Mechanical stability of micropipet-aspirated giant vesicles with fluid phase coexistence

Micropipet aspiration of phase-separated lipid bilayer vesicles can elucidate physicochemical aspects of membrane fluid phase coexistence. Recently, we investigated the composition dependence of line tension at the boundary between liquid-ordered and liquid-disordered phases of giant unilamellar vesicles obtained from ternary lipid mixtures using this approach. Here we examine mechanical equilibria and stability of dumbbell-shaped vesicles deformed by line tension. We present a relationship between the pipet aspiration pressure and the aspiration length in vesicles with two coexisting phases. Using a strikingly simple mechanical model for the free energy of the vesicle, we predict a relation that is in almost quantitative agreement with experiment. The model considers the vesicle free energy to be proportional to line tension and assumes that the vesicle volume, domain area fraction, and total area are conserved during aspiration. We also examine a mechanical instability encountered when releasing a vesicle from the pipet. We find that this releasing instability is observed within the framework of our model that predicts a change of the compressibility of a pipet-aspirated membrane cylinder from positive (i.e., stable) to negative (unstable) values, at the experimental instability. The model furthermore includes an aspiration instability that has also previously been experimentally described. Our method of studying micropipet-induced shape transitions in giant vesicles with fluid domains could be useful for investigating vesicle shape transitions modulated by bending stiffness and line tension.     

Size-dependent properties of small unilamellar vesicles formed by model lipids

The size-dependent behavior of small unilamellar vesicles is explored by dissipative particle dynamics, including the membrane characteristics and mechanical properties. The spontaneously formed vesicles are in the metastable state and the vesicle size is controlled by the concentration of model lipids. As the vesicle size decreases, the bilayer gets thinner and the area density of heads declines. Nonetheless, the area density in the inner leaflet is higher than that in the outer. The packing parameters are calculated for both leaflets. The result indicates that the shape of lipid in the outer leaflet is like a truncated cone but that in the inner leaflet resembles an inverted truncated cone. Based on a local order parameter, our simulations indication that the orientation order of lipid molecules decreases as the size of the vesicle reduces and this fact reveals that the bilayer becoming thinner for smaller vesicle is mainly attributed to the orientation disorder of the lipids. The membrane tension can be obtained through the Young-Laplace equation. The tension is found to grow with reducing vesicle size. Therefore, small vesicles are less stable against fusion. Using the inflation method, the area stretching and bending moduli can be determined and those moduli are found to grow with reducing size. Nonetheless, a general equation with a single numerical constant can relate bending modulus, area stretching modulus, and bilayer thickness irrespective of the vesicle size. Finally, a simple metastable model is proposed to explain the size-dependent behavior of bilayer thickness, orientation, and tension.     

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.     

Endoplasmatic reticulum shaping by generic mechanisms and protein-induced spontaneous curvature

The endoplasmatic reticulum (ER) comprises flattened vesicles (cisternae) with worm holes dubbed with ribosomes coexisting with a network of interconnected tubes which can extend to the cell periphery or even penetrate nerve axons. The coexisting topologies enclose a continuous luminal space. The complex ER topology is specifically controlled by a group of ER-shaping proteins often called reticulons (discovered by the group of Tom Rapoport [1]). They include atlastin, reticulon, REEP and the MT severing protein spastin. A generic ER shape controlling factor is the necessity to maximize the area-to-volume ratio of ER membranes in the highly crowded cytoplasmic space. I present a model of the ER-shaping function of the reticulons based on the Helfrich bending elasticity concept of soft shell shape changes. Common structural motifs of the reticulons are hydrophobic sequences forming wedge shaped hairpins which penetrate the lipid bilayer of the cell membranes. The wedge-like hydrophobic anchors can both induce the high curvature of the tubular ER fraction and ensure the preferred distribution of the reticulons along the tubules. Tubular junctions may be stabilized by the reticulons forming two forceps twisted by 90°. The ER extensions to the cell periphery and the axons are mediated by coupling of the tubes to the microtubules which is mediated by REEP and spastin. At the end I present a model of the tension driven homotype fusion of ER-membranes by atlastin, based on analogies to the SNARE–complexin–SNARE driven heterotype fusion process.     

Rationalizing the membrane interactions of cationic amphipathic antimicrobial peptides by their molecular shape

Biophysical and structural studies of cationic amphipathic antimicrobial peptides have revealed new mechanistic details concerning their membrane interactions. In interfacial environments the peptides adopt amphipathic conformations and the resulting distribution of polar, charged and hydrophobic residues allows them to partition into the bilayer interface. For several helical peptides it was found that their long axis is oriented parallel to the membrane surface, an arrangement which results in considerable perturbations in the packing of the lipid bilayer. Within the molecular shape concept the peptides act as wedge-like structures which impose positive curvature strain on the membrane. As a consequence a wide variety of morphologies are observed of peptide–lipid mixtures which strongly depend on the detailed peptide sequence, the membrane lipid composition, buffer, temperature and other environmental parameters. Therefore, the peptide–lipid systems are best described by phase diagrams, similar to the ones of detergent–lipid mixtures, encompassing on the one extreme regions where the peptide stabilizes the bilayer and on the other extreme regions where membrane lysis occurs. The effects of peptide sequence, membrane penetration depth, lipid composition and membrane surface charge density on membrane-association, -morphology and the resulting phase boundaries are discussed.     

Vesicle shapes from molecular dynamics simulations

Lipid bilayer membranes are known to form various structures such as large sheets or vesicles. When the two leaflets of the bilayer have an equal composition, the membrane preferentially forms a flat sheet or a spherical vesicle. However, a difference in the composition of the two leaflets may result in a curved bilayer or in a wide variety of vesicle shapes. Vesicles with different shapes have already been shown in experiments and diverse vesicle shapes have been predicted theoretically from energy minimization of continuous curves. Here we present a molecular dynamics study of the effect of small changes in the phospholipid headgroups on the spontaneous curvature of the bilayer and on the resulting vesicle shape transformations. Small asymmetries in the bilayers already result in high spontaneous curvature and large vesicle deformations. Vesicle shapes that are formed include ellipsoids, discoids, pear-shaped vesicles, cup-shaped vesicles, as well as budded vesicles. Comparison of these vesicles with theoretically derived vesicle shapes shows both resemblances and differences.     

Heterogeneity and deformation behavior of lipid vesicles

Recent studies on the deformation of lipid vesicles which is a simple model of biological membranes, and the factors that influence it are reviewed. In homogeneous vesicles, the deformation from spherical to various shapes was observed by adjusting the temperature and the osmotic pressure. This is mainly explained by a balance between the bending elasticity and the area difference energy. In phase separated vesicles, the effect of line tension makes a significant contribution to the deformation. In addition, asymmetric distribution of lipid molecules in bilayers caused by lipid sorting determines deformation behaviors including budding, pore, tube, adhesion, and self-reproduction. The change in membrane curvature due to shielding of lipid charges by electrolytes, proteins, peptides, and solid nanoparticles was also reviewed.     

A Membrane Tension-Responsive Mechanosensitive DNA Nanomachine

Membrane curvature reflects physical forces operating on the lipid membrane, which plays important roles in cellular processes. Here, we design a mechanosensitive DNA (MSD) nanomachine that mimics natural mechanosensitive PIEZO channels to convert the membrane tension changes of lipid vesicles with different sizes into fluorescence signals in real time. The MSD nanomachine consists of an archetypical six-helix-bundle DNA nanopore, cholesterol-based membrane anchors, and a solvatochromic fluorophore, spiropyran (SP). We find that the DNA nanopore effectively amplifies subtle variations of the membrane tension, which effectively induces the isomerization of weakly emissive SP into highly emissive merocyanine isomers for visualizing membrane tension changes. By measuring the membrane tension via the fluorescence of MSD nanomachine, we establish the correlation between the membrane tension and the curvature that follows the Young-Laplace equation. This DNA nanotechnology-enabled strategy opens new routes to studying membrane mechanics in physiological and pathological settings.     

Counterion-mediated pattern formation in membranes containing anionic lipids

Most lipid components of cell membranes are either neutral, like cholesterol, or zwitterionic, like phosphatidylcholine and sphingomyelin. Very few lipids, such as sphingosine, are cationic at physiological pH. These generally interact only transiently with the lipid bilayer, and their synthetic analogs are often designed to destabilize the membrane for drug or DNA delivery. However, anionic lipids are common in both eukaryotic and prokaryotic cell membranes. The net charge per anionic phospholipid ranges from − 1 for the most abundant anionic lipids such as phosphatidylserine, to near − 7 for phosphatidylinositol 3,4,5 trisphosphate, although the effective charge depends on many environmental factors. Anionic phospholipids and other negatively charged lipids such as lipopolysaccharides are not randomly distributed in the lipid bilayer, but are highly restricted to specific leaflets of the bilayer and to regions near transmembrane proteins or other organized structures within the plane of the membrane. This review highlights some recent evidence that counterions, in the form of monovalent or divalent metal ions, polyamines, or cationic protein domains, have a large influence on the lateral distribution of anionic lipids within the membrane, and that lateral demixing of anionic lipids has effects on membrane curvature and protein function that are important for biological control.     

Coupling of bending and stretching deformations in vesicle membranes

Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension.     

Deformations of lipid vesicles induced by attached spherical particles

Wrapping of a spherical colloidal particle, located inside and outside a lipid vesicle, by the membrane which forms the wall of the vesicle is investigated. The process is studied for vesicles of different geometries: prolate, oblate, stomatocytes. We focus on the bending energy change and shape transformations induced by binding the membrane to the spherical particles. The ground-state shapes of vesicles are calculated within the framework of a Helfrich curvature energy functional.     

Metabolic control of elastic properties of the inner mitochondrial membrane

A possible physical mechanism for inner mitochondrial membrane shape rearrangements is given. This analytical study shows that high transmembrane potential at the inner mitochondrial membrane brings about specific, substantial, and dynamic electrochemical contributions to lateral tension, bending rigidity constant, and elastic modulus of Gaussian curvature of the membrane. Changes in mitochondrial metabolism dramatically affect the magnitude of these elastic parameters but not necessarily that of proton-motive force. Metabolic-driven variation of mechanical properties of the inner mitochondrial membrane can promote the membrane remodeling between its principal geometric shapes and serve as a negative feedback in control of the oxidative phosphorylation.     

Atomistic simulation of lipid and DiI dynamics in membrane bilayers under tension

Membrane tension modulates cellular processes by initiating changes in the dynamics of its molecular constituents. To quantify the precise relationship between tension, structural properties of the membrane, and the dynamics of lipids and a lipophilic reporter dye, we performed atomistic molecular dynamics (MD) simulations of DiI-labeled dipalmitoylphosphatidylcholine (DPPC) lipid bilayers under physiological lateral tensions ranging from -2.6 mN m(-1) to 15.9 mN m(-1). Simulations showed that the bilayer thickness decreased linearly with tension consistent with volume-incompressibility, and this thinning was facilitated by a significant increase in acyl chain interdigitation at the bilayer midplane and spreading of the acyl chains. Tension caused a significant drop in the bilayer's peak electrostatic potential, which correlated with the strong reordering of water and lipid dipoles. For the low tension regime, the DPPC lateral diffusion coefficient increased with increasing tension in accordance with free-area theory. For larger tensions, free area theory broke down due to tension-induced changes in molecular shape and friction. Simulated DiI rotational and lateral diffusion coefficients were lower than those of DPPC but increased with tension in a manner similar to DPPC. Direct correlation of membrane order and viscosity near the DiI chromophore, which was just under the DPPC headgroup, indicated that measured DiI fluorescence lifetime, which is reported to decrease with decreasing lipid order, is likely to be a good reporter of tension-induced decreases in lipid headgroup viscosity. Together, these results offer new molecular-level insights into membrane tension-related mechanotransduction and into the utility of DiI in characterizing tension-induced changes in lipid packing.     

Simulations of edge behavior in a mixed-lipid bilayer: fluctuation analysis

Coarse-grained molecular dynamics simulations of lipid bilayer ribbons consisting of a mixture of lipids of different tail lengths have been performed to gain insight into bicelle mixtures. The line tension of the bilayer edge decreases as the mole fraction of short-chain lipids in the system is increased, dropping below zero between 30% and 35%. The mole fraction of short-chain lipids in the ribbon interior is lower than the total mole fraction, as the short-chain lipids segregate towards the edge, but continues to rise even after the line tension vanishes, in contrast to predictions of a two-component two-phase model. The fluctuations of the bilayer edge in both high and low line tension regimes have been analyzed to extract information about the factors that influence the length and shape of the edge. At high line tension the wavelength-dependent in-plane fluctuations of the edge are predicted quantitatively using a simple analytical model using only the line tension as input. Where line tension is vanishing, the fluctuations can be modeled as arising from a combination of harmonic fluctuations around a minimum energy contour length and an in-plane bending elasticity. The estimated value of the in-plane bending modulus is of order 10(-29) J m, placing the intrinsic persistence length for the edge near the bilayer thickness of 4 nm.     

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.     

Crystalline protein domains and lipid bilayer vesicle shape transformations

Cellular membranes can take on a variety of shapes to assist biological processes including endocytosis. Membrane-associated protein domains provide a possible mechanism for determining membrane curvature. We study the effect of tethered streptavidin protein crystals on the curvature of giant unilamellar vesicles (GUVs) using confocal, fluorescence, and differential interference contrast microscopy. Above a critical protein concentration, streptavidin domains align and percolate as they form, deforming GUVs into prolate spheroidal shapes in a size-dependent fashion. We propose a mechanism for this shape transformation based on domain growth and jamming. Osmotic deflation of streptavidin-coated GUVs reveals that the relatively rigid streptavidin protein domains resist membrane bending. Moreover, in contrast to highly curved protein domains that facilitate membrane budding, the relatively flat streptavidin domains prevent membrane budding under high osmotic stress. Thus, crystalline streptavidin domains are shown to have a stabilizing effect on lipid membranes. Our study gives insight into the mechanism for protein-mediated stabilization of cellular membranes.     

Computational analysis of local membrane properties

In the field of biomolecular simulations, dynamics of phospholipid membranes is of special interest. A number of proteins, including channels, transporters, receptors and short peptides are embedded in lipid bilayers and tightly interact with phospholipids. While the experimental measurements report on the spatial and/or temporal average membrane properties, simulation results are not restricted to the average properties. In the current study, we present a collection of methods for an efficient local membrane property calculation, comprising bilayer thickness, area per lipid, deuterium order parameters, Gaussian and mean curvature. The local membrane property calculation allows for a direct mapping of the membrane features, which subsequently can be used for further analysis and visualization of the processes of interest. The main features of the described methods are highlighted in a number of membrane systems, namely: a pure dimyristoyl-phosphatidyl-choline (DMPC) bilayer, a fusion peptide interacting with a membrane, voltage-dependent anion channel protein embedded in a DMPC bilayer, cholesterol enriched bilayer and a coarse grained simulation of a curved palmitoyl-oleoyl-phosphatidyl-choline lipid membrane. The local membrane property analysis proves to provide an intuitive and detailed view on the observables that are otherwise interpreted as averaged bilayer properties.     

Correlations in simulated model bilayers

Molecular dynamics simulations of a model bilayer in a solvent are used to determine the structure factors S(q) and other correlations at vanishing lateral tension of the system and at positive and negative tensions as well. The role played by curvature in the absence of surface tension, metastability, and phase transitions, and the dependence on the specific area, are discussed. Possible height-height correlation functions S(q) are examined and tested.     

Electrostatic properties of membrane lipids coupled to metarhodopsin II formation in visual transduction

Changes in lipid composition have recently been shown to exert appreciable influences on the activities of membrane-bound proteins and peptides. We tested the hypothesis that the conformational states of rhodopsin linked to visual signal transduction are related to biophysical properties of the membrane lipid bilayer. For bovine rhodopsin, the meta I-meta II conformational transition was studied in egg phosphatidylcholine (PC) recombinants versus the native rod outer segment (ROS) membranes by means of flash photolysis. Formation of metarhodopsin II was observed by the change in absorbance at 478 nm after a single actinic flash was delivered to the sample. The meta I/meta II ratio was investigated as a function of both temperature and pH. The data clearly demonstrated thermodynamic reversibility of the transition for both the egg PC recombinants and the native ROS membranes. A significant shift of the apparent pK(a) for the acid-base equilibrium to lower values was evident in the egg PC recombinant, with little meta II produced under physiological conditions. Calculations of the membrane surface pH using a Poisson-Boltzmann model suggested the free energies of the meta I and meta II states were significantly affected by electrostatic properties of the bilayer lipids. In the ROS membranes, phosphatidylserine (PS) is needed for full formation of meta II, in combination with phosphatidylethanolamine (PE) and polyunsaturated docosahexaenoic acid (DHA; 22:6omega3) chains. We propose that the PS surface potential leads to an accumulation of hydronium ions, H(3)O(+), in the electrical double layer, which drive the reaction together with the large negative spontaneous curvature (H(0)) conferred by PE plus DHA chains. The elastic stress/strain of the bilayer arises from an interplay of the approximately zero H(0) from PS and the negative H(0) due to the PE headgroups and polyunsaturated chains. The lipid influences are further explained in terms of matching of the bilayer spontaneous curvature to the curvature at the lipid/rhodopsin interface, as formulated by the Helfrich bending energy. These new findings guide current ideas as to how bilayer properties govern the conformational energetics of integral membrane proteins. Moreover, they yield knowledge of how membrane lipid-protein interactions involving acidic phospholipids such as PS and neutral polyunsaturated DHA chains are implicated in key biological functions such as vision.     

Curvature sorting of peripheral proteins on solid-supported wavy membranes

Cellular membrane deformation and the associated redistribution of membrane-bound proteins are important aspects of membrane function. Current model membrane approaches for studying curvature sensing are limited to positive curvatures and often require complex and delicate experimental setups. To overcome these challenges, we fabricated a wavy substrate by imposing a range of curvatures onto an adhering lipid bilayer membrane. We examined the curvature sorting of several peripheral proteins binding to the wavy membrane and observed them to partition into distinct regions of curvature. Furthermore, single-molecule imaging experiments suggested that the curvature sensing of proteins on low-curvature substrates requires cooperative interactions.