Nuclear Magnetic Resonance Solution Structure Research Articles

Structure and conserved RNA binding of the PAZ domain.

The discovery of RNA-mediated gene-silencing pathways, including RNA interference, highlights a fundamental role of short RNAs in eukaryotic gene regulation and antiviral defence. Members of the Dicer and Argonaute protein families are essential components of these RNA-silencing pathways. Notably, these two families possess an evolutionarily conserved PAZ (Piwi/Argonaute/Zwille) domain whose biochemical function is unknown. Here we report the nuclear magnetic resonance solution structure of the PAZ domain from Drosophila melanogaster Argonaute 1 (Ago1). The structure consists of a left-handed, six-stranded beta-barrel capped at one end by two alpha-helices and wrapped on one side by a distinctive appendage, which comprises a long beta-hairpin and a short alpha-helix. Using structural and biochemical analyses, we demonstrate that the PAZ domain binds a 5-nucleotide RNA with 1:1 stoichiometry. We map the RNA-binding surface to the open face of the beta-barrel, which contains amino acids conserved within the PAZ domain family, and we define the 5'-to-3' orientation of single-stranded RNA bound within that site. Furthermore, we show that PAZ domains from different human Argonaute proteins also bind RNA, establishing a conserved function for this domain.

The Octapeptide Repeats in Mammalian Prion Protein Constitute a pH-dependent Folding and Aggregation Site

Structural studies of mammalian prion protein at pH values between 4.5 and 5.5 established that the N-terminal 100 residue domain is flexibly disordered. Here, we show that at pH values between 6.5 and 7.8, i.e. the pH at the cell membrane, the octapeptide repeats in recombinant human prion protein hPrP(23–230) encompassing the highly conserved amino acid sequence PHGGGWGQ are structured. The nuclear magnetic resonance solution structure of the octapeptide repeats at pH 6.2 reveals a new structural motif that causes a reversible pH-dependent PrP oligomerization. Within the aggregation motif the segments HGGGW and GWGQ adopt a loop conformation and a β-turn-like structure, respectively. Comparison with the crystal structure of HGGGW–Cu 2+ indicates that the binding of copper ions induces a conformational transition that presumably modulates PrP aggregation. The knowledge that the cellular prion protein is immobilized on the cell surface along with our results suggests a functional role of aggregation in endocytosis or homophilic cell adhesion.

NMR solution structure determination of membrane proteins reconstituted in detergent micelles

As an alternative to X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy in solution can be used for three-dimensional structure determination of small membrane proteins, preferably proteins with β-barrel fold. This paper reviews recent achievements as well as limiting factors encountered in solution NMR studies of membrane proteins. Our particular interest has been focused on supplementing structure determination with data on the solvation of the proteins in the mixed micelles with detergents that are used to reconstitute membrane proteins for the NMR experiments. For the Escherichia coli outer membrane protein X (OmpX) in dihexanoylphosphatidylcholine (DHPC) micelles, such studies showed that the central part of the protein is covered with a fluid monolayer of lipid molecules, which seems to mimic quite faithfully the embedding of the protein in the lipid phase of the biological membrane. The implication is that the micellar systems used in this instance for the NMR studies of the membrane protein should also be suitable for further investigations of functional interactions with other proteins or low-molecular weight ligands.

ParG, a protein required for active partition of bacterial plasmids, has a dimeric ribbon-helix-helix structure.

The ParG protein (8.6 kDa) is an essential component of the DNA partition complex of multidrug resistance plasmid TP228. ParG is a dimer in solution, interacts with DNA sequences upstream of the parFG genes and also with the ParF partition protein both in the absence and presence of target DNA. Here, the solution nuclear magnetic resonance structure of ParG is reported. The ParG dimer is composed of a folded domain formed by two closely intertwined C-terminal parts (residues 33-76), and two highly mobile tails consisting of N-terminal regions (residues 1-32). The folded part of ParG has the ribbon-helix-helix (RHH) architecture similar to that of the Arc/MetJ superfamily of DNA-binding transcriptional repressors, although the primary sequence similarity is very low. ParG interacts with DNA predominantly via its folded domain; this interaction is coupled with ParG oligomerization. The dimeric RHH structure of ParG suggests that it binds to DNA by inserting the double-stranded beta-sheet into the major groove of DNA, in a manner similar to transcriptional repressors from the Arc/MetJ superfamily, and that ParG can function as a transcriptional repressor itself. A new classification of proteins belonging to the Arc/MetJ superfamily and ParG homologues is proposed, based on the location of a conserved positively charged residue at either the beginning or at the end of the beta-strand which forms part of the DNA recognition motif.

Solution nuclear magnetic resonance structure of a protein disulfide oxidoreductase from Methanococcus jannaschii.

The solution structure of the protein disulfide oxidoreductase Mj0307 in the reduced form has been solved by nuclear magnetic resonance. The secondary and tertiary structure of this protein from the archaebacterium Methanococcus jannaschii is similar to the structures that have been solved for the glutaredoxin proteins from Escherichia coli, although Mj0307 also shows features that are characteristic of thioredoxin proteins. Some aspects of Mj0307's unique behavior can be explained by comparing structure-based sequence alignments with mesophilic bacterial and eukaryotic glutaredoxin and thioredoxin proteins. It is proposed that Mj0307, and similar archaebacterial proteins, may be most closely related to the mesophilic bacterial NrdH proteins. Together these proteins may form a unique subgroup within the family of protein disulfide oxidoreductases.

Solution structure of α-conotoxin SI

The nuclear magnetic resonance solution structure of α-conotoxin SI has been determined at pH 4.2. The 36 lowest energy structures show that α-conotoxin SI exists in a single major solution conformation and is stabilized by six hydrogen bonds. Comparisons are made between the SI solution structure and the solution and crystal structures of α-conotoxin GI. Surprisingly, a high degree of similarity between the backbone conformations of the GI crystal and the SI solution structures is seen in the region of lowest sequence homology, namely residues Gly-8 to Ser-12. This similarity is more surprising when considering that in SI a proline replaces the Arg-9 found in GI. The correspondence in conformation in this region provides the definitive evidence that it is the loss of the arginine basic charge at residue 9 which determines the differences in toxicity between GI and SI, rather than any changes in conformation induced by the cyclic proline residue.

Nuclear magnetic resonance solution structure of truncated human GROβ [5–73] and its structural comparison with CXC chemokine family members GROα and IL-8

The three-dimensional structure of a novel four amino acid truncated form of the CXC chemokine GROβ [5–73] isolated from bone marrow stromal cells with potent hematopoietic and anti-infective activities has been determined by two-dimensional 1H nuclear magnetic resonance (NMR) spectroscopy in solution. On the basis of 1878 upper distance constraints derived from nuclear Overhauser effects (NOE) and 314 dihedral angle constraints, a group of 20 conformers representing the solution structure of the human GROβ [5–73] was computed with the program DYANA. At the concentrations used for NMR study, GROβ [5–73] forms a dimer in solution that is architectured by a six-stranded antiparallel β-sheet (residues 25 to 29, 39 to 44, 49 to 52) and a pair of helices (residues 58 to 68) with 2-fold symmetry, while the C terminus of the protein is disordered. The average of the pairwise root-mean-square deviations of individual NMR conformers relative to the mean coordinates for the backbone atoms N, C α and C′ of residues 5 to 68 is 0.47 Å. Overall, the global fold of GROβ [5–73] is similar to that of the previously reported NMR structure of GROα and the NMR and X-ray structures of interleukin-8. Among these three CXC chemokines, GROβ [5–73] is most similar in structure to GROα. Significant differences between GROβ [5–73], GROα and interleukin-8 are in the N-terminal loop comprising residues 12 to 19. The N-terminal arm containing the conserved ELR motif and the loop of residues 30 to 38 containing the GPH motif are different among these three CXC chemokines. The structural differences in these two regions may be responsible for the specificity of the receptor binding and biological activity of different chemokines.

Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.

A high quality nuclear magnetic resonance solution structure of peptide deformylase from Escherichia coli: application of an automated assignment strategy using GARANT.

The NMR structure of the peptide deformylase (PDF) (1-150) from Escherichia coli, which is an essential enzyme that removes the formyl group from nascent polypeptides and represents a potential target for drug discovery, was determined using 15N/13C doubly labeled protein. Nearly completely automated assignment routines were employed to assign three-dimensional triple resonance, 15N-resolved and 13C-resolved NOESY spectra using the program GARANT. This assignment strategy, demonstrated on a 17 kDa protein, is a significant advance in the automation of NMR data assignment and structure determination that will accelerate future work. A total of 2302 conformational constraints were collected as input for the distance geometry program DYANA. After restrained energy minimization with the program X-PLOR the 20 best conformers characterize a high quality structure with an average of 0.43 A for the root-mean-square deviation calculated from the backbone atoms N, C alpha and C', and 0.81 A for all heavy atoms of the individual conformers relative to the mean coordinates for residues 1 to 150. The globular fold of PDF contains two alpha-helices comprising residues 25-40, 125-138, six beta-strands 57-60, 70-77, 85-88, 98-101, 105-111, 117-123 and one 3(10) helix comprising residues 49-51. The C-terminal helix contains the HEXXH motif positioning a zinc ligand in a similar fashion to other metalloproteases, with the third ligand being cysteine and the fourth presumably a water. The three-dimensional structure of PDF affords insight into the substrate recognition and specificity for N-formylated over N-acetylated substrates and is compared to other PDF structures.

Nuclear magnetic resonance solution structure of the plasminogen-activator protein staphylokinase.

Staphylokinase, a 15.5 kDa protein from Staphylococcus aureus, is a plasminogen activator which is currently undergoing clinical trials for the therapy of myocardial infarction and peripheral thrombosis. The three-dimensional (3D) NMR solution structure has been determined by multidimensional heteronuclear NMR spectroscopy on uniformly 15N- and 15N,13C-labeled samples of staphylokinase. Structural constraints were obtained from 82 3JHNH alpha as well as 22 3JNH beta scalar coupling constants and 2345 NOE cross-peaks, derived from 15N-edited and 13C-edited 3D NOE spectra. NOE cross-peak assignments were confirmed by analysis of ¿15N,13C¿-edited and ¿13C,13C¿-edited 4D NOE spectra. The structure is presented as a family of 20 conformers which show an average rmsd of 1.02 +/- 0.15 A from the mean structure for the backbone atoms. The tertiary structure of staphylokinase shows a well-defined global structure consisting of a central 13-residue alpha-helix flanked by a two-stranded beta-sheet, both of which are located above a five-stranded beta-sheet. Two of the connecting loops exhibit a higher conformational heterogeneity. Overall, staphylokinase shows a strong asymmetry of hydrophilic and hydrophobic surfaces. The N-terminal sequence, including Lys10 which is the site of the initial proteolytic cleavage during activation of plasminogen, folds back onto the protein core, thereby shielding amino acids with functional importance in the plasminogen activation process. From a comparison of the structure with mutational studies, a binding region for plasminogen is proposed.

The NMR solution structure of human glutaredoxin in the fully reduced form

The determination of the nuclear magnetic resonance (NMR) solution structure of fully reduced human glutaredoxin is described. A total of 1159 useful nuclear Overhauser effect (NOE) upper distance constraints and 187 dihedral angle constraints were obtained as the input for the structure calculations for which the torsion angle dynamics program DYANA has been utilized followed by energy minimization in water with the AMBER force field as implemented in the program OPAL. The resulting 20 conformers have an average root-mean-square deviation value relative to the mean coordinates of 0.54 Å for all the backbone atoms N, C α and C′, and of 1.01 Å for all heavy atoms. Human glutaredoxin consists of a four-stranded mixed β-sheet composed of residues 15 to 19, 43 to 47, 72 to 75 and 78 to 81, and five α-helices composed of residues 4 to 9, 24 to 34, 54 to 65, 83 to 91, and 94 to 100. Comparisons with the structures of Escherichia coli glutaredoxin-1, pig liver glutaredoxin and human thioredoxin were made. Electrostatic calculations on the human glutaredoxin structure and that of related proteins provide an understanding of the variation of p K a values for the nucleophilic cysteine in the active site observed among these proteins. In addition, the high-resolution NMR solution structure of human glutaredoxin has been used to model the binding site for glutathione and for ribonucleotide reductase B1 by molecular dynamics simulations.

Nuclear magnetic resonance solution structures of covalent aromatic amine-DNA adducts and their mutagenic relevance.

Nuclear magnetic resonance solution structures of covalent aromatic amine-DNA adducts and their mutagenic relevance.

The NMR solution conformation of unligated human cyclophilin A

The nuclear magnetic resonance (NMR) solution structure of free, unligated cyclophilin A (CypA), which is an 18 kDa protein from human T-lymphocytes that was expressed in Escherichia coli for the present study, was determined using multidimensional heteronuclear NMR techniques. Sequence-specific resonance assignments for 99.5% of all backbone amide protons and non-labile hydrogen atoms provided the basis for collection of an input of 4101 nuclear Overhauser enhancement (NOE) upper distance constraints and 371 dihedral angle constraints for distance geometry calculations and energy minimization with the programs DIANA and OPAL. The average RMSD values of the 20 best energy-refined NMR conformers relative to the mean coordinates are 0.49 Å for the backbone atoms and 0.88 Å for all heavy atoms of residues 2 to 165. The molecular architecture includes an eight-stranded antiparallel β-barrel that is closed by two amphipathic α-helices. Detailed comparisons with the crystal structure of free CypA revealed subtle but significant conformational differences that can in most cases be related to lattice contacts in the crystal structure. 15N spin relaxation times and NMR lineshape analyses for CypA in the free form and complexed with cyclosporin A (CsA) revealed transitions of polypeptide loops surrounding the ligand-binding site from locally flexible conformations in the free protein, some of which include well-defined conformational equilibria, to well-defined spatial arrangements in the CypA-CsA complex. Compared to the crystal structure of free CypA, where the ligand-binding area is extensively involved in lattice contacts, the NMR structure presents a highly relevant reference for studies of changes in structure and internal mobility of the binding pocket upon ligand binding, and possible consequences of this conformational variability for calcineurin recognition by the CypA-CsA complex.

The solution NMR structure of glucosylated N-glycans involved in the early stages of glycoprotein biosynthesis and folding.

Glucosylated oligomannose N-linked oligosaccharides (Glc(x)Man9GlcNAc2 where x = 1-3) are not normally found on mature glycoproteins but are involved in the early stages of glycoprotein biosynthesis and folding as (i) recognition elements during protein N-glycosylation and chaperone recognition and (ii) substrates in the initial steps of N-glycan processing. By inhibiting the first steps of glycan processing in CHO cells using the alpha-glucosidase inhibitor N-butyl-deoxynojirimycin, we have produced sufficient Glc3Man7GlcNAc2 for structural analysis by nuclear magnetic resonance (NMR) spectroscopy. Our results show the glucosyl cap to have a single, well-defined conformation independent of the rest of the saccharide. Comparison with the conformation of Man9GlcNAc2, previously determined by NMR and molecular dynamics, shows the mannose residues to be largely unaffected by the presence of the glucosyl cap. Sequential enzymatic cleavage of the glucose residues does not affect the conformation of the remaining saccharide. Modelling of the Glc3Man9GlcNAc2, Glc2Man9GlcNAc2 and Glc1Man9GlcNAc2 conformations shows the glucose residues to be fully accessible for recognition. A more detailed analysis of the conformations allows potential recognition epitopes on the glycans to be identified and can form the basis for understanding the specificity of the glucosidases and chaperones (such as calnexin) that recognize these glycans, with implications for their mechanisms of action.

The NMR solution structure of the non-classical homeodomain from the rat liver LFB1/HNF1 transcription factor

The nuclear magnetic resonance (NMR) solution structure of the non-classical homeodomain from the rat liver LFB1/HNF1 transcription factor was determined with the program DIANA from an input of 1356 nuclear Overhauser enhancement (NOE) upper distance constraints and 228 dihedral angle constraints collected using experiments with the unlabelled, the uniformly 15N-labelled and the uniformly 13C-labelled protein. Out of a group of 50 independently calculated conformers the 20 conformers with the smallest residual DIANA target function values were refined by energy minimization with the program OPAL and are used to represent the NMR structure. The average of the pairwise root-mean-square deviations (r.m.s.d.) of these 20 individual NMR conformers relative to the mean coordinates is 0.73 Å (1 Å = 0.1 nm) for the backbone atoms N, Cα and C′ of residues 15 to 82. The chain-terminal polypeptide segments 1–14 and 90–99 are disordered in solution. The globular fold contains three well-defined helices comprising the residues 19 to 29, 37 to 53 and 71 to 81, and the third helix is extended by a less well-ordered fourth helix with residues 82 to 89, which coincides with corresponding observations in “classical” homeodomains. Side-chain analysis resulted in 33 “best-defined” side-chains, with global displacements smaller than 1.1 Å, and addition of these side-chains to the global superposition of residues 15 to 82 resulted in a r.m.s.d of 0.81 Å. The protein contains two hydrophobic cores, one of which corresponds to the helical packing seen in classical homeodomains, while the other one stabilizes the conformation of the 21-residue insertion between helices II and III. The individual helices and their relative spatial arrangements are stabilized by a variety of structural motifs, which include medium-range and long-range hydrogen bonds and salt bridges. Detailed comparison with the Antennapedia homeodomain, and studies of the complex formation with an operator DNA half-site provided initial information on the DNA-binding mode of the LFB1/HNF1 homeodomain.

NMR solution structure of the pathogenesis-related protein P14a

The nuclear magnetic resonance (NMR) structure of the 15 kDa pathogenesis-related protein P14a, which displays antifungicidal activity and is induced in tomato leaves as a response to pathogen infection, was determined using 15N/13C doubly labeled and unlabeled protein samples. In all, 2030 conformational constraints were collected as input for the distance geometry program DIANA. After energy-minimization with the program OPAL the 20 best conformers had an average root-mean-square deviation value relative to the mean coordinates of 0.88 Å for the backbone atoms N, Cα and C′, and 1.30 Å for all heavy atoms. P14a contains four α-helices (I to IV) comprising residues 4 to 17, 27 to 40, 64 to 72 and 93 to 98, a short 310-helix of residues 73 to 75 directly following helix III, and a mixed, four-stranded β-sheet with topology +3x, −2x, +1, containing the residues 24-25, 53 to 58, 104 to 111 and 117 to 124. These regular secondary structure elements form a novel, complex α+β topology in which the α-helices I, III and IV and the 310-helix are located above the plane defined by the β-sheet, and the α-helix II lies below this plane. The α-helices and β-strands are thus arranged in three stacked layers, which are stabilized by two distinct hydrophobic cores associated with the two layer interfaces, giving rise to an “α-β-α sandwich”. The three-dimensional structure of P14a provides initial leads for identification of the so far unknown active sites and the mode of action of the protein, which is of direct interest for the generation of transgenic plants with improved host defense properties.

MOLMOL: A program for display and analysis of macromolecular structures

MOLMOL is a molecular graphics program for display, analysis, and manipulation of three-dimensional structures of biological macromolecules, with special emphasis on nuclear magnetic resonance (NMR) solution structures of proteins and nucleic acids. MOLMOL has a graphical user interface with menus, dialog boxes, and on-line help. The display possibilities include conventional presentation, as well as novel schematic drawings, with the option of combining different presentations in one view of a molecule. Covalent molecular structures can be modified by addition or removal of individual atoms and bonds, and three-dimensional structures can be manipulated by interactive rotation about individual bonds. Special efforts were made to allow for appropriate display and analysis of the sets of typically 20–40 conformers that are conventionally used to represent the result of an NMR structure determination, using functions for superimposing sets of conformers, calculation of root mean square distance (RMSD) values, identification of hydrogen bonds, checking and displaying violations of NMR constraints, and identification and listing of short distances between pairs of hydrogen atoms.

Pulmonary surfactant-associated polypeptide SP-C in lipid micelles: CD studies of intact SP-C and NMR secondary structure determination of depalmitoyl-SP-C(1–17)

The surfactant-associated polypeptide C (SP-C) is a 35-residue lipopolypeptide which is essential for the function of surfactants used for therapy of infant respiratory distress. Modeling based on the recently determined nuclear magnetic resonance (NMR) structure of native SP-C in an organic solvent showed that SP-C could readily insert into fluid 1,2-dipalmitoyl- sn-glycero-3-phosphocholine bilayers. The present paper describes further physical-chemical studies of intact SP-C and its N-terminal 17-residue polypeptide fragment, depalmitoyl-SPC(1–17), in the presence of dodecylphosphocholine micelles. The results obtained provide a link between the NMR solution structure and the behaviour of SP-C in an ordered lipid environment, and thus present new insights for rational design of SP-C analogs for therapeutic purposes.

NMR solution structure of the antifungal protein from Aspergillus giganteus: evidence for cysteine pairing isomerism

The solution structure of the antifungal protein (AFP, 51 residues, 4 disulfide bridges) from Aspergillus giganteus has been determined by using experimentally derived interproton distance constraints from nuclear magnetic resonance (NMR) spectroscopy. Complete sequence-specific proton assignments were obtained at pH 5.0 and 35 degrees C. A set of 834 upper limit distance constraints from nuclear Overhauser effect measurements was used as input for the calculation of structures with the program DIANA. An initial family of 40 structures calculated with no disulfide constraints was used to obtain information about the disulfide connectivities, which could not be determined by standard biochemical methods. Three possible disulfide patterns were selected and the corresponding disulfide constraints applied to generate a family of 20 DIANA conformers for each pattern. Following energy minimization, the average pairwise RMSD of the 20 conformers of each family is 1.01, 0.89, and 1.01 A for backbone atoms and 1.82, 1.74, and 1.81 A for all heavy atoms. One of these three families contains the disulfide bridge arrangement actually present in the solution structure of AFP. Although the three families fulfill the NMR constraints, one of the disulfide patterns considered (cysteine pairs 7-33, 14-40, 26-49, 28-51) is favored among the others on the basis of previous chemical studies. It thus probably corresponds to the actual pattern of disulfide bridges present in the protein, and the corresponding family represents the solution structure of AFP. The folding of AFP consists of five antiparallel beta strands connected in a -1, -1, +3, +1 topology and highly twisted, defining a small and compact beta barrel stabilized by four internal disulfide bridges. A cationic site formed by up to three lysine side chains adjacent to a hydrophobic stretch, both at the protein surface, may constitute a potential binding site for phospholipids which would be the basis of its biological function. On the other hand, a second, minor form of AFP has been detected. NMR data, together with results from mass spectrometry, chemical analysis, and sedimentation equilibrium, suggest that this species differs from the major form in the pairs of cysteines involved in the four disulfide bridges.

Direct recognition of the trp operator by the trp holorepressor--a review.

Two different X-ray co-crystal structures of the Escherichia coli trp holorepressor complexed with DNA suggest that the TrpR protein recognizes specific DNA sequences primarily with a network of water-mediated H-bonds. However, the more recent nuclear magnetic resonance (NMR) solution structures of the holorepressor-operator complex show no long-lived, ordered water molecules at the protein-DNA interface and place amino acids in intimate contact with nucleotide bases. Both genetic and biochemical studies support a model in which the trp repressor recognizes specific DNA sequences by a direct mechanism, as seen in the NMR solution structures, not by the 'indirect readout' mechanism initially proposed on the basis of X-ray studies.