Membrane Elastic Properties Research Articles

A One-Dimensional Continuum Elastic Model for Membrane-Embedded Gramicidin Dimer Dissociation

Membrane elastic properties, which are subject to alteration by compounds such as cholesterol, lipid metabolites and other amphiphiles, as well as pharmaceuticals, can have important effects on membrane proteins. A useful tool for measuring some of these effects is the gramicidin A channels, which are formed by transmembrane dimerization of non-conducting subunits that reside in each bilayer leaflet. The length of the conducting channels is less than the bilayer thickness, meaning that channel formation is associated with a local bilayer deformation. Electrophysiological studies have shown that the dimer becomes increasingly destabilized as the hydrophobic mismatch between the channel and the host bilayer increases. That is, the bilayer imposes a disjoining force on the channel, which grows larger with increasing hydrophobic mismatch. The energetic analysis of the channel-bilayer coupling is usually pursued assuming that each subunit, as well as the subunit-subunit interface, is rigid. Here we relax the latter assumption and explore how the bilayer junction responds to changes in this disjoining force using a simple one-dimensional energetic model, which reproduces key features of the bilayer regulation of gramicidin channel lifetimes.

Contribution of Membrane Elastic Energy to Rhodopsin Function

We considered the issue of whether shifts in the metarhodopsin I (MI)-metarhodopsin II (MII) equilibrium from lipid composition are fully explicable by differences in bilayer curvature elastic stress. A series of six lipids with known spontaneous radii of monolayer curvature and bending elastic moduli were added at increasing concentrations to the matrix lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and the MI-MII equilibrium measured by flash photolysis followed by recording UV-vis spectra. The average area-per-lipid molecule and the membrane hydrophobic thickness were derived from measurements of the 2H NMR order parameter profile of the palmitic acid chain in POPC. For the series of ethanolamines with different levels of headgroup methylation, shifts in the MI-MII equilibrium correlated with changes in membrane elastic properties as expressed by the product of spontaneous radius of monolayer curvature, bending elastic modulus, and lateral area per molecule. However, for the entire series of lipids, elastic energy explained the shifts only partially. Additional contributions correlated with the capability of the ethanolamine headgroups to engage in hydrogen bonding with the protein, independent of the state of ethanolamine methylation, with introduction of polyunsaturated sn-2 hydrocarbon chains, and with replacement of the palmitic acid sn-1 chains by oleic acid. The experiments point to the importance of interactions of rhodopsin with particular lipid species in the first layer of lipids surrounding the protein as well as to membrane elastic stress in the lipid-protein domain.

Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell

A two-dimensional computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under steady shear flow. The RBC model consisted of an outer cellular membrane and an inner fluid; the membrane's elastic properties were modeled by springs for stretch/compression and bending to consider the membrane's natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. The proposed simulation model was capable of reproducing tank-treading and tumbling motions of an RBC along with rotational oscillation, which is the transition between the two motions. In simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. Simulation results corresponded to published data from experimental and computational studies. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was approximately 1 at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force. A combination of natural state nonuniformity and elastic spring constant determined that change in the RBC deformation at the transition is that from a large compressive deformation to no deformation, such as rigid body.

Molecular modeling of key elastic properties for inhomogeneous lipid bilayers

Fusion and fission of biological membranes play a crucial role in intracellular transport. Until recently, it was believed that membrane shape transformations involved in these processes are driven by proteins. However, recent evidence shows that lipids, by themselves, can drive membrane deformations. It has been hypothesized that the localized formation of certain lipids changes elastic properties of a membrane in such a way that the membrane deforms spontaneously. This study represents a step towards a systematic investigation of the role of various lipids in local changes of membrane elastic properties. We use coarse-grained molecular dynamics (CGMD) simulations to determine possible effects of addition of phosphatidylinositol-4-phosphate (PI4P) lipids on elastic properties of dipalmitoyl phosphatidyl choline (DPPC) lipid bilayers. We investigate the splay (bending) and the molecular tilt moduli of mixed DPPC/PI4P bilayers, as well as the line tension between domains of pure DPPC and mixed DPPC/PI4P bilayers. Although our results indicate negligible effects of PI4P on elastic properties of DPPC bilayers, the developed methodology can be applied to a wide range of lipid systems.

Effects of incubation pH on the membrane deformation of a single living human red blood cell

Abstract The effects of incubation pH on the morphology, the surface charge and the deformability of a single living human red blood cell (RBC) were studied. A novel multi-dimensional microscope was employed to perform real time, non-invasive in situ measurements on the cell shape and size, as well as the membrane bending and shearing elastic moduli of the cell. A phase-analysis micro-electrophoresis laser scattering technique was used to measure the surface charge density. It was shown that the incubation pH markedly influences the surface charge density and the membrane elastic properties of the RBCs and thus leads to a change in their morphology and deformability.

In vivo areal modulus of elasticity estimation of the human tympanic membrane system: modelling of middle ear mechanical function in normal young and aged ears

The quasi-static elastic properties of the tympanic membrane system can be described by the areal modulus of elasticity determined by a middle ear model. The response of the tympanic membrane to quasi-static pressure changes is determined by its elastic properties. Several clinical problems are related to these, but studies are few and mostly not comparable. The elastic properties of membranes can be described by the areal modulus, and these may also be susceptible to age-related changes reflected by changes in the areal modulus. The areal modulus is determined by the relationship between membrane tension and change of the surface area relative to the undeformed surface area. A middle ear model determined the tension–strain relationship in vivo based on data from experimental pressure–volume deformations of the human tympanic membrane system. The areal modulus was determined in both a younger (n = 10) and an older (n = 10) group of normal subjects. The areal modulus for lateral and medial displacement of the tympanic membrane system was smaller in the older group (mean = 0.686 and 0.828 kN m−1, respectively) compared to the younger group (mean = 1.066 and 1.206 kN m−1, respectively), though not significantly (2p = 0.10 and 0.11, respectively). Based on the model the areal modulus was established describing the summated elastic properties of the tympanic membrane system. Future model improvements include exact determination of the tympanic membrane area accounting for its shape via 3D finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2–3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus.

Elastic properties of biological membranes influenced by attached proteins

Positively charged proteins can attach themselves to the negatively charged outer surface of biological cell membranes and liposomes. In this work, the influence of the intrinsic shape of the membrane-attached proteins on the elastic properties of the membrane is considered theoretically. It is shown that attachment of anisotropic proteins to the outer surface of biological membranes may induce tubulation of the membrane. The attachment of semi-flexible rod-like proteins increases the local bending constant, while the attachment of semi-flexible plate-like anisotropic proteins may also reduce the local bending constant of the membrane. The role of the hydrophobic protrusion of the attached protein which is embedded in the outer membrane layer is also discussed.

Evidence for Specificity in Lipid-Rhodopsin Interactions

The interaction of bovine rhodopsin with poly- and monounsaturated lipids was studied by (1)H MAS NMR with magnetization transfer from rhodopsin to lipid. Experiments were conducted on bovine rod outer segment (ROS) disks and on recombinant membranes containing lipids with polyunsaturated, docosahexaenoyl (DHA) chains. Poly- and monounsaturated lipids interact specifically with different sites on the rhodopsin surface. Rates of magnetization transfer from protein to DHA are lipid headgroup-dependent and increased in the sequence PC < PS < PE. Boundary lipids are in fast exchange with the lipid matrix on a time scale of milliseconds or shorter. All rhodopsin photointermediates transferred magnetization preferentially to DHA-containing lipids, but highest rates were observed for Meta-III rhodopsin. The experiments show clearly that the surface of rhodopsin has sites for specific interaction with lipids. Current theories of lipid-protein interaction do not account for such surface heterogeneity.

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.

Universal Behavior of Membranes with Sterols

Lanosterol is the biosynthetic precursor of cholesterol and ergosterol, sterols that predominate in the membranes of mammals and lower eukaryotes, respectively. These three sterols are structurally quite similar, yet their relative effects on membranes have been shown to differ. Here we study the effects of cholesterol, lanosterol, and ergosterol on 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphatidylcholine lipid bilayers at room temperature. Micropipette aspiration is used to determine membrane material properties (area compressibility modulus), and information about lipid chain order (first moments) is obtained from deuterium nuclear magnetic resonance. We compare these results, along with data for membrane-bending rigidity, to explore the relationship between membrane hydrophobic thickness and elastic properties. Together, such diverse approaches demonstrate that membrane properties are affected to different degrees by these structurally distinct sterols, yet nonetheless exhibit universal behavior.

How proteins produce cellular membrane curvature

Biological membranes exhibit various function-related shapes, and the mechanism by which these shapes are created is largely unclear. Here, we classify possible curvature-generating mechanisms that are provided by lipids that constitute the membrane bilayer and by proteins that interact with, or are embedded in, the membrane. We describe membrane elastic properties in order to formulate the structural and energetic requirements of proteins and lipids that would enable them to work together to generate the membrane shapes seen during intracellular trafficking.

Exploring soft matter: Liposomal vesicles and their tethers

The malleability of soft matter such as vesicular systems, allows their mechanical manipulation into various interesting structures. Their inherent elastic membrane properties can be utilized in fabricating micro-scaled transport machineries. In this paper, we have described several features of research carried out in our laboratory. This includes the self-healing ability of multilamellar liposome on removal of their inner core. The formation of tethers from their outer bilayers into complex networks has been demonstrated. Photo enhancement of images has revealed the apparent existence of narrow channels inside such tethers. The tethers channels were subsequently used as transport conduits to carry solid polystyrene microspheres as well as large liposomes larger than the tether diameter under controllable speeds of up to 2 μm s− 1. The possibility of producing multi-compartment liposomal systems connected to each other directly by fusion or indirectly via tether networks has provided us with a system capable of transporting components from one vesicle entity to another.

Electroendocytosis: Exposure of Cells to Pulsed Low Electric Fields Enhances Adsorption and Uptake of Macromolecules

This study demonstrates alteration of cell surface, leading to enhanced adsorption of macromolecules (bovine serum albumin (BSA), dextran, and DNA), after the exposure of cells to unipolar pulsed low electric fields (LEF). Modification of the adsorptive properties of the cell membrane also stems from the observation of LEF-induced cell-cell aggregation. Analysis of the adsorption isotherms of BSA-fluorescein isothiocyanate (FITC) to the surface of COS 5-7 cells reveals that the stimulated adsorption can be attributed to LEF-induced increase in the capacity of both specific and nonspecific binding. The enhanced adsorption was consequently followed by increased uptake. At 20 V/cm the maximal binding and subsequent uptake of BSA-FITC attached to specific sites are 6.5- and 7.4-fold higher than in controls, respectively. The nonspecific LEF-induced binding and uptake of BSA are 34- and 5.2-fold higher than in controls. LEF-enhanced adsorption is a temperature-independent process, whereas LEF-induced uptake is a temperature-dependent one that is abolished at 4°C. The stimulation of adsorption and uptake is reversible, revealing similar decay kinetics at room temperature. It is suggested that electrophoretic segregation of charged components in the outer leaflet of the cell membrane is responsible for both enhanced adsorption and stimulated uptake via changes of the membrane elastic properties that enhance budding and fission processes.

Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus

We analyze the deformation and bursting process of nonspherical organosiloxane capsules in centrifugal fields. Measurements were performed in a commercial spinning-drop tensiometer at different values of tube rotation. A theoretical analysis of the mechanics of initially ellipsoidal elastic shells subjected to centrifugal forces is developed where the deformation of the capsule is predicted as a function of the initial geometry and membrane elastic properties. For different types of organosiloxane membranes the Poisson number varies between 0 and 0.9. This phenomenon points to a considerable reduction of the membrane thickness at the onset of mechanical stress. Membrane-breaking processes always initiated at one of the pole ends of the capsules. Such rupture processes can be interpreted in terms of the derived theoretical model.

Curvature elasticity of mixed amphiphilic bilayers.

Elastic bending constants of mixed amphiphilic bilayers are calculated using a molecular approach. The free energy is expanded up to quadratic order in curvatures and compositions, choosing a flat symmetrical bilayer as the reference state. Bending constants are then calculated from the derivatives of the free energy evaluated at this reference state. Two-component bilayers are considered. As a novelty, the local compositions are allowed to fully relax upon bending so that the 2 monolayers are at chemical equilibrium with each other at every curvature. The compositional degree of freedom is shown to affect the bending constant k, but not the saddle-splay constant k. The influence on the membrane elastic properties of various chain structural features, such as length, volume, and stiffness, is investigated. This may prove useful to model mixed bilayers composed of hydrocarbon/hydrocarbon and hydrocarbon/fluorocarbon chains.

A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction.

Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.

An experimental/computational approach to identify moduli and residual stress in MEMS radio-frequency switches

In this paper, we identify the Young's modulus and residual stress state of a free-standing thin aluminum membrane, used in MEMS radio-frequency (rf) switches. We have developed a new methodology that combines a membrane deflection experiment (MDE) and three-dimensional numerical simulations. Wafer-level MDE tests were conducted with a commercially available nanoindenter. The accuracy and usefulness of the MDE is confirmed by the repeatability and uniformity of measured load-deflection curves on a number of switches with both wedge and Berkovich tips. It was found that the load-deflection behavior is a function of membrane elastic properties, initial residual stress state and corresponding membrane shape. Furthermore, it was assessed that initial membrane shape has a strong effect on load-deflection curves; hence, its accurate characterization is critical. Through an iterative process and comparison between MDE data and numerical simulations, the Young's modulus and residual stress state, consistent with measured membrane shape, were identified. One important finding from this investigation is that variations in membrane elastic properties and residual stress state affect the load-deflection curve in different regimes. Changes in residual stress state significantly affect the load-deflection slope at small values of deflection. By contrast, variations in Young's modulus result in changes in load-deflection slope at large deflections. These features are helpful to decouple both effects in the identification process.

Osmotic swelling and hole formation in membranes of thalassemic and spherocytic erythrocytes

Osmotic swelling and kinetics of the pore formation in the membranes of spherocytic, thalassemic, and normal erythrocytes were studied by measuring the time-dependent capacitance and conductance at a frequency of 0.2 MHz. No significant difference between the swelling rate of control and spherocytic cells was observed, whereas slower kinetics of swelling were found for thalassemic cells. Time records of the conductance indicate that the probability of the pore formation in the stretched membrances varies in the following order: thalassemia < control < spherocytosis. Based on these findings it was concluded that the erythrocyte swelling is controlled by the initial cell shape, volume, intracellular hemoglobin concentration, and elastic membrane properties, whereas the kinetics of the pore formation depend solely on the resistivity of the stretched membrane of the swollen RBC to the osmotic shock. Therefore, it was assumed that investigations of the pore formation may be used not only for examinations of spherocytic and thalassemic cells, but also for normocytic, normochromic, biconcave-shaped RBCs with altered membrane elasticity.

Interaction of Surfactant Lamellar Phase and a Strictly Alternating Comb-Graft Amphiphilic Polymer Based on PEG

We study the effect of hydrophobically modified polymers (hm-polymers) on the phase behavior and membrane elastic properties of the lyotropic lamellar (Lα) phase of the nonionic surfactant penta(ethylene glycol) dodecyl ether (C12E5). The hm-polymer is a model comb-graft polymer with monodisperse PEG blocks (loops) of 6, 12, or 35 kg/mol connecting C18 stearylamide hydrophobes. The polymer is of interest because both its loops and hydrophobes are biocompatible. The membrane properties are extracted from the small-angle neutron scattering data based on the model of Nallet et al. The monophasic Lα region exists over a narrower membrane volume fraction range but to a higher polymer concentration for hmPEGs with larger PEG spacers. The rigidity of the membranes increases by 40% with decreasing PEG spacer size from 12 to 6 kg/mol or increasing polymer concentration. For hmPEG polymers with 2−3 loops, the effect of finite chain lengths plays a role on the phase behavior and membrane properties.

Interaction of Hydrophobically Modified Polymers and Surfactant Lamellar Phase

We investigate the effect of polysoaps on the phase behavior and membrane elastic properties of the lyotropic lamellar (Lα) phase of the nonionic surfactant penta(ethylene glycol) dodecyl ether (C12E5). The polysoap is a hydrophobically modified polymer (hm-polymer) with n-alkyl side groups randomly grafted to a polyacrylate (PAA) backbone. The membrane properties are extracted from small-angle neutron scattering data based on a model developed by Nallet et al. and the excess area method developed by Roux et al. The phase behavior, membrane rigidity, compression modulus, and bilayer mean bending modulus are found to be independent of molecular weight, polydispersity, and hydrophobe length of hm-polymers. The rigidity and compression moduli of membranes increase with increasing polymer concentration and hydrophobe substitution level. A minimum hydrophobic interaction strength (combination of hydrophobe length and hydrophobe substitution level) is required to produce single phase polysoap/lamellar surfactant systems. A scaling model is proposed that defines the boundaries between homogeneous and biphasic solutions based on two criteria: (1) the surface coverage of chain segments between hydrophobes (i.e. blobs) must be less than the available membrane area and (2) the interlamellar spacing must be larger than the blob size. This simple model captures the essential features of the phase diagrams.