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.

Proton Migration on Top of Charged Membranes.

Proton relay between interfacial water molecules allows rapid two-dimensional diffusion. An energy barrier, ΔGr‡, opposes proton-surface-to-bulk release. The ΔGr‡-regulating mechanism thus far has remained unknown. Here, we explored the effect interfacial charges have on ΔGr‡'s enthalpic and entropic constituents, ΔGH‡ and ΔGS‡, respectively. A light flash illuminating a micrometer-sized membrane patch of a free-standing planar lipid bilayer released protons from an adsorbed hydrophobic caged compound. A lipid-anchored pH-sensitive dye reported protons' arrival at a distant membrane patch. Introducing net-negative charges to the bilayer doubled ΔGH‡, while positive net charges decreased ΔGH‡. The accompanying variations in ΔGS‡ compensated for the ΔGH‡ modifications so that ΔGr‡ was nearly constant. The increase in the entropic component of the barrier is most likely due to the lower number and strength of hydrogen bonds known to be formed by positively charged residues as compared to negatively charged moieties. The resulting high ΔGr‡ ensured interfacial proton diffusion for all measured membranes. The observation indicates that the variation in membrane surface charge alone is a poor regulator of proton traffic along the membrane surface.

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.

Structural Role of Plasma Membrane Sterols in Osmotic Stress Tolerance of Yeast Saccharomyces cerevisiae.

Yeast S. cerevisiae has been shown to suppress a sterol biosynthesis as a response to hyperosmotic stress. In the case of sodium stress, the failure to suppress biosynthesis leads to an increase in cytosolic sodium. The major yeast sterol, ergosterol, is known to regulate functioning of plasma membrane proteins. Therefore, it has been suggested that the suppression of its biosynthesis is needed to adjust the activity of the plasma membrane sodium pumps and channels. However, as the sterol concentration is in the range of thirty to forty percent of total plasma membrane lipids, it is believed that its primary biological role is not regulatory but structural. Here we studied how lowering the sterol content affects the response of a lipid bilayer to an osmotic stress. In accordance with previous observations, we found that a decrease of the sterol fraction increases a water permeability of the liposomal membranes. Yet, we also found that sterol-free giant unilamellar vesicles reduced their volume during transient application of the hyperosmotic stress to a greater extent than the sterol-rich ones. Furthermore, our data suggest that lowering the sterol content in yeast cells allows the shrinkage to prevent the osmotic pressure-induced plasma membrane rupture. We also found that mutant yeast cells with the elevated level of sterol accumulated propidium iodide when exposed to mild hyperosmotic conditions followed by hypoosmotic stress. It is likely that the decrease in a plasma membrane sterol content stimulates a drop in cell volume under hyperosmotic stress, which is beneficial in the case of a subsequent hypo-osmotic one.

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.

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.

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.

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.

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.

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.

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.