Deformation and flow of membrane into tethers extracted from neuronal growth cones.

Membrane tethers are extracted at constant velocity from neuronal growth cones using a force generated by a laser tweezers trap. A thermodynamic analysis shows that as the tether is extended, energy is stored in the tether as bending and adhesion energies and in the cell body as "nonlocal" bending. It is postulated that energy is dissipated by three viscous mechanisms including membrane flow, slip between the two monolayers that form the bilayer, and slip between membrane and cytoskeleton. The analysis predicts and the experiments show a linear relation between tether force and tether velocity. Calculations based on the analytical results and the experimental measurements of a tether radius of approximately 0.2 micron and a tether force at zero velocity of approximately 8 pN give a bending modulus for the tether of 2.7 x 10(-19) N.m and an extraordinarily small "apparent surface tension" in the growth cone of 0.003 mN/m, where the apparent surface tension is the sum of the far-field, in-plane tension and the energy of adhesion. Treatments with cytochalasin B and D, ethanol, and nocodazole affect the apparent surface tension but not bending. ATP depletion affects neither, whereas large concentrations of DMSO affect both. Under conditions of flow, data are presented to show that the dominant viscous mechanism comes from the slip that occurs when the membrane flows over the cytoskeleton. ATP depletion and the treatment with DMSO cause a dramatic drop in the effective viscosity. If it is postulated that the slip between membrane and cytoskeleton occurs in a film of water, then this water film has a mean thickness of only approximately 10 A.     

Coalescence of membrane tethers: experiments, theory, and applications

Tethers are nanocylinders of lipid bilayer membrane, arising in situations ranging from micromanipulation experiments on synthetic vesicles to the formation of dynamic tubular networks in the Golgi apparatus. Relying on the extensive theoretical and experimental works aimed to understand the physics of individual tethers formation, we addressed the problem of the interaction between two nanotubes. By using a combination of micropipette manipulation and optical tweezers, we quantitatively studied the process of coalescence that occurred when the separation distance between both vesicle-tether junctions became smaller than a threshold length. Our experiments, which were supported by an original theoretical analysis, demonstrated that the measurements of the tether force and angle between tethers at coalescence directly yield the bending rigidity, kappa, and the membrane tension, sigma, of the vesicles. Contrary to other methods used to probe the bending rigidity of vesicles, the proposed approach permits a direct measurement of kappa without requiring any control of the membrane tension. Finally, after validation of the method and proposal of possible applications, we experimentally investigated the dynamics of the coalescence process.     

Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles.

The curvature elastic modulus (bending stiffness) of stearoyloleoyl phosphatidylcholine (SOPC) bilayer membrane is determined from membrane tether formation experiments. R. E. Waugh and R. M. Hochmuth 1987. Biophys. J. 52:391-400) have shown that the radius of a bilayer cylinder (tether) is inversely related to the force supported along its axis. The coefficient that relates the axial force on the tether to the tether radius is the membrane bending stiffness. Thus, the bending stiffness can be calculated directly from measurements of the tether radius as a function of force. Giant (10-50-microns diam) thin-walled vesicles were aspirated into a micropipette and a tether was pulled out of the surface by gravitational forces on small glass beads that had adhered to the vesicle surface. Because the vesicle keeps constant surface area and volume, formation of the tether requires displacement of material from the projection of the vesicle in the pipette. Tethers can be made to grow longer or shorter or to maintain equilibrium by adjusting the aspiration pressure in the micropipette at constant tether force. The ratio of the change in the length of the tether to the change in the projection length is proportional to the ratio of the pipette radius to the tether radius. Thus, knowing the density and diameter of the glass beads and measuring the displacement of the projection as a function of tether length, independent determinations of the force on the tether and the tether radius were obtained. The bending stiffness for an SOPC bilayer obtained from these data is approximately 2.0 x 10(-12) dyn cm, for tether radii in the range of 20-100 nm.(ABSTRACT TRUNCATED AT 250 WORDS)     

Local and nonlocal curvature elasticity in bilayer membranes by tether formation from lecithin vesicles.

Bilayer membranes exhibit an elastic resistance to changes in curvature. This resistance depends both on the intrinsic stiffness of the constituent monolayers and on the curvature-induced expansion or compression of the monolayers relative to each other. The monolayers are constrained by hydrophobic forces to remain in contact, but they are capable of independent lateral redistribution to minimize the relative expansion or compression of each leaflet. Therefore, the magnitude of the expansion and compression of the monolayers relative to each other depends on the integral of the curvature over the entire membrane capsule. The coefficient characterizing the membrane stiffness resulting from relative expansion is the nonlocal bending modulus kr. Both the intrinsic (local) bending modulus (kc) and the nonlocal bending modulus (kr) can be measured by the formation of thin cylindrical membrane strands (tethers) from giant phospholipid vesicles. Previously, we reported measurements of kc based on measurements of tether radius as a function of force (Song and Waugh, 1991, J. Biomech. Engr. 112:233). Further analysis has revealed that the contribution from the nonlocal bending stiffness can be detected by measuring the change in the aspiration pressure required to establish equilibrium with increasing tether length. Using this approach, we obtain a mean value for the nonlocal bending modulus kr of approximately 4.1 x 10(-19)J. The range of values is broad (1.1-10.1 x 10(-19)J) and could reflect contributions other than simple mechanical equilibrium. Inclusion of the nonlocal bending stiffness in the calculation of kc results in a value for that modulus of approximately 1.20 +/- 0.17 x 10(-19)J, in close agreement with values obtained by other methods.     

Bilayer membrane bending stiffness by tether formation from mixed PC-PS lipid vesicles

Recently, a new approach to measure the bending stiffness (curvature elastic modulus) of lipid bilayer membrane was developed (Biophys. J., Vol. 55; pp. 509-517, 1989). The method involves the formation of cylindrical membrane strands (tethers) from bilayer vesicles. The bending stiffness (B) can be calculated from measurements of the tether radius (Rt) as a function of the axial force (f) on the tether: B = f.Rt/2 pi. In the present report, we apply this method to determine the bending stiffness of bilayer membranes composed of mixtures of SOPC (1-stearoyl-2-oleoyl phosphatidyl choline) and POPS (1-palmitoyl-2-oleoyl phosphatidyl serine). Three different mixtures were tested: pure SOPC, SOPC plus 2 percent (mol/mol) POPS, and SOPC plus 16 percent POPS. The bending stiffness determined for these three different lipid mixtures were not significantly different (1.6-1.8 x 10(-12) ergs). Because POPS carries a net negative charge, these results indicate that changes in the density of the membrane surface charge have no effect on the intrinsic rigidity of the membrane. The values we obtain are consistent with published values for the bending stiffness of other membranes determined by different methods. Measurements of the aspiration pressure, tether radius and the tether force were used to verify a theoretical relationship among these quantities at equilibrium. The ratio of the theoretical force to the measured force was 1.12 +/- 0.17.     

Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells

The association between the lipid bilayer and the membrane skeleton is important to cell function. In red blood cells, defects in this association can lead to various forms of hemolytic anemia. Although proteins involved in this association have been well characterized biochemically, the physical strength of this association is only beginning to be studied. Formation of a small cylindrical strand of membrane material (tether) from the membrane involves separation of the lipid bilayer from the membrane skeleton. By measuring the force required to form a tether, and knowing the contribution to the force due to the deformation of a lipid bilayer, it is possible to calculate the additional contribution to the work of tether formation due to the separation of membrane skeleton from the lipid bilayer. In the present study, we measured the tethering force during tether formation using a microcantilever (a thin, flexible glass fiber) as a force transducer. Numerical calculations of the red cell contour were performed to examine how the shape of the contour affects the calculation of tether radius, and subsequently separation work per unit area W(sk) and bending stiffness k(c). At high aspiration pressure and small external force, the red cell contour can be accurately modeled as a sphere, but at low aspiration pressure and large external force, the contour deviates from a sphere and may affect the calculation. Based on an energy balance and numerical calculations of the cell contour, values of the membrane bending stiffness k(c) = 2.0 x 10(-19) Nm and the separation work per unit area W(sk) = 0.06 mJ/m2 were obtained.     

Molecular structure of membrane tethers

Membrane tethers are nanotubes formed by a lipid bilayer. They play important functional roles in cell biology and provide an experimental window on lipid properties. Tethers have been studied extensively in experiments and described by theoretical models, but their molecular structure remains unknown due to their small diameters and dynamic nature. We used molecular dynamics simulations to obtain molecular-level insight into tether formation. Tethers were pulled from single-component lipid bilayers by application of an external force to a lipid patch along the bilayer normal or by lateral compression of a confined bilayer. Tether development under external force proceeded by viscoelastic protrusion followed by viscous lipid flow. Weak forces below a threshold value produced only a protrusion. Larger forces led to a crossover to tether elongation, which was linear at a constant force. Under lateral compression, tethers formed from undulations of unrestrained bilayer area. We characterized in detail the tether structure and its formation process, and obtained the material properties of the membrane. To our knowledge, these results provide the first molecular view of membrane tethers.     

Chained vesicles in vascular endothelial cells.

There is extensive ultrastructural evidence in endothelium for the presence of chained vesicles or clusters of attached vesicles, and they are considered to be involved in specific transport mechanisms, such as the formation of trans-endothelial channels. However, few details are known about their mechanical characteristics. In this study, the formation mechanism and mechanical aspects of vascular endothelial chained vesicles are investigated theoretically, based on membrane bending strain energy analysis. The shape of the axisymmetric vesicles was computed on the assumption that the cytoplasmic side of the vesicle has a molecular layer or cytoskeleton attached to the lipid bilayer, which induces a spontaneous curvature in the resting state. The bending strain energy is the only elasticity involved, while the shear elasticity is assumed to be negligible. The surface area of the membrane is assumed to be constant due to constant lipid bilayer thickness. Mechanically stable shapes of chained vesicles are revealed, in addition to a cylindrical tube shape. Unfolding of vesicles into a more flattened shape is associated with increase in bending energy without a significant increase in membrane tension. These results provide insights into the formation mechanism and mechanics of the chained vesicle.     

Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis.

Recent observations indicate that it is possible to form tethers from large phospholipid vesicles. The process of tether formation is analyzed using a continuum mechanical approach to obtain the surface viscosity of the bilayer in terms of experimentally measurable parameters. The membrane is treated as a two-dimensional isotropic material which deforms a constant area. The constitutive equation relates the maximum surface shear resultant to the rate of deformation via the surface viscosity coefficient. The force which acts to increase the tether length is generated by fluid moving past the vesicle. The magnitude of the force is estimated from Stoke's drag equation. The analysis predicts that there is a critical force necessary to produce an increase in the tether length. A dimensionless tether growth parameter is defined, and its value is obtained as a function of the ratio of the applied force on the vesicle to the critical force. This relationship is independent of both the size of the vesicle and the radius of the tether. Knowing the force on the vesicle, the critical force, and the rate of tether growth, the surface viscosity can be calculated.     

Membrane tethers formed from blood cells with available area and determination of their adhesion energy

Fundamental to all mammalian cells is the adherence of the lipid bilayer membrane to the underlying membrane associated cytoskeleton. To investigate this adhesion, we physically detach the lipid membrane from the cell by mechanically forming membrane tethers. For the most part these have been tethers formed from either neutrophils or red cells. Here we do a simple thermodynamic analysis of the tether formation process using the entire cell, including tether, as the control volume. For a neutrophil, we show that the total adhesion energy per unit area between lipid membrane and cytoskeleton depends on the square of the tether force. For a flaccid red cell, we show that the total adhesion energy minus the tension in the spectrin cytoskeleton depends also on the square of the tether force. Finally, we discuss briefly the viscous flow of membrane. Using published data we calculate and compare values for the various adhesion energies and viscosities.     

Accelerated interleaflet transport of phosphatidylcholine molecules in membranes under deformation.

Biological membranes are lamellar structures composed of two leaflets capable of supporting different mechanical stresses. Stress differences between leaflets were generated during micromechanical experiments in which long thin tubes of lipid (tethers) were formed from the surfaces of giant phospholipid vesicles. A recent dynamic analysis of this experiment predicts the relaxation of local differences in leaflet stress by lateral slip between the leaflets. Differential stress may also relax by interleaflet transport of lipid molecules ("flip-flop"). In this report, we extend the former analysis to include interleaflet lipid transport. We show that transmembrane lipid flux will evidence itself as a linear increase in tether length with time after a step reduction in membrane tension. Multiple measurements were performed on 24 different vesicles composed of stearoyl-oleoyl-phosphatidylcholine plus 3% dinitrophenol-linked di-oleoyl-phosphatidylethanolamine. These tethers all exhibited a linear phase of growth with a mean value of the rate of interlayer permeation, cp = 0.009 s-1. This corresponds to a half-time of approximately 8 min for mechanically driven interleaflet transport. This value is found to be consistent with longer times obtained for chemically driven transport if the lipids cross the membrane via transient, localized defects in the bilayer.     

Characteristics of a membrane reservoir buffering membrane tension.

When membrane-attached beads are pulled vertically by a laser tweezers, a membrane tube of constant diameter (tether) is formed. We found that the force on the bead (tether force) did not depend on tether length over a wide range of tether lengths, which indicates that a previously unidentified reservoir of membrane and not stretch of the plasma membrane provides the tether membrane. Plots of tether force vs. tether length have an initial phase, an elongation phase, and an exponential phase. During the major elongation phase, tether force is constant, buffered by the "membrane reservoir." Finally, there is an abrupt exponential rise in force that brings the tether out of the trap, indicating depletion of the membrane reservoir. In chick embryo fibroblasts and 3T3 fibroblasts, the maximum tether lengths that can be pulled at a velocity of 4 microm/s are 5.1 +/- 0. 3 and 5.0 +/- 0.2 microm, respectively. To examine the importance of the actin cytoskeleton, we treated cells with cytochalasin B or D and found that the tether lengths increased dramatically to 13.8 +/- 0.8 and 12.0 +/- 0.7 microm, respectively. Similarly, treatment of the cells with colchicine and nocodazole results in more than a twofold increase in tether length. We found that elevation of membrane tension (through osmotic pressure, a long-term elevation of tether force, or a number of transitory increases) increased reservoir size over the whole cell. Using a tracking system to hold tether force on the bead constant near its maximal length in the exponential phase, the rate of elongation of the tethers was measured as a function of tether force (membrane tension). The rate of elongation of tethers was linearly dependent on the tether force and reflected an increase in size of the reservoir. Increases in the reservoir caused by tension increases on one side of the cell caused increases in reservoir size on the other side of the cell. Thus, we suggest that cells maintain a plasma membrane reservoir to buffer against changes in membrane tension and that the reservoir is increased with membrane tension or disruption of the cytoskeleton.     

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.     

Distinct membrane mechanical properties of human mesenchymal stem cells determined using laser optical tweezers

The therapeutic efficacy of mesenchymal stem cells (MSCs) in tissue engineering and regenerative medicine is determined by their unique biological, mechanical, and physicochemical characteristics, which are yet to be fully explored. Cell membrane mechanics, for example, has been shown to critically influence MSC differentiation. In this study, we used laser optical tweezers to measure the membrane mechanics of human MSCs and terminally differentiated fibroblasts by extracting tethers from the outer cell membrane. The average tether lengths were 10.6+/-1.1 microm (hMSC) and 3.0+/-0.5 microm (fibroblasts). The tether extraction force did not increase during tether formation, which suggests existence of a membrane reservoir intended to buffer membrane tension fluctuations. Cytoskeleton disruption resulted in a fourfold tether length increase in fibroblasts but had no effect in hMSCs, indicating weak association between the cell membrane and hMSC actin cytoskeleton. Cholesterol depletion, known to decrease lipid bilayer stiffness, caused an increase in the tether length both in fibroblasts and hMSCs, as does the treatment of cells with DMSO. We postulate that whereas fibroblasts use both the membrane rigidity and membrane-cytoskeleton association to regulate their membrane reservoir, hMSC cytoskeleton has only a minor impact on stem cell membrane mechanics.     

Role of lamellar membrane structure in tether formation from bilayer vesicles.

A theoretical analysis is presented of the formation of membrane tethers from micropipette-aspirated phospholipid vesicles. In particular, it is taken into account that the phospholipid membrane is composed of two layers which are in contact but unconnected. The elastic energy of the bilayer is taken to be the sum of contributions from area expansivity, relative expansivity of the two monolayers, and bending. The vesicle is aspirated into a pipette and a constant point force is applied at the opposite side in the direction away from the pipette. The shape of the vesicle in approximated as a cylindrical projection into the pipette with a hemispherical cap, a spherical section, and a cylindrical tether with a hemispherical cap. The dimensions of the different regions of the vesicle are obtained by minimizing its elastic energy subject to the condition that the volume of the vesicle is fixed. The range of values for the parameters of the system is determined at which the existence of a tether is possible. Stability analysis is performed showing which of these configurations are stable. The importance of the relative expansion and compression of the constituent monolayers is established by recognizing that local bending energy by itself does not stabilize the vesicle geometry, and that in the limit as the relative expansivity modulus becomes infinitely large, a tether cannot be formed. Predictions are made for the functional relationships among experimentally observable quantities. In a companion report, the results of this analysis are applied to experimental measurements of tether formation, and used to calculate values for the membrane material coefficients.     

Bridging microscopic and mesoscopic simulations of lipid bilayers

A lipid bilayer is modeled using a mesoscopic model designed to bridge atomistic bilayer simulations with macro-scale continuum-level simulation. Key material properties obtained from detailed atomistic-level simulations are used to parameterize the meso-scale model. The fundamental length and time scale of the meso-scale simulation are at least an order of magnitude beyond that used at the atomistic level. Dissipative particle dynamics cast in a new membrane formulation provides the simulation methodology. A meso-scale representation of a dimyristoylphosphatidylcholine membrane is examined in the high and low surface tension regimes. At high surface tensions, the calculated modulus is found to be slightly less than the atomistically determined value. This result agrees with the theoretical prediction that high-strain thermal undulations still persist, which have the effect of reducing the value of the atomistically determined modulus. Zero surface tension simulations indicate the presence of strong thermal undulatory modes, whereas the undulation spectrum and the calculated bending modulus are in excellent agreement with theoretical predictions and experiment.     

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.     

Intramembrane electrostatic interactions destabilize lipid vesicles

Membrane stability is of central concern in many biology and biotechnology processes. It has been suggested that intramembrane electrostatic interactions play a key role in membrane stability. However, due primarily to a lack of supporting experimental evidence, they are not commonly considered in mechanical analyses of lipid membranes. In this paper, we use the micropipette aspiration technique to characterize the elastic moduli and critical tensions of lipid vesicles with varying surface charge. Charge was induced by doping neutral phosphatidylcholine vesicles with anionic lipids phosphatidylglycerol and phosphatidic acid. Measurements were taken in potassium chloride (moderate ion-lipid binding) and tetramethylammonium chloride (low ion-lipid binding) solutions. We show that inclusion of anionic lipid does not appreciably alter the areal dilation elasticity of lipid vesicles. However, the tension required for vesicle rupture decreases with increasing anionic lipid fraction and is a function of electrolyte composition. Using vesicles with 30% charged (i.e., unbound) anionic lipid, we measured critical tension reductions of 75%, demonstrating the important role of electrostatic interactions in membrane stability.     

The Influence of Natural Lipid Asymmetry upon the Conformation of a Membrane-inserted Protein (Perfringolysin O)

Eukaryotic membrane proteins generally reside in membrane bilayers that have lipid asymmetry. However, in vitro studies of the impact of lipids upon membrane proteins are generally carried out in model membrane vesicles that lack lipid asymmetry. Our recently developed method to prepare lipid vesicles with asymmetry similar to that in plasma membranes and with controlled amounts of cholesterol was used to investigate the influence of lipid composition and lipid asymmetry upon the conformational behavior of the pore-forming, cholesterol-dependent cytolysin perfringolysin O (PFO). PFO conformational behavior in asymmetric vesicles was found to be distinct both from that in symmetric vesicles with the same lipid composition as the asymmetric vesicles and from that in vesicles containing either only the inner leaflet lipids from the asymmetric vesicles or only the outer leaflet lipids from the asymmetric vesicles. The presence of phosphatidylcholine in the outer leaflet increased the cholesterol concentration required to induce PFO binding, whereas phosphatidylethanolamine and phosphatidylserine in the inner leaflet of asymmetric vesicles stabilized the formation of a novel deeply inserted conformation that does not form pores, even though it contains transmembrane segments. This conformation may represent an important intermediate stage in PFO pore formation. These studies show that lipid asymmetry can strongly influence the behavior of membrane-inserted proteins.     

Membrane tether formation from outer hair cells with optical tweezers

Optical tweezers were used to characterize the mechanical properties of the outer hair cell (OHC) plasma membrane by pulling tethers with 4.5-microm polystyrene beads. Tether formation force and tether force were measured in static and dynamic conditions. A greater force was required for tether formations from OHC lateral wall (499 +/- 152 pN) than from OHC basal end (142 +/- 49 pN). The difference in the force required to pull tethers is consistent with an extensive cytoskeletal framework associated with the lateral wall known as the cortical lattice. The apparent plasma membrane stiffness, estimated under the static conditions by measuring tether force at different tether length, was 3.71 pN/microm for OHC lateral wall and 4.57 pN/microm for OHC basal end. The effective membrane viscosity was measured by pulling tethers at different rates while continuously recording the tether force, and estimated in the range of 2.39 to 5.25 pN x s/microm. The viscous force most likely results from the viscous interactions between plasma membrane lipids and the OHC cortical lattice and/or integral membrane proteins. The information these studies provide on the mechanical properties of the OHC lateral wall is important for understanding the mechanism of OHC electromotility.