Influence of the completeness of chemical shift assignments on NMR structures obtained with automated NOE assignment

Reliable automated NOE assignment and structure calculation on the basis of a largely complete, assigned input chemical shift list and a list of unassigned NOESY cross peaks has recently become feasible for routine NMR protein structure calculation and has been shown to yield results that are equivalent to those of the conventional, manual approach. However, these algorithms rely on the availability of a virtually complete list of the chemical shifts. This paper investigates the influence of incomplete chemical shift assignments on the reliability of NMR structures obtained with automated NOESY cross peak assignment. The program CYANA was used for combined automated NOESY assignment with the CANDID algorithm and structure calculations with torsion angle dynamics at various degrees of completeness of the chemical shift assignment which was simulated by random omission of entries in the experimental ¹H chemical shift lists that had been used for the earlier, conventional structure determinations of two proteins. Sets of structure calculations were performed choosing the omitted chemical shifts randomly among all assigned hydrogen atoms, or among aromatic hydrogen atoms. For comparison, automated NOESY assignment and structure calculations were performed with the complete experimental chemical shift but under random omission of NOESY cross peaks. When heteronuclear-resolved three-dimensional NOESY spectra are available the current CANDID algorithm yields in the absence of up to about 10% of the experimental ¹H chemical shifts reliable NOE assignments and three-dimensional structures that deviate by less than 2 Å from the reference structure obtained using all experimental chemical shift assignments. In contrast, the algorithm can accommodate the omission of up to 50% of the cross peaks in heteronuclear- resolved NOESY spectra without producing structures with a RMSD of more than 2 Å to the reference structure. When only homonuclear NOESY spectra are available, the algorithm is slightly more susceptible to missing data and can tolerate the absence of up to about 7% of the experimental ¹H chemical shifts or of up to 30% of the NOESY peaks.Abbreviations: BmPBP^A – Bombyx mori pheromone binding protein form A; CYANA – combined assignment and dynamics algorithm for NMR applications; NMR – nuclear magnetic resonance; NOE – nuclear Overhauser effect; NOESY – NOE spectroscopy; RMSD – root-mean-square deviation; WmKT – Williopsis mrakii killer toxin     

ORB, a homology-based program for the prediction of protein NMR chemical shifts

A computer program (ORB) has been developed to predict ¹H,¹³C and ¹⁵N NMR chemical shifts of previouslyunassigned proteins. The program makes use of the information contained in achemical shift database of previously assigned proteins supplemented by astatistically derived averaged chemical shift database in which the shifts arecategorized according to their residue, atom and secondary structure type[Wishart et al. (1991) J. Mol. Biol., 222, 311–333]. The predictionprocess starts with a multiple alignment of all previously assigned proteinswith the unassigned query protein. ORB uses the sequence and secondarystructure alignment program XALIGN for this task [Wishart et al. (1994)CABIOS, 10, 121–132; 687–688]. The prediction algorithm in ORB isbased on a scoring of the known shifts for each sequence. The scores dependon global sequence similarity, local sequence similarity, structuralsimilarity and residue similarity and determine how much weight one particularshift is given in the prediction process. In situations where no applicablepreviously assigned chemical shifts are available, the shifts derived from theaveraged database are used. In addition to supplying the user with predictedchemical shifts, ORB calculates a confidence value for every prediction. Theseconfidence values enable the user to judge which predictions are the mostaccurate and they are particularly useful when ORB is incorporated into acomplete autoassignment package. The usefulness of ORB was tested on threemedium-sized proteins: an interleukin-8 analog, a troponin C synthetic peptideheterodimer and cardiac troponin C. Excellent results are obtained if ORB isable to use the chemical shifts of at least one highly homologous sequence.ORB performs well as long as the sequence identity between proteins with knownchemical shifts and the new sequence is not less than 30%.     

Tools for the automated assignment of high-resolution three-dimensional protein NMR spectra based on pattern recognition techniques

One of the major bottlenecks in the determination of proteinstructures by NMR is in the evaluation of the data produced by theexperiments. An important step in this process is assignment, where thepeaks in the spectra are assigned to specific spins within specificresidues. In this paper, we discuss a spin system assignment tool based onpattern recognition techniques. This tool employs user-specified templatesto search for patterns of peaks in the original spectra; these patterns maycorrespond to side-chain or backbone fragments. Multiple spectra willnormally be searched simultaneously to reduce the impact of noise. Thesearch generates a preliminary list of putative assignments, which arefiltered by a set of heuristic algorithms to produce the final results list.Each result contains a set of chemical shift values plus information aboutthe peaks found. The results may be used as input for combinatorialroutines, such as sequential assignment procedures, in place of peak lists.Two examples are presented, in which (i) HCCH-COSY and -TOCSY spectra arescanned for side-chain spin systems; and (ii) backbone spin systems aredetected in a set of spectra comprising HNCA, HN(CO)CA, HNCO, HN(CA)CO,CBCANH and CBCA(CO)NH.     

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.     

Detecting and accounting for multiple sources of positional variance in peak list registration analysis and spin system grouping

Peak lists derived from nuclear magnetic resonance (NMR) spectra are commonly used as input data for a variety of computer assisted and automated analyses. These include automated protein resonance assignment and protein structure calculation software tools. Prior to these analyses, peak lists must be aligned to each other and sets of related peaks must be grouped based on common chemical shift dimensions. Even when programs can perform peak grouping, they require the user to provide uniform match tolerances or use default values. However, peak grouping is further complicated by multiple sources of variance in peak position limiting the effectiveness of grouping methods that utilize uniform match tolerances. In addition, no method currently exists for deriving peak positional variances from single peak lists for grouping peaks into spin systems, i.e. spin system grouping within a single peak list. Therefore, we developed a complementary pair of peak list registration analysis and spin system grouping algorithms designed to overcome these limitations. We have implemented these algorithms into an approach that can identify multiple dimension-specific positional variances that exist in a single peak list and group peaks from a single peak list into spin systems. The resulting software tools generate a variety of useful statistics on both a single peak list and pairwise peak list alignment, especially for quality assessment of peak list datasets. We used a range of low and high quality experimental solution NMR and solid-state NMR peak lists to assess performance of our registration analysis and grouping algorithms. Analyses show that an algorithm using a single iteration and uniform match tolerances approach is only able to recover from 50 to 80% of the spin systems due to the presence of multiple sources of variance. Our algorithm recovers additional spin systems by reevaluating match tolerances in multiple iterations. To facilitate evaluation of the algorithms, we developed a peak list simulator within our nmrstarlib package that generates user-defined assigned peak lists from a given BMRB entry or database of entries. In addition, over 100,000 simulated peak lists with one or two sources of variance were generated to evaluate the performance and robustness of these new registration analysis and peak grouping algorithms.     

Automated combined assignment of NOESY spectra and three-dimensional protein structure determination

A procedure for automated protein structure determination is presented that is based on an iterative procedure during which the NOESY peak list assignment and the structure calculation are performed simultaneously. The input consists of a list of NOESY peak positions and a list of chemical shifts as obtained from sequence-specific resonance assignment. For the present applications of this approach the previously introduced NOAH routine was implemented in the distance geometry program DIANA. As an illustration, experimental 2D and 3D NOESY cross-peak lists of six proteins have been analyzed, for which complete sequence-specific ¹H assignments are available for the polypeptide backbone and the amino acid side chains. The automated method assigned 70–90% of all NOESY cross peaks, which is on average 10% less than with the interactive approach, and only between 0.8% and 2.4% of the automatically assigned peaks had a different assignment than in the corresponding manually assigned peak lists. The structures obtained with NOAH/DIANA are in close agreement with those from manually assigned peak lists, and with both approaches the residual constraint violations correspond to high-quality NMR structure determinations. Systematic comparisons of the bundles of conformers that represent corresponding automatically and interactively determined structures document the absence of significant bias in either approach, indicating that an important step has been made towards automation of structure determination from NMR spectra.     

Resonance assignment of the NMR spectra of disordered proteins using a multi-objective non-dominated sorting genetic algorithm

A multi-objective genetic algorithm is introduced to predict the assignment of protein solid-state NMR (SSNMR) spectra with partial resonance overlap and missing peaks due to broad linewidths, molecular motion, and low sensitivity. This non-dominated sorting genetic algorithm II (NSGA-II) aims to identify all possible assignments that are consistent with the spectra and to compare the relative merit of these assignments. Our approach is modeled after the recently introduced Monte-Carlo simulated-annealing (MC/SA) protocol, with the key difference that NSGA-II simultaneously optimizes multiple assignment objectives instead of searching for possible assignments based on a single composite score. The multiple objectives include maximizing the number of consistently assigned peaks between multiple spectra (“good connections”), maximizing the number of used peaks, minimizing the number of inconsistently assigned peaks between spectra (“bad connections”), and minimizing the number of assigned peaks that have no matching peaks in the other spectra (“edges”). Using six SSNMR protein chemical shift datasets with varying levels of imperfection that was introduced by peak deletion, random chemical shift changes, and manual peak picking of spectra with moderately broad linewidths, we show that the NSGA-II algorithm produces a large number of valid and good assignments rapidly. For high-quality chemical shift peak lists, NSGA-II and MC/SA perform similarly well. However, when the peak lists contain many missing peaks that are uncorrelated between different spectra and have chemical shift deviations between spectra, the modified NSGA-II produces a larger number of valid solutions than MC/SA, and is more effective at distinguishing good from mediocre assignments by avoiding the hazard of suboptimal weighting factors for the various objectives. These two advantages, namely diversity and better evaluation, lead to a higher probability of predicting the correct assignment for a larger number of residues. On the other hand, when there are multiple equally good assignments that are significantly different from each other, the modified NSGA-II is less efficient than MC/SA in finding all the solutions. This problem is solved by a combined NSGA-II/MC algorithm, which appears to have the advantages of both NSGA-II and MC/SA. This combination algorithm is robust for the three most difficult chemical shift datasets examined here and is expected to give the highest-quality de novo assignment of challenging protein NMR spectra.     

Resolution and sensitivity of high field nuclear magnetic resonance spectroscopy

NMR frequency assignments are usually considered a prerequisite for the analysis of NOESY spectra, in turn required for the calculation of biomolecular structures. In contrast, as we propose here, relatively high numbers of unambiguous NOE identities can be consistently achieved in an automated manner by relying only on grouping resonances into connected spin systems. To achieve this goal, we have developed for proteins two protocols, SPI and BACUS, based on Bayesian inference. SPI (Grishaev and Llinás, 2002c) produces a list of the (1)H resonance frequencies from homo- and hetero-nuclear multidimensional spectra, grouped into effective spin systems. BACUS automatically establishes probabilistic identities of NOESY cross-peaks in terms of the chemical shifts provided by SPI. BACUS requires neither assignment of resonances nor an initial structural model. It successfully copes with chemical shift overlap and does so without cycling through 3D structure calculations. The method exploits the self-consistency of the NOESY graph by taking advantage of a network of J- as well as NOE-connected "reporter" protons sorted via SPI. BACUS was validated by tests on experimental NOESY data recorded for the col 2 and kringle 2 domains.     

Practical use of chemical shift databases for protein solid-state NMR: 2D chemical shift maps and amino-acid assignment with secondary-structure information

We introduce a Python-based program that utilizes the large database of ¹³C and ¹⁵N chemical shifts in the Biological Magnetic Resonance Bank to rapidly predict the amino acid type and secondary structure from correlated chemical shifts. The program, called PACSYlite Unified Query (PLUQ), is designed to help assign peaks obtained from 2D ¹³C–¹³C, ¹⁵N–¹³C, or 3D ¹⁵N–¹³C–¹³C magic-angle-spinning correlation spectra. We show secondary-structure specific 2D ¹³C–¹³C correlation maps of all twenty amino acids, constructed from a chemical shift database of 262,209 residues. The maps reveal interesting conformation-dependent chemical shift distributions and facilitate searching of correlation peaks during amino-acid type assignment. Based on these correlations, PLUQ outputs the most likely amino acid types and the associated secondary structures from inputs of experimental chemical shifts. We test the assignment accuracy using four high-quality protein structures. Based on only the Cα and Cβ chemical shifts, the highest-ranked PLUQ assignments were 40–60 % correct in both the amino-acid type and the secondary structure. For three input chemical shifts (CO–Cα–Cβ or N–Cα–Cβ), the first-ranked assignments were correct for 60 % of the residues, while within the top three predictions, the correct assignments were found for 80 % of the residues. PLUQ and the chemical shift maps are expected to be useful at the first stage of sequential assignment, for combination with automated sequential assignment programs, and for highly disordered proteins for which secondary structure analysis is the main goal of structure determination.     

Assignment of the aliphatic 1H and 13C resonances of the Bacillus subtilis glucose permease IIA domain using double- and triple-resonance heteronuclear three-dimensional NMR spectroscopy.

Nearly complete assignment of the aliphatic 1H and 13C resonances of the IIAglc domain of Bacillus subtilis has been achieved using a combination of double- and triple-resonance three-dimensional (3D) NMR experiments. A constant-time 3D triple-resonance HCA(CO)N experiment, which correlates the 1H alpha and 13C alpha chemical shifts of one residue with the amide 15N chemical shift of the following residue, was used to obtain sequence-specific assignments of the 13C alpha resonances. The 1H alpha and amide 15N chemical shifts had been sequentially assigned previously using principally 3D 1H-15N NOESY-HMQC and TOCSY-HMQC experiments [Fairbrother, W. J., Cavanagh, J., Dyson, H. J., Palmer, A. G., III, Sutrina, S. L., Reizer, J., Saier, M. H., Jr., & Wright, P. E. (1991) Biochemistry 30, 6896-6907]. The side-chain spin systems were identified using 3D HCCH-COSY and HCCH-TOCSY spectra and were assigned sequentially on the basis of their 1H alpha and 13C alpha chemical shifts. The 3D HCCH and HCA(CO)N experiments rely on large heteronuclear one-bond J couplings for coherence transfers and therefore offer a considerable advantage over conventional 1H-1H correlation experiments that rely on 1H-1H 3J couplings, which, for proteins the size of IIAglc (17.4 kDa), may be significantly smaller than the 1H line widths. The assignments reported herein are essential for the determination of the high-resolution solution structure of the IIAglc domain of B. subtilis using 3D and 4D heteronuclear edited NOESY experiments; these assignments have been used to analyze 3D 1H-15N NOESY-HMQC and 1H-13C NOESY-HSQC spectra and calculate a low-resolution structure [Fairbrother, W. J., Gippert, G. P., Reizer, J., Saier, M. H., Jr., & Wright, P. E. (1992) FEBS Lett. 296, 148-152].     

Use of biosynthetic fractional 13C-labeling for backbone NMR assignment of proteins

We describe a simple approach to classify amino acid residue types in NMR spectra of proteins for supporting the backbone resonance assignments. It makes use of the differences in biosynthetic pathways of the 20 amino acids in Escherichia coli. Therefore, it is distinct from the parameters routinely exploited in the backbone resonance assignment such as chemical shifts and spin topology information. The combination of biosynthetically directed fractional 13C-labeling and uniform 15N-labeling enables us to obtain both residue-type specific information and sequential connectivities from a single protein sample. The residue-type classification exploiting biosynthetic pathways can be used for accelerating the conventional backbone assignment procedure.     

A probabilistic approach for validating protein NMR chemical shift assignments

It has been estimated that more than 20% of the proteins in the BMRB are improperly referenced and that about 1% of all chemical shift assignments are mis-assigned. These statistics also reflect the likelihood that any newly assigned protein will have shift assignment or shift referencing errors. The relatively high frequency of these errors continues to be a concern for the biomolecular NMR community. While several programs do exist to detect and/or correct chemical shift mis-referencing or chemical shift mis-assignments, most can only do one, or the other. The one program (SHIFTCOR) that is capable of handling both chemical shift mis-referencing and mis-assignments, requires the 3D structure coordinates of the target protein. Given that chemical shift mis-assignments and chemical shift re-referencing issues should ideally be addressed prior to 3D structure determination, there is a clear need to develop a structure-independent approach. Here, we present a new structure-independent protocol, which is based on using residue-specific and secondary structure-specific chemical shift distributions calculated over small (3–6 residue) fragments to identify mis-assigned resonances. The method is also able to identify and re-reference mis-referenced chemical shift assignments. Comparisons against existing re-referencing or mis-assignment detection programs show that the method is as good or superior to existing approaches. The protocol described here has been implemented into a freely available Java program called “Probabilistic Approach for protein Nmr Assignment Validation (PANAV)” and as a web server () which can be used to validate and/or correct as well as re-reference assigned protein chemical shifts.     

RefDB: a database of uniformly referenced protein chemical shifts

RefDB is a secondary database of reference-corrected protein chemical shifts derived from the BioMagResBank (BMRB). The database was assembled by using a recently developed program (SHIFTX) to predict protein ¹H, ¹³C and ¹⁵N chemical shifts from X-ray or NMR coordinate data of previously assigned proteins. The predicted shifts were then compared with the corresponding observed shifts and a variety of statistical evaluations performed. In this way, potential mis-assignments, typographical errors and chemical referencing errors could be identified and, in many cases, corrected. This approach allows for an unbiased, instrument-independent solution to the problem of retrospectively re-referencing published protein chemical shifts. Results from this study indicate that nearly 25% of BMRB entries with ¹³C protein assignments and 27% of BMRB entries with ¹⁵N protein assignments required significant chemical shift reference readjustments. Additionally, nearly 40% of protein entries deposited in the BioMagResBank appear to have at least one assignment error. From this study it evident that protein NMR spectroscopists are increasingly adhering to recommended IUPAC ¹³C and ¹⁵N chemical shift referencing conventions, however, approximately 20% of newly deposited protein entries in the BMRB are still being incorrectly referenced. This is cause for some concern. However, the utilization of RefDB and its companion programs may help mitigate this ongoing problem. RefDB is updated weekly and the database, along with its associated software, is freely available at http://redpoll.pharmacy.ualberta.ca and the BMRB website.     

MAP-XSII: an improved program for the automatic assignment of methyl resonances in large proteins

NMR studies of large proteins have gathered much interest in recent years, especially after methyl-transverse relaxation optimized spectroscopy was successfully applied to systems as large as ~1 MDa in molecular weight. However, to fully take advantage of these spectra, there is a need for convenient and robust methods for making resonance assignments rapidly. Here, we present an improved version of our program MAP-XS (methyl assignment prediction from X-ray structure) for the automatic assignment of methyl peaks, based on nuclear Overhauser effects (NOE) correlations and chemical shifts together with available structures. No manual analysis of the NOE data is needed in this new version, which helps to further accelerate the assignment process. A refined algorithm as well as more efficient sampling produces results from single runs of MAP-XSII using unanalyzed NOE data are comparable to those achieved by the old version using manually curated data with every NOE peak correctly attributed to the two related methyl peaks; in addition, checking the results from multiple parallel runs against each other provides an effective mechanism for getting rid of the wrong assignments while keeping the correct ones, which significantly improves the reliability of final assignments. The new program is tested against three different proteins and delivers ~95 % correct assignments; positive results are also achieved for tests using different cut-off distances for NOEs, structures of lower resolutions, and ambiguous residue types.     

Automated assignment of NMR chemical shifts using peak-particle dynamics simulation with the DYNASSIGN algorithm

A new algorithm, DYNASSIGN, for the automated assignment of NMR chemical shift resonances was developed in which expected cross peaks in multidimensional NMR spectra are represented by peak-particles and assignment restraints are translated into a potential energy function. Molecular dynamics simulation techniques are used to calculate a trajectory of the system of peak-particles subjected to the potential function in order to find energetically optimal configurations that correspond to correct assignments. Peak-particle dynamics-based simulated annealing was combined with the Hungarian algorithm for local optimization, and a residue-based score was introduced to distinguish between reliable assignments and “unassigned” resonances for which no reliable assignment can be established. The DYNASSIGN algorithm was implemented in the program CYANA and tested with data sets obtained from the experimental NMR data of nine small proteins. With a set of 10 commonly used NMR spectra, on average 82.5% of all backbone and side-chain ¹H, ¹³C and ¹⁵N resonances could be assigned with an average error rate of 3.5%.     

PACES: Protein sequential assignment by computer-assisted exhaustive search

A crucial step in determining solution structures of proteins using nuclear magnetic resonance (NMR) spectroscopy is the process of sequential assignment, which correlates backbone resonances to corresponding residues in the primary sequence of a protein, today, typically using data from triple-resonance NMR experiments. Although the development of automated approaches for sequential assignment has greatly facilitated this process, the performance of these programs is usually less satisfactory for large proteins, especially in the cases of missing connectivity or severe chemical shift degeneracy. Here, we report the development of a novel computer-assisted method for sequential assignment, using an algorithm that conducts an exhaustive search of all spin systems both for establishing sequential connectivities and then for assignment. By running the program iteratively with user intervention after each cycle, ambiguities in the assignments can be eliminated efficiently and backbone resonances can be assigned rapidly. The efficiency and robustness of this approach have been tested with 27 proteins of sizes varying from 76 amino acids to 723 amino acids, and with data of varying qualities, using experimental data for three proteins, and published assignments modified with simulated noise for the other 24. The complexity of sequential assignment with regard to the size of the protein, the completeness of NMR data sets, and the uncertainty in resonance positions has been examined.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1023589029301     

Stereospecific assignment of the asparagine and glutamine sidechain amide protons in proteins from chemical shift analysis

Side chain amide protons of asparagine and glutamine residues in random-coil peptides are characterized by large chemical shift differences and can be stereospecifically assigned on the basis of their chemical shift values only. The bimodal chemical shift distributions stored in the biological magnetic resonance data bank (BMRB) do not allow such an assignment. However, an analysis of the BMRB shows, that a substantial part of all stored stereospecific assignments is not correct. We show here that in most cases stereospecific assignment can also be done for folded proteins using an unbiased artificial chemical shift data base (UACSB). For a separation of the chemical shifts of the two amide resonance lines with differences ≥0.40 ppm for asparagine and differences ≥0.42 ppm for glutamine, the downfield shifted resonance lines can be assigned to H^δ21 and H^ε21, respectively, at a confidence level >95%. A classifier derived from UASCB can also be used to correct the BMRB data. The program tool AssignmentChecker implemented in AUREMOL calculates the Bayesian probability for a given stereospecific assignment and automatically corrects the assignments for a given list of chemical shifts.     

Prospects for resonance assignments in multidimensional solid-state NMR spectra of uniformly labeled proteins

Summary The feasibility of assigning the backbone ¹⁵N and ¹³C NMR chemical shifts in multidimensional magic angle spinning NMR spectra of uniformly isotopically labeled proteins and peptides in unoriented solid samples is assessed by means of numerical simulations. The goal of these simulations is to examine how the upper limit on the size of a peptide for which unique assignments can be made depends on the spectral resolution, i.e., the NMR line widths. Sets of simulated three-dimensional chemical shift correlation spectra for artificial peptides of varying length are constructed from published liquid-state NMR chemical shift data for ubiquitin, a well-characterized soluble protein. Resonance assignments consistent with these spectra to within the assumed spectral resolution are found by a numerical search algorithm. The dependence of the number of consistent assignments on the assumed spectral resolution and on the length of the peptide is reported. If only three-dimensional chemical shift correlation data for backbone ¹⁵N and ¹³C nuclei are used, and no residue-specific chemical shift information, information from amino acid side-chain signals, and proton chemical shift information are available, a spectral resolution of 1 ppm or less is generally required for a unique assignment of backbone chemical shifts for a peptide of 30 amino acid residues.