Bending stiffness of lipid bilayers. I. Bilayer couple or single-layer bending?

To describe the resistance of a bilayer to changes in curvature two mechanisms are distinguished which are termed bilayer couple bending and single-layer bending. In bilayer couple bending, the resistance arises from the 2-D isotropic elasticity of the two layers and their fixed distance. Single-layer bending covers the intrinsic bending stiffness of each monolayer. The two mechanisms are not independent. Even so, the distinction is useful since bilayer couple bending can relax by a slip between the layers from the local to the global fashion. Therefore, the bending stiffness of a bilayer depends on the time scale and on the extent of the deformation imposed on the membrane. Based on experimental data, it is shown by order of magnitude estimates that (a) the bending stiffness determined from thermally induced shape fluctuations of almost spherical vesicles is dominated by single-layer bending; (b) in the tether experiment on lipid vesicles and on red cells, a contribution of local bilayer couple bending can not be excluded; and (c) at the sharp corners at the leading and the trailing edge of tanktreading red cells, local bilayer couple bending appears to be important.     

Minimum Membrane Bending Energies of Fusion Pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of ?0.1 nm^?1 (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43–65 kT. The pore radius of ~2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.     

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.     

The shape of lipid molecules and monolayer membrane fusion

The contact between two bilayer membranes results in their monolayer fusion comprising the formation of a trilaminar structure (a single bilayer connected to two bilayers over the whole perimeter) in the contact region. The time required for monolayer fusion was measured and irreversible electrical breakdown was studied for membranes of different compositions. A theoretical model of the monolayer fusion is suggested to explain the results. It assumes that the structural reorganization underlying the process involves the formation of a stalk between bilayers as a result of local bending of the interacting monolayers. This structural reorganization is similar to the hydrophilic pore formation in a bilayer under irreversible breakdown. However, the directions of the monolayer bending are different in the two processes and, therefore, the bending energies depend oppositely on the effective shape of lipid molecules. Theoretical predictions agree well with experimental data. The applicability of the suggested mechanism to biomembrane fusion is discussed.     

Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape

A possible physical explanation of the echinocyte-spheroechinocyte red blood cell (RBC) shape transformation induced by the intercalation of amphiphilic molecules into the outer layer of the RBC plasma membrane bilayer is given. The stable RBC shape is determined by the minimization of the membrane elastic energy, consisting of the bilayer bending energy, the bilayer relative stretching energy and the skeleton shear elastic energy. It is shown that for a given relative cell volume the calculated number of echinocyte spicula increases while their size decreases as the number of the intercalated amphiphilic molecules in the outer layer of the cell membrane bilayer is increased, which is in agreement with experimental observations. Further, it is shown that the equilibrium difference between the outer and the inner membrane leaflet areas of the stable RBC shapes increases if the amount of the intercalated amphiphiles is increased, thereby verifying theoretically the original bilayer couple hypothesis of Sheetz and Singer (1974) and Evans (1974). Received: 22 August 1997 / Revised version: 25 November 1997 / Accepted: 11 February 1998     

Regulation of sodium channel function by bilayer elasticity: the importance of hydrophobic coupling. Effects of Micelle-forming amphiphiles and cholesterol

Membrane proteins are regulated by the lipid bilayer composition. Specific lipid-protein interactions rarely are involved, which suggests that the regulation is due to changes in some general bilayer property (or properties). The hydrophobic coupling between a membrane-spanning protein and the surrounding bilayer means that protein conformational changes may be associated with a reversible, local bilayer deformation. Lipid bilayers are elastic bodies, and the energetic cost of the bilayer deformation contributes to the total energetic cost of the protein conformational change. The energetics and kinetics of the protein conformational changes therefore will be regulated by the bilayer elasticity, which is determined by the lipid composition. This hydrophobic coupling mechanism has been studied extensively in gramicidin channels, where the channel-bilayer hydrophobic interactions link a "conformational" change (the monomer<-->dimer transition) to an elastic bilayer deformation. Gramicidin channels thus are regulated by the lipid bilayer elastic properties (thickness, monolayer equilibrium curvature, and compression and bending moduli). To investigate whether this hydrophobic coupling mechanism could be a general mechanism regulating membrane protein function, we examined whether voltage-dependent skeletal-muscle sodium channels, expressed in HEK293 cells, are regulated by bilayer elasticity, as monitored using gramicidin A (gA) channels. Nonphysiological amphiphiles (beta-octyl-glucoside, Genapol X-100, Triton X-100, and reduced Triton X-100) that make lipid bilayers less "stiff", as measured using gA channels, shift the voltage dependence of sodium channel inactivation toward more hyperpolarized potentials. At low amphiphile concentration, the magnitude of the shift is linearly correlated to the change in gA channel lifetime. Cholesterol-depletion, which also reduces bilayer stiffness, causes a similar shift in sodium channel inactivation. These results provide strong support for the notion that bilayer-protein hydrophobic coupling allows the bilayer elastic properties to regulate membrane protein function.     

Bilayer balance and regulation of red cell shape changes

Discocytic human red cells undergo discocyte-echinocyte and discocytestomatocyte transformations under the action of a wide variety of lipid-soluble anionic and cationic agents respectively. These shape transformations are explained by the bilayer couple hypothesis of Sheetz and Singer to be the result of preferential distribution of the anionic agents in the outer half of the bilayer and the cationic agents in the inner half of the bilayer. We demonstrate that echinocytogenic effects indeed occur when the naturally occurring phospholipid lysophosphatidylcholine (LPC) is localized in the outer half of the bilayer, and stomatocytogenic effects occur when LPC is in the inner half. However, in contrast to the bilayer couple hypothesis, our results show that simple equivalent membrane surface area expansion on each layer is insufficient to maintain the discocytic shape and there exists a differential concentration effect of LPC on the two halves of the bilayer.     

A computer simulation of free-volume distributions and related structural properties in a model lipid bilayer.

A novel combined approach of molecular dynamics (MD) and Monte Carlo simulations is developed to calculate various free-volume distributions as a function of position in a lipid bilayer membrane at 323 K. The model bilayer consists of 2 x 100 chain molecules with each chain molecule having 15 carbon segments and one head group and subject to forces restricting bond stretching, bending, and torsional motions. At a surface density of 30 A2/chain molecule, the probability density of finding effective free volume available to spherical permeants displays a distribution with two exponential components. Both pre-exponential factors, p1 and p2, remain roughly constant in the highly ordered chain region with average values of 0.012 and 0.00039 A-3, respectively, and increase to 0.049 and 0.0067 A-3 at the mid-plane. The first characteristic cavity size V1 is only weakly dependent on position in the bilayer interior with an average value of 3.4 A3, while the second characteristic cavity size V2 varies more dramatically from a plateau value of 12.9 A3 in the highly ordered chain region to 9.0 A3 in the center of the bilayer. The mean cavity shape is described in terms of a probability distribution for the angle at which the test permeant is in contact with one of and does not overlap with anyone of the chain segments in the bilayer. The results show that (a) free volume is elongated in the highly ordered chain region with its long axis normal to the bilayer interface approaching spherical symmetry in the center of the bilayer and (b) small free volume is more elongated than large free volume. The order and conformational structures relevant to the free-volume distributions are also examined. It is found that both overall and internal motions have comparable contributions to local disorder and couple strongly with each other, and the occurrence of kink defects has higher probability than predicted from an independent-transition model.     

Chain ordering in liquid crystals: II. Structure of bilayer membranes

The ordering of the hydrocarbon chain interior of bilayer membranes has been calculated using the molecular field approximation developed in previous work on liquid crystals. Different statistical averages are evaluated by exact summation over all conformations of a single chain in the field due to neighboring molecules. The internal energy of each conformation, as well as contributions arising from interaction with the molecular field and from a lateral pressure on the chain have been included.The results describe properties of both lipid monolayers and bilayers. For monolayers, the calculated pressure-area relationships are in good agreement with experimental observations. The order parameter for hydrocarbon chains in bilayers (or monolayers) as a function of temperature, lateral pressure and position along the chain, is shown and compared with the available NMR data. Combining the results of calculation and NMR measurements we obtain the value for intrinsic lateral pressure within bilayer membranes, in excellent agreement with direct measurements on surface monolayers.The calculation also gives average length of hydrocarbon chains, thermal expansion coefficient and fraction of bonds in gauche conformations. The effect of cholesterol and proteins within the bilayer is qualitatively described, and the contribution of the bilayer interior to membrane elasticity is determined.     

Equilibrium and kinetic effects of drugs on the shapes of human erythrocytes

We have previously proposed that if the two half-layers of a membrane are different in their protein and lipid compositions, they may respond differently to some membrane perturbation (the bilayer couple hypothesis). This hypothesis has been applied to explain the changes in shape of human erythrocytes that are produced by a variety of amphipathic compounds. These compounds are presumed to intercalate by their hydrophobic ends into the lipid portions of the membrane; if the compounds are anions, the binding is preferentially to the outer half of the bilayer, if cations, to the inner half. It is proposed that such preferential binding causes an expansion of one half-layer relative to the other, with a corresponding change in cell shape. The predicted sidedness of these shape changes is now demonstrated in experiments with methochlorpromazine and 2,4,6-trinitrophenol. Under appropriate nonequilibrium or equilibrium or equilibrium conditions, both of these compounds are shown to be either crenators or cup-formers of the intact erythrocyte, depending upon which side of the membrane they are concentrated in. These results therefore strongly support the bilayer couple hypothesis.     

Structure and energy of fusion stalks: the role of membrane edges

Fusion of lipid bilayers proceeds via a sequence of distinct structural transformations. Its early stage involves a localized, hemifused intermediate in which the proximal but not yet the distal monolayers are connected. Whereas the so-called stalk model most successfully accounts for the properties of the hemifused intermediate, there is still uncertainty about its microscopic structure and energy. We reanalyze fusion stalks using the theory of membrane elasticity. In our calculations, a short (cylindrical micelle-like) tether connects the two proximal monolayers of the hemifused membranes. The shape of the stalk and the length of the tether are calculated such as to minimize the overall free energy and to avoid the formation of voids within the hydrocarbon core. Our free energy expression is based on three internal degrees of freedom of a perturbed lipid layer: thickness, splay, and tilt deformations. Based on exactly the same model, we compare fusion stalks with and without the ability included to form sharp edges at the interfacial region between the hydrocarbon core and the polar environment. Requiring the interface to be smooth everywhere, our detailed calculations recover previous results: the stalk energies are far too high to account for the experimental observation of fusion intermediates. However, if we allow the interface to be nonsmooth, we find a remarkable reduction of the stalk free energy down to more realistic values. The corresponding structure of a nonsmooth stalk exhibits sharp edges at the transition regions between the bilayer and tether parts. In addition to that, a corner is formed at each of the two distal monolayers. We discuss the mechanism how membrane edges reduce the energy of fusion stalks.     

Bending membranes

It is widely assumed that peripheral membrane proteins induce intracellular membrane curvature by the asymmetric insertion of a protein segment into the lipid bilayer, or by imposing shape by adhesion of a curved protein domain to the membrane surface. Two papers now provide convincing evidence challenging these views. The first shows that specific assembly of a clathrin protein scaffold, coupled to the membrane, seems to be the most prevalent mechanism for bending a lipid bilayer in a cell. The second reports that membrane crowding, driven by protein-protein interactions, can also drive membrane bending, even in the absence of any protein insertion into the bilayer.     

Biological membranes as bilayer couples. III. Compensatory shape changes induced in membranes

We have previously proposed the hypothesis that asymmetric membranes behave like bilayer couples: the two layers of the bilayer membrane can respond differently to a particular perturbation. Such a perturbation, for example, can result in the expansion of one layer relative to the other, thereby producing a curvature of that membrane. In experiments with erythrocytes and lymphocytes, we now demonstrate that different membrane perturbations which have opposite effects on membrane curvature can compensate and neutralize one another, as expected from the bilayer couple hypothesis. This provides a rational basis, for example, for understanding the effects of amphipathic drugs on a variety of cellular phenomena which involve shape changes of membranes.     

Phase transition in charged lipid membranes.

Experimental results on the effect of electrostatics on bilayer phase transitions are compared with corresponding data for monolayers and the predictions of electrical double layer theory. The two substantial conclusions which emerge are that: (i) double layer theory based on a continuous surface charge distribution cannot explain all the relevant data, a situation which may be improved by taking into account the discrete nature of the surface charge distribution; (ii) the crystal - liquid crystal phase transition of charged bilayer membranes is always a continuous one which takes place through an intermediate state consisting of both fluid and frozen domains.     

Lateral diffusion and percolation in two-phase, two-component lipid bilayers. Topology of the solid-phase domains in-plane and across the lipid bilayer.

Fluorescence recovery after photobleaching (FRAP) has recently been used to examine the percolation properties of coexisting phases in two-component, two-phase phosphatidylcholine bilayers [Vaz, W. L. C., Melo, E. C. C., & Thompson, T. E. (1989) Biophys. J. 56, 869-876]. We now report the use of FRAP to study two additional problems in similar systems. The first is the effect of solid-phase obstacles on the lateral diffusion in the fluid phase. The second is the question of whether or not, in a single bilayer, solid-phase domains in one monolayer are exactly superimposed on solid domains in the apposing monolayer. To address the first problem, the lateral diffusion of N-(7-nitrobenzoxa-2,3-diazol-4-yl)-1-palmitoyl-2-oleoylphosp hatidylethanolamine (NBD-POPE), a probe soluble only in the fluid phase when solid and fluid phases coexist, has been studied in the mixture N-lignoceroyldihydrogalactosylceramide (LigGalCer)/dipalmitoylphosphatidylcholine (DPPC). Percolation of the fluid phase occurs at a high mass fraction of solid phase. This indicates that the solid domains have a centrosymmetric shape, a characteristic which makes this a good experimental system to test theoretical simulations of diffusion in an archipelago. It is shown that agreement between theory and experiment is poor, a result that had already been observed when the obstacles were integral membrane proteins. We develop an effective-medium model for diffusion in two-phase systems which explains both our results and those obtained with integral proteins. The distinctive feature of the model is the consideration of an annular region around the obstacles where the lipids are more ordered than in the bulk fluid phase. The diffusion coefficient is then calculated by extending the free area model to two-phase systems, taking these annuli into account. The second question, the organization of the solid-phase domains across the lipid bilayer, is examined in the systems LigGalCer/DPPC and dimyristoylphosphatidylcholine (DMPC)/distearoylphosphatidylcholine (DSPC) by comparing the diffusion of a fluid-phase-soluble, gel-phase-insoluble lipid derivative which spans the two monolayers of a bilayer (NBD-membrane-spanning-phosphatidylethanolamine, NBD-msPE) with that of a probe which is restricted to a single monolayer. In LigGalCer/DPPC, 20:80, the distribution of solid domains in one of the monolayers is independent of the distribution in the apposing monolayer. In contrast, in DMPC/DSPC, 50:50, the solid domains in one monolayer are exactly superimposed upon the solid domains existing in the apposing monolayer.     

Sensing with electro-switchable biosurfaces

The conformation of charged molecules tethered to conducting substrates can be controlled efficiently through the application of external voltages. Biomolecules like DNA or oligopeptides can be forced to stretch away from??or fold onto??surfaces biased at moderate potentials of merely hundreds of millivolts. These externally controlled conformation changes can be used to switch the biological function of molecular monolayers on and off, by revealing or concealing molecular recognition sites at will. Moreover, the electrical actuation of biomolecular surface probes bears great potential as a novel, label-free, yet highly sensitive measurement modality for the analysis of molecular interactions. The binding of target molecules to an oscillating probe layer significantly alters the layer??s switching behavior in terms of the conformation switching amplitude and, most remarkably, with respect to the molecular switching dynamics. Analyzing the switching response of target?Cprobe complexes from the low- to the high-frequency regime reveals a wealth of previously inaccessible information. Besides ??classical?? interaction parameters like binding affinities and kinetic rate constants, information on the size, shape, bending flexibility, and elasticity of the target molecule may be obtained in a single assay. This review describes the advent of electrically switchable biosurfaces, focusing on DNA monolayers. The preparation of self-assembled switchable oligonucleotide monolayers and their electrical interactions with charged substrates are highlighted. Special attention is paid to the merits of evaluating the dynamic response of charged biolayers which are operated at high driving frequencies. Several applications of biosensors based on electrically manipulated molecules are exemplified. It is emphasized that the electrical actuation of biomolecules bears many advantages over passive sensor surfaces.     

Chlorpromazine modulates the morphological macro- and microstructure of endothelial cells

Chlorpromazine (CP), anamphipathic, antipsychotic agent, causes concave membrane bending inred blood cells with formation of stomatocytic shapes by modulation ofthe phospholipid bilayer. This study was designed to investigate theeffects of CP on the shape of bovine aortic endothelial cells (BAEC)and their membranes in confluent monolayers with phase-contrast andtransmission electron microscopy. Exposure of BAECs tonanomolar levels of CP leads to membrane curvature changes. Withincreasing CP concentrations, the membrane assumed a shape withenhanced numbers of intracellular caveolae and projection ofpseudopodia at all junctions. At higher CP concentrations (up to 150 µM), the endothelial cells assumed almost spherical shapes. Theevidence suggests that CP may affect lipid bilayer bending of BAECs inanalogy with previous observations on erythrocytes, supporting theformation of caveolae and pseudopodia in BAECs due to the induction ofconcave membrane bending, as well as an effect on endothelialcell membrane adhesion at higher CP concentrations withloss of cellular attachment at junctions.

     

Structure of an adsorbed dimyristoylphosphatidylcholine bilayer measured with specular reflection of neutrons.

Using specular reflection of neutrons, we investigate for the first time the structure of a single dimyristoylphosphatidylcholine bilayer adsorbed to a planar quartz surface in an aqueous environment. We demonstrate that the bilayer is strongly adsorbed to the quartz surface and is stable to phase state changes as well as exchange of the bulk aqueous phase. Our results show that the main phase transition is between the L alpha phase and the metastable L beta'* phase, with formation of the P beta' ripple phase prevented by lateral stress on the adsorbed bilayer. By performing contrast variation experiments, we are able to elucidate substantial detail in the interfacial structure. We measure a bilayer thickness of 43.0 +/- 1.5 A in the L alpha phase (T = 31 degrees C) and 46.0 +/- 1.5 A in the L beta'* phase (T = 20 degrees C). The polar head group is 8.0 +/- 1.5 A thick in the L alpha phase. The water layer between the quartz and bilayer is 30 +/- 10 A for the lipid in both the L alpha and L'* phase. Our results agree well with those previously reported from experiments using lipid vesicles and monolayers, thus establishing the feasibility of our experimental methods.