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.     

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.     

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.     

Domains and Rafts in Membranes – Hidden Dimensions of Selforganization

Both biomembranes and biomimetic membranes such as lipid bilayers withseveral components contain intramembrane domains and rafts.Macromolecules, which are anchored to the membrane but have no tendeney tocluster, induce curved nanodomains. Clustering of membrane componentsleads to larger domains which can grow up to a certain maximal size andthen undergo a budding process. The maximal domain size depends on theinterplay of spontaneous curvature, bending rigidity, and line tension.It is argued that this interplay governs the formation of bothclathrin-coated buds and caveolae. Finally, membrane adhesion often leadsto domain formation within the contact zone.     

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.     

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.     

Prediction of protein domain boundaries from sequence alone

We present here a simple approach to identify domain boundaries in proteins of an unknown three-dimensional structure. Our method is based on the hypothesis that a high-side chain entropy of a region in a protein chain must be compensated by a high-residue interaction energy within the region, which could correlate with a well-structured part of the globule, that is, with a domain unit. For protein domains, this means that the domain boundary is conditioned by amino acid residues with a small value of side chain entropy, which correlates with the side chain size. On the one hand, relatively high Ala and Gly content on the domain boundary results in high conformational entropy of the backbone chain between the domains. On the other hand, the presence of Pro residues leads to the formation of hinges for a relative orientation of domains. The method was applied to 646 proteins with two contiguous domains extracted from the SCOP database with a success rate of 63%. We also report the prediction of domain boundaries for CASP5 targets obtained with the same method.     

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.     

Growth dynamics of domains in ternary fluid vesicles

We have studied the growth dynamics of domains on ternary fluid vesicles composed of saturated (dipalmitoylphosphatidylcholine), unsaturated (dioleoylphosphatidylcholine) phosphatidylcholine lipids, and cholesterol using a fluorescence microscopy. The domain coarsening processes are classified into two types: normal coarsening and trapped coarsening. For the normal coarsening, the domains having flat circular shape grow in a diffusion-and-coalescence manner and phenomenologically the mean size grows as a power law of approximately t(2/3). The observed growth law is not described by a two-dimensional diffusion-and-coalescence growth mechanism following the Saffman and Delbrück theory, which may originate from the two-body hydrodynamic interactions between domains. For trapped coarsening, on the other hand, the domain coarsening is suppressed at a certain domain size because the repulsive interdomain interactions obstruct the coalescence of domains. The two-color imaging of the trapped domains reveals that the repulsive interactions are induced by the budding of domains. The model free energy consisting of the bending energy of domains, the bending energy of matrix, the line energy of domain boundary, and the translation energy of domains can describe the observed trapped coarsening. The trapping of domains is caused by the coupling between the phase separation and the membrane elasticity under the incompressibility constraint.     

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.     

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.     

Domain-induced budding of fluid membranes

Domains within fluid membranes grow by the aggregation of molecules which diffuse laterally within the membrane matrix. A simple theoretical model is introduced which predicts that a flat or weakly curved domain becomes unstable at a certain limiting size and then undergoes a budding or invagination process. This instability is driven by the competition between the bending energy of the domain and the line tension of the domain edge. For lipid bilayers, the budding domain can rupture the membrane and then it pinches off from the matrix. The same mechanism should also drive the budding of non-coated domains in biomembranes, and could even be effective when these domains are covered by a coat of clathrin molecules.     

Line tension and structure of raft boundary calculated from bending,tilt, and lateral compression/stretching

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.     

Thermally induced proliferation of pores in a model fluid membrane.

The growth of thermally induced pores in a two-dimensional model fluid membrane is investigated by Monte Carlo simulation. Holes appear in the membrane via an activated process, and their subsequent growth is controlled by an edge energy per unit length or line tension. The barrier height and line tension, together with a lateral tension, are the independent parameters of the model. In the resulting phase diagram, a rupture transition separates an intact membrane from a disintegrated state. The approach to the ruptured state shows distinct regimes. Reducing the barrier height at large line tension produces multiple, quasi-independent, small holes whose behavior is dominated by their edge energy, whereas at lower line tensions shape fluctuations of the holes facilitate their coalescence into a single large hole. At a small value of line tension and large barrier height, a single hole spontaneously permeabilizes the membrane in an entropically driven phase transition. Entropy dominates pore growth for line tensions not far below those measured for artificial vesicles. Permeabilization of lipid bilayers by certain peptides involves perturbing lipid-lipid cohesive energies, and our simulations show that at small line tensions the entropy of hole shape fluctuations destroys the model membrane's stability.     

Reversible Formation of Nanodomains in Monolayers of DPPC Studied by Kinetic Modeling

Dipalmitoylphosphatidylcholine (DPPC) is the most abundant component in pulmonary surfactants and is believed to be responsible for maintaining low surface tension in alveoli during breathing. In this work, a kinetic model is introduced that describes the phase separation in DPPC films that produces the liquid-condensed (LC) and liquid-expanded (LE) fractions, which differ according to the area density of DPPC. The phase separation in an initially homogeneous film has been investigated numerically. Furthermore, explicit simulations of periodic compression-expansion cycles are reported. In this process, a moderate change of the surface area resulted in a dramatic change in the total amount of LC fraction, as well as in the surface morphology. Depending on the extent of the film's compression, the simulated surface morphologies comprised individual nanosized LC domains embedded in the LE fraction, interconnected networks of such domains, or continuous LC films with nanopores. Equilibration of the total area of the LC nanodomains occurred over a few milliseconds, indicating that the rate of the LE-LC phase transformation is sufficient for maintaining low surface tension during breathing, and that nanoscale LC domains are likely to play a major role in this process. Unlike the total content of the LC fraction, which stabilized quickly, the average size of LC nanodomains showed a tendency to increase slowly, at a rate determined by the diffusivity of DPPC. The computed average domain size seems to be compatible with published experiments for DPPC films. The numeric results also elucidate the distinction between thermodynamically determined and kinetically limited structural properties during phase separation in the major structure-forming component of pulmonary surfactants.     

Flicker spectroscopy of thermal lipid bilayer domain boundary fluctuations

This contribution describes measurements of lipid bilayer domain line tension based on two-dimensional thermal undulations of membranes with liquid ordered/liquid disordered phase coexistence and near-critical composition at room temperature. Lateral inhomogeneity of lipid and protein composition is currently a subject of avid research aimed at determining both fundamental properties and biological relevance of membrane domains. Line tension at fluid lipid bilayer membrane domain boundaries controls the kinetics of domain growth and therefore regulates the size of compositional heterogeneities. High line tension promotes membrane domain budding and fission. Line tension could therefore be an important control parameter regulating functional aspects of biological membranes. Here the established method of fluid domain flicker spectroscopy is applied to examine thermal domain wall fluctuations of phase-separated bilayer membranes. We find a Gaussian probability distribution for the first few excited mode amplitudes, which permits an analysis by means of appropriately specialized capillary wave theory. Time autocorrelation functions are found to decay exponentially, and relaxation times are fitted by means of a hydrodynamic theory relating line tensions and excited mode relaxation kinetics. Line tensions below 1 pN are obtained, with these two approaches yielding similar results. We examine experimental artifacts that perturb the Fourier spectrum of domain traces and discuss ways to identify the number of modes that yield reliable line tension information.     

Construction, purification, and characterization of new interferon gamma (IFN gamma) inhibitor proteins. Three IFN gamma receptor-immunoglobulin hybrid molecules.

Three efficient mouse interferon gamma (MoIFN gamma) inhibitors were constructed, which consist of the MoIFN gamma receptor (MoIFN gamma R) extracellular portion and constant domains of immunoglobulin (Ig) molecules. These are: 1) the constant domain of the mouse kappa chain, 2) the hinge region and the constant domains 2 and 3 of the mouse gamma 2a chain, and 3) the hinge region and the constant domains 2 and 3 of the human gamma 3 chain. The hybrid molecules were expressed in the mouse myeloma cell line J558L and recovered from the supernatants of cell cultures in one purification step. The proteins MoIFN gamma R-M gamma 2a and MoIFN gamma R-H gamma 3 form homodimers, whereas MoIFN gamma R-M kappa is a monomer. All three constructs inhibit the binding of radiolabeled MoIFN gamma to its receptor on L1210 cells. They are biologically active in vitro, neutralizing the action of MoIFN gamma in an antiviral activity assay. The fusions of Ig regions to the soluble MoIFN gamma R do not decrease the affinity of the binding site for the ligand. MoIFN gamma R-M kappa has about the same affinity as the soluble MoIFN gamma R and the cell surface receptor of L1210 cells in situ, which are also monomers, whereas the dimers MoIFN gamma R-M gamma 2a and MoIFN gamma R-H gamma 3 display a 5-10-fold higher affinity for MoIFN gamma than the monomeric molecules. This is best documented in the efficacy of the inhibitors to antagonize the antiviral activity of MoIFN gamma, as the dimeric constructs are about 10 times more active than MoIFN gamma R-M kappa and the soluble MoIFN gamma R. The hybrid constructs can be used as high efficiency MoIFN gamma inhibitors in mouse models of several pathological states in humans, where IFN gamma is thought to play a disease-promoting role.     

Binding free energy landscape of domain-peptide interactions

Peptide recognition domains (PRDs) are ubiquitous protein domains which mediate large numbers of protein interactions in the cell. How these PRDs are able to recognize peptide sequences in a rapid and specific manner is incompletely understood. We explore the peptide binding process of PDZ domains, a large PRD family, from an equilibrium perspective using an all-atom Monte Carlo (MC) approach. Our focus is two different PDZ domains representing two major PDZ classes, I and II. For both domains, a binding free energy surface with a strong bias toward the native bound state is found. Moreover, both domains exhibit a binding process in which the peptides are mostly either bound at the PDZ binding pocket or else interact little with the domain surface. Consistent with this, various binding observables show a temperature dependence well described by a simple two-state model. We also find important differences in the details between the two domains. While both domains exhibit well-defined binding free energy barriers, the class I barrier is significantly weaker than the one for class II. To probe this issue further, we apply our method to a PDZ domain with dual specificity for class I and II peptides, and find an analogous difference in their binding free energy barriers. Lastly, we perform a large number of fixed-temperature MC kinetics trajectories under binding conditions. These trajectories reveal significantly slower binding dynamics for the class II domain relative to class I. Our combined results are consistent with a binding mechanism in which the peptide C terminal residue binds in an initial, rate-limiting step.     

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.