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Theoretical analysis of the effect of the ionic strength of a solution on the surface (zeta) potential of liposomes formed by an anionic phospholipid (cardiolipin) with adsorbed polycations has been carried out. The experimental data were previously measured by the electrokinetic method in the presence of polylysine molecules of different molecular weights and a supporting electrolyte, KCl, at concentrations of 10, 40, and 100 mM. To approximate the experimental dependences of the potential on the amount of polylysine in the suspension, we used a theoretical model with parameters, among which the most physically significant are the thickness of the polymer layer, the adsorption constant, and the fraction of the surface of lipid membranes occupied by the polypeptide at the saturation. The found values of the model parameters demonstrate the effect of the length of the polypeptide molecules on the structure of the polymer layer varying from homogeneous to clustered distribution over the surface. A noticeable decrease in the efficiency of adsorption with an increase in the ionic strength of the solution is explained by the conformational rearrangements of the macromolecules on the surface and a decrease in the area of the surface available for their adsorption upon the saturation.

The formation of through pores in lipid bilayer membranes occurs in a number of cellular processes and is also applied for biotechnological and biomedical purposes. In the classical theory of pore formation, diffusion of membrane defects in space of radii is considered. When the first pore reaches a critical radius, the membrane irreversibly ruptures. It is usually presumed that the diffusion of defects occurs independently; their possible lateral interactions are not taken into account. In this paper, we consider a possible influence of lateral interactions of metastable through pores on their kinetics. It is assumed that the interaction occurs due to the overlap of elastic deformation fields arising at the edges of two pores. The interaction energy of two circular pores was calculated in the Derjaguin approximation for rapidly decaying potentials. The unidimensional potential of interaction of two linear parallel edges of pores formed in membranes of different lipid composition was calculated in the framework of the theory of elasticity of liquid crystals adapted to lipid membranes. It is shown that this interaction should lead to a considerable reduction of the measured line tension of the pore edge. In addition, the lifetime of two optimally situated metastable pores can increase approximately 10 times due to the interaction. Extrapolation of the obtained results to the case of a larger number of interacting pores makes it possible to predict an additional increase in the lifetime by one or two orders of magnitude.

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

It is believed that separation of lipid matrix of biological membranes into ordered and disordered phases plays an important role in the lateral distribution of proteins and transduction of cellular signals through the plasma membrane. In model lipid membranes with symmetric composition of monolayers, such phase separation always leads to formation of bilayer domains. However, the lipid composition of outer and inner monolayers of plasma membranes of cells is different, i.e., these membranes are asymmetric. The mechanism of coupling of monolayer domains into bilayer structures in cells still remains unexplained. The ordered lipid domain is thicker than the surrounding membrane; as a result, elastic deformations occur at their boundary. Minimization of the elastic part of the boundary energy contributes to the coupling of monolayer domains in opposite monolayers. However, this driving force is not enough to ensure that domains will come into register: at a certain fraction of the membrane area occupied by the domains, the elastic energy can reach the minimum in antisymmetric configurations (the ordered domain in the upper monolayer is opposed by disordered monolayer of the surrounding membrane). As an alternative factor of the coupling, we considered curvature thermal fluctuations of the membrane shape. Our theoretical analysis of elastic deformations in a lipid bilayer that is asymmetric in monolayer composition shows that more rigid lipid domains tend to distribute into the region with lower curvature of the monolayer; these regions naturally coincide in opposite monolayers. Thus, the coupling of ordered domains in different monolayers is provided by their greater bending stiffness as compared to the surrounding membrane. At the same time, greater ordering leads to lateral condensation, i.e., to the decrease of the average area per lipid molecule. The difference in area per lipid molecule in the coexisting membrane phases, on the contrary, tends to separate bilayer domains into their monolayer components. To quantify the coupling energy of ordered domains, it is necessary to take both of these effects into account.

The initial stage of viral infection – fusion of viral and target cell membranes – is still a nontrivial system for analysis due to a large number of parameters affecting this process, as well as due to small size of the fusion region, which for a long time made the fusion process difficult for experimental study. A number of recently published papers allowed us to determine features of the geometric structure of fusing membranes, insertion of fusion proteins into the membrane monolayers, and to determine the dependence of fusion efficiency on the membrane composition. Relying on the latest experimental data, on the basis of the theory of elasticity of lipid membranes, we built a fusion model that quantitatively describes these experimental results and in particular, makes it possible to calculate the energy barrier necessary to ensure close contact of fusing membranes, which determines the fusion efficiency. This allows us to adapt the existing fusion theory to these results and for the first time to obtain a quantitative agreement of the effect of the composition of the target cell membrane on the height of the fusion energy barrier.

A theoretical model describing experimental data on the electrophoretic mobility of liposomes, which are formed from mixtures of charged (cardiolipin) and neutral (phosphatidylcholine) lipids and contain polylysine molecules adsorbed on them, is considered. The experimental data show that the ζ potential of the liposomes depends on the concentration of the adsorbed polylysine. The proposed model is used to determine the physically measured characteristics describing the system: the thickness of the adsorbed polymer layer, the surface area fraction occupied by the polymer at saturation, and the polymer–liposome surface binding constant. The performed calculations show that the reversibility of the adsorption dramatically decreases with an increase in the sizes of adsorbed polymer molecules. In addition, the presented model explains the behavior of the point of zero charge upon variations in the system parameters. The considered model is not confined to a specific type of polymers and phospholipids and may be used to study the adsorption of other biologically significant synthetic polycations and polypeptides.

The adsorption of large polycations on a charged lipid membrane is qualitatively different from the small inorganic cations, which almost uniformly populate the membrane surface. We assume that the polycationic adsorption layer might be laterally inhomogeneous starting from a certain polymer length, and this effect can be more visible for membranes with low anionic lipid content. To study systems with inhomogeneous adsorption layers, we carried out electrokinetic measurements of mobility of liposomes containing anionic and neutral phospholipids in the presence of polylysine molecules. Some of these systems were simulated by all-atom molecular dynamics. Here we proposed a theoretical approach accounting for the formation of separated regions at the membrane surface, which differ in charge density and surface potential. Our model allowed us to determine the adsorption layer’s geometric parameters such as surface coverage and surface-bound monomer fraction of polymer, which correlate with the molecular dynamics (MD) simulations. We demonstrated that the configuration polylysine adopts on the membrane surface (tall or planar) depends on the polymer/membrane charge ratio. Both theory and MD indicate a decrease in the anionic lipid content, alongside with a decrease in the bound monomer fraction and corresponding increase in the extension length of the adsorbed polymers.

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.

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 microdomains enriched with sphingomyelin and cholesterol, the so-called rafts, are thicker than the surrounding membrane. To smooth the thickness mismatch, the membrane is deformed, which leads to the formation of a complex asymmetric structure of the raft boundary. The rafts are of great importance in the process of viral infection of the cell: for example, in recent experiments it has been shown that the fusion peptide of human immunodeficiency virus (HIV) tends to be predominantly inserted at the raft boundary, and the effectiveness of the fusion was low in the absence of the rafts. It has been noticed in these studies that such preferential distribution of fusion peptides was not found in the case of influenza virus. In the present paper, we modeled the interaction of fusion peptides with rafts by the methods of elasticity theory of lipid membranes. We have shown that the boundary of the liquid-ordered domains can act as an attractor for the fusion peptides: peptides distribute to the raft boundary and play the role of line-active membrane components. Our model enables to explain the difference of the behavior of different fusion peptides in the presence of rafts in the above mentioned example of the experimental data by different geometry of their insertion into the lipid monolayer. Our results show the fundamental mechanisms by which the geometry of fusion peptide insertion affects their distribution in the lipid membrane.

Signal transduction through cellular membranes requires the highly specific and coordinated work of specialized proteins. Proper functioning of these proteins is provided by an interplay between them and the lipid environment. Liquid-ordered lipid domains are believed to be important players here, however, it is still unclear whether conditions for a phase separation required for lipid domain formation exist in cellular membranes. Moreover, membrane leaflets are compositionally asymmetric, that could be an obstacle for the formation of symmetric domains spanning the lipid bilayer. We theoretically show that the presence of protein in the membrane leads to the formation of a stable liquid-ordered lipid phase around it by the mechanism of protein wetting by lipids, even in the absence of conditions necessary for the global phase separation in the membrane. Moreover, we show that protein shape plays a crucial role in this process, and protein conformational rearrangement can lead to changes in the size and characteristics of surrounding lipid domains.

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.

Here we explored a contribution of fusion proteins to stalk formation, the first stage of membrane fusion, and considered two likely mechanisms, by which these proteins could influence the membrane transformation. One mechanism represents the induction of spontaneous membrane curvature, while another is membrane disturbance by a force generated by attached proteins. The energy barrier arising due to the deformation of approaching membranes and hydration repulsion between them was calculated. In addition, a dependence of an energy barrier height on certain protein features, such as spontaneous curvature, was analyzed. It was found that if fusion proteins do not produce a force directly applied to fusing membranes, they negligibly affect the barrier height irrespective of a value of spontaneous protein curvature. Thus, the overall results provide evidence that if fusion proteins are unable to exert force, they cannot provide monolayer fusion of the membranes.

Experimental curves of lateral pressure and Volta potential previously measured vs. area of dimyristoylphosphatidylserine (DMPS) monolayer (PA diagram) (Ermakov et al., 2010) are analyzed in the framework of the model introduced by Ruckenstein and Li (1996, 1998) for lipid clusters. The same curves are described by some empirical parameters as an alternative mechanistic approach. Both approaches agree with each other and describe the compression diagrams at low and high pressures (high and low areas). Analytical expressions for the asymptotic approximations in the cluster model are suggested. The product of pressure and area (equal to the energy of monolayer compression) as well as Volta potential shown in lateral pressure scale are proposed for experimental data presentation suitable for the quantitative analysis. It is also proposed to represent this function, as well as Volta potential vs. the lateral pressure. Monolayer compressibility module evaluated for the “expanded liquid” area was used to describe the shape of experimental curves. This parameter approximates well the shape of the compression diagrams and Volta potential changes if the interface potential is assumed to be proportional to the mechanical work of the monolayer compression.

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.

We consider the process of fusion of lipid membranes from the stage of stalk with minimal radius to the stage of fusion pore. We assume that stalk directly developed into the fusion pore, omitting the stage of hemifusion diaphragm. Energy of intermediate stages is calculated on the basis of the classical elasticity theory of liquid crystals adapted for lipid membranes. The trajectory of transition from stalk to pore is obtained with regard to hydrophobic and hydration interactions. Continuous change of orientation of lipids in distal monolayers occurs along the trajectory. The orientation changes from the direction along rotational axis of the system specific to stalk to the direction corresponding to the fusion pore. Dependence of energy of intermediate stages on the value of spontaneous curvature of distal monolayers of the fusing membranes is obtained. We demonstrate that the energy barrier of the stalk-to-pore transition decreases when distal monolayers have positive spontaneous curvature, which is in accordance with available experimental data.

The initial stage of membrane fusion under the action of fusion proteins transmitting force to the membrane is considered in the work. Protein inclusions in the membrane create a highly curved bulge, which facilitates fusion of contacting membrane monolayers. Membrane is considered as a liquid-crystal medium subjected to elastic deformations. Deformations of splay and tilt are taken into account and energy is calculated to the second order on these deformations. Protein complexes are modeled as rigid tilted rings embed- ded into the fusing membranes. The energy needed to locally bring membranes together under the action of proteins is calculated. The dependence of the membrane energy on a protein ring radius is shown to have minimum. It means that membrane deformations stabilize the radius of the protein cluster. The main characteristics of the system, such as equilibrium radius of the protein complex and the minimal energy needed to accomplish the first stage of the fusion, are calculated.

Specific domains, called rafts, are formed in cell membranes. Similar lipid domains can be formed in model membranes as a result of phase separation with raft size may remaining small (∼10–100 nm) for a long time. The characteristic lifetime of a nanoraft ensemble strongly depends on the nature of mutual raft interactions. The interaction energy between the boundaries of two rafts has been calculated under the assumption that the thickness of the raft bilayer is greater than that of the surrounding membrane, and elastic deformations appear in order to smooth the thickness mismatch at the boundary. When rafts approach each other, deformations from their boundaries overlap, making interaction energy profile sophisticated. It has been shown that raft merger occurs in two stages: rafts first merge in one monolayer of the lipid bilayer and then in another monolayer. Each merger stage requires overcoming of an energy barrier of about 0.08–0.12 kBT per 1 nm of boundary length. These results allow us to explain the stability of the ensemble of finite sized rafts.

Bilayer thickness in membrane domains enriched with sphingomielin and cholesterol (known as “rafts”) is bigger than thickness of neighboring membrane. Monolayers need to deform to compensate the thicknesses difference in the vicinity of the raft boundary. Line tension of the boundary of rafts associated with elastic deformations originating from the compensation of the thickness mismatch is calculated in the frame-work of the elasticity theory. In the calculations deformations of splay, tilt and lateral stretching/compression are considered. It is assumed that raft consists of two monolayer domains situated in the different membrane monolayers; it is also assumed that the boundaries of domains can shift in the lateral direction with respect to relative to each other. Dependence of the boundary energy of raft on the value of the relative shift of the boundaries is calculated. It is shown that the boundary energy is minimal when shift is equal to 4.5 nm. Dependence of the optimal shift on the mismatch of the monolayer thicknesses of raft and surrounding membrane as well as membrane shape in the vicinity of boundary are calculated. The calculated values of line tension are in a good agreement with available experimental data. Taking into account deformation of stretching/compression increases the accuracy of calculations by 30%; this exceeds the uncertainty of the line tension measurements by modern techniques.

Line tension of the boundary of specific domains (rafts) rich in sphingomyelin was calculated. The line tension was calculated based on macroscopic theory of elasticity under assumption that the bilayer in raft is thicker than in the surrounding membrane. The calculations took into account the possibility of lateral shift of the domain boundaries located in different monolayers of the membrane. The line tension was associated with the energy of elastic deformations appearing in the vicinity of the boundary in order to compensate for the difference in the thickness of the monolayers. Spatial distribution of deformations and the line tension was calculated by minimization of elastic free energy of the system. Dependence of the line tension on the distance between the domains boundaries located in different monolayers was obtained. It was shown that the line tension is minimal if the distance is about 4 nm. Thus, membrane deformations stabilize the bilayer structure of rafts observed experimentally. The calculated value of line tension is about 0.6 pN for the difference between the monolayer thickness of raft and surrounding membrane of about 0.5 nm, which is in agreement with the experimental data available.

The line tension of the edge of the lipid bilayer pore is calculated on the basis of the elastic theory of continuous liquid-crystal medium. Three types of deformations of the membrane were taken into account: bending, lateral stretching/compression, and tilt of the lipidic tails. Various models of structure of the pore edge are considered: models of the cylindrical shape with given radius and optimum radius, “extrapolational” model, “two-coordinate” model, and model with a hydrophobic cavity (“void”). Models can be conventionally divided into two classes. The first class includes models in which membrane monolayers are in contact with each other everywhere. Models of the second class admit appearance of a hydrophobic cavity between monolayers. Models of the first class yield value of the line tension γ, strongly differing from that known from the literature (∼10 pN). For example, the value of the line tension γ obtained in the cylindrical model equals to 21 pN; in the two-coordinate model, 19 pN, and in the extrapolational model, 62 pN. At the same time, the model with cavity gives the value of γ eqal ∼10 pN, provided that surface tension at the boundary of the lipid tails is close to zero. This value is in a good agreement with the literature data.

Our recent publication in this journal [1] challenges the concept that domains in opposing membrane leaflets are in register because of interactions at a membrane midplane. Compelled by the lack of direct experimental proof for (i) midplane interaction via an overhang [2] or (ii) LO and LD phases repelling each other [3] we propose that minimization of line tension γ drives registration (R) [1]. We dismiss antiregistration (AR) as an unlikely event because its twofold larger domain area translates into a 2-fold larger boundary length. Moreover, the line tensions at the LD/LD−LD/LO and LO/LO−LD/LO interfaces (Cartoon 1), γDD and γOO, respectively, exceed the line tension at the LD/LD−LO/LO interface, γR rendering the elastic energy WR of the registered state smaller than the elastic energy WAR of the antiregistered state. Consequently, registration is energetically favorable. Also, γR > γDD, γOO because an isolated LD/LO boundary in only one leaflet leads to membrane bending. As readily observed in the Cartoon, for the membrane to remain flat, a substantial torque must be applied or an LD/LO boundary must be created in the upper monolayer to oppose the LD/LO boundary in the lower monolayer. Cartoon 1 Calculated membrane shape at raft boundary for L = 100nm. The transitional LO/LD zone is tilted. A flat membrane is assured in [1] by boundary conditions (Eq. 6), which set the LO/LO and LD/LD bilayers to a flat horizontal (in Cartoon 1 at x→+∞ and x→−∞, respectively). A tilt was only allowed for the transitional L zone to yield minimal W. Accounting for the spontaneous curvatures of LO, and LD, JO = −0.07 nm−1 and JD = −0.1 nm−1, respectively, in a 1:1:1 mixture of dioleoylphosphatdiylcholine:dipalmitoylphatdiylcholine:cholesterol [4] and assuming hD = 1.3 nm (LD-phase) and hO = 1.6 nm (LO-phase) [5] yields the line tensions (in pN) of γDD=1.06, γOO=1.54, and γR=0.52. This is in stark contrast to Williamson’s and Olmsted’s erroneous assumption [6] that γR−AR = γDD = γOO = γ∞/2. There γ∞ was defined as γR(L→∞). For the specific lipid mixture γ∞ is equal to 0.83 pN. Thus, for the physiological relevant case of small LO domains (signaling platforms = rafts) surrounded by a large area of LD lipids, the ratio WR/WAR=γR/(2γDD)=0.5/1.5≈0.34

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 nor interactions at the membrane midplane.

The close opposition of membranes needed for fusion is initiated by the formation of local protrusions. In viral fusion, the protrusions should be generated by several fusion proteins acting cooperatively within a cluster. We start with two parallel planar membranes and show that membrane elasticity alone can spontaneously cause several fusion proteins to self-organize into a cylindrically symmetric cluster that consists of three to six proteins cluster, independent of specific short-range protein-protein interactions. In essence, fusion proteins induce membrane bending which then brings the proteins together, creating more bending -- a positive feedback system. Calculations of energy minimization yield the following progression of protein arrangements: Three proteins initially arrange at the vertices of an equilateral triangle. Cluster formation continues by three additional proteins symmetrically arranging at the vertices of a more distal equilateral triangle that surrounds the three central proteins. These distal proteins move toward, and the central proteins away, from the center, yielding a cluster of six proteins arranged hexagonally on a circle. The energy needed to bend membranes into protrusions is supplied by the proteins in the cluster; continuum elasticity theory is used to calculate this energy. The total energy consists of the change in elastic energy of membrane deformation and the energy generated by an osmotic pressure difference that arises because the density of proteins outside the cluster is greater than the zero density inside cluster. The minimum energy is 75 kT for a cluster radius of 15 nm. The minimal energy per protein is 12 kT, which is a reasonable estimate.

The structure and line tension of the boundary of a membrane domain (raft) was theoretically examined. A bilayer raft was modeled as two monolayer domains that are in register, directly opposite each other, one domain in each monolayer of a bilayer. It is assumed that rafts are thicker than the surrounding membrane. The macroscopic theory of elasticity was used to calculate line tension and the relative lateral displacement of the boundaries of two opposed monolayer domains. In the absence of deformations at the boundary, hydrophobic portions of a lipid would be exposed to water because rafts are thicker than the surround. The line tension was calculated as the energy required for elastic deformations at the raft boundary to prevent exposure of hydrophobic patches to water. The distribution of the deformations and the boundary energy were determined by minimizing the elastic deformation energy of the system. This yielded the dependence of the line tension on the displacement between the boundaries of the two opposed monolayer domains. It was found that line tension has a minimum when the boundaries of the two monolayer domains are separated by a distance of ∼4 nm. Thus, an experimental predication of the model is that membrane deformations at the boundaries of raft monolayers should stabilize monolayer domains in register; this register is approximate, rather than exact. An applied external lateral tension alters the deformations at the boundary and this leads to an increase in line tension.Supported by the Program of Creation and Development of the National University of Science and Technology «MISiS», and grants from the RFBR #11-04-01001 and #11-04-02087, Russian Federal Targeted Program “Scientific and Scientific-Pedagogical Human Resources of Innovative Russia” (state contract # P337).