Resolution-by-proxy: a simple measure for assessing and comparing the overall quality of NMR protein structures

In protein X-ray crystallography, resolution is often used as a good indicator of structural quality. Diffraction resolution of protein crystals correlates well with the number of X-ray observables that are used in structure generation and, therefore, with protein coordinate errors. In protein NMR, there is no parameter identical to X-ray resolution. Instead, resolution is often used as a synonym of NMR model quality. Resolution of NMR structures is often deduced from ensemble precision, torsion angle normality and number of distance restraints per residue. The lack of common techniques to assess the resolution of X-ray and NMR structures complicates the comparison of structures solved by these two methods. This problem is sometimes approached by calculating "equivalent resolution" from structure quality metrics. However, existing protocols do not offer a comprehensive assessment of protein structure as they calculate equivalent resolution from a relatively small number (<5) of protein parameters. Here, we report a development of a protocol that calculates equivalent resolution from 25 measurable protein features. This new method offers better performance (correlation coefficient of 0.92, mean absolute error of 0.28 ?) than existing predictors of equivalent resolution. Because the method uses coordinate data as a proxy for X-ray diffraction data, we call this measure "Resolution-by-Proxy" or ResProx. We demonstrate that ResProx can be used to identify under-restrained, poorly refined or inaccurate NMR structures, and can discover structural defects that the other equivalent resolution methods cannot detect. The ResProx web server is available at http://www.resprox.ca.     

Determination of three-dimensional protein structures from nuclear magnetic resonance data using fragments of known structures

A method to build a three-dimensional protein model from nuclear magnetic resonance (NMR) data using fragments from a data base of crystallographically determined protein structures is presented. The interproton distances derived from the nuclear Overhauser effect (NOE) data are compared to the precalculated distances in the known protein structures. An efficient search algorithm is used, which arranges the distances in matrices akin to a C alpha diagonal distance plot, and compares the NOE distance matrices for short sequential zones of the protein to the data base matrices. After cluster analysis of the fragments found in this way, the structure is built by aligning fragments in overlapping zones. The sequentially long-range NOEs cannot be used in the initial fragments search but are vital to discriminate between several possible combinations of different groups of fragments. The method has been tested on one simulated NOE data set derived from a crystal structure and one experimental NMR data set. The method produces models that have good local structure, but may contain larger global errors. These models can be used as the starting point for further refinement, e.g., by restrained molecular dynamics or interactive graphics.     

Distance geometry and related methods for protein structure determination from NMR data

Computational tools have been developed in the last few years, to allow a direct determination of protein structures from NMR data. Numerical calculations with simulated and experimental NMR constraints for distances and torsional angles show that data sets available with present NMR techniques carry enough information to determine reliably the global fold of a small protein. The maximum size of a protein for which the direct method can be applied is not limited by the computational tools but rather by the resolution of the two-dimensional spectra. A general estimate of the maximum size would be a molecular weight of about 10,000 (Markley et al. 1984), but parts of larger proteins might be accessible with the method. Effort for improvement of the NMR structures should be concentrated more on the local conformation rather than the global features. The r.m.s. D values for variations of the polypeptide backbone fold are on the order of 1.5-2 A for several of the studied proteins, indicating that the global structure is well determined by the present NMR data and their interpretation. The local structures are sometimes rather poor, with standard deviations for the backbone torsion angles of about 50 degrees. Possible improvements would be stereospecific resonance assignments of individual methylene protons and individual assignments of the methyl groups of the branched side-chains. Accurate estimates of the short-range NOE distance constraints by calibrating the distance constraints, including segmental flexibility effects, and combined use of distance geometry, energy minimization and molecular dynamics calculations, are further tools for improving the structures.     

4D prediction of protein <Superscript>1</Superscript>H chemical shifts

A 4D approach for protein ¹H chemical shift prediction was explored. The 4th dimension is the molecular flexibility, mapped using molecular dynamics simulations. The chemical shifts were predicted with a principal component model based on atom coordinates from a database of 40 protein structures. When compared to the corresponding non-dynamic (3D) model, the 4th dimension improved prediction by 6–7%. The prediction method achieved RMS errors of 0.29 and 0.50 ppm for Hα and HN shifts, respectively. However, for individual proteins the RMS errors were 0.17–0.34 and 0.34–0.65 ppm for the Hα and HN shifts, respectively. X-ray structures gave better predictions than the corresponding NMR structures, indicating that chemical shifts contain invaluable information about local structures. The ¹H chemical shift prediction tool 4DSPOT is available from .     

CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.     

Validation of NMR side-chain conformations by packing calculations

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

NMR of hydrogen bonding in cold-shock protein A and an analysis of the influence of crystallographic resolution on comparisons of hydrogen bond lengths

Hydrogen bonding in cold-shock protein A of Escherichia coli has been investigated using long-range HNCO spectroscopy. Nearly half of the amide protons involved in hydrogen bonds in solution show no measurable protection from exchange in water, cautioning against a direct correspondence between hydrogen bonding and hydrogen exchange protection. The N to O atom distance across a hydrogen bond, R(NO), is related to the size of the (3h)J(NC') trans hydrogen bond coupling constant and the amide proton chemical shift. Both NMR parameters show poorer agreement with the 2.0-A resolution X-ray structure of the cold-shock protein studied by NMR than with a 1.2-A resolution X-ray structure of a homologous cold-shock protein from the thermophile B. caldolyticus. The influence of crystallographic resolution on comparisons of hydrogen bond lengths was further investigated using a database of 33 X-ray structures of ribonuclease A. For highly similar structures, both hydrogen bond R(NO) distance and Calpha coordinate root mean square deviations (RMSD) show systematic increases as the resolution of the X-ray structure used for comparison decreases. As structures diverge, the effects of coordinate errors on R(NO) distance and Calpha coordinate root mean square deviations become progressively smaller. The results of this study are discussed with regard to the influence of data precision on establishing structure similarity relationships between proteins.     

Membrane Protein Structural Validation by Oriented Sample Solid-State NMR: Diacylglycerol Kinase

The validation of protein structures through functional assays has been the norm for many years. Functional assays perform this validation for water-soluble proteins very well, but they need to be performed in the same environment as that used for the structural analysis. This is difficult for membrane proteins that are often structurally characterized in detergent environments, although functional assays for these proteins are most frequently performed in lipid bilayers. Because the structure of membrane proteins is known to be sensitive to the membrane mimetic environment, such functional assays are appropriate for validating the protein construct, but not the membrane protein structure. Here, we compare oriented sample solid-state NMR spectral data of diacylglycerol kinase previously published with predictions of such data from recent structures of this protein. A solution NMR structure of diacylglycerol kinase has been obtained in detergent micelles and three crystal structures have been obtained in a monoolein cubic phase. All of the structures are trimeric with each monomer having three transmembrane and one amphipathic helices. However, the solution NMR structure shows typical perturbations induced by a micelle environment that is reflected in the predicted solid-state NMR resonances from the structural coordinates. The crystal structures show few such perturbations, especially for the wild-type structure and especially for the monomers that do not have significant crystal contacts. For these monomers the predicted and observed data are nearly identical. The thermostabilized constructs do show more perturbations, especially the A41C mutation that introduces a hydrophilic residue into what would be the middle of the lipid bilayer inducing additional hydrogen bonding between trimers. These results demonstrate a general technique for validating membrane protein structures with minimal data obtained from membrane proteins in liquid crystalline lipid bilayers by oriented sample solid-state NMR.     

A large data set comparison of protein structures determined by crystallography and NMR: statistical test for structural differences and the effect of crystal packing

The existence of a large number of proteins for which both nuclear magnetic resonance (NMR) and X-ray crystallographic coordinates have been deposited into the Protein Data Bank (PDB) makes the statistical comparison of the corresponding crystal and NMR structural models over a large data set possible, and facilitates the study of the effect of the crystal environment and other factors on structure. We present an approach for detecting statistically significant structural differences between crystal and NMR structural models which is based on structural superposition and the analysis of the distributions of atomic positions relative to a mean structure. We apply this to a set of 148 protein structure pairs (crystal vs NMR), and analyze the results in terms of methodological and physical sources of structural difference. For every one of the 148 structure pairs, the backbone root-mean-square distance (RMSD) over core atoms of the crystal structure to the mean NMR structure is larger than the average RMSD of the members of the NMR ensemble to the mean, with 76% of the structure pairs having an RMSD of the crystal structure to the mean more than a factor of two larger than the average RMSD of the NMR ensemble. On average, the backbone RMSD over core atoms of crystal structure to the mean NMR is approximately 1 A. If non-core atoms are included, this increases to 1.4 A due to the presence of variability in loops and similar regions of the protein. The observed structural differences are only weakly correlated with the age and quality of the structural model and differences in conditions under which the models were determined. We examine steric clashes when a putative crystalline lattice is constructed using a representative NMR structure, and find that repulsive crystal packing plays a minor role in the observed differences between crystal and NMR structures. The observed structural differences likely have a combination of physical and methodological causes. Stabilizing attractive interactions arising from intermolecular crystal contacts which shift the equilibrium of the crystal structure relative to the NMR structure is a likely physical source which can account for some of the observed differences. Methodological sources of apparent structural difference include insufficient sampling or other issues which could give rise to errors in the estimates of the precision and/or accuracy.     

NMR-pseudoenergy approach to the solution structure of acyl carrier protein

A method for protein structure determination from two-dimensional NMR cross-relaxation data is presented and explored by using short amino acid segments from acyl carrier protein as a test case. The method is based on a molecular mechanics program and incorporates NMR distance constraints in the form of a pseudoenergy term that accurately reflects the distance-dependent precision of NMR cross-relaxation data. When it is used in an indiscriminant fashion, the method has a tendency to produce structures representing local energy minima near starting structures, rather than structures representing a global energy minimum. However, stepwise inclusion of energy terms, beginning with a function heavily weighted by backbone distance constraints, appears to simplify the potential energy surface to a point where convergence to a common backbone structure from a variety of starting structures is possible. In the case of the segment from residues 3 to 15 in acyl carrier protein, a nearly perfect alpha-helix is produced starting with a linear chain, an alpha-helical chain, or a chain having residues with alternating linear and alpha-helical backbone torsional angles. In the case of the segment from residues 26 to 36 a structure having a right-handed loop is produced.     

Conjoined Use of EM and NMR in RNA Structure Refinement

More than 40% of the RNA structures have been determined using nuclear magnetic resonance (NMR) technique. NMR mainly provides local structural information of protons and works most effectively on relatively small biomacromolecules. Hence structural characterization of large RNAs can be difficult for NMR alone. Electron microscopy (EM) provides global shape information of macromolecules at nanometer resolution, which should be complementary to NMR for RNA structure determination. Here we developed a new energy term in Xplor-NIH against the density map obtained by EM. We conjointly used NMR and map restraints for the structure refinement of three RNA systems — U2/U6 small-nuclear RNA, genome-packing motif (Ψ^CD)₂ from Moloney murine leukemia virus, and ribosome-binding element from turnip crinkle virus. In all three systems, we showed that the incorporation of a map restraint, either experimental or generated from known PDB structure, greatly improves structural precision and accuracy. Importantly, our method does not rely on an initial model assembled from RNA duplexes, and allows full torsional freedom for each nucleotide in the torsion angle simulated annealing refinement. As increasing number of macromolecules can be characterized by both NMR and EM, the marriage between the two techniques would enable better characterization of RNA three-dimensional structures.     

GANA--a genetic algorithm for NMR backbone resonance assignment

NMR data from different experiments often contain errors; thus, automated backbone resonance assignment is a very challenging issue. In this paper, we present a method called GANA that uses a genetic algorithm to automatically perform backbone resonance assignment with a high degree of precision and recall. Precision is the number of correctly assigned residues divided by the number of assigned residues, and recall is the number of correctly assigned residues divided by the number of residues with known human curated answers. GANA takes spin systems as input data and uses two data structures, candidate lists and adjacency lists, to assign the spin systems to each amino acid of a target protein. Using GANA, almost all spin systems can be mapped correctly onto a target protein, even if the data are noisy. We use the BioMagResBank (BMRB) dataset (901 proteins) to test the performance of GANA. To evaluate the robustness of GANA, we generate four additional datasets from the BMRB dataset to simulate data errors of false positives, false negatives and linking errors. We also use a combination of these three error types to examine the fault tolerance of our method. The average precision rates of GANA on BMRB and the four simulated test cases are 99.61, 99.55, 99.34, 99.35 and 98.60%, respectively. The average recall rates of GANA on BMRB and the four simulated test cases are 99.26, 99.19, 98.85, 98.87 and 97.78%, respectively. We also test GANA on two real wet-lab datasets, hbSBD and hbLBD. The precision and recall rates of GANA on hbSBD are 95.12 and 92.86%, respectively, and those of hbLBD are 100 and 97.40%, respectively.     

Improving NMR protein structure quality by Rosetta refinement: a molecular replacement study

The structure of human protein HSPC034 has been determined by both solution nuclear magnetic resonance (NMR) spectroscopy and X-ray crystallography. Refinement of the NMR structure ensemble, using a Rosetta protocol in the absence of NMR restraints, resulted in significant improvements not only in structure quality, but also in molecular replacement (MR) performance with the raw X-ray diffraction data using MOLREP and Phaser. This method has recently been shown to be generally applicable with improved MR performance demonstrated for eight NMR structures refined using Rosetta (Qian et al., Nature 2007;450:259-264). Additionally, NMR structures of HSPC034 calculated by standard methods that include NMR restraints have improvements in the RMSD to the crystal structure and MR performance in the order DYANA, CYANA, XPLOR-NIH, and CNS with explicit water refinement (CNSw). Further Rosetta refinement of the CNSw structures, perhaps due to more thorough conformational sampling and/or a superior force field, was capable of finding alternative low energy protein conformations that were equally consistent with the NMR data according to the Recall, Precision, and F-measure (RPF) scores. On further examination, the additional MR-performance shortfall for NMR refined structures as compared with the X-ray structure were attributed, in part, to crystal-packing effects, real structural differences, and inferior hydrogen bonding in the NMR structures. A good correlation between a decrease in the number of buried unsatisfied hydrogen-bond donors and improved MR performance demonstrates the importance of hydrogen-bond terms in the force field for improving NMR structures. The superior hydrogen-bond network in Rosetta-refined structures demonstrates that correct identification of hydrogen bonds should be a critical goal of NMR structure refinement. Inclusion of nonbivalent hydrogen bonds identified from Rosetta structures as additional restraints in the structure calculation results in NMR structures with improved MR performance.     

TASSER-based refinement of NMR structures

The TASSER structure prediction algorithm is employed to investigate whether NMR structures can be moved closer to their corresponding X-ray counterparts by automatic refinement procedures. The benchmark protein dataset includes 61 nonhomologous proteins whose structures have been determined by both NMR and X-ray experiments. Interestingly, by starting from NMR structures, the majority (79%) of TASSER refined models show a structural shift toward their X-ray structures. On average, the TASSER refined models have a root-mean-square-deviation (RMSD) from the X-ray structure of 1.785 A (1.556 A) over the entire chain (aligned region), while the average RMSD between NMR and X-ray structures (RMSD(NMR_X-ray)) is 2.080 A (1.731 A). For all proteins having a RMSD(NMR_X-ray) >2 A, the TASSER refined structures show consistent improvement. However, for the 34 proteins with a RMSD(NMR_X-ray) <2 A, there are only 21 cases (60%) where the TASSER model is closer to the X-ray structure than NMR, which may be due to the inherent resolution of TASSER. We also compare the TASSER models with 12 NMR models in the RECOORD database that have been recalculated recently by Nederveen et al. from original NMR restraints using the newest molecular dynamics tools. In 8 of 12 cases, TASSER models show a smaller RMSD to X-ray structures; in 3 of 12 cases, where RMSD(NMR_X-ray) <1 A, RECOORD does better than TASSER. These results suggest that TASSER can be a useful tool to improve the quality of NMR structures.     

Accurate and automated classification of protein secondary structure with PsiCSI

PsiCSI is a highly accurate and automated method of assigning secondary structure from NMR data, which is a useful intermediate step in the determination of tertiary structures. The method combines information from chemical shifts and protein sequence using three layers of neural networks. Training and testing was performed on a suite of 92 proteins (9437 residues) with known secondary and tertiary structure. Using a stringent cross-validation procedure in which the target and homologous proteins were removed from the databases used for training the neural networks, an average 89% Q3 accuracy (per residue) was observed. This is an increase of 6.2% and 5.5% (representing 36% and 33% fewer errors) over methods that use chemical shifts (CSI) or sequence information (Psipred) alone. In addition, PsiCSI improves upon the translation of chemical shift information to secondary structure (Q3 = 87.4%) and is able to use sequence information as an effective substitute for sparse NMR data (Q3 = 86.9% without (13)C shifts and Q3 = 86.8% with only H(alpha) shifts available). Finally, errors made by PsiCSI almost exclusively involve the interchange of helix or strand with coil and not helix with strand (<2.5 occurrences per 10000 residues). The automation, increased accuracy, absence of gross errors, and robustness with regards to sparse data make PsiCSI ideal for high-throughput applications, and should improve the effectiveness of hybrid NMR/de novo structure determination methods. A Web server is available for users to submit data and have the assignment returned.