The influence of zwitterionic lipids on the electrostatic adsorption of macroions onto mixed lipid membranes

Charged lipid membranes commonly consist of a mixture of charged and zwitterionic lipids. We suggest a model that characterizes the influence of the dipolar nature of the zwitterionic lipid species on the electrostatic adsorption of macroions onto mixed membranes in the fluid state. The model is based on Poisson-Boltzmann theory which we have modified so as to account for the dipolar character of the zwitterionic lipids. In addition the membrane lipids are allowed to adjust their lateral distribution upon macroion adsorption. We consider and compare two experimentally relevant scenarios: cationic macroions adsorbed onto anionic membranes and anionic macroions adsorbed onto cationic membranes. We show that in the former case the adsorption strength is slightly weakened by the presence of the headgroup dipoles of the zwitterionic lipids. Here, macroion-induced lipid demixing is more pronounced and the lipid headgroups tilt away from a cationic macroion upon adsorption. In contrast, for the adsorption of anionic macroions onto a cationic membrane the zwitterionic lipids strongly participate in the electrostatic interaction between membrane and macroion, thus enhancing the adsorption strength significantly (we predict up to 20%). Consistent with that we find less lateral demixing of the charged lipids and a reorientation of the dipoles of the zwitterionic headgroups towards the anionic macroions. Our results may be of importance to understand the differences in the electrostatic adsorption of proteins/peptides onto cellular membranes versus complex formation between cationic membranes and DNA.     

Asymmetry of lipid bilayers induced by monovalent salt: atomistic molecular-dynamics study

Interactions between salt ions and lipid components of biological membranes are essential for the structure, stability, and functions of the membranes. The specific ionic composition of aqueous buffers inside and outside of the cell is known to differ considerably. To model such a situation we perform atomistic molecular-dynamics (MD) simulations of a single-component phosphatidylcholine lipid bilayer which separates two aqueous reservoirs with and without NaCl salt. To implement the difference in electrolyte composition near two membrane sides, a double bilayer setup (i.e., two bilayers in a simulation box) is employed. It turns out that monovalent salt, being in contact with one leaflet only, induces a pronounced asymmetry in the structural, electrostatic, and dynamical properties of bilayer leaflets after 50 ns of MD simulations. Binding of sodium ions to the carbonyl region of the leaflet which is in contact with salt results in the formation of "Na-lipids" complexes and, correspondingly, reduces mobility of lipids of this leaflet. In turn, attractive interactions of chloride ions (mainly located in the aqueous phase close to the water-lipid interface) with choline lipid groups lead to a substantial (more vertical) reorientation of postphatidylcholine headgroups of the leaflet adjoined to salt. The difference in headgroup orientation on two sides of a bilayer, being coupled with salt-induced reorientation of water dipoles, leads to a notable asymmetry in the charge-density profiles and electrostatic potentials of bilayer constitutes of the two leaflets. Although the overall charge density of the bilayer is found to be almost insensitive to the presence of salt, a slight asymmetry in the charge distribution between the two bilayer leaflets results in a nonzero potential difference of about 85 mV between the two water phases. Thus, a transmembrane potential of the order of the membrane potential in a cell can arise without ionic charge imbalance between two aqueous compartments.     

Modeling the influence of adsorbed DNA on the lateral pressure and tilt transition of a zwitterionic lipid monolayer

Certain lipid monolayers at the air-water interface undergo a second-order transition from a tilted to an untilted liquid-crystalline state of their lipid hydrocarbon chains at sufficiently large lateral pressure. Recent experimental observations demonstrate that in the presence of divalent cations DNA adsorbs onto a zwitterionic lipid monolayer and decreases the tilt transition pressure. Lowering of the tilt transition pressure indicates that the DNA condenses the lipid monolayer laterally. To rationalize this finding we analyze a theoretical model that combines a phenomenological Landau approach with an extension of the Poisson-Boltzmann model to zwitterionic lipids. Based on numerical calculations of the mean-field electrostatic free energy of a zwitterionic lipid monolayer-DNA complex in the presence of divalent cations, we analyze the thermodynamic equilibrium of DNA adsorption. We find that adsorbed DNA induces a 10% reduction of the electrostatic contribution to the lateral pressure exerted by the monolayer. This result implies a small but notable decrease in the tilt transition pressure. Additional mechanisms due to ion-ion correlations and headgroup reorientations are likely to further enhance this decrease.     

Effect of lipid headgroup composition on the interaction between melittin and lipid bilayers

The effect of the lipid polar headgroup on melittin-phospholipid interaction was investigated by cryo-TEM, fluorescence spectroscopy, ellipsometry, circular dichroism, electrophoresis and photon correlation spectroscopy. In particular, focus was placed on the effect of the lipid polar headgroup on peptide adsorption to, and penetration into, the lipid bilayer, as well as on resulting colloidal stability effects for large unilamellar liposomes. The effect of phospholipid headgroup properties on melittin-bilayer interaction was addressed by comparing liposomes containing phosphatidylcholine, -acid, and -inositol at varying ionic strength. Increasing the bilayer negative charge leads to an increased liposome tolerance toward melittin which is due to an electrostatic arrest of melittin at the membrane interface. Balancing the electrostatic attraction between the melittin positive charges and the phospholipid negative charges through a hydration repulsion, caused by inositol, reduced this surface arrest and increased liposome susceptibility to the disruptive actions of melittin. Furthermore, melittin was demonstrated to induce liposome structural destabilization on a colloidal scale which coincided with leakage induction for both anionic and zwitterionic systems. The latter findings thus clearly show that coalescence, aggregation, and fragmentation contribute to melittin-induced liposome leakage, and that detailed molecular analyses of melittin pore formation are incomplete without considering also these colloidal aspects.     

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.     

Molecular insight into the electrostatic membrane surface potential by 14n/31p MAS NMR spectroscopy: nociceptin-lipid association

Exploiting naturally abundant (14)N and (31)P nuclei by high-resolution MAS NMR (magic angle spinning nuclear magnetic resonance) provides a molecular view of the electrostatic potential present at the surface of biological model membranes, the electrostatic charge distribution across the membrane interface, and changes that occur upon peptide association. The spectral resolution in (31)P and (14)N MAS NMR spectra is sufficient to probe directly the negatively charged phosphate and positively charged choline segment of the electrostatic P(-)-O-CH(2)-CH(2)-N(+)(CH(3))(3) headgroup dipole of zwitterionic DMPC (dimyristoylphosphatidylcholine) in mixed-lipid systems. The isotropic shifts report on the size of the potential existing at the phosphate and ammonium group within the lipid headgroup while the chemical shielding anisotropy ((31)P) and anisotropic quadrupolar interaction ((14)N) characterize changes in headgroup orientation in response to surface potential. The (31)P/(14)N isotropic chemical shifts for DMPC show opposing systematic changes in response to changing membrane potential, reflecting the size of the electrostatic potential at opposing ends of the P(-)-N(+) dipole. The orientational response of the DMPC lipid headgroup to electrostatic surface variations is visible in the anisotropic features of (14)N and (31)P NMR spectra. These features are analyzed in terms of a modified "molecular voltmeter" model, with changes in dynamic averaging reflecting the tilt of the C(beta)-N(+)(CH)(3) choline and PO(4)(-) segment. These properties have been exploited to characterize the changes in surface potential upon the binding of nociceptin to negatively charged membranes, a process assumed to proceed its agonistic binding to its opoid G-protein coupled receptor.     

A molecular dynamics investigation of the influence of hydration and temperature on structural and dynamical properties of a dimyristoylphosphatidylcholine bilayer

A series of molecular dynamics simulations of dimyristoylphosphatidylcholine bilayers, with different levels of hydration and temperature, were performed to examine the influence of hydration on properties of lipid membranes. Structural and dynamical properties such as area per lipid, electron densities, order parameters for all CH bonds and water, diffusion, and reorientation autocorrelation functions were determined and were all found to be affected by changes in the hydration level. The simulations give an overall picture of the bilayer going to a more ordered state when the hydration level is reduced. Lipid headgroups were found to adopt an orientation more parallel to the membrane plane when the water content was decreased. Dynamical properties such as lipid diffusion and relaxation of reorientation time correlation functions were found to become slower with the removal of water. Our simulation results generally agree with experimental data in cases where such data are available. One important conclusion drawn is that while structural properties are affected only moderately dynamical properties are affected very strongly by a decrease of water content.     

Increasing surface charge density induces interdigitation in vesicles of cationic amphiphile and phosphatidylcholine

Binary vesicles of cationic lipid dihexadecyldimethylammoniumbromide (DHAB) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) were examined by differential scanning calorimetry, fluorescence spectroscopy, and Fourier transform infrared spectroscopy. DHAB/DMPC vesicles demonstrate a complex dependence of the main-transition temperature (T(m)) on their mole proportion of DHAB, with a maximum of 42 degrees C at X(DHAB) = 0.4. An increase of T(m) at X(DHAB) < 0.4 is explained by reorientation of P(-)-N(+) dipoles of the phosphocholine headgroup, resulting in tighter packing of the acyl chains, which increases the thermal energy required for trans --> gauche isomerization. At X(DHAB) > 0.4, Coulombic repulsion between the cationic DHAB headgroups expands the bilayer evident as a decrease in T(m) until a plateau of approximately 28 degrees C at 0.7 < or = X(DHAB) > or = 0.9 is reached, followed by an increment of T(m) to approximately 30 degrees C at X(DHAB) > 0.9. The quenching of DPH-PC fluorescence emission and the decrease in the ratio of peak height intensities of symmetric and antisymmetric -CH(2)- stretching modes suggest an interdigitated phase to form at X(DHAB) > 0.6. Interdigitation allows the membrane to accommodate the augmented Coulombic repulsion between DHAB headgroups because of increasing cationic surface charge density while simultaneously causing tighter packing of the acyl chains evident first as a plateau at 0.7 < or = X(DHAB) > or = 0.9 and subsequently as an increase in T(m) at X(DHAB) > 0.9. Screening of the membrane charges by NaCl abolishes the quenching of DPH emission and decreases T(m), thus revealing electrostatic repulsion as the driving force for interdigitation.     

Relationship between the mobility of phosphocholine headgroups of liposomes and the hydrophobicity at the membrane interface: a characterization with spectrophotometric measurements

In this study, we investigated the dynamics of a membrane interface of liposomes prepared by eight zwitterionic phosphatidylcholines in terms of their headgroup mobility, with spectroscopic methods such as dielectric dispersion analysis (DDA), fluorescence spectroscopy. The DDA measurement is based on the response of the permanent dipole moment to a driving electric field and could give the information on the axial rotational Brownian motion of a headgroup with the permanent dipole moment. This motion depended on kinds of phospholipids, the diameter of the liposomes, and the temperature. The activation energy required to overcome the intermolecular force between headgroups of phospholipids depended on the strength of the interaction between headgroups such as hydrogen bonds and/or dipole-dipole interaction. Hydration at the phosphorous group of phospholipid and the molecular order of lipid membrane impaired the interaction between headgroups. Furthermore, the hydrophobicity of membrane surface increased parallel to the increase in headgroup mobility. It is, therefore, concluded that hydration of headgroup promoted its mobility to make the membrane surface hydrophobic. The lipid membrane in liquid crystalline phase or the lipid membrane with the larger curvature was more hydrophobic.     

Effect of Headgroups on Small‐Ion Permeability across Archaea‐Inspired Tetraether Lipid Membranes

This paper examines the effects of four different polar headgroups on small‐ion membrane permeability from liposomes comprised of Archaea‐inspired glycerolmonoalkyl glycerol tetraether (GMGT) lipids. We found that the membrane‐leakage rate across GMGT lipid membranes varied by a factor of ≤1.6 as a function of headgroup structure. However, the leakage rates of small ions across membranes comprised of commercial bilayer‐forming 1‐palmitoyl‐2‐oleoyl‐sn‐glycerol (PO) lipids varied by as much as 32‐fold within the same series of headgroups. These results demonstrate that membrane leakage from GMGT lipids is less influenced by headgroup structure, making it possible to tailor the structure of the polar headgroups on GMGT lipids while retaining predictable leakage properties of membranes comprised of these tethered lipids.     

Perturbation of phospholipid bilayer properties by ethanol at a high concentration

Atomistic molecular dynamics (MD) simulations have been carried out at 30 degrees C on a fully hydrated liquid crystalline lamellar phase of dimyrystoylphosphatidylcholine (DMPC) lipid bilayer with embedded ethanol molecules at 1:1 composition, as well as on the pure bilayer phase. The ethanol molecules are found to exhibit a preference to occupy regions near the upper part of the lipid acyl chains and the phosphocholine headgroups. The calculations revealed that the phosphocholine headgroup dipoles (P- --> N+) of the lipids prefer to orient more toward the aqueous layer in the presence of ethanol. It is noticed that the ethanol molecules modify the dynamic properties of both lipids as well as the water molecules in the hydration layer of the lipid headgroups. Both the in-plane "rattling" and out-of-plane "protrusion" motions of the lipids have been found to increase in the presence of ethanol. Most importantly, it is observed that the water molecules within the hydration layer of the lipid headgroups exhibit faster translational and rotational motions in the presence of ethanol. This arises due to faster dynamics of hydrogen bonds between lipid headgroups and water in the presence of ethanol.     

SDS对SB3-12胶束表面电荷密度的调控作用及对药物增溶的影响

两性离子甜菜碱表面活性剂(SB3-12)胶束具有较好的生物相容性,由于相反电荷的极性头之间具有静电中和作用,胶束表面具有小的负电荷密度。当加入阴离子的十二烷基硫酸钠(SDS)以后,负离子SD-与SB3-12胶束极性区内层季铵正电荷的静电中和作用,能连续地调节胶束表面磺酸基的负电荷密度,这有利于对药物分子的选择性增溶和调节在生理条件下的药物的输送。等温滴定量热(ITC)研究发现SB3-12和SDS有强的协同效应,混合临界胶束浓度(CMC)和胶束化焓明显降低,并得到两者协同效应的弱静电作用机理。当模型药物分子芦丁(Rutin)与SB3-12/SDS混合胶束作用时,芦丁7位羟基的氢解离后的阴离子与SDS共同作用于SB3-12形成混合胶束。UV-Vis吸收光谱和~1H NMR谱研究发现,在SB3-12胶束中,芦丁分子的A环位于季铵阳离子附近,B环位于两个相反电荷之间的弱极性区域。在SDS胶束中,B环位于栅栏层,而A环和二糖暴露于水相侧。在混合胶束中,随着SDS摩尔分数增加,对A环的静电吸引变弱。离子表面活性剂对两性离子表面活性剂胶束表面电荷密度的调节作用,本质上是对胶束极性区域的物理及化学性质的微调,进而实现对药物的可控增溶。     

Surface properties of mixed monolayers of sulfobetaines and ionic surfactants

To study the influence of the head group in the properties of the mixed monolayers adsorbed at the air-water interface, the surface tension and surface potential of binary mixtures of surfactant have been determined as a function of the surfactant composition. Experiments were carried out with anionic-zwitterionic sodium dodecyl sulfate and dodecyl dimethyl ammoniopropane sulfonate (SDS/DDPS), and cationic-zwitterionic dodecyl trimethylammonium bromide and dodecyl dimethyl ammoniopropane sulfonate (DTAB/DDPS), and dodecyl trimethylammonium bromide and tetradecyl dimethyl ammoniopropane sulfonate (DTAB/TDPS). It was shown that mixed monolayers of cationic-zwitterionic surfactant exhibit small negative deviations of ideal behavior, whereas for SDS/DDPS monolayers show strong negative deviation from the ideality. Deviations of ideal behavior are interpreted by regular solution theory. The surface potential values agree very well with the concentration of the ionic component at the interface. The dynamic surface tension values show that the adsorption kinetics on the interface is a diffusion-controlled process. In monolayers with significant deviation of the ideal behavior, anionic-zwitterionic, there is some evidence of intermolecular attractions after diffusion of both surfactants at the interface.     

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: theory versus experiment

Aqueous dispersions of phosphatidylglycerol (PG) lipids may present an anomalous chain-melting transition at low ionic strengths, as seen by different experimental techniques such as calorimetry or light scattering. The anomaly disappears at high ionic strengths or for longer acyl-chain lengths. In this article, we use a statistical model for the bilayer that distinguishes both lipid chain and headgroup states in order to compare model and experimental thermotropic and electrical properties. The effective van der Waals interactions among hydrophobic chains compete with the electrostatic repulsions between polar headgroups, which may be ionized (counterion dissociated) or electrically neutral (associated with counterions). Electric degrees of freedom introduce new thermotropic charge-ordered phases in which headgroup charges may be spatially ordered, depending on the electrolyte ionic strength, introducing a new rationale for experimental data on PGs. The thermal phases presented by the model for different chain lengths, at fixed ionic strength, compare well with an experimental phase diagram constructed on the basis of differential scanning calorimetry profiles. In the case of dispersions of DMPG (dimyristoyl phosphatidylglycerol) with added monovalent salt, the model properties reproduce the main features displayed by data from differential scanning calorimetry as well as the characteristic profile for the degree of ionization of the bilayer surface across the anomalous transition region, obtained from the theoretical interpretation of electrokinetic (conductivity and electrophoretic mobility) measurements.     

Simulations of lipid vesicle adsorption for different lipid mixtures

Numerous experimental studies of lipid vesicle adsorption on solid surfaces show that electrostatic interactions play an important role for the kinetics and end result. The latter can, e.g., be intact vesicles or supported lipid bilayers (SLB). Despite an accumulated quite large experimental data base, the understanding of the underlying processes is still poor, and mathematical models are scarce. We have developed a phenomenological model of a vesicle adsorbing on a substrate, where the charge of the surface and the charge and polar state of the lipid headgroup can be varied. With physically reasonable assumptions and input parameters, we reproduce many key experimental observations, clarify the details of some experiments, and give predictions and suggestions for future experiments. Specifically, we have investigated the influence of different lipid mixtures (different charges of the headgroups) in the vesicle on the outcome of a vesicle adsorption event. For different mixtures of zwitterionic lipids with positive and negative lipids, we investigated whether the vesicle adsorbs or not, and--if it adsorbs--to what extent it gets deformed and when it ruptures spontaneously. Diffusion of neutral vesicles on different types of negatively charged substrates was also simulated. The mean surface charge density of the substrate was varied, including or excluding local fluctuations in the surface charge density. The simulations are compared to available experiments. A consistent picture of the influence of different lipid mixtures in the vesicle on adsorption, and the influence of different types of substrates on vesicle diffusion, appear as a result of the simulation data.     

Extension of CAVS coarse‐grained model to phospholipid membranes: The importance of electrostatics

It is evident from experiment that electrostatic potential (or dipole potential) is positive inside PC or PE lipid bilayers in the absence of ions. MARTINI coarse‐grained (CG) model, which has been widely used in simulating physical properties of lipid bilayers, fails to reproduce the positive value for the dipole potential in the membrane interior. Although the total dipole potential can be correctly described by the BMW/MARTINI model, the contribution from the ester dipoles, playing a nontrivial role in the electrostatic potential across lipid membranes, is neglected by this hybrid approach. In the ELBA CG model, the role of the ester dipoles is considered, but it is overweighed because various atomistic models have consistently shown that water is actually the leading contributor of dipole potential. Here, we present a CG approach by combining the BMW‐like water model (namely CAVS model) with the ELBA‐like lipid model proposed in this work. Our CG model was designed not only to correctly reproduce the positive values for the dipole potential inside PC and PE lipid bilayers but also to properly balance the individual contributions from the ester dipoles and water, surmounting the limitations of current CG models in the calculations of dipole potential. © 2017 Wiley Periodicals, Inc.     

Modification of the CHARMM force field for DMPC lipid bilayer

The CHARMM force field for DMPC lipids was modified in order to improve agreement with experiment for a number of important properties of hydrated lipid bilayer. The modification consists in introduction of a scaling factor 0.83 for 1-4 electrostatic interactions (between atoms separated by three covalent bonds), which provides correct transgauche ratio in the alkane tails, and recalculation of the headgroup charges on the basis of HF/6-311(d,p) ab-initio computations. Both rigid TIP3P and flexible SPC water models were used with the new lipid model, showing similar results. The new model in a 75 ns simulation has shown a correct value of the area per lipid at zero surface tension, as well as good agreement with the experiment for the electron density, structure factor, and order parameters, including those in the headgroup part of lipids.     

Activity of synthetic ion channels is influenced by cation-pi interactions with phospholipid headgroups

A suite of synthetic hydraphile ion channels has been used to probe the possibility of cation-pi interactions between the channel and the phospholipid bilayer. The hydraphiles selected for this study contained either no sidearm, aliphatic sidearms or aromatic sidearms that varied in electron-richness. An ion selective electrode (ISE) method was used to evaluate the ion transport ability of these hydraphiles across synthetic bilayers. Transport was dependent on sidearm identity. Ion transport activity for the aromatic sidechained compounds was greatest when the sidearms were electron rich and vesicles were prepared from 100% DOPC (trimethylammonium cation headgroup, overall neutral). When the lipid headgroups were made more negative by changing the composition from DOPC to 70 : 30 (w/w) DOPC : DOPA, transport by the aromatic-sidechained channels was reduced. Fluorescence studies showed that when the lipid composition changed, the headgroups experienced a different polarity, suggesting reorientation. The data are in accord with a stabilizing cation-pi interaction between the aromatic sidearm of the hydraphile channel and the ammonium phospholipid headgroup.     

Interrelation between hydration and interheadgroup interaction in phospholipids

The stability and the ionic conductivity of biological membranes and of lipid bilayers depend on their hydration. A small number of water molecules adhere strongly to the different residues of the lipid headgroups and are oriented by them. An additional number of water molecules adhere more weakly, preserving their freedom of rotation, but are essential for bestowing the thermodynamic properties of hydrated bilayers and of biological membranes. Around six water molecules are attached so strongly to the headgroups of different phospholipids (PL) that they are rendered unfreezable, or their freezing is extended over such a wide range of temperatures that it cannot be detected by differential scanning calorimetry (DSC). If cholesterol is added to the PL above the concentration at which phase separation of the cholesterol phase occurs, the number of unfreezable water molecules per PL increases, indicating that the PL molecules on the border line between the two phases attach nearly twice as many water molecules as those in the middle of the phase. The orientation of about seven or eight water molecules attached to PL headgroups (seven to phosphatidyl serine (PS)) can be detected by polarized FTIR. The dichroic ratio of the successively adhering water molecules to the headgroup of PS fluctuates between 2.6 and 2.9, with the cumulative value of about 2.8 for the seven water molecules adhering to the headgroup of PS. In addition, in this case, the number of water molecules oriented by PL molecule residues on the border line of the two phases is much larger ( approximately 13 for PS). Interaction between two opposite negatively charged layers containing PS approaching each other may lead, after correlated electrostatic attraction, to change in the conformation of the headgroups with concomitant dehydration. This process is enhanced by Ca(+) and by Li(+), but it may also occur with Na(+) and K(+) as counter-ions if the layers are mutually aligned. This process may be important in the fusion mechanism of biological membranes, and its molecular modeling has been carried out.