Universal similarity measure for comparing protein structures

We introduce a new variant of the root mean square distance (RMSD) for comparing protein structures whose range of values is independent of protein size. This new dimensionless measure (relative RMSD, or RRMSD) is zero between identical structures and one between structures that are as globally dissimilar as an average pair of random polypeptides of respective sizes. The RRMSD probability distribution between random polypeptides converges to a universal curve as the chain length increases. The correlation coefficients between aligned random structures are computed as a function of polypeptide size showing two characteristic lengths of 4.7 and 37 residues. These lengths mark the separation between phases of different structural order between native protein fragments. The implications for threading are discussed.     

A tail strength measure for assessing the overall univariate significance in a dataset

We propose an overall measure of significance for a set of hypothesis tests. The 'tail strength' is a simple function of the p-values computed for each of the tests. This measure is useful, for example, in assessing the overall univariate strength of a large set of features in microarray and other genomic and biomedical studies. It also has a simple relationship to the false discovery rate of the collection of tests. We derive the asymptotic distribution of the tail strength measure, and illustrate its use on a number of real datasets.     

New metrics for comparing and assessing discrepancies between RNA 3D structures and models

To benchmark progress made in RNA three-dimensional modeling and assess newly developed techniques, reliable and meaningful comparison metrics and associated tools are necessary. Generally, the average root-mean-square deviations (RMSDs) are quoted. However, RMSD can be misleading since errors are spread over the whole molecule and do not account for the specificity of RNA base interactions. Here, we introduce two new metrics that are particularly suitable to RNAs: the deformation index and deformation profile. The deformation index is calibrated by the interaction network fidelity, which considers base–base-stacking and base–base-pairing interactions within the target structure. The deformation profile highlights dissimilarities between structures at the nucleotide scale for both intradomain and interdomain interactions. Our results show that there is little correlation between RMSD and interaction network fidelity. The deformation profile is a tool that allows for rapid assessment of the origins of discrepancies.     

Crystallographic and NMR spectroscopic protein structures: the inter-residue contacts

Inter-residue pair contacts have been analyzed in detail for the four pairs of protein structures determined both by X-ray analysis (X-ray) and nuclear magnetic resonance (NMR). At contact distances < or = 4.0 angstroms in the four NMR structures the overall number of pair contacts are less by 4-9% and pair contacts are in average shorter by 0.02-0.16 angstroms than those in corresponding X-ray structures. In each of four structure pairs 83-94% of common pair contacts are formed by the same residues in both structures and rest 6-17% ones are longer own pair contacts formed by the different residues in the NMR and X-ray structures. The amount of the longer own contacts is higher in the X-ray structure of the pair. In the each NMR structure there are three types of common pair contacts, which are shorter, longer or equal length in comparison with identical pair contacts in the X-ray structure of the same protein. The methodological different shortened common pair contacts predominate in the known distant dependence of the inter-residue contact densities of the 60-61 pair of the NMR/X-ray structure. Among four pairs analyzed the contact shortening proceeds upon the energy minimization of the crambin NMR structure and upon the resolving by the program X-PLOR with decreased atom van der Waals radius of the NMR structures of ubiquitin, hen lysozyme and monomeric hemoglobin. An extent of the NMR contact shortening decreased as the amount of NMR information upon the calculation of the NMR structures increased. Among 60-61 pairs of NMR/X-ray structures the main difference between alpha-helical and beta-structural proteins on the inter-residue distant dependence of the average contact densities arises from the strong alpha/beta difference in the local backbone geometry.     

COCO: a simple tool to enrich the representation of conformational variability in NMR structures

NMR structures are typically deposited in databases such as the PDB in the form of an ensemble of structures. Generally, each of the models in such an ensemble satisfies the experimental data and is equally valid. No unique solution can be calculated because the experimental NMR data is insufficient, in part because it reflects the conformational variability and dynamical behavior of the molecule in solution. Even for relatively rigid molecules, the limited number of structures that are typically deposited cannot completely encompass the structural diversity allowed by the observed NMR data, but they can be chosen to try and maximize its representation. We describe here the adaptation and application of techniques more commonly used to examine large ensembles from molecular dynamics simulations, to the analysis of NMR ensembles. The approach, which is based on principal component analysis, we call COCO ("Complementary Coordinates"). The COCO approach analyses the distribution of an NMR ensemble in conformational space, and generates a new ensemble that fills "gaps" in the distribution. The method is very rapid, and analysis of a 25-member ensemble and generation of a new 25 member ensemble typically takes 1-2 min on a conventional workstation. Applied to the 545 structures in the RECOORD database, we find that COCO generates new ensembles that are as structurally diverse-both from each other and from the original ensemble-as are the structures within the original ensemble. The COCO approach does not explicitly take into account the NMR restraint data, yet in tests on selected structures from the RECOORD database, the COCO ensembles are frequently good matches to this data, and certainly are structures that can be rapidly refined against the restraints to yield high-quality, novel solutions. COCO should therefore be a useful aid in NMR structure refinement and in other situations where a richer representation of conformational variability is desired-for example in docking studies. COCO is freely accessible via the website www.ccpb.ac.uk/COCO.     

GENFOLD: a genetic algorithm for folding protein structures using NMR restraints.

We report the development and validation of the program GENFOLD, a genetic algorithm that calculates protein structures using restraints obtained from NMR, such as distances derived from nuclear Overhauser effects, and dihedral angles derived from coupling constants. The program has been tested on three proteins: the POU domain (a small three-helix DNA-binding protein), bovine pancreatic trypsin inhibitor (BPTI), and the starch-binding domain from Aspergillus niger glucoamylase I, a 108-residue beta-sheet protein. Structures were calculated for each protein using published NMR restraints. In addition, structures were calculated for BPTI using artificial restraints generated from a high-resolution crystal structure. In all cases the fittest calculated structures were close to the target structure, and could be refined to structures indistinguishable from the target structures by means of a low-temperature simulated annealing refinement. The effectiveness of the program is similar to that of distance geometry and simulated annealing methods, and it is capable of using a very wide range of restraints as input. It can thus be readily extended to the calculation of structures of large proteins, for which few NOE restraints may be available.     

A fast method of comparing protein structures

Comparative studies on protein structures form an integral part of protein crystallography. Here, a fast method of comparing protein structures is presented. Protein structures are represented as a set of secondary structural elements. The method also provides information regarding preferred packing arrangements and evolutionary dynamics of secondary structural elements. This information is not easily obtained from previous methods. In contrast to those methods, the present one can be used only for proteins with some secondary structure. The method is illustrated with globin folds, cytochromes and dehydrogenases as examples.     

Chemically accurate protein structures: Validation of protein NMR structures by comparison of measured and predicted pK a 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 pK _a values of acidic residues, and protein structure. The accurate and fast empirical computational method employed by the PROPKA program () allows the user to test the ability of a given structure to reproduce known pK _a 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 pK _a 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.     

Network compression as a quality measure for protein interaction networks

With the advent of large-scale protein interaction studies, there is much debate about data quality. Can different noise levels in the measurements be assessed by analyzing network structure? Because proteomic regulation is inherently co-operative, modular and redundant, it is inherently compressible when represented as a network. Here we propose that network compression can be used to compare false positive and false negative noise levels in protein interaction networks. We validate this hypothesis by first confirming the detrimental effect of false positives and false negatives. Second, we show that gold standard networks are more compressible. Third, we show that compressibility correlates with co-expression, co-localization, and shared function. Fourth, we also observe correlation with better protein tagging methods, physiological expression in contrast to over-expression of tagged proteins, and smart pooling approaches for yeast two-hybrid screens. Overall, this new measure is a proxy for both sensitivity and specificity and gives complementary information to standard measures such as average degree and clustering coefficients.     

Crystallographic and NMR spectroscopic protein structures: Interresidue contacts

Interresidue pair contacts were analyzed in detail for four pairs of protein structures solved using X-ray analysis (X-ray) and nuclear magnetic resonance (NMR). In the four NMR structures, at distances of ≤4.0 Å, the total number of pair contacts was 4–9% lower and, in general, the pair contacts were 0.02–0.16 Å shorter compared to the X-ray structures. Each of the four structural pairs contained 83–94% common pair contacts (CPCs), which were formed by identical residues in both structures; the other 6–17% were longer intrinsic pair contacts (IPCs) formed by different residues in NMR and X-ray structures, while the latter contained more IPC. Every NMR structure contained three types of CPC that were shorter, longer, or equal to the identical contact pairs in the X-ray structure of this protein. Methodologically different short CPCs prevailed at a known distance dependence of the interresidue contact density in 60–61 pairs of NMR/X-ray structures. Among the analyzed four structural pairs, contact shortening appeared upon the energy minimization of the crambin NMR structure and upon solving the ubiquitin, hen lysozyme, and monomeric hemoglobin NMR structures using X-PLOR software with decreased van der Waals atomic radii. The degree of contact shortening in the NMR structures diminished with an increase in the NMR data used to solve these structures. Among the 60 pairs of NMR/X-ray structures, the major difference between α-helical and β-structural proteins in the dependences on interresidue distances of average contact density appeared due to strong α/β differences in the backbone local geometry.     

A method for determining overall protein fold from NMR distance restraints

Summary We describe a simple method for determining the overall fold of a polypeptide chain from NOE-derived distance restraints. The method uses a reduced representation consisting of two particles per residue, and a force field containing pseudo-bond and pseudo-angle terms, an electrostatic term, but no van der Waals or hard shell repulsive terms. The method is fast and robust, requiring relatively few distance restraints to approximate the correct fold, and the correct mirror image is readily determined. The method is easily implemented using commercially available molecular modeling software.     

Paramagnetic effects in NMR for protein structures and ensembles: Studies of metalloproteins

Paramagnetic effects on the NMR spectra are known to encode information on structure, electronic properties and dynamics hardly accessible with any other technique, especially in the field of biological systems. Paramagnetism-based restraints are conveniently used for the de novo determination of protein structures, the structural refinement starting from crystallographic models, and for the determination of the internal arrangement of domains with known structures. Conformational variability can also be profitably interrogated including the possibility of uncovering the presence of states with very low population. The recent advances in the quantum chemistry treatment of paramagnetic NMR effects has provided new momentum to the field, allowing for the refinement of protein structures at the metal coordination site to an unprecedented resolution.     

A normalized root-mean-square distance for comparing protein three-dimensional structures.

The degree of similarity of two protein three-dimensional structures is usually measured with the root-mean-square distance between equivalent atom pairs. Such a similarity measure depends on the dimension of the proteins, that is, on the number of equivalent atom pairs. The present communication presents a simple procedure to make the root-mean-square distances between pairs of three-dimensional structures independent of their dimensions. This normalization may be useful in evolutionary and fold classification studies as well as in simple comparisons between different structural models.     

An overview of tools for the validation of protein NMR structures

Biomolecular structures at atomic resolution present a valuable resource for the understanding of biology. NMR spectroscopy accounts for 11 % of all structures in the PDB repository. In response to serious problems with the accuracy of some of the NMR-derived structures and in order to facilitate proper analysis of the experimental models, a number of program suites are available. We discuss nine of these tools in this review: PROCHECK-NMR, PSVS, GLM-RMSD, CING, Molprobity, Vivaldi, ResProx, NMR constraints analyzer and QMEAN. We evaluate these programs for their ability to assess the structural quality, restraints and their violations, chemical shifts, peaks and the handling of multi-model NMR ensembles. We document both the input required by the programs and output they generate. To discuss their relative merits we have applied the tools to two representative examples from the PDB: a small, globular monomeric protein (Staphylococcal nuclease from S. aureus, PDB entry 2kq3) and a small, symmetric homodimeric protein (a region of human myosin-X, PDB entry 2lw9).     

Method for comparing the structures of protein ligand-binding sites and application for predicting protein-drug interactions

Many drugs, even ones that are designed to act selectively on a target protein, bind unintended proteins. These unintended bindings can explain side effects or indicate additional mechanisms for a drug's medicinal properties. Structural similarity between binding sites is one of the reasons for binding to multiple targets. We developed a method for the structural alignment of atoms in the solvent-accessible surface of proteins that uses similarities in the local atomic environment, and carried out all-against-all structural comparisons for 48,347 potential ligand-binding regions from a nonredundant protein structure subset (nrPDB, provided by NCBI). The relationships between the similarity of ligand-binding regions and the similarity of the global structures of the proteins containing the binding regions were examined. We found 10,403 known ligand-binding region pairs whose structures were similar despite having different global folds. Of these, we detected 281 region pairs that had similar ligands with similar binding modes. These proteins are good examples of convergent evolution. In addition, we found a significant correlation between Z-score of structural similarity and true positive rate of "active" entries in the PubChem BioAssay database. Moreover, we confirmed the interaction between ibuprofen and a new target, porcine pancreatic elastase, by NMR experiment. Finally, we used this method to predict new drug-target protein interactions. We obtained 540 predictions for 105 drugs (e.g., captopril, lovastatin, flurbiprofen, metyrapone, and salicylic acid), and calculated the binding affinities using AutoDock simulation. The results of these structural comparisons are available at http://www.tsurumi.yokohama-cu.ac.jp/fold/database.html.     

MaxSub: an automated measure for the assessment of protein structure prediction quality

MOTIVATION: Evaluating the accuracy of predicted models is critical for assessing structure prediction methods. Because this problem is not trivial, a large number of different assessment measures have been proposed by various authors, and it has already become an active subfield of research (Moult et al. (1997,1999) and CAFASP (Fischer et al. 1999) prediction experiments have demonstrated that it has been difficult to choose one single, 'best' method to be used in the evaluation. Consequently, the CASP3 evaluation was carried out using an extensive set of especially developed numerical measures, coupled with human-expert intervention. As part of our efforts towards a higher level of automation in the structure prediction field, here we investigate the suitability of a fully automated, simple, objective, quantitative and reproducible method that can be used in the automatic assessment of models in the upcoming CAFASP2 experiment. Such a method should (a) produce one single number that measures the quality of a predicted model and (b) perform similarly to human-expert evaluations. RESULTS: MaxSub is a new and independently developed method that further builds and extends some of the evaluation methods introduced at CASP3. MaxSub aims at identifying the largest subset of C(alpha) atoms of a model that superimpose 'well' over the experimental structure, and produces a single normalized score that represents the quality of the model. Because there exists no evaluation method for assessment measures of predicted models, it is not easy to evaluate how good our new measure is. Even though an exact comparison of MaxSub and the CASP3 assessment is not straightforward, here we use a test-bed extracted from the CASP3 fold-recognition models. A rough qualitative comparison of the performance of MaxSub vis-a-vis the human-expert assessment carried out at CASP3 shows that there is a good agreement for the more accurate models and for the better predicting groups. As expected, some differences were observed among the medium to poor models and groups. Overall, the top six predicting groups ranked using the fully automated MaxSub are also the top six groups ranked at CASP3. We conclude that MaxSub is a suitable method for the automatic evaluation of models.