Stabilization of bilayer structure of raft due to elastic deformations of membrane

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.     

Line tension and interaction energies of membrane rafts calculated from lipid splay and tilt

Membrane domains known as rafts are rich in cholesterol and sphingolipids, and are thought to be thicker than the surrounding membrane. If so, monolayers should elastically deform so as to avoid exposure of hydrophobic surfaces to water at the raft boundary. We calculated the energy of splay and tilt deformations necessary to avoid such hydrophobic exposure. The derived value of energy per unit length, the line tension gamma, depends on the elastic moduli of the raft and the surrounding membrane; it increases quadratically with the initial difference in thickness between the raft and surround; and it is reduced by differences, either positive or negative, in spontaneous curvature between the two. For zero spontaneous curvature, gamma is approximately 1 pN for a monolayer height mismatch of approximately 0.3 nm, in agreement with experimental measurement. Our model reveals conditions that could prevent rafts from forming, and a mechanism that can cause rafts to remain small. Prevention of raft formation is based on our finding that the calculated line tension is negative if the difference in spontaneous curvature for a raft and the surround is sufficiently large: rafts cannot form if gamma < 0 unless molecular interactions (ignored in the model) are strong enough to make the total line tension positive. Control of size is based on our finding that the height profile from raft to surround does not decrease monotonically, but rather exhibits a damped, oscillatory behavior. As an important consequence, the calculated energy of interaction between rafts also oscillates as it decreases with distance of separation, creating energy barriers between closely apposed rafts. The height of the primary barrier is a complex function of the spontaneous curvatures of the raft and the surround. This barrier can kinetically stabilize the rafts against merger. Our physical theory thus quantifies conditions that allow rafts to form, and further, defines the parameters that control raft merger.     

Effect of hydrophobic mismatch on phase behavior of lipid membranes

We investigate the competing effects of hydrophobic mismatch and chain stretching on the morphology and evolution of domains in lipid membranes via Monte Carlo techniques. We model the membrane as a binary mixture of particles that differ in their preferred lengths, with the shorter particles mimicking unsaturated nonraft lipids and the longer particles mimicking saturated raft lipids. We find that phase separation can be induced upon increasing either the ratio J/kappa of the hydrophobic surface tension J to the compressibility modulus kappa. J/kappa determines the decay length for thickness changes. When this decay length is larger than the system size the membrane remains mixed. Furthermore, increasing the thickness relaxation time can induce transient phase separation.     

Lateral redistribution of transmembrane proteins and liquid-ordered domains in lipid membranes with inhomogeneous curvature

A number of processes in living cells are accompanied by significant changes of the geometric curvature of lipid membranes. In turn, heterogeneity of the lateral curvature can lead to spatial redistribution of membrane components, most important of which are transmembrane proteins and liquid-ordered lipid-protein domains. These components have a so-called hydrophobic mismatch: the length of the transmembrane domain of the protein, or the thickness of the bilayer of the domain differ from the thickness of the surrounding membrane. In this work we consider redistribution of membrane components with hydrophobic mismatch in membranes with non-uniform geometric curvature. Dependence of the components’ energy on the curvature is calculated in terms of theory of elasticity of liquid crystals adapted to lipid membranes. According to the calculations, transmembrane proteins prefer regions of the membrane with zero curvature. Liquid-ordered domains having a size of a few nm distribute mainly into regions of the membrane with small negative curvature appearing in the cell plasma membrane in the process of endocytosis. The distribution of domains of a large radius is determined by a decrease of their perimeter upon bending; these domains distribute into membrane regions with relatively large curvature.     

Coupling between line tension and domain contact angle in heterogeneous membranes

The compositional differences between domains in phase-separated membranes are associated with differences in bilayer thickness and moduli. The resulting packing deformation at the phase boundary gives rise to a line tension, the one dimensional equivalent of surface tension. In this paper we calculate the line tension between a large membrane domain and a continuous phase as a function of the thickness mismatch and the contact angle between the phases. We find that the packing-induced line tension is sensitive to the contact angle, reaching a minimum at a specific value. The difference in the line tension between a flat domain (that is within the plane of the continuous phase) and a domain at the optimal contact angle may be of order 40%. This could explain why previous calculations of the thickness mismatch based line tension tend to yield values that are higher than those measured experimentally.     

Coupling between line tension and domain contact angle in heterogeneous membranes

The compositional differences between domains in phase-separated membranes are associated with differences in bilayer thickness and moduli. The resulting packing deformation at the phase boundary gives rise to a line tension, the one dimensional equivalent of surface tension. In this paper we calculate the line tension between a large membrane domain and a continuous phase as a function of the thickness mismatch and the contact angle between the phases. We find that the packing-induced line tension is sensitive to the contact angle, reaching a minimum at a specific value. The difference in the line tension between a flat domain (that is within the plane of the continuous phase) and a domain at the optimal contact angle may be of order 40%. This could explain why previous calculations of the thickness mismatch based line tension tend to yield values that are higher than those measured experimentally.     

Effect of line tension on the lateral organization of lipid membranes

The principles of organization and functioning of cellular membranes are currently not well understood. The raft hypothesis suggests the existence of domains or rafts in cell membranes, which behave as protein and lipid platforms. They have a functional role in important cellular processes, like protein sorting or cell signaling, among others. Theoretical work suggests that the interfacial energy at the domain edge, also known as line tension, is a key parameter determining the distribution of domain sizes, but there is little evidence of how line tension affects membrane organization. We have investigated the effects of the line tension on the formation and stability of liquid ordered domains in model lipid bilayers with raft-like composition by means of time-lapse confocal microscopy coupled to atomic force microscopy. We varied the hydrophobic mismatch between the two phases, and consequently the line tension, by modifying the thickness of the disordered phase with phosphatidylcholines of different acyl chain length. The temperature of domain formation, the dynamics of domain growth, and the distribution of domain sizes depend strongly on the thickness difference between the domains and the surrounding membrane, which is related to line tension. When considering line tension calculated from a theoretical model, our results revealed a linear increase of the temperature of domain formation and domain growth rate with line tension. Domain budding was also shown to depend on height mismatch. Our experiments contribute significantly to our knowledge of the physical-chemical parameters that control membrane organization. Importantly, the general trends observed can be extended to cellular membranes.     

Line tension and stability of domains in cell-adhesion zones mediated by long and short receptor-ligand complexes

Submicron scale domains of membrane-anchored receptors play an important role in cell signaling. Central questions concern the stability of these microdomains, and the mechanisms leading to the domain formation. In immune-cell adhesion zones, microdomains of short receptor-ligand complexes form next to domains of significantly longer receptor-ligand complexes. The length mismatch between the receptor-ligand complexes leads to membrane deformations and has been suggested as a possible cause of the domain formation. The domain formation is a nucleation and growth process that depends on the line tension and free energy of the domains. Using a combination of analytical calculations and Monte Carlo simulations, we derive here general expressions for the line tension between domains of long and short receptor-ligand complexes and for the adhesion free energy of the domains. We argue that the length mismatch of receptor-ligand complexes alone is sufficient to drive the domain formation, and obtain submicron-scale minimum sizes for stable domains that are consistent with the domain sizes observed during immune-cell adhesion.     

A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch.

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness dP, embedded in a lipid bilayer of unperturbed thickness doL. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when dP > doL) in order to bridge over the lipid-protein hydrophobic mismatch (dP-doL). The bilayer's hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isometric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy delta F is calculated as a function of dP-doL. Most calculations are for C14 amphiphiles which, in the absence of a protein, pack at an average area per head-group ao approximately equal to 32 A2 (doL approximately 24.5 A), corresponding to the fluid state of the membrane. When dP = doL, delta F > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When dP > doL, the interaction free energy is further increased due to the enhanced stretching of the tails. When dP < doL, chain flexibility (entropy) increases, but this contribution to delta F is overcounted by the increase in the interfacial free energy. Thus, delta F obtains a minimum at dP-doL approximately 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the discussion.     

Entropic part of the boundary energy in a lipid membrane

Two-phase lipid membrane is modeled with lipids of different bending rigidity of hydrophobic tails: domains consist of “rigid” lipid liquid condensed phase and are surrounded by the “flexible” lipid liquid expanded phase. Within the framework of the earlier proposed model of flexible strings, entropic contribution not including mismatch energy is calculated analytically. “Entropic” line tension is found to be weakly dependent on the domain radius. According to the model, it is shown that merely “entropic mismatch” is not enough for the domain formation. In the paper it is assumed that lipids at the boundary, on the average, have larger area than the ones in the volume. This leads to an increase of energy of boundary lipids. Cases of lipids with nearly the same bending rigidities and with strongly different ones are considered. Free energy is calculated using Taylor expansion on the difference of area of lipids at the domain’s boundary and in the volume. Based on the calculated boundary energy domain stability in the finite system is estimated.     

Calculation of line tension in various models of lipid bilayer pore edge

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.     

Raft composition at physiological temperature and pH in the absence of detergents

Biological rafts were identified and isolated at 37°C and neutral pH. The strategy for isolating rafts utilized membrane tension to generate large domains. For lipid compositions that led only to microscropically unresolvable rafts in lipid bilayers, membrane tension led to the appearance of large, observable rafts. The large rafts converted back to small ones when tension was relieved. Thus, tension reversibly controls raft enlargement. For cells, application of membrane tension resulted in several types of large domains; one class of the domains was identified as rafts. Tension was generated in several ways, and all yielded raft fractions that had essentially the same composition, validating the principle of tension as a means to merge small rafts into large rafts. It was demonstrated that sphingomyelin-rich vesicles do not rise during centrifugation in sucrose gradients because they resist lysis, necessitating that, contrary to current experimental practice, membrane material be placed toward the top of a gradient for raft fractionation. Isolated raft fractions were enriched in a GPI-linked protein, alkaline phosphatase, and were poor in Na⁺-K⁺ ATPase. Sphingomyelin and gangliosides were concentrated in rafts, the expected lipid raft composition. Cholesterol, however, was distributed equally between raft and nonraft fractions, contrary to the conventional view.     

Ganglioside GM1 increases line tension at raft boundary in model membranes

Gangliosides are significant participants in suppression of immune system during tumor processes. It was shown that they can induce apoptosis of T-lymphocytes in a raft-dependent manner. Fluorescence confocal microscopy was used to study distribution and influence of ganglioside GM1 on raft properties in giant unilamellar vesicles. Both raft and non-raft phase markers were utilized. No visible phase separation was observed without GM1 unless lateral tension was applied to the membrane. At 2 mol % of GM1 large domains appeared indicating macroscopic phase separation. Increase of GM1 content to 5 mol % resulted in shape transformation of the domains consistent with growth of line tension at the domain boundary. At 10 mol % of GM1 almost all domains were pinched out from vesicles, forming their own homogeneous liposomes. Estimations showed that the change of the GM1 content from 2 to 5–10 mol % resulted in a several-fold increase of line tension. This finding provides a possible mechanism of apoptosis induction by GM1. Incorporation of GM1 into a membrane leads to an increase of the line tension. This results in a growth of the average size of rafts due to coalescence or merger of small domains. Thus, necessary proteins can find themselves in one common raft and start the corresponding cascade of reactions. The article is published in the original.     

Lipid-protein interactions alter line tensions and domain size distributions in lung surfactant monolayers

The size distribution of domains in phase-separated lung surfactant monolayers influences monolayer viscoelasticity and compressibility which, in turn, influence monolayer collapse and set the compression at which the minimum surface tension is reached. The surfactant-specific protein SP-B decreases the mean domain size and polydispersity as shown by fluorescence microscopy. From the images, the line tension and dipole density difference are determined by comparing the measured size distributions with a theory derived by minimizing the free energy associated with the domain energy and mixing entropy. We find that SP-B increases the line tension, dipole density difference, and the compressibility modulus at surface pressures up to the squeeze-out pressure. The increase in line tension due to SP-B indicates the protein avoids domain boundaries due to its solubility in the more fluid regions of the film.     

The determinants of hydrophobic mismatch response for transmembrane helices

Hydrophobic mismatch arises from a difference in the hydrophobic thickness of a lipid membrane and a transmembrane protein segment, and is thought to play an important role in the folding, stability and function of membrane proteins. We have investigated the possible adaptations that lipid bilayers and transmembrane α-helices undergo in response to mismatch, using fully-atomistic molecular dynamics simulations totaling 1.4 μs. We have created 25 different tryptophan-alanine-leucine transmembrane α-helical peptide systems, each composed of a hydrophobic alanine–leucine stretch, flanked by 1–4 tryptophan side chains, as well as the β-helical peptide dimer, gramicidin A. Membrane responses to mismatch include changes in local bilayer thickness and lipid order, varying systematically with peptide length. Adding more flanking tryptophan side chains led to an increase in bilayer thinning for negatively mismatched peptides, though it was also associated with a spreading of the bilayer interface. Peptide tilting, bending and stretching were systematic, with tilting dominating the responses, with values of up to ~ 45° for the most positively mismatched peptides. Peptide responses were modulated by the number of tryptophan side chains due to their anchoring roles and distributions around the helices. Potential of mean force calculations for local membrane thickness changes, helix tilting, bending and stretching revealed that membrane deformation is the least energetically costly of all mismatch responses, except for positively mismatched peptides where helix tilting also contributes substantially. This comparison of energetic driving forces of mismatch responses allows for deeper insight into protein stability and conformational changes in lipid membranes.     

Energetics of inclusion-induced bilayer deformations.

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning proteins perturb the structure of the surrounding bilayer. This coupling between the protein and the bilayer arises from hydrophobic interactions between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between the length of the protein's hydrophobic exterior surface and the average thickness of the bilayer's hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deformation is described as the sum of three contributions: compression-expansion, splay-distortion, and surface tension. When evaluating the interdependence among the energy components, one modulus renormalizes the other: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion energy. The surface tension contribution always is negligible in thin solvent-free bilayers. When evaluating the energy per unit distance (away from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion component is more prominent further away from the boundary. Despite this complexity, the bilayer deformation energy in many cases can be described by a linear spring formalism. The results show that, for a protein embedded in a membrane with an initial hydrophobic mismatch of only 1 A, an increase in hydrophobic mismatch to 1.3 A can increase the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.     

Theoretical analysis of hydrophobic matching and membrane-mediated interactions in lipid bilayers containing gramicidin.

We present a quantitative analysis of the effects of hydrophobic matching and membrane-mediated protein-protein interactions exhibited by gramicidin embedded in dimyristoylphosphatidylcholine (DMPC) and dilauroylphosphatidylcholine (DLPC) bilayers (Harroun et al., 1999. Biophys. J. 76:937-945). Incorporating gramicidin, at 1:10 peptide/lipid molar ratio, decreases the phosphate-to-phosphate (PtP) peak separation in the DMPC bilayer from 35.3 A without gramicidin to 32.7 A. In contrast, the same molar ratio of gramicidin in DLPC increases the PtP from 30.8 A to 32.1 A. Concurrently, x-ray in-plane scattering showed that the most probable nearest-neighbor separation between gramicidin channels was 26.8 A in DLPC, but reduced to 23.3 A in DMPC. In this paper we review the idea of hydrophobic matching in which the lipid bilayer deforms to match the hydrophobic surface of the embedded proteins. We use a simple elasticity theory, including thickness compression, tension, and splay terms to describe the membrane deformation. The energy of membrane deformation is compared with the energy cost of hydrophobic mismatch. We discuss the boundary conditions between a gramicidin channel and the lipid bilayer. We used a numerical method to solve the problem of membrane deformation profile in the presence of a high density of gramicidin channels and ran computer simulations of 81 gramicidin channels to find the equilibrium distributions of the channels in the plane of the bilayer. The simulations contain four parameters: bilayer thickness compressibility 1/B, bilayer bending rigidity Kc, the channel-bilayer mismatch Do, and the slope of the interface at the lipid-protein boundary s. B, Kc, and Do were experimentally measured; the only free parameter is s. The value of s is determined by the requirement that the theory produces the experimental values of bilayer thinning by gramicidin and the shift in the peak position of the in-plane scattering due to membrane-mediated channel-channel interactions. We show that both hydrophobic matching and membrane-mediated interactions can be understood by the simple elasticity theory.     

The Mechanism of Collapse of Heterogeneous Lipid Monolayers

Collapse of homogeneous lipid monolayers is known to proceed via wrinkling/buckling, followed by folding into bilayers in water. For heterogeneous monolayers with phase coexistence, the mechanism of collapse remains unclear. Here, we investigated collapse of lipid monolayers with coexisting liquid-liquid and liquid-solid domains using molecular dynamics simulations. The MARTINI coarse-grained model was employed to simulate monolayers of ∼80 nm in lateral dimension for 10–25 μs. The monolayer minimum surface tension decreased in the presence of solid domains, especially if they percolated. Liquid-ordered domains facilitated monolayer collapse due to the spontaneous curvature induced at a high cholesterol concentration. Upon collapse, bilayer folds formed in the liquid (disordered) phase; curved domains shifted the nucleation sites toward the phase boundary. The liquid (disordered) phase was preferentially transferred into bilayers, in agreement with the squeeze-out hypothesis. As a result, the composition and phase distribution were altered in the monolayer in equilibrium with bilayers compared to a flat monolayer at the same surface tension. The composition and phase behavior of the bilayers depended on the degree of monolayer compression. The monolayer-bilayer connection region was enriched in unsaturated lipids. Percolation of solid domains slowed down monolayer collapse by several orders of magnitude. These results are important for understanding the mechanism of two-to-three-dimensional transformations in heterogeneous thin films and the role of lateral organization in biological membranes. The study is directly relevant for the function of lung surfactant, and can explain the role of nanodomains in its surface activity and inhibition by an increased cholesterol concentration.     

Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime.

The deformation free energy of a lipid bilayer is presented based on the principle of a continuum theory. For small deformations, the free energy consists of a layer-compression term, a splay-distortion term, and a surface-tension term, equivalent to the elastic free energy of a two-layer smectic liquid crystal with surface tension. Minimization of the free energy leads to a differential equation that, with boundary conditions, determines the elastic deformation of a bilayer membrane. When a dimeric gramicidin channel is formed in a membrane of thickness greater than the length of the channel, the membrane deformation reduces the stability of the channel. Previously this effect was studied by comparing the variation of channel lifetime with the surface tension of bilayers (Elliott, J. R., D. Needham, J. P. Dilger, and D. A. Hayden, 1983, Biochim. Biophys. Acta, 735:95-103). The tension was assumed to pull a dimer for a distance z before the channel loses ion conductivity. To account for the data, z was found to be 18 A. With the deformation free energy, the data can be accounted for with z less than or approximately to 1 A, which is consistent with the breaking of hydrogen bonds in a dimer dissociation. Increasing the strength of lipid-protein interactions is not the only consequence of the complete free energy compared with the previous discussions. It also changes the shape of membrane deformation around an embedded channel from convex to concave, and increases the range of deformation from less than 10 A to greater than 20 A. Clearly these will be important factors in the general considerations of lipid-protein interactions and membrane-mediated interactions between proteins. In addition, thermal fluctuations of a membrane are calculated; in particular, we calculate the relations between the intrinsic thickness and the experimentally measured values. The experimental parameters of monoolein-squalene membranes are used for quantitative analyses.     

Micrometric segregation of fluorescent membrane lipids: relevance for endogenous lipids and biogenesis in erythrocytes

Micrometric membrane lipid segregation is controversial. We addressed this issue in attached erythrocytes and found that fluorescent boron dipyrromethene (BODIPY) analogs of glycosphingolipids (GSLs) [glucosylceramide (BODIPY-GlcCer) and monosialotetrahexosylganglioside (GM1BODIPY)], sphingomyelin (BODIPY-SM), and phosphatidylcholine (BODIPY-PC inserted into the plasma membrane spontaneously gathered into distinct submicrometric domains. GM1BODIPY domains colocalized with endogenous GM1 labeled by cholera toxin. All BODIPY-lipid domains disappeared upon erythrocyte stretching, indicating control by membrane tension. Minor cholesterol depletion suppressed BODIPY-SM and BODIPY-PC but preserved BODIPY-GlcCer domains. Each type of domain exchanged constituents but assumed fixed positions, suggesting self-clustering and anchorage to spectrin. Domains showed differential association with 4.1R versus ankyrin complexes upon antibody patching. BODIPY-lipid domains also responded differentially to uncoupling at 4.1R complexes [protein kinase C (PKC) activation] and ankyrin complexes (in spherocytosis, a membrane fragility disease). These data point to micrometric compartmentation of polar BODIPY-lipids modulated by membrane tension, cholesterol, and differential association to the two nonredundant membrane:spectrin anchorage complexes. Micrometric compartmentation might play a role in erythrocyte membrane deformability and fragility.