The dimeric nature of the gramicidin A transmembrane channel: Conductance and fluorescence energy transfer studies of hybrid channels

Gramicidin A, a linear peptide antibiotic, makes membranes permeable to alkali cations and hydrogen ions by forming transmembrane channels. We report here conductance and fluorescence energy transfer studies of channels containing two kinds of gramicidin. These studies of hybrid channels were designed to determine the number of molecules in a channel. The gramicidins studied were gramicidin A, dansyl gramicidin C, the p-phenylazobenzene sulfonyl derivative of gramicidin C (PABS⁴ gramicidin C), and the 4-(diethylamino)-phenylazobenzene-4-sulfonyl chloride derivative of gramicidin C (DPBS gramicidin C). The dansyl, PABS and DPBS groups were linked to the hydroxyl group of tyrosine 11 in gramicidin C. The single-channel conductance of PABS gramicidin C in planar bilayer membranes is 0.68 that of gramicidin A. Membranes containing both PABS gramicidin C and gramicidin A exhibit three kinds of channels: a pure gramicidin A, a pure PABS gramicidin C channel, and a hybrid channel with an intermediate conductance (0.82 that of gramicidin A). The dependence of the frequencies of these three kinds of channels on the mole fractions of gramicidin A and PABS gramicidin C in the membrane-forming solution fits a dimer model. Fluorescence energy transfer was used as a complementary means of ascertaining the frequency of hybrid channels. Dansyl gramicidin C was the fluorescent energy donor and DPBS gramicidin C was the energy acceptor. The efficiency of energy transfer between these chromophores in hybrid channels in liposomes was 75%. The relative quantum yield of the dansyl fluorescence was measured as a function of the mole fraction of DPBS gramicidin C. These fluorescence studies, like the single-channel conductance measurements, showed that there are two molecules of gramicidin in a channel. The study of hybrid species by conductance and fluorescence techniques should be generally useful in elucidating the subunit structure of oligomeric assemblies in membranes.     

Single-channel parameters of gramicidin A,B, and C.

The single-channel conductance lambda and the mean channel lifetime gamma of natural and synthetic gramicidins A, B, and C has been studied. Significant differences in delta were found between gramicidin A and B; both gramicidins differ only in one amino acid (tryptophan replaced by phenylaline). The distribution of lambda is narrow in glycerylmonooleate membranes but considerably broader in dioleoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine membranes. The ratio of the single-channel conductances in glycerylmonooleate and dioleoyl phosphatidylcholine membranes is only about two and is considerable smaller than the conductance ratio of nonactin-mediated cation transport. This finding suggests that dipolar potentials at the membrane/solution interface have little influence on the conductance of the gramicidin channel.     

Single-channel parameters of gramicidin a,b, and c

The single-channel conductance Λ and the mean channel lifetime τ1 of natural and synthetic gramicidins A, B, and C has been studied. Significant differences in Λ were found between gramicidin A and B; both gramicidins differ only in one amino acid (tryptophan replaced by phenylalinine). The distribution of Λ is narrow in glycerylmonooleate membranes but considerably broader in dioleoyl phosphatidylcholine and dioleoyl phosphatidylethanolamine membranes. The ratio of the single-channel conductances in glycerylmonooleate and dioleoyl phosphatidylcholine membranes is only about two and is considerable smaller than the conductance ratio of nonactin-mediated cation transport. This finding suggests that dipolar potentials at the membrane/solution interface have little influence on the conductance of the gramicidin channel.     

Hydrophobic coupling of lipid bilayer energetics to channel function

The hydrophobic coupling between membrane-spanning proteins and the lipid bilayer core causes the bilayer thickness to vary locally as proteins and other "defects" are embedded in the bilayer. These bilayer deformations incur an energetic cost that, in principle, could couple membrane proteins to each other, causing them to associate in the plane of the membrane and thereby coupling them functionally. We demonstrate the existence of such bilayer-mediated coupling at the single-molecule level using single-barreled as well as double-barreled gramicidin channels in which two gramicidin subunits are covalently linked by a water-soluble, flexible linker. When a covalently attached pair of gramicidin subunits associates with a second attached pair to form a double-barreled channel, the lifetime of both channels in the assembly increases from hundreds of milliseconds to a hundred seconds--and the conductance of each channel in the side-by-side pair is almost 10% higher than the conductance of the corresponding single-barreled channels. The double-barreled channels are stabilized some 100,000-fold relative to their single-barreled counterparts. This stabilization arises from: first, the local increase in monomer concentration around a single-barreled channel formed by two covalently linked gramicidins, which increases the rate of double-barreled channel formation; and second, from the increased lifetime of the double-barreled channels. The latter result suggests that the two barrels of the construct associate laterally. The underlying cause for this lateral association most likely is the bilayer deformation energy associated with channel formation. More generally, the results suggest that the mechanical properties of the host bilayer may cause the kinetics of membrane protein conformational transitions to depend on the conformational states of the neighboring proteins.     

Gramicidin K, a new linear channel-forming gramicidin from Bacillus brevis

A new gramicidin has been isolated from a commercial mixture of gramicidins A, B, and C. This new molecule, designated gramicidin K, contains formyl and ethanolamine blocking groups, has a molecular weight approximately 20% higher than gramicidin A, and is strongly retained on reversed-phase liquid chromatographic columns. Gramicidin K can be resolved into two components, one of which contains tyrosine. In lipid bilayer membranes, both components form channels of considerably longer lifetime and somewhat lower conductance than gramicidin A. Gramicidin K appears to be a lipopeptide that consists of a fatty acyl chain attached to the ethanolamine of gramicidin A.     

Gramicidins A, B, and C form structurally equivalent ion channels.

The membrane structure of the naturally occurring gramicidins A, B, and C was investigated using circular dichroism (CD) spectroscopy and single-channel recording techniques. All three gramicidins form channels with fairly similar properties (Bamberg, E., K. Noda, E. Gross, and P. L?uger. 1976. Biochim. Biophys. Acta. 419:223-228.). When incorporated into lysophosphatidylcholine micelles, however, the CD spectrum of gramicidin B is different from that of gramicidin A or C (cf. Prasad, K. U., T. L. Trapane, D. Busath, G. Szabo, and D. W. Urry. 1983. Int. J. Pept. Protein Res. 22:341-347.). The structural identity of the channels formed by gramicidin B has, therefore, been uncertain. We find that when gramicidins A and B are incorporated into dipalmitoylphosphatidylcholine vesicles, their CD spectra are fairly similar, suggesting that the two channel structures could be similar. In planar bilayers, gramicidins A, B, and C all form hybrid channels with each other. The properties of the hybrid channels are intermediate to those of the symmetric channels, and the appearance rates of the hybrid channels (relative to the symmetric channels) corresponds to what would be predicted if all three gramicidin molecules were to form structurally equivalent channels. These results allow us to interpret the different behavior of channels formed by the three gramicidins solely on the basis of the amino acid substitution at position 11.     

Energetics of gramicidin hybrid channel formation as a test for structural equivalence. Side-chain substitutions in the native sequence.

To determine whether amino acid side-chain substitutions in linear gramicidins after the structure of membrane-spanning channels formed by the modified peptides, we have developed a quantitative measure of structural equivalence of the peptide backbone among gramicidin channels based on functional (single-channel) measurements. The experiments exploit the fact that gramicidin channels are symmetrical dimers, and that channels formed by different gramicidin analogues can be distinguished on the basis of their single-channel current amplitudes or durations. It is thereby possible to determine whether hybrid channels can form between chemically dissimilar peptides, i.e. whether the peptides can adapt to each other. Further, since the relative rates of channel formation as well as the relative concentrations of pure and hybrid channel types can be measured in the same membrane, these experiments provide a quantitative measure of the energetic cost of hybrid channel formation relative to the formation of the pure channels. For a wide variety of different side-chains, we find that substitutions as extreme as glycine to phenylalanine at position 1, at the join between the two monomers in a membrane-spanning dimer, incur no energetic cost for channel formation, which implies that channels formed by each of the modified peptides are structurally equivalent. In addition, the average durations of the hybrid channels (except those having tyrosine or hexafluorovaline at position 1) are intermediate to the average durations of the respective pure channel types, thus providing further evidence for structural equivalence among channels formed by sequence-substituted gramicidins.     

Tryptophan photolysis is responsible for gramicidin-channel inactivation by ultraviolet light

The decay of gramicidin fluorescence resulting from ultraviolet exposure was compared to the decay of conductance from gramicidin-containing planar bilayer membranes under the same conditions of illumination. The decay rate was the same for both processes. The fluorescence decay was identical whether gramicidin was dissolved in methanol or incorporated into lipid vesicles, indicating that the peptide conformation does not affect the sensitivity of gramicidin to photolysis. The correlation of fluorescence decay and conductance decay imply that conductance loss from gramicidin-doped membranes illuminated with ultraviolet light is due to photochemical modifications of the channel tryptophans rather than simply to disturbance of the conformation of gramicidin channels.     

Formation of ion channels by a negatively charged analog of gramicidin A.

O-pyromellitylgramicidin is a derivative of gramicidin in which three carboxyl groups are introduced at the terminal hydroxyl end of the peptide. Experiments with artificial lipid membranes indicate that this negatively charged analog forms ion-permeable channels in a way similar to that of gramicidin. If O-pyromellitylgramicidin is added to only one aqueous solution, the membrane conductance remains small, but increases by several orders of magnitude if the same amount is also added to the other side. In accordance with the dimer model of the channel, the membrane conductance under symmetrical conditions is proportional to the square of the aqueous concentration of O-pyromellitylgramicidin over a wide range. The ratio lambdaPG/lambdaG of the single-channel conductance of O-pyromellitylgramicidin to that of gramicidin is close to unity at high ionic strength, but increases more than fivefold at smaller ionic strength (0.01 M). This observation is explained in terms of an electrostatic effect of the fixed negative charges localized near the mouth of the channel. In a mixture of O-pyromellitylgramicidin and gramicidin, unit conductance steps of intermediate size are observed in addition to the conductance steps corresponding to the pure compounds, indicating the formation of hybrid channels. Hybrid channels with preferred orientation may be formed if small amounts of gramicicin and O-pyromellitylgramicidin are added to opposite sides of the membrane. These hybrid channels show a distinct asymmetry in the current-voltage characteristic.     

Ion channels formed by chemical analogs of gramicidin A.

Channel-forming peptides such as gramicidin A offer the opportunity to study the relationship between chemical structure and transport properties of an ion channel. This article summarizes a number of recent experiments with chemical analogs and derivatives of gramicidin A using artificial lipid bilayer membranes. The introduction of negative charges near the channel mouth leads to an increase in the cation transport rate. Hybrid channels consisting of a neutral and a negatively charged or of a positively and a negatively charged half-channel may be formed. The current-voltage characteristic of these hybrid channels exhibits a pronounced asymmetry.Experiments with charged derivatives of gramicidin A have been used in order to distinguish between different structural models of the dimeric channel; these studies strongly support Urry's model of a single-stranded, head-to-head associated helical dimer. In a further set of experiments gramicidin analogs with modified amino acid sequence were studied. It was found that a single substitution (tryptophan replaced by phenylalanine) leads to marked changes in the conductance of the channel. Analogs with a simplified amino acid sequence such as (L-Trp-D-Leu)7-L-Trp or L-Trp-Gly-(L-Trp-D-Leu)6-L-Trp are able to form cation permeable channels with similar properties as gramicidin A.     

Low conductance gramicidin A channels are head-to-head dimers of beta 6.3-helices.

Weakly conductive, atypical channels were observed to form from highly purified Val1-gramicidin A in planar lipid bilayer membranes. The structure of these low-conductance channels (minis) was investigated by a detailed study of their channel forming characteristics. The possibility that minis originate from primary structural analogs or degradation products of gramicidin was considered and ruled out. In particular, spontaneous conductance changes in single channels demonstrated that minis can derive directly and reversibly from "standard" channels having the most common conductance level. The fraction of channels which are minis does not vary with changes in membrane gramicidin concentration, indicating that mini and standard channels have the same molecularity, that is, both are dimers. The mean lifetime of mini channels is only slightly shorter than that of standard channels, indicating that the six hydrogen bonds that stabilize the head-to-head dimer are minimally affected in minis. The fraction of channels which are minis is unaffected by the ionic strength, ionic composition, or pH of the bathing solution; it is also unaffected by the lipid composition of the bilayer. These findings are consistent with the hypothesis that minis arise from minor changes in the conformation of the Val1-gramicidin A molecule near the channel entrance or exit.     

Gramicidin Channels Are Internally Gated

Gramicidin channels are archetypal molecular subjects for solid-state NMR studies and investigations of single-channel or cation conductance. Until now, the transitions between on and off conductance states have been thought, based on multichannel studies, to represent monomer ↔ dimer reactions. Here we use a single-molecule deposition method (vesicle fusion to a planar bilayer) to show that gramicidin dimer channels do not normally dissociate when conductance terminates. Furthermore, the observation of two ¹³C peaks in solid-state NMR indicates very stable dichotomous conformations for both the first and second peptide bonds in the monomers, and a two-dimensional chemical exchange spectrum with a 12-s mixing time demonstrates that the Val₁ carbonyl conformations exchange slowly, with lifetimes of several seconds. It is proposed that gramicidin channels are gated by small conformational changes in the channel near the permeation pathway. These studies demonstrate how regulation of conformations governing closed ↔ open transitions may be achieved and studied at the molecular level.     

Preparation and properties of O-dansyltyrosine gramicidin C.

Gramicidins A, B, and C are a family of poly-peptide antibiotics which facilitate the passive diffusion of alkali cations and protons through lipid bilayer membranes. It is clear that gramicidin forms a multimeric transmembrane channel and it has been suggested that the channel is an io-conducting dimer in equilibrium on the membrane with non-conducting monomer. We describe the preparation and purification of a derivative of gramicidin C in which the phenolic hydroxyl of the tyrosine at position 11 has been esterified to 8-dimethylaminonaphthalene-1-sulfonate (dansyl). This derivative fluoresces strongly in the visible with an emission maximun in dioxane of 530 nm, an emission lifetime of 16 ns, and a quantum yield of 0.8. Veatch et al. ((1975),J. Mol. Biol. 99, 75) have shown this 0-dansyltyrosine gamicidin C to be a fully active analogue of gramicidin A in artificial lipid bilayer membranes. We here utilize this derivative to further characterize the state of aggregation and rotational mobility of the four interconvertible conformational species formed by gramicidin in nonpolar organic solvents (Veatch et al. (1974), Biochemsitry 13, 5249; Veatch and Blout (1974), Biochemistry 13, 5257). Fluorescence energy transfer from the tryptophans of gramicidin A to the 0-dansyltyrosine of this derivatives supports the conclusion that all of these gramicidin isolated species are aggregates. Decay of fluorescence polarization anisotropy measurements yield a rotational correlation time of 1 ns for the 0-dansyltyrosine chromophore in ethanol in good agreement with the more detailed information previously obtained by 13C-nuclear magnetic resonance for the monomer in dimethyl sulfoxide (Fossel et al. (1974), Biochemistry 13, 5264). However, it is likely that the chromophore has much more rotational mobility than the rest of the gramicidin molecule in the aggregated comformational states.     

Calcium-dependent association of annexins with lipid bilayers modifies gramicidin A channel parameters

In order to examine whether calcium-dependent binding of annexin to acidic phospholipids could change the lipid bilayer environment sufficiently to perturb channel-mediated transmembrane ion-transport, gramicidin A channel activity in planar lipid bilayers was investigated in the presence of calcium and annexins II, III or V. The experiments were performed with membranes consisting of phosphatidylcholine, phosphatidylethanolamine and phosphatidylserine in 300 mM KCl solution buffered to pH 7.4 and with either 0.1 or 1 mM calcium added to the solution. Annexin (1 microM) was subsequently applied to the cis side of the membrane. All three annexins (II, III and V) when tested at 1 mM calcium decreased the gramicidin single-channel conductance. Annexins II and III increased the mean lifetime of the channels whereas annexin V seemed to have no influence on the mean lifetime. Since the lifetime of gramicidin A channels is a function of the rate constant for dissociation of the gramicidin dimer, which is dependent on the physical properties of the lipid phase, binding of annexins II and III seems to stabilize the gramicidin channel owing to a change of the bilayer structure.     

Small-Molecule Photostabilizing Agents are Modifiers of Lipid Bilayer Properties

Small-molecule photostabilizing or protective agents (PAs) provide essential support for the stability demands on fluorescent dyes in single-molecule spectroscopy and fluorescence microscopy. These agents are employed also in studies of cell membranes and model systems mimicking lipid bilayer environments, but there is little information about their possible effects on membrane structure and physical properties. Given the impact of amphipathic small molecules on bilayer properties such as elasticity and intrinsic curvature, we investigated the effects of six commonly used PAs—cyclooctatetraene (COT), para-nitrobenzyl alcohol (NBA), Trolox (TX), 1,4-diazabicyclo[2.2.2]octane (DABCO), para-nitrobenzoic acid (pNBA), and n-propyl gallate (nPG)—on bilayer properties using a gramicidin A (gA)-based fluorescence quench assay to probe for PA-induced changes in the gramicidin monomer↔dimer equilibrium. The experiments were done using fluorophore-loaded large unilamellar vesicles that had been doped with gA, and changes in the gA monomer↔dimer equilibrium were assayed using a gA channel-permeable fluorescence quencher (Tl⁺). Changes in bilayer properties caused by, e.g., PA adsorption at the bilayer/solution interface that alter the equilibrium constant for gA channel formation, and thus the number of conducting gA channels in the large unilamellar vesicle membrane, will be detectable as changes in the rate of Tl⁺ influx—the fluorescence quench rate. Over the experimentally relevant millimolar concentration range, TX, NBA, and pNBA, caused comparable increases in gA channel activity. COT, also in the millimolar range, caused a slight decrease in gA channel activity. nPG increased channel activity at submillimolar concentrations. DABCO did not alter gA activity. Five of the six tested PAs thus alter lipid bilayer properties at experimentally relevant concentrations, which becomes important for the design and analysis of fluorescence studies in cells and model membrane systems. We therefore tested combinations of COT, NBA, and TX; the combinations altered the fluorescence quench rate less than would be predicted assuming their effects on bilayer properties were additive. The combination of equimolar concentrations of COT and NBA caused minimal changes in the fluorescence quench rate.     

On the supramolecular organization of gramicidin channels. The elementary conducting unit is a dimer.

The question, whether the conducting channels formed by the linear gramicidins are dimers (as is generally believed) or tetramers (as has been recently proposed [Stark G., M. Strässle, and Z. Takacz. 1986. J. Membr. Biol. 89:23-37; Strässle, M., G. Stark, M. Wilhelm, P. Daumas, F. Heitz, and R. Lazaro. 1989. Biochim. Biophys. Acta. 980:305-314]) has been addressed in single-channel experiments. The experimental approach was based on the ability of electrophysiological (single-channel) experiments to resolve the number of hybrid channel types that could form between gramicidin A or C and O-pyromellityl-gramicidin A or C (in which a pyromellitic acid residue has been esterified to the ethanolamine-OH group [Apell, H.-J., E. Bamberg, H. Alpes, and P. Läuger. 1977. J. Membr. Biol. 31:171-188]). The presence of the bulky, negatively charged pyromellityl group at the channel entrances endows the hybrid channels with characteristically different features and thus facilitates the resolution of the different hybrid channel types. Only two hybrid channel types were detected, indicating that the conducting channels are membrane-spanning dimers. There was likewise no evidence for lateral association between conducting channels and nonconducting monomers. These results can be reconciled with those of Stark et al. (op. cit.) if gramicidin channel formation involves a (slow) folding into beta 6.3-helical monomers followed by the dimerization step.     

Formation of ion channels by a negatively charged analog of gramicidin a

Summary O-pyromellitylgramicidin is a derivative of gramicidin in which three carboxyl groups are introduced at the terminal hydroxyl end of the peptide. Experiments with artificial lipid membranes indicate that this negatively charged analog forms ion-permeable channels in a way similar to that of gramicidin. If O-pyromellitylgramicidin is added to only one aqueous solution, the membrane conductance remains small, but increases by several orders of magnitude if the same amount is also added to the other side. In accordance with the dimer model of the channel, the membrane conductance under symmetrical conditions is proportional to the square of the aqueous concentration of O-pyromellitylgramicidin over a wide range. The ratio _PG/ _G of the single-channel conductance of O-pyromellitylgramicidin to that of gramicidin is close to unity at high ionic strength, but increases more than fivefold at smaller ionic strength (0.01m). This observation is explained in terms of an electrostatic effect of the fixed negative charges localized near the mouth of the channel. In a mixture of O-pyromellitylgramicidin and gramicidin, unit conductance steps of intermediate size are observed in addition to the conductance steps corresponding to the pure compounds, indicating the formation of hybrid channels. Hybrid channels with preferred orientation may be formed if small amounts of gramicidin and O-pyromellitylgramicidin are added to opposite sides of the membrane. These hybrid channels show a distinct asymmetry in the current-voltage characteristic.     

Channel formation kinetics of gramicidin A in lipid bilayer membranes

Summary Previous studies have given evidence that the active form of gramicidin A in lipid bilayer membranes is a dimer which acts as an ion channel; it has been further shown that the mean lifetime of the channel strongly depends on the membrane thickness. As the thickness slightly decreases when a voltage is applied to the membrane, the equilibrium between conducting dimers and nonconducting monomers may be displaced by a voltage jump. From the relaxation of the electrical current after the voltage jump, information about the kinetics of channel formation is obtained. For a dioleoyllecithin/n-decane membrane the rate constant of association is found to be 2×10¹⁴ cm² mole^–1 sec^–1, which is by three orders of magnitude below the limiting value of a diffusion-controlled reaction in a two-dimensional system. The dissociation rate constant is equal to 2 sec^–1, a value which is consistent with the channel lifetime as obtained from electrical fluctuation measurements.     

Formamidinium-induced dimer stabilization and flicker block behavior in homo- and heterodimer channels formed by gramicidin A and N-acetyl gramicidin A.

Compared to the N-formyl gramicidin A (GA), the N-acetyl gramicidin A (NAG) channel has unchanged conductance in 1 M NH4+ (gamma NN/gamma GG = 1, conductance ratio) but reduced conductance in 1 M K+ (gamma NN/gamma GG = 0.6) methylammonium (gamma NN/gamma GG = 0.3), and formamidinium (gamma NN/gamma GG = 0.1) solutions. Except with formamidinium, "flicker blocks" are evident even at low cutoff frequencies. For all cations studied, channel lifetimes of N-acetyl homodimers (NN) are approximately 50-fold shorter than those of the GA homodimer (GG). The novel properties of GA channels in formamidinium solution (supralinear current-voltage relations and dimer stabilization (Seoh and Busath, 1993)) also appear in NN channels. The average single channel lifetime in 1 M formamidinium solution at 100 mV is 6-7-fold longer than in K+ and methylammonium solutions and, like in the GA channel, significantly decreases with increasing membrane potential. Experiments with mixtures of the two peptides, GA and NAG, showed three main conductance peaks. Oriented hybrids were formed utilizing the principle that monomers remain in one leaflet of the bilayer (O'Connell et al., 1990). With GA at the polarized side and NAG at the grounded side, at positive potentials (in which case hybrids were designated GN) and at negative potentials (in which case hybrids were designated NG), channels had the same conductances and channel properties at all potentials studied. Flicker blocks were not evident in the hybrid channels, which suggests that both N-acetyl methyl groups at the junction of the dimer are required to cause flickers. Channel lifetimes in hybrids are only approximately threefold shorter than those of the GG channels, and channel conductances are similar to those of GG rather than NN channels. We suggest that acetyl-acetyl crowding at the dimeric junction in NN channels cause dimer destabilization, flickers, and increased selectivity in N-acetyl gramicidin channels.     

Millimeter microwave effect on ion transport across lipid bilayer membranes

The effects of millimeter microwaves in the frequency range of 54–76 GHz on capacitance and conductance of lipid bilayer membranes (BLM) were studied. Some of the membranes were modified by gramicidin A and amphotericin B or by tetraphenylboron anions (TPhB_?). The millimeter microwaves were pulse-modulated (PW) at repetition rates ranging from 1 to 100 pps, PW at 1000 pps, or unmodulated continuous waves (CW). The maximum output power at the waveguide outlet was 20 mW. It was found that CW irradiation decreased the unmodified BLM capacitance by 1.2% ± 0.5%. At the same time, membrane current induced by TPhB transport increased by 5% ± 1%. The changes in conductance of ionic channels formed by gramicidin A and amphotericin B were small (0.6% ± 0.4%). No “resonance-like” effects of mm-wave irradiation on membrane capacitance, ionic channel currents, or TPhB transport were detected. All changes in membrane capacitance and currents were independent of the modulation employed and were equivalent to heating by approximately 1.1 °C. © 1995 Wiley-Liss, Inc.