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     

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.     

CAMRA: Chemical shift based computer aided protein NMR assignments

A suite of programs called CAMRA (Computer Aided Magnetic Resonance Assignment) has been developed for computer assisted residue-specific assignments of proteins. CAMRA consists of three units: ORB, CAPTURE and PROCESS. ORB predicts NMR chemical shifts for unassigned proteins using a chemical shift database of previously assigned homologous proteins supplemented by a statistically derived chemical shift database in which the shifts are categorized according to their residue, atom and secondary structure type. CAPTURE generates a list of valid peaks from NMR spectra by filtering out noise peaks and other artifacts and then separating the derived peak list into distinct spin systems. PROCESS combines the chemical shift predictions from ORB with the spin systems identified by CAPTURE to obtain residue specific assignments. PROCESS ranks the top choices for an assignment along with scores and confidence values. In contrast to other auto-assignment programs, CAMRA does not use any connectivity information but instead is based solely on matching predicted shifts with observed spin systems. As such, CAMRA represents a new and unique approach for the assignment of protein NMR spectra. CAMRA will be particularly useful in conjunction with other assignment methods and under special circumstances, such as the assignment of flexible regions in proteins where sufficient NOE information is generally not available. CAMRA was tested on two medium-sized proteins belonging to the chemokine family. It was found to be effective in predicting the assignment providing a database of previously assigned proteins with at least 30% sequence identity is available. CAMRA is versatile and can be used to include and evaluate heteronuclear and three-dimensional experiments.     

Automated assignment of NOESY NMR spectra using a knowledge based method (KNOWNOE)

Automated assignment of NOESY spectra is a prerequisite for automated structure determination of biological macromolecules. With the program KNOWNOE we present a novel, knowledge based approach to this problem. KNOWNOE is devised to work directly with the experimental spectra without interference of an expert. Besides making use of routines already implemented in AUREMOL, it contains as a central part a knowledge driven Bayesian algorithm for solving ambiguities in the NOE assignments. These ambiguities mainly arise from chemical shift degeneration which allows multiple assignments of cross peaks. Using a set of 326 protein NMR structures, statistical tables in the form of atom-pairwise volume probability distributions (VPDs) were derived. VPDs for all assignment possibilities relevant to the assignments of interproton NOEs were calculated. With these data for a given cross peak with N possible assignments A _i(i = 1,...,N) the conditional probabilities P(A _i, a|V ₀) can be calculated that the assignment A _idetermines essentially all (a-times) of the cross peak volume V ₀. An assignment A _kwith a probability P(A _k, a|V ₀) higher than 0.8 is transiently considered as unambiguously assigned. With a list of unambiguously assigned peaks a set of structures is calculated. These structures are used as input for a next cycle of iteration where a distance threshold D _maxis dynamically reduced. The program KNOWNOE was tested on NOESY spectra of a medium size protein, the cold shock protein (TmCsp) from Thermotoga maritima. The results show that a high quality structure of this protein can be obtained by automated assignment of NOESY spectra which is at least as good as the structure obtained from manual data evaluation.     

Peak picking multidimensional NMR spectra with the contour geometry based algorithm CYPICK

The automated identification of signals in multidimensional NMR spectra is a challenging task, complicated by signal overlap, noise, and spectral artifacts, for which no universally accepted method is available. Here, we present a new peak picking algorithm, CYPICK, that follows, as far as possible, the manual approach taken by a spectroscopist who analyzes peak patterns in contour plots of the spectrum, but is fully automated. Human visual inspection is replaced by the evaluation of geometric criteria applied to contour lines, such as local extremality, approximate circularity (after appropriate scaling of the spectrum axes), and convexity. The performance of CYPICK was evaluated for a variety of spectra from different proteins by systematic comparison with peak lists obtained by other, manual or automated, peak picking methods, as well as by analyzing the results of automated chemical shift assignment and structure calculation based on input peak lists from CYPICK. The results show that CYPICK yielded peak lists that compare in most cases favorably to those obtained by other automated peak pickers with respect to the criteria of finding a maximal number of real signals, a minimal number of artifact peaks, and maximal correctness of the chemical shift assignments and the three-dimensional structure obtained by fully automated assignment and structure calculation.     

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%.     

CISA: combined NMR resonance connectivity information determination and sequential assignment

A nearly complete sequential resonance assignment is a key factor leading to successful protein structure determination via NMR spectroscopy. Assuming the availability of a set of NMR spectral peak lists, most of the existing assignment algorithms first use the differences between chemical shift values for common nuclei across multiple spectra to provide the evidence that some pairs of peaks should be assigned to sequentially adjacent amino acid residues in the target protein. They then use these connectivities as constraints to produce a sequential assignment. At various levels of success, these algorithms typically generate a large number of potential connectivity constraints, and it grows exponentially as the quality of spectral data decreases. A key observation used in our sequential assignment program, CISA, is that chemical shift residual signature information can be used to improve the connectivity determination, and thus to dramatically decrease the number of predicted connectivity constraints. Fewer connectivity constraints lead to less ambiguities in the sequential assignment. Extensive simulation studies on several large test datasets demonstrated that CISA is efficient and effective, compared to three most recently proposed sequential resonance assignment programs RANDOM, PACES, and MARS.     

Automation of peak-tracking analysis of stepwise perturbed NMR spectra

We describe a new algorithmic approach able to automatically pick and track the NMR resonances of a large number of 2D NMR spectra acquired during a stepwise variation of a physical parameter. The method has been named Trace in Track (TinT), referring to the idea that a gaussian decomposition traces peaks within the tracks recognised through 3D mathematical morphology. It is capable of determining the evolution of the chemical shifts, intensity and linewidths of each tracked peak.The performances obtained in term of track reconstruction and correct assignment on realistic synthetic spectra were high above 90% when a noise level similar to that of experimental data were considered. TinT was applied successfully to several protein systems during a temperature ramp in isotope exchange experiments. A comparison with a state-of-the-art algorithm showed promising results for great numbers of spectra and low signal to noise ratios, when the graduality of the perturbation is appropriate. TinT can be applied to different kinds of high throughput chemical shift mapping experiments, with quasi-continuous variations, in which a quantitative automated recognition is crucial.     

APART: automated preprocessing for NMR assignments with reduced tedium

MOTIVATION: High-throughput NMR structure determination is a goal that will require progress on many fronts, one of which is rapid resonance assignment. An important rate-limiting step in the resonance assignment process is accurate identification of resonance peaks in the NMR spectra. Peak-picking schemes range from incomplete (which lose essential assignment connectivities) to noisy (which obscure true connectivities with many false ones). We introduce an automated preassignment process that removes false peaks from noisy peak lists by requiring consensus between multiple NMR experiments and exploiting a priori information about NMR spectra. This process is designed to accept multiple input formats and generate multiple output formats, in an effort to be compatible with a variety of user preferences. RESULTS: Automated preprocessing with APART rapidly identifies and removes false peaks from initial peak lists, reduces the burden of manual data entry, and documents and standardizes the peak filtering process. Successful preprocessing is demonstrated by the increased number of correct assignments obtained when data are submitted to an automated assignment program. AVAILABILITY: APART is available from http://sir.lanl.gov/NMR/APART.htm CONTACT: npawley@lanl.gov; rmichalczyk@lanl.gov SUPPLEMENTARY INFORMATION: Manual pages with installation instructions, procedures and screen shots can also be found at http://sir.lanl.gov/NMR/APART_Manual1.pdf.     

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.     

Peakmatch: a simple and robust method for peak list matching

Peak lists are commonly used in NMR as input data for various software tools such as automatic assignment and structure calculation programs. Inconsistencies of chemical shift referencing among different peak lists or between peak and chemical shift lists can cause severe problems during peak assignment. Here we present a simple and robust tool to achieve self-consistency of the chemical shift referencing among a set of peak lists. The Peakmatch algorithm matches a set of peak lists to a specified reference peak list, neither of which have to be assigned. The chemical shift referencing offset between two peak lists is determined by optimizing an assignment-free match score function using either a complete grid search or downhill simplex optimization. It is shown that peak lists from many different types of spectra can be matched reliably as long as they contain at least two corresponding dimensions. Using a simulated peak list, the Peakmatch algorithm can also be used to obtain the optimal agreement between a chemical shift list and experimental peak lists. Combining these features makes Peakmatch a useful tool that can be applied routinely before automatic assignment or structure calculation in order to obtain an optimized input data set.     

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.     

Assignment of MS-based metabolomic datasets via compound interaction pair mapping

Assignment of physical meaning to mass spectrometry (MS) data peaks is an important scientific challenge for metabolomics investigators. Improvements in instrumental mass accuracy reduce the number of spurious database matches, however, this alone is insufficient for accurate, unique high-throughput assignment. We present a method for clustering MS instrumental artifacts and a stochastic local search algorithm for the automated assignment of large, complex MS-based metabolomic datasets. Artifact peaks and their associated source peaks are grouped into “instrumental clusters.” Instrumental clusters, peaks grouped together by shared peak shape in the temporal domain, serve as a guide for the number of assignments necessary to completely explain a given dataset. We refine mass only assignments through the intersection of peak correlation pairs with a database of biochemically relevant interaction pairs. Further refinement is achieved through a stochastic local search optimization algorithm that selects individual assignments for each instrumental cluster. The algorithm works by choosing the peak assignment that maximally explains the connectivity of a given cluster. We demonstrate that this methodology provides a significant advantage over standard methods for the assignment of metabolites in a UPLC-MS diabetes dataset. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Reliability of exclusively NOESY-based automated resonance assignment and structure determination of proteins

Protein structure determination by NMR can in principle be speeded up both by reducing the measurement time on the NMR spectrometer and by a more efficient analysis of the spectra. Here we study the reliability of protein structure determination based on a single type of spectra, namely nuclear Overhauser effect spectroscopy (NOESY), using a fully automated procedure for the sequence-specific resonance assignment with the recently introduced FLYA algorithm, followed by combined automated NOE distance restraint assignment and structure calculation with CYANA. This NOESY-FLYA method was applied to eight proteins with 63–160 residues for which resonance assignments and solution structures had previously been determined by the Northeast Structural Genomics Consortium (NESG), and unrefined and refined NOESY data sets have been made available for the Critical Assessment of Automated Structure Determination of Proteins by NMR project. Using only peak lists from three-dimensional ¹³C- or ¹⁵N-resolved NOESY spectra as input, the FLYA algorithm yielded for the eight proteins 91–98 % correct backbone and side-chain assignments if manually refined peak lists are used, and 64–96 % correct assignments based on raw peak lists. Subsequent structure calculations with CYANA then produced structures with root-mean-square deviation (RMSD) values to the manually determined reference structures of 0.8–2.0 Å if refined peak lists are used. With raw peak lists, calculations for 4 proteins converged resulting in RMSDs to the reference structure of 0.8–2.8 Å, whereas no convergence was obtained for the four other proteins (two of which did already not converge with the correct manual resonance assignments given as input). These results show that, given high-quality experimental NOESY peak lists, the chemical shift assignments can be uncovered, without any recourse to traditional through-bond type assignment experiments, to an extent that is sufficient for calculating accurate three-dimensional structures.     

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.     

Computational assignment of protein backbone NMR peaks by efficient bounding and filtering

NMR resonance assignment is one of the key steps in solving an NMR protein structure. The assignment process links resonance peaks to individual residues of the target protein sequence, providing the prerequisite for establishing intra- and inter-residue spatial relationships between atoms. The assignment process is tedious and time-consuming, which could take many weeks. Though there exist a number of computer programs to assist the assignment process, many NMR labs are still doing the assignments manually to ensure quality. This paper presents a new computational method based on the combination of a suite of algorithms for automating the assignment process, particularly the process of backbone resonance peak assignment. We formulate the assignment problem as a constrained weighted bipartite matching problem. While the problem, in the most general situation, is NP-hard, we present an efficient solution based on a branch-and-bound algorithm with effective bounding techniques using two recently introduced approximation algorithms. We also devise a greedy filtering algorithm for reducing the search space. Our experimental results on 70 instances of (pseudo) real NMR data derived from 14 proteins demonstrate that the new solution runs much faster than a recently introduced (exhaustive) two-layer algorithm and recovers more correct peak assignments than the two-layer algorithm. Our result demonstrates that integrating different algorithms can achieve a good tradeoff between backbone assignment accuracy and computation time.     

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.     

Protein NMR structure determination with automated NOE assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA

Combined automated NOE assignment and structure determination module (CANDID) is a new software for efficient NMR structure determination of proteins by automated assignment of the NOESY spectra. CANDID uses an iterative approach with multiple cycles of NOE cross-peak assignment and protein structure calculation using the fast DYANA torsion angle dynamics algorithm, so that the result from each CANDID cycle consists of exhaustive, possibly ambiguous NOE cross-peak assignments in all available spectra and a three-dimensional protein structure represented by a bundle of conformers. The input for the first CANDID cycle consists of the amino acid sequence, the chemical shift list from the sequence-specific resonance assignment, and listings of the cross-peak positions and volumes in one or several two, three or four-dimensional NOESY spectra. The input for the second and subsequent CANDID cycles contains the three-dimensional protein structure from the previous cycle, in addition to the complete input used for the first cycle. CANDID includes two new elements that make it robust with respect to the presence of artifacts in the input data, i.e. network-anchoring and constraint-combination, which have a key role in de novo protein structure determinations for the successful generation of the correct polypeptide fold by the first CANDID cycle. Network-anchoring makes use of the fact that any network of correct NOE cross-peak assignments forms a self-consistent set; the initial, chemical shift-based assignments for each individual NOE cross-peak are therefore weighted by the extent to which they can be embedded into the network formed by all other NOE cross-peak assignments. Constraint-combination reduces the deleterious impact of artifact NOE upper distance constraints in the input for a protein structure calculation by combining the assignments for two or several peaks into a single upper limit distance constraint, which lowers the probability that the presence of an artifact peak will influence the outcome of the structure calculation. CANDID test calculations were performed with NMR data sets of four proteins for which high-quality structures had previously been solved by interactive protocols, and they yielded comparable results to these reference structure determinations with regard to both the residual constraint violations, and the precision and accuracy of the atomic coordinates. The CANDID approach has further been validated by de novo NMR structure determinations of four additional proteins. The experience gained in these calculations shows that once nearly complete sequence-specific resonance assignments are available, the automated CANDID approach results in greatly enhanced efficiency of the NOESY spectral analysis. The fact that the correct fold is obtained in cycle 1 of a de novo structure calculation is the single most important advance achieved with CANDID, when compared with previously proposed automated NOESY assignment methods that do not use network-anchoring and constraint-combination.     

Four-dimensional heteronuclear correlation experiments for chemical shift assignment of solid proteins

Chemical shift assignment is the first step in all established protocols for structure determination of uniformly labeled proteins by NMR. The explosive growth in recent years of magic-angle spinning (MAS) solid-state NMR (SSNMR) applications is largely attributable to improved methods for backbone and side-chain chemical shift correlation spectroscopy. However, the techniques developed so far have been applied primarily to proteins in the size range of 5–10 kDa, despite the fact that SSNMR has no inherent molecular weight limits. Rather, the degeneracy inherent to many 2D and 3D SSNMR spectra of larger proteins has prevented complete unambiguous chemical shift assignment. Here we demonstrate the implementation of 4D backbone chemical shift correlation experiments for assignment of solid proteins. The experiments greatly reduce spectral degeneracy at a modest cost in sensitivity, which is accurately described by theory. We consider several possible implementations and investigate the CANCOCX pulse sequence in detail. This experiment involves three cross polarization steps, from H to CA[i], CA[i] to N[i], and N[i] to C′[i−1], followed by a final homonuclear mixing period. With short homonuclear mixing times (<20 ms), backbone correlations are observed with high sensitivity; with longer mixing times (>200 ms), long-range correlations are revealed. For example, a single 4D experiment with 225 ms homonuclear mixing time reveals ∼200 uniquely resolved medium and long-range correlations in the 56-residue protein GB1. In addition to experimental demonstrations in the 56-residue protein GB1, we present a theoretical analysis of anticipated improvements in resolution for much larger proteins and compare these results in detail with the experiments, finding good agreement between experiment and theory under conditions of stable instrumental performance.