Electrostatic Potentials Caused by the Release of Protons from Photoactivated Compound Sodium 2-Methoxy-5-nitrophenyl Sulfate at the Surface of Bilayer Lipid Membrane

Lateral transport and release of protons at the water-membrane interface play crucial roles in cell bioenergetics. Therefore, versatile techniques need to be developed for investigating as well as clarifying the main features of these processes at the molecular level. Here, we experimentally measured the kinetics of binding of protons released from the photoactivated compound sodium 2-methoxy-5-nitrophenyl sulfate (MNPS) at the surface of a bilayer lipid membrane (BLM). We developed a theoretical model of this process describing the damage of MNPS coupled with the release of the protons at the membrane surface, as well as the exchange of MNPS molecules and protons between the membrane and solution. We found that the total change in the boundary potential difference across the membrane, ∆ϕb, is the sum of opposing effects of adsorption of MNPS anions and release of protons at the membrane-water interface. Steady-state change in the ∆ϕb due to protons decreased with the concentration of the buffer and increased with the pH of the solution. The change in the concentration of protons evaluated from measurements of ∆ϕb was close to that in the unstirred water layer near the BLM. This result, as well as rate constants of the proton exchange between the membrane and the bulk solution, indicated that the rate-limiting step of the proton surface to bulk release is the change in the concentration of protons in the unstirred layer. This means that the protons released from MNPS remain in equilibrium between the BLM surface and an adjacent water layer.

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.

Influenza A Virus M1 Protein Non-Specifically Deforms Charged Lipid Membranes and Specifically Interacts with the Raft Boundary

Topological rearrangements of biological membranes, such as fusion and fission, often require a sophisticated interplay between different proteins and cellular membranes. However, in the case of fusion proteins of enveloped viruses, even one molecule can execute membrane restructurings. Growing evidence indicates that matrix proteins of enveloped viruses can solely trigger the membrane bending required for another crucial step in virogenesis, the budding of progeny virions. For the case of the influenza A virus matrix protein M1, different studies report both in favor and against M1 being able to produce virus-like particles without other viral proteins. Here, we investigated the physicochemical mechanisms of M1 membrane activity on giant unilamellar vesicles of different lipid compositions using fluorescent confocal microscopy. We confirmed that M1 predominantly interacts electrostatically with the membrane, and its ability to deform the lipid bilayer is non-specific and typical for membrane-binding proteins and polypeptides. However, in the case of phase-separating membranes, M1 demonstrates a unique ability to induce macro-phase separation, probably due to the high affinity of M1's amphipathic helices to the raft boundary. Thus, we suggest that M1 is tailored to deform charged membranes with a specific activity in the case of phase-separating membranes.

Planar aggregation of the influenza viral fusion peptide alters membrane structure and hydration, promoting poration

To infect, enveloped viruses employ spike protein, spearheaded by its amphipathic fusion peptide (FP), that upon activation extends out from the viral surface to embed into the target cellular membrane. Here we report that synthesized influenza virus FPs are membrane active, generating pores in giant unilamellar vesicles (GUV), and thus potentially explain both influenza virus' hemolytic activity and the liposome poration seen in cryo-electron tomography. Experimentally, FPs are heterogeneously distributed on the GUV at the time of poration. Consistent with this heterogeneous distribution, molecular dynamics (MD) simulations of asymmetric bilayers with different numbers of FPs in one leaflet show FP aggregation. At the center of FP aggregates, a profound change in the membrane structure results in thinning, higher water permeability, and curvature. Ultimately, a hybrid bilayer nanodomain forms with one lipidic leaflet and one peptidic leaflet. Membrane elastic theory predicts a reduced barrier to water pore formation when even a dimer of FPs thins the membrane as above, and the FPs of that dimer tilt, to continue the leaflet bending initiated by the hydrophobic mismatch between the FP dimer and the surrounding lipid.

A Model of Lipid Monolayer-Bilayer Fusion of Lipid Droplets and Peroxisomes

Lipid droplets are unique organelles that store neutral lipids encapsulated by the lipid monolayer. In some processes of cellular metabolism, lipid droplets interact with peroxisomes resulting in the fusion of their envelopes and the formation of protrusions of the peroxisome monolayer, called pexopodia. The formation of pexopodia is facilitated by free fatty acids generated during lipolysis within lipid droplets. In this work, we studied the fusion of monolayer and bilayer membranes during the interaction between lipid droplets and peroxisomes. To this end, we built the energy trajectory of this process using the continuum elasticity theory and investigated the molecular details of the fusion structures utilizing molecular dynamics. We divided the fusion process into two stages: formation of a stalk and its consequent expansion into pexopodia. We found that in the considered system, the stalk was energetically more stable and had a lower energy barrier of formation compared to the case of bilayer fusion. The further evolution of the stalk depended on the value of the spontaneous curvature of the membrane in a threshold manner. We attributed the possible expansion of the stalk to the incorporation of free fatty acids into the stalk region. The developed model allowed describing quantitatively the process of monolayer-bilayer fusion.

Lysolipids regulate raft size distribution

The lipid matrix of cellular membranes, directly and indirectly, regulates many vital functions of the cell. The diversity of lipids in membranes leads to the formation of ordered domains called rafts, which play a crucial role in signal transduction, protein sorting and other cellular processes. Rafts are believed to impact the development of different neurodegenerative diseases, such as Alzheimer’s, Parkinson’s, Huntington’s ones, amyotrophic lateral sclerosis, some types of cancer, etc. These diseases correlate with the change in the membrane lipid composition resulting from an oxidative stress, age-related processes, dysfunction of proteins, and many others. In particular, a lot of studies report a significant rise in the level of lysolipids. Physicochemical properties of rafts are determined by membrane composition, in particular, by the content of lysolipids. Lysolipids may thus regulate raft-involving processes. However, the exact mechanism of such regulation is unknown. Although studying rafts in vivo still seems to be rather complicated, liquid-ordered domains are well observed in model systems. In the present study, we used atomic force microscopy (AFM) to examine how lysophospholipids influence the liquid-ordered domains in model ternary membranes. We demonstrated that even a small amount of lysolipids in a membrane significantly impacts domain size depending on the saturation of the lysolipid hydrocarbon tails and the amount of cholesterol. The mixture with the bigger relative fraction of cholesterol was more susceptible to the action of lysolipids. This data helped us to generalize our previous theoretical model of the domain size regulation by lipids with particular molecular shape expanding it to the case of lysolipids and dioleoylglycerol.

Determinants of Lipid Domain Size

Lipid domains less than 200 nm in size may form a scaffold, enabling the concerted function of plasma membrane proteins. The size-regulating mechanism is under debate. We tested the hypotheses that large values of spontaneous monolayer curvature are incompatible with micrometer-sized domains. Here, we used the transition of photoswitchable lipids from their cylindrical conformation to a conical conformation to increase the negative curvature of a bilayer-forming lipid mixture. In contrast to the hypothesis, pre-existing micrometer-sized domains did not dissipate in our planar bilayers, as indicated by fluorescence images and domain mobility measurements. Elasticity theory supports the observation by predicting the zero free energy gain for splitting large domains into smaller ones. It also indicates an alternative size-determining mechanism: The cone-shaped photolipids reduce the line tension associated with lipid deformations at the phase boundary and thus slow down the kinetics of domain fusion. The competing influence of two approaching domains on the deformation of the intervening lipids is responsible for the kinetic fusion trap. Our experiments indicate that the resulting local energy barrier may restrict the domain size in a dynamic system.

Heterogeneity in Lateral Distribution of Polycations at the Surface of Lipid Membrane: From the Experimental Data to the Theoretical Model

Natural and synthetic polycations of different kinds attract substantial attention due to an increasing number of their applications in the biomedical industry and in pharmacology. The key characteristic determining the effectiveness of the majority of these applications is the number of macromolecules adsorbed on the surface of biological cells or their lipid models. Their study is complicated by a possible heterogeneity of polymer layer adsorbed on the membrane. Experimental methods reflecting the structure of the layer include the electrokinetic measurements in liposome suspension and the boundary potential of planar bilayer lipid membranes (BLM) and lipid monolayers with a mixed composition of lipids and the ionic media. In the review, we systematically analyze the methods of experimental registration and theoretical description of the laterally heterogeneous structures in the polymer layer published in the literature and in our previous studies. In particular, we consider a model based on classical theory of the electrical double layer, used to analyze the available data of the electrokinetic measurements in liposome suspension with polylysines of varying molecular mass. This model suggests a few parameters related to the heterogeneity of the polymer layer and allows determining the conditions for its appearance at the membrane surface. A further development of this theoretical approach is discussed.

Amphipathic Peptides Impede Lipid Domain Fusion in Phase-Separated Membranes

Cell membranes are heterogeneous in lipid composition which leads to the phase separation with the formation of nanoscopic liquid-ordered domains, also called rafts. There are multiple cell processes whereby the clustering of these domains into a larger one might be involved, which is responsible for such important processes as signal transduction, polarized sorting, or immune response. Currently, antimicrobial amphipathic peptides are considered promising antimicrobial, antiviral, and anticancer therapeutic agents. Here, within the framework of the classical theory of elasticity adapted for lipid membranes, we investigate how the presence of the peptides in a phase-separated membrane influences the fusion of the domains. We show that the peptides tend to occupy the boundaries of liquid-ordered domains and significantly increase the energy barrier of the domain-domain fusion, which might lead to misregulation of raft clustering and adverse consequences for normal cell processes.

Photoswitching of model ion channels in lipid bilayers

Membrane proteins can be regulated by alterations in material properties intrinsic to the hosting lipid bilayer. Here, we investigated whether the reversible photoisomerization of bilayer-embedded diacylglycerols (OptoDArG) with two azobenzene-containing acyl chains may trigger such regulatory events. We observed an augmented open probability of the mechanosensitive model channel gramicidin A (gA) upon photoisomerizing OptoDArG's acyl chains from trans to cis: integral planar bilayer conductance brought forth by hundreds of simultaneously conducting gA dimers increased by typically >50% - in good agreement with the observed increase in single-channel lifetime. Further, (i) increments in the electrical capacitance of planar lipid bilayers and protrusion length of aspirated giant unilamellar vesicles into suction pipettes, as well as (ii) changes of small-angle X-ray scattering of multilamellar vesicles indicated that spontaneous curvature, hydrophobic thickness, and bending elasticity decreased upon switching from trans- to cis-OptoDArG. Our bilayer elasticity model for gA supports the causal relationship between changes in gA activity and bilayer material properties upon photoisomerization. Thus, we conclude that photolipids are deployable for converting bilayers of potentially diverse origins into light-gated actuators for mechanosensitive proteins.

Nonlinear material and ionic transport through membrane nanotubes

Membrane nanotubes (NTs) and their networks play an important role in intracellular membrane transport and intercellular communications. The transport characteristics of the NT lumen resemble those of conventional solid-state nanopores. However, unlike the rigid pores, the soft membrane wall of the NT can be deformed by forces driving the transport through the NT lumen. This intrinsic coupling between the NT geometry and transport properties remains poorly explored. Using synchronized fluorescence microscopy and conductance measurements, we revealed that the NT shape was changed by both electric and hydrostatic forces driving the ionic and solute fluxes through the NT lumen. Far from the shape instability, the strength of the force effect is determined by the lateral membrane tension and is scaled with membrane elasticity so that the NT can be operated as a linear elastic sensor. Near shape instabilities, the transport forces triggered large-scale shape transformations, both stochastic and periodic. The periodic oscillations were coupled to a vesicle passage along the NT axis, resembling peristaltic transport. The oscillations were parametrically controlled by the electric field, making NT a highly nonlinear nanofluidic circuitry element with biological and technological implications.

Membrane-Mediated Lateral Interactions Regulate the Lifetime of Gramicidin Channels

The lipid matrix of cellular membranes is an elastic liquid crystalline medium. Its deformations regulate the functionality and interactions of membrane proteins,f membrane-bound peptides, lipid and protein-lipid domains. Gramicidin A (gA) is a peptide, which incorporates into membrane leaflets as a monomer and may form a transmembrane dimer. In both configurations, gA deforms the membrane. The transmembrane dimer of gA is a cation-selective ion channel. Its electrical response strongly depends on the elastic properties of the membrane. The gA monomer and dimer deform the membrane differently; therefore, the elastic energy contributes to the activation barriers of the dimerization and dissociation of the conducting state. It is shown experimentally that channel characteristics alter if gA molecules have been located in the vicinity of the conducting dimer. Here, based on the theory of elasticity of lipid membranes, we developed a quantitative theoretical model which allows explaining experimentally observed phenomena under conditions of high surface density of gA or its analogues, i.e., in the regime of strong lateral interactions of gA molecules, mediated by elastic deformations of the membrane. The model would be useful for the analysis and prediction of the gA electrical response in various experimental conditions. This potentially widens the possible applications of gA as a convenient molecular sensor of membrane elasticity.

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.

Continuum Models of Membrane Fusion: Evolution of the Theory

Starting from fertilization, through tissue growth, hormone secretion, synaptic transmission, and sometimes morbid events of carcinogenesis and viral infections, membrane fusion regulates the whole life of high organisms. Despite that, a lot of fusion processes still lack well-established models and even a list of main actors. A merger of membranes requires their topological rearrangements controlled by elastic properties of a lipid bilayer. That is why continuum models based on theories of membrane elasticity are actively applied for the construction of physical models of membrane fusion. Started from the view on the membrane as a structureless film with postulated geometry of fusion intermediates, they developed along with experimental and computational techniques to a powerful tool for prediction of the whole process with molecular accuracy. In the present review, focusing on fusion processes occurring in eukaryotic cells, we scrutinize the history of these models, their evolution and complication, as well as open questions and remaining theoretical problems. We show that modern approaches in this field allow continuum models of membrane fusion to stand shoulder to shoulder with molecular dynamics simulations, and provide the deepest understanding of this process in multiple biological systems.

Cyclopentane rings in hydrophobic chains of a phospholipid enhance the bilayer stability to electric breakdown

Archaeal lipids ensure unprecedented stability of archaea membranes in extreme environments. Here, we incorporate a characteristic structural feature of an archaeal lipid, the cyclopentane ring, into hydrocarbon chains of a short-chain (C12) phosphatidylcholine to explore whether the insertion would allow such a lipid (1,2-di-(3-(3-hexylcyclopentyl)-propanoate)-sn-glycero-3-phosphatidylcholine, diC12cp-PC) to form stable bilayers at room temperature. According to fluorescence-based assays, in water diC12cp-PC formed liquid-crystalline bilayers at room temperature. Liposomes produced from diC12cp-PC retained calcein for over a week when stored at +4 °C. diC12cp-PC could also form model bilayer lipid membranes that were by an order of magnitude more stable to electrical breakdown than egg PC membranes. Molecular dynamics simulation showed that the cyclopentane fragment fixes five carbon atoms (or four C-C bonds), which is compensated by the higher mobility of the rest of the chain. This was found to be the reason for the remarkable stability of the diC12cp-PC bilayer: restricted conformational mobility of a chain segment increases the membrane bending modulus (compared to a normal hydrocarbon chain of the same length). Here, higher stiffness practically does not affect the line tension of a membrane pore edge. Rather it makes it more difficult for diC12cp-PC to rearrange in order to line the edge of a hydrophilic pore; therefore, fewer pores are formed.

Ordered Lipid Domains Assemble via Concerted Recruitment of Constituents from Both Membrane Leaflets

Lipid rafts serve as anchoring platforms for membrane proteins. Thus far they escaped direct observation by light microscopy due to their small size. Here we used differently colored dyes as reporters for the registration of both ordered and disordered lipids from the two leaves of a freestanding bilayer. Photoswitchable lipids dissolved or reformed the domains. Measurements of domain mobility indicated the presence of 120 nm wide ordered and 40 nm wide disordered domains. These sizes are in line with the predicted roles of line tension and membrane undulation as driving forces for alignment.

Elastic deformations mediate interaction of the raft boundary with membrane inclusions leading to their effective lateral sorting

Liquid-ordered lipid domains represent a lateral inhomogeneity in cellular membranes. These domains have elastic and physicochemical properties different from those of the surrounding membrane. In particular, their thickness exceeds that of the disordered membrane. Thus, elastic deformations arise at the domain boundary in order to compensate for the thickness mismatch. In equilibrium, the deformations lead to an incomplete register of monolayer ordered domains: the elastic energy is minimal if domains in opposing monolayers lie on the top of each other, and their boundaries are laterally shifted by about 3 nm. This configuration introduces a region, composed of one ordered and one disordered monolayers, with an intermediate bilayer thickness. Besides, a jump in a local monolayer curvature takes place in this intermediate region, concentrating here most of the elastic stress. This region can participate in a lateral sorting of membrane inclusions by offering them an optimal bilayer thickness and local curvature conditions. In the present study, we consider the sorting of deformable lipid inclusions, undeformable peripheral and deeply incorporated peptide inclusions, and undeformable transmembrane inclusions of different molecular geometry. With rare exceptions, all types of inclusions have an affinity to the ordered domain boundary as compared to the bulk phases. The optimal lateral distribution of inclusions allows relaxing the elastic stress at the boundary of domains.

Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent

The theory of elasticity of lipid membranes is used widely to describe processes of cell membrane remodeling. Classically, the functional of a membrane's elastic energy is derived under assumption of small deformations; the membrane is considered as an infinitely thin film. This functional is quadratic on membrane surface curvature, with half of the splay modulus as its proportionality coefficient; it is generally applicable for small deformations only. Any validity of this functional for the regime of strong deformations should be verified experimentally. Recently, research using molecular dynamics simulations challenged the validity of this classic, linear model, i.e. the constancy of the splay modulus for strongly bent membranes. Here we demonstrate that the quadratic energy functional still can be applied for calculation of the elastic energy of strongly deformed membranes without introducing higher order terms with additional elastic moduli, but only if applied separately for each lipid monolayer. For cylindrical membranes, both classic and monolayerwise models yield equally accurate results. For cylindrical deformations we experimentally show that the elastic energy of lipid monolayers is additive: a low molecular weight solvent leads to an approximately twofold decrease in the membrane bending stiffness. Accumulation of solvent molecules in the inner monolayer of a membrane cylinder can explain these results, as the solvent partially prevents lipid molecules from splaying there. Thus, the linear theory of elasticity can be expanded through the range from weak to strong deformations-its simplicity and physical transparency describe various membrane phenomena.

Archaeal cyclopentane fragment in a surfactant's hydrophobic tail decreases the Krafft point

Archaea are prokaryotic microorganisms famous for their ability to adapt to extreme environments, including low and high temperatures. Archaeal lipids often are macrocycles with two polar heads and a hydrophobic core that contains methyl groups and in-line cycles. Here we present the design of novel general-purpose surfactants that have inherited features of archaeal lipids. These are C12 and C14 carboxylic acids containing in-line cyclopentanes. The cyclopentanes disturb the chain packing, which results in remarkable expansion of the operational range of the surfactant into the low-temperature region. We report synthesis and properties of these novel archaea-like surfactants and details of their chain packing derived from thermodynamics model predictions, molecular dynamics simulations, and experimental data on CMC and Krafft points.

Membrane-mediated interaction of amphipathic peptides can be described by a one-dimensional approach

Amphipathic alpha-helical peptides, among other peripheral components of plasma membranes, are promising antimicrobial agents. Partial incorporation of a peptide into a lipid monolayer causes elastic deformations. Deformations induced by two peptides distant from each other are independent; when peptides get closer, interference between the deformations causes effective lateral interaction. We quantified the energy of membrane deformations for arbitrary configuration of two amphipathic peptides on the membrane surface. The global minimum of the deformation energy proved to be achieved when two parallel peptides are in registry at the distance of about 6 nm between the axes of peptides. The energy calculated in the unidimensional approach provides a good approximation for the dependence of the energy of peptides being in the registered configuration upon the distance between them, valid for a broad range of peptide lengths. The effective interactional length of peptides for the unidimensional approach is close to their actual length. If two parallel peptides are shifted along their axes with respect to each other, the interaction energy is also well approximated by the unidimensional potential, within the projection of one peptide onto the other. In the case when the axes of alpha helices cross at a substantial angle, the main contribution to peptide interactions comes from their edges: the effective length of peptides for the unidimensional approach is almost equal to the characteristic length of decay of deformations. Based on the results we obtained it can be concluded that interaction of membrane inclusions is quite adequately described by the potential calculated in the unidimensional approach.

Phospholipidic Colchicinoids as Promising Prodrugs Incorporated into Enzyme-Responsive Liposomes: Chemical, Biophysical, and Enzymological Aspects

Enzyme-responsive liposomes release their cargo in response to pathologically increased levels of enzymes at the target site. We report herein an assembly of phospholipase A2-responsive liposomes based on colchicinoid lipid prodrugs incorporated into lipid bilayer of the nanosized vesicles. The liposomes were constructed to addresses two important issues: (i) the lipid prodrugs were designed to fit the structure of the enzyme binding site; and (ii) the concept of lateral pressure profile was used to design lipid prodrugs that introduce almost no distortions into the lipid bilayer packing, thus ensuring that corresponding liposomes are stable. The colchicinoid agents exhibit antiproliferative activity in subnanomolar range of concentrations.

Membrane Elastic Deformations Modulate Gramicidin A Transbilayer Dimerization and Lateral Clustering

Gramicidin A (gA) is a short β-helical peptide known to form conducting channels in lipid membranes because of transbilayer dimerization. The gA conducting dimer, being shorter than the lipid bilayer thickness, deforms the membrane in its vicinity, and the bilayer elastic energy contributes to the gA dimer formation energy. Likewise, membrane incorporation of a gA monomer, which is shorter than the lipid monolayer thickness, creates a void, thereby forcing surrounding lipid molecules to tilt to fill it. The energy of membrane deformation was calculated in the framework of the continuum elasticity theory, taking into account splay, tilt, lateral stretching/compression, Gaussian splay deformations, and external membrane tension. We obtained the interaction energy profiles for two gA monomers located either in the same or in the opposite monolayers. The profiles demonstrated the long-range attraction and short-range repulsion behavior of the monomers resulting from the membrane deformation. Analysis of the profile features revealed conditions under which clusters of gA monomers would not dissipate because of diffusion. The calculated dependence of the dimer formation and decay energy barriers on the membrane elastic properties was in good agreement with the available experimental data and suggested an explanation for a hitherto contentious phenomenon.

Lateral Membrane Heterogeneity Regulates Viral-Induced Membrane Fusion during HIV Entry

Sphingomyelin- and cholesterol- enriched membrane domains, commonly referred to as “rafts” play a crucial role in a large number of intra- and intercellular processes. Recent experiments suggest that not only the volumetric inhomogeneity of lipid distribution in rafts, but also the arrangement of the 1D boundary between the raft and the surrounding membrane is important for the membrane-associated processes. The reason is that the boundary preferentially recruits different peptides, such as HIV (human immunodeficiency virus) fusion peptide. In the present work, we report a theoretical investigation of mechanisms of influence of the raft boundary arrangement upon virus-induced membrane fusion. We theoretically predict that the raft boundary can act as an attractor for viral fusion peptides, which preferentially distribute into the vicinity of the boundary, playing the role of ‘line active components’ of the membrane (‘linactants’). We have calculated the height of the fusion energy barrier and demonstrated that, in the case of fusion between HIV membrane and the target cell, presence of the raft boundary in the vicinity of the fusion site facilitates fusion. The results we obtained can be further generalized to be applicable to other enveloped viruses.

Influenza virus Matrix Protein M1 preserves its conformation with pH, changing multimerization state at the priming stage due to electrostatics

Influenza A virus matrix protein M1 plays an essential role in the virus lifecycle, but its functional and structural properties are not entirely defined. Here we employed small-angle X-ray scattering, atomic force microscopy and zeta-potential measurements to characterize the overall structure and association behavior of the full-length M1 at different pH conditions. We demonstrate that the protein consists of a globular N-terminal domain and a flexible C-terminal extension. The globular N-terminal domain of M1 monomers appears preserved in the range of pH from 4.0 to 6.8, while the C-terminal domain remains flexible and the tendency to form multimers changes dramatically. We found that the protein multimerization process is reversible, whereby the binding between M1 molecules starts to break around pH 6. A predicted electrostatic model of M1 self-assembly at different pH revealed a good agreement with zeta-potential measurements, allowing one to assess the role of M1 domains in M1-M1 and M1-lipid interactions. Together with the protein sequence analysis, these results provide insights into the mechanism of M1 scaffold formation and the major role of the flexible and disordered C-terminal domain in this process.

Pore formation in lipid membrane II: Energy landscape under external stress

Lipid membranes are extremely stable envelopes allowing cells to survive in various environments and to maintain desired internal composition. Membrane permeation through formation of transversal pores requires substantial external stress. Practically, pores are usually formed by application of lateral tension or transmembrane voltage. Using the same approach as was used for obtaining continuous trajectory of pore formation in the stress-less membrane in the previous article, we now consider the process of pore formation under the external stress. The waiting time to pore formation proved a non-monotonous function of the lateral tension, dropping from infinity at zero tension to a minimum at the tension of several millinewtons per meter. Transmembrane voltage, on the contrary, caused the waiting time to decrease monotonously. Analysis of pore formation trajectories for several lipid species with different spontaneous curvatures and elastic moduli under various external conditions provided instrumental insights into the mechanisms underlying some experimentally observed phenomena.

Pore formation in lipid membrane I: Continuous reversible trajectory from intact bilayer through hydrophobic defect to transversal pore

Lipid membranes serve as effective barriers allowing cells to maintain internal composition differing from that of extracellular medium. Membrane permeation, both natural and artificial, can take place via appearance of transversal pores. The rearrangements of lipids leading to pore formation in the intact membrane are not yet understood in details. We applied continuum elasticity theory to obtain continuous trajectory of pore formation and closure, and analyzed molecular dynamics trajectories of pre-formed pore reseal. We hypothesized that a transversal pore is preceded by a hydrophobic defect: intermediate structure spanning through the membrane, the side walls of which are partially aligned by lipid tails. This prediction was confirmed by our molecular dynamics simulations. Conversion of the hydrophobic defect into the hydrophilic pore required surmounting some energy barrier. A metastable state was found for the hydrophilic pore at the radius of a few nanometers. The dependence of the energy on radius was approximately quadratic for hydrophobic defect and small hydrophilic pore, while for large radii it depended on the radius linearly. The pore energy related to its perimeter, line tension, thus depends of the pore radius. Calculated values of the line tension for large pores were in quantitative agreement with available experimental data.

Undulations Drive Domain Registration from the Two Membrane Leaflets

Phase separation in biological membranes plays an important role in protein targeting and transmembrane signaling. Its occurrence in both membrane leaflets commonly gives rise to matching liquid or liquid-ordered domains in the opposing monolayers. The underlying mechanism of such co-localization is not fully understood. The decrease of the line tension around the thicker ordered domain constitutes an important driving force. Yet, robust domain coupling requires an additional energy source, which we have now identified as thermal undulations. Our theoretical analysis of elastic deformations in a lipid bilayer shows that stiffer lipid domains tend to distribute into areas with lower fluctuations of monolayer curvature. These areas naturally align in the opposing monolayers. Thus, coupling requires both membrane leafs to display a heterogeneity in splay rigidities. The heterogeneity may either originate from intrinsic lipid properties or be acquired by adsorption of peripheral molecules. Undulations and line tension act synergistically: the gain in energy due a minimized line tension is proportional to domain radius and thus primarily fuels the registration of smaller domains; whereas the energetic contribution of undulations increases with membrane area and thus primarily acts to coalesce larger domains.

Line Activity of Ganglioside GM1 Regulates the Raft Size Distribution in a Cholesterol-Dependent Manner

Liquid-ordered lipid domains, also called rafts, are assumed to be important players in different cellular processes, mainly signal transduction and membrane trafficking. They are thicker than the disordered part of the membrane and are thought to form to compensate for the hydrophobic mismatch between transmembrane proteins and the lipid environment. Despite the existence of such structures in vivo still being an open question, they are observed in model systems of multicomponent lipid bilayers. Moreover, the predictions obtained from model experiments allow the explanation of different physiological processes possibly involving rafts. Here we present the results of the study of the regulation of raft size distribution by ganglioside GM1. Combining atomic force microscopy with theoretical considerations based on the theory of membrane elasticity, we predict that this glycolipid should change the line tension of raft boundaries in two different ways, mainly depending on the cholesterol content. These results explain the shedding of gangliosides from the surface of tumor cells and the following ganglioside-induced apoptosis of T-lymphocytes in a raft-dependent manner. Moreover, the generality of the model allows the prediction of the line activity of different membrane components based on their molecular geometry.

Elastic deformations of bolalipid membranes

Archaeal membranes have unique mechanical properties that enable these organisms to survive under extremely aggressive environmental conditions. The so-called bolalipids contribute to this exceptional stability. They have two polar heads joined by two hydrocarbon chains. The two headgroups can face different sides of the membrane (O-shape conformation) or the same side (U-shape conformation). We have developed an elasticity theory for bolalipid membranes and show that the energetic contributions of (i) tilt deformations, (ii) area compression/stretching deformations, (iii) as well as those of Gaussian splay from the two membrane surfaces are additive, while splay deformations yield a cross-term. The presence of a small fraction of U-shaped molecules resulted in spontaneous membrane curvature. We estimated the tilt modulus to be approximately equal to that of membranes in eukaryotic cells. In contrast to conventional lipids, the bolalipid membrane possesses two splay moduli, one of which is estimated to be an order of magnitude larger than that of conventional lipids. The projected values of elastic moduli act to hamper pore formation and to decelerate membrane fusion and fission.

Metabolic Precursor of Cholesterol Causes Formation of Chained Aggregates of Liquid-Ordered Domains

7-Dehydrocholesterol, an immediate metabolic predecessor of cholesterol, can accumulate in tissues due to some metabolic abnormalities, causing an array of symptoms known as Smith-Lemli-Opitz syndrome. Enrichment of cellular membranes with 7-dehydrocholesterol interferes with normal cell-signaling processes, which involve interaction between rafts and formation of the so-called signaling platforms. In model membranes, cholesterol-based ordered domains usually merge upon contact. According to our experimental data, ordered domains in the model systems where cholesterol is substituted for 7-dehydrocholesterol never merge on the time scale of the experiment, but clusterize into necklace-like aggregates. We attribute such different dynamical behavior to altered properties of the domain boundary. In the framework of thickness mismatch model, we analyzed changes of interaction energy profiles of two approaching domains caused by substitution of cholesterol by 7-dehydrocholesterol. The energy barrier for domain merger is shown to increase notably, with simultaneous appearance of another distinct local energy minimum. Such energy profile is in perfect qualitative agreement with the experimental observations. The observed change of domain dynamics can impair proper interaction between cellular rafts underlying pathologies associated with deviations in cholesterol metabolism.

Elastic Membrane Deformations Govern Interleaflet Coupling of Lipid-Ordered Domains

The mechanism responsible for domain registration in two membrane leaflets has thus far remained enigmatic. Using continuum elasticity theory, we show that minimum line tension is achieved along the rim between thicker (ordered) and thinner (disordered) domains by shifting the rims in opposing leaflets by a few nanometers relative to each other. Increasing surface tension yields an increase in line tension, resulting in larger domains. Because domain registration is driven by lipid deformation energy, it does not require special lipid components or interactions at the membrane midplane.