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1.
Sharpe S  Yau WM  Tycko R 《Biochemistry》2006,45(3):918-933
We report solid-state nuclear magnetic resonance (NMR) measurements on the peptide Vpu(1-40), comprising residues 1-40 of the 81-residue type 1 integral membrane protein Vpu encoded by the HIV-1 genome. On the basis of a combination of 13C and 15N NMR chemical shifts under magic-angle spinning (MAS), effects of local mobility on NMR signal intensities, site-specific MAS NMR line widths, and NMR-detected hydrogen-deuterium exchange, we develop a model for the structure and dynamics of the Vpu(1-40) monomer in phospholipid bilayer membranes. Our data are largely consistent with earlier structural studies of Vpu peptides by Opella and co-workers, in which solution NMR and solid-state NMR without MAS were used, but our data provide new information about local variations in the degree of mobility and structural order. In addition, our data indicate that the transmembrane alpha-helix of Vpu(1-40) extends beyond the hydrophobic core of the bilayer. We find no evidence for heterogeneity in the conformation and intermolecular contacts of the transmembrane alpha-helix, with the exception of two distinct chemical shifts observed for the C alpha and C beta atoms of A18 that may reflect distinct modes of helix-helix interaction. These results have possible implications for the supramolecular structure of Vpu oligomers that form cation-selective ion channels.  相似文献   

2.
Montal M 《FEBS letters》2003,552(1):47-53
Vpu, a membrane protein from human immunodeficiency virus-1, folds into two distinct structural domains with different biological activities: a transmembrane (TM) helical domain involved in the budding of new virions from infected cells, and a cytoplasmic domain encompassing two amphipathic helices, which is implicated in CD4 degradation. The molecular mechanism by which Vpu facilitates virion budding is not clear. This activity of Vpu requires an intact TM helical domain. And it is known that oligomerization of the VPU TM domain results in the formation of sequence-specific, cation-selective channels. It has been shown that the channel activity of Vpu is confined to the TM domain, and that the cytoplasmic helices regulate the lifetime of the Vpu channel in the conductive state. Structure-function correlates based on the convergence of information about the channel activity of Vpu reconstituted in lipid bilayers and on its 3-D structure in membranes by a combination of solution and solid-state nuclear magnetic resonance spectroscopy may provide valuable insights to understand the role of Vpu in the pathogenesis of AIDS and for drug design aimed to block channel activity.  相似文献   

3.
Abstract

The role of histidine in channel-forming transmembrane (TM) helices was investigated by comparing the TM helices from Virus protein ‘u' (Vpu) and the M2 proton channel. Both proteins are members of the viroporin family of small membrane proteins that exhibit ion channel activity, and have a single TM helix that is capable of forming oligomers. The TM helices from both proteins have a conserved tryptophan towards the C-terminus. Previously, alanine 18 of Vpu was mutated to histidine in order to artificially introduce the same HXXXW motif that is central to the proton channel activity of M2. Interestingly, the mutated Vpu TM resulted in an increase in helix tilt angle of 11° in lipid bilayers compared to the wild-type Vpu TM. Here, we find the reverse, when histidine 37 of the HXXXW motif in M2 was mutated to alanine, it decreased the helix tilt by 10° from that of wild-type M2. The tilt change is independent of both the helix length and the presence of tryptophan. In addition, compared to wild-type M2, the H37A mutant displayed lowered sensitivity to proton concentration. We also found that the solvent accessibility of histidine-containing M2 is greater than without histidine. This suggests that the TM helix may increase the solvent exposure by changing its tilt angle in order to accommodate a polar/charged residue within the hydrophobic membrane region. The comparative results of M2, Vpu and their mutants demonstrated the significance of histidine in a transmembrane helix and the remarkable plasticity of the function and structure of ion channels stemming from changes at a single amino acid site.  相似文献   

4.
5.
Tatulian SA  Tamm LK 《Biochemistry》2000,39(3):496-507
Influenza virus hemagglutinin (HA), the viral envelope glycoprotein that mediates fusion between the viral and cellular membranes, is a homotrimer of three subunits, each containing two disulfide-linked polypeptide chains, HA(1) and HA(2). Each HA(2) chain spans the viral membrane with a single putative transmembrane alpha-helix near its C-terminus. Fusion experiments with recombinant HAs suggest that this sequence is required for a late step of membrane fusion, as a glycosylphosphatidylinositol-anchored analogue of HA only mediates "hemifusion" of membranes, i.e., the merging of the proximal, but not distal, leaflets of the two juxtaposed lipid bilayers [Kemble et al. (1994) Cell 76, 383-391]. To find a structural explanation for the function of the transmembrane domain of HA(2) in membrane fusion, we have studied the secondary structure, orientation, oligomerization, and lipid interactions of a synthetic peptide representing the transmembrane segment of X:31 HA (TMX31) by circular dichroism and attenuated total reflection Fourier transform infrared spectroscopy and by gel electrophoresis. The peptide was predominantly alpha-helical in detergent micelles and in phospholipid bilayers. The helicity was increased in lipid bilayers composed of acidic lipids compared to pure phosphatidylcholine bilayers. In planar lipid bilayers, the helices were oriented close to the membrane normal. TMX31 aggregated into small heat-resistant oligomers composed of two to five subunits in SDS micelles. Amide hydrogen exchange experiments indicated that a large fraction of the helical residues were accessible to water, suggesting the possibility that TMX31 forms pores in lipid bilayers. Finally, the peptide increased the acyl chain order in lipid bilayers, which may be related to the preferential association of HA with lipid "rafts" in the cell surface and which may be an important prerequisite for complete membrane fusion.  相似文献   

6.
Vpu, an 81-residue membrane protein encoded by the genome of HIV-1, is involved in CD4 degradation and facilitates virion budding from infected cells. The latter activity requires an intact transmembrane (TM) domain; however, the mechanism remains unclear. Vpu forms ion channels, an activity linked to the TM domain and envisioned to arise by oligomerization. The precise number of Vpu monomers that structure the channel is not yet known. To address this issue, we have synthesized tetrameric and pentameric proteins consisting of a carrier template to which four or five peptides corresponding to the TM domain of Vpu are attached. Ketoxime-forming chemoselective ligation efficiently ligated four and five copies, respectively, of the linear transmembrane peptide that was solubilized by the addition of a cleavable polyethylene glycol-polyamide auxiliary to a template. Purified tetrameric and pentameric proteins, denoted as T(4)Vpu and T(5)Vpu, exhibit the predicted mass as determined by MS analysis and fold with a high helical content as evidenced by CD. Both T(4)Vpu and T(5)Vpu, after reconstitution in lipid bilayers, form discrete ion channels of distinct conductance and high propensity to be open. The most frequent openings have a single channel conductance of 42 +/- 5 pS for T(4)Vpu and 76 +/- 5 pS for T(5)Vpu in 0.5m KCl. These findings validate the notion that the channels formed by Vpu result from the self-assembly of monomers. We conclude that a five-helix bundle of the TM of Vpu may approximate the structural motif underlying the oligomeric state of the conductive channel.  相似文献   

7.
Part of the genome of the human immunodeficiency virus type 1 (HIV-1) encodes for a short membrane protein Vpu, which has a length of 81 amino acids. It has two functional roles: (i) to downregulate CD4 and (ii) to support particle release. These roles are attributed to two distinct domains of the peptide, the cytoplasmic and transmembrane (TM) domains, respectively. It has been suggested that the enhanced particle release function is linked to the ion channel activity of Vpu, with a slight preference for cations over anions. To allow ion flux across the membrane Vpu would be required to assemble in homooligomers to form functional water-filled pores. In this study molecular dynamics simulations are used to address the role of particular amino acids in 4, 5, and 6 TM helix bundle structures. The helices (Vpu(6-33)) are extended to include hydrophilic residues such as Glu, Tyr, and Arg (EYR motif). Our simulations indicate that this motif destabilizes the bundles at their C-terminal ends. The arginines point into the pore to form a positive charged ring that could act as a putative selectivity filter. The helices of the bundles adopt slightly higher average tilt angles with decreasing number of helices. We also suggest that the helices are kinked. Conductance measurements on a peptide (Vpu(1-32)) reconstituted into lipid membranes show that the peptide forms ion channels with several conductance levels.  相似文献   

8.
Towards a mechanism of function of the viral ion channel Vpu from HIV-1   总被引:1,自引:0,他引:1  
Vpu, an integral membrane protein encoded in HIV-1, is implicated in the release of new virus particles from infected cells, presumably mediated by ion channel activity of homo-oligomeric Vpu bundles. Reconstitution of both full length Vpu(1-81) and a short, the transmembrane (TM) domain comprising peptide Vpu(1-32) into bilayers under a constant electric field results in an asymmetric orientation of those channels. For both cases, channel activity with similar kinetics is observed. Channels can open and remain open within a broad series of conductance states even if a small or no electric potential is applied. The mean open time for Vpu peptide channels is voltage-independent. The rate of channel opening shows a biphasic voltage activation, implicating that the gating is influenced by the interaction of the dipole moments of the TM helices with an electric field.  相似文献   

9.
Peptides were designed that are based on candidate transmembrane sequences of the V o-sector from the vacuolar H (+)-ATPase of Saccharomyces cerevisiae. Spin-label EPR studies of lipid-protein interactions were used to characterize the state of oligomerization, and polarized IR spectroscopy was used to determine the secondary structure and orientation, of these peptides in lipid bilayer membranes. Peptides corresponding to the second and fourth transmembrane domains (TM2 and TM4) of proteolipid subunit c (Vma3p) and of the putative seventh transmembrane domain (TM7) of subunit a (Vph1p) are wholly, or predominantly, alpha-helical in membranes of dioleoyl phosphatidylcholine. All three peptides self-assemble into oligomers of different sizes, in which the helices are differently inclined with respect to the membrane normal. The coassembly of rotor (Vma3p TM4) and stator (Vph1p TM7) peptides, which respectively contain the glutamate and arginine residues essential to proton transport by the rotary ATPase mechanism, is demonstrated from changes in the lipid interaction stoichiometry and helix orientation. Concanamycin, a potent V-ATPase inhibitor, and a 5-(2-indolyl)-2,4-pentadienoyl inhibitor that exhibits selectivity for the osteoclast subtype, interact with the membrane-incorporated Vma3p TM4 peptide, as evidenced by changes in helix orientation; concanamycin additionally interacts with Vph1p TM7, suggesting that both stator and rotor elements contribute to the inhibitor site within the membrane. Comparison of the peptide behavior in lipid bilayers is made with membranous subunit c assemblies of the 16-kDa proteolipid from Nephrops norvegicus, which can substitute functionally for Vma3p in S. cerevisiae.  相似文献   

10.
We report constraints on the supramolecular structure of amyloid fibrils formed by the 40-residue beta-amyloid peptide associated with Alzheimer's disease (A beta(1-40)) obtained from solid-state nuclear magnetic resonance (NMR) measurements of intermolecular dipole-dipole couplings between (13)C labels at 11 carbon sites in residues 2 through 39. The measurements are carried out under magic-angle spinning conditions, using the constant-time finite-pulse radiofrequency-driven recoupling (fpRFDR-CT) technique. We also present one-dimensional (13)C magic-angle spinning NMR spectra of the labeled A beta(1-40) samples. The fpRFDR-CT data reveal nearest-neighbor intermolecular distances of 4.8 +/- 0.5 A for carbon sites from residues 12 through 39, indicating a parallel alignment of neighboring peptide chains in the predominantly beta-sheet structure of the amyloid fibrils. The one-dimensional NMR spectra indicate structural order at these sites. The fpRFDR-CT data and NMR spectra also indicate structural disorder in the N-terminal segment of A beta(1-40), including the first nine residues. These results place strong constraints on any molecular-level structural model for full-length beta-amyloid fibrils.  相似文献   

11.
The structure of the membrane anchor domain (VpuMA) of the HIV-1-specific accessory protein Vpu has been investigated in solution and in lipid bilayers by homonuclear two-dimensional and solid-state nuclear magnetic resonance spectroscopy, respectively. Simulated annealing calculations, using the nuclear Overhauser enhancement data for the soluble synthetic peptide Vpu1-39 (positions Met-1-Asp-39) in an aqueous 2,2,2-trifluoroethanol (TFE) solution, afford a compact well-defined U-shaped structure comprised of an initial turn (residues 1-6) followed by a linker (7-9) and a short helix on the N-terminal side (10-16) and a further longer helix on the C-terminal side (22-36). The side chains of the two aromatic residues (Trp-22 and Tyr-29) in the longer helix are directed toward the center of the molecule around which the hydrophobic core of the folded VpuMA is positioned. As the observed solution structure is inconsistent with the formation of ion-conductive membrane pores defined previously for VpuMA in planar lipid bilayers, the isolated VpuMA domain as peptide Vpu1-27 was investigated in oriented phospholipid bilayers by proton-decoupled 15N cross polarization solid-state NMR spectroscopy. The line widths and chemical shift data of three selectively 15N-labeled peptides are consistent with a transmembrane alignment of a helical polypeptide. Chemical shift tensor calculations imply that the data sets are compatible with a model in which the nascent helices of the folded solution structure reassemble to form a more regular linear alpha-helix that lies parallel to the bilayer normal with a tilt angle of 相似文献   

12.
Bechinger B 《FEBS letters》2001,504(3):161-165
Helical peptides reconstituted into oriented phospholipid bilayers were studied by proton-decoupled 15N solid-state NMR spectroscopy. Whereas hydrophobic channel peptides, such as the N-terminal region of Vpu of HIV-1, adopt transmembrane orientations, amphipathic peptide antibiotics are oriented parallel to the bilayer surface. The interaction contributions that determine the alignment of helical peptides in lipid membranes were analysed using model sequences, and peptides that change their topology in a pH-dependent manner have been designed. The energy contributions of histidines, lysines, leucines and alanines as well as the alignment of peptides and phospholipids under conditions of hydrophobic mismatch have been investigated in considerable detail.  相似文献   

13.
The three-dimensional backbone structure of the transmembrane domain of Vpu from HIV-1 was determined by solid-state NMR spectroscopy in two magnetically-aligned phospholipid bilayer environments (bicelles) that differed in their hydrophobic thickness. Isotopically labeled samples of Vpu(2-30+), a 36-residue polypeptide containing residues 2-30 from the N-terminus of Vpu, were incorporated into large (q = 3.2 or 3.0) phospholipid bicelles composed of long-chain ether-linked lipids (14-O-PC or 16-O-PC) and short-chain lipids (6-O-PC). The protein-containing bicelles are aligned in the static magnetic field of the NMR spectrometer. Wheel-like patterns of resonances characteristic of tilted transmembrane helices were observed in two-dimensional (1)H/(15)N PISEMA spectra of uniformly (15)N-labeled Vpu(2-30+) obtained on bicelle samples with their bilayer normals aligned perpendicular or parallel to the direction of the magnetic field. The NMR experiments were performed at a (1)H resonance frequency of 900 MHz, and this resulted in improved data compared to lower-resonance frequencies. Analysis of the polarity-index slant-angle wheels and dipolar waves demonstrates the presence of a transmembrane alpha-helix spanning residues 8-25 in both 14-O-PC and 16-O-PC bicelles, which is consistent with results obtained previously in micelles by solution NMR and mechanically aligned lipid bilayers by solid-state NMR. The three-dimensional backbone structures were obtained by structural fitting to the orientation-dependent (15)N chemical shift and (1)H-(15)N dipolar coupling frequencies. Tilt angles of 30 degrees and 21 degrees are observed in 14-O-PC and 16-O-PC bicelles, respectively, which are consistent with the values previously determined for the same polypeptide in mechanically-aligned DMPC and DOPC bilayers. The difference in tilt angle in C14 and C16 bilayer environments is also consistent with previous results indicating that the transmembrane helix of Vpu responds to hydrophobic mismatch by changing its tilt angle. The kink found in the middle of the helix in the longer-chain C18 bilayers aligned on glass plates was not found in either of these shorter-chain (C14 or C16) bilayers.  相似文献   

14.
The HIV-1-encoded protein Vpu forms an oligomeric ion channel/pore in membranes and interacts with host proteins to support the virus lifecycle. However, Vpu molecular mechanisms are currently not well understood. Here, we report on the Vpu oligomeric organization under membrane and aqueous conditions and provide insights into how the Vpu environment affects the oligomer formation. For these studies, we designed a maltose-binding protein (MBP)-Vpu chimera protein and produced it in E. coli in soluble form. We analyzed this protein using analytical size-exclusion chromatography (SEC), negative staining electron microscopy (nsEM), and electron paramagnetic resonance (EPR) spectroscopy. Surprisingly, we found that MBP-Vpu formed stable oligomers in solution, seemingly driven by Vpu transmembrane domain self-association. A coarse modeling of nsEM data as well as SEC and EPR data suggests that these oligomers most likely are pentamers, similar to what was reported regarding membrane-bound Vpu. We also noticed reduced MBP-Vpu oligomer stability upon reconstitution of the protein in β-DDM detergent and mixtures of lyso-PC/PG or DHPC/DHPG. In these cases, we observed greater oligomer heterogeneity, with MBP-Vpu oligomeric order generally lower than in solution; however, larger oligomers were also present. Notably, we found that in lyso-PC/PG, above a certain protein concentration, MBP-Vpu assembles into extended structures, which had not been reported for Vpu. Therefore, we captured various Vpu oligomeric forms, which can shed light on Vpu quaternary organization. Our findings could be useful in understanding Vpu organization and function in cellular membranes and could provide information regarding the biophysical properties of single-pass transmembrane proteins.  相似文献   

15.
The human immunodeficiency virus type I (HIV-1) Vpu protein is 81 residues long and has two cytoplasmic and one transmembrane (TM) helical domains. The TM domain oligomerizes to form a monovalent cation selective ion channel and facilitates viral release from host cells. Exactly how many TM domains oligomerize to form the pore is still not understood, with experimental studies indicating the existence of a variety of oligomerization states. In this study, molecular dynamics (MD) simulations were performed to investigate the propensity of the Vpu TM domain to exist in tetrameric, pentameric, and hexameric forms. Starting with an idealized α-helical representation of the TM domain, a thorough search for the possible orientations of the monomer units within each oligomeric form was carried out using replica-exchange MD simulations in an implicit membrane environment. Extensive simulations in a fully hydrated lipid bilayer environment on representative structures obtained from the above approach showed the pentamer to be the most stable oligomeric state, with interhelical van der Waals interactions being critical for stability of the pentamer. Atomic details of the factors responsible for stable pentamer structures are presented. The structural features of the pentamer models are consistent with existing experimental information on the ion channel activity, existence of a kink around the Ile17, and the location of tetherin binding residues. Ser23 is proposed to play an important role in ion channel activity of Vpu and possibly in virus propagation.  相似文献   

16.
The channel-forming trans-membrane domain of Vpu (Vpu TM) from HIV-1 is known to enhance virion release from the infected cells and is a potential target for ion-channel blockers. The substitution of alanine at position 18 by a histidine (A18H) has been shown to render HIV-1 infections susceptible to rimantadine, a channel blocker of M2 protein from the influenza virus. In order to describe the influence of the mutation on the structure and rimantadine susceptibility of Vpu, we determined the structure of A18H Vpu TM, and compared it to those of wild-type Vpu TM and M2 TM. Both isotropic and orientationally dependent NMR frequencies of the backbone amide resonance of His18 were perturbed by rimantadine, and those of Ile15 and Trp22 were also affected, suggesting that His18 is the key residue for rimantadine binding and that residues located on the same face of the TM helix are also involved. A18H Vpu TM has an ideal, straight alpha-helix spanning residues 6-27 with an average tilt angle of 41 degrees in C14 phospholipid bicelles, indicating that the tilt angle is increased by 11 degrees compared to that of wild-type Vpu TM. The longer helix formed by the A18H mutation has a larger tilt angle to compensate for the hydrophobic mismatch with the length of the phospholipids in the bilayer. These results demonstrate that the local change of the primary structure plays an important role in secondary and tertiary structures of Vpu TM in lipid bilayers and affects its ability to interact with channel blockers.  相似文献   

17.
Abstract

Vpu, an integral membrane protein encoded in HIV-1, is implicated in the release of new virus particles from infected cells, presumably mediated by ion channel activity of homo- oligomeric Vpu bundles.

Reconstitution of both full length Vpu1–81 and a short, the transmembrane (TM) domain comprising peptide Vpu1-32 into bilayers under a constant electric field results in an asymmetric orientation of those channels. For both cases, channel activity with similar kinetics is observed. Channels can open and remain open within a broad series of conductance states even if a small or no electric potential is applied.

The mean open time for Vpu peptide channels is voltage-independent. The rate of channel opening shows a biphasic voltage activation, implicating that the gating is influenced by the interaction of the dipole moments of the TM helices with an electric field.  相似文献   

18.
Mehnert T  Routh A  Judge PJ  Lam YH  Fischer D  Watts A  Fischer WB 《Proteins》2008,70(4):1488-1497
Vpu from HIV-1 is an 81 amino acid type I integral membrane protein which consists of a cytoplasmic and a transmembrane (TM) domain. The TM domain is known to alter membrane permeability for ions and substrates when inserted into artificial membranes. Peptides corresponding to the TM domain of Vpu (Vpu(1-32)) and mutant peptides (Vpu(1-32)-W23L, Vpu(1-32)-R31V, Vpu(1-32)-S24L) have been synthesized and reconstituted into artificial lipid bilayers. All peptides show channel activity with a main conductance level of around 20 pS. Vpu(1-32)-W23L has a considerable flickering pattern in the recordings and longer open times than Vpu(1-32). Whilst recordings for Vpu(1-32)-R31V are almost indistinguishable from those of the WT peptide, recordings for Vpu(1-32)-S24L do not exhibit any noticeable channel activity. Recordings of WT peptide and Vpu(1-32)-W23L indicate Michaelis-Menten behavior when the salt concentration is increased. Both peptide channels follow the Eisenman series I, indicative for a weak ion channel with almost pore like characteristics.  相似文献   

19.
Vpu is a small phosphorylated integral membrane protein encoded by the human immunodeficiency virus type 1 genome and found in the endoplasmic reticulum and Golgi membranes of infected cells. It has been linked to roles in virus particle budding and degradation of CD4 in the endoplasmic reticulum. However, the molecular mechanisms employed by Vpu in performance of these functions are unknown. Structural similarities between Vpu and the M2 protein of influenza A virus have raised the question of whether the two proteins are functionally analogous: M2 has been demonstrated to form cation-selective ion channels in phospholipid membranes. In this paper we provide evidence that Vpu, purified after expression in Escherichia coli, also forms ion channels in planar lipid bilayers. The channels are approximately five- to sixfold more permeable to sodium and potassium cations than to chloride or phosphate anions. A bacterial cross-feeding assay was used to demonstrate that Vpu can also form sodium-permeable channels in vivo in the E. coli plasma membrane.  相似文献   

20.
K Weisz  G Gr?bner  C Mayer  J Stohrer  G Kothe 《Biochemistry》1992,31(4):1100-1112
The influence of cholesterol on the dynamic organization of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) bilayers was studied by deuteron nuclear magnetic resonance (2H NMR) using unoriented and macroscopically aligned samples. Analysis of the various temperature- and orientation-dependent experiments were performed using a comprehensive NMR model based on the stochastic Liouville equation. Computer simulations of the relaxation data obtained from phospholipids deuterated at the 6-, 13- and 14-position of the sn-2 chain and cholesterol labeled at the 3 alpha-position of the rigid steroid ring system allowed the unambiguous assignment of the various motional modes and types of molecular order present in the system. Above the phospholipid gel-to-liquid-crystalline phase transition, TM, 40 mol % cholesterol was found to significantly increase the orientational and conformational order of the phospholipid with substantially increased trans populations even at the terminal sn-2 acyl chain segments. Lowering the temperature continuously increases both inter- and intramolecular ordering, yet indicates less ordered chains than found for the pure phospholipid in its paracrystalline gel phase. Trans-gauche isomerization rates on all phospholipid alkyl chain segments are slowed down by incorporated cholesterol to values characteristic of gel-state lipid. However, intermolecular dynamics remain fast on the NMR time scale up to 30 K below TM, with rotational correlation times tau R parallel for DMPC ranging from 10 to 100 ns and an activation energy of ER = 35 kJ/mol. Below 273 K a continuous noncooperative condensation of both phospholipid and cholesterol is observed in the mixed membranes, and at about 253 K only a motionally restricted component is left, exhibiting slow fluctuations with correlation times of tau R perpendicular greater than 1 microsecond. In the high-temperature region (T greater than TM), order director fluctuations are found to constitute the dominant transverse relaxation process. Analysis of these collective lipid motions provides the viscoelastic parameters of the membranes. The results (T = 318 K) show that cholesterol significantly reduces the density of the cooperative motions by increasing the average elastic constant of the membrane from K = 1 x 10(-11) N for the pure phospholipid bilayers to K = 3.5 x 10(-11) N for the mixed system.  相似文献   

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