Assessing precision and accuracy of protein structures derived from NMR data

The accuracy of NMR protein structures in the Protein Data Bank

The program ANSURR measures the accuracy of NMR structures by comparing rigidity obtained from experimental backbone chemical shifts and from structures. We report on ANSURR analysis of 7,000 PDB NMR ensembles within the Protein Data Bank, which can be found at ansurr.com. The accuracy of NMR structures progressively improved up until 2005, but since then, it has plateaued. Most structures have accurate secondary structure, but are generally too floppy, particularly in loops. Thus, there is a need for more experimental restraints in loops. Currently, the best predictors of accuracy are Ramachandran distribution and the number of NOE restraints per residue. The precision of structures within the ensemble correlates well with accuracy, as does the number of hydrogen bond restraints per residue. Structure accuracy is improved when other components (such as additional polypeptide chains or ligands) are included.

A method for validating the accuracy of NMR protein structures

We present a method that measures the accuracy of NMR protein structures. It compares random coil index [RCI] against local rigidity predicted by mathematical rigidity theory, calculated from NMR structures [FIRST], using a correlation score (which assesses secondary structure), and an RMSD score (which measures overall rigidity). We test its performance using: structures refined in explicit solvent, which are much better than unrefined structures; decoy structures generated for 89 NMR structures; and conventional predictors of accuracy such as number of restraints per residue, restraint violations, energy of structure, ensemble RMSD, Ramachandran distribution, and clashscore. Restraint violations and RMSD are poor measures of accuracy. Comparisons of NMR to crystal structures show that secondary structure is equally accurate, but crystal structures are typically too rigid in loops, whereas NMR structures are typically too floppy overall. We show that the method is a useful addition to existing measures of accuracy.

In Silico Identification of Mimicking Molecules as Defense Inducers Triggering Jasmonic Acid Mediated Immunity against Alternaria Blight Disease in Brassica Species

Alternaria brassicae and Alternaria brassicicola are two major phytopathogenic fungi which cause Alternaria blight, a recalcitrant disease on Brassica crops throughout the world, which is highly destructive and responsible for significant yield losses. Since no resistant source is available against Alternaria blight, therefore, efforts have been made in the present study to identify defense inducer molecules which can induce jasmonic acid (JA) mediated defense against the disease. It is believed that JA triggered defense response will prevent necrotrophic mode of colonization of Alternaria brassicae fungus. The JA receptor, COI1 is one of the potential targets for triggering JA mediated immunity through interaction with JA signal. In the present study, few mimicking compounds more efficient than naturally occurring JA in terms of interaction with COI1 were identified through virtual screening and molecular dynamics simulation studies. A high quality structural model of COI1 was developed using the protein sequence of Brassica rapa. This was followed by virtual screening of 767 analogs of JA from ZINC database for interaction with COI1. Two analogs viz. ZINC27640214 and ZINC43772052 showed more binding affinity with COI1 as compared to naturally occurring JA. Molecular dynamics simulation of COI1 and COI1-JA complex, as well as best screened interacting structural analogs of JA with COI1 was done for 50 ns to validate the stability of system. It was found that ZINC27640214 possesses efficient, stable, and good cell permeability properties. Based on the obtained results and its physicochemical properties, it is capable of mimicking JA signaling and may be used as defense inducers for triggering JA mediated resistance against Alternaria blight, only after further validation through field trials.

Crystal structure of DPF3b in complex with an acetylated histone peptide

Histone acetylation plays an important role in chromatin dynamics and is associated with active gene transcription. This modification is written by acetyltransferases, erased by histone deacetylases and read out by bromodomain containing proteins, and others such as tandem PHD fingers of DPF3b. Here we report the high resolution crystal structure of the tandem PHD fingers of DPF3b in complex with an H3K14ac peptide. In the complex structure, the histone peptide adopts an α-helical conformation, unlike previously observed by NMR, but similar to a previously reported MOZ-H3K14ac complex structure. Our crystal structure adds to existing evidence that points to the α-helix as a natural conformation of histone tails as they interact with histone-associated proteins.

A community resource of experimental data for NMR / X-ray crystal structure pairs

We have developed an online NMR / X-ray Structure Pair Data Repository. The NIGMS Protein Structure Initiative (PSI) has provided many valuable reagents, 3D structures, and technologies for structural biology. The Northeast Structural Genomics Consortium was one of several PSI centers. NESG used both X-ray crystallography and NMR spectroscopy for protein structure determination. A key goal of the PSI was to provide experimental structures for at least one representative of each of hundreds of targeted protein domain families. In some cases, structures for identical (or nearly identical) constructs were determined by both NMR and X-ray crystallography. NMR spectroscopy and X-ray diffraction data for 41 of these "NMR / X-ray" structure pairs determined using conventional triple-resonance NMR methods with extensive sidechain resonance assignments have been organized in an online NMR / X-ray Structure Pair Data Repository. In addition, several NMR data sets for perdeuterated, methyl-protonated protein samples are included in this repository. As an example of the utility of this repository, these data were used to revisit questions about the precision and accuracy of protein NMR structures first outlined by Levy and coworkers several years ago (Andrec et al., Proteins 2007;69:449-465). These results demonstrate that the agreement between NMR and X-ray crystal structures is improved using modern methods of protein NMR spectroscopy. The NMR / X-ray Structure Pair Data Repository will provide a valuable resource for new computational NMR methods development.

NMR data-driven structure determination using NMR-I-TASSER in the CASD-NMR experiment

NMR-I-TASSER, an adaption of the I-TASSER algorithm combining NMR data for protein structure determination, recently joined the second round of the CASD-NMR experiment. Unlike many molecular dynamics-based methods, NMR-I-TASSER takes a molecular replacement-like approach to the problem by first threading the target through the PDB to identify structural templates which are then used for iterative NOE assignments and fragment structure assembly refinements. The employment of multiple templates allows NMR-I-TASSER to sample different topologies while convergence to a single structure is not required. Retroactive and blind tests of the CASD-NMR targets from Rounds 1 and 2 demonstrate that even without using NOE peak lists I-TASSER can generate correct structure topology with 15 of 20 targets having a TM-score above 0.5. With the addition of NOE-based distance restraints, NMR-I-TASSER significantly improved the I-TASSER models with all models having the TM-score above 0.5. The average RMSD was reduced from 5.29 to 2.14 Å in Round 1 and 3.18 to 1.71 Å in Round 2. There is no obvious difference in the modeling results with using raw and refined peak lists, indicating robustness of the pipeline to the NOE assignment errors. Overall, despite the low-resolution modeling the current NMR-I-TASSER pipeline provides a coarse-grained structure folding approach complementary to traditional molecular dynamics simulations, which can produce fast near-native frameworks for atomic-level structural refinement.

Outcome of the First wwPDB Hybrid/Integrative Methods Task Force Workshop

Structures of biomolecular systems are increasingly computed by integrative modeling that relies on varied types of experimental data and theoretical information. We describe here the proceedings and conclusions from the first wwPDB Hybrid/Integrative Methods Task Force Workshop held at the European Bioinformatics Institute in Hinxton, UK, on October 6 and 7, 2014. At the workshop, experts in various experimental fields of structural biology, experts in integrative modeling and visualization, and experts in data archiving addressed a series of questions central to the future of structural biology. How should integrative models be represented? How should the data and integrative models be validated? What data should be archived? How should the data and models be archived? What information should accompany the publication of integrative models?

NMR structure validation in relation to dynamics and structure determination

NMR spectroscopy is a key technique for understanding the behaviour of proteins, especially highly dynamic proteins that adopt multiple conformations in solution. Overall, protein structures determined from NMR spectroscopy data constitute just over 10% of the Protein Data Bank archive. This review covers the validation of these NMR protein structures, but rather than describing currently available methodology, it focuses on concepts that are important for understanding where and how validation is most relevant. First, the inherent characteristics of the protein under study have an influence on quality and quantity of the distinct types of data that can be acquired from NMR experiments. Second, these NMR data are necessarily transformed into a model for use in a structure calculation protocol, and the protein structures that result from this reflect the types of NMR data used as well as the protein characteristics. The validation of NMR protein structures should therefore take account, wherever possible, of the inherent behavioural characteristics of the protein, the types of available NMR data, and the calculation protocol. These concepts are discussed in the context of 'knowledge based' and 'model versus data' validation, with suggestions for questions to ask and different validation categories to consider. The principal aim of this review is to stimulate discussion and to help the reader understand the relationships between the above elements in order to make informed decisions on which validation approaches are the most relevant in particular cases.

Protein NMR structures refined with Rosetta have higher accuracy relative to corresponding X-ray crystal structures

We have found that refinement of protein NMR structures using Rosetta with experimental NMR restraints yields more accurate protein NMR structures than those that have been deposited in the PDB using standard refinement protocols. Using 40 pairs of NMR and X-ray crystal structures determined by the Northeast Structural Genomics Consortium, for proteins ranging in size from 5-22 kDa, restrained Rosetta refined structures fit better to the raw experimental data, are in better agreement with their X-ray counterparts, and have better phasing power compared to conventionally determined NMR structures. For 37 proteins for which NMR ensembles were available and which had similar structures in solution and in the crystal, all of the restrained Rosetta refined NMR structures were sufficiently accurate to be used for solving the corresponding X-ray crystal structures by molecular replacement. The protocol for restrained refinement of protein NMR structures was also compared with restrained CS-Rosetta calculations. For proteins smaller than 10 kDa, restrained CS-Rosetta, starting from extended conformations, provides slightly more accurate structures, while for proteins in the size range of 10-25 kDa the less CPU intensive restrained Rosetta refinement protocols provided equally or more accurate structures. The restrained Rosetta protocols described here can improve the accuracy of protein NMR structures and should find broad and general for studies of protein structure and function.

Definition and classification of evaluation units for CASP10

For the 10th experiment on Critical Assessment of the techniques of protein Structure Prediction (CASP), the prediction target proteins were broken into independent evaluation units (EUs), which were then classified into template-based modeling (TBM) or free modeling (FM) categories. We describe here how the EUs were defined and classified, what issues arose in the process, and how we resolved them. EUs are frequently not the whole target proteins but the constituting structural domains. However, the assessors from CASP7 on combined more than one domain into 1 EU for some targets, which implied that the assessment also included evaluation of the prediction of the relative position and orientation of these domains. In CASP10, we followed and expanded this notion by defining multidomain EUs for a number of targets. These included 3 EUs, each made of two domains of familiar fold but arranged in a novel manner and for which the focus of evaluation was the interdomain arrangement. An EU was classified to the TBM category if a template could be found by sequence similarity searches and to FM if a structural template could not be found by structural similarity searches. The EUs that did not fall cleanly in either of these cases were classified case-by-case, often including consideration of the overall quality and characteristics of the predictions.

Recommendations of the wwPDB NMR Validation Task Force

As methods for analysis of biomolecular structure and dynamics using nuclear magnetic resonance spectroscopy (NMR) continue to advance, the resulting 3D structures, chemical shifts, and other NMR data are broadly impacting biology, chemistry, and medicine. Structure model assessment is a critical area of NMR methods development, and is an essential component of the process of making these structures accessible and useful to the wider scientific community. For these reasons, the Worldwide Protein Data Bank (wwPDB) has convened an NMR Validation Task Force (NMR-VTF) to work with wwPDB partners in developing metrics and policies for biomolecular NMR data harvesting, structure representation, and structure quality assessment. This paper summarizes the recommendations of the NMR-VTF, and lays the groundwork for future work in developing standards and metrics for biomolecular NMR structure quality assessment.

MOTOR: model assisted software for NMR structure determination

Eukaryotic proteins with important biological function can be partially unstructured, conformational flexible, or heterogenic. Crystallization trials often fail for such proteins. In NMR spectroscopy, parts of the polypeptide chain undergoing dynamics in unfavorable time regimes cannot be observed. De novo NMR structure determination is seriously hampered when missing signals lead to an incomplete chemical shift assignment resulting in an information content of the NOE data insufficient to determine the structure ab initio. We developed a new protein structure determination strategy for such cases based on a novel NOE assignment strategy utilizing a number of model structures but no explicit reference structure as it is used for bootstrapping like algorithms. The software distinguishes in detail between consistent and mutually exclusive pairs of possible NOE assignments on the basis of different precision levels of measured chemical shifts searching for a set of maximum number of consistent NOE assignments in agreement with 3D space. Validation of the method using the structure of the low molecular-weight-protein tyrosine phosphatase A (MptpA) showed robust results utilizing protein structures with 30-45% sequence identity and 70% of the chemical shift assignments. About 60% of the resonance assignments are sufficient to identify those structural models with highest conformational similarity to the real structure. The software was benchmarked by de novo solution structures of fibroblast growth factor 21 (FGF21) and the extracellular fibroblast growth factor receptor domain FGFR4 D2, which both failed in crystallization trials and in classical NMR structure determination.

Solution NMR refinement of a metal ion bound protein using metal ion inclusive restrained molecular dynamics methods

Correctly calculating the structure of metal coordination sites in a protein during the process of nuclear magnetic resonance (NMR) structure determination and refinement continues to be a challenging task. In this study, we present an accurate and convenient means by which to include metal ions in the NMR structure determination process using molecular dynamics (MD) simulations constrained by NMR-derived data to obtain a realistic and physically viable description of the metal binding site(s). This method provides the framework to accurately portray the metal ions and its binding residues in a pseudo-bond or dummy-cation like approach, and is validated by quantum mechanical/molecular mechanical (QM/MM) MD calculations constrained by NMR-derived data. To illustrate this approach, we refine the zinc coordination complex structure of the zinc sensing transcriptional repressor protein Staphylococcus aureus CzrA, generating over 130 ns of MD and QM/MM MD NMR-data compliant sampling. In addition to refining the first coordination shell structure of the Zn(II) ion, this protocol benefits from being performed in a periodically replicated solvation environment including long-range electrostatics. We determine that unrestrained (not based on NMR data) MD simulations correlated to the NMR data in a time-averaged ensemble. The accurate solution structure ensemble of the metal-bound protein accurately describes the role of conformational sampling in allosteric regulation of DNA binding by zinc and serves to validate our previous unrestrained MD simulations of CzrA. This methodology has potentially broad applicability in the structure determination of metal ion bound proteins, protein folding and metal template protein-design studies.

CING: an integrated residue-based structure validation program suite

We present a suite of programs, named CING for Common Interface for NMR Structure Generation that provides for a residue-based, integrated validation of the structural NMR ensemble in conjunction with the experimental restraints and other input data. External validation programs and new internal validation routines compare the NMR-derived models with empirical data, measured chemical shifts, distance- and dihedral restraints and the results are visualized in a dynamic Web 2.0 report. A red-orange-green score is used for residues and restraints to direct the user to those critiques that warrant further investigation. Overall green scores below ~20 % accompanied by red scores over ~50 % are strongly indicative of poorly modelled structures. The publically accessible, secure iCing webserver ( https://nmr.le.ac.uk ) allows individual users to upload the NMR data and run a CING validation analysis.

Accurate protein structure modeling using sparse NMR data and homologous structure information

While information from homologous structures plays a central role in X-ray structure determination by molecular replacement, such information is rarely used in NMR structure determination because it can be incorrect, both locally and globally, when evolutionary relationships are inferred incorrectly or there has been considerable evolutionary structural divergence. Here we describe a method that allows robust modeling of protein structures of up to 225 residues by combining (1)H(N), (13)C, and (15)N backbone and (13)Cβ chemical shift data, distance restraints derived from homologous structures, and a physically realistic all-atom energy function. Accurate models are distinguished from inaccurate models generated using incorrect sequence alignments by requiring that (i) the all-atom energies of models generated using the restraints are lower than models generated in unrestrained calculations and (ii) the low-energy structures converge to within 2.0 Å backbone rmsd over 75% of the protein. Benchmark calculations on known structures and blind targets show that the method can accurately model protein structures, even with very remote homology information, to a backbone rmsd of 1.2-1.9 Å relative to the conventional determined NMR ensembles and of 0.9-1.6 Å relative to X-ray structures for well-defined regions of the protein structures. This approach facilitates the accurate modeling of protein structures using backbone chemical shift data without need for side-chain resonance assignments and extensive analysis of NOESY cross-peak assignments.

Protein structure validation by generalized linear model root-mean-square deviation prediction

Large-scale initiatives for obtaining spatial protein structures by experimental or computational means have accentuated the need for the critical assessment of protein structure determination and prediction methods. These include blind test projects such as the critical assessment of protein structure prediction (CASP) and the critical assessment of protein structure determination by nuclear magnetic resonance (CASD-NMR). An important aim is to establish structure validation criteria that can reliably assess the accuracy of a new protein structure. Various quality measures derived from the coordinates have been proposed. A universal structural quality assessment method should combine multiple individual scores in a meaningful way, which is challenging because of their different measurement units. Here, we present a method based on a generalized linear model (GLM) that combines diverse protein structure quality scores into a single quantity with intuitive meaning, namely the predicted coordinate root-mean-square deviation (RMSD) value between the present structure and the (unavailable) "true" structure (GLM-RMSD). For two sets of structural models from the CASD-NMR and CASP projects, this GLM-RMSD value was compared with the actual accuracy given by the RMSD value to the corresponding, experimentally determined reference structure from the Protein Data Bank (PDB). The correlation coefficients between actual (model vs. reference from PDB) and predicted (model vs. "true") heavy-atom RMSDs were 0.69 and 0.76, for the two datasets from CASD-NMR and CASP, respectively, which is considerably higher than those for the individual scores (-0.24 to 0.68). The GLM-RMSD can thus predict the accuracy of protein structures more reliably than individual coordinate-based quality scores.

Solving a generalized distance geometry problem for protein structure determination

We propose a new approach to the problem of determining an ensemble of protein structures with a set of interatomic distance bounds in NMR protein modeling. Similarly to X-ray crystallography, we assume that the protein has an equilibrium structure and the atoms fluctuate around their equilibrium positions. Then, the problem can be formulated as a generalized distance geometry problem, to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling.

Advances in automated NMR protein structure determination

Around half of all protein structures solved nowadays using solution-state nuclear magnetic resonance (NMR) spectroscopy have been because of automated data analysis. The pervasiveness of computational approaches in general hides, however, a more nuanced view in which the full variety and richness of the field appears. This review is structured around a comparison of methods associated with three NMR observables: classical nuclear Overhauser effect (NOE) constraint gathering in contrast with more recent chemical shift and residual dipole coupling (RDC) based protocols. In each case, the emphasis is placed on the latest research, covering mainly the past 5 years. By describing both general concepts and representative programs, the objective is to map out a field in which--through the very profusion of approaches--it is all too easy to lose one's bearings.

NMR Constraints Analyser: a web-server for the graphical analysis of NMR experimental constraints

Nuclear magnetic resonance (NMR) spectroscopy together with X-ray crystallography, are the main techniques used for the determination of high-resolution 3D structures of biological molecules. The output of an NMR experiment includes a set of lower and upper limits for the distances (constraints) between pairs of atoms. If the number of constraints is high enough, there will be a finite number of possible conformations (models) of the macromolecule satisfying the data. Thus, the more constraints are measured, the better defined these structures will be. The availability of a user-friendly tool able to help in the analysis and interpretation of the number of experimental constraints per residue, is thus of valuable importance when assessing the levels of structure definition of NMR solved biological macromolecules, in particular, when high-quality structures are needed in techniques such as, computational biology approaches, site-directed mutagenesis experiments and/or drug design. Here, we present a free publicly available web-server, i.e. NMR Constraints Analyser, which is aimed at providing an automatic graphical analysis of the NMR experimental constraints atom by atom. The NMR Constraints Analyser server is available from the web-page http://molsim.sci.univr.it/constraint.

Protein flexibility: coordinate uncertainties and interpretation of structural differences

Valid interpretations of conformational movements in protein structures determined by X-ray crystallography require that the movement magnitudes exceed their uncertainty threshold. Here, it is shown that such thresholds can be obtained from the distance difference matrices (DDMs) of 1014 pairs of independently determined structures of bovine ribonuclease A and sperm whale myoglobin, with no explanations provided for reportedly minor coordinate differences. The smallest magnitudes of reportedly functional motions are just above these thresholds. Uncertainty thresholds can provide objective criteria that distinguish between true conformational changes and apparent 'noise', showing that some previous interpretations of protein coordinate changes attributed to external conditions or mutations may be doubtful or erroneous. The use of uncertainty thresholds, DDMs, the newly introduced CDDMs (contact distance difference matrices) and a novel simple rotation algorithm allows a more meaningful classification and description of protein motions, distinguishing between various rigid-fragment motions and nonrigid conformational deformations. It is also shown that half of 75 pairs of identical molecules, each from the same asymmetric crystallographic cell, exhibit coordinate differences that range from just outside the coordinate uncertainty threshold to the full magnitude of large functional movements. Thus, crystallization might often induce protein conformational changes that are comparable to those related to or induced by the protein function.

Assessing the accuracy of protein structures by quantum mechanical computations of 13C(alpha) chemical shifts

Two major techniques have been used to determine the three-dimensional structures of proteins: X-ray diffraction and NMR spectroscopy. In particular, the validation of NMR-derived protein structures is one of the most challenging problems in NMR spectroscopy. Therefore, researchers have proposed a plethora of methods to determine the accuracy and reliability of protein structures. Despite these proposals, there is a growing need for more sophisticated, physics-based structure validation methods. This approach will enable us to (a) characterize the "quality" of the NMR-derived ensemble as a whole by a single parameter, (b) unambiguously identify flaws in the sequence at a residue level, and (c) provide precise information, such as sets of backbone and side-chain torsional angles, that we can use to detect local flaws. Rather than reviewing all of the existing validation methods, this Account describes the contributions of our research group toward a solution of the long-standing problem of both global and local structure validation of NMR-derived protein structures. We emphasize a recently introduced physics-based methodology that makes use of observed and computed (13)C(alpha) chemical shifts (at the density functional theory (DFT) level of theory) for an accurate validation of protein structures in solution and in crystals. By assessing the ability of computed (13)C(alpha) chemical shifts to reproduce observed (13)C(alpha) chemical shifts of a single structure or ensemble of structures in solution and in crystals, we accomplish a global validation by using the conformationally averaged root-mean-square deviation, ca-rmsd, as a scoring function. In addition, the method enables us to provide local validation by identifying a set of individual amino acid conformations for which the computed and observed (13)C(alpha) chemical shifts do not agree within a certain error range and may represent a nonreliable fold of the protein model. Although it is computationally intensive, our validation method has several advantages, which we illustrate through a series of applications. This method makes use of the (13)C(alpha) chemical shifts, not shielding, that are ubiquitous to proteins and can be computed precisely from the phi, psi, and chi torsional angles. There is no need for a priori knowledge of the oligomeric state of the protein, and no knowledge-based information or additional NMR data are required. The primary limitation at this point is the computational cost of such calculations. However, we anticipate that enhancements in the speed of calculating these chemical shifts coupled with the ever-increasing computational power should soon make this a standard method accessible to the general NMR community.

Automated protein structure calculation from NMR data

Current software is almost at the stage to permit completely automatic structure determination of small proteins of <15 kDa, from NMR spectra to structure validation with minimal user interaction. This goal is welcome, as it makes structure calculation more objective and therefore more easily validated, without any loss in the quality of the structures generated. Moreover, it releases expert spectroscopists to carry out research that cannot be automated. It should not take much further effort to extend automation to ca 20 kDa. However, there are technological barriers to further automation, of which the biggest are identified as: routines for peak picking; adoption and sharing of a common framework for structure calculation, including the assembly of an automated and trusted package for structure validation; and sample preparation, particularly for larger proteins. These barriers should be the main target for development of methodology for protein structure determination, particularly by structural genomics consortia.

Distance matrix-based approach to protein structure prediction

Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r(ij)(2)] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r (ij) is greater or less than a cutoff value r (cutoff). We have performed spectral decomposition of the distance matrices D = sigma lambda(k)V(k)V(kT), in terms of eigenvalues lambda kappa and the corresponding eigenvectors v kappa and found that it contains at most five nonzero terms. A dominant eigenvector is proportional to r (2)--the square distance of points from the center of mass, with the next three being the principal components of the system of points. By predicting r (2) from the sequence we can approximate a distance matrix of a protein with an expected RMSD value of about 7.3 A, and by combining it with the prediction of the first principal component we can improve this approximation to 4.0 A. We can also explain the role of hydrophobic interactions for the protein structure, because r is highly correlated with the hydrophobic profile of the sequence. Moreover, r is highly correlated with several sequence profiles which are useful in protein structure prediction, such as contact number, the residue-wise contact order (RWCO) or mean square fluctuations (i.e. crystallographic temperature factors). We have also shown that the next three components are related to spatial directionality of the secondary structure elements, and they may be also predicted from the sequence, improving overall structure prediction. We have also shown that the large number of available HIV-1 protease structures provides a remarkable sampling of conformations, which can be viewed as direct structural information about the dynamics. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM) that is based on the contact matrix C (related to D), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to atomic molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide a similar sampling of conformations. Finally, we use distance constraints from databases of known protein structures for structure refinement. We use the distributions of distances of various types in known protein structures to obtain the most probable ranges or the mean-force potentials for the distances. We then impose these constraints on structures to be refined or include the mean-force potentials directly in the energy minimization so that more plausible structural models can be built. This approach has been successfully used by us in 2006 in the CASPR structure refinement (http://predictioncenter.org/caspR).

Neural networks predict protein structure and function

Both supervised and unsupervised neural networks have been applied to the prediction of protein structure and function. Here, we focus on feedforward neural networks and describe how these learning machines can be applied to protein prediction. We discuss how to select an appropriate data set, how to choose and encode protein features into the neural network input, and how to assess the predictor's performance.

Mixture models for protein structure ensembles

MOTIVATION

Protein structure ensembles provide important insight into the dynamics and function of a protein and contain information that is not captured with a single static structure. However, it is not clear a priori to what extent the variability within an ensemble is caused by internal structural changes. Additional variability results from overall translations and rotations of the molecule. And most experimental data do not provide information to relate the structures to a common reference frame. To report meaningful values of intrinsic dynamics, structural precision, conformational entropy, etc., it is therefore important to disentangle local from global conformational heterogeneity.

RESULTS

We consider the task of disentangling local from global heterogeneity as an inference problem. We use probabilistic methods to infer from the protein ensemble missing information on reference frames and stable conformational sub-states. To this end, we model a protein ensemble as a mixture of Gaussian probability distributions of either entire conformations or structural segments. We learn these models from a protein ensemble using the expectation-maximization algorithm. Our first model can be used to find multiple conformers in a structure ensemble. The second model partitions the protein chain into locally stable structural segments or core elements and less structured regions typically found in loops. Both models are simple to implement and contain only a single free parameter: the number of conformers or structural segments. Our models can be used to analyse experimental ensembles, molecular dynamics trajectories and conformational change in proteins.

AVAILABILITY

The Python source code for protein ensemble analysis is available from the authors upon request.

Knowledge-based versus experimentally acquired distance and angle constraints for NMR structure refinement

Nuclear Overhauser effects (NOE) distance constraints and torsion angle constraints are major conformational constraints for nuclear magnetic resonance (NMR) structure refinement. In particular, the number of NOE constraints has been considered as an important determinant for the quality of NMR structures. Of course, the availability of torsion angle constraints is also critical for the formation of correct local conformations. In our recent work, we have shown how a set of knowledge-based short-range distance constraints can also be utilized for NMR structure refinement, as a complementary set of conformational constraints to the NOE and torsion angle constraints. In this paper, we show the results from a series of structure refinement experiments by using different types of conformational constraints--NOE, torsion angle, or knowledge-based constraints--or their combinations, and make a quantitative assessment on how the experimentally acquired constraints contribute to the quality of structural models and whether or not they can be combined with or substituted by the knowledge-based constraints. We have carried out the experiments on a small set of NMR structures. Our preliminary calculations have revealed that the torsion angle constraints contribute substantially to the quality of the structures, but require to be combined with the NOE constraints to be fully effective. The knowledge-based constraints can be functionally as crucial as the torsion angle constraints, although they are statistical constraints after all and are not meant to be able to replace the latter.

Comparison of multiple crystal structures with NMR data for engrailed homeodomain

Two methods are currently available to solve high resolution protein structures-X-ray crystallography and nuclear magnetic resonance (NMR). Both methods usually produce highly similar structures, but small differences between both solutions are always observed. Here the raw NMR data as well as the solved NMR structure were compared to the multiple crystal structures solved for the WT 60 residue three helix bundle engrailed homeodomain (EnHD) and single point mutants. There was excellent agreement between TALOS-predicted and crystal structure-observed dihedral angles and a good agreement for the (3) J(H ( N ) H ( alpha )) couplings for the multiple crystal structures. Around 1% of NOEs were violated for any crystal structure, but no NOE was inconsistent with all of the crystal structures. Violations usually occurred for surface residues or for residues for which multiple discreet conformations were observed between the crystal structures. Comparison of the disorder shown in the multiple crystal structures shows little correlation with dynamics under native conditions for this protein.

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 and X-ray analysis of structural additivity in metal binding site-swapped hybrids of rubredoxin

Background

Chimeric hybrids derived from the rubredoxins of Pyrococcus furiosus (Pf) and Clostridium pasteurianum (Cp) provide a robust system for the characterization of protein conformational stability and dynamics in a differential mode. Interchange of the seven nonconserved residues of the metal binding site between the Pf and Cp rubredoxins yields a complementary pair of hybrids, for which the sum of the thermodynamic stabilities is equal to the sum for the parental proteins. Furthermore, the increase in amide hydrogen exchange rates for the hyperthermophile-derived metal binding site hybrid is faithfully mirrored by a corresponding decrease for the complementary hybrid that is derived from the less thermostable rubredoxin, indicating a degree of additivity in the conformational fluctuations that underlie these exchange reactions.

Results

Initial NMR studies indicated that the structures of the two complementary hybrids closely resemble "cut-and-paste" models derived from the parental Pf and Cp rubredoxins. This protein system offers a robust opportunity to characterize differences in solution structure, permitting the quantitative NMR chemical shift and NOE peak intensity data to be analyzed without recourse to the conventional conversion of experimental NOE peak intensities into distance restraints. The intensities for 1573 of the 1652 well-resolved NOE crosspeaks from the hybrid rubredoxins were statistically indistinguishable from the intensities of the corresponding parental crosspeaks, to within the baseplane noise level of these high sensitivity data sets. The differences in intensity for the remaining 79 NOE crosspeaks were directly ascribable to localized dynamical processes. Subsequent X-ray analysis of the metal binding site-swapped hybrids, to resolution limits of 0.79 Å and 1.04 Å, demonstrated that the backbone and sidechain heavy atoms in the NMR-derived structures lie within the range of structural variability exhibited among the individual molecules in the crystallographic asymmetric unit (~0.3 Å), indicating consistency with the "cut-and-paste" structuring of the hybrid rubredoxins in both crystal and solution.

Conclusion

Each of the significant energetic interactions in the metal binding site-swapped hybrids appears to exhibit a 1-to-1 correspondence with the interactions present in the corresponding parental rubredoxin structure, thus providing a structural basis for the observed additivity in conformational stability and dynamics. The congruence of these X-ray and NMR experimental data offers additional support for the interpretation that the conventional treatment of NOE distance restraints contributes substantially to the systematic differences that are commonly reported between NMR- and X-ray-derived protein structures.

Prediction of protein loop geometries in solution

The ability to determine the structure of a protein in solution is a critical tool for structural biology, as proteins in their native state are found in aqueous environments. Using a physical chemistry based prediction protocol, we demonstrate the ability to reproduce protein loop geometries in experimentally derived solution structures. Predictions were run on loops drawn from (1)NMR entries in the Protein Databank (PDB), and from (2) the RECOORD database in which NMR entries from the PDB have been standardized and re-refined in explicit solvent. The predicted structures are validated by comparison with experimental distance restraints, a test of structural quality as defined by the WHAT IF structure validation program, root mean square deviation (RMSD) of the predicted loops to the original structural models, and comparison of precision of the original and predicted ensembles. Results show that for the RECOORD ensembles, the predicted loops are consistent with an average of 95%, 91%, and 87% of experimental restraints for the short, medium and long loops respectively. Prediction accuracy is strongly affected by the quality of the original models, with increases in the percentage of experimental restraints violated of 2% for the short loops, and 9% for both the medium and long loops in the PDB derived ensembles. We anticipate the application of our protocol to theoretical modeling of protein structures, such as fold recognition methods; as well as to experimental determination of protein structures, or segments, for which only sparse NMR restraint data is available.

Outer membrane proteins: comparing X-ray and NMR structures by MD simulations in lipid bilayers

The structures of three bacterial outer membrane proteins (OmpA, OmpX and PagP) have been determined by both X-ray diffraction and NMR. We have used multiple (7 x 15 ns) MD simulations to compare the conformational dynamics resulting from the X-ray versus the NMR structures, each protein being simulated in a lipid (DMPC) bilayer. Conformational drift was assessed via calculation of the root mean square deviation as a function of time. On this basis the 'quality' of the starting structure seems mainly to influence the simulation stability of the transmembrane beta-barrel domain. Root mean square fluctuations were used to compare simulation mobility as a function of residue number. The resultant residue mobility profiles were qualitatively similar for the corresponding X-ray and NMR structure-based simulations. However, all three proteins were generally more mobile in the NMR-based than in the X-ray simulations. Principal components analysis was used to identify the dominant motions within each simulation. The first two eigenvectors (which account for >50% of the protein motion) reveal that such motions are concentrated in the extracellular loops and, in the case of PagP, in the N-terminal alpha-helix. Residue profiles of the magnitude of motions corresponding to the first two eigenvectors are similar for the corresponding X-ray and NMR simulations, but the directions of these motions correlate poorly reflecting incomplete sampling on a approximately 10 ns timescale.

Evaluating protein structures determined by structural genomics consortia

Structural genomics projects are providing large quantities of new 3D structural data for proteins. To monitor the quality of these data, we have developed the protein structure validation software suite (PSVS), for assessment of protein structures generated by NMR or X-ray crystallographic methods. PSVS is broadly applicable for structure quality assessment in structural biology projects. The software integrates under a single interface analyses from several widely-used structure quality evaluation tools, including PROCHECK (Laskowski et al., J Appl Crystallog 1993;26:283-291), MolProbity (Lovell et al., Proteins 2003;50:437-450), Verify3D (Luthy et al., Nature 1992;356:83-85), ProsaII (Sippl, Proteins 1993;17: 355-362), the PDB validation software, and various structure-validation tools developed in our own laboratory. PSVS provides standard constraint analyses, statistics on goodness-of-fit between structures and experimental data, and knowledge-based structure quality scores in standardized format suitable for database integration. The analysis provides both global and site-specific measures of protein structure quality. Global quality measures are reported as Z scores, based on calibration with a set of high-resolution X-ray crystal structures. PSVS is particularly useful in assessing protein structures determined by NMR methods, but is also valuable for assessing X-ray crystal structures or homology models. Using these tools, we assessed protein structures generated by the Northeast Structural Genomics Consortium and other international structural genomics projects, over a 5-year period. Protein structures produced from structural genomics projects exhibit quality score distributions similar to those of structures produced in traditional structural biology projects during the same time period. However, while some NMR structures have structure quality scores similar to those seen in higher-resolution X-ray crystal structures, the majority of NMR structures have lower scores. Potential reasons for this "structure quality score gap" between NMR and X-ray crystal structures are discussed.

NMR structure and binding studies confirm that PA4608 from Pseudomonas aeruginosa is a PilZ domain and a c-di-GMP binding protein

PA4608 is a 125 residue protein from Pseudomonas aeruginosa with a recent identification as a PilZ domain and putative bis-(3'-5')-cyclic dimeric guanosine monophosphate (c-di-GMP) adaptor protein that plays a role in bacterial second-messenger regulated processes. The nuclear magnetic resonance (NMR) structure of PA4608 has been determined and c-di-GMP binding has been confirmed by NMR titration studies. The monomeric core structure of PA4608 contains a six-stranded anti-parallel beta barrel flanked by three helices. Conserved surface residues among PA4608 homologs suggest the c-di-GMP binding site is at one end of the barrel and includes residues in the helices as well as in the unstructured N-terminus. Chemical shift changes in PA4608 resonances upon titration with c-di-GMP confirm binding. This evidence supports the hypothesis that proteins containing PilZ domains are the long-sought c-di-GMP adaptor proteins.

Chemically accurate protein structures: validation of protein NMR structures by comparison of measured and predicted pKa values

A new method is presented for evaluating the quality of protein structures obtained by NMR. This method exploits the dependence between measurable chemical properties of a protein, namely pKa values of acidic residues, and protein structure. The accurate and fast empirical computational method employed by the PROPKA program ( http://www.propka.chem.uiowa.edu) allows the user to test the ability of a given structure to reproduce known pKa values, which in turn can be used as a criterion for the selection of more accurate structures. We demonstrate the feasibility of this novel idea for a series of proteins for which both NMR and X-ray structures, as well as pKa values of all ionizable residues, have been determined. For the 17 NMR ensembles used in this study, this criterion is shown effective in the elimination of a large number of NMR structure ensemble members.

Traditional biomolecular structure determination by NMR spectroscopy allows for major errors

One of the major goals of structural genomics projects is to determine the three-dimensional structure of representative members of as many different fold families as possible. Comparative modeling is expected to fill the remaining gaps by providing structural models of homologs of the experimentally determined proteins. However, for such an approach to be successful it is essential that the quality of the experimentally determined structures is adequate. In an attempt to build a homology model for the protein dynein light chain 2A (DLC2A) we found two potential templates, both experimentally determined nuclear magnetic resonance (NMR) structures originating from structural genomics efforts. Despite their high sequence identity (96%), the folds of the two structures are markedly different. This urged us to perform in-depth analyses of both structure ensembles and the deposited experimental data, the results of which clearly identify one of the two models as largely incorrect. Next, we analyzed the quality of a large set of recent NMR-derived structure ensembles originating from both structural genomics projects and individual structure determination groups. Unfortunately, a visual inspection of structures exhibiting lower quality scores than DLC2A reveals that the seriously flawed DLC2A structure is not an isolated incident. Overall, our results illustrate that the quality of NMR structures cannot be reliably evaluated using only traditional experimental input data and overall quality indicators as a reference and clearly demonstrate the urgent need for a tight integration of more sophisticated structure validation tools in NMR structure determination projects. In contrast to common methodologies where structures are typically evaluated as a whole, such tools should preferentially operate on a per-residue basis.

Three-dimensional biomolecular structures provide an invaluable source of biologically relevant information. To be able to learn the most of the wealth of information that these structures can provide us, it is of great importance that the quality and accuracy of the protein structure models deposited in the Protein Data Bank are as high as possible. In this work, the authors describe an analysis that illustrates that this is unfortunately not the case for many protein structures solved using nuclear magnetic resonance spectroscopy. They present an example in which two strikingly different models describing the same protein are analyzed using commonly available structure validation tools, and the results of this analysis show one of the two models to be incorrect. Subsequently, using a large set of recently determined structures, the authors demonstrate that unfortunately this example does not stand on its own. The analyses and examples clearly illustrate that relying solely on the experimental data to evaluate structural quality can provide a false sense of correctness and the combination of multiple sophisticated structure validation tools is required to detect the presence of errors in protein nuclear magnetic resonance structures.

Definition of a new information-based per-residue quality parameter

For biomolecular NMR structures typically only a poor correspondence is observed between statistics derived from the experimental input data and structural quality indicators obtained from the structure ensembles. Here, we investigate the relationship between the amount of available NMR data and structure quality. By generating datasets with a predetermined information content and evaluating the quality of the resulting structure ensembles we show that there is, in contrast to previous findings, a linear relation between the information contained in experimental data and structural quality. From this relation, a new quality parameter is derived that provides direct insight, on a per-residue basis, into the extent to which structural quality is governed by the experimental input data.