Detection of membrane biointeractions based on fluorescence superquenching

Assays for biointeractions of molecules with supported lipid bilayers using fluorescence superquenching are described. A conjugated cationic polymer was adsorbed on to silica microspheres, which were then coated with an anionic lipid bilayer. The lipid bilayer attenuated superquenching by acting as a barrier between the conjugated polymer and its quencher. Biointeractions of the lipid bilayer with a membrane lytic peptide, melittin, were detected and quantitated by superquenching of the conjugated polyelectrolyte in flow cytometric and microfluidic bioassays. A higher sensitivity for detecting melittin lysis of the lipid bilayer at lower concentrations and shorter times for melittin action was found using flow cytometry in this study in comparison to other existing methods. This study combined the sensitivity of superquenching and flow cytometry to detect biointeractions with a lipid bilayer, which serves as a platform for developing functional assays for sensor applications, lipid enzymology, and investigations of molecular interactions. In addition, this study demonstrated proof-of-concept for using superquenching detected as a result of lipid bilayer disruption in a microfluidic format.     

Nonintercalating nanosubstrates create asymmetry between bilayer leaflets

The physical properties of lipid bilayers can be remodeled by a variety of environmental factors. Here we investigate using molecular dynamics simulations the specific effects of nanoscopic substrates or external contact points on lipid membranes. We expose palmitoyl-oleoyl phosphatidylcholine bilayers unilaterally and separately to various model nanosized substrates differing in surface hydroxyl densities. We find that a surface hydroxyl density as low as 10% is sufficient to keep the bilayer juxtaposed to the substrate. The bilayer interacts with the substrate indirectly through multiple layers of water molecules; however, despite such buffered interaction, the bilayers exhibit certain properties different from unsupported bilayers. The substrates modify transverse lipid fluctuations, charge density profiles, and lipid diffusion rates, although differently in the two leaflets, which creates an asymmetry between bilayer leaflets. Other properties that include lipid cross-sectional areas, component volumes, and order parameters are minimally affected. The extent of asymmetry that we observe between bilayer leaflets is well beyond what has been reported for bilayers adsorbed on infinite solid supports. This is perhaps because the bilayers are much closer to our nanosized finite supports than to infinite solid supports, resulting in a stronger support-bilayer electrostatic coupling. The exposure of membranes to nanoscopic contact points, therefore, cannot be considered as a simple linear interpolation between unsupported membranes and membranes supported on infinite supports. In the biological context, this suggests that the exposure of membranes to nonintercalating proteins, such as those belonging to the cytoskeleton, should not always be considered as passive nonconsequential interactions.     

Lipid bilayer disruption by polycationic polymers: the roles of size and chemical functional group

Polycationic polymers are used extensively in biology to disrupt cell membranes and thus enhance the transport of materials into the cell. The highly polydisperse nature of many of these materials makes obtaining a mechanistic understanding of the disruption processes difficult. To design an effective mechanistic study, a monodisperse class of polycationic polymers, poly(amidoamine) (PAMAM) dendrimers, has been studied in the context of supported dimyristoylphosphatidylcholine (DMPC) lipid bilayers using atomic force microscopy (AFM). Aqueous solutions of amine-terminated generation 7 (G7) PAMAM dendrimers caused the formation of 15-40-nm-diameter holes in lipid bilayers. This effect was significantly reduced for smaller G5 dendrimers. For G3, no hole formation was observed. In addition to dendrimer size, surface chemistry had a strong influence on dendrimer-lipid bilayer interactions. In particular, acetamide-terminated G5 did not cause hole formation in bilayers. In all instances, the edges of bilayer defects proved to be points of highest dendrimer activity. A proposed mechanism for the removal of lipids by dendrimers involves the formation of dendrimer-filled lipid vesicles. By considering the thermodynamics, interaction free energy, and geometry of these self-assembled vesicles, a model that explains the influence of polymer particle size and surface chemistry on the interactions with lipid membranes was developed. These results are of general significance for understanding the physical and chemical properties of polycationic polymer interactions with membranes that lead to the transport of materials across cell membranes.     

In situ formation and characterization of poly(ethylene glycol)-supported lipid bilayers on gold surfaces

Inclusion of a polymer cushion between a lipid bilayer membrane and a solid surface has been suggested as a means to provide a soft, deformable layer that will allow for transmembrane protein insertion and mobility. In this study, mobile, tethered lipid bilayers were formed on a poly(ethylene glycol) (PEG) support via a two-step adsorption process. The PEG films were prepared by coadsorbing a heterofunctional, telechelic PEG lipopolymer (1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-poly(ethylene glycol)-2000-N-[3-(2-(pyridyldithio)propionate]) (DSPE-PEG-PDP) and a nonlipid functionalized PEG-PDP from an ethanol/water mixture, as described in a previous paper (Munro, J. C.; Frank, C. W. Langmuir 2004, 20, 3339-3349). Then a two-step lipid adsorption strategy was used. First, lipids were adsorbed onto the PEG support from a hexane solution. Second, vesicles were adsorbed and fused on the surface to create a bilayer in an aqueous environment. Fluorescence recovery after photobleaching experiments show that this process results in mobile bilayers with diffusion coefficients on the order of 2 microm2/s. The mobility of the bilayers is decreased slightly by increasing the density of tethered lipids. The formation of bilayers, and not multilayer structures, is also confirmed by surface plasmon resonance, which was used to determine in situ film thickness, and by fluorimetry, which was used to determine quantitatively the fluorescence intensity for each 18 by 18 mm sample. Unfortunately, fluorescence microscopy also shows that there are large defects on the samples, which limits the utility of this system.     

Measuring lipid asymmetry in planar supported bilayers by fluorescence interference contrast microscopy

There is substantial scientific and practical interest in engineering supported lipid bilayers with asymmetric lipid distributions as models for biological cell membranes. In principle, it should be possible to make asymmetric supported lipid bilayers by either the Langmuir-Blodgett/Schafer (LB/LS) or Langmuir-Blodgett/vesicle fusion (LB/VF) techniques (Kalb et al. Biochim. Biophys. Acta 1992, 1103, 307-316). However, the retention of asymmetry in biologically relevant lipid bilayers has never been experimentally examined in any of these systems. In the present work, we developed a technique that is based on fluorescence interference contrast (FLIC) microscopy to measure lipid asymmetry in supported bilayers. We compared the final degree of lipid asymmetry in LB/LS and LB/VF bilayers with and without cholesterol in liquid-ordered (l(o)) and liquid-disordered (l(d)) phases. Of five different fluorescent lipid probes that were examined, 1,2-dipalmitoyl-phosphatidylethanolamine-N-[lissamine rhodamine B] was the best for studying supported bilayers of complex composition and phase by FLIC microscopy. An asymmetrically labeled bilayer made by the LB/LS method was found to be at best 70-80% asymmetric once completed. In LB/LS bilayers of either l(o) or l(d) phase, cholesterol increased the degree of lipid mixing between the opposing monolayers. The use of a tethered polymer support for the initial monolayer did not improve lipid asymmetry in the resulting bilayer. However, asymmetric LB/VF bilayers retained nearly 100% asymmetric label, with or without the use of a tethered polymer support. Finally, lipid mixing across the center of LB/LS bilayers was found to have drastic effects on the appearance of l(d)-l(o) phase coexistence as shown by epifluorescence microscopy.     

Weakly coupled lipid bilayer membranes on multistimuli-responsive poly(N-isopropylacrylamide) copolymer cushions

Polymer-cushioned lipid bilayers are frequently used to mimic the native environment of cellular membranes in respect to the extracellular matrix and intracellular structures. With the aim to actively tune lipid membrane characteristics, we pursue the approach to use temperature and pH responsive polymer thin films of poly(N-isopropylacrylamide-co-carboxyacrylamide) (PNIPAAm-co-carboxyAAM) as cushions for supported lipid bilayers. A cationic lipid bilayer composed of dioleoylphosphatidylcholine (DOPC) and dioleoyltrimethylammoniumpropane (DOTAP) (9:1) was formed on top of the polymer thin film in a drying/rehydration process. Fluorescence recovery after photobleaching (FRAP) yielded higher lipid diffusion coefficients (6.3-9.6 μm(2) s(-1)) on polymer cushions in comparison to solid glass supports (3.0-5.9 μm(2) s(-1)). No correlation of the lipid mobility was found with the swelling state of (PNIPAAm-co-carboxyAAM), which is ascribed to restrained interfacial electrostatic interactions and dispersion forces. The results revealed a minimal coupling of the lipid bilayer with the polymer cushions, and thus, bilayers supported by (PNIPAAm-co-carboxyAAM) provide interesting opportunities for unperturbed lipid diffusion combined with control of transmembrane protein mobility due to the impact of a tunable frictional drag.     

Lipid bilayer deposition and patterning via air bubble collapse

We report a new method for forming patterned lipid bilayers on solid substrates. In bubble collapse deposition (BCD), an air bubble is first "inked" with a monolayer of phospholipid molecules and then touched to the surface of a thermally oxidized silicon wafer and the air is slowly withdrawn. As the bubble shrinks, the lipid monolayer pressure increases. Once the monolayer exceeds the collapse pressure, it folds back on itself, depositing a stable lipid bilayer on the surface. These bilayer disks have lateral diffusion coefficients consistent with high quality supported bilayers. By sequentially depositing bilayers in overlapping areas, fluid connections between bilayers of different compositions are formed. Performing vesicle rupture on the open substrate surrounding this bilayer patch results in a fluid but spatially isolated bilayer. Very little intermixing was observed between the vesicle rupture and bubble-deposited bilayers.     

Using bicellar mixtures to form supported and suspended lipid bilayers on silicon chips

Bicellar mixtures, planar lipid bilayer assemblies comprising long- and short-chain phosphatidylcholine lipids in suspension, were used to form supported lipid bilayers on flat silicon substrate and on nanotextured silicon substrates containing arrays of parallel troughs (170 nm wide, 380 nm deep, and 300 nm apart). Confocal fluorescence and atomic force microscopies were used to characterize the resulting lipid bilayer. Formation of a continuous biphasic undulating lipid bilayer membrane, where the crests and troughs corresponded to supported and suspended lipid bilayer regions, is demonstrated. The use of interferometric lithography to fabricate nanotexured substrates provides an advantage over other nanotextured substrates such as nanoporous alumina by offering flexibility in designing different geometries for suspending lipid bilayers.     

Impact of Strong and Weak Lipid–Protein Interactions on the Structure of a Lipid Bilayer on a Gold Electrode Surface

A lipid bilayer deposited on an electrode surface can serve as a benchmark system to investigate lipid–protein interactions in the presence of physiological electric fields. Recoverin and myelin‐associated glycoprotein (MAG) are used to study the impact of strong and weak protein–lipid interactions on the structure of model lipid bilayers, respectively. The structural changes in lipid bilayers are followed using electrochemical polarization modulation infrared reflection–absorption spectroscopy (PM IRRAS). Recoverin contains a myristoyl group that anchors in the hydrophobic part of a cell membrane. Insertion of the protein into the 1,2‐dimyristoyl‐sn‐glycero‐3‐phosphatidylcholine (DMPC)–cholesterol lipid bilayer leads to an increase in the capacitance of the lipid film adsorbed on a gold electrode surface. The stability and kinetics of the electric‐field‐driven adsorption–desorption process are not affected by the interaction with protein. Upon interaction with recoverin, the hydrophobic hydrocarbon chains become less ordered. The polar head groups are separated from each other, which allows for recoverin association in the membrane. MAG is known to interact with glycolipids present on the surface of a cell membrane. Upon probing the interaction of the DMPC–cholesterol–glycolipid bilayer with MAG a slight decrease in the capacity of the adsorbed lipid film is observed. The stability of the lipid bilayer increases towards negative potentials. At the molecular scale this interaction results in minor changes in the structure of the lipid bilayer. MAG causes small ordering in the hydrocarbon chains region and an increase in the hydration of the polar head groups. Combining an electrochemical approach with a structure‐sensitive technique, such as PM IRRAS, is a powerful tool to follow small but significant changes in the structure of a supramolecular assembly.     

Diffusive dynamics of vesicles tethered to a fluid supported bilayer by single-particle tracking

We recently introduced a method to tether intact phospholipid vesicles onto a fluid supported lipid bilayer using DNA hybridization (Yoshina-Ishii, C.; Miller, G. P.; Kraft, M. L; Kool, E. T.; Boxer, S. G. J. Am. Chem. Soc. 2005, 127, 1356-1357). Once tethered, the vesicles can diffuse in two dimensions parallel to the supported membrane surface. The average diffusion coefficient, D, is typically 0.2 microm(2)/s; this is 3-5 times smaller than for individual lipid or DNA-lipid conjugate diffusion in supported bilayers. In this article, we investigate the origin of this difference in the diffusive dynamics of tethered vesicles by single-particle tracking under collision-free conditions. D is insensitive to tethered vesicle size from 30 to 200 nm, as well as a 3-fold change in the viscosity of the bulk medium. The addition of macromolecules such as poly(ethylene glycol) reversibly stops the motion of tethered vesicles without causing the exchange of lipids between the tethered vesicle and supported bilayer. This is explained as a depletion effect at the interface between tethered vesicles and the supported bilayer. Ca ions lead to transient vesicle-vesicle interactions when tethered vesicles contain negatively charged lipids, and vesicle diffusion is greatly reduced upon Ca ion addition when negatively charged lipids are present both in the supported bilayer and tethered vesicles. Both effects are interesting in their own right, and they also suggest that tethered vesicle-supported bilayer interactions are possible; this may be the origin of the reduction in D for tethered vesicles. In addition, the effects of surface defects that reversibly trap diffusing vesicles are modeled by Monte Carlo simulations. This shows that a significant reduction in D can be observed while maintaining normal diffusion behavior on the time scale of our experiments.     

Composition of supported model membranes determined by neutron reflection

We have investigated the formation of supported bilayers by coadsorption of dipalmitoyl phosphatidylcholine (DPPC) with the nonionic surfactant beta-D-dodecyl maltoside. The adsorption of mixed phospholipid-surfactant micelles on hydrophilic silica surfaces at 25 degrees C was followed as a function of bulk concentration by neutron reflection. Using chain-deuterated d(25)-beta-D-dodecyl maltoside and d(62)-DPPC, we demonstrate that it is possible to determine the composition of the bilayers at each stage of a sequential dilution process, which enriches the adsorbed layer in phospholipid and leads to complete elimination of the surfactant. The final supported bilayers have thicknesses of 51 +/- 3 A and are stable to heating to 37 degrees C once all surfactant has been removed, and the structures agree well with other published data on DPPC supported bilayers. The coadsorption of cholesterol in a DPPC-surfactant mixture was also achieved, and the location and volume fraction of cholesterol in the DPPC bilayer was determined. Cholesterol is located in a 18 +/- 1 A thick layer below the lipid headgroup region and leads to an increased bilayer thickness of 58 +/- 2 A at 26 mol % of cholesterol.     

STABILIZATION OF LIPID BILAYERS ON SURFACES THROUGH CHARGED POLYMERS

ABSTRACT

It is our concept to use a polymer as a hydrophilic cushion to stabilize a lipid bilayer on a solid support. This can be accomplished by using polyacrylamides with disulfides and DMPE anchors as a hydrophilic cushion. These polymers have the additional functionalities to chemisorb on gold surfaces through the disulfides and to bind a lipid bilayer on it through the insertion of the lipid anchors into the lipid bilayer. This paper shows that a polymer with the additional functionality of charged groups increases the attraction of vesicles to form a tethered supported lipid bilayer. By varying the amount of charged groups in the polymer, we are able to control the hydrophilic behavior of the polymer and therefore are able to change the wetting on a surface. This was examined by measuring the contact angles. Using the technique of the surface plasmon spectroscopy, we are able to monitor the process of vesicle fusion on the polymer support.     

Interaction of polyacrylic acid with lipid bilayers: effect of polymer mass

Polyanion‐coated lipid vesicles are proposed to have an appreciable potential for drug delivery because of their ability to control the permeability of lipid bilayers by environmental parameters such as pH and temperature. However, details of the interaction of this class of polymers with lipids and their mechanisms of induced permeability are still being debated. In this work, we applied ¹H NOESY to study details of the interaction of polyacrylic acid (PAA) fractions of molecular weights 5 and 240 kDa with dimyristoylphosphatidylcholine vesicles. We showed that PAA of two different molecular masses modifies lipid bilayers increasing disorder and probability of close contact between polar and hydrophobic groups. PAA molecules adsorb near the interface of lipid bilayers but do not penetrate into the hydrophobic core of the bilayer and, thus, cannot participate in formation of transbilayer channels, proposed in earlier works. Increasing the molecular mass of PAA from 5 kDa to 240 kDa does not change the effect of PAA on the bilayer, although PAA240 forms a more compact structure (either intra‐molecular or inter‐molecular) and interacts more strongly with interface lipid protons. Copyright © 2013 John Wiley & Sons, Ltd.     

Interactions of lipid bilayers with supports: a coarse-grained molecular simulation study

The study of lipid structure and phase behavior at the nanoscale is of utmost importance due to implications in understanding the role of the lipids in biochemical membrane processes. Supported lipid bilayers play a key role in understanding real biological systems, but they are vastly underrepresented in computational studies. In this paper, we discuss molecular dynamics simulations of supported lipid bilayers using a coarse-grained model. We first focus on the technical implications of modeling solid supports for biomembrane simulations. We then describe noticeable influences of the support on the systems. We are able to demonstrate that the bilayer system behavior changes when supported by a hydrophilic surface. We find that the thickness of the water layer between the support and the bilayer (the inner-water region in the latter part of this paper) adapts through water permeation on the microsecond time scale. Additionally, we discuss how different surface topologies affect the bilayer. Finally, we point out the differences between the two leaflets induced by the support.     

Ultra-high vacuum surface analysis study of rhodopsin incorporation into supported lipid bilayers

Planar supported lipid bilayers that are stable under ambient atmospheric and ultra-high-vacuum conditions were prepared by cross-linking polymerization of bis-sorbylphosphatidylcholine (bis-SorbPC). X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) were employed to investigate bilayers that were cross-linked using either redox-initiated radical polymerization or ultraviolet photopolymerization. The redox method yields a more structurally intact bilayer; however, the UV method is more compatible with incorporation of transmembrane proteins. UV polymerization was therefore used to prepare cross-linked bilayers with incorporated bovine rhodopsin, a light-activated, G-protein-coupled receptor (GPCR). A previous study (Subramaniam, V.; Alves, I. D.; Salgado, G. F. J.; Lau, P. W.; Wysocki, R. J.; Salamon, Z.; Tollin, G.; Hruby, V. J.; Brown, M. F.; Saavedra, S. S. J. Am. Chem. Soc. 2005, 127, 5320-5321) showed that rhodopsin retains photoactivity after incorporation into UV-polymerized bis-SorbPC, but did not address how the protein is associated with the bilayer. In this study, we show that rhodopsin is retained in supported bilayers of poly(bis-SorbPC) under ultra-high-vacuum conditions, on the basis of the increase in the XPS nitrogen concentration and the presence of characteristic amino acid peaks in the ToF-SIMS data. Angle-resolved XPS data show that the protein is inserted into the bilayer, rather than adsorbed on the bilayer surface. This is the first study to demonstrate the use of ultra-high-vacuum techniques for structural studies of supported proteolipid bilayers.     

Stability of DNA-tethered lipid membranes with mobile tethers

We recently introduced two approaches for tethering planar lipid bilayers as membrane patches to either a supported lipid bilayer or DNA-functionalized surface using DNA hybridization (Chung, M.; Lowe, R. D.; Chan, Y-H. M.; Ganesan, P. V.; Boxer, S. G. J. Struct. Biol.2009, 168, 190-9). When mobile DNA tethers are used, the tethered bilayer patches become unstable, while they are stable if the tethers are fixed on the surface. Because the mobile tethers between a patch and a supported lipid bilayer offer a particularly interesting architecture for studying the dynamics of membrane-membrane interactions, we have investigated the sources of instability, focusing on membrane composition. The most stable patches were made with a mixture of saturated lipids and cholesterol, suggesting an important role for membrane stiffness. Other factors such as the effect of tether length, lateral mobility, and patch membrane edge were also investigated. On the basis of these results, a model for the mechanism of patch destruction is developed.     

Synthetic and natural polycationic polymer nanoparticles interact selectively with fluid-phase domains of DMPC lipid bilayers

Polycationic polymers are known to disrupt lipid bilayers. In this letter, we report the dependence of this disruption on the lipid structural phase. DMPC bilayers are exposed to two polycationic polymeric nanoparticles, PAMAM dendrimers and MSI-78. We find that regions of the bilayer that are in the gel phase are unaffected by the presence of polymers, whereas the liquid phase is disrupted.     

Role of lipid charge in organization of water/lipid bilayer interface: insights via computer simulations

Anionic unsaturated lipid bilayers represent suitable model systems that mimic real cell membranes: they are fluid and possess a negative surface charge. Understanding of detailed molecular organization of water-lipid interfaces in such systems may provide an important insight into the mechanisms of proteins' binding to membranes. Molecular dynamics (MD) of full-atom hydrated lipid bilayers is one of the most powerful tools to address this problem in silico. Unfortunately, wide application of computational methods for such systems is limited by serious technical problems. They are mainly related to correct treatment of long-range electrostatic effects. In this study a physically reliable model of an anionic unsaturated bilayer of 1,2-dioleoyl-sn-glycero-3-phosphoserine (DOPS) was elaborated and subjected to long-term MD simulations. Electrostatic interactions were treated with two different algorithms: spherical cutoff function and particle-mesh Ewald summation (PME). To understand the role of lipid charge in the system behavior, similar calculations were also carried out for zwitterionic bilayer composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). It was shown that, for the charged DOPS bilayer, the PME protocol performs much better than the cutoff scheme. In the last case a number of artifacts in the structural organization of the bilayer were observed. All of them were attributed to inadequate treatment of electrostatic interactions of lipid headgroups with counterions. Electrostatic properties, along with structural and dynamic parameters, of both lipid bilayers were investigated. Comparative analysis of the MD data reveals that the water-lipid interface of the DOPC bilayer is looser than that for DOPS. This makes possible deeper penetration of water molecules inside the zwitterionic (DOPC) bilayer, where they strongly interact with carbonyls of lipids. This can lead to thickening of the membrane interface in zwitterionic as compared to negatively charged bilayers.     

Supported lipid bilayers on biocompatible polysaccharide multilayers

Formation of supported lipid bilayers on soft polymer cushions is a useful approach to decouple the membrane from the substrate for applications involving membrane proteins. We prepared biocompatible polymer cushions by the layer-by-layer assembly of two polysaccharide polyelectrolytes, chitosan (CHI) and hyaluronic acid, on glass and silicon substrates. (CHI/HA)(5) films were characterized by atomic force microscopy, giving an average thickness of 57 nm and roughness of 25 nm in aqueous solution at pH 6.5. Formation of zwitterionic lipid bilayers by the vesicle fusion method was attempted using DOPC vesicles at pH 4 and 6.5 on (CHI/HA)(5) films. At higher pH adsorbed lipids had low mobility and large immobile lipid fractions; a combination of fluorescence and AFM indicated that this was attributable to formation of poor quality membranes with defects and pinned lipids rather than to a layer of surface-adsorbed vesicles. By contrast, more uniform bilayers with mobile lipids were produced at pH 4. Fluorescence recovery after photobleaching gave diffusion coefficients that were similar to those for bilayers on PEG cushions and considerably higher than those measured on other polyelectrolyte films. The results suggest that the polymer surface charge is more important than the surface roughness in controlling formation of mobile supported bilayers. These results demonstrate that polysaccharides provide a useful alternative to other polymer cushions, particularly for applications where biocompatibility is important.     

Protein adsorption on supported phospholipid bilayers

Quartz crystal microbalance with dissipation (QCM-D) measurements were used to investigate the adsorption of human fibrinogen, human serum albumin, bovine hemoglobin, horse heart cytochrome c, human immunoglobulin (hIgG), and 10% fetal bovine serum on supported bilayers of egg-phosphatidylcholine (eggPC) lipids. For comparison the adsorption of fibrinogen and hIgG to eggPC bilayers was also studied with surface plasmon resonance (SPR). The supported bilayers were formed in situ by vesicle adhesion and spontaneous fusion onto a SiO(2) surface. The supported lipid bilayer is highly protein resistant: The irreversible adsorption measured with the QCM-D technique was below the detection level, while reversible protein adsorption was detected for all the proteins in the range 0.3-4% of the saturation coverage on a hydrophobic thiol monolayer on gold. The adsorbed amounts were slightly higher for the SPR measurements. Possible mechanisms for the protein resistance of eggPC bilayers are briefly discussed.