthermore, the rupture time of the vesicle shows a nonlinear decrease with an increase in the dimensionless shear rate, and the confinement also contributes to the rupture. The results are very useful for guiding the application of vesicles in a flow environment.

Remodeling of Membrane Shape and Topology by Curvature Elasticity and Membrane Tension

Cellular membranes exhibit a fascinating variety of different morphologies, which are continuously remodeled by transformations of membrane shape and topology. This remodeling is essential for important biological processes (cell division, intracellular vesicle trafficking, endocytosis) and can be elucidated in a systematic and quantitative manner using synthetic membrane systems. Here, recent insights obtained from such synthetic systems are reviewed, integrating experimental observations and molecular dynamics simulations with the theory of membrane elasticity. The study starts from the polymorphism of biomembranes as observed for giant vesicles by optical microscopy and small nanovesicles in simulations. This polymorphism reflects the unusual elasticity of fluid membranes and includes the formation of membrane necks or fluid 'worm holes'. The proliferation of membrane necks generates stable multi-spherical shapes, which can form tubules and tubular junctions. Membrane necks are also essential for the remodeling of membrane topology via membrane fission and fusion. Neck fission can be induced by fine-tuning of membrane curvature, which leads to the controlled division of giant vesicles, and by adhesion-induced membrane tension as observed for small nanovesicles. Challenges for future research include the interplay of curvature elasticity and membrane tension during membrane fusion and the localization of fission and fusion processes within intramembrane domains.

Role of Endocytosis Pathways in Electropermeablization of MCF7 Cells Using Low Voltage and High Frequency Electrochemotherapy

Objective

The cell membrane is a major barrier for delivery of hydrophilic drugs and molecules into the cells. Although low voltage and high frequency electric fields (LVHF) are proposed to overcome the cell membrane barrier, the mechanism of membrane permeabilization is unclear. The aim of study is to investigate endocytosis pathways as a possible mechanism for enhancing uptake of bleomycin by LVHF.

Materials and Methods

In this experimental study, MCF-7 cells were exposed to bleomycin or to electric fields with various strengths (10-80 V/cm), frequency of 5 kHz, 4000 electric pulse and 100 µs duration in the presence and absence of three endocytosis inhibitors-chlorpromazine (Cpz), amiloride (Amilo) and genistein (Geni). We determined the efficiency of these chemotherapeutic agents in each group.

Results

LVHF, depending on the intensity, induced different endocytosis pathways. Electric field strengths of 10 and 20 V/cm stimulated the macropinocytosis route. Clathrin-mediated endocytosis was observed at electric field intensities of 10, 30, 60 and 70 V/cm, whereas induction of caveolae-mediated endocytosis was observed only at the lowest electric field intensity (10 V/cm).

Conclusion

The results of this study imply that LVHF can induce different endocytosis pathways in MCF-7 cells, which leads to an increase in bleomycin uptake.

Quantifying Membrane Curvature Sensing of Peripheral Proteins by Simulated Buckling and Umbrella Sampling

Membrane curvature plays an essential role in the organization and trafficking of membrane associated proteins. Comparison or prediction of the experimentally resolved protein concentrations adopted at different membrane curvatures requires direct quantification of the relative partitioning free energy. Here, we present a highly efficient and simple to implement a free-energy calculation method which is able to directly resolve the relative partitioning free energy of proteins as a direct function of membrane curvature, i.e., a curvature sensing profile, within (coarse-grained) molecular dynamics simulations. We demonstrate its utility by resolving these profiles for two known curvature sensing peptides, namely ALPS and α-synuclein, for a membrane curvature ranging from -1/6.5 to +1/6.5 nm^-1. We illustrate that the difference in relative partitioning (binding) free energy between these two extrema is only about 13 k_BT for both peptides, illustrating that the driving force of curvature sensing is subtle. Furthermore, we illustrate that ALPS and α-synuclein sense curvature via a contrasting mechanism, which is differentially affected by membrane composition. In addition, we demonstrate that the intrinsic spontaneous curvature of both of these peptides lies beyond the range of membrane curvature accessible in micropipette aspiration experiments, being about 1/7 nm ^-1. Our approach offers an efficient and simple to implement in silico tool for exploring and screening the membrane curvature sensing mechanisms of proteins.

Cholera Toxin as a Probe for Membrane Biology

Cholera toxin B-subunit (CTxB) has emerged as one of the most widely utilized tools in membrane biology and biophysics. CTxB is a homopentameric stable protein that binds tightly to up to five GM1 glycosphingolipids. This provides a robust and tractable model for exploring membrane structure and its dynamics including vesicular trafficking and nanodomain assembly. Here, we review important advances in these fields enabled by use of CTxB and its lipid receptor GM1.

Budding and Fission of Nanovesicles Induced by Membrane Adsorption of Small Solutes

Membrane budding and fission are essential cellular processes that produce new membrane compartments during cell and organelle division, for intracellular vesicle trafficking as well as during endo- and exocytosis. Such morphological transformations have also been observed for giant lipid vesicles with a size of many micrometers. Here, we report budding and fission processes of lipid nanovesicles with a size below 50 nm. We use coarse-grained molecular dynamics simulations, by which we can visualize the morphological transformations of individual vesicles. The budding and fission processes are induced by low concentrations of small solutes that absorb onto the outer leaflets of the vesicle membranes. In addition to the solute concentration, we identify the solvent conditions as a second key parameter for these processes. For good solvent conditions, the budding of a nanovesicle can be controlled by reducing the vesicle volume for constant solute concentration or by increasing the solute concentration for constant vesicle volume. After the budding process is completed, the budded vesicle consists of two membrane subcompartments which are connected by a closed membrane neck. The budding process is reversible as we demonstrate explicitly by reopening the closed neck. For poor solvent conditions, on the other hand, we observe two unexpected morphological transformations of nanovesicles. Close to the binodal line, at which the aqueous solution undergoes phase separation, the vesicle exhibits recurrent shape changes with closed and open membrane necks, reminiscent of flickering fusion pores (kiss-and-run) as observed for synaptic vesicles. As we approach the binodal line even closer, the recurrent shape changes are truncated by the fission of the membrane neck which leads to the division of the nanovesicle into two daughter vesicles. In this way, our simulations reveal a nanoscale mechanism for the budding and fission of nanovesicles, a mechanism that arises from the interplay between membrane elasticity and solute-mediated membrane adhesion.

Transport mechanisms of SARS-CoV-E viroporin in calcium solutions: Lipid-dependent Anomalous Mole Fraction Effect and regulation of pore conductance

The envelope protein E of the SARS-CoV coronavirus is an archetype of viroporin. It is a small hydrophobic protein displaying ion channel activity that has proven highly relevant in virus-host interaction and virulence. Ion transport through E channel was shown to alter Ca²⁺ homeostasis in the cell and trigger inflammation processes. Here, we study transport properties of the E viroporin in mixed solutions of potassium and calcium chloride that contain a fixed total concentration (mole fraction experiments). The channel is reconstituted in planar membranes of different lipid compositions, including a lipid mixture that mimics the endoplasmic reticulum-Golgi intermediate compartment (ERGIC) membrane where the virus localizes within the cell. We find that the E ion conductance changes non-monotonically with the total ionic concentration displaying an Anomalous Mole Fraction Effect (AMFE) only when charged lipids are present in the membrane. We also observe that E channel insertion in ERGIC-mimic membranes – including lipid with intrinsic negative curvature – enhances ion permeation at physiological concentrations of pure CaCl₂ or KCl solutions, with a preferential transport of Ca²⁺ in mixed KCl-CaCl₂ solutions. Altogether, our findings demonstrate that the presence of calcium modulates the transport properties of the E channel by interacting preferentially with charged lipids through different mechanisms including direct Coulombic interactions and possibly inducing changes in membrane morphology.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength L_np or curvature mismatch μ = R_c/R_np, where R_c and R_np are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either L_np or μ. NPs with curvature larger than that of the tubule (μ > 1) lie perpendicularly to the tubule's axis. However, for μ smaller than a specific arclength-dependent mismatch μ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing μ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for μ > 1 and high values of L_np, the NPs self-assemble into linear chains, and lie side-by-side. For μ < μ* and high L_np, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Introduction to remodeling of biomembranes

In general, biomembranes and giant vesicles can respond to cues in their aqueous environment by remodeling their molecular composition, shape, or topology. This themed collection focuses on remodeling of membrane shape which is intimately related to membrane curvature. In this introductory contribution, we clarify the different notions of curvature and describe the general nanoscopic mechanisms for curvature generation and membrane scaffolding. At the end, we give a brief outlook on membrane tension.

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.

Emerging applications at the interface of DNA nanotechnology and cellular membranes: Perspectives from biology, engineering, and physics

DNA nanotechnology has proven exceptionally apt at probing and manipulating biological environments as it can create nanostructures of almost arbitrary shape that permit countless types of modifications, all while being inherently biocompatible. Emergent areas of particular interest are applications involving cellular membranes, but to fully explore the range of possibilities requires interdisciplinary knowledge of DNA nanotechnology, cell and membrane biology, and biophysics. In this review, we aim for a concise introduction to the intersection of these three fields. After briefly revisiting DNA nanotechnology, as well as the biological and mechanical properties of lipid bilayers and cellular membranes, we summarize strategies to mediate interactions between membranes and DNA nanostructures, with a focus on programmed delivery onto, into, and through lipid membranes. We also highlight emerging applications, including membrane sculpting, multicell self-assembly, spatial arrangement and organization of ligands and proteins, biomechanical sensing, synthetic DNA nanopores, biological imaging, and biomelecular sensing. Many critical but exciting challenges lie ahead, and we outline what strikes us as promising directions when translating DNA nanostructures for future in vitro and in vivo membrane applications.

In vitro Analysis of O-Antigen-Specific Bacteriophage P22 Inactivation by Salmonella Outer Membrane Vesicles

Bacteriophages use a large number of different bacterial cell envelope structures as receptors for surface attachment. As a consequence, bacterial surfaces represent a major control point for the defense against phage attack. One strategy for phage population control is the production of outer membrane vesicles (OMVs). In Gram-negative host bacteria, O-antigen-specific bacteriophages address lipopolysaccharide (LPS) to initiate infection, thus relying on an essential outer membrane glycan building block as receptor that is constantly present also in OMVs. In this work, we have analyzed interactions of Salmonella (S.) bacteriophage P22 with OMVs. For this, we isolated OMVs that were formed in large amounts during mechanical cell lysis of the P22 S. Typhimurium host. In vitro, these OMVs could efficiently reduce the number of infective phage particles. Fluorescence spectroscopy showed that upon interaction with OMVs, bacteriophage P22 released its DNA into the vesicle lumen. However, only about one third of the phage P22 particles actively ejected their genome. For the larger part, no genome release was observed, albeit the majority of phages in the system had lost infectivity towards their host. With OMVs, P22 ejected its DNA more rapidly and could release more DNA against elevated osmotic pressures compared to DNA release triggered with protein-free LPS aggregates. This emphasizes that OMV composition is a key feature for the regulation of infective bacteriophage particles in the system.

Membrane-Sugar Interactions Probed by Low-Frequency Raman Spectroscopy: The Monolayer Adsorption Model

Small sugars are known to stabilize biological membranes under extreme conditions of freezing and desiccation. The proposed mechanisms of stabilization suggest membrane-sugar interactions to be either attractive or repulsive. To obtain new insight into the problem, we use a recently developed low-frequency Raman scattering approach which allows detecting membrane mechanical vibrations. For model membranes of palmitoyl-oleoyl-glycero-phosphocholine (POPC) hydrated in aqueous sucrose and trehalose solutions, we studied the Raman peak between 12 and 15 cm^-1 that is attributed to an eigenmode of the normal mechanical vibrations of a lipid monolayer. For both sugars, similar results were obtained. With an increase in sugar concentration in solution, the frequency position of the peak was found to decrease by ∼13% which was interpreted as a consequence of the membrane thickening due sugar monolayer adsorption on the membrane surface. The concentration dependence of the peak frequency position was satisfactorily described by a Langmuir monolayer adsorption model. It is concluded that, at small sugar concentrations (less than 0.2 M), the membrane-sugar interactions are attractive, while at higher concentrations (more than 0.4 M) the attraction disappears. The data obtained show that one sugar molecule on the surface interacts with approximately 3-4 polar lipid heads.

Newton-Cartan submanifolds and fluid membranes

We develop the geometric description of submanifolds in Newton-Cartan spacetime. This provides the necessary starting point for a covariant spacetime formulation of Galilean-invariant hydrodynamics on curved surfaces. We argue that this is the natural geometrical framework to study fluid membranes in thermal equilibrium and their dynamics out of equilibrium. A simple model of fluid membranes that only depends on the surface tension is presented and, extracting the resulting stresses, we show that perturbations away from equilibrium yield the standard result for the dispersion of elastic waves. We also find a generalization of the Canham-Helfrich bending energy for lipid vesicles that takes into account the requirements of thermal equilibrium.

Membrane constriction and thinning by sequential ESCRT-III polymerization

The endosomal sorting complexes required for transport (ESCRTs) mediate diverse membrane remodeling events. These typically require ESCRT-III proteins to stabilize negatively curved membranes; however, recent work has indicated that certain ESCRT-IIIs also participate in positive-curvature membrane-shaping reactions. ESCRT-IIIs polymerize into membrane-binding filaments, but the structural basis for negative versus positive membrane remodeling by these proteins remains poorly understood. To learn how certain ESCRT-IIIs shape positively curved membranes, we determined structures of human membrane-bound CHMP1B-only, membrane-bound CHMP1B + IST1, and IST1-only filaments by cryo-EM. Our structures show how CHMP1B first polymerizes into a single-stranded helical filament, shaping membranes into moderate-curvature tubules. Subsequently, IST1 assembles a second strand on CHMP1B, further constricting the membrane tube and reducing its diameter nearly to the fission point. Each step of constriction thins the underlying bilayer, lowering the barrier to membrane fission. Our structures reveal how a two-component, sequential polymerization mechanism drives membrane tubulation, constriction and bilayer thinning.

Simple sugars shape giant vesicles into multispheres with many membrane necks

Simple sugars such as glucose and sucrose are ubiquitous in all organisms. One remarkable property of these small solutes is their ability to protect biomembranes against dehydration damage. This property, which reflects the underlying sugar-lipid interactions, has been intensely studied for lipid bilayers interacting with a single sugar at low hydration. Here, we use giant vesicles to investigate fully hydrated lipid membranes in contact with two sugars, glucose and sucrose. The vesicles were osmotically balanced, with the same total sugar concentration in the interior and exterior aqueous solutions. However, the two solutions differed in their composition: the interior solution contained only sucrose whereas the exterior one contained primarily glucose. This sugar asymmetry generated a striking variety of multispherical or "multi-balloon" vesicle shapes. Each multisphere involved only a single membrane that formed several spherical segments, which were connected by narrow, hourglass-shaped membrane necks. These morphologies revealed that the sugar-lipid interactions generated a significant spontaneous curvature with a magnitude of about 1 μm^-1. Such a spontaneous curvature can be generated both by depletion and by adsorption layers of the sugar molecules arising from effectively repulsive and attractive sugar-lipid interactions. All multispherical shapes are stable over a wide range of parameters, with a substantial overlap between the different stability regimes, reflecting the rugged free energy landscape in shape space. One challenge for future studies is to identify pathways within this landscape that allow us to open and close the membrane necks of these shapes in a controlled and reliable manner. We will then be able to apply these multispheres as metamorphic chambers for chemical reactions and nanoparticle growth.

Spontaneous Curvature, Differential Stress, and Bending Modulus of Asymmetric Lipid Membranes

Lipid bilayers can exhibit asymmetric states, in which the physical characteristics of one leaflet differ from those of the other. This most visibly manifests in a different lipid composition, but it can also involve opposing lateral stresses in each leaflet that combine to an overall vanishing membrane tension. Here, we use theoretical modeling and coarse-grained simulation to explore the interplay between a compositional asymmetry and a nonvanishing differential stress. Minimizing the total elastic energy leads to a preferred spontaneous curvature that balances torques due to both bending moments and differential stress, with sometimes unexpected consequences. For instance, asymmetric flat bilayers, whose specific areas in each leaflet are matched to those of corresponding tensionless symmetric flat membranes, still exhibit a residual differential stress because the conditions of vanishing area strain and vanishing bending moment differ. We also measure the curvature rigidity of asymmetric bilayers and find that a sufficiently strong differential stress, but not compositional asymmetry alone, can increase the bending modulus. The likely cause is a stiffening of the compressed leaflet, which appears to be related to its gel transition but not identical with it. We finally show that the impact of cholesterol on differential stress depends on the relative strength of elastic and thermodynamic driving forces: if cholesterol solvates equally well in both leaflets, it will redistribute to cancel both leaflet tensions almost completely, but if its partitioning free energy prefers one leaflet over the other, the resulting distribution bias may even create differential stress. Because cells keep most of their lipid bilayers in an asymmetric nonequilibrium steady state, our findings suggest that biomembranes are elastically more complex than previously thought: besides a spontaneous curvature, they might also exhibit significant differential stress, which could strongly affect their curvature energetics.

Interaction Mechanisms of Giant Unilamellar Vesicles with Hydrophobic Glass Surfaces and Silicone Oil-Water Interfaces: Adsorption, Deformation, Rupture, Dynamic Shape Changes, Internal Vesicle Formation, and Desorption

Phospholipid monolayers at oil-water interfaces are often obtained via vesicle adsorption. However, the interaction mechanisms of vesicles with these oil-water interfaces remain unclear. Herein, we studied the adsorption of giant unilamellar vesicles (GUVs) of approximately 2-5 μm diameter onto silicone oil-water interfaces and glass surfaces modified with hexamethyldisilazane (HMDS) and octadecyltrimethoxysilane (ODTMS) using fluorescence microscopy. The GUVs exhibited various modes of interaction, adsorbing on the silanized glass surfaces without sizable deformation, whereas GUVs bound to the silicone oil-water interface exhibited large deformation. After adsorption, GUV rupture occurred within 350, 110, and 3 ms on HMDS-modified glass, ODTMS-modified glass, and silicone oil-water interface, respectively. On glass surfaces, GUV rupture was often initiated and proceeded with pore formation near the surface. The monolayer patches formed by GUV rupture on HMDS-modified glass remained for at least 1 h over an area approximately twice of that estimated from the original GUV. On the ODTMS-modified glass and silicone oil surfaces, the monolayer patch structures disappeared in milliseconds owing to lipid diffusion across the interface. When adsorbed on the oil-water interface, the GUVs spontaneously underwent dynamic shape changes, internal vesicle formation, and desorption without rupture. Thus, it can be concluded that these different pathways arose from different lipid-surface affinities.