Membrane stretching elasticity and thermal shape fluctuations of nearly spherical lipid vesicles.

One of the most widely used methods for determination of the bending elasticity modulus of model lipid membranes is the analysis of the shape fluctuations of nearly spherical lipid vesicles. The theoretical basis of this analysis is given by Milner and Safran [Phys. Rev. A 36, 4371 (1987)0556-279110.1103/PhysRevA.36.4371]. In their theory the stretching effects are not considered. In the present study we generalized their approach including the stretching effects deduced after application of the statistical mechanics to vesicles.

Digital holographic microscopy as a tool to study the thermal shape fluctuations of lipid vesicles.

The bending elasticity modulus of lipid membranes is obtained by applying for the first time, to the best of our knowledge, a novel experimental technique based on digital holographic microscopy. The fluctuations of the radius with time were extracted by tracking and measuring the optical thickness at the vesicle poles. The temporal autocorrelation function of the vesicle diameter computed for each of the studied vesicles was then fitted with the theoretical expression to deduce the membrane's tension and bending constant. For the bending elasticity modulus of SOPC bilayers, the value of (0.93 ± 0.03) × 10(-12) erg was obtained. This result is in accordance with values previously obtained by means of other conventional methods for the same type of lipid membrane in the presence of sugar molecules in aqueous medium. The obtained results encourage the future development of the digital holographic microscopy as a technique suitable for the measurement of the bending elasticity of lipid membranes.

Bending elasticity of vesicle membranes studied by Monte Carlo simulations of vesicle thermal shape fluctuations.

The membrane bending stiffness of nearly spherical lipid vesicles can be deduced from the analysis of their thermal shape fluctuations. The theoretical basis of this analysis [Milner and Safran, Phys. Rev. A: At., Mol., Opt. Phys., 1987, 36, 4371-4379] uses the mean field approximation. In this work we apply Monte Carlo simulations and estimate the error in the determination of the bending stiffness due to the approximations applied in the theory. It is less than 10%. The method presented in this work can also be used to determine the changes of the bending stiffness of biological membranes due to their chemical and/or structural modifications.

Bending elasticity modulus of giant vesicles composed of aeropyrum pernix k1 archaeal lipid.

Thermally induced shape fluctuations were used to study elastic properties of giant vesicles composed of archaeal lipids C25,25-archetidyl (glucosyl) inositol and C25,25-archetidylinositol isolated from lyophilised Aeropyrum pernix K1 cells. Giant vesicles were created by electroformation in pure water environment. Stroboscopic illumination using a xenon flash lamp was implemented to remove the blur effect due to the finite integration time of the camera and to obtain an instant picture of the fluctuating vesicle shape. The mean weighted value of the bending elasticity modulus kc of the archaeal membrane determined from the measurements meeting the entire set of qualification criteria was (1.89 ± 0.18) × 10-19 J, which is similar to the values obtained for a membrane composed of the eukaryotic phospholipids SOPC (1.88 ± 0.17) × 10-19 J and POPC (2.00 ± 0.21) ´ 10-19 J. We conclude that membranes composed of archaeal lipids isolated from Aeropyrum pernix K1 cells have similar elastic properties as membranes composed of eukaryotic lipids. This fact, together with the importance of the elastic properties for the normal circulation through blood system, provides further evidence in favor of expectations that archaeal lipids could be appropriate for the design of drug delivery systems.

Registration and analysis of the shape fluctuations of nearly spherical lipid vesicles.

The analysis of shape fluctuations of giant nearly spherical lipid vesicles observed via optical microscopy is one of the widely used methods for the determination of the bending elasticity of lipid membranes. Although the method has been used already for three decades, the values of this material constant, obtained by different groups for membranes of the same composition, in identical conditions, differ significantly. The aim of the present work is the development of the method, enabling us to avoid the influence of artifacts on the value of the measured bending modulus. This is achieved by rejection of some images of the vesicle or the whole vesicle when they do not satisfy the requirements (selection criteria) of the applied theory. The bending modulus of 1-stearoyl-2-oleoyl-sn-glycerol-3-phosphocholine lipid membranes is determined via the advanced method described here. The results are compared with the values in the literature and their difference is discussed.

Shape fluctuations of nearly spherical lipid vesicles and emulsion droplets.

It is known that the relaxation of the shape fluctuations of nearly spherical lipid vesicles is accompanied by a lateral displacement of the monolayers, comprising their bilayers. In this work a dissipation mechanism of the mechanical energy stored in the fluctuation is revealed that concerns the viscous friction of the flow in the liquid around the vesicle caused by this displacement. The time correlation functions of each of the vesicle's fluctuation modes are calculated as a function of the mechanical and rheological properties of the system which are the tension of the vesicle bilayer, its bending elasticities at free and blocked flip-flop, the viscosities of the liquids bathing the bilayer, the friction coefficient between the two monolayers, as well as the vesicle's dimensions: its bilayer thickness and radius. The correlations of the shape fluctuations of nearly spherical emulsion droplets are also calculated for different viscosities of the liquid inside and outside the droplet.

Alamethicin influence on the membrane bending elasticity.

We investigate the bending elasticity of lipid membranes with the increase of the alamethicin concentrations in the membrane via analysis of the thermally induced shape fluctuations of quasi-spherical giant vesicles. Our experimental results prove the strong influence of alamethicin molecules on the bending elasticity of diphytanoyl phosphatidylcholine and dilauroyl phosphatidylcholine membranes even in the range of very low peptide concentrations (less than 10(-3) mol/mol in the membrane). The results presented in this work, testify to the peripheral orientation of alamethicin molecules at low peptide concentrations in the membrane for both types of lipid bilayers. An upper limit of the concentration of the peptide in the membrane is determined below which the system behaves as an ideal two-dimensional solution and the peptide molecules have a planar orientation in the membrane.

Fields and forces acting on a planar membrane with a conducting channel.

Modeling electric fields and forces around a channel in a planar membrane is still an open problem. Until now, most of the existing theories have oversimplified the electric field distribution by placing the electrode directly at the entry of the channel. However, in any relevant experimental setup the electrodes are placed far away in the electrolyte solution. We demonstrate that long-range deformation of the electric field distribution appears around the membrane, spanning on distances of the order of the distance between the membrane and the electrode. The forces acting due to this distribution are in most of the cases negligible. They can be important for channels with radii of the order of the thickness of the layer of structured water at the oil-water interface.

Permeability and the hidden area of lipid bilayers.

The passive water permeability of a lipid vesicle membrane was studied, related to the hydrostatic (not osmotic) pressure difference between the inner and the outer side of the vesicle in a water environment without additives. Each pressure difference was created by sucking a vesicle into a micropipette at a given sucking pressure. The part of the membrane sucked into the micropipette (the projection length) was measured as a function of time. The time dependence can be divided into two intervals. We put forward the idea that smoothing of membrane defects, accompanied by an increase of the membrane area, takes place during the initial time interval, which results in a faster increase of the projection length. In the second time interval the volume of the vesicle decreases due to the permeability of its membrane and the increase of the projection length is slower. The hidden area and the water permeability of a typical lipid bilayer were estimated. The measured permeability, conjugated to the hydrostatic pressure difference, is an order of magnitude higher than the known value of the permeability, conjugated to the osmotic pressure difference. A hypothesis, based on pore formation, is proposed as an explanation of this experimental result.

Bending elasticity and bending fluctuations of lipid bilayer containing an additive.

The static and dynamic behavior of a bilayer containing an additive is examined theoretically. We have proved that the amplitudes of the thermal shape fluctuations of a quasi spherical lipid vesicle depend on the value of the bending elasticity of the vesicle's membrane at free exchange of molecules between its constituent monolayers. The dependence is calculated of this bending elasticity as a function of the concentration of the additive in the low concentration domain. In the same domain, the autocorrelation function of each vesicle fluctuation mode is found to be dependent on the two-dimensional diffusion coefficient of the bilayer additive.