Determination of solid-state NMR structures of proteins by means of three-dimensional 15N-13C-13C dipolar correlation spectroscopy and chemical shift analysis

In this paper, a three-dimensional (3D) NMR-based approach for the determination of the fold of moderately sized proteins by solid-state magic-angle spinning (MAS) NMR is presented and applied to the alpha-spectrin SH3 domain. This methodology includes the measurement of multiple (13)C-(13)C distance restraints on biosynthetically site-directed (13)C-enriched samples, obtained by growing bacteria on [2-(13)C]glycerol and [1,3-(13)C]glycerol. 3D (15)N-(13)C-(13)C dipolar correlation experiments were applied to resolve overlap of signals, in particular in the region where backbone carbon-carbon correlations of the C(alpha)-C(alpha), CO-CO, C(alpha)-CO, and CO-C(alpha) type appear. Additional restraints for confining the structure were obtained from phi and psi backbone torsion angles of 29 residues derived from C(alpha), C(beta), CO, NH, and H(alpha) chemical shifts. Using both distance and angular restraints, a refined structure was calculated with a backbone root-mean-square deviation of 0.7 A with respect to the average structure.     

Pressure-dependent <Superscript>13</Superscript>C chemical shifts in proteins: origins and applications

Pressure-dependent ¹³C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH₃, CH₂ and CH carbon shifts change on average by +0.23, −0.09 and −0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the γ-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual ¹³Cα shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas ¹³Cβ shifts retain significant dependence on local compression, making them less useful as structural restraints.     

Automated amino acid side-chain NMR assignment of proteins using <Superscript>13</Superscript>C- and <Superscript>15</Superscript>N-resolved 3D [<Superscript>1</Superscript>H,<Superscript>1</Superscript>H]-NOESY

ASCAN is a new algorithm for automatic sequence-specific NMR assignment of amino acid side-chains in proteins, which uses as input the primary structure of the protein, chemical shift lists of (1)H(N), (15)N, (13)C(alpha), (13)C(beta) and possibly (1)H(alpha) from the previous polypeptide backbone assignment, and one or several 3D (13)C- or (15)N-resolved [(1)H,(1)H]-NOESY spectra. ASCAN has also been laid out for the use of TOCSY-type data sets as supplementary input. The program assigns new resonances based on comparison of the NMR signals expected from the chemical structure with the experimentally observed NOESY peak patterns. The core parts of the algorithm are a procedure for generating expected peak positions, which is based on variable combinations of assigned and unassigned resonances that arise for the different amino acid types during the assignment procedure, and a corresponding set of acceptance criteria for assignments based on the NMR experiments used. Expected patterns of NOESY cross peaks involving unassigned resonances are generated using the list of previously assigned resonances, and tentative chemical shift values for the unassigned signals taken from the BMRB statistics for globular proteins. Use of this approach with the 101-amino acid residue protein FimD(25-125) resulted in 84% of the hydrogen atoms and their covalently bound heavy atoms being assigned with a correctness rate of 90%. Use of these side-chain assignments as input for automated NOE assignment and structure calculation with the ATNOS/CANDID/DYANA program suite yielded structure bundles of comparable quality, in terms of precision and accuracy of the atomic coordinates, as those of a reference structure determined with interactive assignment procedures. A rationale for the high quality of the ASCAN-based structure determination results from an analysis of the distribution of the assigned side chains, which revealed near-complete assignments in the core of the protein, with most of the incompletely assigned residues located at or near the protein surface.     

Solution structure of the soluble domain of the NfeD protein YuaF from <Emphasis Type="Italic">Bacillus subtilis</Emphasis>

The transmembrane protein YuaF from B. subtilis is a member of the NfeD-like clan with a potential role in maintaining membrane integrity during conditions of cellular stress. nfeD-genes are primarily found in highly conserved operon structures together with the gene of another membrane protein belonging to the SPFH superfamily, in this case YuaG. This strongly suggests a functional if not physical interaction between YuaF and YuaG. Secondary structure predictions of NfeD proteins that accompany SPFH proteins all indicate a high content of beta-sheets in the C-terminal domains indicating a conserved core structure despite very low homology at the level of primary structure. Here we report the high-resolution solution structure of YuaF's soluble C-terminal domain derived from NMR data (sYuaF, residues 97-174 of full-length YuaF). Full backbone and side chain assignments of sYuaF were obtained from triple-resonance spectra. The structure was determined from distance restraints derived from 3D NOESY spectra collected at 600 MHz and 800 MHz, together with phi, psi, and chi(1) torsion angle restraints based on the analysis of (1)H(N), (15)N, (1)H(alpha), (13)C(alpha), (13)CO, and (13)C(beta) chemical shifts, and HNHA, HNHB and HACAHB-COSY spectra. Structures were calculated using CYANA 2.0 and refined in AMBER 8. sYuaF is composed of an extended N-terminal alpha-helix and a beta-barrel formed by five beta-strands. This beta-sheet core structure is well known from the diverse class of OB-fold proteins and can also be found in the distantly related NfeD protein Ph0471 from the archaeon P. horikoshii. Despite significant differences of their amino acid sequences the structural homology of these proteins suggests a conserved function of SPFH-associated NfeD proteins.     

Direct amide <Superscript>15</Superscript>N to <Superscript>13</Superscript>C transfers for solid-state assignment experiments in deuterated proteins

The assignment of protein backbone and side-chain NMR chemical shifts is the first step towards the characterization of protein structure. The recent introduction of proton detection in combination with fast MAS has opened up novel opportunities for assignment experiments. However, typical 3D sequential-assignment experiments using proton detection under fast MAS lead to signal intensities much smaller than the theoretically expected ones due to the low transfer efficiency of some of the steps. Here, we present a selective 3D experiment for deuterated and (amide) proton back-exchanged proteins where polarization is directly transferred from backbone nitrogen to selected backbone or sidechain carbons. The proposed pulse sequence uses only ¹H–¹⁵N cross-polarization (CP) transfers, which are, for deuterated proteins, about 30% more efficient than ¹H–¹³C CP transfers, and employs a dipolar version of the INEPT experiment for N–C transfer. By avoiding H^N–C (H^N stands for amide protons) and C–C CP transfers, we could achieve higher selectivity and increased signal intensities compared to other pulse sequences containing long-range CP transfers. The REDOR transfer is designed with an additional selective π pulse, which enables the selective transfer of the polarization to the desired ¹³C spins.     

<Superscript>1</Superscript>H, <Superscript>15</Superscript>N, <Superscript>13</Superscript>C backbone resonance assignment of the C-terminal domain of enzyme I from <Emphasis Type="Italic">Thermoanaerobacter tengcongensis</Emphasis>

Phosphoenolpyruvate binding to the C-terminal domain (EIC) of enzyme I of the bacterial phosphotransferase system (PTS) initiates a phosphorylation cascade that results in sugar translocation across the cell membrane and controls a large number of essential pathways in bacterial metabolism. EIC undergoes an expanded to compact conformational equilibrium that is regulated by ligand binding and determines the phosphorylation state of the overall PTS. Here, we report the backbone ¹H, ¹⁵N and ¹³C chemical shift assignments of the 70 kDa EIC dimer from the thermophilic bacterium Thermoanaerobacter tengcongensis. Assignments were obtained at 70 °C by heteronuclear multidimensional NMR spectroscopy. In total, 90% of all backbone resonances were assigned, with 264 out of a possible 299 residues assigned in the ¹H–¹⁵N TROSY spectrum. The secondary structure predicted from the assigned backbone resonance using the program TALOS+ is in good agreement with the X-ray crystal structure of T. tengcongensis EIC. The reported assignments will allow detailed structural and thermodynamic investigations on the coupling between ligand binding and conformational dynamics in EIC.     

Empirical correlation between protein backbone <Superscript>15</Superscript>N and <Superscript>13</Superscript>C secondary chemical shifts and its application to nitrogen chemical shift re-referencing

The linear analysis of chemical shifts (LACS) has provided a robust method for identifying and correcting ¹³C chemical shift referencing problems in data from protein NMR spectroscopy. Unlike other approaches, LACS does not require prior knowledge of the three-dimensional structure or inference of the secondary structure of the protein. It also does not require extensive assignment of the NMR data. We report here a way of extending the LACS approach to ¹⁵N NMR data from proteins, so as to enable the detection and correction of inconsistencies in chemical shift referencing for this nucleus. The approach is based on our finding that the secondary ¹⁵N chemical shift of the backbone nitrogen atom of residue i is strongly correlated with the secondary chemical shift difference (experimental minus random coil) between the alpha and beta carbons of residue i − 1. Thus once alpha and beta ¹³C chemical shifts are available (their difference is referencing error-free), the ¹⁵N referencing can be validated, and an appropriate offset correction can be derived. This approach can be implemented prior to a structure determination and can be used to analyze potential referencing problems in database data not associated with three-dimensional structure. Application of the LACS algorithm to the current BMRB protein chemical shift database, revealed that nearly 35% of the BMRB entries have δ ¹⁵N values mis-referenced by over 0.7 ppm and over 25% of them have δ ¹H^N values mis-referenced by over 0.12 ppm. One implication of the findings reported here is that a backbone ¹⁵N chemical shift provides a better indicator of the conformation of the preceding residue than of the residue itself. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Relationship between1H and13C NMR chemical shifts and the secondary and tertiary structure of a zinc finger peptide

Summary Essentially complete assignments have been obtained for the¹H and protonated¹³C NMR spectra of the zinc finger peptide Xfin-31 in the presence and absence of zinc. The patterns observed for the¹H and¹³C chemical shifts of the peptide in the presence of zinc, relative to the shifts in the absence of zinc, reflect the zinc-mediated folding of the unstructured peptide into a compact globular structure with distinct elements of secondary structure. Chemical shifts calculated from the 3D solution structure of the peptide in the presence of zinc and the observed shifts agree to within ca. 0.2 and 0.6 ppm for the backbone C^aH and NH protons, respectively. In addition, homologous zinc finger proteins exhibit similar correlations between their¹H chemical shifts and secondary structure.     

(3, 2)D <Superscript>1</Superscript>H, <Superscript>13</Superscript>C BIRD<Superscript>r,X</Superscript>-HSQC-TOCSY for NMR structure elucidation of mixtures: application to complex carbohydrates

Overlap of NMR signals is the major cause of difficulties associated with NMR structure elucidation of molecules contained in complex mixtures. A 2D homonuclear correlation spectroscopy in particular suffers from low dispersion of ¹H chemical shifts; larger dispersion of ¹³C chemical shifts is often used to reduce this overlap, while still providing the proton–proton correlation information e.g. in the form of a 2D ¹H, ¹³C HSQC-TOCSY experiment. For this methodology to work, ¹³C chemical shift must be resolved. In case of ¹³C chemical shifts overlap, ¹H chemical shifts can be used to achieve the desired resolution. The proposed (3, 2)D ¹H, ¹³C BIRD^r,X-HSQC-TOCSY experiment achieves this while preserving singlet character of cross peaks in the F₁ dimension. The required high-resolution in the ¹³C dimension is thus retained, while the cross peak overlap occurring in a regular HSQC-TOCSY experiment is eliminated. The method is illustrated on the analysis of a complex carbohydrate mixture obtained by depolymerisation of a fucosylated chondroitin sulfate isolated from the body wall of the sea cucumber Holothuria forskali.     

Structure of an elastin-mimetic polypeptide by solid-state NMR chemical shift analysis

The conformation of an elastin-mimetic recombinant protein, [(VPGVG)4(VPGKG)]39, is investigated using solid-state NMR spectroscopy. The protein is extensively labeled with 13C and 15N, and two-dimensional 13C-13C and 15N-13C correlation experiments were carried out to resolve and assign the isotropic chemical shifts of the various sites. The Pro 15N, 13Calpha, and 13Cbeta isotropic shifts, and the Gly-3 Calpha isotropic and anisotropic chemical shifts support the predominance of type-II beta-turn structure at the Pro-Gly pair but reject a type-I beta-turn. The Val-1 preceding Pro adopts mostly beta-sheet torsion angles, while the Val-4 chemical shifts are intermediate between those of helix and sheet. The protein exhibits a significant conformational distribution, shown by the broad line widths of the 15N and 13C spectra. The average chemical shifts of the solid protein are similar to the values in solution, suggesting that the low-hydration polypeptide maintains the same conformation as in solution. The ability to measure these conformational restraints by solid-state NMR opens the possibility of determining the detailed structure of this class of fibrous proteins through torsion angles and distances.     

<Superscript>1</Superscript>H, <Superscript>15</Superscript>N,and <Superscript>13</Superscript>C chemical shift assignments of the regulatory domain of human calcineurin

Calcineurin (CaN) plays an important role in T-cell activation, cardiac system development and nervous system function. Previous studies have demonstrated that the regulatory domain (RD) of CaN binds calmodulin (CaM) towards the N-terminal end. Calcium-loaded CaM activates the serine/threonine phosphatase activity of CaN by binding to the RD, although the mechanistic details of this interaction remain unclear. It is thought that CaM binding at the RD displaces the auto-inhibitory domain (AID) from the active site of CaN, activating phosphatase activity. In the absence of calcium-loaded CaM, the RD is disordered, and binding of CaM induces folding in the RD. In order to provide mechanistic detail about the CaM–CaN interaction, we have undertaken an NMR study of the RD of CaN. Complete ¹³C, ¹⁵N and ¹H assignments of the RD of CaN were obtained using solution NMR spectroscopy. The backbone of RD has been assigned using a combination of ¹³C-detected CON-IPAP experiments as well as traditional HNCO, HNCA, HNCOCA and HNCACB-based 3D NMR spectroscopy. A ¹⁵N-resolved TOCSY experiment has been used to assign Hα and Hβ chemical shifts.     

Protein structure determination from pseudocontact shifts using ROSETTA

Paramagnetic metal ions generate pseudocontact shifts (PCSs) in nuclear magnetic resonance spectra that are manifested as easily measurable changes in chemical shifts. Metals can be incorporated into proteins through metal binding tags, and PCS data constitute powerful long-range restraints on the positions of nuclear spins relative to the coordinate system of the magnetic susceptibility anisotropy tensor (Δχ-tensor) of the metal ion. We show that three-dimensional structures of proteins can reliably be determined using PCS data from a single metal binding site combined with backbone chemical shifts. The program PCS-ROSETTA automatically determines the Δχ-tensor and metal position from the PCS data during the structure calculations, without any prior knowledge of the protein structure. The program can determine structures accurately for proteins of up to 150 residues, offering a powerful new approach to protein structure determination that relies exclusively on readily measurable backbone chemical shifts and easily discriminates between correctly and incorrectly folded conformations.     

Protein backbone chemical shifts predicted from searching a database for torsion angle and sequence homology

Chemical shifts of nuclei in or attached to a protein backbone are exquisitely sensitive to their local environment. A computer program, SPARTA, is described that uses this correlation with local structure to predict protein backbone chemical shifts, given an input three-dimensional structure, by searching a newly generated database for triplets of adjacent residues that provide the best match in phi/psi/chi(1 )torsion angles and sequence similarity to the query triplet of interest. The database contains (15)N, (1)H(N), (1)H(alpha), (13)C(alpha), (13)C(beta) and (13)C' chemical shifts for 200 proteins for which a high resolution X-ray (< or =2.4 A) structure is available. The relative importance of the weighting factors for the phi/psi/chi(1) angles and sequence similarity was optimized empirically. The weighted, average secondary shifts of the central residues in the 20 best-matching triplets, after inclusion of nearest neighbor, ring current, and hydrogen bonding effects, are used to predict chemical shifts for the protein of known structure. Validation shows good agreement between the SPARTA-predicted and experimental shifts, with standard deviations of 2.52, 0.51, 0.27, 0.98, 1.07 and 1.08 ppm for (15)N, (1)H(N), (1)H(alpha), (13)C(alpha), (13)C(beta) and (13)C', respectively, including outliers.     

Assigning large proteins in the solid state: a MAS NMR resonance assignment strategy using selectively and extensively <Superscript>13</Superscript>C-labelled proteins

In recent years, solid-state magic-angle spinning nuclear magnetic resonance spectroscopy (MAS NMR) has been growing into an important technique to study the structure of membrane proteins, amyloid fibrils and other protein preparations which do not form crystals or are insoluble. Currently, a key bottleneck is the assignment process due to the absence of the resolving power of proton chemical shifts. Particularly for large proteins (approximately >150 residues) it is difficult to obtain a full set of resonance assignments. In order to address this problem, we present an assignment method based upon samples prepared using [1,3-¹³C]- and [2-¹³C]-glycerol as the sole carbon source in the bacterial growth medium (so-called selectively and extensively labelled protein). Such samples give rise to higher quality spectra than uniformly [¹³C]-labelled protein samples, and have previously been used to obtain long-range restraints for use in structure calculations. Our method exploits the characteristic cross-peak patterns observed for the different amino acid types in ¹³C-¹³C correlation and 3D NCACX and NCOCX spectra. An in-depth analysis of the patterns and how they can be used to aid assignment is presented, using spectra of the chicken α-spectrin SH3 domain (62 residues), αB-crystallin (175 residues) and outer membrane protein G (OmpG, 281 residues) as examples. Using this procedure, over 90% of the Cα, Cβ, C′ and N resonances in the core domain of αB-crystallin and around 73% in the flanking domains could be assigned (excluding 24 residues at the extreme termini of the protein). Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Backbone structure confirmation and side chain conformation refinement of a bradykinin mimic BKM-824 by comparing calculated (1)H, (13)C and (19)F chemical shifts with experiment

Calculated and experimental (1)H, (13)C and (19)F chemical shifts were compared in BKM-824, a cyclic bradykinin antagonist mimic, c[Ava(1)-Igl(2)-Ser(3)-DF5F(4)-Oic(5)-Arg(6)] (Ava=5-aminovaleric acid, Igl=alpha-(2-indanyl)glycine, DF5F=pentafluorophenylalanine, Oic=(2S,3aS,7aS)-octahydroindole-2-carboxylic acid). The conformation of BKM-824 has been studied earlier by NMR spectroscopy (M. Miskolzie et al., J. Biomolec. Struct. Dyn. 17, 947-955 (2000)). All NMR structures have qualitatively the same backbone structure but there is considerable variation in the side chain conformations. We have carried out quantum mechanical optimization for three representative NMR structures at the B3LYP/6-31G* level, constraining the backbone dihedral angles at their NMR structure values, followed by NMR chemical shift calculations at the optimized structures with the 6-311G** basis set. There is an intramolecular hydrogen bond at Ser(3) in the optimized structures. The experimental (13)C chemical shifts at five C(alpha) positions as well as at the Cbeta, Cgamma and Cdelta position of Ava(1), which forms part of the backbone, are well reproduced by the calculations, confirming the NMR backbone structure. A comparison between the calculated and experimental H(beta) chemical shifts in Igl(2) shows that the dominant conformation at this residue is gauche. Changes of proton chemical shifts with the scan of the chi(1) angle in DF5F(4) suggest that chi(1)180 degrees. The calculated (1)H and (13)C chemical shifts are in good agreement with experiment at the rigid residue Oic(5). None of the models gives accurate results for Arg(6), presumably because of its positive charge. Our study indicates that calculated NMR shifts can be used as additional constraints in conjunction with NMR data to determine protein conformations. However, to be computationally effective, a database of chemical shifts in small peptide fragments should be precalculated.     

<Superscript>1</Superscript>H, <Superscript>13</Superscript>C and <Superscript>15</Superscript>N resonance assignment of human guanylate kinase

Human guanylate kinase (hGMPK) is a critical enzyme that, in addition to phosphorylating its physiological substrate (d)GMP, catalyzes the second phosphorylation step in the conversion of anti-viral and anti-cancer nucleoside analogs to their corresponding active nucleoside analog triphosphates. Until now, a high-resolution structure of hGMPK is unavailable and thus, we studied free hGMPK by NMR and assigned the chemical shift resonances of backbone and side chain ¹H, ¹³C, and ¹⁵N nuclei as a first step towards the enzyme’s structural and mechanistic analysis with atomic resolution.     

Probing multiple effects on 15N, 13C alpha, 13C beta,and 13C' chemical shifts in peptides using density functional theory

We have used density functional calculations on model peptides to study conformational effects on (15)N, (13)C alpha, (13)C beta, and (13)C' chemical shifts, associated with hydrogen bonding, backbone conformation, and side-chain orientation. The results show a significant dependence on the backbone torsion angles of the nearest three residues. Contributions to (15)N chemical shifts from hydrogen bonding (up to 8 ppm), backbone conformation (up to 13 ppm), side-chain orientation and neighborhood residue effects (up to 22 ppm) are significant, and a unified theory will be required to account for their behavior in proteins. In contrast to this, the dependence on sequence and hydrogen bonding is much less for (13)C alpha and (13)C beta chemical shifts (<0.5 ppm), and moderate for carbonyl carbon shifts (<2 ppm). The effects of side-chain orientation are mainly limited to the residue itself for both nitrogen and carbon, but the chi(1) effect is also significant for the nitrogen shift of the following residue and for the (13)C' shift of the preceding residue. The calculated results are used, in conjunction with an additive model of chemical shift contributions, to create an algorithm for prediction of (15)N and (13)C shifts in proteins from their structure; this includes a model to extrapolate results to regions of torsion angle space that have not been explicitly studied by density functional theory (DFT) calculations. Crystal structures of 20 proteins with measured shifts have been used to test the prediction scheme. Root mean square deviations between calculated and experimental shifts 2.71, 1.22, 1.31, and 1.28 ppm for N, C alpha, C beta, and C', respectively. This prediction algorithm should be helpful in NMR assignment, crystal and solution structure comparison, and structure refinement.     

Residual backbone and side-chain <Superscript>13</Superscript>C and <Superscript>15</Superscript>N resonance assignments of the intrinsic transmembrane light-harvesting 2 protein complex by solid-state Magic Angle Spinning NMR spectroscopy

This study reports the sequence specific chemical shifts assignments for 76 residues of the 94 residues containing monomeric unit of the photosynthetic light-harvesting 2 transmembrane protein complex from Rhodopseudomonas acidophila strain 10050, using Magic Angle Spinning (MAS) NMR in combination with extensive and selective biosynthetic isotope labeling methods. The sequence specific chemical shifts assignment is an essential step for structure determination by MAS NMR. Assignments have been performed on the basis of 2-dimensional proton-driven spin diffusion ¹³C–¹³C correlation experiments with mixing times of 20 and 500 ms and band selective ¹³C–¹⁵N correlation spectroscopy on a series of site-specific biosynthetically labeled samples. The decreased line width and the reduced number of correlation signals of the selectively labeled samples with respect to the uniformly labeled samples enable to resolve the narrowly distributed correlation signals of the backbone carbons and nitrogens involved in the long -helical transmembrane segments. Inter-space correlations between nearby residues and between residues and the labeled BChl a cofactors, provided by the ¹³C–¹³C correlation experiments using a 500 ms spin diffusion period, are used to arrive at sequence specific chemical shift assignments for many residues in the protein complex. In this way it is demonstrated that MAS NMR methods combined with site-specific biosynthetic isotope labeling can be used for sequence specific assignment of the NMR response of transmembrane proteins.     

Structure determination of proteins in <Superscript>2</Superscript>H<Subscript>2</Subscript>O solution aided by a deuterium-decoupled 3D HCA(N)CO experiment

We developed an NMR pulse sequence, 3D HCA(N)CO, to correlate the chemical shifts of protein backbone ¹Hα and ¹³Cα to those of ¹³C′ in the preceding residue. By applying ²H decoupling, the experiment was accomplished with high sensitivity comparable to that of HCA(CO)N. When combined with HCACO, HCAN and HCA(CO)N, the HCA(N)CO sequence allows the sequential assignment using backbone ¹³C′ and amide ¹⁵N chemical shifts without resort to backbone amide protons. This assignment strategy was demonstrated for ¹³C/¹⁵N-labeled GB1 dissolved in ²H₂O. The quality of the GB1 structure determined in ²H₂O was similar to that determined in H₂O in spite of significantly smaller number of NOE correlations. Thus this strategy enables the determination of protein structures in ²H₂O or H₂O at high pH values.