Detailed mechanics of membrane-membrane adhesion and separation. II. Discrete kinetically trapped molecular cross-bridges

In general, membrane-membrane adhesion involves specific molecular binding and cross-bridging reactions. The ideal, classical view is that near equilibrium the forces required to separate adhesive contacts are essentially equal to those induced in the membrane when the contact is formed. In contrast to the classical view, experimental observations often show that negligible levels of tension are induced by the adhesive contact even though the tension required to separate the contact is large enough to rupture the membrane. The deviation in tension levels associated with contact formation and separation appears to be due to the sparse distribution of strong molecular cross-bridges. Here, the mechanics of membrane-membrane adhesion and separation is developed for the case of discrete, kinetically trapped cross-bridges. The solution is obtained by numerical computation of the membrane contour that minimizes the total free energy (membrane elastic energy of deformation plus cross-bridge energies) in the contact zone. This solution is matched with the analytical solution for membrane stresses and geometry derived for the adjacent, unbridged zone. The results yield specific values of the macroscopic tension applied to the membrane in the plane region away from the contact zone and the microscopic angle at the edge of the contact zone. Two disparate values of the macroscopic tension are found: (a) the minimum tension required to separate the adherent membranes; and (b) the maximum tension induced in the membranes when the contact is formed (i.e., the level of tension at which the contact will just begin to spread).(ABSTRACT TRUNCATED AT 250 WORDS)     

Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges

The mechanics of membrane-membrane adhesion are developed for the approximation that the molecular cross-bridging forces are continuously distributed as a normal stress (force per unit area). The significance of the analysis is that the finite range of the cross-bridging forces and the microscopic contact angle are not assumed negligible. Since the cross-bridging and adhesion forces are finite range interactions, there are two membrane regions: a free zone where the membranes are not subject to attractive forces; and an adherent zone where the membranes are held together by attractive stresses. The membrane is treated as an elastic continuum. The approach is to analyze the mechanics for each zone separately and then to require continuity of the solutions at the interface between the zones. Final solution yields the membrane contour and stresses proximal to and within the contact zone as well as the microscopic contact angle at the edge of the contact zone. It is demonstrated that the classical Young equation is consistent with this model. The results show that the microscopic contact angle becomes appreciable when the strength of adhesion is large or the length of the cross-bridge is large; however, the microscopic contact angle approaches zero as the membrane elastic stiffness increases. The solution predicts the width of the contact zone over which molecular bonds are stretched. It is this boundary region where increased biochemical activity is expected. In the classical model presented here, the level of tension necessary to oppose spreading of the contact is equal to the minimal level of tension required to separate the adherent membranes. This behavior is in contrast with that derived for the case of discrete molecular cross-bridges where the possibility of different levels of tension associated with adhesion and separation is introduced. The discrete cross-bridge case is the subject of a companion paper.     

Adhesion-induced receptor segregation and adhesion plaque formation: A model membrane study.

A model system to study the control of cell adhesion by receptor-mediated specific forces, universal interactions, and membrane elasticity is established. The plasma membrane is mimicked by reconstitution of homophilic receptor proteins into solid supported membranes and, together with lipopolymers, into giant vesicles with the polymers forming an artificial glycocalix. The homophilic cell adhesion molecule contact site A, a lipid-anchored glycoprotein from cells of the slime mold Dictyostelium discoideum, is used as receptor. The success of the reconstitution, the structure and the dynamics of the model membranes are studied by various techniques including film balance techniques, micro fluorescence, fluorescence recovery after photobleaching, electron microscopy, and phase contrast microscopy. The interaction of the functionalized giant vesicles with the supported bilayer is studied by reflection interference contrast microscopy, and the adhesion strength is evaluated quantitatively by a recently developed technique. At low receptor concentrations adhesion-induced receptor segregation in the membranes leads to decomposition of the contact zone between membranes into domains of strong (receptor-mediated) adhesion and regions of weak adhesion while continuous zones of strong adhesion form at high receptor densities. The adhesion strengths (measured in terms of the spreading pressure S) of the various states of adhesion are obtained locally by analysis of the vesicle contour near the contact line in terms of elastic boundary conditions of adhesion: the balance of tensions and moments. The spreading pressure of the weak adhesion zones is S approximately 10(-9) J/m(2) and is determined by the interplay of gravitation and undulation forces whereas the spreading pressure of the tight adhesion domains is of the order S approximately 10(-6) J/m(2).     

Internal forces, tension and energy density in tethered cellular membranes

We analyze tethered cellular membranes by considering the membrane resultants, tension and densities of two modes of energy, bending and adhesion. These characteristics are determined based on a computational (finite-difference) analysis of membrane shape. We analyze the relative contribution and distribution of the membrane characteristics in four typical zones of the membrane surface. Using an axisymmetric model, we found that the meridional and circumferential components of the resultant are different near the tether body and they converge to the value of membrane tension farther from the tether. At the beginning of the area of membrane detachment from the cytoskeleton, the density of bending energy is on the same order of magnitude as membrane tension (resultant). Away from the tether, the bending energy density quickly decreases and becomes of the same order as that of the adhesion energy in the membrane-cytoskeleton attachment area. In that area, both modes of energy are significantly smaller than the membrane tension. We also consider the effect of the membrane bending modulus on the distribution of the membrane characteristics. An increase in the bending modulus results in changing the length and position on the membrane surface of zone 1 characterized by significant evolution of the resultant components. It also results in shortening zone 2 that covers the rest of the area of membrane detachment. The obtained results can help in a better interpretation of the measurements of membrane mechanical properties as well as in analyses of proteins and channels in curved membranes.     

Mechanics of spreading cells probed by atomic force microscopy

Cellular adhesion and motility are fundamental processes in biological systems such as morphogenesis and tissue homeostasis. During these processes, cells heavily rely on the ability to deform and supply plasma membrane from pre-existing membrane reservoirs, allowing the cell to cope with substantial morphological changes. While morphological changes during single cell adhesion and spreading are well characterized, the accompanying alterations in cellular mechanics are scarcely addressed. Using the atomic force microscope, we measured changes in cortical and plasma membrane mechanics during the transition from early adhesion to a fully spread cell. During the initial adhesion step, we found that tremendous changes occur in cortical and membrane tension as well as in membrane area. Monitoring the spreading progress by means of force measurements over 2.5 h reveals that cortical and membrane tension become constant at the expense of excess membrane area. This was confirmed by fluorescence microscopy, which shows a rougher plasma membrane of cells in suspension compared with spread ones, allowing the cell to draw excess membrane from reservoirs such as invaginations or protrusions while attaching to the substrate and forming a first contact zone. Concretely, we found that cell spreading is initiated by a transient drop in tension, which is compensated by a decrease in excess area. Finally, all mechanical parameters become almost constant although morphological changes continue. Our study shows how a single cell responds to alterations in membrane tension by adjusting its overall membrane area. Interference with cytoskeletal integrity, membrane tension and excess surface area by administration of corresponding small molecular inhibitors leads to perturbations of the spreading process.     

Membrane tether formation from blebbing cells

Membrane tension has been proposed to be important in regulating cell functions such as endocytosis and cell motility. The apparent membrane tension has been calculated from tether forces measured with laser tweezers. Both membrane-cytoskeleton adhesion and membrane tension contribute to the tether force. Separation of the plasma membrane from the cytoskeleton occurs in membrane blebs, which could remove the membrane-cytoskeleton adhesion term. In renal epithelial cells, tether forces are significantly lower on blebs than on membranes that are supported by cytoskeleton. Furthermore, the tether forces are equal on apical and basolateral blebs. In contrast, tether forces from membranes supported by the cytoskeleton are greater in apical than in basolateral regions, which is consistent with the greater apparent cytoskeletal density in the apical region. We suggest that the tether force on blebs primarily contains only the membrane tension term and that the membrane tension may be uniform over the cell surface. Additional support for this hypothesis comes from observations of melanoma cells that spontaneously bleb. In melanoma cells, tether forces on blebs are proportional to the radius of the bleb, and as large blebs form, there are spikes in the tether force in other cell regions. We suggest that an internal osmotic pressure inflates the blebs, and the pressure calculated from the Law of Laplace is similar to independent measurements of intracellular pressures. When the membrane tension term is subtracted from the apparent membrane tension over the cytoskeleton, the membrane-cytoskeleton adhesion term can be estimated. In both cell systems, membrane-cytoskeleton adhesion was the major factor in generating the tether force.     

Electro-mechanical permeabilization of lipid vesicles. Role of membrane tension and compressibility.

A simple micropipet technique was used to determine the critical electric field strength for membrane breakdown as a function of the applied membrane tension for three different reconstituted membranes: stearoyloleoylphosphatidylcholine (SOPC), red blood cell (RBC) lipid extract, and SOPC cholesterol (CHOL), 1:1. For these membranes the elastic area expansivity modulus increases from approximately 200 to 600 dyn/cm, and the tension at lysis increases from 5.7 to 13.2 dyn/cm, i.e., the membranes become more cohesive with increasing cholesterol content. The critical membrane voltage, Vc, required for breakdown was also found to increase with increasing cholesterol from 1.1 to 1.8 V at zero membrane tension. We have modeled the behavior in terms of the bilayer expansivity. Membrane area can be increased by either tensile or electrocompressive stresses. Both can store elastic energy in the membrane and eventually cause breakdown at a critical area dilation or critical energy. The model predicts a relation between tension and voltage at breakdown and this relation is verified experimentally for the three reconstituted membrane systems studied here.     

Adhesively-tensed cell membranes: lysis kinetics and atomic force microscopy probing

Membrane tension underlies a range of cell physiological processes. Strong adhesion of the simple red cell is used as a simple model of a spread cell with a finite membrane tension-a state which proves useful for studies of both membrane rupture kinetics and atomic force microscopy (AFM) probing of native structure. In agreement with theories of strong adhesion, the cell takes the form of a spherical cap on a substrate densely coated with poly-L-lysine. The spreading-induced tension, sigma, in the membrane is approximately 1 mN/m, which leads to rupture over many minutes; and sigma is estimated from comparable rupture times in separate micropipette aspiration experiments. Under the sharpened tip of an AFM probe, nano-Newton impingement forces (10-30 nN) are needed to penetrate the tensed erythrocyte membrane, and these forces increase exponentially with tip velocity ( approximately nm/ms). We use the results to clarify how tapping-mode AFM imaging works at high enough tip velocities to avoid rupturing the membrane while progressively compressing it to a approximately 20-nm steric core of lipid and protein. We also demonstrate novel, reproducible AFM imaging of tension-supported membranes in physiological buffer, and we describe a stable, distended network consistent with the spectrin cytoskeleton. Additionally, slow retraction of the AFM tip from the tensed membrane yields tether-extended, multipeak sawtooth patterns of average force approximately 200 pN. In sum we show how adhesive tensioning of the red cell can be used to gain novel insights into native membrane dynamics and structure.     

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.     

Attraction, deformation and contact of membranes induced by low frequency electric fields

The force of attraction between erythrocyte ghosts induced by low frequency electric fields (60 Hz) was measured as a function of the intermembrane separation. It varied from 10(-14) N for separation of the order of the cell diameter to 10(-12) N for close approach and contact in 20 mM sodium phosphate buffers (conductivity 260 mS/m, pH 8.5). For large separations the interaction force followed a dependence on separation as predicted for dipole-dipole interactions. For small separation an empirical formula was obtained. The membranes deformed at close approach (less than 1 microns) before making contact. The contact area increased with time until reaching the final equilibrium state. The ghosts separated reversibly after switching off the electric field. The membrane tension induced by the ghost interaction at contact was estimated to be of the order of 0.1 mN/m. These first quantitative measurements of the force/separation dependence for intermembrane interactions induced by low frequency electric fields indicate that attractive forces, membrane deformation and contact area of cells depend strongly on intermembrane separation and field strength. The quantitative relationship between them are important for measuring membrane surface and mechanical properties, intermembrane forces and understanding mechanisms of membrane adhesion, instability and fusion in electric fields and in general.     

Neutrophil adhesive contact dependence on impingement force

Neutrophil capture and recruitment from the circulation requires the formation of specific receptor/ligand bonds under hydrodynamic forces. In the present study we examine bond formation between beta2-integrins on neutrophils and immobilized ICAM-1 while using micropipettes to control the force of contact between the cell and substrate. Magnesium was used to induce the high affinity conformation of the integrins, and bond formation was assessed by measuring the probability of adhesion during repeated contacts. Increasing the impingement force caused an increase in the contact area and led to a proportional increase in adhesion probability (from approximately 20 to 50%) over the range of forces tested (50-350 pN). In addition, different-sized beads were used to change the force per unit area in the contact zone (contact stress). We conclude that for a given contact stress, the rate of bond formation increases linearly with contact area, but that increasing contact stress results in higher intrinsic rates of bond formation.     

Resonance energy transfer imaging of phospholipid vesicle interaction with a planar phospholipid membrane: undulations and attachment sites in the region of calcium-mediated membrane--membrane adhesion

Membrane fusion of a phospholipid vesicle with a planar lipid bilayer is preceded by an initial prefusion stage in which a region of the vesicle membrane adheres to the planar membrane. A resonance energy transfer (RET) imaging microscope, with measured spectral transfer functions and a pair of radiometrically calibrated video cameras, was used to determine both the area of the contact region and the distances between the membranes within this zone. Large vesicles (5-20 microns diam) were labeled with the donor fluorophore coumarin- phosphatidylethanolamine (PE), while the planar membrane was labeled with the acceptor rhodamine-PE. The donor was excited with 390 nm light, and separate images of donor and acceptor emission were formed by the microscope. Distances between the membranes at each location in the image were determined from the RET rate constant (kt) computed from the acceptor:donor emission intensity ratio. In the absence of an osmotic gradient, the vesicles stably adhered to the planar membrane, and the dyes did not migrate between membranes. The region of contact was detected as an area of planar membrane, coincident with the vesicle image, over which rhodamine fluorescence was sensitized by RET. The total area of the contact region depended biphasically on the Ca2+ concentration, but the distance between the bilayers in this zone decreased with increasing [Ca2+]. The changes in area and separation were probably related to divalent cation effects on electrostatic screening and binding to charged membranes. At each [Ca2+], the intermembrane separation varied between 1 and 6 nm within each contact region, indicating membrane undulation prior to adhesion. Intermembrane separation distances < or = 2 nm were localized to discrete sites that formed in an ordered arrangement throughout the contact region. The area of the contact region occupied by these punctate attachment sites was increased at high [Ca2+]. Membrane fusion may be initiated at these sites of closest membrane apposition.     

Tyrosine phosphorylation of membrane proteins mediates cellular invasion by transformed cells

Tyrosine phosphorylation of membrane-associated proteins is involved at two distinct sites of contact between cells and the extracellular matrix: adhesion plaques (cell adhesion and de-adhesion) and invadopodia (invasion into the extracellular matrix). Adhesion plaques from chicken embryonic fibroblasts or from cells transformed by Rous sarcoma virus contain low levels of tyrosine-phosphorylated proteins (YPPs) which were below the level of detection in 0.5-microns thin, frozen sections. In contrast, intense localization of YPPs was observed at invadopodia of transformed cells at sites of degradation and invasion into the fibronectin-coated gelatin substratum, but not in membrane extensions free of contact with the extracellular matrix. Local extracellular matrix degradation and formation of invadopodia were blocked by genistein, an inhibitor of tyrosine-specific kinases, but cells remained attached to the substratum and retained their free-membrane extensions. Invadopodia reduced or lost YPP labeling after treatment of the cells with genistein, but adhesion plaques retained YPP labeling. The plasma membrane contact fractions of normal and transformed cells have been isolated form cells grown on gelatin cross-linked substratum using a novel fractionation scheme, and analyzed by immunoblotting. Four major YPPs (150, 130, 81, and 77 kD) characterize invadopodial membranes in contact with the matrix, and are probably responsible for the intense YPP labeling associated with invadopodia extending into sites of matrix degradation. YPP150 may be an invadopodal-specific YPP since it is approximately 3.6-fold enriched in the invasive contact fraction relative to the cell body fraction and is not observed in normal contacts. YPP130 is enriched in transformed cell contacts but may also be present in normal contacts. The two major YPPs of normal contacts (130 and 71 kD) are much lower in abundance than the major tyrosine-phosphorylated bands associated with invadopodial membranes, and likely represent major adhesion plaque YPPs. YPP150, paxillin, and tensin appear to be enriched in the cell contact fractions containing adhesion plaques and invadopodia relative to the cell body fraction, but are also present in the soluble supernate fraction. However, vinculin, talin, and alpha-actinin that are localized at invadopodia, are equally concentrated in cell bodies and cell contacts as is the membrane-adhesion receptor beta 1 integrin. Thus, tyrosine phosphorylation of the membrane-bound proteins may contribute to the cytoskeletal and plasma membrane events leading to the formation and function of invadopodia that contact and proteolytically degrade the extracellular matrix; we have identified several candidate YPPs that may participate in the regulation of these processes.     

Thermodynamics of short-term cell adhesion in vitro.

A thermodynamic theory of short-term (less than 2 hr) in vitro cell adhesion has been developed which allows calculation of reversible work of adhesion and estimation of a term proportional to cell-substrate contact area. The theory provides a means of determining a parameter related to membrane wetting tension for microscopic cells that does not require special manipulations which might desiccate or denature delicate cell membranes. Semiquantitative agreement between predicted and experimentally-measured cell adhesion obtained for three different cell types (MDCK, RBL-1, and HCT-15) in two different liquid phase compositions of surfactants (Tween-80 and fetal bovine serum) supports concepts and approximations utilized in development of theory. Cell-substrate contact areas were largest for wettable surfaces treated with ionizing corona or plasma discharges and smallest for hydrophobic materials for each cell type studied. Contact area for the continuous dog-kidney cell line MDCK was larger than that of either the leukemic blood cell RBL-1 or the anaplastic human colon cell HCT-15.     

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.     

Lipid-glass adhesion in giga-sealed patch-clamped membranes.

Adhesion between patch-clamped lipid membranes and glass micropipettes is measured by high contrast video imaging of the mechanical response to the application of suction pressure across the patch. The free patch of membrane reversibly alters both its contact angle and radius of curvature on pressure changes. The assumption that an adhesive force between the membrane and the pipette can sustain normal tension up to a maximum Ta at the edge of the free patch accounts for the observed mechanical responses. When the normal component of the pressure-induced membrane tension exceeds Ta membrane at the contact point between the free patch and the lipid-glass interface is pulled away from the pipette wall, resulting in a decreased radius of curvature for the patch and an increased contact angle. Measurements of the membrane radius of curvature as a function of the suction pressure and pipette radius determine line adhesion tensions Ta which range from 0.5 to 4.0 dyn/cm. Similar behavior of patch-clamped cell membranes implies similar adhesion mechanics.     

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.     

Membrane bending modulus and adhesion energy of wild-type and mutant cells of Dictyostelium lacking talin or cortexillins.

We have employed an interferometric technique for the local measurement of bending modulus, membrane tension, and adhesion energy of motile cells adhering to a substrate. Wild-type and mutant cells of Dictyostelium discoideum were incubated in a flow chamber. The flow-induced deformation of a cell near its adhesion area was determined by quantitative reflection interference contrast microscopy (RICM) and analyzed in terms of the elastic boundary conditions: equilibrium of tensions and bending moments at the contact line. This technique was employed to quantify changes caused by the lack of talin, a protein that couples the actin network to the plasma membrane, or by the lack of cortexillin I or II, two isoforms of the actin-bundling protein cortexillin. Cells lacking either cortexillin I or II exhibited reduced bending moduli of 95 and 160 k(B)T, respectively, as compared to 390 k(B)T, obtained for wild-type cells. No significant difference was found for the adhesion energies of wild-type and cortexillin mutant cells. In cells lacking talin, not only a strongly reduced bending modulus of 70 k(B)T, but also a low adhesion energy one-fourth of that in wild-type cells was measured.     

Formation and maintenance of tubular membrane projections require mechanical force, but their elongation and shortening do not require additional force

Living cells develop their own characteristic shapes depending on their physiological functions, and their morphologies are based on the mechanical characteristics of the cytoskeleton and of membranes. To investigate the role of lipid membranes in morphogenesis, we constructed a simple system that can manipulate liposomes and measure the forces required to transform their shapes. Two polystyrene beads (1 microm in diameter) were encapsulated in giant liposomes and were manipulated using double-beam laser tweezers. Without any specific interaction between the lipid membrane and beads, mechanical forces could be applied to the liposome membrane from the inside. Spherical liposomes transformed into a lemon shape with increasing tension, and tubular membrane projections were subsequently generated in the tips at either end. This process is similar to the liposomal transformation caused by elongation of encapsulated cytoskeletons. In the elongation stage of lemon-shaped liposomes, the force required for the transformation became larger as the end-to-end length increased. Just before the tubular membrane was generated, the force reached the maximum strength (approximately 11 pN). However, immediately after the tubular membrane developed, the force suddenly decreased and was maintained at a constant strength (approximately 4 pN) that was independent of further tube elongation or shortening, even though there was no excess membrane reservoir as occurs in living cells. When the tube length was shortened to approximately 2 microm, the liposome reversed to a lemon shape and the force temporarily increased (to approximately 7 pN). These results indicate that the simple application of mechanical force is sufficient to form a protrusion in a membrane, that a critical force and length is needed to form and to maintain the protrusion, and suggest that the lipid bilayer itself has the ability to buffer the membrane tension.     

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.