Transport methods for probing the barrier domain of lipid bilayer membranes.

Two experimental techniques have been utilized to explore the barrier properties of lecithin/decane bilayer membranes with the aim of determining the contributions of various domains within the bilayer to the overall barrier. The thickness of lecithin/decane bilayers was systematically varied by modulating the chemical potential of decane in the annulus surrounding the bilayer using different mole fractions of squalene in decane. The dependence of permeability of a model permeant (acetamide) on the thickness of the solvent-filled region of the bilayer was assessed in these bilayers to determine the contribution of this region to the overall barrier. The flux of acetamide was found to vary linearly with bilayer area with Pm = (2.9 +/- 0.3) x 10(-4) cm s-1, after correcting for diffusion through unstirred water layers. The ratio between the overall membrane permeability coefficient and that calculated for diffusion through the hydrocarbon core in membranes having maximum thickness was 0.24, suggesting that the solvent domain contributes only slightly to the overall barrier properties. Consistent with these results, the permeability of acetamide was found to be independent of bilayer thickness. The relative contributions of the bilayer interface and ordered hydrocarbon regions to the transport barrier may be evaluated qualitatively by exploring the effective chemical nature of the barrier microenvironment. This may be probed by comparing functional group contributions to transport with those obtained for partitioning between water and various model bulk solvents ranging in polarity or hydrogen-bonding potential. A novel approach is described for obtaining group contributions to transport using ionizable permeants and pH adjustment. Using this approach, bilayer permeability coefficients of p-toluic acid and p-hydroxymethyl benzoic acid were determined to be 1.1 +/- 0.2 cm s-1 and (1.6 +/- 0.4) x 10(-3) cm s-1, respectively. From these values, the -OH group contribution to bilayer transport [delta(delta G0-OH)] was found to be 3.9 kcal/mol. This result suggests that the barrier region of the bilayer does not resemble the hydrogen-bonding environment found in octanol, but is somewhat less selective (more polar) than a hydrocarbon solvent.     

Permeability of membranes to amino acids and modified amino acids: Mechanisms involved in translocation

Summary The amino acid permeability of membranes is of interest because they are one of the key solutes involved in cell function. Membrane permeability coefficients (P) for amino acid classes, including neutral, polar, hydrophobic, and charged species, have been measured and compared using a variety of techniques. Decreasing lipid chain length increased permeability slightly (5-fold), while variations in pH had only minor effects on the permeability coefficients of the amino acids tested in liposomes. Increasing the membrane surface charge increased the permeability of amino acids of the opposite charge, while increasing the cholesterol content decreased membrane permeability. The permeability coefficients for most amino acids tested were surprisingly similar to those previously measured for monovalent cations such as sodium and potassium (approximately 10^–12–10^–13 cm · s^–1). This observation suggests that the permeation rates for the neutral, polar and charged amino acids are controlled by bilayer fluctuations and transient defects, rather than partition coefficients and Born energy barriers. Hydrophobic amino acids were 10² more permeable than the hydrophilic forms, reflecting their increased partition coefficient values.External pH had dramatic effects on the permeation rates for the modified amino acid lysine methyl ester in response to transmembrane pH gradients. It was established that lysine methyl ester and other modified short peptides permeate rapidly (P = 10^–2 cm · s^–1) as neutral (deprotonated) molecules. It was also shown that charge distributions dramatically alter permeation rates for modified di-peptides. These results may relate to the movement of peptides through membranes during protein translocation and to the origin of cellular membrane transport on the early Earth.Abbreviations DCP dicetylphosphate - DMPC dimyristoyl phosphatidylcholine - EPC egg phosphatidylcholine - LUV large unilamellar vesicle - MLV multilamellar vesicle - PLM planar lipid membrane - SUV small unilamellar vesicle - pH transmembrane pH gradient     

Cellular lipidomics

The cellular lipidome comprises over 1000 different lipids. Most lipids look similar having a polar head and hydrophobic tails. Still, cells recognize lipids with exquisite specificity. The functionality of lipids is determined by their local concentration, which varies between organelles, between the two leaflets of the lipid bilayer and even within the lateral plane of the membrane. To incorporate function, cellular lipidomics must not only determine which lipids are present but also the concentration of each lipid at each specific intracellular location in time and the lipid's interaction partners. Moreover, cellular lipidomics must include the enzymes of lipid metabolism and transport, their specificity, localization and regulation. Finally, it requires a thorough understanding of the physical properties of lipids and membranes, especially lipid-lipid and lipid-protein interactions. In the context of a cell, the complex relationships between metabolites can only be understood by viewing them as an integrated system. Cellular lipidomics provides a framework for understanding and manipulating the vital role of lipids, especially in membrane transport and sorting and in cell signaling.     

Effect of incorporation of drugs,vitamins and peptides on the structure and dynamics of lipid assemblies

The characteristics of vesicles formed from Dipalmitoyl Phosphatidyl Choline (DPPC) are sensitive to the presence of perturbing molecules such as drugs, peptides, hormones and vitamins. We have used ESR spin labeling and NMR techniques for studying interaction of such molecules with lipid bilayers. ESR spin labeling has been used to monitor thermotropic behaviour of model membranes. Different NMR probes such as¹H,³¹P,¹³C have been used to gather information regarding the mode of interaction. It has been observed that the model membrane systems respond differently depending upon the localization of the perturbing molecules in the lipid bilayer. Small molecules such as neurotransmitters epinephrine and norepinephrine decrease gel to liquid crystalline phase transition temperature significantly even when present in small amounts. Vitamine E acetate having a hydrophobic hydrocarbon tail orients parallel to the lipid molecule and thereby exhibits dynamics similar to palmitate chain. When the acetate group is replaced by hydroxyl group (-tocopherol), the phase transition becomes broad and the lipid molecules loose freedom of lateral diffusion. This can be attributed to formation of hydrogen bond between the hydroxyl group of -tocopherol and phosphate moiety of lipid. The conformation of antidepressants nitroxazepine and imipramine is significantly altered when embedded in lipid bilayer. Anaesthetic etomidate not only modifies thermotropic characteristics but also induces polymorphism. The normal bilayer arrangement of lipids gets transformed into hexagonal packing. Amino acid tryptophan induces cubic phases in the normal bilayer arrangement of DPPC dispersions. Peptide gonadoliberin shows a reduced internal motion due to the lipid peptide interaction.The major consequences of binding of lipids with externally added molecules are changes in the fluidity and permeability properties of membranes. It has been shown that permeability is effected by the presence of molecules such as propranolol, -tocopherol and its analogue, neurotransmitters, etc. The magnetic resonance methods have thus evolved as power techniques in the study of membrane structure and function.     

The effect of the polar moiety of lipids on the ion permeability of bilayer membranes

Summary Bilayer membranes were prepared with the negatively charged lipids phosphatidylglycerol and diphosphatidylglycerol, the positively charged lipid lysyl phosphatidylglycerol, the zwitterionic lipid phosphatidylethanolamine, and an uncharged glycolipid, diglucosyldiglyceride, all isolated from gram-positive bacteria. Bilayer membranes of all these lipids manifested specific resistances of 10⁷ to 10⁹ cm² and capacitances of 0.3 to 0.4 F cm^–2. The membrane potentials of these bilayers were measured as a function of the sodium chloride, potassium chloride, and hydrogen chloride transmembrane concentration gradients (0.01 to 0.10m) and were found to be linear with the logarithm of the salt activity gradients. Membranes made from lysyl phosphatidylglycerol (one net positive charge) were almost completely chloride selective, whereas membranes from phosphatidylglycerol and diphosphatidylglycerol (one and two net negative charges, respectively) were highly cation selective. Membranes prepared with either diglucosyldiglyceride or phosphatidylethanolamine showed only slight cation selectivity. These findings indicate that the charge on the polar head group of membrane lipids plays an important role in controlling the ion-selective permeability of the bilayer.     

Permeability and electrical properties of planar lipid membranes from thylakoid lipids.

Electrical measurements were carried out on planar lipid membranes from thylakoid lipids. The specific capacitance of membranes formed from decane-containing monogalactosyldiacylglycerol (MGDG), which accounts for 57% of the total lipid content of thylakoids, showed that it adopted a bilayer structure. Solvent-free bilayers of MGDG were not formed, with very rare exceptions, indicating that decane is required to stabilize the planar conformation. However, this cone-shaped lipid produces bilayer structures in combination with other cylindrical thylakoid lipids even in the absence of organic solvent. We compared the properties of solvent-free and decane-containing bilayers from MGDG, soybean lecithin, and the quaternary mixture of lipids similar to that found in vivo. The conductance of decane-MGDG was 26 times higher than that of decane-lecithin. The flux through the decane-lecithin bilayer was found to be slightly dependent on pH, whereas the decane-MGDG membrane was not. The specific conductance of bilayers formed from the quaternary mixture of lipids was 5 to 10 times larger than lecithin (with alkane or not). Further experiments with bilayers made in the presence of a KCl gradient showed that decane-MGDG, decane-MGDG/DGDG/SQDG/PG, and solvent-free MGDG/DGDG/SQDG/PG were cation-selective. The permeability coefficient for potassium ranged from 4.9 to 8.3 x 10(-11) cm s-1. The permeability coefficient for protons in galactolipids, however, was determined to be about six orders of magnitude higher than the value for potassium ions. The HCl permeation mechanism through the lipid membranes was determined from diffusion potentials measured in HCl gradients. Our results suggest that HCl was not transported as neutral molecules. The data is discussed with regard to the function of galactolipids in the ion transport through thylakoid membranes.     

Permeation of membranes by the neutral form of amino acids and peptides: Relevance to the origin of peptide translocation

The flux of amino acids and other nutrient solutes such as phosphate across lipid bilayers (liposomes) is 10⁵ slower than facilitated inward transport across biological membranes. This suggests that primitive cells lacking highly evolved transport systems would have difficulty transporting sufficient nutrients for cell growth to occur. There are two possible ways by which early life may have overcome this difficulty: (1) The membranes of the earliest cellular life-forms may have been intrinsically more permeable to solutes; or (2) some transport mechanism may have been available to facilitate transbilayer movement of solutes essential for cell survival and growth prior to the evolution of membrane transport proteins. Translocation of neutral species represents one such mechanism. The neutral forms of amino acids modified by methylation (creating protonated weak bases) permeate membranes up to 10¹⁰ times faster than charged forms. This increased permeability when coupled to a transmembrane pH gradient can result in significantly increased rates of net unidirectional transport. Such pH gradients can be generated in vesicles used to model protocells that preceded and were presumably ancestral to early forms of life. This transport mechanism may still play a role in some protein translocation processes (e.g., for certain signal sequences, toxins and thylakoid proteins) in vivo.Abbreviations LUV large unilamellar vesicle - pH transmembrane pH gradient - PAH polyaromatic hydrocarbon Correspondence to: A.C. Chakrabarti     

A Theoretical Model for the Association Probabilities of Saturated Phospholipids from Two-Component Bilayer Lipid Membranes

The non-random mixing of biomembrane components, especially saturated phospholipids, exhibits important consequences in molecular biology. Particularly, the distribution of lipids within natural and model membranes is strongly determined by the selective association processes. These processes of phospholipids take place due to the cooperative modes in multiparticle systems as well as the specific lipid-lipid interactions both in the hydrophobic core and in the region of the polar headgroups. We demonstrated that the investigation of the selective association processes of saturated phospholipids might contribute to the insight of the lipid domains appearance inside the bilayer membranes. The association probabilities of like-pairs and cross-pairs from a binary mixture of saturated phospholipids were tested for both parallel and anti-parallel alignments of the polar headgroups. The present model confirms the experimental evidence for saturated phospholipids to have a high tendency for association in parallel configuration of the electric dipole moments of the polar headgroups whether the cross-sectional area of the polar headgroup is in an usual range of 25-55 2. There are three major lipid domains in a binary mixture of saturated phospholipids: (i) lipid domains in non-mixed phase of the first mixture component, in parallel alignment of the polar headgroups; (ii) lipid domains in non-mixed phase of the second mixture component, in anti-parallel alignment of the polar headgroups; (iii) lipid domains in mixed phase. We think that the selective association processes of phospholipids are neither exclusively, nor only involved in promoting the lipid domains appearance through bilayer phospholipid membranes.     

Attracted to membranes: lipid-binding domains in plants

Membranes are essential for cells and organelles to function. As membranes are impermeable to most polar and charged molecules, they provide electrochemical energy to transport molecules across and create compartmentalized microenvironments for specific enzymatic and cellular processes. Membranes are also responsible for guided transport of cargoes between organelles and during endo- and exocytosis. In addition, membranes play key roles in cell signaling by hosting receptors and signal transducers and as substrates and products of lipid second messengers. Anionic lipids and their specific interaction with target proteins play an essential role in these processes, which are facilitated by specific lipid-binding domains. Protein crystallography, lipid-binding studies, subcellular localization analyses, and computer modeling have greatly advanced our knowledge over the years of how these domains achieve precision binding and what their function is in signaling and membrane trafficking, as well as in plant development and stress acclimation.

Lipid-binding domains represent essential motifs within proteins that allow them to bind specific lipids in membranes in a spatial and temporal manner for signaling and trafficking purposes.     

Effect of fatty acids and monoglycerides on permeability of lipid bilayer

The effect of fatty acids and monoglycerides on barrier properties of liposomal membranes prepared from egg phosphatidylcholine was investigated. The incorporation of these lipids as liposomal membrane components induced the alteration of the permeability to less permeable liposomally entrapped drugs, sulfanilic acid and procainamide ethobromide (PAEB). Monoolein caused greatly increased permeability of both drugs and unsaturated fatty acids markedly enhanced the release rate of PAEB, while saturated fatty acids caused a small increase in the release rate.Electron spin resonance (ESR) investigation with 5-nitroxide stearic acid showed that fatty acids disordered the hydrophobic region of the lipid bilayer and the disordering effect of unsaturated fatty acids was greater than that of saturated ones. It was demonstrated that the incorporated fatty acids and monoglycerides interacted with the polar region of the membranes by ESR study with cholestane label and ¹H-NMR study. These results indicated that the increase in the membrane permeability caused by fatty acids and monoglycerides associated with the disorder in the membranes' interior and the interaction of the incorporated lipid with the polar head group of phospholipid.     

α-Synuclein Oligomers: an Amyloid Pore?

In many human diseases, oligomeric species of amyloid proteins may play a pivotal role in cytotoxicity. Many lines of evidence indicate that permeabilization of cellular membranes by amyloid oligomers may be the key factor in disrupting cellular homeostasis. However, the exact mechanisms by which the membrane integrity is impaired remain elusive. One prevailing hypothesis, the so-called amyloid pore hypothesis, assumes that annular oligomeric species embed into lipid bilayers forming transbilayer protein channels. Alternatively, an increased membrane permeability could be caused by thinning of the hydrophobic core of the lipid bilayer due to the incorporation of the oligomers between the tightly packed lipids, which would facilitate the transport of small molecules across the membrane. In this review, we briefly recapitulate our findings on the structure of α-synuclein oligomers and the factors influencing their interaction with lipid bilayers. Our results, combined with work from other groups, suggest that α-synuclein oligomers do not necessarily form pore-like structures. The emerging consensus is that local structural rearrangements of the protein lead to insertion of specific regions into the hydrophobic core of the lipid bilayer, thereby disrupting the lipid packing.     

Mechanism of human erythrocyte hemolysis induced by short-chain phosphatidylcholines and lysophosphatidylcholine

The incorporation and accumulation of a certain amount of short-chain phosphatidylcholine or lysophosphatidylcholine into lipid bilayers of erythrocyte membranes is the first step causing membrane perturbation in the process of hemolysis. Accumulation of dilauroylglycerophosphocholine into membranes makes human erythrocytes "permeable cells"; Ions such as Na+ or K+ can permeate through the membrane, though large molecules such as hemoglobin can not. The "pore" formation was partially reproduced in liposomes prepared from lipids extracted from human erythrocyte membranes; C12:0PC induced the release of glucose from liposomes but did not significantly induce the release of dextran. It was suggested that the phase boundary between dilauroylglycerophosphocholine and the host membrane bilayer or dilauroylglycerophosphocholine rich domain itself behaves as "pores." Erythrocytes could expand to 1.5 times the original cell volume without any appreciable hemolysis when incubated with C12:0PC at 37 degrees C. The capacity of the erythrocytes to expand was temperature dependent. The capacity may play an important role in the resistance of the cells against lysis. The "permeable cell" stage could be hardly observed when erythrocytes were treated with didecanoylglycerophosphocholine and lysophosphatidylcholine. Perturbation induced by accumulation of didecanoylglycerophosphocholine or lysophosphatidylcholine may cause non specific destruction of membranes rather than formation of a kind of "pore."     

The effects of a cyclic polyether on the electrical properties of phospholipid bilayer membranes

Summary The cyclic polyether XXXII, a neutral, lipid soluble molecule, produces large increases in the conductance of bilayer membranes formed from a variety of lipids. The conductance increases linearly with the concentration of alkali metal cation but with the square, and at higher concentrations the cube, of the polyether concentration. This implies that two or three polyether molecules combine with a single cation to carry it across the membrane. In the presence of XXXII the bilayer is permeable solely to cations and the membrane potential is described by an equation of the Goldman-Hodgkin-Katz type. The permeability ratios determined from potential measurements are independent of salt concentration, decrease in the sequence Cs>Rb>K>NH₄>Na>Li(1.0,0.25, 0.15, 0.075, 0.007, 0.0013) and are equal to the conductance ratios at low (e.g. 10^–3 m) salt concentration. At higher salt concentrations, the permeability and conductance ratios are not equal and maxima in the conductancevs. salt concentration curves are observed. Both these phenomena are postulated to be caused by the formation of relatively impermeant 11 polyether cation complexes in the aqueous phase. The 11 aqueous association constants deduced from bilayer measurements decrease in the sequence K>Rb>Na>NH₄>Cs>Li (120, 34, 26, 19, 12, 4 liters per mole) and agree quantitatively with the literature values for the more water soluble polyether XXXI, which lacks only thet-butyl groups of XXXII.     

Bipolar tetraether lipids: chain flexibility and membrane polarity gradients from spin-label electron spin resonance

Membranes of thermophilic Archaea are composed of unique tetraether lipids in which C40, saturated, methyl-branched biphytanyl chains are linked at both ends to polar groups. In this paper, membranes composed of bipolar lipids P2 extracted from the acidothermophile archaeon Sulfolobus solfataricus are studied. The biophysical basis for the membrane formation and thermal stability is investigated by using electron spin resonance (ESR) of spin-labeled lipids. Spectral anisotropy and isotropic hyperfine couplings are used to determine the chain flexibility and polarity gradients, respectively. For comparison, similar measurements have been carried out on aqueous dispersions of diacyl reference lipid dipalmitoyl phosphatidylcholine and also of diphytanoyl phosphatidylcholine, which has methyl-branched chains. At a given temperature, the bolaform lipid chains are more ordered and less flexible than in normal bilayer membranes. Only at elevated temperatures (80 degrees C) does the flexibility of the chain environment in tetraether lipid assemblies approach that of fluid bilayer membranes. The height of the hydrophobic barrier formed by a monolayer of archaebacterial lipids is similar to that in conventional fluid bilayer membranes, and the permeability barrier width is comparable to that formed by a bilayer of C16 lipid chains. At a mole ratio of 1:2, the tetraether P2 lipids mix well with dipalmitoyl phosphatidylcholine lipids and stabilize conventional bilayer membranes. The biological as well as the biotechnological relevance of the results is discussed.     

The permeability of the frog choroid plexus to nonelectrolytes

Summary Anin vitro preparation of the frog choroid plexus has been used to measure the permeability of the choroidal epithelium to 50 nonelectrolytes by an osmotic method. The method involves the measurement of nonelectrolyte reflection coefficients () by a rapid electrical procedure. For the majority of compounds tested, there was a good correlation between the rate of solute permeation and the solute's bulk-phase lipid: water partition coefficients; i.e., the higher the partition coefficient the greater the permeability. The membrane lipids of the choroid plexus differ from the membrane lipids of the gall bladder in at least three ways: (1) the lipids of the choroid plexus cannot distinguish between branched chain solutes and their straight chain isomers; (2) small polar solutes such as urea and acetamide permeate via the membrane lipids to a significant extent; and (3) the smaller selectivity ratios suggest that the lipids of the choroid plexus contain more hydrogen bonding sites (i.e., there are stronger solute: lipid intermolecular forces in the choroid plexus). The permeability characteristics of the choroid plexus are qualitatively similar to those of most other cell membranes. In addition, there is evidence for the presence of a special mechanism for the transport of sugar across this epithelium.     

The magnitude of nonelectrolyte selectivity in the gallbladder epithelium

Summary The permeability of the rabbit gallbladder epithelium to nonelectrolytes was determinted by radioactive tracer techniques and by a rapid osmotic procedure. As expected from empirical and theoretical considerations, there was a good agreement between the selectivity sequences obtained by the two methods for the sixteen compounds used in this study. Although the permeability coefficients are directly related to their bulk-phase partition coefficients, the gallbladder behaves as if the membranes controlling selectivatity are more hydrophilic than isobutanol. The relation between permeability coefficients and molecular weight also show that these membranes are less viscous than other single cell membranes. Small polar solutes exhibit lower apparent activiation energies for permeation than larger solutes, and this is taken as support for the view that small polar molecules permeate across this tissue via a polar pathway. Inutin and sucrose permeability coefficients are in the ratio of their free-solution diffusion coefficients, and the apparent surcose activation energy is indistinguishable from that reported for diffusion in aqueous solution. These latter observations may be explained by the presence of a few large pores in the epithelium.     

Lipid requirements for endocytosis in yeast

Endocytosis is, besides secretion, the most prominent membrane transport pathway in eukaryotic cells. In membrane transport, defined areas of the donor membranes engulf solutes of the compartment they are bordering and bud off with the aid of coat proteins to form vesicles. These transport vehicles are guided along cytoskeletal paths, often matured and, finally, fuse to the acceptor membrane they are targeted to. Lipids and proteins are equally important components in membrane transport pathways. Not only are they the structural units of membranes and vesicles, but both classes of molecules also participate actively in membrane transport processes. Whereas proteins form the cytoskeleton and vesicle coats, confer signals and constitute attachment points for membrane-membrane interaction, lipids modulate the flexibility of bilayers, carry protein recognition sites and confer signals themselves. Over the last decade it has been realized that all classes of bilayer lipids, glycerophospholipids, sphingolipids and sterols, actively contribute to functional membrane transport, in particular to endocytosis. Thus, abnormal bilayer lipid metabolism leads to endocytic defects of different severity. Interestingly, there seems to be a great deal of interdependence and interaction among lipid classes. It will be a challenge to characterize this plenitude of interactions and find out about their impact on cellular processes.     

Atomic-scale structure and electrostatics of anionic palmitoyloleoylphosphatidylglycerol lipid bilayers with Na+ counterions

Anionic palmitoyloleoylphosphatidylglycerol (POPG) is one of the most abundant lipids in nature, yet its atomic-scale properties have not received significant attention. Here we report extensive 150-ns molecular dynamics simulations of a pure POPG lipid membrane with sodium counterions. It turns out that the average area per lipid of the POPG bilayer under physiological conditions is approximately 19% smaller than that of a bilayer built from its zwitterionic phosphatidylcholine analog, palmitoyloleoylphosphatidylcholine. This suggests that there are strong attractive interactions between anionic POPG lipids, which overcome the electrostatic repulsion between negative charges of PG headgroups. We demonstrate that interlipid counterion bridges and strong intra- and intermolecular hydrogen bonding play a key role in this seemingly counterintuitive behavior. In particular, the substantial strength and stability of ion-mediated binding between anionic lipid headgroups leads to complexation of PG molecules and ions and formation of large PG-ion clusters that act in a concerted manner. The ion-mediated binding seems to provide a possible molecular-level explanation for the low permeability of PG-containing bacterial membranes to organic solvents: highly polar interactions at the water/membrane interface are able to create a high free energy barrier for hydrophobic molecules such as benzene.     

Protonophore anion permeability of the human red cell membrane determined in the presence of valinomycin

Summary A transport model for translocation of the protonophore CCCP across the red cell membrane has been established and cellular CCCP binding parameters have been determined. The time course of the CCCP redistribution across the red cell membrane, following a jump in membrane potential induced by valinomycin addition, has been characterized by fitting values of preequilibrium extracellular pHvs. time to the transport model. It is demonstrated, that even in the presence of valinomycin, the CCCP-anion is well behaved, in that the translocation can be described by simple electrodiffusion. The translocation kinetics conform to an Eyring transport model, with a single activation energy barrier, contrary to translocation across lipid bilayers, that is reported to follow a transport model with a plateau in the activation energy barrier. The CCCP anion permeability across the red cell membrane has been calculated to be close to 2.0×10^–4 cm/sec at 37°C with small variations between donors. Thus the permeability of CCCP in the human red cell membrane deviates from that found in black lipid membranes, in which the permeability is found to be a factor of 10 higher.