Influence of rigid inclusions on the bending elasticity of a lipid membrane

Anisotropic interactions for continuum modeling of protein-membrane systems

In this work, a model for anisotropic interactions between proteins and cellular membranes is proposed for large-scale continuum simulations. The framework of the model is based on dynamic density functional theory, which provides a formalism to describe the lipid densities within the membrane as continuum fields while still maintaining the fidelity of the underlying molecular interactions. Within this framework, we extend recent results to include the anisotropic effects of protein-lipid interactions. As applications, we consider two membrane proteins of biological interest: a RAS-RAF complex tethered to the membrane and a membrane embedded G protein-coupled receptor. A strong qualitative and quantitative agreement is found between the numerical results and the corresponding molecular dynamics simulations. Combining the scope of continuum level simulations with the details from molecular level particle simulations enables research into protein-membrane behaviors at a more biologically relevant scale, which crucially can also be accessed via experiment.

Magnetoresponsive liposomes applications in nanomedicine: A comprehensive review

Safe and effective cancer therapy requires a suitable nanocarrier that can target particular sites, such as cancer cells, in a selective manner. With the tremendous growth in nanotechnology, liposomes, among various competing nanocarriers, have shown promising advances in cancer therapy. Magnetic nanoparticles and metal ions are wide-reaching candidates for conferring magnetic properties and for incorporation into liposomes. Combining liposomes with magnetic structures enables construction of magnetoresponsive liposomes, allowing stimuli-responsiveness to an alternating magnetic field, magnetic targeting, and tracking by magnetic resonance imaging, which could all occur in parallel. This review presents a comprehensive analysis of the practical advances and novel aspects of design, synthesis and engineering magnetoresponsive liposomes, emphasizing their diverse properties for various applications. Our work explores the innovative uses of these structures, extending beyond drug delivery to include smart contrast agents, cell labeling, biosensing, separation, and filtering. By comparing new findings with earlier studies, we showcase significant improvements in efficiency and uncover new potentials, setting a new benchmark for future research in the field of magnetoresponsive liposomes.

Membrane curvature sensing and symmetry breaking of the M2 proton channel from Influenza A

The M2 proton channel aids in the exit of mature influenza viral particles from the host plasma membrane through its ability to stabilize regions of high negative Gaussian curvature (NGC) that occur at the neck of budding virions. The channels are homo-tetramers that contain a cytoplasm-facing amphipathic helix (AH) that is necessary and sufficient for NGC generation; however, constructs containing the transmembrane spanning helix, which facilitates tetramerization, exhibit enhanced curvature generation. Here, we used all-atom molecular dynamics (MD) simulations to explore the conformational dynamics of M2 channels in lipid bilayers revealing that the AH is dynamic, quickly breaking the fourfold symmetry observed in most structures. Next, we carried out MD simulations with the protein restrained in four- and twofold symmetric conformations to determine the impact on the membrane shape. While each pattern was distinct, all configurations induced pronounced curvature in the outer leaflet, while conversely, the inner leaflets showed minimal curvature and significant lipid tilt around the AHs. The MD-generated profiles at the protein-membrane interface were then extracted and used as boundary conditions in a continuum elastic membrane model to calculate the membrane-bending energy of each conformation embedded in different membrane surfaces characteristic of a budding virus. The calculations show that all three M2 conformations are stabilized in inward-budding, concave spherical caps and destabilized in outward-budding, convex spherical caps, the latter reminiscent of a budding virus. One of the C2-broken symmetry conformations is stabilized by 4 kT in NGC surfaces with the minimum energy conformation occurring at a curvature corresponding to 33 nm radii. In total, our work provides atomistic insight into the curvature sensing capabilities of M2 channels and how enrichment in the nascent viral particle depends on protein shape and membrane geometry.

Surfactin molecules with a cone-like structure promote the formation of membrane domains with negative spontaneous curvature and induce membrane invaginations

Surfactin uniquely influences lipid bilayer structure by initially inducing membrane invaginations before solubilization. In this study, we exposed DOPC giant vesicles to various surfactin concentrations at different temperatures and observed surfactin-induced membrane invaginations by using differential interference contrast and confocal laser fluorescence microscopy. These invaginations were stable at room temperature but not at higher temperatures. Surfactin molecules induce membrane nanodomains with negative spontaneous curvature and membrane invaginations despite their intrinsic conical shape and intrinsic positive curvature. Considering the experimentally observed capacity of surfactin to fluidize lipid acyl chains and induce partial dehydration of lipid headgroups, we propose that the resulting surfactin-lipid complexes exhibit a net negative spontaneous curvature. We further conducted 3D numerical Monte Carlo (MC) simulations to investigate the behaviour of vesicles containing negative curvature nanodomains within their membrane at varying temperatures. MC simulations demonstrated strong agreement with experimental results, revealing that invaginations are preferentially formed at low temperatures, while being less pronounced at elevated temperatures. Our findings go beyond the expectations of the Israelachvili molecular shape and packing concepts analysis. These concepts do not take into account the influence of specific interactions between neighboring molecules on the inherent shapes of molecules and their arrangement within curved membrane nanodomains. Our work contributes to a more comprehensive understanding of the complex factors governing vesicle morphology and membrane organization and provides insight into the role of detergent-lipid interactions in modulating vesicle morphology.

Rotation of the c-Ring Promotes the Curvature Sorting of Monomeric ATP Synthases

ATP synthases are proteins that catalyse the formation of ATP through the rotatory movement of their membrane-spanning subunit. In mitochondria, ATP synthases are found to arrange as dimers at the high-curved edges of cristae. Here, a direct link is explored between the rotatory movement of ATP synthases and their preference for curved membranes. An active curvature sorting of ATP synthases in lipid nanotubes pulled from giant vesicles is found. Coarse-grained simulations confirm the curvature-seeking behaviour of rotating ATP synthases, promoting reversible and frequent protein-protein contacts. The formation of transient protein dimers relies on the membrane-mediated attractive interaction of the order of 1.5 kB T produced by a hydrophobic mismatch upon protein rotation. Transient dimers are sustained by a conic-like arrangement characterized by a wedge angle of θ ≈ 50°, producing a dynamic coupling between protein shape and membrane curvature. The results suggest a new role of the rotational movement of ATP synthases for their dynamic self-assembly in biological membranes.

Dependence of protein-induced lipid bilayer deformations on protein shape

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

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.

Alteration of lipid bilayer mechanics by volatile anesthetics: Insights from μs-long molecular dynamics simulations

Very few drugs in clinical practice feature the chemical diversity, narrow therapeutic window, unique route of administration, and reversible cognitive effects of volatile anesthetics. The correlation between their hydrophobicity and their potency and the increasing amount of evidence suggesting that anesthetics exert their action on transmembrane proteins, justifies the investigation of their effects on phospholipid bilayers at the molecular level, given the strong functional and structural link between transmembrane proteins and the surrounding lipid matrix. Molecular dynamics simulations of a model lipid bilayer in the presence of ethylene, desflurane, methoxyflurane, and the nonimmobilizer 1,2-dichlorohexafluorocyclobutane (also called F6 or 2N) at different concentrations highlight the structural consequences of VA partitioning in the lipid phase, with a decrease of lipid order and bilayer thickness, an increase in overall lipid lateral mobility and area-per-lipid, and a marked reduction in the mechanical stiffness of the membrane, that strongly correlates with the compounds' hydrophobicity.

Universal properties of active membranes

We put forward a general field theory for nearly flat fluid membranes with embedded activators and analyze their critical properties using renormalization group techniques. Depending on the membrane-activator coupling, we find a crossover between acoustic and diffusive scaling regimes, with mean-field dynamical critical exponents z=1 and 2, respectively. We argue that the acoustic scaling, which is exact in all spatial dimensions, leads to an early-time behavior, which is representative of the spatiotemporal patterns observed at the leading edge of motile cells, such as oscillations superposed on the growth of the membrane width. In the case of mean-field diffusive scaling, one-loop corrections to the mean-field exponents reveal universal behavior distinct from the Kardar-Parisi-Zhang scaling of passive interfaces and signs of strong-coupling behavior.

Renormalization group study of the dynamics of active membranes: Universality classes and scaling laws

Motivated by experimental observations of patterning at the leading edge of motile eukaryotic cells, we introduce a general model for the dynamics of nearly-flat fluid membranes driven from within by an ensemble of activators. We include, in particular, a kinematic coupling between activator density and membrane slope which generically arises whenever the membrane has a nonvanishing normal speed. We unveil the phase diagram of the model by means of a perturbative field-theoretical renormalization group analysis. Due to the aforementioned kinematic coupling the natural early-time dynamical scaling is acoustic, that is the dynamical critical exponent is 1. However, as soon as the the normal velocity of the membrane is tuned to zero, the system crosses over to diffusive dynamic scaling in mean field. Distinct critical points can be reached depending on how the limit of vanishing velocity is realized: in each of them corrections to scaling due to nonlinear coupling terms must be taken into account. The detailed analysis of these critical points reveals novel scaling regimes which can be accessed with perturbative methods, together with signs of strong coupling behavior, which establishes a promising ground for further nonperturbative calculations. Our results unify several previous studies on the dynamics of active membrane, while also identifying nontrivial scaling regimes which cannot be captured by passive theories of fluctuating interfaces and are relevant for the physics of living membranes.

On the Role of Electrostatic Repulsion in Topological Defect-Driven Membrane Fission

Within a modified Langevin Poisson–Boltzmann model of electric double layers, we derived an analytical expression for osmotic pressure between two charged surfaces. The orientational ordering of the water dipoles as well as the space dependencies of electric potentials, electric fields, and osmotic pressure between two charged spheres were taken into account in the model. Thus, we were able to capture the interaction between the parent cell and connected daughter vesicle or the interactions between neighbouring beads in necklace-like membrane protrusions. The predicted repulsion between them can facilitate the topological antidefect-driven fission of membrane daughter vesicles and the fission of beads of undulated membrane protrusions.

The Elucidation of the Molecular Mechanism of the Extrusion Process

Extrusion is a popular method for producing homogenous population of unilamellar liposomes. The technique relies on forcing a lipid suspension through cylindrical pores in a polycarbonate membrane. The quantification of the extrusion and/or recalibration processes make possible the acquisition of experimental data, which can be correlated with the mechanical properties of the lipid bilayer. In this work, the force needed for the extrusion process was correlated with the mechanical properties of a lipid bilayer derived from other experiments. Measurements were performed using a home-made dedicated device capable of maintaining a stable volumetric flux of a liposome suspension through well-defined pores and to continuously measure the extrusion force. Based on the obtained results, the correlation between the lipid bilayer bending rigidity and extrusion force was derived. Specifically, it was found that the bending rigidity of liposomes formed from well-defined lipid mixtures agrees with data obtained by others using flicker-noise spectroscopy or micromanipulation. The other issue addressed in the presented studies was the identification of molecular mechanisms leading to the formation of unilamellar vesicles in the extrusion process. Finally, it was demonstrated that during the extrusion, lipids are not exchanged between vesicles, i.e., vesicles can divide but no membrane fusion or lipid exchange between bilayers was detected.

Mechanical and Electrical Interaction of Biological Membranes with Nanoparticles and Nanostructured Surfaces

In this review paper, we theoretically explain the origin of electrostatic interactions between lipid bilayers and charged solid surfaces using a statistical mechanics approach, where the orientational degree of freedom of lipid head groups and the orientational ordering of the water dipoles are considered. Within the modified Langevin Poisson–Boltzmann model of an electric double layer, we derived an analytical expression for the osmotic pressure between the planar zwitterionic lipid bilayer and charged solid planar surface. We also show that the electrostatic interaction between the zwitterionic lipid head groups of the proximal leaflet and the negatively charged solid surface is accompanied with a more perpendicular average orientation of the lipid head-groups. We further highlight the important role of the surfaces’ nanostructured topography in their interactions with biological material. As an example of nanostructured surfaces, we describe the synthesis of TiO₂ nanotubular and octahedral surfaces by using the electrochemical anodization method and hydrothermal method, respectively. The physical and chemical properties of these nanostructured surfaces are described in order to elucidate the influence of the surface topography and other physical properties on the behavior of human cells adhered to TiO₂ nanostructured surfaces. In the last part of the paper, we theoretically explain the interplay of elastic and adhesive contributions to the adsorption of lipid vesicles on the solid surfaces. We show the numerically predicted shapes of adhered lipid vesicles corresponding to the minimum of the membrane free energy to describe the influence of the vesicle size, bending modulus, and adhesion strength on the adhesion of lipid vesicles on solid charged surfaces.

Creasing of flexible membranes at vanishing tension

The properties of freestanding tensionless interfaces and membranes at low bending rigidity κ are dominated by strong fluctuations and self-avoidance and are thus outside the range of standard perturbative analysis. We analyze this regime by a simple discretized, self-avoiding membrane model on a frame subject to periodic boundary conditions by use of Monte Carlo simulation and dynamically triangulated surface techniques. We find that at low bending rigidities, the membrane properties fall into three regimes: Below the collapse transition κ_{BP} it is subject to branched polymer instability where the framed surface is not defined, in a range below a threshold rigidity κ_{c} the conformational correlation function are characterized by power-law behavior with a continuously varying exponent α, 2<α≤4 and above κ_{c}, α=4 characteristic for linearized bending excitations. Response functions specific heat and area compressibility display pronounced peaks close to κ_{c}. The results may be important for the description of soft interface systems, such as microemulsions and membranes with in-plane cooperative phenomena.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Impact of Quercetin Encapsulation with Added Phytosterols on Bilayer Membrane and Photothermal-Alteration of Novel Mixed Soy Lecithin-Based Liposome

This study used highly lipophilic agents with an aim to increase the oxidant inhibitory activity and enhance photothermal stability of a novel mixed soy lecithin (ML)-based liposome by changing the composition of formulation within the membrane. Specifically, the development and optimization of the liposome intended for improving Trolox equivalent antioxidant capacity (TEAC) value and %TEAC loss was carried out by incorporating a natural antioxidant, quercetin (QU). In this context, a focus was set on QU encapsulation in ML-based liposomes and the concentration-dependent solubility of QU was investigated and calculated as encapsulation efficiency (EE). To explore the combined effects of the incorporation of plant sterols on the integrity and entrapment capacity of mixed phospholipid vesicles, conjugation of two types of phytosterols (PSs), namely β-sitosterol (βS) and stigmasterol (ST), to mixed membranes at different ratios was also performed. The EE measurement revealed that QU could be efficiently encapsulated in the stable ML-based liposome using 0.15 and 0.1 g/100 mL of βS and ST, respectively. The aforementioned liposome complex exhibited a considerable TEAC (197.23%) and enhanced TEAC loss (30.81%) when exposed to ultraviolet (UV) light (280-320 nm) over a 6 h duration. It appeared that the presence and type of PSs affect the membrane-integration characteristics as well as photodamage transformation of the ML-based liposome. The association of QU with either βS or ST in the formulation was justified by their synergistic effects on the enhancement of the EE of liposomes. Parallel to this, it was demonstrated that synergistic PS effects could be in effect in the maintenance of membrane order of the ML-based liposome. The findings presented in this study provided useful information for the development and production of stable QU-loaded ML-based liposomes for food and nutraceutical applications and could serve as a potential mixed lipids-based delivery system in the disease management using antioxidant therapy.

Additional contributions to elastic energy of lipid membranes: Tilt-curvature coupling and curvature gradient

Lipid bilayer membranes under biologically relevant conditions are flexible thin laterally fluid films consisting of two unimolecular layers (monolayers) each about 2 nm thick. On spatial scales much larger than the bilayer thickness, the membrane elasticity is well determined by its shape. The classical Helfrich theory considers the membrane as an elastic two-dimensional (2D) film, which has no particular internal structure. However, various local membrane heterogeneities can result in a lipids tilt relative to the membrane surface normal. On the basis of the classical elasticity theory of 3D bodies, Hamm and Kozlov [Eur. Phys. J. E 3, 323 (2000)10.1007/s101890070003] derived the most general energy functional, taking into account the tilt and lipid monolayer curvature. Recently, Terzi and Deserno [J. Chem. Phys. 147, 084702 (2017)10.1063/1.4990404] showed that Hamm and Kozlov's derivation was incomplete because the tilt-curvature coupling term had been missed. However, the energy functional derived by Terzi and Deserno appeared to be unstable, thereby being invalid for applications that require minimizations of the overall energy of deformations. Here, we derive a stable elastic energy functional, showing that the squared gradient of the curvature was missed in both of these works. This change in the energy functional arises from a more accurate consideration of the transverse shear deformation terms and their influence on the membrane stability. We also consider the influence of the prestress terms on the stability of the energy functional, and we show that it should be considered small and the effective Gaussian curvature should be neglected because of the stability requirements. We further generalize the theory, including the stretching-compressing deformation modes, and we provide the geometrical interpretation of the terms that were previously missed by Hamm and Kozlov. The physical consequences of the new terms are analyzed in the case of a membrane-mediated interaction of two amphipathic peptides located in the same monolayer. We also provide the expression for director fluctuations, comparing it with that obtained by Terzi and Deserno.

Confinement in Nanodiscs Anisotropically Modifies Lipid Bilayer Elastic Properties

Lipid nanodiscs are small synthetic lipid bilayer structures that are stabilized in solution by special circumscribing (or scaffolding) proteins or polymers. Because they create native-like environments for transmembrane proteins, lipid nanodiscs have become a powerful tool for structural determination of this class of systems when combined with cryo-electron microscopy or nuclear magnetic resonance. The elastic properties of lipid bilayers determine how the lipid environment responds to membrane protein perturbations, and how the lipid in turn modifies the conformational state of the embedded protein. However, despite the abundant use of nanodiscs in determining membrane protein structure, the elastic material properties of even pure lipid nanodiscs (i.e., without embedded proteins) have not yet been quantitatively investigated. A major hurdle is due to the inherently nonlocal treatment of the elastic properties of lipid systems implemented by most existing methods, both experimental and computational. In addition, these methods are best suited for very large “infinite” size lipidic assemblies, or ones that contain periodicity, in the case of simulations. We have previously described a computational analysis of molecular dynamics simulations designed to overcome these limitations, so it allows quantification of the bending rigidity (K_C) and tilt modulus (κ_t) on a local scale even for finite, nonperiodic systems, such as lipid nanodiscs. Here we use this computational approach to extract values of K_C and κ_t for a set of lipid nanodisc systems that vary in size and lipid composition. We find that the material properties of lipid nanodiscs are different from those of infinite bilayers of corresponding lipid composition, highlighting the effect of nanodisc confinement. Nanodiscs tend to show higher stiffness than their corresponding macroscopic bilayers, and moreover, their material properties vary spatially within them. For small-size MSP1 nanodiscs, the stiffness decreases radially, from a value that is larger in their center than the moduli of the corresponding bilayers by a factor of ∼2–3. The larger nanodiscs (MSP1E3D1 and MSP2N2) show milder spatial changes of moduli that are composition dependent and can be maximal in the center or at some distance from it. These trends in moduli correlate with spatially varying structural properties, including the area per lipid and the nanodisc thickness. Finally, as has previously been reported, nanodiscs tend to show deformations from perfectly flat circular geometries to varying degrees, depending on size and lipid composition. The modulations of lipid elastic properties that we find should be carefully considered when making structural and functional inferences concerning embedded proteins.

Magneto-mechanical actuation of barium-hexaferrite nanoplatelets for the disruption of phospholipid membranes

HYPOTHESIS

The magneto-mechanical actuation (MMA) of magnetic nanoparticles with a low-frequency alternating magnetic field (AMF) can be used to destroy cancer cells. So far, MMA was tested on different cells using different nanoparticles and different field characteristics, which makes comparisons and any generalizations about the results of MMA difficult. In this paper we propose the use of giant unilamellar vesicles (GUVs) as a simple model system to study the effect of MMA on a closed lipid bilayer membrane, i.e., a basic building block of any cell.

EXPERIMENTS

The GUVs were exposed to barium-hexaferrite nanoplatelets (NPLs, ~50 nm wide and 3 nm thick) with unique magnetic properties dominated by a permanent magnetic moment that is perpendicular to the platelet, at different concentrations (1-50 µg/mL) and pH values (4.2-7.4) of the aqueous suspension. The GUVs were observed with an optical microscope while being exposed to a uniaxial AMF (3-100 Hz, 2.2-10.6 mT).

FINDINGS

When the NPLs were electrostatically attached to the GUV membranes, the MMA induced cyclic fluctuations of the GUVs' shape corresponding to the AMF frequency at the low NPL concentration (1 µm/mL), whereas the GUVs were bursting at the higher concentration (10 µg/mL). Theoretical considerations suggested that the bursting of the GUVs is a consequence of the local action of an assembly of several NPLs, rather than a collective effect of all the absorbed NPLs.

Saddle-curvature instability of lipid bilayer induced by amphipathic peptides: a molecular model

Amphipathic peptides that partition into lipid bilayers affect the curvature elastic properties of their host. Some of these peptides are able to shift the Gaussian modulus to positive values, thus triggering an instability with respect to the formation of saddle curvatures. To characterize the generic aspects of the underlying mechanism, we employ a molecular lipid model that accounts for the interfacial tension between the polar and apolar regions of the membrane, for interactions between the lipid headgroups, and for the energy to stretch or compress the hydrocarbon chains. Peptides are modeled as cylinders that partition into the host membrane in a parallel orientation where they diminish the space available to the lipid headgroups and chains. The penetration depth into the membrane is determined by the angular size of the peptide's hydrophilic region. We demonstrate that only peptides with a small angular size of their hydrophilic region have an intrinsic tendency to render the Gaussian modulus more positive, and we identify conditions at which the Gaussian modulus adopts a positive sign upon increasing the peptide concentration. Our model allows us to also incorporate electrostatic interactions between cationic peptides and anionic lipids on the level of the linear Debye-Hückel model. We show that electrostatic interactions tend to shift the Gaussian modulus toward more positive values. Steric and electrostatic lipid-peptide interactions jointly decrease the effective interaction strength in the headgroup region of the host membrane thus suggesting a generic mechanisms of how certain amphipathic peptides are able to induce the formation of saddle curvatures.

Origin of lipid tilt in flat monolayers and bilayers

This paper continues the series of our works devoted to the liquid-gel phase transition in lipid membranes. Previously we described a variation of area per lipid, membrane thickness, and diffusion coefficient at the temperature-driven liquid-gel phase transition in bilayers. Here we expand the application of our analytic model approach to include a description of the lipid tilt and also extend the investigation to include Langmuir and self-assembled monolayers. The theory describes tilt formation at the temperature-driven liquid-gel phase transition in bilayers and the pressure-driven phase transition in Langmuir monolayers. Neither uniform tilt nor liquid-gel phase transition is found in self-assembled monolayers chemically bonded to the substrate.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Clustering and separation of hydrophobic nanoparticles in lipid bilayer explained by membrane mechanics

Small hydrophobic gold nanoparticles with diameter lower than the membrane thickness can form clusters or uniformly distribute within the hydrophobic core of the bilayer. The coexistence of two stable phases (clustered and dispersed) indicates the energy barrier between nanoparticles. We calculated the distance dependence of the membrane-mediated interaction between two adjacent nanoparticles. In our model we consider two deformation modes: the monolayer bending and the hydroxycarbon chain stretching. Existence of an energy barrier between the clustered and the separated state of nanoparticles was predicted. Variation analysis of the membrane mechanical parameters revealed that the energy barrier between two membrane embedded nanoparticles is mainly the consequence of the bending deformation and not change of the thickness of the bilayer in the vicinity of nanoparticles. It is shown, that the forces between the nanoparticles embedded in the biological membrane could be either attractive or repulsive, depending on the mutual distance between them.

Cell penetrating peptide modulation of membrane biomechanics by Molecular dynamics

The efficacy of a pharmaceutical treatment is often countered by the inadequate membrane permeability, that prevents drugs from reaching their specific intracellular targets. Cell penetrating peptides (CPPs) are able to route across cells' membrane various types of cargo, including drugs and nanoparticles. However, CPPs internalization mechanisms are not yet fully understood and depend on a wide variety of aspects. In this contest, the entry of a CPP into the lipid bilayer might induce molecular conformational changes, including marked variations on membrane's mechanical properties. Understanding how the CPP does influence the mechanical properties of cells membrane is crucial to design, engineer and improve new and existing penetrating peptides. Here, all atom Molecular Dynamics (MD) simulations were used to investigate the interaction between different types of CPPs embedded in a lipid bilayer of dioleoyl phosphatidylcholine (DOPC). In a greater detail, we systematically highlighted how CPP properties are responsible for modulating the membrane bending modulus. Our findings highlighted the CPP hydropathy strongly correlated with penetration of water molecules in the lipid bilayer, thus supporting the hypothesis that the amount of water each CPP can route inside the membrane is modulated by the hydrophobic and hydrophilic character of the peptide. Water penetration promoted by CPPs leads to a local decrease of the lipid order, which emerges macroscopically as a reduction of the membrane bending modulus.

Lipid-packing perturbation of model membranes by pH-responsive antimicrobial peptides

The indiscriminate use of conventional antibiotics is leading to an increase in the number of resistant bacterial strains, motivating the search for new compounds to overcome this challenging problem. Antimicrobial peptides, acting only in the lipid phase of membranes without requiring specific membrane receptors as do conventional antibiotics, have shown great potential as possible substituents of these drugs. These peptides are in general rich in basic and hydrophobic residues forming an amphipathic structure when in contact with membranes. The outer leaflet of the prokaryotic cell membrane is rich in anionic lipids, while the surface of the eukaryotic cell is zwitterionic. Due to their positive net charge, many of these peptides are selective to the prokaryotic membrane. Notwithstanding this preference for anionic membranes, some of them can also act on neutral ones, hampering their therapeutic use. In addition to the electrostatic interaction driving peptide adsorption by the membrane, the ability of the peptide to perturb lipid packing is of paramount importance in their capacity to induce cell lysis, which is strongly dependent on electrostatic and hydrophobic interactions. In the present research, we revised the adsorption of antimicrobial peptides by model membranes as well as the perturbation that they induce in lipid packing. In particular, we focused on some peptides that have simultaneously acidic and basic residues. The net charges of these peptides are modulated by pH changes and the lipid composition of model membranes. We discuss the experimental approaches used to explore these aspects of lipid membranes using lipid vesicles and lipid monolayer as model membranes.

New Continuum Approaches for Determining Protein-Induced Membrane Deformations

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, it has been argued that continuum models cannot reproduce the distortions observed in fully atomistic molecular dynamics simulations. We suggest that this failure can be overcome by using chemically and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel's orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution.

On the role of external force of actin filaments in the formation of tubular protrusions of closed membrane shapes with anisotropic membrane components

Biological membranes are composed of different components and there is no a priori reason to assume that all components are isotropic. It was previously shown that the anisotropic properties of membrane components may explain the stability of membrane tubular protrusions even without the application of external force. Our theoretical study focuses on the role of anisotropic membrane components in the stability of membrane tubular structures generated or stabilized by actin filaments. We show that the growth of the actin cytoskeleton inside the vesicle can induce the partial lateral segregation of different membrane components. The entropy of mixing of membrane components hinders the total lateral segregation of the anisotropic and isotropic membrane components. Self-assembled aggregates formed by anisotropic membrane components facilitate the growth of long membrane tubular protrusions. Protrusive force generated by actin filaments favors strong segregation of membrane components by diminishing the opposing effect of mixing entropy.

Continuum descriptions of membranes and their interaction with proteins: Towards chemically accurate models

Biological membranes deform in response to resident proteins leading to a coupling between membrane shape and protein localization. Additionally, the membrane influences the function of membrane proteins. Here we review contributions to this field from continuum elastic membrane models focusing on the class of models that couple the protein to the membrane. While it has been argued that continuum models cannot reproduce the distortions observed in fully-atomistic molecular dynamics simulations, we suggest that this failure can be overcome by using chemically accurate representations of the protein. We outline our recent advances along these lines with our hybrid continuum-atomistic model, and we show the model is in excellent agreement with fully-atomistic simulations of the nhTMEM16 lipid scramblase. We believe that the speed and accuracy of continuum-atomistic methodologies will make it possible to simulate large scale, slow biological processes, such as membrane morphological changes, that are currently beyond the scope of other computational approaches. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Controlled assembly of magnetic nanoparticles on microbubbles for multimodal imaging

Magnetic microbubbles (MMBs) consisting of microbubbles (MBs) and magnetic nanoparticles (MNPs) were synthesized for use as novel markers for improving multifunctional biomedical imaging. The MMBs were fabricated by assembling MNPs in different concentrations on the surfaces of MBs. The relationships between the structure, magnetic properties, stability of the MMBs, and their use in magnetic resonance/ultrasound (MR/US) dual imaging applications were determined. The MNPs used were NPs of 3-aminopropyltriethoxysilane (APTS)-functionalized superparamagnetic iron oxide γ-Fe2O3 (SPIO). SPIO was assembled on the surfaces of polymer MBs using a "surface-coating" approach. An analysis of the underlying mechanism showed that the synergistic effects of covalent coupling, electrostatic adsorption, and aggregation of the MNPs allowed them to be unevenly assembled in large amounts on the surfaces of the MBs. With an increase in the MNP loading amount, the magnetic properties of the MMBs improved significantly; in this way, the shell structure and mechanical properties of the MMBs could be modified. For surface densities ranging from 2.45 × 10(-7) μg per MMB to 8.45 × 10(-7) μg per MMB, in vitro MR/US imaging experiments showed that, with an increase in the number of MNPs on the surfaces of the MBs, the MMBs exhibited better T2 MR imaging contrast, as well as an increase in the US contrast for longer durations. In vivo experiments also showed that, by optimizing the structure of the MMBs, enhanced MR/US dual-modality image signals could be obtained for mouse tumors. Therefore, by adjusting the shell composition of MBs through the assembly of MNPs in different concentrations, MMBs with good magnetic and acoustic properties for MR/US dual-modality imaging contrast agents could be obtained.

Membrane shape modulates transmembrane protein distribution

Although membrane shape varies greatly throughout the cell, the contribution of membrane curvature to transmembrane protein targeting is unknown because of the numerous sorting mechanisms that take place concurrently in cells. To isolate the effect of membrane shape, we used cell-sized giant unilamellar vesicles (GUVs) containing either the potassium channel KvAP or the water channel AQP0 to form membrane nanotubes with controlled radii. Whereas the AQP0 concentrations in flat and curved membranes were indistinguishable, KvAP was enriched in the tubes, with greater enrichment in more highly curved membranes. Fluorescence recovery after photobleaching measurements showed that both proteins could freely diffuse through the neck between the tube and GUV, and the effect of each protein on membrane shape and stiffness was characterized using a thermodynamic sorting model. This study establishes the importance of membrane shape for targeting transmembrane proteins and provides a method for determining the effective shape and flexibility of membrane proteins.

Influence of nanoparticle-membrane electrostatic interactions on membrane fluidity and bending elasticity

The aim of this work is to investigate the effect of electrostatic interactions between the nanoparticles and the membrane lipids on altering the physical properties of the liposomal membrane such as fluidity and bending elasticity. For this purpose, we have used nanoparticles and lipids with different surface charges. Positively charged iron oxide (γ-Fe2O3) nanoparticles, neutral and negatively charged cobalt ferrite (CoFe2O4) nanoparticles were encapsulated in neutral lipid 1-stearoyl-2-oleoyl-sn-glycero-3-phosphocholine and negatively charged 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine lipid mixture. Membrane fluidity was assessed through the anisotropy measurements using the fluorescent probe 1,6-diphenyl-1,3,5-hexatriene. Though the interaction of both the types of nanoparticles reduced the membrane fluidity, the results were more pronounced in the negatively charged liposomes encapsulated with positively charged iron oxide nanoparticles due to strong electrostatic attractions. X-ray photoelectron spectroscopy results also confirmed the presence of significant quantity of positively charged iron oxide nanoparticles in negatively charged liposomes. Through thermally induced shape fluctuation measurements of the giant liposomes, a considerable reduction in the bending elasticity modulus was observed for cobalt ferrite nanoparticles. The experimental results were supported by the simulation studies using modified Langevin-Poisson-Boltzmann model.

Calculating the Bending Modulus for Multicomponent Lipid Membranes in Different Thermodynamic Phases

We establish a computational approach to extract the bending modulus, KC , for lipid membranes from relatively small-scale molecular simulations. Fluctuations in the splay of individual pairs of lipids faithfully inform on KC in multicomponent membranes over a large range of rigidities in different thermodynamic phases. Predictions are validated by experiments even where the standard spectral analysis-based methods fail. The local nature of this method potentially allows its extension to calculations of KC in protein-laden membranes.

How sterol tilt regulates properties and organization of lipid membranes and membrane insertions

Serving as a crucial component of mammalian cells, cholesterol critically regulates the functions of biomembranes. This review focuses on a specific property of cholesterol and other sterols: the tilt modulus χ that quantifies the energetic cost of tilting sterol molecules inside the lipid membrane. We show how χ is involved in determining properties of cholesterol-containing membranes, and detail a novel approach to quantify its value from atomistic molecular dynamics (MD) simulations. Specifically, we link χ with other structural, thermodynamic, and mechanical properties of cholesterol-containing lipid membranes, and delineate how this useful parameter can be obtained from the sterol tilt probability distributions derived from relatively small-scale unbiased MD simulations. We demonstrate how the tilt modulus quantitatively describes the aligning field that sterol molecules create inside the phospholipid bilayers, and we relate χ to the bending rigidity of the lipid bilayer through effective tilt and splay energy contributions to the elastic deformations. Moreover, we show how χ can conveniently characterize the "condensing effect" of cholesterol on phospholipids. Finally, we demonstrate the importance of this cholesterol aligning field to the proper folding and interactions of membrane peptides. Given the relative ease of obtaining the tilt modulus from atomistic simulations, we propose that χ can be routinely used to characterize the mechanical properties of sterol/lipid bilayers, and can also serve as a required fitting parameter in multi-scaled simulations of lipid membrane models to relate the different levels of coarse-grained details.

Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers

We present a unified continuum-level model for bilayer energetics that includes the effects of bending, compression, lipid orientation (tilting relative to the monolayer surface normal), and microscopic noise (protrusions). Expressions for thermal fluctuation amplitudes of several physical quantities are derived. These predictions are shown to be in good agreement with molecular simulations.

On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures

Recent studies have demonstrated that actin filaments are not crucial for the short-term stability of tubular membrane protrusions originating from the cell surface. It has also been demonstrated that prominin nanodomains and curvature inducing I-BAR proteins could account for the stability of the membrane protrusion. Here we constructed an axisymmetric model of a membrane protrusion that excludes actin filaments in order to investigate the contributions of prominin nanodomains (rafts) and I-BAR proteins to the membrane protrusion stability. It was demonstrated that prominin nanodomains and I-BAR proteins can stabilize the membrane protrusion only over a specific range of spontaneous curvature. On the other hand, high spontaneous curvature and/or high density of I-BAR proteins could lead to system instability and to non-uniform contraction in the radial direction of the membrane protrusion. In agreement with previous studies, it was also shown that the isotropic bending energy of lipids is not sufficient to explain the stability of the observed tubular membrane protrusion without actin filaments.

Membrane morphology induced by anisotropic proteins

There are a great many proteins that localize to and collectively generate curvature in biological fluid membranes. We study changes in the topology of fluid membranes due to the presence of highly anisotropic, curvature-inducing proteins. Generically, we find a surprisingly rich phase diagram with phases of both positive and negative Gaussian curvature. As a concrete example modeled on experiments, we find that a lamellar phase in a negative Gaussian curvature regime exhibits a propensity to form screw dislocations of definite Burgers scalar but of both chiralities.

Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids

Research investigating lipid membrane curvature generation and sensing is a rapidly developing frontier in membrane physical chemistry and biophysics. The fast recent progress is based on the discovery of a plethora of proteins involved in coupling membrane shape to cellular membrane function, the design of new quantitative experimental techniques to study aspects of membrane curvature, and the development of analytical theories and simulation techniques that allow a mechanistic interpretation of quantitative measurements. The present review first provides an overview of important classes of membrane proteins for which function is coupled to membrane curvature. We then survey several mechanisms that are assumed to underlie membrane curvature sensing and generation. Finally, we discuss relatively simple thermodynamic/mechanical models that allow quantitative interpretation of experimental observations.

Post-prandial rise of microvesicles in peripheral blood of healthy human donors

Background

Microvesicles isolated from body fluids are membrane - enclosed fragments of cell interior which carry information on the status of the organism. It is yet unclear how metabolism affects the number and composition of microvesicles in isolates from the peripheral blood.

Aim

To study the post - prandial effect on microvesicles in isolates from the peripheral blood of 21 healthy donors, in relation to blood cholesterol and blood glucose concentrations.

Results

The average number of microvesicles in the isolates increased 5 hours post - prandially by 52%; the increase was statistically significant (p = 0.01) with the power P = 0.68, while the average total blood cholesterol concentration, average low density lipoprotein cholesterol concentration (LDL-C) and average high density lipoprotein cholesterol concentration (HDL-C) all remained within 2% of their fasting values. We found an 11% increase in triglycerides (p = 0.12) and a 6% decrease in blood glucose (p < 0.01, P = 0.74). The post - prandial number of microvesicles negatively correlated with the post - fasting total cholesterol concentration (r = - 0.46, p = 0.035) while the difference in the number of microvesicles in the isolates between post - prandial and post - fasting states negatively correlated with the respective difference in blood glucose concentration (r = - 0.39, p = 0.05).

Conclusions

In a population of healthy human subjects the number of microvesicles in isolates from peripheral blood increased in the post - prandial state. The increase in the number of microvesicles was affected by the fasting concentration of cholesterol and correlated with the decrease in blood glucose.

Echinophilic proteins stomatin, sorcin, and synexin locate outside gangliosideM1 (GM1) patches in the erythrocyte membrane

The detergent (Triton X-100, 4°C)-resistant membrane (DRM)-associated membrane proteins stomatin, sorcin, and synexin (anexin VII) exposed on the cytoplasmic side of membrane were investigated for their lateral distribution in relation to induced ganglioside(M1) (GM1) raft patches in flat (discocytic) and curved (echinocytic) human erythrocyte membrane. In discocytes, no accumulation of stomatin, sorcin, and synexin in cholera toxin subunit B (CTB) plus anti-CTB-induced GM1 patches was detected by fluorescence microscopy. In echinocytes, stomatin, sorcin, and synexin showed a similar curvature-dependent lateral distribution as GM1 patches by accumulating to spiculae induced by ionophore A23187 plus calcium. Stomatin was partly and synexin and sorcin were fully recruited to the spiculae. However, the DRM-associated proteins only partially co-localized with GM1 and were frequently distributed into different spiculae than GM1. The study indicates that stomatin, sorcin, and synexin are echinophilic membrane components that mainly locate outside GM1 rafts in the human erythrocyte membrane. Echinophilicity is suggested to contribute to the DRM association of a membrane component in general.

Lamellar stacking split by in-membrane clustering of bulky glycolipids

We developed a simple model to investigate the effect of lipid clustering on the local interlayer distance in a cluster of interacting lamellae. The model, based on nonequilibrium thermodynamics and linear stability theories, explores the early stages of the lamella-lamella phase separation process where the lateral diffusion is much faster than the interlamellar lipid exchange. Results indicate, in the early stages, the presence of locally distorted regions with a higher concentration of one lipid component and an anomalous repeat distance. Experimental cases are presented, consisting of multilamellar-oriented depositions of phospholipids containing minority amounts of ganglioside or sphingomyelin under a low-hydration condition. The minority components are known to form domains within the phospholipid bilayer matrix. The low water content inhibits the lipid exchange among nearby lamellae and strengthens lamella-lamella interaction, allowing for a straightforward comparison with the model. Small-angle and wide-angle neutron diffraction experiments were performed in order to detect interlayer distances and local chain order, respectively. Lamellar stacking splitting has been observed for the ganglioside-containing lamellae, induced by in-phase lipid clustering. In excess water and after long equilibration times, these local structures may further evolve, leading to coexisting lamellar phases with different lipid compositions and interlayer distances.

Membrane-protein interactions in a generic coarse-grained model for lipid bilayers

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed.