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

Membrane Remodeling Driven by Shallow Helix Insertions via a Cooperative Mechanism

Helix-membrane interactions are key to membrane deformation and play significant biological roles. However, systematic studies on the mechanisms behind these interactions are limited. This study uses a continuum membrane model to investigate how shallowly inserted helices interact with biological membranes, focusing on membrane deformation and the cooperative effects of multiple helices. Our findings show that even short helices (2 nm in length) can induce anisotropic membrane deformation. Longer helices and deeper insertions result in more significant deformations, and the spatial arrangement of helices affects the nature of these deformations. The perturbation area (PA) and perturbation extent (PE) are quantified to describe membrane deformation, revealing stronger cooperative effects in parallel insertions and more complex deformations in other arrangements. Additionally, membrane properties, such as lipid composition, influence the extent of deformation. In multi-helix systems, we observe local clustering behavior when perturbations are strong enough, with cooperativity varying based on helix length, insertion depth, and membrane composition. This study provides criteria for helix cooperativity, advancing our understanding of helix-membrane interactions and their biological significance in processes like membrane remodeling.

Continuum elasticity and molecular dynamics of a pore in archaeal bolalipid membranes

Archaea are famous for their ability to survive in extremely harsh environments, probably due to the unprecedented stability of their lipid membranes. Key features of archaeal lipids (bolalipids) that confer their stability are methyl side groups and cyclopentanes in the alkyl chains, as well as the specific shape of the molecule, which has two headgroups connected by two tails. However, the contribution of each structural parameter to membrane stability and the underlying physical mechanism remain unknown. Here, we used molecular dynamics simulations to develop a method for measuring the energy of pore formation in bolalipid membranes as an assessment of their stability. In addition, we improved our previously developed continuum model by introducing a new term responsible for the rigidity of the alkyl chain. We calculated the pore edge energy and evaluated the membrane stability in terms of membrane elasticity. We demonstrated that increased stability of bolalipid membranes resulted both from hindered lateral mobility of these amphiphilic molecules and increased pore energy due to specific structure of bolalipids. Methyl side groups of bolalipids reduce the mobility of the molecules and increase the pore line tension in the same way as in the case of conventional phytanyl lipids. Chain rigidity hinders the formation of the bend molecules at the pore edge, thus additionally increasing the pore formation energy.

Predicting protein curvature sensing across membrane compositions with a bilayer continuum model

Cytoplasmic proteins must recruit to membranes to function in processes such as endocytosis and cell division. Many of these proteins recognize not only the chemical structure of the membrane lipids, but the curvature of the surface, binding more strongly to more highly curved surfaces, or 'curvature sensing'. Curvature sensing by amphipathic helices is known to vary with membrane bending rigidity, but changes to lipid composition can simultaneously alter membrane thickness, spontaneous curvature, and leaflet symmetry, thus far preventing a systematic characterization of lipid composition on such curvature sensing through either experiment or simulation. Here we develop and apply a bilayer continuum membrane model that can tractably address this gap, quantifying how controlled changes to each material property can favor or disfavor protein curvature sensing. We evaluate both energetic and structural changes to vesicles upon helix insertion, with strong agreement to new in vitro experiments and all-atom MD simulations, respectively. Our membrane model builds on previous work to include both monolayers of the bilayer via representation by continuous triangular meshes. We introduce a coupling energy that captures the incompressibility of the membrane and the established energetics of lipid tilt. In agreement with experiment, our model predicts stronger curvature sensing in membranes with distinct tail groups (POPC vs DOPC vs DLPC), despite having identical head-group chemistry; the model shows that the primary driving force for weaker curvature sensing in DLPC is that it is thinner, and more wedge shaped. Somewhat surprisingly, asymmetry in lipid shape composition between the two leaflets has a negligible contribution to membrane mechanics following insertion. Our multi-scale approach can be used to quantitatively and efficiently predict how changes to membrane composition in flat to highly curved surfaces alter membrane energetics driven by proteins, a mechanism that helps proteins target membranes at the correct time and place.

Membrane Activity and Viroporin Assembly for the SARS-CoV-2 E Protein Are Regulated by Cholesterol

The SARS-CoV-2 E protein is an enigmatic viral structural protein with reported viroporin activity associated with the acute respiratory symptoms of COVID-19, as well as the ability to deform cell membranes for viral budding. Like many viroporins, the E protein is thought to oligomerize with a well-defined stoichiometry. However, attempts to determine the structure of the protein complex have yielded inconclusive results, suggesting several possible oligomers, ranging from dimers to pentamers. Here, we combined patch-clamp, confocal fluorescence microscopy on giant unilamellar vesicles, and atomic force microscopy to show that E protein can exhibit two modes of membrane activity depending on membrane lipid composition. In the absence or the presence of a low content of cholesterol, the protein forms short-living transient pores, which are seen as semi-transmembrane defects in a membrane by atomic force microscopy. Approximately 30 mol% cholesterol is a threshold for the transition to the second mode of conductance, which could be a stable pentameric channel penetrating the entire lipid bilayer. Therefore, the E-protein has at least two different types of activity on membrane permeabilization, which are regulated by the amount of cholesterol in the membrane lipid composition and could be associated with different types of protein oligomers.

Alteration of Average Thickness of Lipid Bilayer by Membrane-Deforming Inclusions

Thickness of lipid bilayer membranes is a key physical parameter determining membrane permeability and stability with respect to formation of through pores. Most membrane inclusions or impurities like amphipathic peptides, transmembrane peptides, lipid inclusions of a different molecular shape, lipid domains, and protein-lipid domains, locally deform the membrane. The detailed structure of the locally deformed region of the membrane is a kind of "fingerprint" for the inclusion type. However, most experimental methods allow determining only averaged parameters of membranes with incorporated inclusions, thus preventing the direct obtaining of the characteristics of the inclusion. Here we developed a model that allows the obtaining of characteristic parameters of three types of membrane inclusions (amphipathic peptides, transmembrane peptides, monolayer lipid patches) from experimentally observable dependencies of the average thickness of lipid bilayer on the surface concentration of the inclusions. In the case of amphipathic peptides, the model provided the peptide parameters that were in qualitative agreement with the available experimental data.

The Membrane-Mediated Interaction of Liquid-Ordered Lipid Domains in the Presence of Amphipathic Peptides

The lipid membranes of living cells are composed of a large number of lipid types and can undergo phase separation with the formation of nanometer-scale liquid-ordered lipid domains, also called rafts. Raft coalescence, i.e., the fusion of lipid domains, is involved in important cell processes, such as signaling and trafficking. In this work, within the framework of the theory of elasticity of lipid membranes, we explore how amphipathic peptides adsorbed on lipid membranes may affect the domain-domain fusion processes. We show that the elastic deformations of lipid membranes drive amphipathic peptides to the boundary of lipid domains, which leads to an increase in the average energy barrier of the domain-domain fusion, even if the surface concentration of amphipathic peptides is low and the domain boundaries are only partially occupied by the peptides. This inhibition of the fusion of lipid domains may lead to negative side effects of using amphipathic peptides as antimicrobial agents.

Initiation and evolution of pores formed by influenza fusion peptides probed by lysolipid inclusion

The fusion peptide (FP) domain is necessary for the fusogenic activity of spike proteins in a variety of enveloped viruses, allowing the virus to infect the host cell, and is the only part of the protein that interacts directly with the target membrane lipid tails during fusion. There are consistent findings of poration by this domain in experimental model membrane systems, and, in certain conditions, the isolated FPs can generate pores. Here, we use molecular dynamics simulations to investigate the specifics of how these FP-induced pores form in membranes with different compositions of lysolipid and POPC. The simulations show that pores form spontaneously at high lysolipid concentrations via hybrid intermediates, where FP aggregates in the cis leaflet tilt to form a funnel-like structure that spans the leaflet and locally reduces the hydrophobic thickness that must be traversed by water to form a pore. By restraining a single FP within an FP aggregate to this tilted conformation, pores can be formed in lower-lysolipid-content membranes, including pure POPC, on the 100-ns timescale, much more rapidly than in unbiased simulations in bilayers with the same composition. The pore formation pathway is similar to the spontaneous formation in high lysolipid concentrations. Depending on the membrane composition, the pores can be metastable (as seen in POPC) or lead to membrane rupture.

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.

Hydrophobic Mismatch Controls the Mode of Membrane-Mediated Interactions of Transmembrane Peptides

Various cellular processes require the concerted cooperative action of proteins. The possibility for such synchronization implies the occurrence of specific long-range interactions between the involved protein participants. Bilayer lipid membranes can mediate protein-protein interactions via relatively long-range elastic deformations induced by the incorporated proteins. We considered the interactions between transmembrane peptides mediated by elastic deformations using the framework of the theory of elasticity of lipid membranes. An effective peptide shape was assumed to be cylindrical, hourglass-like, or barrel-like. The interaction potentials were obtained for membranes of different thicknesses and elastic rigidities. Cylindrically shaped peptides manifest almost neutral average interactions-they attract each other at short distances and repel at large ones, independently of membrane thickness or rigidity. The hourglass-like peptides repel each other in thin bilayers and strongly attract each other in thicker bilayers. On the contrary, the barrel-like peptides repel each other in thick bilayers and attract each other in thinner membranes. These results potentially provide possible mechanisms of control for the mode of protein-protein interactions in membrane domains with different bilayer thicknesses.

Physico-Chemical Mechanisms of the Functioning of Membrane-Active Proteins of Enveloped Viruses

Over the past few years, the attention of the whole world has been riveted to the emergence of new dangerous strains of viruses, among which a special place is occupied by coronaviruses that have overcome the interspecies barrier in the past 20 years: SARS viruses (SARS), Middle East respiratory syndrome (MERS), as well as a new coronavirus infection (SARS-CoV-2), which caused the largest pandemic since the Spanish flu in 1918. Coronaviruses are members of a class of enveloped viruses that have a lipoprotein envelope. This class also includes such serious pathogens as human immunodeficiency virus (HIV), hepatitis, Ebola virus, influenza, etc. Despite significant differences in the clinical picture of the course of disease caused by enveloped viruses, they themselves have a number of characteristic features, which determine their commonality. Regardless of the way of penetration into the cell—by endocytosis or direct fusion with the cell membrane—enveloped viruses are characterized by the following stages of interaction with the target cell: binding to receptors on the cell surface, interaction of the surface glycoproteins of the virus with the membrane structures of the infected cell, fusion of the lipid envelope of the virion with plasma or endosomal membrane, destruction of the protein capsid and its dissociation from the viral nucleoprotein. Subsequently, within the infected cell, the newly synthesized viral proteins must self-assemble on various membrane structures to form a progeny virion. Thus, both the initial stages of viral infection and the assembly and release of new viral particles are associated with the activity of viral proteins in relation to the cell membrane and its organelles. This review is devoted to the analysis of physicochemical mechanisms of functioning of the main structural proteins of a number of enveloped viruses in order to identify possible strategies for the membrane activity of such proteins at various stages of viral infection of the cell.

Regulation of Antimicrobial Peptide Activity via Tuning Deformation Fields by Membrane-Deforming Inclusions

Antimicrobial peptides (AMPs) are considered prospective antibiotics. Some AMPs fight bacteria via cooperative formation of pores in their plasma membranes. Most AMPs at their working concentrations can induce lysis of eukaryotic cells as well. Gramicidin A (gA) is a peptide, the transmembrane dimers of which form cation-selective channels in membranes. It is highly toxic for mammalians as being majorly hydrophobic gA incorporates and induces leakage of both bacterial and eukaryotic cell membranes. Both pore-forming AMPs and gA deform the membrane. Here we suggest a possible way to reduce the working concentrations of AMPs at the expense of application of highly-selective amplifiers of AMP activity in target membranes. The amplifiers should alter the deformation fields in the membrane in a way favoring the membrane-permeabilizing states. We developed the statistical model that allows describing the effect of membrane-deforming inclusions on the equilibrium between AMP monomers and cooperative membrane-permeabilizing structures. On the example of gA monomer-dimer equilibrium, the model predicts that amphipathic peptides and short transmembrane peptides playing the role of the membrane-deforming inclusions, even in low concentration can substantially increase the lifetime and average number of gA channels.

Characteristic lengths of transmembrane peptides controlling their tilt and lateral distribution between membrane domains

Lipids and proteins of plasma membranes of eukaryotic cells are supposed to form protein-lipid domains, characterized by a different molecular order, bilayer thickness, and elastic parameters. Several mechanisms of preferable distribution of transmembrane proteins to the ordered or disordered membrane domains have been revealed. The mismatch between the length of the protein transmembrane domain and hydrophobic thickness of the lipid bilayer is considered to be an important driving force of protein lateral sorting. Utilizing the continuum theory of elasticity, we analyzed optimal configurations and preferable membrane domains for single-pass transmembrane peptides of various hydrophobic lengths and effective molecular shapes. We obtained that short transmembrane peptides stand perpendicularly to the membrane plane. The exceedance of a certain characteristic length leads to the tilt of the peptide. This length depends on the bilayer thickness. Thus, in the membrane with coexisting ordered (thicker) and disordered (thinner) phases tilting of the peptide in each phase is governed by its individual characteristic length. The lateral distribution of the peptides between ordered and disordered membrane domains is shown to be described by two additional characteristic lengths. The exceedance of the smaller one drives the peptide towards a more ordered and thicker membrane, while the exceedance of the larger characteristic length switches the preferable membrane domain from ordered and thicker to disordered and thinner. Thus, membrane proteins with long enough transmembrane domains are predicted to accumulate in the thinner disordered membrane as compared to the thicker ordered bilayer. For hourglass-like and barrel-like shaped transmembrane peptides the specific regime of sorting was obtained: the peptides distributed almost equally between the phases in a wide range of peptide lengths. This finding allowed explaining the experimental data on lateral distribution of transmembrane peptide tLAT.

Peptide-induced membrane elastic deformations decelerate gramicidin dimer-monomer equilibration

Gramicidin A (gA) is a hydrophobic pentadecapeptide readily incorporating into a planar bilayer lipid membrane (BLM), thereby inducing a large macroscopic current across the BLM. This current results from ion-channel formation due to head-to-head transbilayer dimerization of gA monomers with rapidly established monomer-dimer equilibrium. Any disturbance of the equilibrium, e.g., by sensitized photoinactivation of a portion of gA monomers, causes relaxation toward a new equilibrium state. According to previous studies, the characteristic relaxation time of the gA-mediated electric current decreases as the current increases upon elevating the gA concentration in the membrane. Here, we report data on the current relaxation kinetics for gA analogs with N-terminal valine replaced by glycine or tyrosine. Surprisingly, the relaxation time increased rather than decreased upon elevation of the total membrane conductance induced by these gA analogs, thus contradicting the classical kinetic scheme. We developed a general theoretical model that accounts for lateral interaction of monomers and dimers mediated by membrane elastic deformations. The modified kinetic scheme of the gramicidin dimerization predicts the reverse dependence of the relaxation time on membrane conductance for gA analogs, with a decreased dimerization constant that is in a good agreement with our experimental data. The equilibration process may be also modulated by incorporation of other peptides ("impurities") into the lipid membrane.

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.

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.

Ectodomain Pulling Combines with Fusion Peptide Inserting to Provide Cooperative Fusion for Influenza Virus and HIV

Enveloped viruses include the most dangerous human and animal pathogens, in particular coronavirus, influenza virus, and human immunodeficiency virus (HIV). For these viruses, receptor binding and entry are accomplished by a single viral envelope protein (termed the fusion protein), the structural changes of which trigger the remodeling and merger of the viral and target cellular membranes. The number of fusion proteins required for fusion activity is still under debate, and several studies report this value to range from 1 to 9 for type I fusion proteins. Here, we consider the earliest stage of viral fusion based on the continuum theory of membrane elasticity. We demonstrate that membrane deformations induced by the oblique insertion of amphipathic fusion peptides mediate the lateral interaction of these peptides and drive them to form into a symmetric fusion rosette. The pulling force produced by the structural rearrangements of the fusion protein ectodomains gives additional torque, which deforms the membrane and additionally stabilizes the symmetric fusion rosette, thus allowing a reduction in the number of fusion peptides needed for fusion. These findings can resolve the large range of published cooperativity indices for HIV, influenza, and other type I fusion proteins.

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.

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.