GTPase cycle of dynamin is coupled to membrane squeeze and release, leading to spontaneous fission.

The GTPase dynamin is critically involved in membrane fission during endocytosis. How does dynamin use the energy of GTP hydrolysis for membrane remodeling? By monitoring the ionic permeability through lipid nanotubes (NT), we found that dynamin was capable of squeezing NT to extremely small radii, depending on the NT lipid composition. However, long dynamin scaffolds did not produce fission: instead, fission followed GTPase-dependent cycles of assembly and disassembly of short dynamin scaffolds and involved a stochastic process dependent on the curvature stress imposed by dynamin. Fission happened spontaneously upon NT release from the scaffold, without leakage. Our calculations revealed that local narrowing of NT could induce cooperative lipid tilting, leading to self-merger of the inner monolayer of NT (hemifission), consistent with the absence of leakage. We propose that dynamin transmits GTP's energy to periodic assembling of a limited curvature scaffold that brings lipids to an unstable intermediate.

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.

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.

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.

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.

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.

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.

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.

Phosphatidylcholine Membrane Fusion Is pH-Dependent.

Membrane fusion mediates multiple vital processes in cell life. Specialized proteins mediate the fusion process, and a substantial part of their energy is used for topological rearrangement of the membrane lipid matrix. Therefore, the elastic parameters of lipid bilayers are of crucial importance for fusion processes and for determination of the energy barriers that have to be crossed for the process to take place. In the case of fusion of enveloped viruses (e.g., influenza) with endosomal membrane, the interacting membranes are in an acidic environment, which can affect the membrane's mechanical properties. This factor is often neglected in the analysis of virus-induced membrane fusion. In the present work, we demonstrate that even for membranes composed of zwitterionic lipids, changes of the environmental pH in the physiologically relevant range of 4.0 to 7.5 can affect the rate of the membrane fusion notably. Using a continual model, we demonstrated that the key factor defining the height of the energy barrier is the spontaneous curvature of the lipid monolayer. Changes of this parameter are likely to be caused by rearrangements of the polar part of lipid molecules in response to changes of the pH of the aqueous solution bathing the membrane.

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.

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.

Helix-helix interactions in membrane domains of bitopic proteins: Specificity and role of lipid environment.

Interaction between transmembrane helices often determines biological activity of membrane proteins. Bitopic proteins, a broad subclass of membrane proteins, form dimers containing two membrane-spanning helices. Some aspects of their structure-function relationship cannot be fully understood without considering the protein-lipid interaction, which can determine the protein conformational ensemble. Experimental and computer modeling data concerning transmembrane parts of bitopic proteins are reviewed in the present paper. They highlight the importance of lipid-protein interactions and resolve certain paradoxes in the behavior of such proteins. Besides, some properties of membrane organization provided a clue to understanding of allosteric interactions between distant parts of proteins. Interactions of these kinds appear to underlie a signaling mechanism, which could be widely employed in the functioning of many membrane proteins. Treatment of membrane proteins as parts of integrated fine-tuned proteolipid system promises new insights into biological function mechanisms and approaches to drug design. This article is part of a Special Issue entitled: Lipid order/lipid defects and lipid-control of protein activity edited by Dirk Schneider.

Switching between Successful and Dead-End Intermediates in Membrane Fusion.

Fusion of cellular membranes during normal biological processes, including proliferation, or synaptic transmission, is mediated and controlled by sophisticated protein machinery ensuring the preservation of the vital barrier function of the membrane throughout the process. Fusion of virus particles with host cell membranes is more sparingly arranged and often mediated by a single fusion protein, and the virus can afford to be less discriminative towards the possible different outcomes of fusion attempts. Formation of leaky intermediates was recently observed in some fusion processes, and an alternative trajectory of the process involving formation of π-shaped structures was suggested. In this study, we apply the methods of elasticity theory and Lagrangian formalism augmented by phenomenological and molecular geometry constraints and boundary conditions to investigate the traits of this trajectory and the drivers behind the choice of one of the possible scenarios depending on the properties of the system. The alternative pathway proved to be a dead end, and, depending on the parameters of the participating membranes and fusion proteins, the system can either reversibly enter the corresponding "leaky" configuration or be trapped in it. A parametric study in the biologically relevant range of variables emphasized the fusion protein properties crucial for the choice of the fusion scenario.

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 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.

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.

Long and short lipid molecules experience the same interleaflet drag in lipid bilayers.

Membrane interleaflet viscosity ηe affects tether formation, phase separation into domains, cell shape changes, and budding. Contrary to the expected contribution to interleaflet coupling from interdigitation, the slide of lipid patches in opposing monolayers conferred the same value ηe≈3×10(9) J s m-4 for the friction experienced by the ends of both short and long chain fluorescent lipid analogues. Consistent with the weak dependence of the translational diffusion coefficient on lipid length, the in-layer viscosity was, albeit length dependent, much smaller than ηe.

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.