Conformational studies of poly(L-tyrosine). A helix–coil transition in dimethyl sulfoxide–dichloroacetic acid mixtures

Poly(L -tyrosine) is a random coil in dimethyl sulfoxide. Upon addition of dichloroacetic acid, poly(L -tyrosine) undergoes a conformational transition centered at about 10% dichloroacetic acid. The transition is nearly complete at 20% dichloroacetic acid. Further addition of dichloroacetic acid leads to precipitation of poly(L -tyrosine). We have characterized this transition by optical rotation, viscosity, circular dichroism, and infrared. The optical rotation at 350 nm and the intrinsic viscosity increase sharply to values that are consistent with a transition to the α-helix conformation. The circular dichroism of poly(L -tyrosine) in dimethyl sulfoxide and in dimethyl sulfoxide/dichloroacetic acid (80:20 v/v) agrees with previous reports for random-coil and α-helix conformations, respectively. The infrared spectrum of poly(L -tyrosine) in dimethyl sulfoxide/dichloroacetic acid (80:20 v/v) shows no evidence of β-structure. We conclude that the transition on going from dimethyl sulfoxide to 20% dichloroacetic acid in dimethyl sulfoxide is a coil → α-helix transition. The amide-I band of poly(L -tyrosine) in dimethyl sulfoxide/dichloroacetic acid (80:20) is found to be at 1662 cm^?1. It has been suggested that this high frequency may be indicative of a left-handed α-helix. However, this high amide-I frequency is consistent with conformational energy calculations of Scheraga and co-workers. The mechanism of the dichloroacetic acid-induced transition to an α-helix is discussed. Dichloroacetic acid and dimethyl sulfoxide interact strongly and the transition presumably involves a marked decrease in the ability of dimethyl sulfoxide to solvate the peptide backbone and aromatic side chains upon complex formation with dichloroacetic acid.     

What does it mean to be natively unfolded?

Natively unfolded or intrinsically unstructured proteins constitute a unique group of the protein kingdom. The evolutionary persistence of such proteins represents strong evidence in the favor of their importance and raises intriguing questions about the role of protein disorders in biological processes. Additionally, natively unfolded proteins, with their lack of ordered structure, represent attractive targets for the biophysical studies of the unfolded polypeptide chain under physiological conditions in vitro. The goal of this study was to summarize the structural information on natively unfolded proteins in order to evaluate their major conformational characteristics. It appeared that natively unfolded proteins are characterized by low overall hydrophobicity and large net charge. They possess hydrodynamic properties typical of random coils in poor solvent, or premolten globule conformation. These proteins show a low level of ordered secondary structure and no tightly packed core. They are very flexible, but may adopt relatively rigid conformations in the presence of natural ligands. Finally, in comparison with the globular proteins, natively unfolded polypeptides possess 'turn out' responses to changes in the environment, as their structural complexities increase at high temperature or at extreme pH.     

Pressure‐induced conformational switch of an interfacial protein

A special class of proteins adopts an inactive conformation in aqueous solution and activates at an interface (such as the surface of lipid droplet) by switching their conformations. Lipase, an essential enzyme for breaking down lipids, serves as a model system for studying such interfacial proteins. The underlying conformational switch of lipase induced by solvent condition is achieved through changing the status of the gated substrate‐access channel. Interestingly, a lipase was also reported to exhibit pressure activation, which indicates it is drastically active at high hydrostatic pressure. To unravel the molecular mechanism of this unusual phenomenon, we examined the structural changes induced by high hydrostatic pressures (up to 1500 MPa) using molecular dynamics simulations. By monitoring the width of the access channel, we found that the protein undergoes a conformational transition and opens the access channel at high pressures (>100 MPa). Particularly, a disordered amphiphilic α5 region of the protein becomes ordered at high pressure. This positive correlation between the channel opening and α5 ordering is consistent with the early findings of the gating motion in the presence of a water–oil interface. Statistical analysis of the ensemble of conformations also reveals the essential collective motions of the protein and how these motions contribute to gating. Arguments are presented as to why heightened sensitivity to high‐pressure perturbation can be a general feature of switchable interfacial proteins. Further mutations are also suggested to validate our observations. Proteins 2016; 84:820–827. © 2016 Wiley Periodicals, Inc.     

Spectroscopic studies of oligomers containing 2,5-trans furanoid sugar amino acids

Sugar amino acids and their oligomers, known as carbopeptoids, are commonly studied as foldamers. However, study of their conformational preference is often challenging when the adopted conformations are extended and/or disordered. This study is the first to explore the disordered nature of such carbopeptoids by utilizing a family of 2,5-trans carbopeptoids. An array of spectroscopic techniques has been used to investigate the conformational preference of these carbopeptoids. However, using this data alone it has not been possible to assign conformational preference as an ordered extended conformation or as a disordered family of closely related conformations. Computational methods need to be employed to achieve reliable interpretation of the spectroscopic data.     

A method for estimating the nature and relative proportions of amorphous, single, and double-helical components in starch granules by (13)C CP/MAS NMR

An improved method to analyze the (13)C NMR spectra of native starches, which considers the contribution of the V-type conformation and the nature of the amorphous component, has been developed. Starch spectra are separated into amorphous and ordered subspectra, using intensity at 84 ppm as a reference point. The ordered subspectra of high amylose starches show the presence of both V-type single helices and B-type double helices. Relative proportions of amorphous, single, and double-helical conformations are estimated by apportioning intensity of C1 peak areas between conformational types on the basis of ordered and amorphous subspectra of the native starch. Quantitative analysis shows that the V-type single-helical component increases with amylose content of starches. Different amorphous subspectra are needed to provide a consistent analysis of granular starches from diverse sources. The method of preparation was found to be more important than the starch botanical origin in determining (13)C NMR spectral features of amorphous samples.     

Influence of the pyruvate content of xanthan on macromolecular association in solution

The unusual increase in viscosity and pseudoplasticity often observed when salts are added to moderately concentrated aqueous solutions of xanthan gum is shown to arise from an increase in the extent of macromolecular association. The fractional change in viscosity on addition of KCl to salt-free 1% (w/v) solutions of purified polysaccharide in the K⁺ salt form is found to be positive only when the degree of pyruvate substitution (fraction of side chains which carry pyruvate ketal substituents) exceeds ≈0.31. Above this value, the fractional change in viscosity increases with further increase in the degree of pyruvate substitution. These differences cannot arise from different degrees of conformational ordering, since the magnitude of the thermally induced order disorder transition (monitored by optical rotation at low ionic strength) is independent of pyruvate content. The temperature at the transition midpoint, however, falls with increasing degree of pyruvate substitution. This is attributed to destabilization of the ordered structure by intramolecular electrostatic repulsion between pyruvate groups, and stabilization through apolar interactions of acetate methyl groups. Viscosity-concentration relationships show changes of slope which mark the onset of macromolecular association. Association commences at lower concentrations when ionic strength and degree of pyruvate substitution are high. It is suggested that once electrostatic repulsions have been diminished at high ionic strength, association is promoted by intermolecular apolar interactions of pyruvate methyl groups, which are suitably near the periphery of the helical conformation.     

CD, 1H NMR and molecular modeling studies of the interaction of Ca2+ with substance P and Ala7-substance P in a non-polar solvent.

The biologically relevant conformation of substance P is likely to be dictated by the lipid milieu wherein the hormone would interact with its receptor. Assuming that specific constraints to the hormone structure may be imparted by its interaction with Ca2+ ions in the low dielectric lipid medium, the interaction of substance P and its inactive analog, Ala7-substance P, has been characterized in a lipid-mimetic solvent. Circular dichroism (CD) and NMR spectral methods were employed to study the conformation of the free and Ca2+-bound forms of the peptides and the conformational changes that occur on Ca2+ binding. The results show that both peptides assume a helical structure in the non-polar solvent used, a mixture of acetonitrile and trifluoroethanol. The N-terminal region is, however, less ordered in the analog peptide compared with the native hormone. Ca2+ addition causes significant conformational changes in both the peptides. However, while substance P binds two Ca2+ ions in a cooperative manner, Ala7-substance P binds only one Ca2+ ion with a relatively weaker affinity. Computations of the minimum-energy conformations of the free and Ca2+-bound peptides were performed using interproton distances derived from nuclear Overhauser enhancement spectra of the two peptides, as well as the information provided by changes in proton chemical shifts caused by Ca2+ addition. Taken together, the results of this study suggest that differences in the interaction of substance P and Ala7-substance P with Ca2+ in the non-polar milieu, which in turn leads to differences in their Ca2+-bound conformations, may be the basis for the differences in their biological potencies.     

Association of proteins in acidic solutions—a case study with β-globulin

The investigation of the effect of acid pH on the structure of beta-globulin indicated several transitions as a function of pH. Upon reducing the pH from 7.0, the beta-globulin molecule underwent an expansion due to hydration up to pH 5.0, and a further increase in H+ concentration resulted in unfolding. This is a single step cooperative denaturation as indicated by the viscosity profile. At extreme acid pH values (below pH 2.0) the protein associates or folds to a different conformational motif as shown by blue shift of ultraviolet fluorescence emission maximum and decrease in reduced viscosity values by more than 30% due to an entropically driven hydrophobic interaction. The conformational analysis of beta-globulin showed a decrease up to pH 3.0, followed by an increase in the ordered structure at low pH values indicating that the low pH values stabilized this new conformation. These results are discussed in view of the molten globule structure of proteins.     

Nuclear magnetic resonance conformational studies on the chemotactic tripeptide formyl-L-methionyl-L-leucyl-L-phenylalanine. A small beta sheet.

Previous work by several groups has shown that the combination of spin--spin coupling constants and spectral density components (derived from spin--lattice relaxation and/or nuclear Overhauser measurements) may aid in the task of conformational determination of peptides in solution. Using the peptide formyl-L-methionyl-L-leucyl-L-phenylalanine, which is a potent specific chemotactic agent for leucocytes, we show the following: (a) that 3JNHCH coupling constants are consistent with a high degree of rigidity in the peptide backbone in solution, (b) that 3H isotopic substitution in combination with relaxation data taken at different Larmor frequencies enables spectral density, and thence conformational, information to be obtained, (c) that side-chain conformations for this molecule mirror, in some aspects, those found in the solid state for other peptides containing the same residues, and (d) that temperature dependence of amide chemical shifts does not have direct implication concerning the existence of intramolecular hydrogen bonds in peptides. We are able to propose a family of conformations which appear to interchange rapidly on the NMR time scale and are characterized by a distribution of side-chain rotamers. The basic backbone conformation is, or closely approximates, a small beta antiparallel pleated sheet and as such suggests a possible mode of receptor--chemotactic peptide interaction.     

Solution structure and conformational heterogeneity of acylphosphatase from Bacillus subtilis

Acylphosphatase is a small enzyme that catalyzes the hydrolysis of acyl phosphates. Here, we present the solution structure of acylphosphatase from Bacillus subtilis (BsAcP), the first from a Gram-positive bacterium. We found that its active site is disordered, whereas it converted to an ordered state upon ligand binding. The structure of BsAcP is sensitive to pH and it has multiple conformations in equilibrium at acidic pH (pH < 5.8). Only one main conformation could bind ligand, and the relative population of these states is modulated by ligand concentration. This study provides direct evidence for the role of ligand in conformational selection.     

Estimating the Contributions of Selection and Self-Organization in RNA Secondary Structure

In addition to characteristic structural properties imposed by evolutionary modification, evolved, single-stranded RNAs also display characteristic structural properties imposed by intrinsic physical constraints on RNA polymer folding. The balance of intrinsic and functionally selected characters in the folded conformation of evolved secondary structures was determined by comparing the predicted secondary structures of evolved and unevolved (random) RNA sequences. Though evolved conformations are significantly more ordered than conformations of random-sequence RNA, this analysis demonstrates that the majority of conformational order within evolved structures results not from evolutionary optimization but from constraints imposed by rules intrinsic to RNA polymer folding. Received: 25 November 1998 / Accepted: 12 February 1999     

江浙蝮蛇毒酸性与碱性磷脂酶A_2溶液构象变化的差示扫描量热法研究

运用差示扫描量热法,在不同ｐＨ值的缓冲溶液内和各种浓度的碱土族氯化物溶液内,研究了来自江浙蝮蛇（ＡｇｋｉｓｔｒｏｄｏｎｈａｌｙｓＰａｌｌａｓ）毒的酸性与碱性磷脂酶外Ａ２（ＰＬＡ２）的热变性过程。得到表征这两种酶溶液构象变化的热力学参数。依据这些参数研究了两者的溶液构象及其变化。在ｐＨ４．５以下,分子净荷正电的这两种酶在溶液中不形成可热致伸展的有序构象;ｐＨ高于４．５时,Ａｓｐ和Ｇｌｕ的侧链羧基以负离子形式存在有利于有序构象的稳定。Ｈｉｓ是决定ＰＬＡ２活力和热稳定性的重要残基。磷酸根离子和这两种酶有结合作用而降低有序构象的热稳定性。碱土族阳离子除和这两种酶结合外,还以依赖于离子强度的方式复杂地影响酶的溶液构象,但其作用不完全是静电性的,是或多或少地随离子的不同而不同的。计算给出酸性ＰＬＡ２的△Ｈｃｄ．     

Beta-hairpin conformation of fibrillogenic peptides: structure and alpha-beta transition mechanism revealed by molecular dynamics simulations

Understanding the conformational transitions that trigger the aggregation and amyloidogenesis of otherwise soluble peptides at atomic resolution is of fundamental relevance for the design of effective therapeutic agents against amyloid-related disorders. In the present study the transition from ideal alpha-helical to beta-hairpin conformations is revealed by long timescale molecular dynamics simulations in explicit water solvent, for two well-known amyloidogenic peptides: the H1 peptide from prion protein and the Abeta(12-28) fragment from the Abeta(1-42) peptide responsible for Alzheimer's disease. The simulations highlight the unfolding of alpha-helices, followed by the formation of bent conformations and a final convergence to ordered in register beta-hairpin conformations. The beta-hairpins observed, despite different sequences, exhibit a common dynamic behavior and the presence of a peculiar pattern of the hydrophobic side-chains, in particular in the region of the turns. These observations hint at a possible common aggregation mechanism for the onset of different amyloid diseases and a common mechanism in the transition to the beta-hairpin structures. Furthermore the simulations presented herein evidence the stabilization of the alpha-helical conformations induced by the presence of an organic fluorinated cosolvent. The results of MD simulation in 2,2,2-trifluoroethanol (TFE)/water mixture provide further evidence that the peptide coating effect of TFE molecules is responsible for the stabilization of the soluble helical conformation.     

Downhill versus Barrier-Limited Folding of BBL: 3. Heterogeneity of the Native State of the BBL Peripheral Subunit Binding Domain and Its Implications for Folding Mechanisms

Protein folding studies are generally predicated on Anfinsen's dogma that there is a unique native state of a protein. However, this is not always the case. NMR measurements of BBL, for example, find a decrease in helicity of helix 2 surrounding His166 on its protonation, which, with other experimental data, suggests that the native state can occupy two or more conformations. Here, we analysed the native structure of BBL as a function of pH, temperature and ionic strength, along with a truncated BBL construct, by extensive all-atom molecular dynamics simulations in explicit solvent, corresponding to at least 400 ns of trajectories collected for each set of conditions. The native state was heterogeneous under a variety of conditions, consisting of two predominant conformations. This equilibrium changed with conditions: protonation of His166 at low pH shifted the equilibrium in favour of a less ordered conformer, while high ionic strength at neutral pH shifted the equilibrium to a more ordered conformer. Furthermore, high temperature and truncation of the sequence also shifted the equilibrium toward the less ordered conformer. Importantly, conformational heterogeneity in a native structure that changes with conditions will lead to deviations from the classic two-state behaviour during the barrier-limited unfolding of a protein. In particular, some regions of the protein will appear to unfold asynchronously and some residues will have anomalous thermal titration curves and unusual baseline behaviour monitored microscopically by NMR spectroscopy and macroscopically by calorimetry and other techniques. Such data could otherwise be interpreted as evidence for barrier-free downhill folding. Any biological significance of downhill folding of BBL appears to be ruled out by recent crystallographic studies on the reaction cycle of the BBL-equivalent domain in a pyruvate dehydrogenase multienzyme complex in which the domain remains of constant structure.     

β‐Hairpin folding and stability: molecular dynamics simulations of designed peptides in aqueous solution

The structural properties of a 10‐residue and a 15‐residue peptide in aqueous solution were investigated by molecular dynamics simulation. The two designed peptides, SYINSDGTWT and SESYINSDGTWTVTE, had been studied previously by NMR at 278 K and the resulting model structures were classified as 3:5 β‐hairpins with a type I + G1 β‐bulge turn. In simulations at 278 K, starting from the NMR model structure, the 3:5 β‐hairpin conformers proved to be stable over the time period evaluated (30 ns). Starting from an extended conformation, simulations of the decapeptide at 278 K, 323 K and 353 K were also performed to study folding. Over the relatively short time scales explored (30 ns at 278 K and 323 K, 56 ns at 353 K), folding to the 3:5 β‐hairpin could only be observed at 353 K. At this temperature, the collapse to β‐hairpin‐like conformations is very fast. The conformational space accessible to the peptide is entirely dominated by loop structures with different degrees of β‐hairpin character. The transitions between different types of ordered loops and β‐hairpins occur through two unstructured loop conformations stabilized by a single side‐chain interaction between Tyr2 and Trp9, which facilitates the changes of the hydrogen‐bond register. In agreement with previous experimental results, β‐hairpin formation is initially driven by the bending propensity of the turn segment. Nevertheless, the fine organization of the turn region appears to be a late event in the folding process. Copyright © 2004 European Peptide Society and John Wiley & Sons, Ltd.     

Prediction of the native conformation of a polypeptide by a statistical-mechanical procedure. II. Average backbone structure of enkephalin

The average conformation of Met-enkephalin was determined by using an adaptive, importance-sampling Monte Carlo algorithm (SMAPPS—Statistical Mechanical Algorithm for Predicting Protein Structure). In the calculation, only the backbone dihedral angles (? and ψ) were allowed to vary; i.e., all side-chain (χ) and peptide-bond (ω) dihedral angles were kept fixed at the values corresponding to a low-energy structure of the pentapeptide. The total conformational energy for each randomly generated structure of the polypeptide was obtained by summing over the interaction energies of all pairs of nonbonded atoms of the whole molecule. The interaction energies were computed by the program ECEPP/2 (Empirical Conformational Energy Program for Peptides). Solvent effects were not included in the computation. The calculation was repeated until a total of 10 independent average conformations were established. The regions of conformational space occupied by the average structures were compared with the regions of low conditional free energy obtained by SMAPPS in the first paper of this series. Such a comparison provides an analysis of the capacity of SMAPPS to adjust the Monte Carlo search to regions of highest probability. The results demonstrate that the ability of SMAPPS to focus the Monte Carlo search is excellent. Finally, the 10 independent average conformations and the mean of the 10 average structures were utilized as the initial conformations for a direct energy minimization of the pentapeptide. Of the 11 final energy-minimized structures, three of the conformations were found to be equivalent to the conformation of lowest energy determined previously. In addition, all but two of the remaining energy-minimized structures were found to correspond to one of the two other conformations of high probability obtained in the first paper of this series. These results indicate that a set of independent average conformations can provide a rational, unbiased choice for the initial conformation, to be used in a direct energy minimization of a polypeptide. The final energy-minimized structures consequently constitute a set of low-energy conformations, which include the global energy minimum.     

The conformational equilibria of a renin inhibitor peptide in solution

The conformational equilibrium of a decapeptide renin inhibitor (Renin Inhibitory Peptide (RIP), NH-P-H-P-F-H-F-F-V-Y-K-CO2H) in water, methanol and trifluoroethanol has been investigated. The value of a combined spectroscopic approach was apparent, with the need to define conformational states that were mixtures of conformational forms. Similarities between this study and that of the Melanin Concentrating Hormone (MCH) core peptide (5-14) are notable [1]. In water, two beta-turn conformations and an extended form were found to be in equilibrium, with cis/trans isomerism at Pro-3. Extended conformations associated with the P(II) helix and irregular forms were more favoured in aqueous environments. In MeOH and TFE, two beta-turn conformations associated with overlapping sequences and cis/trans isomerism at Pro-3 amide bond were seen to be in equilibrium. 2D ROESY and chemical-exchange cross-peaks were detected by 1H NMR and used to build up detailed models of the interconverting beta-turn conformations of RIP.     

Raman studies of nucleic acids. XII. Conformations of oligonucleotides and deuterated polynucleotides

Laser Raman spectra of the trinucleoside diphoshate ApApA and dinucleoside phosphates ApU, UpA, GpC, CpG, and GpU are reported and discussed. Assignments of conformationally sensitive frequencies are-facilitated by comparison with spectra reported here of poly(rA), poly(rC), and poly(rU) in deuterium oxide solutions. The significant spectral differences between ApU and UpA, and between GpC and CpG, reveal that the sequence isomers have nonidentical conformations in aqueous solution. In UpA at low temperature the bases are stacked and the backbone conformation is similar to that found in ordered polynucleotide structures and RNA. In ApU no base stacking can be detected and the backbone conformation differs from that found in UpA, both in the orientation of phosphodiester linkages and in the internal conformation of ribose. At the conditions employed neither ApU nor UpA exhibits base pairing in aqueous solutions. In both GpC and CpG the bases are stacked and the phosphodiester conformations are similar to those encountered for UpA and RNA. However, major differences between spectra of GpC and CpG indicate that the geometries of stacking and ribosyl conformations are different. In GpC the Raman data favor the formation of hydrogen bonded dimers containing GC pairs. Protonation of C in GpC is sufficient to eliminate the ordered conformation detected by Raman spectroscopy. Despite the ordered backbone conformation evident in GpU, this dinucleoside apparently contains neither stacked nor hydrogen bonded bases at the conditions employed here. The Raman data also confirm the stacking interactions in ApApA, poly(rA), and poly(rC) but suggest that the backbone conformation in poly(rC) differs qualitatively from that found in most ordered polynucleotide structures and is thermally more stable. The present results demonstrate the sensitivity of the Raman technique to sequence-related structural differences in oligonucleotides and provide additional spectra–structure correlations for future conformational studies of RNA by laser Raman spectroscopy.     

Relating protein conformational changes to packing efficiency and disorder

Changes in protein conformation play key roles in facilitating various biochemical processes, ranging from signaling and phosphorylation to transport and catalysis. While various factors that drive these motions such as environmental changes and binding of small molecules are well understood, specific causative effects on the structural features of the protein due to these conformational changes have not been studied on a large scale. Here, we study protein conformational changes in relation to two key structural metrics: packing efficiency and disorder. Packing has been shown to be crucial for protein stability and function by many protein design and engineering studies. We study changes in packing efficiency during conformational changes, thus extending the analysis from a static context to a dynamic perspective and report some interesting observations. First, we study various proteins that adopt alternate conformations and find that tendencies to show motion and change in packing efficiency are correlated: residues that change their packing efficiency show larger motions. Second, our results suggest that residues that show higher changes in packing during motion are located on the changing interfaces which are formed during these conformational changes. These changing interfaces are slightly different from shear or static interfaces that have been analyzed in previous studies. Third, analysis of packing efficiency changes in the context of secondary structure shows that, as expected, residues buried in helices show the least change in packing efficiency, whereas those embedded in bends are most likely to change packing. Finally, by relating protein disorder to motions, we show that marginally disordered residues which are ordered enough to be crystallized but have sequence patterns indicative of disorder show higher dislocation and a higher change in packing than ordered ones and are located mostly on the changing interfaces. Overall, our results demonstrate that between the two conformations, the cores of the proteins remain mostly intact, whereas the interfaces display the most elasticity, both in terms of disorder and change in packing efficiency. By doing a variety of tests, we also show that our observations are robust to the solvation state of the proteins.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.