Interactions of antibody aromatic residues with a peptide of cholera toxin observed by two-dimensional transferred nuclear Overhauser effect difference spectroscopy

The interactions between a peptide of cholera toxin and the aromatic amino acids of the TE33 antipeptide antibody, cross-reactive with the toxin, have been studied by NOESY difference spectroscopy. The 2D difference between the NOESY spectrum of the Fab with a 4-fold excess of the peptide and that of the peptide-saturated Fab reveals cross-peaks growing with excess of the peptide. These cross-peaks are due to magnetization transfer between the Fab and neighboring bound peptide protons, and a further transfer to the free peptide protons by exchange between bound and free peptide (transferred NOE). Additional cross-peaks appearing in the difference spectrum are due to a combination of intramolecular interactions between bound peptide protons and exchange between bound and free peptide. Assignment of cross-peaks is attained by specific deuteration of antibody aromatic amino acids using also the resonance assignment of the free peptide, deduced from the COSY spectrum of the peptide solution. The antibody combining site is found to be highly aromatic. We have identified one or two histidine, two tyrosine, and two tryptophan residues and one phenylalanine residue of the antibody interacting with valine-3, proline-4, glycine-5, glutamine-7, histidine-8, and aspartate-10 of the peptide. The 2D TRNOE difference spectroscopy can be used to study protein-ligand interactions, given that the ligand off rate is fast relative to the spin-lattice relaxation time of the protein and ligand protons (about 1 s). The resolution obtained in the difference spectra implies that the technique is equally applicable for studying proteins having a molecular weight larger than 50,000.(ABSTRACT TRUNCATED AT 250 WORDS)     

Complete assignment of the imino protons of Escherichia coli valine transfer RNA: two-dimensional NMR studies in water

The imino proton spectrum of Escherichia coli valine tRNA has been studied by two-dimensional nuclear Overhauser effect spectroscopy (NOESY) in H2O solution. The small nuclear Overhauser effects from the imino proton of an internal base pair to the imino protons of each nearest neighbor can be observed as off-diagonal cross-peaks. In this way most of the sequential NOE connectivity trains for all the helices in this molecule can be determined in a single experiment. AU resonances can be distinguished from GC resonances by the AU imino NOE to the aromatic adenine C2-H, thus leading to specific base-pair assignments. In general, the NOESY spectrum alone is not capable of assigning every imino proton resonance even in well-resolved tRNA spectra. Multiple proton peaks exhibit more than two cross-peaks, resulting in ambiguous connectivities, and coupling between protons with similar chemical shifts produces cross-peaks that are incompletely resolved from the diagonal. The sequence of the particular tRNA determines the occurrence of the latter problem, which can often be solved by careful one-dimensional experiments. The complete imino proton assignments of E. coli valine tRNA are presented.     

The differences in the T2 relaxation rates of the protons in the partially-deuteriated and fully protonated sugar residues in a large oligo-DNA ('NMR-window') gives complementary structural information.

Selective incorporation of the stereospecifically deuteriated sugar moieties (> 97 atom % 2H enhancements at H2', H2', H3' and H5'/5' sites, approximately 85 atom % 2H enhancement at H4' and approximately 20 atom % 2H enhancement at H1') in DNA and RNA by the 'NMR-window' approach has been shown to solve the problem of the resonance overlap [refs. 1, 2 & 3]. Such specific deuterium labelling gives much improved resolution and sensitivity of the residual sugar proton (i.e. H1' or H4') vicinal to the deuteriated centers (ref. 3). The T2 relaxation time of the residual protons also increases considerably in the partially-deuteriated (shown by underline) sugar residues in dinucleotides [d(CpG), d(GpC), d(ApT), d(TpA)], trinucleotide r(A2'p5'A2'p5'A) and 20-mer DNA duplex 5'd(C1G2C3-G4C5G6C7G8A9A10T11T12C13G14C15G16C17G18C19G20)(2) 3'. The protons with shorter T2 can be filtered away using a number of different NMR experiments such as ROESY, MINSY or HAL. The NOE intensity of the cross-peaks in these experiments includes only straight pathway from H1' to aromatic proton (i-i and i-i + 1) without any spin-diffusion. The volumes of these NOE cross-peaks could be measured with high accuracy as their intensity is 3 to 4 times larger than the corresponding peaks in the fully protonated residues in the normal NOESY spectra. The structural informations thus obtainable from the residual protons in the partially-deuteriated part of the duplex and the fully protonated part in the 'NMR window' can indeed complement each other.     

Conformational microheterogeneity in a DNA double helix: structure of restriction endonuclease Bam H1 recognition site

Structural studies using 500 MHz 1H NMR spectroscopy on Bam H1 recognition site d(GGATCC)2 in solution at 19 degrees is reported. The resonances from the sugar ring and base protons have been assigned from the 2D-COSY and NOESY spectra. Analyses of the NOESY cross-peaks between the base protons H8/H6 and sugar protons H2'/H2", H3' reveal that the nucleotide units G2, A3 and C6 adopt (C3'-endo, chi = 200 degrees-220 degrees) conformation while G1, T4 and C5 exhibit (C2'-endo, chi = 240 degrees-260 degrees) conformation. NMR data clearly suggest that the two strands of d(GGATCC)2 are conformationally equivalent and there is a structural two-fold between the two A-T pairs. The above information and the NOESY data are used to generate a structural model of d(GGATCC)2. The important features are: (i) G1-G2 stack, the site of cleavage, shows an alternation in sugar pucker i.e. C2'-endo, C3'-endo as in a B-A junction, (ii) G2-A3 stack adopts a mini A-DNA, both the sugars being C3'-endo, (iii) A3-T4 stack, the site of two-fold, displays an A-B junction with alternation in sugar pucker as C3'-endo, C2'-endo, (iv) T4-C5 stack adopts a mini B-DNA both the sugars being C2'-endo and (v) C5-C6 stack exhibits a B-A junction with C2'-endo, C3'-endo sugar puckers. Thus, our studies demonstrate that conformational microheterogeneity with a structural two fold, is present in the Bam H1 recognition site.     

Selective diagonal-free 13C,13C-edited aliphatic–aromatic NOESY experiment with non-uniform sampling

A band-selective aromatic–aliphatic C,C-edited four-dimensional NOESY experiment is proposed here. Its key advantage is the absence of auto-correlation signals which makes it very attractive for joint use with non-uniform sampling. It is demonstrated here that the sensitivity of the experiment is not significantly affected by utilization of selective pulses (for either aromatic-13C or aliphatic-13C spins). The method was applied to the sample of E32Q mutant of human S100A1 protein, a homodimer of total molecular mass ~20 kDa. High-resolution 4D spectra were obtained from ~1.5 % of sampling points required conventionally. It is shown that superior resolution facilitates unambiguous assignment of observed aliphatic–aromatic cross-peaks. Additionally, the addition of aliphatic-13C dimension enables to resolve peaks with degenerated aliphatic ¹H chemical shifts. All observed cross-peaks were validated against previously determined 3D structure of E32Q mutant of S100A1 protein (PDB 2LHL). The increased reliability of structural constraints obtained from the proposed high-resolution 4D 13C(ali),13C(aro)-edited NOESY can be exploited in the automated protocols of structure determination of proteins.     

NMR and CD studies on the interaction of Alzheimer beta-amyloid peptide (12-28) with beta-cyclodextrin

Polymerization of the amyloid beta-peptide (Abeta) has been identified as a major feature of the pathogenesis of Alzheimer's disease (AD). Inhibition of the formation of these toxic polymers of Abeta has emerged as an approach for developing therapeutics for AD. NMR and CD spectra were used to investigate the interaction between cyclodextrin and Abeta(12-28) peptide, which was reported to be an important region for forming amyloid fibrils. CD spectral analyses show that of the alpha-, beta- and gamma-cyclodextrins only beta-cyclodextrin inhibits the aggregation of Abeta(12-28) at pH 5.0. Analysis of the one-dimensional proton NMR spectra of Abeta(12-28) and the mixture of Abeta(12-28) with beta-cyclodextrin clearly indicates that there are chemical shift changes in the aromatic ring of Phe19 and the methyl groups of Val18 in the peptide. The NOESY spectra show cross-peaks between H-3 and H-5 of beta-cyclodextrin and the aromatic protons of Phe19 and Phe20. These chemical shift differences and NOEs demonstrate that there is an interaction between Abeta(12-28) and beta-cyclodextrin. Analysis of the cross-peak intensity in the NOESY spectra reveals that the aromatic rings of Phe19 and 20 are generally inserted into beta-cyclodextrin at the broad side and are oriented toward the narrow side of the cavity.     

NMR-based fluxomics: quantitative 2D NMR methods for isotopomers analysis

We have investigated the reliability of 2D-COSY and 2D-TOCSY experiments to provide accurate measurements of (13)C-enrichments in complex mixtures of (13)C-labelled metabolites. This was done from both theoretical considerations and experimental investigations. The results showed that 2D-TOCSY but not 2D-COSY could provide accurate measurements of (13)C-enrichments, provided efficient zero-quantum filters were applied during the mixing period. This approach extends the range of NMR methods applicable in (13)C-labelling experiments and is suitable to investigating the dynamic behaviour of metabolic systems.     

Three-dimensional homonuclear NOESY-TOCSY of an intramolecular pyrimidine.purine.pyrimidine DNA triplex containing a central G.TA triple: nonexchangeable proton assignments and structural implications.

Two- and three-dimensional homonuclear 1H NMR spectroscopic techniques have been applied to obtain nearly complete nonexchangeable proton assignments for a 31-residue intramolecular pyrimidine.purine.pyrimidine DNA triplex containing a central G.TA triple in D2O. An assignment strategy for obtaining resonance assignments for DNA protons from a 3D NOESY-TOCSY spectrum is proposed. The strategy utilizes the H1'/H5 omega 3 planes and relies on the recognition of cross-peak patterns for obtaining both intraresidue as well as sequential assignments. On the basis of the cross-peaks observed in the 2D and 3D spectra, a few structural features of the triplex have been delineated qualitatively. All three strands of the triplex adopt a right-handed helical conformation, and, despite the introduction of a central purine guanosine, there is no evidence for major structural distortions in the protonated third strand on the basis of a qualitative interpretation of NMR data. Several interstrand contacts between the purine and the Hoogsteen pyrimidine strands are observed which define the relative orientation of the bases and sugars in these two strands. The presence of strong NOEs between the methyl protons of thymine and the H1' proton of guanosine defines the preferred base-pairing alignment of guanosine at the G.TA triple site. The general approaches illustrated in this study extend the range of DNA molecules accessible for detailed structural investigation by high-resolution NMR spectroscopy.     

Nuclear magnetic resonance studies of lipid hydration in monomethyldioleoylphosphatidylethanolamine dispersions.

Solid-state proton nuclear magnetic resonance has been used to examine surface hydration in suspensions of monomethyldioleoylphosphatidylethanolamine (MeDOPE). The magic-angle spinning (MAS) 1H spectra for aqueous suspensions of MeDOPE in the L alpha phase exhibited two resonances of roughly equal intensity that could be ascribed to water protons, but both their spin-lattice relaxation times and chemical shifts converged upon conversion to the hexagonal phase. Only a single water peak was observed for analogous samples of dioleoylphosphatidylcholine (DOPC). MAS-assisted two-dimensional nuclear Overhauser effect spectroscopy (NOESY) was conducted for multibilayers of both MeDOPE and DOPC. Through-space interactions were identified between pairs of lipid protons, as expected from their chemical structure. For lamellar suspensions of MeDOPE, positive NOESY cross-peaks were observed between the downfield-shifted water resonance (only) and both CH2N and NH2CH3+ protons of the lipid headgroup. These cross-peaks were not observed in the NOESY spectra of MeDOPE in its hexagonal or cubic phases or for lamellar DOPC reference samples. Taken together, the observation of two water peaks, spin-lattice relaxation behavior, and NOESY connectivities in MeDOPE suspensions support the interpretation that the low-field water peak corresponds to hydrogen-bonded interlamellar water interacting strongly with the lipid. Such a population of water molecules exists in association with MeDOPE in the lamellar phase but not for its inverted phases or for lamellar dispersions of DOPC.     

A 500 MHz proton NMR study of stacking interactions: binding of tripeptide Lys-Tyr-Lys to tetradeoxynucleotide d-GpCpGpC.

The complete sequential assignment and conformation of d-GpCpGpC in D2O has been determined from 1D NMR spectra at 285-320 K and room temperature 2D-COSY and NOESY spectra. The tetradeoxynucleotide exists primarily as a right handed double helix at 285 K, having Tm as 314 K. On binding to a tripeptide Lys-Tyr-Lys in a concentration equimolar to tetranucleotide duplex, the Tyr ring protons shift upfield by 0.14 ppm at 285 K. The increase in Tm on binding suggests stabilization of duplex. The existence of intermolecular NOEs between C4 sugar protons and Tyr alpha C and Lys alpha C protons give direct evidence of proximity of Tyr residue to the C4 base of d-GpCpGpC. The conformation of d-GpCpGpC remains unchanged on binding. The observed results are interpreted in terms of preferential stacking of aromatic ring of Tyr residue with proximal base-pair of d-GpCpGpC, stabilized by electrostatic interaction of Lysine side chains with backbone phosphates. This is in contrast to intercalculation of aromatic dyes within base-pairs resulting in a change in sugar conformation at the binding site.     

Monitoring anthracycline binding to nucleotides by two dimensional cosy NMR experiments.

The nucleotide binding ability of the novel anthracycline drug, 3-fluoro-4-demethoxydaunomycin, has been studied by two dimensional 1H NMR correlated spectroscopy (COSY). In the COSY spectrum of the nucleotide mini-helix d(CTGCAG)2 cross-peaks are observed from the spin-coupled H6 and H5 protons of the cytidine bases. Additional cytidine H6/H5 cross-peaks are observed in the COSY spectrum of the anthracycline-d(CTGCAG)2 complex. These additional cytidine cross-peaks enable the identification of the anthracycline binding sites and the determination of the relative kinetic stability of the bound drug at each binding site.     

Position of residues in transmembrane peptides with respect to the lipid bilayer: A combined lipid NOEs and water chemical exchange approach in phospholipid bicelles

The model transmembrane peptide P16 (Ac-KKGLLLALLLLALLLALLLKKA-NH₂) was incorporated into small unaligned phospholipid bicelles, which provide a `native-like' lipid bilayer compatible with high-resolution solution NMR techniques. Using amide-water chemical exchange and amide-lipid cross-relaxation measurements, the interactions between P16 and bicelles were investigated. Distinctive intermolecular NOE patterns observed in band-selective 2D-NOESY spectra of bicellar solutions with several lipid deuteration schemes indicated that P16 is preferentially interacting with the `bilayered' region of the bicelle rather than with the rim. Furthermore, when amide-lipid NOEs were combined with amide-water chemical exchange cross-peaks of selectively ¹⁵N-labeled P16 peptides, valuable information was obtained about the position of selected residues relative to the membrane-water interface. Specifically, three main classes were identified. Class I residues lie outside the bilayer and show amide-water exchange cross-peaks but no amide-lipid NOEs. Class II residues reside in the bilayer-water interface and show both amide-water exchange cross-peaks and amide-lipid NOEs. Class III residues are embedded within the hydrophobic core of the membrane and show no amide-water exchange cross-peaks but strong amide-lipid NOEs.     

NMR studies of the variant-3 neurotoxin from Centruroides sculpturatus Ewing

We report a preliminary high-resolution proton nuclear magnetic resonance characterization of the variant-3 toxin from the scorpion Centruroides sculpturatus Ewing (range Southwestern USA). This toxin assumes a well defined folded conformation in aqueous solutions at room temperature and undergoes reversible thermal denaturation. A number of amide hydrogens exhibit exchange life times varying from several minutes to several hours. A few tentative assignments of the low field aromatic CH resonances has been made on the basis of 2D-COSY and NOE experiments. The upfield shifts exhibited by Trp-47 suggest a unique microenvironment for this residue. The NMR data suggest that there is some degree of correlation between the solution structure of the variant-3 toxin and its crystallographic structure. Our studies provide a basis for a detailed elucidation of the structure-function relationships of these interesting scorpion toxins which bind to the sodium channels of excitable membranes and delay sodium current inactivation.     

High-resolution mono- and multidimensional magic angle spinning 1H nuclear magnetic resonance of membrane peptides in nondeuterated lipid membranes and H2O.

High-speed (14 kHz) solid-state magic angle spinning (MAS) 1H NMR has been applied to several membrane peptides incorporated into nondeuterated dilauroyl or dimyristoylphosphatidylcholine membranes suspended in H2O. It is shown that solvent suppression methods derived from solution NMR, such as presaturation or jump-return, can be used to reduce water resonance, even at relatively high water content. In addition, regioselective excitation of 1H peptide resonances promotes an efficient suppression of lipid resonances, even in cases where these are initially two orders of magnitude more intense. As a consequence, 1H MAS spectra of the peptide low-field region are obtained without interference from water and lipid signals. These display resonances from amide and other exchangeable 1H as well as from aromatic nonexchangeable 1H. The spectral resolution depends on the specific types of resonance and membrane peptide. For small amphiphilic or hydrophobic oligopeptides, resolution of most individual amide resonance is achieved, whereas for the transmembrane peptide gramicidin A, an unresolved amide spectrum is obtained. Partial resolution of aromatic 1H occurs in all cases. Multidimensional 1H-MAS spectra of membrane peptides can also be obtained by using water suppression and regioselective excitation. For gramicidin A, F2-regioselective 2D nuclear Overhauser effect spectroscopy (NOESY) spectra are dominated by intermolecular through-space connectivities between peptide aromatic or formyl 1H and lipid 1H. These appear to be compatible with the known structure and topography of the gramicidin pore. On the other hand, for the amphiphilic peptide leucine-enkephalin, F2-regioselective NOESY spectra mostly display cross-peaks originating from though-space proximities of amide or aromatic 1H with themselves and with aliphatic 1H. F3-regioselective 3D NOESY-NOESY spectra can be used to obtain through-space correlations within aliphatic 1H. Such intrapeptide proximities should allow determination of the conformation of the peptide in membranes. It is suggested that high-speed MAS multidimensional 1H NMR of peptides in nondeuterated membranes and in H2O can be used for studies of both peptide structure and lipid-peptide interactions.     

Study on steroidal oximinoethers: synthesis and stereostructure by NMR spectroscopy.

The condensation of O-substituted hydroxylamines with conjugated 3-oxo-4-en steroids results in a mixture of syn-anti configurations. Syn-anti ratios are influenced by sterical hindrance between the oximino substituents (e.g. O-benzyl) and the steroidal skeleton. Stereostructures and isomeric ratios were proved by detailed 1H and 13C NMR studies and also by using 2D-COSY, 2D-HSC, DEPT, 2D-COLOC and DNOE measurements.     

Synthesis,G-Quadruplex DNA binding and cytotoxic properties of naphthalimide substituted styryl dyes

G-Quadruplex DNAs, formed by G-rich DNA sequences in human genes, are promising targets for design of cancer drugs. In this study, two naphthalimide substituted styryl dyes with different sizes of aromatic groups were synthesized. The spectral analysis showed that the dye X-2 with a large aromatic group formed aggregates in buffer solution displaying very weak fluorescence intensity, and disaggregated in the presence of G-Quadruplex DNAs with large intensity enhancements (up to ~1800 fold). Moreover, X-2 displayed good selectivity to G-Quadruplex DNAs. In contrast, dye X-3 with the smaller aromatic group had much lower fluorescence enhancements and poor selectivity to G-Quadruplex DNAs, suggesting that the suitably sized aromatic ring was essential for the interaction with G-Quadruplex. Further binding studies suggested that X-2 mainly bound on G-quartet surface through end-stacking mode. Cytotoxicity assay showed that both of the two dyes showed good anti-proliferative activities against the cancer cell lines and less cytotoxicity in non-malignant cell lines, which were better than a standard drug 5-fluorouracil. In addition, living cell imaging was also studied and demonstrated the potential applications of the new dye X-2 in bioassays and cell imaging.     

1H-15N-NMR studies of bacteriorhodopsin Halobacterium halobium. Conformational dynamics of the four-helical bundle.

Series of uniformly and selectively 15N-labeled bacteriorhodopsins of Halobacterium halobium (strain ET 1001) were obtained and a 1H-15N-NMR study was performed in methanol/chloroform (1:1) and 0.1 M NH4CHOO, medium which mimics that in the membrane in vivo. Less than half of the cross-peaks expected from the amino acid sequence of uniformly 15N-labeled bacteriorhodopsin were observed, using heteronuclear 1H-15N coherence spectroscopy. In order to assign the observed cross-peaks, a selective 15N-labeling of amino acid residues (Tyr, Phe, Trp, Lys, Gly, Leu, Val or Ile) was carried out and 1H-15N-NMR spectra of bacteriorhodopsin and its fragments C1 (residues (72-231), C2 (residues 1-71), B1 (residues 1-155) and BP2 (residues 163-231) were investigated. By this procedure, all observed 1H-15N cross-peaks of the entire bacteriorhodopsin were found to belong to the transmembrane segments A, B and G. The cross-peaks from four (C, D, E and F) helical bundles (79-189 residues) were missed. These results clearly indicate that dynamic processes occur in the four helice bundle. The significance of this, in respect to bacteriorhodopsin functioning, is discussed.     

Combination of heteronuclear 1H-15N and 1H-13C three-dimensional nuclear magnetic resonance experiments for amide-directed sequential assignment in larger proteins

A new strategy for the sequential assignment of backbone proton resonances in larger proteins involving a unique combination of four types of heteronuclear three-dimensional (3D) NMR spectroscopies is reported. This method relies on the uniform labeling of amide nitrogens with 15N and of alpha-carbons with 13C. Heteronuclear 1H-15N TOCSY-HMQC and NOESY-HMQC experiments can reveal connections between cross-peaks arising from the NHi-C alpha Hi-1 and NHi-C alpha Hi connectivities in the finger-print region in in general. They also specifically reveal the sequential amide-amide connectivities among the amide cross-peaks for the alpha-helices. Heteronuclear 1H-13C HMQC-TOCSY and HMQC-NOESY experiments can reveal connections between cross-peaks arising from the NHi-C alpha Hi and NHi+1-C alpha Hi connectivities in the finger-print region in general. The combination of the two sets of results reveals the complete unambiguous sequential connection of cross-peaks for the proton resonances in the peptide backbone. The application of the new strategy is reported for a protein, ribonuclease H, with a molecular weight of 17.6 kDa.     

Minor groove hydration of DNA in aqueous solution: sequence-dependent next neighbor effect of the hydration lifetimes in d(TTAA)2 segments measured by NMR spectroscopy.

The hydration in the minor groove of double stranded DNA fragments containing the sequences 5'-dTTAAT, 5'-dTTAAC, 5'-dTTAAA and 5'-dTTAAG was investigated by studying the decanucleotide duplex d(GCATTAATGC)2 and the singly cross-linked decameric duplexes 5'-d(GCATTAACGC)-3'-linker-5'-d(GCGTTAATGC)-3' and 5'-d(GCCTTAAAGC)-3'-linker-5'-d(GCTTTAAGGC)-3' by NMR spectroscopy. The linker employed consisted of six ethyleneglycol units. The hydration water was detected by NOEs between water and DNA protons in NOESY and ROESY spectra. NOE-NOESY and ROE-NOESY experiments were used to filter out intense exchange cross-peaks and to observe water-DNA NOEs with sugar 1' protons. Positive NOESY cross-peaks corresponding to residence times longer than approximately 0.5 ns were observed for 2H resonances of the central adenine residues in the duplex containing the sequences 5'-dTTAAT and 5'-dTTAAC, but not in the duplex containing the sequences 5'-dTTAAA and 5'-dTTAAG. In all nucleotide sequences studied here, the hydration water in the minor groove is significantly more mobile at both ends of the AT-rich inner segments, as indicated by very weak or negative water-A 2H NOESY cross-peaks. No positive NOESY cross-peaks were detected with the G 1'H and C 1'H resonances, indicating that the minor groove hydration water near GC base pairs is kinetically less restrained than for AT-rich DNA segments. Kinetically stabilized minor groove hydration water was manifested by positive NOESY cross-peaks with both A 2H and 1'H signals of the 5'-dTTAA segment in d(GCATTAATGC)2. More rigid hydration water was detected near T4 in d(GCATTAATGC)2 as compared with 5'-d(GCATTAACGC)-3'-linker-5'-d(GCGTTAATGC)-3', although the sequences differ only in a single base pair. This illustrates the high sensitivity of water-DNA NOEs towards small conformational differences.     

Reconstruction of the three-dimensional NMR spectrum of a protein from a set of plane projections

Three-dimensional protein NMR spectra can be obtained significantly faster than by traditional methods by a projection-reconstruction procedure related to X-ray tomography. First, two orthogonal projections are acquired in quick two-dimensional experiments with the evolution parameters t₁ or t₂ set to zero. These projections define a three-dimensional lattice; all cross-peaks must lie on this lattice but not all lattice points are occupied. A third experiment with t₁ and t₂ incremented simultaneously and in a fixed ratio, generates a projection onto a tilted plane and thus establishes the positions of all the cross-peaks unambiguously. This projection-reconstruction technique has been tested on the 500 MHz three-dimensional HNCO spectrum of ubiquitin.