A biophysical study of the interactions between the antimicrobial peptide indolicidin and lipid model systems

The naturally occurring peptide indolicidin from bovine neutrophils exhibits strong biological activity against a broad spectrum of microorganisms. This is believed to arise from selective interactions with the negatively charged cytoplasmic lipid membrane found in bacteria. We have investigated the peptide interaction with supported lipid model membranes using a combination of complementary surface sensitive techniques: neutron reflectometry (NR), atomic force microscopy (AFM), and quartz crystal microbalance with dissipation monitoring (QCM-D). The data are compared with small-angle X-ray scattering (SAXS) results obtained with lipid vesicle/peptide solutions. The peptide membrane interaction is shown to be significantly concentration dependent. At low concentrations, the peptide inserts at the outer leaflet in the interface between the headgroup and tail core. Insertion of the peptide results in a slight decrease in the lipid packing order of the bilayer, although not sufficient to cause membrane thinning. By increasing the indolicidin concentration well above the physiologically relevant conditions, a deeper penetration of the peptide into the bilayer and subsequent lipid removal take place, resulting in a slight membrane thinning. The results suggest that indolicidin induces lipid removal and that mixed indolicidin-lipid patches form on top of the supported lipid bilayers. Based on the work presented using model membranes, indolicidin seems to act through the interfacial activity model rather than through the formation of stable pores.     

Mechanisms of antimicrobial peptide action: studies of indolicidin assembly at model membrane interfaces by in situ atomic force microscopy

We report here on an in situ atomic force microscopy study of the interaction of indolicidin, a tryptophan-rich antimicrobial peptide, with phase-segregated zwitterionic DOPC/DSPC supported planar bilayers. By varying the peptide concentration and bilayer composition through the inclusion of anionic lipids (DOPG or DSPG), we found that indolicidin interacts with these model membranes in one of two concentration-dependent manners. At low peptide concentrations, indolicidin forms an amorphous layer on the fluid domains when these domains contain anionic lipids. At high peptide concentrations, indolicidin appears to initiate a lowering of the gel-phase domains independent of the presence of an anionic lipid. Similar studies performed using membrane-raft mimetic bilayers comprising 30mol% cholesterol/1:1 DOPC/egg sphingomyelin revealed that indolicidin does not form a carpet-like layer on the zwitterionic DOPC domains at low peptide concentrations and does not induce membrane lowering of the liquid-ordered sphingomyelin/cholesterol-rich domains at high peptide concentration. Simultaneous AFM-confocal microscopy imaging did however reveal that indolicidin preferentially inserts into the fluid-phase DOPC domains. These data suggest that the indolicidin-membrane association is influenced greatly by specific electrostatic interactions, lipid fluidity, and peptide concentration. These insights provide a glimpse into the mechanism of the membrane selectivity of antibacterial peptides and suggest a powerful correlated approach for characterizing peptide-membrane interactions.     

Molecular dynamics simulations of indolicidin association with model lipid bilayers

Identifying the mechanisms responsible for the interaction of peptides with cell membranes is critical to the design of new antimicrobial peptides and membrane transporters. We report here the results of a computational simulation of the interaction of the 13-residue peptide indolicidin with single-phase lipid bilayers of dioleoylphosphatidylcholine, distearoylphosphatidylcholine, dioleoylphosphatidylglycerol, and distearoylphosphatidylglycerol. Ensemble analysis of the membrane-bound peptide revealed that, in contrast to the extended, linear backbone structure reported for indolicidin in sodium dodecyl sulphate detergent micelles, the peptide adopts a boat-shaped conformation in both phosphatidylglycerol and phosphatidylcholine lipid bilayers, similar to that reported for dodecylphosphocholine micelles. In agreement with fluorescence and NMR experiments, simulations confirmed that the peptide localizes in the membrane interface, with the distance between phosphate headgroups of each leaflet being reduced in the presence of indolicidin. These data, along with a concomitant decrease in lipid order parameters for the upper-tail region, suggest that indolicidin binding results in membrane thinning, consistent with recent in situ atomic force microscopy studies.     

Membrane binding and permeation by indolicidin analogs studied by a biomimetic lipid/polydiacetylene vesicle assay

Membrane binding and relative penetration of indolicidin analogs were studied using lipid/polydiacetylene (PDA) chromatic biomimetic membranes. Colorimetric and fluorescence analyses determined that an indolicidin analog with a proline and tryptophan residue substituted with lysines showed more pronounced bilayer surface interactions, while indolicidin and particularly an indolicidin analog in which all prolines were replaced with alanine residues exhibited deeper insertion into the lipid bilayer. The colorimetric data demonstrated that more pronounced blue-red transitions were observed when the chromatic vesicles incorporated lipopolysaccharide (LPS) within the lipid bilayer, indicating that LPS promoted preferred binding and incorporation of the peptides at the lipid/water interface. The fluorescence quenching experiments further confirmed this outcome. The results indicate that the antibacterial activity of indolicidin most likely requires initial binding to the LPS moieties within bacterial membranes, as well as disruption of the bilayer interface. The degree of hemolysis induced by the analogs, on the other hand, correlated to the extent of penetration into the hydrophobic core of the lipid assembly.     

Interaction Between Amyloid-β (1-42) Peptide and Phospholipid Bilayers: A Molecular Dynamics Study

The amyloid-β (Aβ) peptide is a key aggregate species in Alzheimer's disease. Although important aspects of Aβ peptide aggregation are understood, the initial stage of aggregation from monomer to oligomer is still not clear. One potential mediator of this early aggregation process is interactions of Aβ with anionic cell membranes. We used unconstrained and umbrella sampling molecular dynamics simulations to investigate interactions between the 42-amino acid Aβ peptide and model bilayers of zwitterionic dipalmitoylphosphatidylcholine (DPPC) lipids and anionic dioleoylphosphatidylserine (DOPS) lipids. Using these methods, we determined that Aβ is attracted to the surface of DPPC and DOPS bilayers over the small length scales used in these simulations. We also found supporting evidence that the charge on both the bilayer surface and the peptide affects the free energy of binding of the peptide to the bilayer surface and the distribution of the peptide on the bilayer surface. Our work demonstrates that interactions between the Aβ peptide and lipid bilayer promotes a peptide distribution on the bilayer surface that is prone to peptide-peptide interactions, which can influence the propensity of Aβ to aggregate into higher-order structures.     

Antimicrobial activity of the indolicidin‐derived novel synthetic peptide In‐58

Natural peptides with antimicrobial activity are extremely diverse, and peptide synthesis technologies make it possible to significantly improve their properties for specific tasks. Here, we investigate the biological properties of the natural peptide indolicidin and the indolicidin‐derived novel synthetic peptide In‐58. In‐58 was generated by replacing all tryptophan residues on phenylalanine in D‐configuration; the α‐amino group in the main chain also was modified by unsaturated fatty acid. Compared with indolicidin, In‐58 is more bactericidal, more resistant to proteinase K, and less toxic to mammalian cells. Using molecular physics approaches, we characterized the action of In‐58 on bacterial cells at the cellular level. Also, we have found that studied peptides damage bacterial membranes. Using the Escherichia coli luminescent biosensor strain MG1655 (pcolD’::lux), we investigated the action of indolicidin and In‐58 at the subcellular level. At subinhibitory concentrations, indolicidin and In‐58 induced an SOS response. Our data suggest that indolicidin damages the DNA, but bacterial membrane perturbation is its principal mode of action. Copyright © 2017 European Peptide Society and John Wiley & Sons, Ltd.     

Interactions of tryptophan-rich cathelicidin antimicrobial peptides with model membranes studied by differential scanning calorimetry

The 13-residue cathelicidins indolicidin and tritrpticin are part of a group of relatively short tryptophan-rich antimicrobial peptides that hold potential as future substitutes for antibiotics. Differential scanning calorimetry (DSC) has been applied here to study the effect of indolicidin and tritrpticin as well as five tritrpticin analogs on the phase transition behaviour of model membranes made up of zwitterionic dimyristoylphosphatidylcholine (DMPC, DMPC/cholesterol) and anionic dimyristoylphosphatidyl glycerol (DMPG) phospholipids. Most of the peptides studied significantly modified the phase transition profile, suggesting the importance of hydrophobic forces for the peptide interactions with the lipid bilayers and their insertion into the bilayer. Indolicidin and tritrpticin are both known to be flexible in aqueous solution, but they adopt turn-turn structures when they bind to and insert in a membrane surface. Pro-to-Ala substitutions in tritrpticin, which result in the formation of a stable α-helix in this peptide, lead to a substantial increase in the peptide interactions with both zwitterionic and anionic phospholipid vesicles. In contrast, the substitution of the three Trp residues by Tyr or Phe resulted in a significant decrease of the peptide's interaction with anionic vesicles and virtually eliminated binding of these peptides to the zwitterionic vesicles. An increase of the cationic charge of the peptide induced much smaller changes to the peptide interaction with all lipid systems than substitution of particular amino acids or modification of the peptide conformation. The presence of multiple lipid domains with a non-uniform peptide distribution was noticed. Slow equilibration of the lipid-peptide systems due to peptide redistribution was observed in some cases. Generally good agreement between the present DSC data and peptide antimicrobial activity data was obtained.     

Lipid tails modulate antimicrobial peptide membrane incorporation and activity

Membrane disrupting antimicrobial peptides (AMPs) are often amphipathic peptides that interact directly with lipid bilayers. AMPs are generally thought to interact mostly with lipid head groups, but it is less clear how the lipid alkyl chain length and saturation modulate interactions with membranes. Here, we used native mass spectrometry to measure the stoichiometry of three different AMPs—LL-37, indolicidin, and magainin-2—in lipid nanodiscs. We also measured the activity of these AMPs in unilamellar vesicle leakage assays. We found that LL-37 formed specific hexamer complexes but with different intermediates and affinities that depended on the bilayer thickness. LL-37 was also most active in lipid bilayers containing longer, unsaturated lipids. In contrast, indolicidin incorporated to a higher degree into more fluid lipid bilayers but was more active with bilayers with thinner, less fluid lipids. Finally, magainin-2 incorporated to a higher degree into bilayers with longer, unsaturated alkyl chains and showed more activity in these same conditions. Together, these data show that higher amounts of peptide incorporation generally led to higher activity and that AMPs tend to incorporate more into longer unsaturated lipid bilayers. However, the activity of AMPs was not always directly related to amount of peptide incorporated.     

Interactions of tryptophan-rich cathelicidin antimicrobial peptides with model membranes studied by differential scanning calorimetry

The 13-residue cathelicidins indolicidin and tritrpticin are part of a group of relatively short tryptophan-rich antimicrobial peptides that hold potential as future substitutes for antibiotics. Differential scanning calorimetry (DSC) has been applied here to study the effect of indolicidin and tritrpticin as well as five tritrpticin analogs on the phase transition behaviour of model membranes made up of zwitterionic dimyristoylphosphatidylcholine (DMPC, DMPC/cholesterol) and anionic dimyristoylphosphatidyl glycerol (DMPG) phospholipids. Most of the peptides studied significantly modified the phase transition profile, suggesting the importance of hydrophobic forces for the peptide interactions with the lipid bilayers and their insertion into the bilayer. Indolicidin and tritrpticin are both known to be flexible in aqueous solution, but they adopt turn-turn structures when they bind to and insert in a membrane surface. Pro-to-Ala substitutions in tritrpticin, which result in the formation of a stable alpha-helix in this peptide, lead to a substantial increase in the peptide interactions with both zwitterionic and anionic phospholipid vesicles. In contrast, the substitution of the three Trp residues by Tyr or Phe resulted in a significant decrease of the peptide's interaction with anionic vesicles and virtually eliminated binding of these peptides to the zwitterionic vesicles. An increase of the cationic charge of the peptide induced much smaller changes to the peptide interaction with all lipid systems than substitution of particular amino acids or modification of the peptide conformation. The presence of multiple lipid domains with a non-uniform peptide distribution was noticed. Slow equilibration of the lipid-peptide systems due to peptide redistribution was observed in some cases. Generally good agreement between the present DSC data and peptide antimicrobial activity data was obtained.     

Interaction of indolicidin, a 13-residue peptide rich in tryptophan and proline and its analogues with model membranes

Indolicidin is a 13-residue broad-spectrum antibacterial peptide isolated from bovine neutrophils. The primary structure of the peptide ILPWKWPWWPWRR-amide (IL) reveals an unusually high percentage of tryptophan residues. IL and its analogues where proline residues have been replaced by alanine (ILA) and trp replaced by phe (ILF) show comparable antibacterial activitieso While IL and ILA are haemolytic, ILF does not have this property. Since aromatic residues would strongly favour partitioning of the peptide into the lipid bilayer interface, the biological activities of IL and its analogues could conceivably arise due perturbation of the lipid bilayer of membranes. We have therefore investigated the interaction of IL and its analogues with lipid vesicles. Peptides IL and ILA bind to lipid vesicles composed of phosphatidylcholine and phosphatidylethanol amine: phosphatidyl glycerol: cardiolipin. The position of λ_max and I^- quenching experiments suggest that the trp residues are localized at the membrane interface and not associated with the hydrophobic core of the lipid bilayer in both the peptides. Hence, membrane permeabilization is likely to occur due to deformation of the membrane surface rather than formation of transmembrane channels by indolicidin and its analogues. Peptides ILA, IL and ILF cause the release of entrapped carboxyfluorescein from phosphatidyl choline vesicles. The peptide-lipid ratios indicate that ILF is less effective than IL and ILA in permeabilizing lipid vesicles, correlating with their haemolytic activities. An erratum to this article is available at .     

Membrane perturbation by the antimicrobial peptide PMAP-23: A fluorescence and molecular dynamics study

Several bioactive peptides exert their biological function by interacting with cellular membranes. Structural data on their location inside lipid bilayers are thus essential for a detailed understanding of their mechanism of action. We propose here a combined approach in which fluorescence spectroscopy and molecular dynamics (MD) simulations were applied to investigate the mechanism of membrane perturbation by the antimicrobial peptide PMAP-23. Fluorescence spectra, depth-dependent quenching experiments, and peptide-translocation assays were employed to determine the location of the peptide inside the membrane. MD simulations were performed starting from a random mixture of water, lipids and peptide, and following the spontaneous self-assembly of the bilayer. Both experimental and theoretical data indicated a peptide location just below the polar headgroups of the membrane, with an orientation essentially parallel to the bilayer plane. These findings, together with experimental results on peptide-induced leakage from large and giant vesicles, lipid flip-flop and peptide exchange between vesicles, support a mechanism of action consistent with the “carpet” model. Furthermore, the atomic detail provided by the simulations suggested the occurrence of an additional, more specific and novel mechanism of bilayer destabilization by PMAP-23, involving the unusual insertion of charged side chains into the hydrophobic core of the membrane.     

Structural Plasticity in the Topology of the Membrane-Interacting Domain of HIV-1 gp41

We use a number of computational and experimental approaches to investigate the membrane topology of the membrane-interacting C-terminal domain of the HIV-1 gp41 fusion protein. Several putative transmembrane regions are identified using hydrophobicity analysis based on the Wimley-White scales, including the membrane-proximal external region (MPER). The MPER region is an important target for neutralizing anti-HIV monoclonal antibodies and is believed to have an interfacial topology in the membrane. To assess the possibility of a transmembrane topology of MPER, we examined the membrane interactions of a peptide corresponding to a 22-residue stretch of the MPER sequence (residues 662–683) using fluorescence spectroscopy and oriented circular dichroism. In addition to the previously reported interfacial location, we identify a stable transmembrane conformation of the peptide in synthetic lipid bilayers. All-atom molecular dynamics simulations of the MPER-derived peptide in a lipid bilayer demonstrate a stable helical structure with an average tilt of 24 degrees, with the five tryptophan residues sampling different environments inside the hydrocarbon core of the lipid bilayer, consistent with the observed spectral properties of intrinsic fluorescence. The degree of lipid bilayer penetration obtained by computer simulation was verified using depth-dependent fluorescence quenching of a selectively attached fluorescence probe. Overall, our data indicate that the MPER sequence can have at least two stable conformations in the lipid bilayer, interfacial and transmembrane, and suggest a possibility that external perturbations can switch the topology during physiological functioning.     

Recombinant expression of indolicidin concatamers in Escherichia coli

Antimicrobial peptides are part of the innate immune system of vertebrates and invertebrates. They are active against gram-negative and gram-positive bacteria, fungi, and protozoa. Currently, most antimicrobial peptides are extracted from host organisms or produced by solid-phase peptide synthesis. Recombinant protein expression in Escherichia coli is a tool for greater production yields at a decreased cost and reduces the use of hazardous materials. We have constructed a concatamer of indolicidin and successfully expressed a fusion product with thioredoxin in E. coli BL21DE3. Codons for methionine residues flanking individual indolicidin genes were incorporated for cyanogen bromide cleavage of the fusion protein and liberation of active monomeric indolicidin. Peptide yields of 150 μg/l monomeric indolicidin were achieved in this first report of recombinant production of indolicidin with demonstrated antimicrobial activity.     

Surface binding of alamethicin stabilizes its helical structure: molecular dynamics simulations.

Alamethicin is an amphipathic alpha-helical peptide that forms ion channels. An early event in channel formation is believed to be the binding of alamethicin to the surface of a lipid bilayer. Molecular dynamics simulations are used to compare the structural and dynamic properties of alamethicin in water and alamethicin bound to the surface of a phosphatidylcholine bilayer. The bilayer surface simulation corresponded to a loosely bound alamethicin molecule that interacted with lipid headgroups but did not penetrate the hydrophobic core of the bilayer. Both simulations started with the peptide molecule in an alpha-helical conformation and lasted 2 ns. In water, the helix started to unfold after approximately 300 ps and by the end of the simulation only the N-terminal region of the peptide remained alpha-helical and the molecule had collapsed into a more compact form. At the surface of the bilayer, loss of helicity was restricted to the C-terminal third of the molecule and the rod-shaped structure of the peptide was retained. In the surface simulation about 10% of the peptide/water H-bonds were replaced by peptide/lipid H-bonds. These simulations suggest that some degree of stabilization of an amphipathic alpha-helix occurs at a bilayer surface even without interactions between hydrophobic side chains and the acyl chain core of the bilayer.     

Bilayer conformation of fusion peptide of influenza virus hemagglutinin: a molecular dynamics simulation study

Unraveling the conformation of membrane-bound viral fusion peptides is essential for understanding how those peptides destabilize the bilayer topology of lipids that is important for virus-cell membrane fusion. Here, molecular dynamics (MD) simulations were performed to investigate the conformation of the 20 amino acids long fusion peptide of influenza hemagglutinin of strain X31 bound to a dimyristoyl phosphatidylcholine (DMPC) bilayer. The simulations revealed that the peptide adopts a kinked conformation, in agreement with the NMR structures of a related peptide in detergent micelles. The peptide is located at the amphipathic interface between the headgroups and hydrocarbon chains of the lipid by an energetically favorable arrangement: The hydrophobic side chains of the peptides are embedded into the hydrophobic region and the hydrophilic side chains are in the headgroup region. The N-terminus of the peptide is localized close to the amphipathic interface. The molecular dynamics simulations also revealed that the peptide affects the surrounding bilayer structure. The average hydrophobic thickness of the lipid phase close to the N-terminus is reduced in comparison with the average hydrophobic thickness of a pure dimyristoyl phosphatidylcholine bilayer.     

Effect of salt on the interactions of antimicrobial peptides with zwitterionic lipid bilayers

The effect of salt on the binding of the antimicrobial peptide magainin to POPC lipid bilayers is studied by 40-50 ns molecular dynamics simulations of a POPC bilayer in the presence of different concentrations of Na+ and Cl− ions, corresponding to effective concentrations of 0, 100, 150, 200, 250 and 300 millimolar NaCl, with and without a single molecule of antimicrobial peptide magainin. Simulations without magainin showed that increasing salt concentration leads to the decrease in the area per lipid, a decrease in the head group tilt of the lipids, as well as increased order of lipid tails, in agreement with other recent simulations. Simulations with magainin show that peptide binding to the lipids is stronger at lower concentrations of salt. The peptides disorder the lipids in their immediate vicinity, but this effect is diminished as the salt concentration increases. Our studies indicate that while 50 ns simulations give information on peptide hydrogen bonding and lipid tail ordering that is insensitive to the initial peptide orientation, this run time is not sufficient to equilibrate the peptide position and orientation within the bilayer.     

Molecular dynamics simulations predict a tilted orientation for the helical region of dynorphin A(1-17) in dimyristoylphosphatidylcholine bilayers

The structural properties of the endogenous opioid peptide dynorphin A(1-17) (DynA), a potential analgesic, were studied with molecular dynamics simulations in dimyristoylphosphatidylcholine bilayers. Starting with the known NMR structure of the peptide in dodecylphosphocholine micelles, the N-terminal helical segment of DynA (encompassing residues 1-10) was initially inserted in the bilayer in a perpendicular orientation with respect to the membrane plane. Parallel simulations were carried out from two starting structures, systems A and B, that differ by 4 A in the vertical positioning of the peptide helix. The complex consisted of approximately 26,400 atoms (dynorphin + 86 lipids + approximately 5300 waters). After >2 ns of simulation, which included >1 ns of equilibration, the orientation of the helical segment of DynA had undergone a transition from parallel to tilted with respect to the bilayer normal in both the A and B systems. When the helix axis achieved a approximately 50 degrees angle with the bilayer normal, it remained stable for the next 1 ns of simulation. The two simulations with different starting points converged to the same final structure, with the helix inserted in the bilayer throughout the simulations. Analysis shows that the tilted orientation adopted by the N-terminal helix is due to specific interactions of residues in the DynA sequence with phospholipid headgroups, water, and the hydrocarbon chains. Key elements are the "snorkel model"-type interactions of arginine side chains, the stabilization of the N-terminal hydrophobic sequence in the lipid environment, and the specific interactions of the first residue, Tyr. Water penetration within the bilayer is facilitated by the immersed DynA, but it is not uniform around the surface of the helix. Many water molecules surround the arginine side chains, while water penetration near the helical surface formed by hydrophobic residues is negligible. A mechanism of receptor interaction is proposed for DynA, involving the tilted orientation observed from these simulations of the peptide in the lipid bilayer.     

An Antibody as Surrogate Receptor Reveals Determinants of Activity of an Innate Immune Peptide Antibiotic

Drug discovery initiatives often depend critically on knowledge of ligand-receptor interactions. However, the identity or structure of the target receptor may not be known in every instance. The concept of receptor surrogate, a molecular environment mimic of natural receptor, may prove beneficial under such circumstances. Here, we demonstrate the potential of monoclonal antibodies (mAbs) to act as surrogate receptors for a class of innate immune peptide antibiotics, a strategy that can help comprehend their action mechanism and identify chemical entities crucial for activity. A panel of antibody surrogates was raised against indolicidin, a tryptophan-rich cationic broad spectrum antimicrobial peptide of innate immune origin. Employing an elegant combination of thermodynamics, crystallography, and molecular modeling, interactions of the peptide with a high affinity anti-indolicidin monoclonal antibody were analyzed and were used to identify a motif that contained almost the entire antibiotic activity of native indolicidin. The analysis clarified the interaction of the peptide with previously proposed targets such as bacterial cell membrane and DNA and could further be correlated with antimicrobial compounds whose actions involve varied other mechanisms. These features suggest a multipronged assault pathway for indolicidin. Remarkably, the anti-indolicidin mAb surrogate was able to isolate additional independent bactericidal sequences from a random peptide library, providing compelling evidence as to the physiological relevance of surrogate receptor concept and suggesting applications in receptor-based pharmacophore research.     

Structural and DNA-binding studies on the bovine antimicrobial peptide, indolicidin: evidence for multiple conformations involved in binding to membranes and DNA

Indolicidin, a l3-residue antimicrobial peptide-amide, which is unusually rich in tryptophan and proline, is isolated from the cytoplasmic granules of bovine neutrophils. In this study, the structures of indolicidin in 50% D₃-trifluoroethanol and in the absence and presence of SDS and D₃₈-dodecylphosphocholine were determined using NMR spectroscopy. Multiple conformations were found and were shown to be due to different combinations of contact between the two WPW motifs. Although indolicidin is bactericidal and able to permeabilize bacterial membranes, it does not lead to cell wall lysis, showing that there is more than one mechanism of antimicrobial action. The structure of indolicidin in aqueous solution was a globular and amphipathic conformation, differing from the wedge shape adopted in lipid micelles, and these two structures were predicted to have different functions. Indolicidin, which is known to inhibit DNA synthesis and induce filamentation of bacteria, was shown to bind DNA in gel retardation and fluorescence quenching experiments. Further investigations using surface plasmon resonance confirmed the DNA-binding ability and showed the sequence preference of indolicidin. Based on our biophysical studies and previous results, we present a diagram illustrating the DNA-binding mechanism of the antimicrobial action of indolicidin and explaining the roles of the peptide when interacting with lipid bilayers at different concentrations.