Gramicidin A as a mechanical sensor for mixed nonideal lipid membranes.

Gramicidin A (gA) is a short hydrophobic ß-helical peptide that forms cation-selective channels in lipid membranes in the course of transbilayer dimerization. The length of the gA helix is smaller than the thickness of a typical lipid monolayer. Consequently, elastic deformations of the membrane arise in the configurations of gA monomers, conducting dimer, and the intermediate state of coaxial pair, where gA monomers from opposing membrane monolayers are located one on top of the other. The gA channel is characterized by the average lifetime of the conducting state. The elastic properties of the membrane influence the average lifetime, thus making gA a convenient sensor of membrane elasticity. However, the utilization of gA to investigate the elastic properties of mixed membranes comprising two or more components frequently relies on the assumption of ideality, namely that the elastic parameters of mixed-lipid bilayers depend linearly on the concentrations of the components. Here, we developed a general approach that does not rely on the aforementioned assumption. Instead, we explicitly accounted for the possibility of inhomogeneous lateral distribution of all lipid components, as well as for membrane-mediated lateral interactions of gA monomers, dimer, coaxial pair, and minor lipid components. This approach enabled us to derive unknown elastic parameters of lipid monolayer from experimentally determined lifetimes of gA channel in mixed-lipid bilayers. A general algorithm was formulated that allows the unknown elastic parameters of a lipid monolayer to be obtained using gA as a mechanical sensor.

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.

Effect of solid support and membrane tension on adsorption and lateral interaction of amphipathic peptides.

A wide class of antimicrobial amphipathic peptides is aimed to selectively form through pores in bacterial membranes. The partial incorporation of the peptides into the lipid monolayer leads to elastic deformation of the membrane. The deformation influences both the adsorption of the peptides and their lateral interaction. Detailed study of pore formation mechanisms requires an accurate determination of the surface concentration of the peptides at their given bulk concentration. Widely used methods to register the adsorption are atomic force microscopy (AFM), surface plasmon resonance refractometry (SPRR), and inner field compensation (IFC). AFM and SPRR utilize membranes deposited onto a solid support, while IFC operates with model membranes under substantial lateral tension. Here, we theoretically studied the effect of the solid support and lateral tension on the elastic deformations of the membrane induced by partially incorporated amphipathic peptides and thus on the peptide adsorption energy and lateral interaction. We demonstrated that, under conditions typical for AFM, SPRR, and IFC, the adsorption energy can increase by up to 1.5 kBT per peptide leading to about 4 times decreased surface concentration as compared to free-standing tensionless membranes. In addition, the effective lateral size of the peptide molecule increases by about 10%, which can have an impact on the quantitative description of the adsorption isotherms. Our results allow estimating the effects of the solid support and lateral tension on the adsorption and interaction of amphipathic peptides at the membrane surface and taking them into account in interpretation of experimental observations.

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.

A Mechanism of Double-Membrane Vesicle Formation from Liquid-Ordered/Liquid-Disordered Phase Separated Spherical Membrane.

Genome replication of coronaviruses takes place in specific cellular compartments, in so-called double-membrane vesicles (DMVs), formed from the endoplasmic reticulum (ER). An intensive production of DMVs is induced by non-structural viral proteins. Here, we proposed a possible mechanism of the DMV formation from ER-derived spherical vesicles where liquid-ordered and liquid-disordered lipid phases coexist. These vesicles are supposed to divide into two homogeneous liquid-ordered and liquid-disordered vesicles. The formation of two spherical vesicles constituting DMV requires a mechanical work to be performed. We considered the excess energy of the boundary between the coexisting lipid phases as the main driving force behind the division of the initial vesicle. Explicitly accounting for the energy of elastic deformations and the interphase boundary energy, we analyzed a range of physical parameters where the DMV formation is possible. We concluded that this process can principally take place in a very narrow range of system parameters. The most probable diameter of DMVs formed according to the proposed mechanism appeared to be approximately 220 nm, in an agreement with the average diameter of DMVs observed in vivo. Our consideration predicts the DMV size to be strongly limited from above. The developed analysis can be utilized for the production of DMVs in model systems.

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.

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.

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.

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.

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.

Membrane Elastic Deformations Modulate Gramicidin A Transbilayer Dimerization and Lateral Clustering.

Gramicidin A (gA) is a short ß-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.

Probing absolute spin polarization at the nanoscale.

Probing absolute values of spin polarization at the nanoscale offers insight into the fundamental mechanisms of spin-dependent transport. Employing the Zeeman splitting in superconducting tips (Meservey-Tedrow-Fulde effect), we introduce a novel spin-polarized scanning tunneling microscopy that combines the probing capability of the absolute values of spin polarization with precise control at the atomic scale. We utilize our novel approach to measure the locally resolved spin polarization of magnetic Co nanoislands on Cu(111). We find that the spin polarization is enhanced by 65% when increasing the width of the tunnel barrier by only 2.3 Å due to the different decay of the electron orbitals into vacuum.