Membrane Bending Modulus Research Articles

Influenza viral membrane fusion is sensitive to sterol concentration but surprisingly robust to sterol chemical identity.

Influenza virions are enriched in cholesterol relative to the plasma membrane from which they bud. Previous work has shown that fusion between influenza virus and synthetic liposomes is sensitive to the amount of cholesterol in either the virus or the target membrane. Here, we test the chemical properties of cholesterol required to promote influenza fusion by replacing cholesterol with other sterols and assaying viral fusion kinetics. We find that influenza fusion with liposomes is surprisingly robust to sterol chemical identity, showing no significant dependence on sterol identity in target membranes for any of the sterols tested. In the viral membrane, lanosterol slowed fusion somewhat, while polar sterols produced a more pronounced slowing and inhibition of fusion. No other sterols tested showed a significant perturbation in fusion rates, including ones previously shown to alter membrane bending moduli or phase behavior. Although fusion rates depend on viral cholesterol, they thus do not require cholesterol’s ability to support liquid-liquid phase coexistence. Using electron cryo-microscopy, we further find that sterol-dependent changes to hemagglutinin spatial patterning in the viral membrane do not require liquid-liquid phase coexistence. We therefore speculate that local sterol-hemagglutinin interactions in the viral envelope may control the rate-limiting step of fusion.

Atomic Force Microscopic Analysis of the Effect of Lipid Composition on Liposome Membrane Rigidity.

Mechanical rigidity of the liposome membrane is often defined by the membrane bending modulus and is one of the determinants of liposome stability, but the quantitative experimental data are still limited to a few kinds of liposomes. Here, we used atomic force microscopy to investigate the membrane bending moduli of liposomes by immobilizing them on bovine serum albumin-coated glass in aqueous medium. The following lipids were used for liposome preparation: egg yolk phosphatidylcholine, dioleoylphosphatidylcholine, hydrogenated soybean phosphatidylcholine, dipalmitoylphosphatidylcholine, 1,2-dioleoyl-3-trimethylammonium-propane, cholesterol, and N-(carbonylmethoxypoly(ethylene glycol) 2000)-1,2-distearoyl-sn-glycero-3-phosphoethanolamine. By using liposomes of various compositions, we showed that the thermodynamic phase state of the membrane rather than the electric potential or liposome surface modification with poly(ethylene glycol) is the predominant determinant of the bending modulus, which decreased in the following order: solid ordered > liquid ordered > liquid disordered. By using the generalized polarization value of the Laurdan fluorescent probe, we investigated membrane rigidity in terms of membrane fluidity. Atomic force microscopic analysis was superior to the Laurdan method, especially in evaluating the membrane rigidity of liposomes containing hydrogenated soybean phosphatidylcholine and cholesterol. Positively charged liposomes with a large bending modulus were taken up by cells more efficiently than those with a small bending modulus. These findings offer a quantitative method of analyzing the membrane rigidity of nanosized liposomes with different lipid compositions and will contribute to the control of liposome stability and cellular uptake efficiency of liposomal formulations intended for clinical use.

Influence of Charge on the Elastic Properties of Lipid Membranes

Lipid membrane elastic properties play an important role in the membrane deformations and dynamic morphological transitions necessary for cell function. A key elastic property underlying these dynamics is the bending rigidity, motivating significant research efforts to quantify the effects of lipid structure and additives on the membrane bending modulus. To date, the majority of experimental research has focused on the dynamics of model membrane systems composed of zwitterionic lipids; however, most biomembranes are negatively charged at physiological conditions due to the presence of charged lipid headgroups. Here we study the bending dynamics of negatively-charged phosphatidylglycerol (PG) bilayers using neutron spin echo spectroscopy. Our results show that the charged lipid bilayers are softer than analogous zwitterionic phosphatidylcholine (PC) bilayers in both the gel and fluid phases at low ionic strength conditions. Interestingly, theoretical predictions indicate that the opposite should be true and that the bending rigidity should increase with increasing surface charge. We propose that this discrepancy is due to charged-related differences in the area per headgroup and lipid hydration between PG and PC bilayers that are not considered by existing theoretical models. Our results provide new insights into the influence of charge on the membrane elastic properties and demonstrate how these dynamics are coupled to charge effects on the membrane structure.

Understanding Lipid Bilayer Dynamics: Relating Bending and Thickness Fluctuations to Membrane Elasticity

Lipid membranes are highly complex systems with a hierarchy of structure and dynamics that span several decades in length and time scales which in turn have a huge influence on membrane functions. While a large body of research has been dedicated to multiscale structural investigations in such systems, dynamical characterization has lagged far behind. The experimental challenge here is the need to simultaneously access the desired length and time scales for the motions of interest. Over the past decade, neutron spin echo spectroscopy (NSE) has proven to be a unique tool for capturing the collective lipid membrane dynamics on the nanometer and nanosecond scales. For example, lipid membrane bending moduli have been estimated from the relaxation time of single membrane fluctuations in unilamellar vesicles. More recently, lipid membrane thickness fluctuations have also been measured with relaxation times on the order of 100 ns and with amplitudes of a few tenths of nanometers in fluid lipid bilayers. Here we use deformation free energy calculations to connect the experimentally measured thickness fluctuation amplitude to the bilayer elastic parameters: the compressibility modulus and wavelength of the fluctuations. The compressibility modulus is on the order of 10ˆ6 Pa irrespective of saturated tail length in zwitterionic bilayers; however, this value decreases upon mixing lipids with different tail length. Similarly, the fluctuation wavelength is also influenced by lipid composition and is on the order on 20 nm in single component bilayers and increases with temperature in mixed lipid bilayers. It is interesting to note that these fluctuation wavelengths are on the same size scale as laterally inhomogeneous bilayer structures such as the ripple phase and raft domains, which may hint at an interplay between the structure and dynamics in lipid bilayers.

A computer simulation approach to quantify the true area and true area compressibility modulus of biological membranes.

We present a new computational approach to quantify the area per lipid and the area compressibility modulus of biological membranes. Our method relies on the analysis of the membrane fluctuations using our recently introduced coupled undulatory (CU) mode [Tarazona et al., J. Chem. Phys. 139, 094902 (2013)], which provides excellent estimates of the bending modulus of model membranes. Unlike the projected area, widely used in computer simulations of membranes, the CU area is thermodynamically consistent. This new area definition makes it possible to accurately estimate the area of the undulating bilayer, and the area per lipid, by excluding any contributions related to the phospholipid protrusions. We find that the area per phospholipid and the area compressibility modulus features a negligible dependence with system size, making possible their computation using truly small bilayers, involving a few hundred lipids. The area compressibility modulus obtained from the analysis of the CU area fluctuations is fully consistent with the Hooke's law route. Unlike existing methods, our approach relies on a single simulation, and no a priori knowledge of the bending modulus is required. We illustrate our method by analyzing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers using the coarse grained MARTINI force-field. The area per lipid and area compressibility modulus obtained with our method and the MARTINI forcefield are consistent with previous studies of these bilayers.

Electrohydrodynamic instability of a capacitive elastic membrane

The electrohydrodynamic instability of a leaky (weakly conducting) capacitive elastic membrane driven by a direct current electric field, both perpendicular and parallel to the membrane in a micro-fluidic channel, is investigated theoretically. In the leaky dielectric framework, electric charges can accumulate on either side of the membrane, and the effect of the accumulated surface charge depends on the ratio of charge relaxation time in the bulk to the membrane charging time. Under a parallel electric field, a non-conducting membrane can become unstable while under a perpendicular electric field a non-conducting capacitive membrane is always stable and membrane conductance is essential for the membrane instability. The effects of membrane conductance, bending modulus, and charge relaxation time on the membrane instability are elucidated for several combinations of conductivity ratio and permittivity ratio in the bulk fluids. Regions of instability are computed for both the parallel and perpendicular electric fields. The tangential electric field acts similarly to the membrane tension in terms of its damping effects at small length scales (high wave number), while either bending or membrane tension is needed to damp out the small-scale perturbations under a perpendicular electric field.

Membrane Bending Modulus for Ternary Mixture Models of the Cell Plasma Membrane

Ternary mixtures of high-melting lipid, low-melting lipid, and cholesterol exhibit a region of liquid-ordered + liquid-disordered phase coexistence analogous to raft + non-raft behavior in cells. These coexisting phases manifest domain sizes that range from a few nanometers to many microns, depending strongly on the nature of the low-melting lipid. When POPC, which gives rise to nanodomains, is replaced by DOPC, which yields macrodomains, an intermediate region is observed of patterned, or modulated phases. This domain morphology can be explained as a competition between line tension and bending energies with patterns occurring when the two are nearly balanced. Necessary for testing this model are measurements of line tension, and bending moduli for both phases. Here we report the bending moduli of coexisting Lo and Ld phases from mixtures that produce domains ranging in size from nanoscopic to macroscopic. Measurements were made by shape analysis of giant unilamellar vesicles with both fluorescence and phase contrast microscopy. Vesicles of a single phase were made by the gentle hydration method to obtain a more narrow distribution of vesicle tensions than is obtained by electroformation. A transmembrane helical peptide, WALP23, strongly partitions to the liquid disordered phase, and changes the size of coexisting Lo + Ld domains. We are currently investigating the effects of WALP23 on membrane mechanical properties and line tension.

Deployable and Conformal Planar Micro-Devices: Design and Model Validation

We report a design concept for a deployable planar microdevice and the modeling and experimental validation of its mechanical behavior. The device consists of foldable membranes that are suspended between flexible stems and actuated by push-pull wires. Such a deployable device can be introduced into a region of interest in its compact “collapsed” state and then deployed to conformally cover a large two-dimensional surface area for minimally invasive biomedical operations and other engineering applications. We develop and experimentally validate theoretical models based on the energy minimization approach to examine the conformality and figures of merit of the device. The experimental results obtained using model contact surfaces agree well with the prediction and quantitatively highlight the importance of the membrane bending modulus in controlling surface conformality. The present study establishes an early foundation for the mechanical design of this and related deployable planar microdevice concepts.

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.

Two-dimensional strain-hardening membrane model for large deformation behavior of multiple red blood cells in high shear conditions

BackgroundComputational modeling of Red Blood Cell (RBC) flow contributes to the fundamental understanding of microhemodynamics and microcirculation. In order to construct theoretical RBC models, experimental studies on single RBC mechanics have presented a material description for RBC membranes based on their membrane shear, bending and area moduli. These properties have been directly employed in 3D continuum models of RBCs but practical flow analysis with 3D models have been limited by their computationally expensive nature. As such, various researchers have employed 2D models to efficiently and qualitatively study microvessel flows. Currently, the representation of RBC dynamics using 2D models is a limited methodology that breaks down at high shear rates due to excessive and unrealistic stretching.MethodsWe propose a localized scaling of the 2D elastic moduli such that it increases with RBC local membrane strain, thereby accounting for effects such as the Poisson effect and membrane local area incompressibility lost in the 2D simplification. Validation of our 2D Large Deformation (2D-LD) RBC model was achieved by comparing the predicted RBC deformation against the 3D model from literature for the case of a single RBC in simple shear flow under various shear rates (dimensionless shear rate G = 0.05, 0.1, 0.2, 0.5). The multi-cell flow of RBCs (38% Hematocrit) in a 20 μm width microchannel under varying shear rates (50, 150, 150 s-1) was then simulated with our proposed model and the popularly-employed 2D neo-Hookean model in order to evaluate the efficacy of our proposed 2D-LD model.ResultsThe validation set indicated similar RBC deformation for both the 2D-LD and the 3D models across the studied shear rates, highlighting the robustness of our model. The multi-cell simulation indicated that the 2D neo-Hookean model predicts noodle-like RBC shapes at high shear rates (G = 0.5) whereas our 2D-LD model maintains sensible RBC deformations.ConclusionThe ability of the 2D-LD model to limit RBC strain even at high shear rates enables this proposed model to be employed in practical simulations of high shear rate microfluidic flows such as blood separation channels.

Probing Membrane Biomechanics of Erythrocytes Parasitized by <italic>Salmonella paratyphi B</italic> Using Atomic Force Microscopy

Parasitization by Salmonella paratyphi B ( Sp B ) leads to morphological, structural, biochemical component, and mechanical deformation alterations to the host erythrocytes. To probe these modifications at the nanoscale, we apply atomic force microscopy and diffraction phase microscopy to measure the mechanical properties of red blood cell (RBC) membrane infected by Sp B , including deformability, shear modulus and bending modulus. Combining the two techniques with a new mathematical model describing RBC membrane is very sensitive to the invader of parasitic Sp B . The results demonstrated that the growing parasite in their host RBCs caused structure changes and decreased deformation. Coincident with this morphological transition, there is a significant increase in the membrane's shear and bending moduli. This mechanical transition can alter cell circulation and impede oxygen delivery. The results indicated that proteins transported from invading organisms, such as the Ivirulent parasitic Sp B , to specific binding sites in the spectrin network are considered to introduce significant alterations to RBC membrane skeleton network, dynamics and mechanical response. These changes could provide insights into possible mechanistic pathways in the pathogenesis of parasitic Sp B , which may provide new ideas on further experiments and analyses.

Bending rigidity of phosphatidylserine-containing lipid bilayers in acidic aqueous solutions

The elastic properties of anion lipid-containing bilayers were studied in aqueous solutions with fixed ionic strength at pH ≤5. Giant vesicles from stearoyl-oleoyl-phosphatidylcholine (SOPC) with various contents of dioleoyl-phosphatidylserine (DOPS) were obtained via electroformation and observed in phase contrast and fluorescence. Two structural phases were found to coexist in vesicle membranes. Thermal fluctuation spectroscopy of quasispherical vesicles with homogeneous liquid membranes was applied for the quantification of their bending rigidity. The white-noise contribution, significantly influencing the calculated value of the bending modulus, was taken into account in the analysis of the thermal shape fluctuations of vesicles. Electrokinetic measurements with SOPC/DOPS liposomes provided information about their surface potential dependence on pH and also as a function of the DOPS molar content in bilayers. The experimentally obtained values for the bending rigidity of SOPC bilayers containing various amounts of DOPS are reported and discussed in the light of the existing theory for the electrostatic contribution to the bending modulus of charged lipid membranes.

Molecular origins of bending rigidity in lipids with isolated and conjugated double bonds: The effect of cholesterol

We examine the effects of cholesterol (Chol) on the mechanical properties of membranes consisting of 16:0/18:1 POPC lipid and of lipids with conjugated linoleic acid (CLA), cis-9/trans-11 CLA (C9T11) and trans-10/cis-12 CLA (T10C12). Atomistic molecular dynamics (MD) simulations of POPC–Chol and CLA-Chol mixtures at various Chol concentrations are employed within a recently developed and validated computational methodology (Khelashvili et al., 2013) that calculates from MD trajectories the bending rigidity (KC) for these systems. We have found that the addition of 30% Chol stiffens POPC lipid membranes much more significantly (2.3-fold) than it does C9T11 (1.5-fold) or T10C12 (1.75-fold) lipid bilayers. Extensive comparative structural analysis of the simulated mixtures supports a molecular mechanism for the differential effects of cholesterol, whereby the sterol molecules tilt more significantly in CLA membranes where they also insert deeper inside the hydrocarbon core. The observed distinct arrangement of Chol molecules in CLA and POPC bilayers, in turn, is dictated by the interplay between the specific location of the trans double bond in the two CLA lipid isomers and the preferential interaction of the rigid Chol ring with the saturated segments of the lipid tails. The simulations and analysis described in this paper provide novel insights into the specific modes of molecular interaction in bilayers composed of mixtures of Chol and unsaturated lipids that drive emergent macroscopic properties, such as the membrane's bending modulus.

Hiv-1 Tat Membrane Translocation Probed by Low- and Wide-Angle X-Ray Scattering, Neutron Scattering, CD Spectroscopy and MD Simulations

In an effort to understand membrane translocation of a cell-penetrating peptide, interactions of HIV-1 Tat peptide (GRKKRRQRRRPPQ) with DOPC, DOPC/DOPE, DOPC/DOPS, and nuclear membrane mimics were investigated using low- and wide-angle x-ray scattering (LAXS and WAXS), neutron scattering, and circular dichroism (CD) spectroscopy. The diffuse scattering analysis applied to LAXS collected at CHESS revealed that Tat-membrane interactions reduce the membrane thickness by ∼1 A. In DOPC and DOPC/DOPE membranes, the position of Tat was found to transition from the vicinity of the glycerol-carbonyl headgroup to the phosphate headgroup as Tat mole fraction was increased from 0.009 to 0.06. The area per lipid for DOPC and DOPC/DOPE membranes increased by ∼2 A2 at the highest Tat mole fraction. The membrane bending modulus was found to decrease by roughly a factor of 2 at the highest Tat mole fraction except for the nuclear mimic. The chain-orientational order parameter, Sxray, calculated from WAXS and corrected for mosaic spread, showed Tat slightly disordered chains. Neutron scattering collected at NIST from fully hydrated samples consisting of DOPC:DOPE (3:1) membranes and Tat at 0.06 mole fraction showed a prominent, broad peak corresponding to a Tat-membrane correlation of ∼100 A. The secondary structure of Tat calculated from CD spectra using DichroWEB was found to be the same in pure water as in lipid thin films and primarily consisted of β-sheet and random coil with small helical content. Our findings are consistent with the results from MD simulations by Herce and Garcia, which suggested that Tat interacts with phosphate headgroups across the bilayer, facilitating the formation of pores. The ensemble of configurations obtained from a new MD simulation allows visualization of Tat/membrane interactions. Funded by GM44976, GM86801, DMR-0936384(CHESS), and DOE(NIST).

APPLICATION OF DISSIPATIVE PARTICLE DYNAMICS TO THE STUDY OF A RED BLOOD CELL IN SIMPLE SHEAR FLOW

The present work reports an attempt to apply the dissipative particle dynamics (DPD) method to study the dynamic behaviors of a red blood cell (RBC) in simple shear flow. The simulation system is discretized into four types of particles, namely wall particles, fluid particles, membrane particles and internal particles. The particle interaction is modeled by the DPD method, and the membrane particles are connected into a viscoelastic triangular network to represent the RBC membrane. As benchmarking tests, we simulate the deformation of a spherical capsule in shear flow and compare it with the past study, and also examine the effect of computational domain size. After that, we investigate the dynamics of a RBC in shear flow at different membrane shear and bending moduli. Our simulations reproduce the tank-treading, trembling and tumbling motions of the RBC at the shear modulus Es = 6, 60 and 600 μN/m, respectively. Moreover, we find that the RBC undergoes a trembling motion when its bending modulus is large enough, where the obvious stretching and smoothing of the RBC occur alternately in shape.

Robust Measurement of Membrane Bending Moduli Using Light Sheet Fluorescence Imaging of Vesicle Fluctuations

The mechanical rigidity of lipid membranes is a key determinant of the energetics of cellular membrane deformation. Measurements of membrane bending moduli remain rare, however, and show a large variance, a situation that can be addressed by the development of improved techniques and by comparisons between disparate techniques applied to the same systems. We introduce here the use of selective plane illumination microscopy (SPIM, also known as light sheet fluorescence microscopy) to image thermal fluctuations of giant vesicles. The optical sectioning of SPIM enables high-speed fluorescence imaging of freely suspended vesicles and quantification of edge localization precision, yielding robust fluctuation spectra and rigidity estimates. For both lipid-only membranes and membranes bound by the intracellular trafficking protein Sar1p, which lowers membrane rigidity in a concentration-dependent manner, we show that the resulting bending modulus values are in close agreement with those derived from an independent assay based on membrane tether pulling. We also show that the fluctuation spectra of vesicles bound by the mammalian Sar1A protein, which stiffens membranes at high concentrations, are not well fit by a model of homogeneous quasi-spherical vesicles, suggesting that SPIM-based analysis can offer insights into spatially inhomogeneous properties induced by protein assemblies.

Multiphasic Effects of Cholesterol on Influenza Fusion Kinetics Reflect Multiple Mechanistic Roles

The envelope lipid composition of influenza virus differs from that of the cellular plasma membrane from which it buds. Viruses also appear to fuse preferentially to specific membrane compartments, suggesting that the lipid environment may influence permissiveness for fusion. Here, we investigated the influence of the membrane environment on fusion, focusing on cholesterol composition. Strikingly, manipulating cholesterol levels in the viral membrane had different effects on fusion kinetics compared with analogous changes to the target membrane. Increasing cholesterol content in target vesicles increased lipid- and contents-mixing rates. Moderate cholesterol depletion from the viral membrane sped fusion rates, whereas severe depletion slowed the process. The pleiotropic effects of cholesterol include alterations in both membrane-bending moduli and lateral organization. Because influenza virions have demonstrated cholesterol-dependent lateral organization, to separate these effects, we deliberately selected a target vesicle composition that does not support lateral heterogeneity. We therefore postulate that the monotonic response of fusion kinetics to target membrane cholesterol reflects bending and curvature effects, whereas the multiphasic response to viral cholesterol levels reflects the combined effects of lateral organization and material properties.

Determining the bending modulus of a lipid membrane by simulating buckling

The force needed to buckle a thin elastic surface is proportional to its bending rigidity. This fact suggests using a buckling setup to measure the bending modulus of lipid membranes. Extending the work of Noguchi [Phys. Rev. E 83, 061919 (2011)], we systematically derive highly accurate analytical expressions for the forces along and perpendicular to the buckle, and we elucidate some of their counterintuitive properties using the framework of a surface stress tensor. Furthermore, we estimate the corrections to buckling forces due to thermal fluctuations and find them significant only for stresses along the ridges. We then apply this buckling protocol to four different lipid membrane models, which widely differ in their level of resolution and the treatment of solvent, and show that in all cases buckling is a reliable and accurate means for measuring their rigidity. Finally, we show that monitoring both stresses and energies during a simulation offers additional insights into the thermodynamics of curvature elasticity and permits one to predict the bending rigidity for a range of temperatures around the actual simulation temperature.

Optical stretching as a tool to investigate the mechanical properties of lipid bilayers.

Measurements of lipid bilayer bending modulus by various techniques produce widely divergent results. We attempt to resolve some of this ambiguity by measuring bending modulus in a system that can rapidly process large numbers of samples, yielding population statistics. This system is based on optical stretching of giant unilamellar vesicles (GUVs) in a microfluidic dual-beam optical trap (DBOT). The microfluidic DBOT system is used here to measure three populations of GUVs with distinct lipid compositions. We find that gel-phase membranes are significantly stiffer than liquid-phase membranes, consistent with previous reports. We also find that the addition of cholesterol does not alter the bending modulus of membranes composed of a monounsaturated phospholipid.

Experimental study of the bending elasticity of charged lipid bilayers in aqueous solutions with pH5

Exposure to high concentrations of contaminations due to air polluting gases, vapours and aerosols and possibly altering the normal pH in the body could lead to undesirable changes in the properties of biological cells. Here, we study experimentally the mechanical properties of synthetic phospholipid bilayers containing increasing molar fractions (up to 0.15) of charged lipid (synthetic phosphatidylserine) in aqueous solutions with controlled ionic strength and at pH 5, which is slightly lower than the physiological values of pH. Our observations in phase contrast and fluorescence testified to the coexistence of two phases in membranes for temperatures below 29°C. Micro-sized inhomogeneities in vesicle membranes were systematically observed at temperatures lower than 29°C and for molar fractions of phosphatidylserine in the bilayer higher than 0.1. For the quantitative determination of the membrane bending rigidity, we applied thermal fluctuation analysis of the shape of quasispherical lipid vesicles. As far as the liquid-crystalline state of the bilayer is a necessary condition for the application of the experimental method, only vesicles satisfying this requirement were processed for determination of their membrane bending rigidity. The value obtained for the bending modulus of bilayers with 0.15 molar content of charged lipid is about two times higher than the bending modulus of uncharged membranes in the same bathing solution. These findings are in qualitative agreement with our previous results for the bending rigidity of charged bilayers, measured by vesicle micromanipulation.