Influence of thermally driven surface undulations on tethers formed from bilayer membranes

Tether formation is a powerful method to study the mechanical properties of soft lipid bilayer membranes. The force required to maintain a tether at a given length depends upon both membrane elastic properties and tension. In this report, we develop a theoretical analysis that considers the contribution of thermally driven surface undulations and the corresponding entropically driven tensions on the conformation of tethers formed from unaspirated lipid vesicles. In this model, thermal undulations of the vesicle surface provide the excess area required for tether formation. Energy minimization demonstrates the dependence of equilibrium tether conformation on membrane tension and provides an analytical relationship between tether force and radius. If the contributions of nonlocal bending are not considered, an analytical relationship between tether force and length can also be obtained. The predictions of the model are compared to recently reported experimental data, and a value for the initial vesicle tension is obtained. Since most analyses of tether formation from cells and unaspirated vesicles neglect the contributions of nonlocal bending, the appropriateness of this assumption is analyzed. The effect of surface microvesiculations on the tether force-length relation is also considered.     

Effect of salicylate on the elasticity, bending stiffness, and strength of SOPC membranes

Salicylate is a small amphiphilic molecule which has diverse effects on membranes and membrane-mediated processes. We have utilized micropipette aspiration of giant unilamellar vesicles to determine salicylate's effects on lecithin membrane elasticity, bending rigidity, and strength. Salicylate effectively reduces the apparent area compressibility modulus and bending modulus of membranes in a dose-dependent manner at concentrations above 1 mM, but does not greatly alter the actual elastic compressibility modulus at the maximal tested concentration of 10 mM. The effect of salicylate on membrane strength was investigated using dynamic tension spectroscopy, which revealed that salicylate increases the frequency of spontaneous defect formation and lowers the energy barrier for unstable hole formation. The mechanical and dynamic tension experiments are consistent and support a picture in which salicylate disrupts membrane stability by decreasing membrane stiffness and membrane thickness. The tension-dependent partitioning of salicylate was utilized to calculate the molecular volume of salicylate in the membrane. The free energy of transfer for salicylate insertion into the membrane and the corresponding partition coefficient were also estimated, and indicated favorable salicylate-membrane interactions. The mechanical changes induced by salicylate may affect several biological processes, especially those associated with membrane curvature and permeability.     

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.     

Mechanics of the Formation,Interaction, and Evolution of Membrane Tubular Structures

Membrane nanotubes, also known as membrane tethers, play important functional roles in many cellular processes, such as trafficking and signaling. Although considerable progresses have been made in understanding the physics regulating the mechanical behaviors of individual membrane nanotubes, relatively little is known about the formation of multiple membrane nanotubes due to the rapid occurring process involving strong cooperative effects and complex configurational transitions. By exerting a pair of external extraction upon two separate membrane regions, here, we combine molecular dynamics simulations and theoretical analysis to investigate how the membrane nanotube formation and pulling behaviors are regulated by the separation between the pulling forces and how the membrane protrusions interact with each other. As the force separation increases, different membrane configurations are observed, including an individual tubular protrusion, a relatively less deformed protrusion with two nanotubes on its top forming a V shape, a Y-shaped configuration through nanotube coalescence via a zipper-like mechanism, and two weakly interacting tubular protrusions. The energy profile as a function of the separation is determined. Moreover, the directional flow of lipid molecules accompanying the membrane shape transition is analyzed. Our results provide new, to our knowledge, insights at a molecular level into the interaction between membrane protrusions and help in understanding the formation and evolution of intra- and intercellular membrane tubular networks involved in numerous cell activities.     

Quantitative analysis of the native presynaptic cytomatrix by cryoelectron tomography

The presynaptic terminal contains a complex network of filaments whose precise organization and functions are not yet understood. The cryoelectron tomography experiments reported in this study indicate that these structures play a prominent role in synaptic vesicle release. Docked synaptic vesicles did not make membrane to membrane contact with the active zone but were instead linked to it by tethers of different length. Our observations are consistent with an exocytosis model in which vesicles are first anchored by long (>5 nm) tethers that give way to multiple short tethers once vesicles enter the readily releasable pool. The formation of short tethers was inhibited by tetanus toxin, indicating that it depends on soluble N-ethyl-maleimide sensitive fusion protein attachment protein receptor complex assembly. Vesicles were extensively interlinked via a set of connectors that underwent profound rearrangements upon synaptic stimulation and okadaic acid treatment, suggesting a role of these connectors in synaptic vesicle mobilization and neurotransmitter release.     

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.     

Deformability of multilamellar vesicles

Although a free unilamellar vesicle has zero or almost zero genuine surface tension, the multilamellar vesicle ("onion") exhibits a nonzero effective surface tension sigma(eff). The expression for sigma(eff) used in the literature is sigma(eff) approximately square root of kappaB/d(0), where B is the interaction modulus between the vesicle bilayers, d(0) the repeating distance between the bilayers in the droplet, and kappa their bending rigidity. In this paper we calculate the contributions to the effective surface tension of a lamellar droplet in the case when the layers interact with one another and when they are free. It is shown that the interaction contribution to the surface tension is small and sigma(eff) is determined mainly by kappa, the radius of the droplet R(0), and the number of the shape undulation modes l(max). A nonzero surface tension of the layers is also included in the calculation which is necessary when the vesicle membrane is stressed in the complex of other membranes.     

The role of sterols in the lipid vesicle response induced by the pore-forming agent nystatin

The influences of ergosterol and cholesterol on the activity of the nystatin were investigated experimentally in a POPC model membrane as well as theoretically. The behavior of giant unilamellar vesicles (GUVs) under osmotic stress due to the formation of transmembrane pores was observed on single vesicles at different nystatin concentrations using phase-contrast microscopy. A significant shift of the typical vesicle behavior, i.e., morphological alterations, membrane bursts, slow vesicle ruptures and explosions, towards lower nystatin concentrations was detected in the ergosterol-containing vesicles and a slight shift towards higher nystatin concentrations was detected in the cholesterol-containing membranes. In addition, the nystatin activity was shown to be significantly affected by the ergosterol membrane’s molar fraction in a non-proportional manner. The observed tension-pore behavior was interpreted using a theoretical model based on the osmotic phenomena induced by the occurrence of size-selective nystatin pores. The number of nystatin pores for different vesicle behavior was theoretically determined and the role of the different mechanical characteristics of the membrane, i.e., the membrane's expansivity and bending moduli, the line tension and the lysis tension, in the tension-pore formation process was quantified. The sterol-induced changes could not be explained adequately on the basis of the different mechanical characteristics, and were therefore interpreted mainly by the direct influences of the membrane sterols on the membrane binding, the partition and the pore-formation process of nystatin.     

Dynamic tension spectroscopy and strength of biomembranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01-100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermally-activated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallow-curved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a two-dimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.     

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.     

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.     

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.     

Cholesterol reduces membrane electroporation and electric deformation of small bilayer vesicles

Electric fields, similar in the order of magnitude of the natural membrane fields of cellular lipid/protein membranes, and chemical relaxation spectrometry can be used as tools to quantify the rigidifying effect of cholesterol in membranes. Small unilamellar vesicles of radius a=50+/-3 nm, prepared form phosphatidylcholine, phosphatidylserine and phosphatidyl-glycerol in the molar ratio 1:1:1 and containing the optical lipid probe molecule 2-(3-diphenyl-hexatrienyl) propanoyl)-1-palmitoyl-sn-glycerol-3-phosphocholine (beta-DPH pPC), serve as examples for curved lipid membranes. The data of electrooptical turbidity and absorbance relaxations at the wavelength lambda=365 nm are analysed in terms of membrane bending rigidity kappa and membrane stretching modulus K. Both kappa and K increase with increasing mole fraction x of cholesterol up to x=0.5. The cholesterol induced denser packing of the lipids reduces the extent of both membrane electroporation (ME) and electroelongation of the vesicles. Further on, cholesterol in the lipid phase and sucrose in the aqueous suspension reduce the extent of membrane undulation and electro-stretching.     

Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.     

Linking membrane physical properties and low temperature tolerance in arthropods

Maintenance of membrane fluidity is of crucial importance in ectotherms experiencing thermal changes. This maintenance has in ectotherms most often been indicated using indirect measures of biochemical changes of phospholipid membranes, which is then assumed to modulate the physico-chemical properties of the membrane. Here, we measure bending rigidity characterizing the membrane flexibility of re-constituted membrane vesicles to provide a more direct link between membrane physical characteristics and low temperature tolerance. Bending rigidity of lipid bilayers was measured in vitro using Giant Unilamellar Vesicles formed from phospholipid extracts of the springtail, Folsomia candida. The bending rigidity of these membranes decreased when exposed to 0.4 vol% ethanol (0.23 mM/L). Springtails exposed to ethanol for 24 h significantly increased their cold shock tolerance. Thus, by chemically inducing decreased membrane rigidity, we have shown a direct link between the physico-chemical properties of the membranes and the capacity to tolerate low temperature in a chill-susceptible arthropod.     

Theoretical model for the formation of caveolae and similar membrane invaginations

We study a physical model for the formation of bud-like invaginations on fluid lipid membranes under tension, and apply this model to caveolae formation. We demonstrate that budding can be driven by membrane-bound proteins, provided that they exert asymmetric forces on the membrane that give rise to bending moments. In particular, caveolae formation does not necessarily require forces to be applied by the cytoskeleton. Our theoretical model is able to explain several features observed experimentally in caveolae, where proteins in the caveolin family are known to play a crucial role in the formation of caveolae buds. These include 1), the formation of caveolae buds with sizes in the 100-nm range and 2), that certain N- and C-termini deletion mutants result in vesicles that are an order-of-magnitude larger. Finally, we discuss the possible origin of the morphological striations that are observed on the surfaces of the caveolae.     

Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity

Sterols are regulators of both biological function and structure. The role of cholesterol in promoting the structural and mechanical stability of membranes is widely recognized. Knowledge of how the related sterols, lanosterol and ergosterol, affect membrane mechanical properties is sparse. This paper presents a comprehensive comparison of the effects of cholesterol, lanosterol, and ergosterol upon the bending elastic properties of 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine giant unilamellar vesicles. Measurements are made using vesicle fluctuation analysis, a nonintrusive technique that we have recently improved for determining membrane bending rigidity. Giving a detailed account of the vesicle fluctuation analysis technique, we describe how the gravitational stabilization of the vesicles enhances image contrast, vesicle yield, and the quality of data. Implications of gravity on vesicle behaviour are also discussed. These recent modifications render vesicle fluctuation analysis an efficient and accurate method for determining how cholesterol, lanosterol, and ergosterol increase membrane bending rigidity.     

Electroporation of curved lipid membranes in ionic strength gradients

A thermodynamic theory for the membrane electroporation of curved membranes such as those of lipid vesicles and cylindrical membrane tubes has been developed. The theory covers in particular the observation that electric pore formation and shape deformation of vesicles and cells are dependent on the salt concentration of the suspending solvent. It is shown that transmembrane salt gradients can appreciably modify the electrostatic part of Helfrich's spontaneous curvature, elastic bending rigidity and Gaussian curvature modulus of charged membranes. The Gibbs reaction energy of membrane electroporation can be explicitely expressed in terms of salt gradient-dependent contributions of bending, the ionic double layers and electric surface potentials and dielectric polarisation of aqueous pores. In order to cover the various physical contribution to the chemical process of electroporation-resealing, we have introduced a generalised chemophysical potential covering all generalised forces and generalised displacements in terms of a transformed Gibbs energy formalism. Comparison with, and analysis of, the data of electrooptical relaxation kinetic studies show that the Gibbs reaction energy terms can be directly determined from turbidity dichroism (Planck's conservative dichroism). The approach also quantifies the electroporative cross-membrane material exchange such as electrolyte release, electrohaemolysis of red blood cells or uptake of drugs and dyes and finally gene DNA by membrane electroporation.     

Membrane Elastic Properties and Cell Function

Recent studies indicate that the cell membrane, interacting with its attached cytoskeleton, is an important regulator of cell function, exerting and responding to forces. We investigate this relationship by looking for connections between cell membrane elastic properties, especially surface tension and bending modulus, and cell function. Those properties are measured by pulling tethers from the cell membrane with optical tweezers. Their values are determined for all major cell types of the central nervous system, as well as for macrophage. Astrocytes and glioblastoma cells, which are considerably more dynamic than neurons, have substantially larger surface tensions. Resting microglia, which continually scan their environment through motility and protrusions, have the highest elastic constants, with values similar to those for resting macrophage. For both microglia and macrophage, we find a sharp softening of bending modulus between their resting and activated forms, which is very advantageous for their acquisition of phagocytic functions upon activation. We also determine the elastic constants of pure cell membrane, with no attached cytoskeleton. For all cell types, the presence of F-actin within tethers, contrary to conventional wisdom, is confirmed. Our findings suggest the existence of a close connection between membrane elastic constants and cell function.