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1.
Lipid peroxidation plays an important role in cell membrane damage. We investigated the effect of lipid peroxidation on the properties of 1-palmitoyl-2-linoleoyl-sn-glycero-3-phosphatidylcholine (PLPC) lipid bilayers using molecular dynamics simulations. We focused on four main oxidation products of linoleic acid with either a hydroperoxide or an aldehyde group: 9-trans, cis-hydroperoxide linoleic acid, 13-trans, cis-hydroperoxide linoleic acid, 9-oxo-nonanoic acid, and 12-oxo-9-dodecenoic acid. These oxidized chains replaced the sn-2 linoleate chain. The properties of PLPC lipid bilayers were characterized as a function of the concentration of oxidized lipids, with concentrations from 2.8% to 50% for each oxidation product. The introduction of oxidized functional groups in the lipid tail leads to an important conformational change in the lipids: the oxidized tails bend toward the water phase and the oxygen atoms form hydrogen bonds with water and the polar lipid headgroup. This conformational change leads to an increase in the average area per lipid and, correspondingly, to a decrease of the bilayer thickness and the deuterium order parameters for the lipid tails, especially evident at high concentrations of oxidized lipid. Water defects are observed in the bilayers more frequently as the concentration of the oxidized lipids is increased. The changes in the structural properties of the bilayer and the water permeability are associated with the tendency of the oxidized lipid tails to bend toward the water interface. Our results suggest that one mechanism of cell membrane damage is the increase in membrane permeability due to the presence of oxidized lipids.  相似文献   

2.
Song Y  Guallar V  Baker NA 《Biochemistry》2005,44(41):13425-13438
Salicylate, an amphiphilic molecule and a popular member of the nonsteroidal anti-inflammatory drug family, is known to affect hearing through reduction of the electromechanical coupling in the outer hair cells of the ear. This reduction of electromotility by salicylate has been widely studied, but the molecular mechanism of the phenomenon is still unknown. In this study, we investigated one aspect of salicylate's action, namely the perturbation of electrical and mechanical membrane properties by salicylate in the absence of cytoskeletal or membrane-bound motor proteins such as prestin. In particular, we simulated the interaction of salicylate with a dipalmitoylphosphatidylcholine (DPPC) bilayer via atomically detailed molecular dynamics simulations to observe the effect of salicylate on the microscopic and mesoscopic properties of the bilayer. The results demonstrate that salicylate interacts with the bilayer by associating at the water-DPPC interface in a nearly perpendicular orientation and penetrating more deeply into the bilayer than either sodium or chloride. This association has several affects on the membrane properties. First, binding of salicylate to the membrane displaces chloride from the bilayer-water interface. Second, salicylate influences the electrostatic potential and dielectric properties of the bilayer, with significant changes at the water-lipid bilayer interface. Third, salicylate association results in structural changes, including decreased headgroup area per lipid and increased lipid tail order. However, salicylate does not significantly alter the mechanical properties of the DPPC bilayer; bulk compressibility, area compressibility, and bending modulus were only perturbed by small, statistically insignificant amounts by the presence of salicylate. The observations from these simulations are in qualitative agreement with experimental data and support the conclusion that salicylate influences the electrical but not the mechanical properties of DPPC membranes.  相似文献   

3.
We report small angle X-ray scattering (SAXS) data from large unilamellar vesicles as model membranes composed of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocoline (POPC) and two oxidized species, namely its hydroperoxidized form POPC-OOH and 1-palmitoyl-2-azelaoyl-sn-glycero-3-phosphocholine (PazePC) lipid that has a carboxyl group at the end of its truncated sn-2 chain. The replacement of POPC by either POPC-OOH (POPC-OOHxPOPC1−x) or PazePC (PazePCxPOPC1−x), with oxidized lipid molar ratio x varying from 0.00 up to 1.00, permits to experimentally inspect changes in the membrane structural properties due to oxidation. The volume fraction distribution of each lipid chemical group along the bilayer is determined. The results quantify that 95% of the hydroperoxide group lies in the membrane polar moiety, near the carbonyl and phosphate groups, whereas just 5% of OOH group experiences the polar/apolar interface, for all values of x studied. In the case of PazePC up to x = 0.33, a bimodal distribution of the carboxyl group in the interior and polar regions of the lipid membrane is obtained, probably due to a dynamic movement of the shortened alkyl chain towards the water interface. The mean molecular area A gradually increases from 65.4 ± 0.4 Å2 for POPC bilayers to 78 ± 2 Å2 for pure POPC-OOH bilayers, whereas POPC-OOH membrane thickness resulted to be 20% thinner than the non-oxidized POPC membrane. For PazePC up to x = 0.33, A increases to 67 ± 2 Å2 with 10% of membrane thinning. The SAXS results thus demonstrate how the lipid oxidation progress affects the membrane structural features, thus paving the way to better understand membrane damage under oxidative stress.  相似文献   

4.
Giant bilayer vesicles were reconstituted from several lipids and lipid/cholesterol (CHOL) mixtures: stearolyloleoylphosphatidylcholine (SOPC), bovine sphingomyelin (BSM), diarachidonylphosphatidylcholine (DAPC), SOPC/CHOL, BSM/CHOL, DAPC/CHOL, and extracted red blood cell (RBC) lipids with native cholesterol. Single-walled vesicles were manipulated by micropipette suction and several membrane material properties were determined. The properties measured were the elastic area compressibility modulus K, the critical areal strain alpha c, and the tensile strength tau lys, from which the failure energy or membrane toughness Tf was calculated. The elastic area expansion moduli for these lipid and lipid/cholesterol bilayers ranged from 57 dyn/cm for DAPC to 1,734 dyn/cm for BSM/CHOL. The SOPC/CHOL series and RBC lipids had intermediate values. The results indicated that the presence of cholesterol is the single most influential factor in increasing bilayer cohesion, but only for lipids where both chains are saturated, or mono- or diunsaturated. Multiple unsaturation in both lipid chains inhibits the condensing effect of cholesterol in bilayers. The SOPC/CHOL system was studied in more detail. The area expansion modulus showed a nonlinear increase with increasing cholesterol concentration up to a constant plateau, indicating a saturation limit for cholesterol in the bilayer phase of approximately 55 mol% CHOL. The membrane compressibility was modeled by a property-averaging composite theory involving two bilayer components, namely, uncomplexed lipid and a lipid/cholesterol complex of stoichiometry 1/1.22. The area expansion modulus of this molecular composite membrane was evaluated by a combination of the expansion moduli of each component scaled by their area fractions in the bilayer. Bilayer toughness, which is the energy stored in the bilayer at failure, showed a maximum value at approximately 40 mol% CHOL. This breakdown energy was found to be only a fraction of the available thermal energy, implying that many molecules (approximately 50-100) may be involved in forming the defect structure that leads to failure. The area expansion modulus of extracted RBC lipids with native cholesterol was compared with recent measurements of intact RBC membrane compressibility. The natural membrane was also modeled as a simple composite made up to a compressible lipid/cholesterol matrix containing relatively incompressible transmembrane proteins. It appears that the interaction of incompressible proteins with surrounding lipid confers enhanced compressibility on the composite structure.  相似文献   

5.
At the 2017 meeting of the Australian Society for Biophysics, we presented the combined results from two recent studies showing how hydronium ions (H3O+) modulate the structure and ion permeability of phospholipid bilayers. In the first study, the impact of H3O+ on lipid packing had been identified using tethered bilayer lipid membranes in conjunction with electrical impedance spectroscopy and neutron reflectometry. The increased presence of H3O+ (i.e. lower pH) led to a significant reduction in membrane conductivity and increased membrane thickness. A first-order explanation for the effect was assigned to alterations in the steric packing of the membrane lipids. Changes in packing were described by a critical packing parameter (CPP) related to the interfacial area and volume and shape of the membrane lipids. We proposed that increasing the concentraton of H3O+ resulted in stronger hydrogen bonding between the phosphate oxygens at the water–lipid interface leading to a reduced area per lipid and slightly increased membrane thickness. At the meeting, a molecular model for these pH effects based on the result of our second study was presented. Multiple μs-long, unrestrained molecular dynamic (MD) simulations of a phosphatidylcholine lipid bilayer were carried out and showed a concentration dependent reduction in the area per lipid and an increase in bilayer thickness, in agreement with experimental data. Further, H3O+ preferentially accumulated at the water–lipid interface, suggesting the localised pH at the membrane surface is much lower than the bulk bathing solution. Another significant finding was that the hydrogen bonds formed by H3O+ ions with lipid headgroup oxygens are, on average, shorter in length and longer-lived than the ones formed in bulk water. In addition, the H3O+ ions resided for longer periods in association with the carbonyl oxygens than with either phosphate oxygen in lipids. In summary, the MD simulations support a model where the hydrogen bonding capacity of H3O+ for carbonyl and phosphate oxygens is the origin of the pH-induced changes in lipid packing in phospholipid membranes. These molecular-level studies are an important step towards a better understanding of the effect of pH on biological membranes.  相似文献   

6.
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.  相似文献   

7.
SGTx1 is a gating-modifier toxin that has been shown to inhibit the voltage-gated potassium channel Kv2.1. SGTx1 is thought to bind to the S3b-S4a region of the voltage-sensor, and is believed to alter the energetics of gating. Gating-modifier toxins such as SGTx1 are of interest as they can be used to probe the structure and dynamics of their target channels. Although there are experimental data for SGTx1, its interaction with lipid bilayer membranes remains to be characterized. We performed atomistic and coarse-grained molecular dynamics simulations to study the interaction of SGTx1 with a POPC and a 3:1 POPE/POPG lipid bilayer membrane. We reveal the preferential partitioning of SGTx1 into the water/membrane interface of the bilayer. We also show that electrostatic interactions between the charged residues of SGTx1 and the lipid headgroups play an important role in stabilizing SGTx1 in a bilayer environment.  相似文献   

8.
SGTx1 is a gating-modifier toxin that has been shown to inhibit the voltage-gated potassium channel Kv2.1. SGTx1 is thought to bind to the S3b-S4a region of the voltage-sensor, and is believed to alter the energetics of gating. Gating-modifier toxins such as SGTx1 are of interest as they can be used to probe the structure and dynamics of their target channels. Although there are experimental data for SGTx1, its interaction with lipid bilayer membranes remains to be characterized. We performed atomistic and coarse-grained molecular dynamics simulations to study the interaction of SGTx1 with a POPC and a 3:1 POPE/POPG lipid bilayer membrane. We reveal the preferential partitioning of SGTx1 into the water/membrane interface of the bilayer. We also show that electrostatic interactions between the charged residues of SGTx1 and the lipid headgroups play an important role in stabilizing SGTx1 in a bilayer environment.  相似文献   

9.
Phosphoinositides like phosphatidylinositol 4,5-bisphosphate (PIP2) are negatively charged lipids that play a pivotal role in membrane trafficking, signal transduction, and protein anchoring. We have designed a force field for the PIP2 headgroup using quantum mechanical methods and characterized its properties inside a lipid bilayer using molecular dynamics simulations. Macroscopic properties such as area/headgroup, density profiles, and lipid order parameters calculated from these simulations agree well with the experimental values. However, microscopically, the PIP2 introduces a local perturbation of the lipid bilayer. The average PIP2 headgroup orientation of 45° relative to the bilayer normal induces a unique, distance-dependent organization of the lipids that surround PIP2. The headgroups of these lipids preferentially orient closer to the bilayer normal. This perturbation creates a PIP2 lipid microdomain with the neighboring lipids. We propose that the PIP2 lipid microdomain enables the PIP2 to function as a membrane-bound anchoring molecule.  相似文献   

10.
Interactions of the hydrophobic anticancer drug tamoxifen (TAM) with lipid model membranes were studied using calcein-encapsulated vesicle leakage, attenuated total reflection Fourier transform infrared (FTIR) spectroscopy, small-angle neutron scattering (SANS), atomic force microscopy (AFM) based force spectroscopy, and all-atom molecular dynamics (MD) simulations. The addition of TAM enhances membrane permeability, inducing calcein to translocate from the interior to the exterior of lipid vesicles. A large decrease in the FTIR absorption band’s magnitude was observed in the hydrocarbon chain region, suggesting suppressed bond vibrational dynamics. Bilayer thickening was determined from SANS data. Force spectroscopy measurements indicate that the lipid bilayer area compressibility modulus KA is increased by a large amount after the incorporation of TAM. MD simulations show that TAM decreases the lipid area and increases chain order parameters. Moreover, orientational and positional analyses show that TAM exhibits a highly dynamic conformation within the lipid bilayer. Our detailed experimental and computational studies of TAM interacting with model lipid membranes shed new light on membrane modulation by TAM.  相似文献   

11.
New molecular-dynamic topology of phosphatidylcholine bilayer (DPPC) in total atomic OPLS force field was developed and used to study the structural characteristics of liquid-crystalline and gel state of lipid bilayer in the absence and in the presence of Na+ and Be2+ cations adsorbed at the interface and different in their affinity. The parameters of bilayer geometry, the amount of surface water, and the electrostatic potential distribution were estimated quantitatively from the simulation in both phase states. The azimuthal angle of hydrocarbon chains was found nearly the same in the region of each monolayer in gel state. The amount of surface water decreases upon bilayer “freezing” mainly by loss of water molecules not participating in H-bonds between lipid headgroups. The cation adsorption was shown to have a small effect on these H-bonded water molecules, whereas Be2+ appeared to retain surface water in the bilayer upon its freezing. The electric potential distribution in the normal direction to the membrane-water interface had a similar shape in any bilayer phase state regardless of the presence of the adsorbed cations. Analysis of the microscopic nature of the electric potential revealed a mutual compensation of the contributions of the main structural components of the system (lipids, water, and ions). The boundary potential increased by 116 mV for pure DPPC, by 212 mV in the presence of Na+, and by 133 mV in the presence of Be2+ upon the phase transition of bilayer to the gel state. The boundary potential difference in the presence of Na+ and Be2+ and its change at the bilayer phase transition are in a good agreement with the experimental data published earlier [Ermakov Yu.A., 1993].  相似文献   

12.
The affinity of ionized fatty acids for the Na,K-ATPase is used to determine the transmembrane profile of water penetration at the protein-lipid interface. The standardized intensity of the electron spin echo envelope modulation (ESEEM) from 2H-hyperfine interaction with D2O is determined for stearic acid, n-SASL, spin-labeled systematically at the C-n atoms throughout the chain. In both native Na,K-ATPase membranes from shark salt gland and bilayers of the extracted membrane lipids, the D2O-ESEEM intensities of fully charged n-SASL decrease progressively with position down the fatty acid chain toward the terminal methyl group. Whereas the D2O intensities decrease sharply at the n = 9 position in the lipid bilayers, a much broader transition region in the range n = 6 to 10 is found with Na,K-ATPase membranes. Correction for the bilayer population in the membranes yields the intrinsic D2O-intensity profile at the protein-lipid interface. For positions at either end of the chains, the D2O concentrations at the protein interface are greater than in the lipid bilayer, and the positional profile is much broader. This reveals the higher polarity, and consequently higher intramembrane water concentration, at the protein-lipid interface. In particular, there is a significant water concentration adjacent to the protein at the membrane midplane, unlike the situation in the bilayer regions of this cholesterol-rich membrane. Experiments with protonated fatty acid and phosphatidylcholine spin labels, both of which have a considerably lower affinity for the Na,K-ATPase, confirm these results.  相似文献   

13.
The affinity of ionized fatty acids for the Na,K-ATPase is used to determine the transmembrane profile of water penetration at the protein-lipid interface. The standardized intensity of the electron spin echo envelope modulation (ESEEM) from 2H-hyperfine interaction with D2O is determined for stearic acid, n-SASL, spin-labeled systematically at the C-n atoms throughout the chain. In both native Na,K-ATPase membranes from shark salt gland and bilayers of the extracted membrane lipids, the D2O-ESEEM intensities of fully charged n-SASL decrease progressively with position down the fatty acid chain toward the terminal methyl group. Whereas the D2O intensities decrease sharply at the n = 9 position in the lipid bilayers, a much broader transition region in the range n = 6 to 10 is found with Na,K-ATPase membranes. Correction for the bilayer population in the membranes yields the intrinsic D2O-intensity profile at the protein-lipid interface. For positions at either end of the chains, the D2O concentrations at the protein interface are greater than in the lipid bilayer, and the positional profile is much broader. This reveals the higher polarity, and consequently higher intramembrane water concentration, at the protein-lipid interface. In particular, there is a significant water concentration adjacent to the protein at the membrane midplane, unlike the situation in the bilayer regions of this cholesterol-rich membrane. Experiments with protonated fatty acid and phosphatidylcholine spin labels, both of which have a considerably lower affinity for the Na,K-ATPase, confirm these results.  相似文献   

14.
Cationic lipid membranes are known to form compact complexes with DNA and to be effective as gene delivery agents both in vitro and in vivo. Here we employ molecular dynamics simulations for a detailed atomistic study of lipid bilayers consisting of a mixture of cationic dimyristoyltrimethylammonium propane (DMTAP) and zwitterionic dimyristoylphosphatidylcholine (DMPC). Our main objective is to examine how the composition of the DMPC/DMTAP bilayers affects their structural and electrostatic properties in the liquid-crystalline phase. By varying the mole fraction of DMTAP, we have found that the area per lipid has a pronounced nonmonotonic dependence on the DMTAP concentration, with a minimum around the point of equimolar DMPC/DMTAP mixture. We show that this behavior has an electrostatic origin and is driven by the interplay between positively charged TAP headgroups and the zwitterionic phosphatidylcholine (PC) heads. This interplay leads to considerable reorientation of PC headgroups for an increasing DMTAP concentration, and gives rise to major changes in the electrostatic properties of the lipid bilayer, including a significant increase of total dipole potential across the bilayer and prominent changes in the ordering of water in the vicinity of the membrane. Moreover, chloride counterions are bound mostly to PC nitrogens implying stronger screening of PC heads by Cl ions compared to TAP headgroups. The implications of these findings are briefly discussed.  相似文献   

15.
We present molecular dynamics simulations of a multicomponent, asymmetric bilayer in mixed aqueous solutions of sodium and potassium chloride. Because of the geometry of the system, there are two aqueous solution regions in our simulations: one mimics the intracellular region, and one mimics the extracellular region. Ion-specific effects are evident at the membrane/aqueous solution interface. Namely, at equal concentrations of sodium and potassium, sodium ions are more strongly adsorbed to carbonyl groups of the lipid headgroups. A significant concentration excess of potassium is needed for this ion to overwhelm the sodium abundance at the membrane. Ion-membrane interactions also lead to concentration-dependent and cation-specific behavior of the electrostatic potential in the intracellular region because of the negative charge on the inner leaflet. In addition, water permeation across the membrane was observed on a timescale of ∼100 ns. This study represents a step toward the modeling of realistic biological membranes at physiological conditions in intracellular and extracellular environments.  相似文献   

16.
The higher harmonics of the alternating current in bilayer lipid membranes induced by a sinusoidal voltage applied to the membrane were measured. The bilayer lipid membranes were prepared from diphytanoylphosphatidylcholine in decane and tetradecane; a 16-bit analog-to-digital converter was used for the measurements. A sinusoidal voltage was formed with a 16-bit digital-to-analog converter. The dynamic measurement range reached 90 dB. The coefficients α and β of the expansion of capacitance C in terms of the membrane voltage U—C = C 0(1 + αU 2 + βU 4)—were determined from the measurement results. It was shown within the framework of the electrostriction model that a certain ratio of the coefficients α and β characterizes the inhomogeneity of the membrane with respect to its thickness and Young’s modulus of elasticity.  相似文献   

17.
Model bilayer systems from individual purified chloroplast thylakoid membrane lipids, from reconstituted mixtures of these purified lipids, and from leaf total polar lipid extracts have been prepared in water, and the longitudinal relaxation times (T's1) of the individual carbon atoms of the fatty acyl chains measured by 13C-NMR spectroscopy. The T's1 increasing distance of the carbon atoms from the polar headgroups in all cases, and as the results from each of the preparations are similar, all can be used as models of chloroplast membrane bilayers. Relaxation time measurements on intact chloroplast thylakoid membranes indicate the presence of chlorophyll resonances in the 13C-NMR spectrum of the membrane.  相似文献   

18.
We applied precise densimetry and ultrasound velocimetry methods to study the interaction of a synthetic α-helical transmembrane peptide, acetyl-K2-L24-K2-amide (L24), with model bilayer lipid membranes. The large unilamellar vesicles (LUVs) utilized were composed of a homologous series of n-saturated diacylphosphatidylcholines (PCs). PCs whose hydrocarbon chains contained from 13 to 16 carbon atoms, thus producing phospholipid bilayers of different thicknesses and gel to liquid-crystalline phase transition temperatures. This allowed us to analyze how the difference between the hydrophobic length of the peptide and the hydrophobic thickness of the lipid bilayer influences the thermodynamical and mechanical properties of the membranes. We showed that the incorporation of L24 decreases the temperature and cooperativity of the main phase transition of all LUVs studied. The presence of L24 in the bilayer also caused an increase of the specific volume and of the volume compressibility in the gel state bilayers. In the liquid crystalline state, the peptide decreases the specific volume at relatively higher peptide concentration (mole ratio L24:PC = 1:50). The overall volume compressibility of the peptide-containing lipid bilayers in the liquid-crystalline state was in general higher in comparison with pure membranes. There was, however, a tendency for the volume compressibility of these lipid bilayers to decrease with higher peptide content in comparison with bilayers of lower peptide concentration. For one lipid composition, we also compared the thermodynamical and mechanical properties of LUVs and large multilamellar vesicles (MLVs) with and without L24. As expected, a higher cooperativity of the changes of the thermodynamical and mechanical parameters took place for MLVs in comparison with LUVs. These results are in agreement with previously reported DSC and 2H NMR spectroscopy study of the interaction of the L24 and structurally related peptides with phosphatidylcholine bilayers. An apparent discrepancy between 2H NMR spectroscopy and compressibility data in the liquid crystalline state may be connected with the complex and anisotropic nature of macroscopic mechanical properties of the membranes. The observed changes in membrane mechanical properties induced by the presence of L24 suggest that around each peptide a distorted region exists that involves at least 2 layers of lipid molecules.  相似文献   

19.
Surface areas and fluctuations evaluated from 50 ns molecular dynamics simulations of fully hydrated dipalmitoylphosphatidylcholine (DPPC) bilayers in a 1:2 trehalose:lipid ratio carried out at surface tensions 10, 17 and 25 dyn/cm/leaflet are compared with those of pure bilayers under the same conditions. Trehalose increases the surface area, as consistent with the surface tension lowering observed in simulations at constant area. The system bulk elastic modulus K b  = 1.5 ± 0.3 × 1010 dyn/cm2. It is independent of bilayer surface area and trehalose content within statistical error. In contrast, the area elastic modulus K a shows a strong area dependence. At 64 Å2/lipid (the experimental surface area), K a  = 138 ± 26 dyn/cm for a pure DPPC bilayer and 82 ± 10 dyn/cm for one with trehalose; i.e. trehalose increases fluidity of the bilayer surface at this area per lipid.  相似文献   

20.
A mathematic–physical model of the interaction between cell membrane bilayer leaflets is proposed based on the Casimir effect in dielectrics. This model explains why the layers of a lipid membrane gently slide one past another rather than penetrate each other. The presented model reveals the dependence of variations in the free energy of the system on the membrane thickness. This function is characterized by the two close minima corresponding to the different levels of interdigitation of the lipids from neighbor layers. The energy barrier of the compressing transition between the predicted minima is estimated to be 5.7 kT/lipid, and the return energy is estimated to be 3.1 kT/lipid. The proposed model enables estimation of the value of the membrane elastic thickness modulus of compressibility, which is 1.7 × 109 N/m2, and the value of the interlayer friction coefficient, which is 1.9 × 108 Ns/m3.  相似文献   

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