Membrane hydrophobicity determines the activation free energy of passive lipid transport

The collective behavior of lipids with diverse chemical and physical features determines a membrane’s thermodynamic properties. Yet, the influence of lipid physicochemical properties on lipid dynamics, in particular interbilayer transport, remains underexplored. Here, we systematically investigate how the activation free energy of passive lipid transport depends on lipid chemistry and membrane phase. Through all-atom molecular dynamics simulations of 11 chemically distinct glycerophospholipids, we determine how lipid acyl chain length, unsaturation, and headgroup influence the free energy barriers for two elementary steps of lipid transport: lipid desorption, which is rate limiting, and lipid insertion into a membrane. Consistent with previous experimental measurements, we find that lipids with longer, saturated acyl chains have increased activation free energies compared to lipids with shorter, unsaturated chains. Lipids with different headgroups exhibit a range of activation free energies; however, no clear trend based solely on chemical structure can be identified, mirroring difficulties in the interpretation of previous experimental results. Compared to liquid-crystalline phase membranes, gel phase membranes exhibit substantially increased free energy barriers. Overall, we find that the activation free energy depends on a lipid’s local hydrophobic environment in a membrane and that the free energy barrier for lipid insertion depends on a membrane’s interfacial hydrophobicity. Both of these properties can be altered through changes in lipid acyl chain length, lipid headgroup, and membrane phase. Thus, the rate of lipid transport can be tuned through subtle changes in local membrane composition and order, suggesting an unappreciated role for nanoscale membrane domains in regulating cellular lipid dynamics.     

Lipid-protein interactions

Intrinsic membrane proteins are solvated by a shell of lipid molecules interacting with the membrane-penetrating surface of the protein; these lipid molecules are referred to as annular lipids. Lipid molecules are also found bound between transmembrane α-helices; these are referred to as non-annular lipids. Annular lipid binding constants depend on fatty acyl chain length, but the dependence is less than expected from models based on distortion of the lipid bilayer alone. This suggests that hydrophobic matching between a membrane protein and the surrounding lipid bilayer involves some distortion of the transmembrane α-helical bundle found in most membrane proteins, explaining the importance of bilayer thickness for membrane protein function. Annular lipid binding constants also depend on the structure of the polar headgroup region of the lipid, and hotspots for binding anionic lipids have been detected on some membrane proteins; binding of anionic lipid molecules to these hotspots can be functionally important. Binding of anionic lipids to non-annular sites on membrane proteins such as the potassium channel KcsA can also be important for function. It is argued that the packing preferences of the membrane-spanning α-helices in a membrane protein result in a structure that matches nicely with that of the surrounding lipid bilayer, so that lipid and protein can meet without either having to change very much.     

Partitioning and membrane disordering effects of dopamine antagonists: influence of lipid peroxidation, temperature, and drug concentration.

The effect of four dopamine antagonists (spiperone, haloperidol, pimozide, and domperidone) on the lipid order of caudate nucleus microsomal membranes and on liposomes from membrane lipid extracts was evaluated and related to the partition coefficients (Kp) of the drugs. Lipid membrane order was determined by fluorescence polarization using 1,6-diphenyl-1,3,5-hexatriene (DPH) as a probe of the membrane core and 1-[4-(trimethylammonium)phenyl]-6-phenyl-1,3,5-hexatriene (TMA-DPH) as a probe of the membrane surface. Dopamine antagonists decrease the fluorescence polarization of both probes, indicating that they disorder the membrane lipids at different depths. Pimozide and domperidone, the drugs with higher Kp values, are more effective at decreasing the polarization of DPH, a probe of the membrane core, than that of TMA-DPH. In contrast, spiperone and haloperidol, which have lower values for Kp, induce more significant decreases in TMA-DPH depolarization, a probe of the membrane surface. These findings indicate that higher partition coefficients of the drugs are directly correlated with an increase of fluidity in the hydrophobic core of brain membranes. Ascorbate/Fe(2+)-induced membrane lipid peroxidation increases membrane order. Membrane lipid peroxidation decreases the partition coefficients of the dopamine antagonists tested. Increasing temperature (4-37 degrees C) decreases membrane order, but temperature effect is less evident after lipid peroxidation. The disordering effect of dopamine antagonists increases with increasing drug concentrations (1-15 microM), a maximum being observed at 10 microM. However, this effect is also less evident after membrane lipid peroxidation. We can conclude that dopamine antagonists and membrane lipid peroxidation affect membrane lipid order and that the action of these drugs is dependent on initial bilayer fluidity. Membrane lipid peroxidation increases membrane order while dopamine antagonists show a disordering effect of membrane phospholipids. This disordering effect can indirectly influence the activity of membrane proteins and it is one of the mechanisms through which membrane function can be altered by these drugs.     

Folding and assembly of beta-barrel membrane proteins

Beta-barrel membrane proteins occur in the outer membranes of Gram-negative bacteria, mitochondria and chloroplasts. The membrane-spanning sequences of beta-barrel membrane proteins are less hydrophobic than those of alpha-helical membrane proteins, which is probably the main reason why completely different folding and membrane assembly pathways have evolved for these two classes of membrane proteins. Some beta-barrel membrane proteins can be spontaneously refolded into lipid bilayer model membranes in vitro. They may also have this ability in vivo although lipid and protein chaperones likely assist with their assembly in appropriate target membranes. This review summarizes recent work on the thermodynamic stability and the mechanism of membrane insertion of beta-barrel membrane proteins in lipid model and biological membranes. How lipid compositions affect folding and assembly of beta-barrel membrane proteins is also reviewed. The stability of these proteins in membranes is not as large as previously thought (<10 kcal/mol) and is modulated by elastic forces of the lipid bilayer. Detailed kinetic studies indicate that beta-barrel membrane proteins fold in distinct steps with several intermediates that can be characterized in vitro. Formation of the barrel is synchronized with membrane insertion and all beta-hairpins insert simultaneously in a concerted pathway.     

Lipid-protein interactions in biological membranes: a structural perspective

Lipid molecules bound to membrane proteins are resolved in some high-resolution structures of membrane proteins. An analysis of these structures provides a framework within which to analyse the nature of lipid-protein interactions within membranes. Membrane proteins are surrounded by a shell or annulus of lipid molecules, equivalent to the solvent layer surrounding a water-soluble protein. The lipid bilayer extends right up to the membrane protein, with a uniform thickness around the protein. The surface of a membrane protein contains many shallow grooves and protrusions to which the fatty acyl chains of the surrounding lipids conform to provide tight packing into the membrane. An individual lipid molecule will remain in the annular shell around a protein for only a short period of time. Binding to the annular shell shows relatively little structural specificity. As well as the annular lipid, there is evidence for other lipid molecules bound between the transmembrane α-helices of the protein; these lipids are referred to as non-annular lipids. The average thickness of the hydrophobic domain of a membrane protein is about 29 Å, with a few proteins having significantly smaller or greater thicknesses than the average. Hydrophobic mismatch between a membrane protein and the surrounding lipid bilayer generally leads to only small changes in membrane thickness. Possible adaptations in the protein to minimise mismatch include tilting of the helices and rotation of side chains at the ends of the helices. Packing of transmembrane α-helices is dependent on the chain length of the surrounding phospholipids. The function of membrane proteins is dependent on the thickness of the surrounding lipid bilayer, sometimes on the presence of specific, usually anionic, phospholipids, and sometimes on the phase of the phospholipid.     

多不饱和脂肪酸对细胞膜功能影响的研究进展

多不饱和脂肪酸是细胞膜磷脂的重要组成成份,影响细胞膜的稳定性.它具有广泛的生物学功能,包括细胞内信号传导通路、基因表达和细胞凋亡的调控等.主要从细胞膜脂质的组成,细胞膜的流动性及膜脂质过氧化等方面对多不饱和脂肪酸对细胞膜功能的影响进行了综述.     

Lipid-protein interactions in biological membranes: a structural perspective

Lipid molecules bound to membrane proteins are resolved in some high-resolution structures of membrane proteins. An analysis of these structures provides a framework within which to analyse the nature of lipid-protein interactions within membranes. Membrane proteins are surrounded by a shell or annulus of lipid molecules, equivalent to the solvent layer surrounding a water-soluble protein. The lipid bilayer extends right up to the membrane protein, with a uniform thickness around the protein. The surface of a membrane protein contains many shallow grooves and protrusions to which the fatty acyl chains of the surrounding lipids conform to provide tight packing into the membrane. An individual lipid molecule will remain in the annular shell around a protein for only a short period of time. Binding to the annular shell shows relatively little structural specificity. As well as the annular lipid, there is evidence for other lipid molecules bound between the transmembrane alpha-helices of the protein; these lipids are referred to as non-annular lipids. The average thickness of the hydrophobic domain of a membrane protein is about 29 A, with a few proteins having significantly smaller or greater thicknesses than the average. Hydrophobic mismatch between a membrane protein and the surrounding lipid bilayer generally leads to only small changes in membrane thickness. Possible adaptations in the protein to minimise mismatch include tilting of the helices and rotation of side chains at the ends of the helices. Packing of transmembrane alpha-helices is dependent on the chain length of the surrounding phospholipids. The function of membrane proteins is dependent on the thickness of the surrounding lipid bilayer, sometimes on the presence of specific, usually anionic, phospholipids, and sometimes on the phase of the phospholipid.     

How lipids and proteins interact in a membrane: a molecular approach

Membrane proteins in a biological membrane are surrounded by a shell or annulus of 'solvent' lipid molecules. These lipid molecules in general interact rather non-specifically with the protein molecules, although a few 'hot-spots' may be present on the protein where anionic lipids bind with high affinity. Because of the low structural specificity of most of the annular sites, the composition of the lipid annulus will be rather similar to the bulk lipid composition of the membrane. The structures of the solvent lipid molecules are important in determining the conformational state of a membrane protein, and hence its activity, through charge and hydrogen bonding interactions between the lipid headgroups and residues in the protein, and through hydrophobic matching between the protein and the surrounding lipid bilayer. Evidence is also accumulating for the presence of 'co-factor' lipid molecules binding with high specificity to membrane proteins, often between transmembrane alpha-helices, and often being essential for activity.     

Lipid trafficking to the outer membrane of Gram-negative bacteria

The envelope of Gram-negative bacteria is composed of two distinct lipid membranes: an inner membrane and outer membrane. The outer membrane is an asymmetric bilayer with an inner leaflet of phospholipids and an outer leaflet of lipopolysaccharide. Most of the steps of lipid synthesis occur within the cytoplasmic compartment of the cell. Lipids must then be transported across the inner membrane and delivered to the outer membrane. These topological features combined with the ability to apply the tools of biochemistry and genetics make the Gram-negative envelope a fascinating model for the study of lipid trafficking. In addition, as lipopolysaccharide is essential for growth of most strains and is a potent inducer of the mammalian innate immune response via activation of Toll-like receptors, Gram-negative lipid transport is also a promising target for the development of novel antibacterial and anti-inflammatory compounds. This review focuses on recent developments in our understanding of lipid transport across the inner membrane and to the outer membrane of Gram-negative bacteria.     

HIV gp41 Fusion Peptide Increases Membrane Ordering in a Cholesterol-Dependent Fashion

Fusion between viral envelopes and host cell membranes, which is mediated by special glycoproteins anchored on the viral membrane, is required for HIV viral entry and infection. The HIV gp41 fusion peptide (FP), which initiates membrane fusion, adopts either an α-helical or β-sheeted structure depending on the cholesterol concentration. We used phosphocholine spin labels on the lipid headgroup and different positions on the acyl chain to detect its perturbation on lipid bilayers containing different cholesterol concentrations by electron-spin resonance. Our findings were as follows. 1), gp41 FP affects the lipid order in the same manner as previously shown for influenza hemagglutinin FP, i.e., it has a cooperative effect versus the peptide/lipid ratio, supporting our hypothesis that membrane ordering is a common prerequisite for viral membrane fusion. 2), gp41 FP induces membrane ordering in all lipid compositions studied, whereas a nonfusion mutant FP perturbs lipid order to a significantly smaller extent. 3), In high-cholesterol-containing lipid bilayers, where gp41 FP is in the β-aggregation conformation, its effect on the lipid ordering reaches deeper into the bilayer. The different extent to which the two conformers perturb is correlated with their fusogenicity. The possible role of the two conformers in membrane fusion is discussed.     

Electrochemical and NMR spectroscopic investigations of the influence of the probe molecule Eu(fod)3 on the permeability of lipid membranes to ions

Investigating the action of the fluorinated europium complex Eu(fod)3 on lipid membranes we found that the complex facilitates the ion transfer through the membrane. Electric measurements on planar lipid membranes showed that the membrane conductivity increases considerably by insertion of the complex into the membrane. The increase in the conductivity was only obtained if both layers of the membrane were modified with the complex. 1H NMR spectroscopic studies using DOPC liposomes gave information about the location of the modifier complex in the lipid membrane. From chemical shift effects we concluded that the complex resides in the choline head group region of the membrane and also in the membrane interior near the -C =C- lipid double bond, but not in the center of the bilayer. For understanding of the mentioned conductivity effect we assume that the europium complex induces defects of yet unknown structure in the lipid matrix which provide paths for the ion transfer through the membrane. As appropriate measurements revealed, these paths seem to conduct cations predominantly. Investigating the current voltage behavior of the modified lipid membranes in dependence on the ion concentration we obtained different shaped current-voltage curves. Calculation showed that a model with only one energy barrier inside the membrane is unable to describe these curves kinetically. However, by assuming two energy barriers--one barrier in each membrane lipid layer--the observed curve can be described satisfactorily.     

uPA binding increases UPAR localization to lipid rafts and modifies the receptor microdomain composition

UPAR is a GPI anchored protein, which is found in both lipid rafts and in more fluid regions of the plasma membrane. We have studied the role of the ligand uPA on uPAR localization and on the composition of the lipid membrane microdomains. We have analyzed the glycosphingolipid environment of uPAR in detergent resistant membrane (DRM) fractions prepared by cell lysis with 1% Triton X-100 and fractionated by sucrose gradient centrifugation obtained from HEK293-uPAR cells. The uPAR specific lipid membrane microdomain has been separated from the total DRM fraction by immunoprecipitation with an anti-uPAR specific antibody under conditions that preserve membrane integrity. We have also tested uPA-induced ERK phosphorylation in the presence of methyl-beta-cyclodextrin, which is known to disrupt lipid rafts by sequestering cholesterol from such domains. Our results show that uPAR is partially associated with DRM and this association is increased by ligands, is independent of the catalytic activity of uPA, and is required for intracellular signalling. In the absence of ligands, uPAR experiences a lipid environment very similar to that of total DRM, enriched in sphingomyelin and glycosphingolipids. However, after treatment of cells with uPA or ATF the lipid environment is strongly impoverished of neutral glycosphingolipids.     

uPA binding increases UPAR localization to lipid rafts and modifies the receptor microdomain composition

UPAR is a GPI anchored protein, which is found in both lipid rafts and in more fluid regions of the plasma membrane. We have studied the role of the ligand uPA on uPAR localization and on the composition of the lipid membrane microdomains. We have analyzed the glycosphingolipid environment of uPAR in detergent resistant membrane (DRM) fractions prepared by cell lysis with 1% Triton X-100 and fractionated by sucrose gradient centrifugation obtained from HEK293-uPAR cells. The uPAR specific lipid membrane microdomain has been separated from the total DRM fraction by immunoprecipitation with an anti-uPAR specific antibody under conditions that preserve membrane integrity. We have also tested uPA-induced ERK phosphorylation in the presence of methyl-β-cyclodextrin, which is known to disrupt lipid rafts by sequestering cholesterol from such domains. Our results show that uPAR is partially associated with DRM and this association is increased by ligands, is independent of the catalytic activity of uPA, and is required for intracellular signalling. In the absence of ligands, uPAR experiences a lipid environment very similar to that of total DRM, enriched in sphingomyelin and glycosphingolipids. However, after treatment of cells with uPA or ATF the lipid environment is strongly impoverished of neutral glycosphingolipids.     

Use of fluorescence polarization to monitor intracellular membrane changes during temperature acclimation. Correlation with lipid compositional and ultrastructural changes.

Fluorescence polarization of 1,6-diphenylhexatriene (DPH) was used to study the effects of temperature acclimation on Tetrahymena membranes. The physical properties of membrane lipids were found to be highly dependent on cellular growth temperature. DPH polarization in lipids from three different membrane fractions correlated well with earlier freeze-fracture and electron spin resonance observations showing that membrane fluidity progressively decreases in the order microsomes greater than pellicles greater than cilia throughout a wide range of growth temperatures. Changes in membrane lipid fluidity following a shift from high to low growth temperatures proceed rapidly in the microsomes, whereas there is a pronounced lag in the changes of peripheral cell membrane lipids. These data support previous observations that adaptive changes in membrane fluidity proceed via lipid modifications in the endoplasmic reticulum, followed by dissemination of lipid components to other cell membranes. The rapid changes in polarization observed in the microsomal lipids following a temperature shift correspond closely with the time-dependent alterations in both lipid fatty acid composition and freeze-fracture patterns of membrane particle distribution, suggesting that, in the endoplasmic reticulum, lipid phase separation is the primary cause of membrane particle rearrangements.     

Effect of cholesterol on the interaction of the HIV GP41 fusion peptide with model membranes. Importance of the membrane dipole potential

Fusion of viral and cell membranes is a key event in the process by which the human immunodeficiency virus (HIV) enters the target cell. Membrane fusion is facilitated by the interaction of the viral gp41 fusion peptide with the cell membrane. Using synthetic peptides and model membrane systems, it has been established that the sequence of events implies the binding of the peptide to the membrane, followed by a conformational change (transformation of unordered and helical structures into beta-aggregates) which precedes lipid mixing. It is known that this process can be influenced by the membrane lipid composition. In the present work we have undertaken a systematic study in order to determine the influence of cholesterol (abundant in the viral membrane) in the sequence of events leading to lipid mixing. Besides its effect on membrane fluidity, cholesterol can affect a less known physical parameter, the membrane dipole potential. Using the dipole potential fluorescent sensor di-8-ANEPPS together with other biophysical techniques, we show that cholesterol increases the affinity of the fusion peptide for the model membranes, and although it lowers the extent of lipid mixing, it increases the mixing rate. The influence of cholesterol on the peptide affinity and the lipid mixing rate are shown to be mainly due to its influence of the membrane dipole potential, whereas the lipid mixing extent and peptide conformational changes seem to be more dependent on other membrane parameters such as membrane fluidity and hydration.     

Interaction of carbonylcyanide <Emphasis Type="Italic">p</Emphasis>-trifluoromethoxyphenylhydrazone (FCCP) with lipid membrane systems: a biophysical approach with relevance to mitochondrial uncoupling

FCCP (carbonylcyanide p-trifluoromethoxyphenylhydrazone), a classical uncoupler of mitochondrial oxidative phosphorylation, is used in this study as a model to clarify how interactions of uncouplers with membrane lipid bilayers may influence membrane biophysics and their protonophoric activity itself. In order to disclose putative effects that may be important when considering using uncouplers for pharmacological purposes, an extensive characterization of FCCP membrane lipid interactions using accurate biophysical approaches and simple model lipid systems was carried out. Differential scanning calorimetry studies showed that FCCP molecules disturb lipid bilayers and favor lateral phase separation in mixed lipid systems. ³¹P NMR assays indicated that FCCP alters the curvature elastic properties of membrane models containing non-bilayer lipids, favoring lamellar/H_II transition, probably by alleviation of hydrocarbon-packing constraints in the inverted hexagonal phase. Taking advantage of FCCP quenching effects on the fluorescent probes DPH (1,6-diphenyl-1,3,5-hexatriene) and DPH-PA (3-(p-(6-phenyl)-1,3,5-hexatrienyl)phenylpropionic acid), it is demonstrated that FCCP distributes across the bilayer thickness in both a single and a ternary lipid system mimicking the inner mitochondrial membrane. This behavior is consistent with the ability of the compound to migrate through the thickness of the inner mitochondrial membrane, an event required for its protonophoric activity. Finally, the study of the membrane fluidity in different lipid systems, as reported by the rotational correlation time (θ) of DPH or DPH-PA, showed that the extension at which FCCP disturbs membrane properties associated with the dynamics and the order of lipid molecules depends on the lipid composition of the model lipid system assayed.     

Membrane organization and lipid rafts

Cell membranes are composed of a lipid bilayer, containing proteins that span the bilayer and/or interact with the lipids on either side of the two leaflets. Although recent advances in lipid analytics show that membranes in eukaryotic cells contain hundreds of different lipid species, the function of this lipid diversity remains enigmatic. The basic structure of cell membranes is the lipid bilayer, composed of two apposing leaflets, forming a two-dimensional liquid with fascinating properties designed to perform the functions cells require. To coordinate these functions, the bilayer has evolved the propensity to segregate its constituents laterally. This capability is based on dynamic liquid-liquid immiscibility and underlies the raft concept of membrane subcompartmentalization. This principle combines the potential for sphingolipid-cholesterol self-assembly with protein specificity to focus and regulate membrane bioactivity. Here we will review the emerging principles of membrane architecture with special emphasis on lipid organization and domain formation.     

Structure of planar membrane formed from liposomes

Lipid vesicles with incorporated ion channels from polyene antibiotic amphotericin B were used to investigate structures of planar membranes formed by Shindler's techniques. A planar membrane assembled on the aperture in a lavsan film from two layers generated at the air-aqueous liposome suspension interface is not a simple bilayer but a bimolecular membrane containing numerous partly fused liposomes. A complete fusion of liposomal membranes with the planar bilayer is an unlikely event during membrane formation. A planar bimolecular lipid membrane without incorporated liposomes can be made by a method consisting of three stages: formation of a lipid layer on the air-water interface of a suspension containing liposomes, transfer of this layer along the surface of the solution into a chamber containing a solution without liposomes where a lipid monomolecular layer forms gradually (within about 20 min) at the air-water interface, assembling of the planar bilayer membrane from this monolayer. The knowledge of the planar membrane structure may be useful in experiments on incorporation of membrane proteins into a planar lipid bilayer.     

Structural changes in vesicle membranes and mixed micelles of various lipid compositions after binding of different bile salts

Binding equilibria of common bile salts (BS) and different mixtures of membrane lipids were correlated with BS-induced structural changes of large unilamellar vesicles, with transition of vesicles to mixed micelles (MM), and with successive transformations of MM. At very low BS concentrations, in the outer vesicle monolayer definite BS/lipid aggregates are formed, the size and BS binding strength of which depend on the BS and lipid species involved. At increasing BS concentrations, binding to the membranes is hampered, and above a critical BS content, membrane stress due to asymmetric BS binding leads to formation of transient membrane holes, as shown by inulin release from the vesicles. Independent of the BS and lipid species, membrane solubilization starts at a ratio r = 0.3 of bound BS/lipid. Increasing phosphatidylserine, phosphatidylethanolamine, and cholesterol contents stabilize the lecithin membrane against BS to different degrees and in different ways, whereas the destabilization by sphingomyelin is probably due to the enhancement of the membrane gel-liquid transition temperature. Conjugation of the BS with glycine or taurine has a modulating effect on membrane hole formation, rather than on lipid solubilization. Diphenylhexatriene fluorescence anisotropy indicates a BS-induced drop of the internal membrane order and its restoration during membrane solubilization. At higher concentrations ursodeoxycholate induces additional condensation, whereas the other BS cause internal disorder in the MM. Above ratios r of approximately 8:1, we found a release of BS from these MM and suggest a rodlike structure for them. The results were discussed with respect to BS/membrane interactions during lipid excretion from the liver cell.     

Regulation of transbilayer plasma membrane phospholipid asymmetry

Lipids in biological membranes are asymmetrically distributed across the bilayer; the amine-containing phospholipids are enriched on the cytoplasmic surface of the plasma membrane, while the choline-containing and sphingolipids are enriched on the outer surface. The maintenance of transbilayer lipid asymmetry is essential for normal membrane function, and disruption of this asymmetry is associated with cell activation or pathologic conditions. Lipid asymmetry is generated primarily by selective synthesis of lipids on one side of the membrane. Because passive lipid transbilayer diffusion is slow, a number of proteins have evolved to either dissipate or maintain this lipid gradient. These proteins fall into three classes: 1) cytofacially-directed, ATP-dependent transporters ("flippases"); 2) exofacially-directed, ATP-dependent transporters ("floppases"); and 3) bidirectional, ATP-independent transporters ("scramblases"). The flippase is highly selective for phosphatidylserine and functions to keep this lipid sequestered from the cell surface. Floppase activity has been associated with the ABC class of transmembrane transporters. Although they are primarily nonspecific, at least two members of this class display selectivity for their substrate lipid. Scramblases are inherently nonspecific and function to randomize the distribution of newly synthesized lipids in the endoplasmic reticulum or plasma membrane lipids in activated cells. It is the combined action of these proteins and the physical properties of the membrane bilayer that generate and maintain transbilayer lipid asymmetry.