The effect of heme-linked ionizable groups on cyanide binding to methemoglobin

The pH dependence of the kinetics of the binding of cyanide ion to methemoglobins A and S and to guinea pig and pigeon methemoglobins appears to be not directly correlated with the net charges on the proteins. The kinetics can, however, be adequately explained in terms of three sets of heme-linked ionizable groups with pK1 ranging between 4.9 and 5.3, pK2 between 6.2 and 7.9, and pK3 between 8.0 and 8.5 at 20 degrees C. pK1 is assigned to carboxylic acid groups, pK2 to histidines and terminal amino groups, and pK3 to the acid-alkaline methemoglobin transition. Kinetic second order rate constants have also been determined for the binding of cyanide ion by the four sets of methemoglobin species present in solution. The pKi values and the rate constants of methemoglobin S are strikingly different from those of methemoglobin A. This result is explained in terms of different electrostatic contributions to the free energy of heme linkage arising from differences in the environments of ionizable groups at the surfaces of the two molecules.     

The uptake of protons by heme-linked ionizable groups on azide binding to methemoglobin

When azide ion reacts with methemoglobin in unbuffered solution the pH of the solution increases. This phenomenon is associated with increases in the pK values of heme-linked ionizable groups on the protein which give rise to an uptake of protons from solution. We have determined as a functional of pH the proton uptake, delta h+, on azide binding to methemoglobin at 20 degrees C. Data for methemoglobins A (human), guinea pig and pigeon are fitted to a theoretical expression based on the electrostatic effect of these sets of heme-linked ionizable groups on the binding of the ligand. From these fits the pK values of heme-linked ionizable groups are obtained for liganded and unliganded methemoglobins. In unliganded methemoglobin pK1, which is associated with carboxylic acid groups, ranges between 4.0 and 5.5 for the three methemoglobins; pK2, which is associated with histidines and terminal amino groups, ranges from 6.2 to 6.7. In liganded methemoglobin pK1 lies between 5.8 and 6.3 and pK2 varies from 8.1 to 8.5. The pH dependences of the apparent equilibrium constants for azide binding to the three methemoglobins at 20 degrees C are well accounted for with the pK values calculated from the variation of delta h+ with pH.     

Activated conformers of Escherichia coli sulfite reductase heme protein subunit

The heme protein subunit of Escherichia coli sulfite reductase shows enhanced reactivity with its substrate and a number of other ligands after a cycle of reduction and reoxidation at alkaline pH. At pH 9.5 this variant of the enzyme possesses at least four EPR-detectable, chloride-sensitive high-spin conformers, in contrast to the single chloride-insensitive species observed in the oxidized, resting enzyme at pH 7.7. Quantitative reversal of the spectral and ligand-binding properties of the "activated" enzyme to those of the resting enzyme is observed on reacidification to pH 7.7. At intermediate pH values, there occurs an acid-catalyzed relaxation of the activated enzyme to the resting form. This reaction is distinct from the one responsible for the accelerated ligand binding and production of multiple EPR conformers, which appears to be regulated by a process with a pK of 8.5.     

Retardation of proton transfer caused by binding of the transition metal ion to the bacterial reaction center is due to pKa shifts of key protonatable residues

Transition metal ions bind to the reaction center (RC) protein of the photosynthetic bacterium Rhodobacter sphaeroides and slow the light-induced electron and proton transfer to the secondary quinone, Q(B). We studied the properties of the metal ion-RC complex by measuring the pH dependence of the dissociation constant and the stoichiometry of proton release upon ligand formation. We investigated the mechanism of inhibition by measuring the stoichiometry and kinetics of flash-induced proton binding, the transfer of (first and second) electrons to Q(B), and the rate of steady-state turnover of the RC in the absence and presence of Cd(2+) and Ni(2+) on a wide pH range. The following results were obtained. (1) The complexation of transition metal ions Cd(2+) and Ni(2+) with the bacterial RC showed strong pH dependence. This observation was explained by different (pH-dependent) states of the metal-ligand cluster: the complex formation was strong when the ligand (Asp and His residues) was deprotonated and was much weaker if the ligand was partly (or fully) protonated. A direct consequence of the model was the pH-dependent proton release upon complexation. (2) The retardation of transfer of electrons and protons to Q(B) was also strongly pH-dependent. The effect was large in the neutral pH range and decreased toward the acidic and alkaline pH values. (3) Steady-state turnover measurements indicated that the rate of the second proton transfer was much less inhibited than that of the first one, which became the rate-limiting step in continuous turnover of the RC. (4) Sodium azide partly recovered the proton transfer rate. The effect is not due to removal of the bound metal ion by azide but probably by formation of a proton-transporting azide network similarly as water molecules may build up proton pathways. (5) We argue that the inhibition comes mainly from pK(a) shifts of key protonatable residues that control the proton transfer along the H-bond network to Q(B). The electrostatic interaction between the metal ion and these residues may result in acidic pK(a) shifts between 1.5 and 2.0 that account for the observed retardation of the electron and proton transfer.     

Kinetic studies on redox reactions of hemoproteins. II. Reduction of thermoresistant cytochrome c-552 and horse heart cytochrome c by ascorbic acid.

The reductions of thermoresistant cytochrome c-552 and horse heart cytochrome c by ascorbic acid were studied by the stopped-flow method between pH 4 and 10. The results were as follows (1) The reduction of horse heart cytochrome c showed two relaxation decays above pH 8.5, one of which was pseudo-first order, as was the case below pH 8, while the other was nearly concentration-independent. These results were consistent with those reported by Greenwood and Palmer (J. Biol. Chem. (1965) 240, 3660-3663). (2) For the reduction of cytochrome c-552, only a single relaxational decay that obeyed pseudo-first order kinetics was observed. (3) It seems most reasonable to assume that the concentration-independent relaxation process can be attributed to the isomerization reaction accompanying ligand exchange, since it is known that only horse heart cytochrome c exhibits ligand exchange, involving a residue with pK 9.3.     

Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3'-O-(N-methylantraniloyl)-5'-diphosphate to the E. coli DnaC protein.     

Coordination geometry of heme in lactoperoxidase: pH-dependent 1H relaxivity and optical spectral studies

Molar relaxivity of water proton in lactoperoxidase solution was studied as a function of pH in the range of 2-13 by spin-lattice relaxation time measurements on a Bruker AM 500 MHz nuclear magnetic resonance (NMR) spectrometer. It was shown by comparison with the molar relaxivities of met myoglobin (Mb) and horseradish peroxidase (HRP) solutions that the sixth coordination position of the heme pocket in lactoperoxidase (LPO) is vacant. Distance of the water proton in the heme pocket from ferric ion was deduced to be 2.7, 3.6 and 4.3 A for Mb, HRP, and LPO, respectively. Acid-alkaline transition for met myoglobin, horseradish peroxidase, and lactoperoxidase determined from the pH dependence of changes in the Soret absorptions were found to be characterized by pK of 8.8, 10.9, and 12.1, respectively. Proton NMR of LPO at pH = 12.2 was found to have single broad resonance considerably upfield shifted as compared to that of LPO at neutral pH. By comparison with the proton NMR of HRP and Mb at pH greater than their respective pK of acid-alkaline transition, the upfield shifted proton resonance of LPO at pH = 12.2 was assigned to be due to low-spin LPO.     

A 1H-NMR study of electronic structure of the active site of Galeorhinus japonicus metmyoglobin

The ferric high-spin form of the myoglobin from the shark Galeorhinus japonicus, which possesses a Gln residue at the distal site instead of the usual His residue, has been studied by 1H-NMR spectroscopy. Using the heme meso-proton (C5H, C10H, C15H and C20H) resonance shift as a diagnostic probe for identifying the coordination system of the iron center in ferric high-spin form of hemoprotein, it has been shown that G. japonicus metmyoglobin (metMb) possesses the pentacoordinated active site. The pH-dependence study of NMR spectra of G. japonicus metMb revealed the appearance of the hydroxyl form of metMb at high pH, indicating that the protein undergoes the transition between the acidic and alkaline forms. The pK value and the rate for this acid-alkaline transition in G. japonicus metMb were found to be approximately 10 and much less than 4 x 10(2) s-1, respectively. Since the pK value of the acid-alkaline transition for the pentacoordinated heme in Aplysia limacina metMb is 7.8 [Giacometti, G.M., Das Ros, A., Antonini, E. & Brunori, M. (1975) Biochemistry 14, 1584-1588] and that of the hexacoordinated heme in sperm whale metMb is 9.1 [Brunori, M., Antonini, E., Fasella, P., Wyman, J. & Rossi-Fanelli, A. (1968) J. Mol. Biol. 34, 497-504], the OH- affinity of the ferric heme iron does not appear to depend on its coordination system. The acid-alkaline transition rate in A. limacina metMb was reported to be much less than 1.5 x 10(2) s-1 [Pande, U., La Mar, G.N., Lecomte, J.T.J., Ascoli, F., Brunori, M., Smith, K.M., Pandey, R.K., Parish, D.W. & Thanabal, V. (1986) Biochemistry 25, 5638-5646] and therefore a slow transition rate may be unique to the pentacoordinated active site of Mb.     

Equilibrium and kinetic evidence for a transition between six- and five-coordinate ferrous heme in the nitric oxide derivative of Aplysia myoglobin

The pH dependence in the range 3--7 of the optical absorption and electron paramagnetic resonance of the nitric oxide adduct of ferrous Aplysia myoglobin is reported. Optical spectra in the Soret region show a transition between two conformers with an apparent pK in the range 3.5--5 depending on the presence of carboxylic anions as third component. In the same pH range, the EPR spectrum undergoes a change from a 9-line to a 3-line hyperfine pattern in the g. region, similar to that reported for synthetic heme derivatives and for other hemoproteins. The structural interpretation of the pH-induced transition experienced by Aplysia myoglobin nitric oxide is that of a proton-linked cleavage of the proximal bond as suggested by several lines of evidence. Temperature-jump measurements allowed an estimation of the relaxation time for the process, which is of the order of 0.3 ms at 25 degrees C.     

Mechanism of azide binding to chloroperoxidase and horseradish peroxidase: use of an iodine laser temperature-jump apparatus

The kinetics of azide binding to chloroperoxidase have been studied at eight pH values ranging from 3.0 to 6.6 at 9.5 +/- 0.2 degrees C and ionic strength of 0.4 M in H2O. The same reaction was studied in D2O at pD 4.36. In addition, results were obtained on azide binding to horseradish peroxidase at pD 4.36 and pH 4.56. Typical relaxation times were in the range 10-40 microseconds. The value of kH/kD(on) for chloroperoxidase is 1.16, and kH/kD(off) is 1.7; corresponding values for horseradish peroxidase are 1.10 and 2.4. The H/D solvent isotope effects indicate proton transfer is partially rate controlling and is more important in the dissociation of azide from the enzyme-ligand complex. A mechanism is proposed in which hydrazoic acid binds to chloroperoxidase in a concerted process in which its proton is transferred to a distal basic group. Hydrogen bonding from the newly formed distal acid to the bound azide facilitates formation of hydrazoic acid as the leaving group in the dissociation process. The binding rate constant data, kon, can be fit to the equation kon = k3/(1 + KA/[H+]), where k3 = 7.6 X 10(7) M-1 S-1 and KA, the dissociation constant of hydrazoic acid, is 2.5 X 10(-5) M. The same mechanism probably is valid for the ligand binding to horseradish peroxidase.     

Kinetics of oxygen and carbon monoxide binding to liver fluke (Dicrocoelium dendriticum) hemoglobin. An extreme case?

The kinetics of oxygen and carbon monoxide binding to the monomeric liver fluke (Dicrocoelium dendriticum) hemoglobin have been studied. The ligand association rates are approximately 1 X 10(8) and approximately 3 X 10(8) M-1 s-1, respectively, for CO and O2 and show no pH dependence. On the contrary the ligand dissociation rates decrease by lowering the pH below 7, the pK of the transition being around 5.5. These findings, together with spectroscopic properties of the protein, are discussed in relation to the fact that, in this hemoglobin, the distal histidine is replaced by a glycine.     

Thermodynamics of the reaction of ferric myoglobin from Aplysia limacina with azide and fluoride. Dependence of enthalpy changes on pH

The effect of pH on the enthalpy changes for binding of azide and fluoride to ferric myoglobin from Aplysia limacina, which lacks the distal histidine, has been investigated. Over the whole pH range explored (3.8 to 9.5), -delta H degrees values for the formation of the hemoprotein-ligand complexes are: (1) much greater than the variations in -delta G degrees; (2) always negative; and (3) show a dependence upon pH characterized by a maximum for azide and a minimum for fluoride binding, centered at pH 4.55 (identical to pHch). This value agrees well with that expected from the linear correlation between pHch and the simple function "Lys+Arg-Glu-Asp-2" proposed by Beetlestone and others. Data reported here greatly extend the pH range for which the linear correlation between the net charge of the macromolecule and pHch has been found to hold, and indicate unequivocally that the pH dependence of -delta H degree for the binding of anionic ligands does not uniquely require the presence of the histidyl residue at the distal position.     

Quaternary structure of methemoglobin. Pulse radiolysis study of the binding of oxygen to the valence hybrid.

The pulse radiolysis of solutions of adult human methemogolbin was used in order to reduce a single heme iron within the protein tetramers. The valence hybrids thus formed were reacted with oxygen. Kinetics of the reactions were studied. The effects of pH and inositol hexaphosphate were examined. The kinetics of the ligation of oxygen to stripped valence hybrids showed a single phase behavior at the pH range 6.5 to 9. As the pH was lowered below 6.5, a second, slower phase became apparent. In the presence of inositol hexaphosphate, above pH 8, the kinetics of oxygen binding was of a single phase. As the pH was lowered, a transition to a second, slower phase was noticed. Below pH 7, the slower phase was the only detectable one. The analysis of the relative contribution of the faster phase to the total reaction as a function of the pH showed a typical transition curve characterized by a pK = 7.5 and a Hill parameter n = 2.9. On this basis, it is concluded that human adult stripped methemoglobin resides in an R quarternary structure, while the presence of IHP stabilizes the T structure at pH below 7.5. This transition between the quaternary structures of methemoglobin cannot be accounted for by the switch between the high spin and the low spin states of the ferric iron. This switch of spin state takes place at pH greater than 8.2.     

Folding and stability of trp aporepressor from Escherichia coli

Equilibrium and kinetic studies of the urea-induced unfolding of trp aporepressor from Escherichia coli were performed to probe the folding mechanism of this intertwined, dimeric protein. The equilibrium unfolding transitions at pH 7.6 and 25 degrees C monitored by difference absorbance, fluorescence, and circular dichroism spectroscopy are coincident within experimental error. All three transitions are well described by a two-state model involving the native dimer and the unfolded monomer; the free energy of folding in the absence of denaturant and under standard-state conditions is estimated to be 23.3 +/- 0.9 kcal/mol of dimer. The midpoint of the equilibrium unfolding transition increases with increasing protein concentration in the manner expected from the law of mass action for the two-state model. We find no evidence for stable folding intermediates. Kinetic studies reveal that unfolding is governed by a single first-order reaction whose relaxation time decreases exponentially with increasing urea concentration and also decreases with increasing protein concentration in the transition zone. Refolding involves at least three phases that depend on both the protein concentration and the final urea concentration in a complex manner. The relaxation time of the slowest of these refolding phases is identical with that for the single phase in unfolding in the transition zone, consistent with the results expected for a reaction that is kinetically reversible. The two faster refolding phases are presumed to arise from slow isomerization reactions in the unfolded form and reflect parallel folding channels.     

Probing the dynamics of a His73-heme alkaline transition in a destabilized variant of yeast iso-1-cytochrome c with conformationally gated electron transfer methods

The alkaline transition of cytochrome c involves substitution of the Met80 heme ligand of the native state with a lysine ligand from a surface Ω-loop (residues 70 to 85). The standard mechanism for the alkaline transition involves a rapid deprotonation equilibrium followed by the conformational change. However, recent work implicates multiple ionization equilibria and stable intermediates. In previous work, we showed that the kinetics of formation of a His73-heme alkaline conformer of yeast iso-1-cytochrome c requires ionization of the histidine ligand (pK(HL) ~ 6.5). Furthermore, the forward and backward rate constants, k(f) and k(b), respectively, for the conformational change are modulated by two auxiliary ionizations (pK(H1) ~ 5.5, and pK(H2) ~ 9). A possible candidate for pK(H1) is His26, which has a strongly shifted pK(a) in native cytochrome c. Here, we use the AcH73 iso-1-cytochrome c variant, which contains an H26N mutation, to test this hypothesis. pH jump experiments on the AcH73 variant show no change in k(obs) for the His73-heme alkaline transition from pH 5 to 8, suggesting that pK(H1) has disappeared. However, direct measurement of k(f) and k(b) using conformationally gated electron transfer methods shows that the pH independence of k(obs) results from coincidental compensation between the decrease in k(b) due to pK(H1) and the increase in k(f) due to pK(HL). Thus, His26 is not the source of pK(H1). The data also show that the H26N mutation enhances the dynamics of this conformational transition from pH 5 to 10, likely as a result of destabilization of the protein.     

Aplysia oxymyoglobin with an unusual stability property: involvement of two kinds of carboxyl groups

Unlike mammalian oxymyoglobins, Aplysia MbO2 is extremely susceptible to autoxidation, and its pH dependence is also unusual. Kinetic formulation has revealed that two kinds of dissociable group with pK1 = 4.3 and pK2 = 6.1, respectively, at 25 degrees C are involved in the stability property of Aplysia MbO2. In order to characterize thermodynamically these dissociation processes involved, the effect of temperature on K1 and K2 was studied by analyzing the pH dependence for the autoxidation rate of Aplysia MbO2 in 0.1 M buffer over the pH range of 4-11, and at 15, 25 and 35 degrees C. The resulting thermodynamic parameters for each group were both those to be expected for the ionization of a carboxyl group; the delta H degrees value being numerically much less than 1 kcal.mol-1, or zero in practice, but being associated with a large negative value of delta S degrees of the order of -20 cal.mol-1.K-1. Taking into account the fact that Aplysia myoglobin contains only a single histidine residue corresponding to the heme-binding proximal one, we can unequivocally conclude that the two kinds of the dissociable group involved in the unusual stability of Aplysia MbO2 must both be carboxyl groups, the protonation of these groups being responsible for an increase in its autoxidation rate in the acidic pH range.     

Electrogenic proton exchange between cytochrome a3 active center and M-aqueous phase. Evidence for cytochrome a3-associated input proton well

The rate of cyanide binding with the oxidized cytochrome-c oxidase in proteoliposomes is controlled by ionization of a protein group with pK approximately 6.7, the ligand reacting with the protonated enzyme only [(1983) Bioorg. Chem. (USSR) 9, 216-227]. As shown here, the kinetics of cyanide binding depends on the pH inside the proteoliposomes. The reaction rate is affected by the electrical potential difference across the proteoliposome membranes as if the a3-linked ionizable group exchanged H+ with the proteoliposome interior electrogenically. The data corroborate a hypothesis on the existence of a proton well communicating cytochrome oxidase O2-reducing center with the M-aqueous phase.     

Spin-label study of conformational changes induced by pH and ligands in leghemoglobin from yellow lupine root nodules

Conformational changes induced by ligands and pH in lupine ferrileghemoglobin selectively modified at Tyr-E16 by the imidazolide spin label has been studied by the method of electron spin resonance in the pH range 6-13. It is shown that in the alkaline pH region the bound spin label registers a local conformational transition which precedes the alkaline denaturation of the protein. In aquamet, cyanide and nicotinate complexes of ferrileghemoglobin this transition occurs with pK 10.5, in acetate and azide complexes with pK 11. In all these ligand derivatives the transition is induced by alteration in the ionization state of one group (delta nH+ approximately equal to 1), most probably, the epsilon-amino group of Lys-GH3. The latter is linked with the Glu-A14 residue and this bond is essential for maintaining the native conformation of leghemoglobin. The ligand-induced conformational changes in the vicinity of the label are small and consist, most likely, in some alteration of the mutual arrangement of the AE and GH helical complexes. No correlation has been revealed between the spin state of the heme iron and the conformation of leghemoglobin in the region under study.     

Structural dynamics in the active site of murine neuroglobin and its effects on ligand binding

We have examined the effects of active site residues on ligand binding to the heme iron of mouse neuroglobin using steady-state and time-resolved visible spectroscopy. Absorption spectra of the native protein, mutants H64L and K67L and double mutant H64L/K67L were recorded for the ferric and ferrous states over a wide pH range (pH 4-11), which allowed us to identify a number of different species with different ligands at the sixth coordination, to characterize their spectroscopic properties, and to determine the pK values of active site residues. In flash photolysis experiments on CO-ligated samples, reaction intermediates and the competition of ligands for the sixth coordination were studied. These data provide insights into structural changes in the active site and the role of the key residues His64 and Lys67. His64 interferes with exogenous ligand access to the heme iron. Lys67 sequesters the distal pocket from the solvent. The heme iron is very reactive, as inferred from the fast ligand binding kinetics and the ability to bind water or hydroxyl ligands to the ferrous heme. Fast bond formation favors geminate rebinding; yet the large fraction of bimolecular rebinding observed in the kinetics implies that ligand escape from the distal pocket is highly efficient. Even slight pH variations cause pronounced changes in the association rate of exogenous ligands near physiological pH, which may be important in functional processes.     

Interstrand loops CD and EF act as pH-dependent gates to regulate fatty acid ligand binding in tear lipocalin

Tear lipocalin (TL), a major component of human tears, shows pH-dependent endogenous ligand binding. The structural and conformational changes associated with ligand release in the pH range of 7.5-3.0 are monitored by circular dichroism spectroscopy and site-directed tryptophan fluorescence. In the transition from pH 7.5 to pH 5.5, the ligand affinity for 16-(9-anthroyloxy)palmitic acid (16AP) and 8-anilino-1-naphthalenesulfonic acid is reduced. At pH 4.0 these ligands no longer bind within the TL calyx. From pH 7.3 to pH 3.0, the residues on loops CD and EF, which overhang the calyx entrance, show reduced accessibility to acrylamide. In addition resonance energy transfer is enhanced between residues on the two loops; the distance between the loops narrows. These findings suggest that apposition of the loops at low pH excludes the ligand from the intracavitary binding site. The conformational changes observed in transition from pH 7.3 to pH 3.0 for loops CD and EF are quite different. The CD loop shows less population reshuffling than the EF loop with an acidic environment, probably because backbone motion is restrained by the adjacent disulfide bond. The Trp fluorescence wavelength maximum (lambda(max)) reflects internal electrostatic interactions for positions on loops CD and EF. The titration curves of lambda(max) for mutants on the EF loop fit the Hendersen-Hasselbalch equation for two apparent pK(a) values, while the CD loop positions fit satisfactorily with one pK(a) value. Midpoints of transition for the binding affinity of TL tryptophan mutants to 16AP occur at pH 5.5-6.1. Replacement of each amino acid on either loop by single tryptophan mutation does not disrupt the pH-dependent binding affinity to 16AP. Taken together the data suggest that pH-driven ligand release involves ionization changes in several titratable residues associated with CD and EF loop apposition and occlusion of the calyx.