Dipalmitoylphosphatidylcholine Bilayers Research Articles

Calcium and Zinc Differentially Affect the Structure of Lipid Membranes.

Interactions of calcium (Ca2+) and zinc (Zn2+) cations with biomimetic membranes made of dipalmitoylphosphatidylcholine (DPPC) were studied by small angle neutron diffraction (SAND). Experiments show that the structure of these lipid bilayers is differentially affected by the two divalent cations. Initially, both Ca2+ and Zn2+ cause DPPC bilayers to thicken, while further increases in Ca2+ concentration result in the bilayer thinning, eventually reverting to having the same thickness as pure DPPC. The binding of Zn2+, on the other hand, causes the bilayers to swell to a maximum thickness, and the addition of more Zn2+ does not result in a further thickening of the membrane. Agreement between our results obtained using oriented planar membranes and those from vesicular samples implies that the effect of cations on bilayer thickness is the result of electrostatic interactions, rather than geometrical constraints due to bilayer curvature. This notion is further reinforced by MD simulations. Finally, the radial distribution functions reveal a strong interaction between Ca2+ and the phosphate oxygens, while Zn2+ shows a much weaker binding specificity.

Exploring the interactions of irbesartan and irbesartan–2-hydroxypropyl-β-cyclodextrin complex with model membranes

The interactions of irbesartan (IRB) and irbesartan–2-hydroxypropyl-β-cyclodextrin (HP-β-CD) complex with dipalmitoyl phosphatidylcholine (DPPC) bilayers have been explored utilizing an array of biophysical techniques ranging from differential scanning calorimetry (DSC), small angle X-ray scattering (SAXS), ESI mass spectrometry (ESI-MS) and solid state nuclear magnetic resonance (ssNMR). Molecular dynamics (MD) calculations have been also conducted to complement the experimental results. Irbesartan was found to be embedded in the lipid membrane core and to affect the phase transition properties of the DPPC bilayers. SAXS studies revealed that irbesartan alone does not display perfect solvation since some coexisting irbesartan crystallites are present. In its complexed form IRB gets fully solvated in the membranes showing that encapsulation of IRB in HP-β-CD may have beneficial effects in the ADME properties of this drug. MD experiments revealed the topological and orientational integration of irbesartan into the phospholipid bilayer being placed at about 1nm from the membrane centre.

Conformational Space of a Polyphilic Molecule with a Fluorophilic Side Chain Integrated in a DPPC Bilayer.

We investigate the conformational space of a polyphilic molecule with hydrophilic, lipophilic and fluorophilic parts inserted as a transmembrane agent into a dipalmitoylphosphatidylcholine bilayer by means of all-atom molecular dynamics simulations. Special focus is put on the competing structural driving forces arising from the hydrophilic, lipophilic and fluorophilic side chains and the aromatic backbone of the polyphile. We observe a significant difference between the lipophilic and the fluorophilic side chains regarding their intramembrane distribution. While the lipophilic groups remain membrane-centered, the fluorophilic parts tend to orient toward the phosphate headgroups. This trend is important for understanding the influence of polyphile agents on the properties of phospholipid membranes. From a fundamental point of view, our computed distribution functions of the side chains are related to the interplay of sterical, enthalpic and entropic driving forces. Our findings illustrate the potential of rationally designed membrane additives which can be exploited to tune the properties of phospholipid membranes. © 2017 Wiley Periodicals, Inc.

Hysteresis and the Cholesterol-Dependent Melting Transition of the Martini Model

Extensive Martini simulation data, totaling 5 ms, is presented for binary mixtures of dipalmitoyl phosphatidylcholine (DPPC) and cholesterol. Using simulations initiated from both gel and liquid-disordered (L d ) phases, significant and strongly cholesterol-dependent hysteresis in the enthalpy as a function of temperature is observed for cholesterol mole fractions from 0 to 20 mol% — adding just a single cholesterol to each leaflet of a pure DPPC bilayer more than doubles the width of the hysteresis loop relative to a pure DPPC bilayer.

A refined polarizable water model for the coarse-grained MARTINI force field with long-range electrostatic interactions.

We present a refined version of the polarizable Martini water model - coined refPOL - designed specifically for the use with long-range electrostatics. The refPOL model improves the agreement with the experimentally measured dielectric constant and the mass density of water at room temperature compared to the original polarizable Martini water force field when particle mesh Ewald electrostatics are employed. Our study reveals that the model remains applicable with various commonly used settings for the non-bonded interactions, including reaction field electrostatics. The oil/water partitioning behavior of uncharged Martini bead types is thoroughly investigated: Lennard-Jones interactions between the refPOL model and the remaining Martini beads are adjusted to reproduce the hydration free energies obtained with the original polarizable water model, while free energies of solvation in apolar media remain unchanged. The cross-interactions with charged bead types are parameterized to agree with the experimentally observed area per lipid of a fully solvated dipalmitoylphosphatidylcholine bilayer. We additionally verify the model by analyzing the potentials of mean force between different sample pairs in refPOL water and comparing the results to reference data obtained using the original polarizable Martini water model as well as fully atomistic simulations. Based on the results, we suggest to replace the original polarizable Martini water model with the new refPOL model for future applications.

Interaction of aurein 1.2 and its analogue with DPPC lipid bilayer.

Antibacterial peptides have potential as novel therapeutic agents for bacterial infections. Aurein 1.2 is one of the smallest antibacterial peptides extracted from an anuran. LLAA is a more active analogue of aurein 1.2. Antibacterial peptides usually accomplish their function by interacting with bacterial membrane selectively. In this study, we tried to find the reasons for the stronger antibacterial activity of LLAA compared with aurein 1.2. For this purpose, the interaction of aurein 1.2 and LLAA with dipalmitoylphosphatidylcholine (DPPC) was investigated by molecular dynamics (MD) simulation. In addition, the structure of peptides and their antibacterial activity were investigated by circular dichroism (CD) and dilution test method, respectively. MD results showed that LLAA is more flexible compared with aurein 1.2. Furthermore, LLAA loses its structure more than aurein 1.2 in the DPPC bilayer. A higher amount of water molecules penetrate into bilayer in the presence of LLAA relative to aurein 1.2. According to the antibacterial result that indicated LLAA is remarkably more active than aurein 1.2, it can be concluded that flexibility of the peptide is a determining factor in antibacterial activity. Probably, flexibility of the peptides facilitates formation of effective pores in the lipid bilayer.

Lipid and Peptide Diffusion in Bilayers: The Saffman-Delbrück Model and Periodic Boundary Conditions.

The periodic Saffman-Delbrück (PSD) model, an extension of the Saffman-Delbrück model developed to describe the effects of periodic boundary conditions on the diffusion constants of lipids and proteins obtained from simulation, is tested using the coarse-grained Martini and all-atom CHARMM36 (C36) force fields. Simulations of pure Martini dipalmitoylphosphatidylcholine (DPPC) bilayers and those with one embedded gramicidin A (gA) dimer or one gA monomer with sizes ranging from 512 to 2048 lipids support the PSD model. Underestimates of D∞ (the value of the diffusion constant for an infinite system) from the 512-lipid system are 35% for DPPC, 45% for the gA monomer, and 70% for the gA dimer. Simulations of all-atom DPPC and dioleoylphosphatidylcholine (DOPC) bilayers yield diffusion constants not far from experiment. However, the PSD model predicts that diffusion constants at the sizes of the simulation should underestimate experiment by approximately a factor of 3 for DPPC and 2 for DOPC. This likely implies a deficiency in the C36 force field. A Bayesian method for extrapolating diffusion constants of lipids and proteins in membranes obtained from simulation to infinite system size is provided.

Probing Lipid Bilayers under Ionic Imbalance

Biological membranes are normally under a resting transmembrane potential (TMP), which originates from the ionic imbalance between extracellular fluids and cytosols, and serves as electric power storage for cells. In cell electroporation, the ionic imbalance builds up a high TMP, resulting in the poration of cell membranes. However, the relationship between ionic imbalance and TMP is not clearly understood, and little is known about the effect of ionic imbalance on the structure and dynamics of biological membranes. In this study, we used coarse-grained molecular dynamics to characterize a dipalmitoylphosphatidylcholine bilayer system under ionic imbalances ranging from 0 to ∼0.06 e charges per lipid (e/Lip). We found that the TMP displayed three distinct regimes: 1) a linear regime between 0 and 0.045 e/Lip, where the TMP increased linearly with ionic imbalance; 2) a yielding regime between ∼0.045 and 0.060 e/Lip, where the TMP displayed a plateau; and 3) a poration regime above ∼0.060 e/Lip, where we observed pore formation within the sampling time (80 ns). We found no structural changes in the linear regime, apart from a nonlinear increase in the area per lipid, whereas in the yielding regime the bilayer exhibited substantial thinning, leading to an excess of water and Na+ within the bilayer, as well as significant misalignment of the lipid tails. In the poration regime, lipid molecules diffused slightly faster. We also found that the fluid-to-gel phase transition temperature of the bilayer dropped below the normal value with increased ionic imbalances. Our results show that a high ionic imbalance can substantially alter the essential properties of the bilayer, making the bilayer more fluid like, or conversely, depolarization of a cell could in principle lead to membrane stiffening.

Water populations in restricted environments of lipid membrane interphases.

We employ molecular dynamics simulations to study the hydration properties of Dipalmitoylphosphatidylcholine (DPPC) bilayers, both in the gel and the liquid crystalline states. We show that while the tight hydration centers (PO and CO moieties) are significantly hydrated in both phases, the gel-fluid transition involves significant changes at the second hydration shell, particularly at the buried region between the hydrocarbon tails. Thus, while almost no buried water population exists in the gel state below the carbonyls, this hydrophobic region becomes partially water accesible in the liquid crystalline state. We shall also show that such water molecules present a lower H-bond coordination as compared to the molecules at the primary hydration shell. This means that, while the latter are arranged in relatively compact nanoclusters (as already proposed), the buried water molecules tend to organize themselves in less compact structures, typically strings or branched strings, with a scarce population of isolated molecules. This behavior is similar to that observed in other hydration contexts, like water penetrating carbon nanotubes or model hydrophobic channels or pores, and reflects the reluctance of water to sacrifice HB coordination.

Resveratrol induces chain interdigitation in DPPC cell membrane model systems

Resveratrol is a natural polyphenol found in various plants with potential therapeutic activity as anti-oxidant, anti-inflammatory, cardioprotective and anti-tumoral. Lipid membranes are among cellular components that are targets of its action. In this work ESR of chain labeled lipids, calorimetry, X-ray diffraction and molecular docking are used to study the interaction of resveratrol with membrane model systems of dipalmitoylphosphatidylcholine (DPPC) as a function of resveratrol concentration (0–30 mol% of the lipid) and temperature (10–50°C). Resveratrol incorporated in DPPC bilayers induces considerable motional restriction at the lipid tail termini, removing the gradient of increasing mobility along the chain found in DPPC bilayers in the gel phase. In contrast, it leaves unperturbed the DPPC chain flexibility profile in the liquid-crystalline phase. At low concentration, resveratrol progressively reduces the pre-transition temperature and eliminates the pre-transition for content ≥5mol%. A reduced cooperativity and a downshift of the main transition temperature are observed, especially at high content. The typical diffraction pattern of DPPC multibilayers in the Lβ′ phase is converted to a lamellar pattern with reduced d-spacing of untilted lipid chain in a hexagonal packing at 30 mol% of resveratrol. Molecular docking indicates that the energetically favoured anchoring site is the polar headgroup region, where resveratrol acts as a spacer. The overall results are consistent with the formation in DPPC of an interdigitated Lβi gel phase induced by 30 mol% resveratrol.

The partition and transport behavior of cytotoxic ionic liquids (ILs) through the DPPC bilayer: Insights from molecular dynamics simulation.

A molecular dynamics (MD) simulation with atomistic details was performed to examine the partitioning and transport behavior of moderately cytotoxic ionic liquids (ILs), namely choline bis(2-ethylhexyl) phosphate (CBEH), choline bis(2,4,4-trimethylpentyl) phosphinate (CTMP) and choline O,O-diethyl dithiophosphate (CDEP) in a fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer in the fluid phase at 323 K. The structure of ILs was so selected to understand if the role of dipole and dispersion forces in the ILs distribution in the membrane can be possible. Several analyses including mass density, electrostatic potential, order parameter, diffusion coefficients and hydrogen bond formation, was carried out to determine the precise location of the anionic species inside the membrane. Moreover, the potential of the mean force (PMF) method was used to calculate free energy profile for transferring anionic species from the DPPC membrane into the bulk water. While less cytotoxic DEP is located within the bulk water, more cytotoxic TMP and BEH ILs were found to remain in the membrane and the energy barrier for crossing through the bilayer center of BEH was higher. Various ILs have no significant effect on P-N vector. The thickness of lipid bilayer decreased in all systems comprising ILs, while area per lipid increased.

Cholesterol–Ceramide Interactions in Phospholipid and Sphingolipid Bilayers As Observed by Positron Annihilation Lifetime Spectroscopy and Molecular Dynamics Simulations

Free volume voids in lipid bilayers can be measured by positron annihilation lifetime spectroscopy (PALS). This technique has been applied, together with differential scanning calorimetry and molecular dynamics (MD) simulations, to study the effects of cholesterol (Chol) and ceramide (Cer) on free volume voids in sphingomyelin (SM) or dipalmitoylphosphatidylcholine (DPPC) bilayers. Binary lipid samples with Chol were studied (DPPC:Chol 60:40, SM:Chol 60:40 mol ratio), and no phase transition was detected in the 20-60 °C range, in agreement with calorimetric data. Chol-driven liquid-ordered phase showed an intermediate free volume void size as compared to gel and fluid phases. For SM and SM:Cer (85:15 mol:mol) model membranes measured in the 20-60 °C range the gel-to-fluid phase transition could be observed with a related increase in free volume, which was more pronounced for the SM:Cer sample. MD simulations suggest a hitherto unsuspected lipid tilting in SM:Cer bilayers but not in pure SM. Ternary samples of DPPC:Cer:Chol (54:23:23) and SM:Cer:Chol (54:23:23) were measured, and a clear pattern of free volume increase was observed in the 20-60 °C because of the gel-to-fluid transition. Interestingly, MD simulations showed a tendency of Cer to change its distribution along the membrane to make room for Chol in ternary mixtures. The results suggest that the gel phase formed in these ternary mixtures is stabilized by Chol-Cer interactions.

Influence of cytotoxic butyltin complexes with 2-sulfobenzoic acid on the thermotropic phase behavior of lipid model membranes

In the previous study, we showed that butyltin complexes with 2-sulfobenzoic acid (commonly referred to as BTsbz) exhibit a very wide biological activity. The BTsbz in vitro are very active cytotoxic agents against tumor cells—more effective than cisplatin and carboplatin (traditional anticancer drugs). These complexes are antibacterial agents against gram-positive and gram-negative bacteria, as well. The aim of the present study was to investigate the influence of BTsbz on the thermotropic phase behavior of dipalmitoylphosphatidylcholine (DPPC) model membranes. The effect of this compound on the multilamellar liposomes was studied mainly by the means of differential scanning calorimetry and additionally by the steady-state fluorimetry and infrared spectroscopy. All investigated butyltin complexes with 2-sulfobenzoic acid change the thermotropic properties of lipid model membranes: The temperature of the main phase transition of DPPC is slightly decreased, and the transition’s cooperativity of the peak is very much reduced. With increasing concentration, all investigated compounds abolished the pretransition. The results suggest that BTsbz are very active in the hydrophilic area of DPPC bilayer and at the same time have an effect on membrane fluidity.

Specific electrical capacitance and voltage breakdown as a function of temperature for different planar lipid bilayers

The breakdown voltage and specific electrical capacitance of planar lipid bilayers formed from lipids isolated from the membrane of archaeon Aeropyrum pernix K1 as a function of temperature were studied and compared with data obtained previously in MD simulation studies. Temperature dependence of breakdown voltage and specific electrical capacitance was measured also for dipalmitoylphosphatidylcholine (DPPC) bilayers and bilayers formed from mixture of diphytanoylphosphocholine (DPhPC) and DPPC in ratio 80:20.The breakdown voltage of archaeal lipids planar lipid bilayers is more or less constant until 50°C, while at higher temperatures a considerable drop is observed, which is in line with the results from MD simulations. The breakdown voltage of DPPC planar lipid bilayer at melting temperature is considerably higher than in the gel phase. Specific electrical capacitance of planar lipid bilayers formed from archaeal lipids is approximately constant for temperatures up to 40°C and then gradually decreases. The difference with MD simulation predictions is discussed. Specific electrical capacitance of DPPC planar lipid bilayers in fluid phase is 1.75 times larger than that of the gel phase and it follows intermediated phases before phase transition. Increase in specific electrical capacitance while approaching melting point of DPPC is visible also for DPhPC:DPPC mixture.

The Localization of Phenolic Compounds in Liposomal Bilayers and Their Effects on Surface Characteristics and Colloidal Stability.

The interactions with and effects of five chemically distinct, bioactive phenolic compounds on the lipid bilayers of model dipalmitoylphosphatidylcholine (DPPC) liposomes were investigated. Complementary analytical techniques, including differential scanning calorimetry (DSC) and phosphorus and proton nuclear magnetic resonance spectroscopy (NMR), were employed in order to determine the location of the compounds within the bilayer and to correlate location with their effects on bilayer characteristics and liposomal stability. As compared to the phenolic compounds localized in the glycerol region of the DPPC head group within the bilayer, which enhanced the colloidal stability of the liposomes, compounds located closer to the center of the bilayer reduced vesicle stability as a function of time. Molecules present in the upper region of liposomal DPPC acyl chains (C1-C10) inhibited liposomal aggregation and size increase, perhaps due to tighter packing of adjoining DPPC molecules and increased surface exposure of DPPC phosphate head groups. These data may be useful for designing liposomal systems containing hydrophobic phenols and other small molecules, selecting appropriate analytical methods for determining their location within liposomal bilayers, and predicting their effects on liposome characteristics early in the liposome formulation development process.

Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer

Extensive microscopic molecular dynamics simulations have been performed to study the effects of tow β-blocker drugs (Propranolol, Oxprenolol) on fully hydrated dipalmitoylphosphatidylcholine (DPPC) in the fluid phase at 323K. Simulation of 4 systems containing varying concentrations of drugs was carried out. For the purpose of comparison, a fully hydrated DPPC bilayer without drugs was also studied at the same level of simulation technique which has been done on 4 other systems. The length of each simulation was 100ns. The effects of concentrations of both drugs were analyzed on lipid bilayer properties, such as electrostatic potential, order parameter, diffusion coefficients, and hydrogen bond formation, etc. Penetration of water in the bilayer system was also investigated using radial distribution function analysis. Efficacy of varying concentrations of both drugs has no significant effect on P–N vector. Consistent with experimental results, by increasing the concentration of Propranolol, the thickness of the bilayer was increased.

Structural perturbation of a dipalmitoylphosphatidylcholine (DPPC) bilayer by warfarin and its bolaamphiphilic analogue: A molecular dynamics study

Compounds with nominally similar biological activity may exhibit differential toxicity due to differences in their interactions with cell membranes. Many pharmaceutical compounds are amphiphilic and can be taken up by phospholipid bilayers, interacting strongly with the lipid–aqueous interface whether or not subsequent permeation through the bilayer is possible. Bolaamphiphilic compounds, which possess two hydrophilic ends and a hydrophobic linker, can likewise undergo spontaneous uptake by bilayers. While membrane-spanning bolaamphiphiles can stabilize membranes, small molecules with this characteristic have the potential to create membrane defects via disruption of bilayer structure and dynamics. When compared to the amphiphilic therapeutic anticoagulant, warfarin, the bolaamphiphilic analogue, brodifacoum, exhibits heightened toxicity that goes beyond superior inhibition of the pharmacological target enzyme. We explore, herein, the consequences of anticoagulant accumulation in a dipalmitoylphosphatidylcholine (DPPC) bilayer. Coarse-grained molecular dynamics simulations reveal that permeation of phospholipid bilayers by brodifacoum causes a disruption of membrane barrier function that is driven by the bolaamphiphilic nature and size of this molecule. We find that brodifacoum partitioning into bilayers causes membrane thinning and permeabilization and promotes lipid flip-flop – phenomena that are suspected to play a role in triggering cell death. These phenomena are either absent or less pronounced in the case of the less toxic, amphiphilic compound, warfarin.

Naphthalene Derivatives Induce Acyl Chain Interdigitation in Dipalmitoylphosphatidylcholine Bilayers.

The interdigitated phase of the lipid bilayer results when acyl chains from opposing monolayers fully interpenetrate such that the terminal methyl groups of the respective lipid chains are located at the interfacial region on the opposite sides of the bilayer. Usually, chain interdigitation is not encountered in a symmetric chain phosphatidylcholine (PC) membrane but can be induced under certain special conditions. In this article, we elucidate the contribution of small amphiphatic molecules in altering the physical properties of a symmetric chain PC bilayer membrane, which results in acyl chain interdigitation. Using small-angle X-ray scattering (SAXS), we have carried out a systematic investigation of the physical interactions of three naphthalene derivatives containing hydroxyl groups: β-naphthol, 2,3-dihydroxynaphthalene, and 2,7-dihydroxynaphthalene, with dipalmitoylphosphatidylcholine (DPPC) bilayers. On the basis of the diffraction patterns, we have determined the temperature-composition phase diagrams of these binary mixtures. The present study not only enables us to gain insight into the role played by small molecules in altering the packing arrangement of the acyl chains of the constituting PC lipids of the bilayer but also brings to light some important features that have not yet been reported hitherto. One such feature is the stabilization of the enigmatic asymmetric ripple phase over a wide temperature and concentration range. The results presented here strongly point toward a clear correlation between chain interdigitation and the stability of the ripple phase.

Phase transition behaviors of the supported DPPC bilayer investigated by sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM).

The phase transition behaviors of a supported bilayer of dipalmitoylphosphatidyl-choline (DPPC) have been systematically evaluated by in situ sum frequency generation (SFG) vibrational spectroscopy and atomic force microscopy (AFM). By using an asymmetric bilayer composed of per-deuterated and per-protonated monolayers, i.e., DPPC-d75/DPPC and a symmetric bilayer of DPPC/DPPC, we were able to probe the molecular structural changes during the phase transition process of the lipid bilayer by SFG spectroscopy. It was found that the DPPC bilayer is sequentially melted from the top (adjacent to the solution) to bottom leaflet (adjacent to the substrate) over a wide temperature range. The conformational ordering of the supported bilayer does not decrease (even slightly increases) during the phase transition process. The conformational defects in the bilayer can be removed after the complete melting process. The phase transition enthalpy for the bottom leaflet was found to be approximately three times greater than that for the top leaflet, indicating a strong interaction of the lipids with the substrate. The present SFG and AFM observations revealed similar temperature dependent profiles. Based on these results, the temperature-induced structural changes in the supported lipid bilayer during its phase transition process are discussed in comparison with previous studies.

A comparative differential scanning calorimetry study of the effects of cholesterol and various oxysterols on the thermotropic phase behavior of dipalmitoylphosphatidylcholine bilayer membranes

We have carried out a comparative differential scanning calorimetric (DSC) study of the effects of cholesterol (C) and the eight most physiologically relevant oxysterols on the thermotropic phase behavior of dipalmitoylphosphatidylcholine (DPPC) bilayer membranes. The structures of these oxysterols differ from that of C by the presence of additional hydroxyl, keto or epoxy groups on the steroid ring system or by the presence of a hydroxyl group in the alkyl side chain. In general, the progressive incorporation of these oxysterols reduces the temperature, cooperativity and enthalpy of the pretransition of DPPC to a greater extent than C, indicating that their presence thermally destabilizes and disorders the gel states of DPPC bilayers to a greater extent than C. Similarly, the incorporation of these oxysterols either increases the temperature of the broad component of the main phase transition to a smaller extent than C or actually decreases it. Again, this indicates that the presence of these compounds is less effective at thermally stabilizing and ordering the sterol-rich domains of DPPC bilayers than is C itself. Moreover, the incorporation of these oxysterols decrease the cooperativity and enthalpy of the main phase transition of DPPC to a smaller extent than C, indicating that they are somewhat less miscible in fluid DPPC bilayers than is C. Particularly notable in this regard is 25-hydroxycholesterol, which exhibits a markedly reduced miscibility in both gel and fluid DPPC bilayers compared to C itself. In general, the effectiveness of these oxysterols in stabilizing and ordering DPPC bilayers decreases as their rate of interbilayer exchange and the polarity of the oxysterol increases. We close by providing a tentative molecular explanation for the results of our DSC studies and of those of previous biophysical studies of the effects of various oxysterol on lipid bilayer model membranes.