Patterns in Protein Flexibility: A Comparison of NMR "Ensembles", MD Trajectories, and Crystallographic B-Factors.

Proteins are molecular machines requiring flexibility to function. Crystallographic B-factors and Molecular Dynamics (MD) simulations both provide insights into protein flexibility on an atomic scale. Nuclear Magnetic Resonance (NMR) lacks a universally accepted analog of the B-factor. However, a lack of convergence in atomic coordinates in an NMR-based structure calculation also suggests atomic mobility. This paper describes a pattern in the coordinate uncertainties of backbone heavy atoms in NMR-derived structural "ensembles" first noted in the development of FindCore2 (previously called Expanded FindCore: DA Snyder, J Grullon, YJ Huang, R Tejero, GT Montelione, Proteins: Structure, Function, and Bioinformatics 82 (S2), 219-230) and demonstrates that this pattern exists in coordinate variances across MD trajectories but not in crystallographic B-factors. This either suggests that MD trajectories and NMR "ensembles" capture motional behavior of peptide bond units not captured by B-factors or indicates a deficiency common to force fields used in both NMR and MD calculations.

Covariance NMR: Theoretical concerns, practical considerations, contemporary applications and related techniques.

The family of resolution enhancement and spectral reconstruction techniques collectively known as covariance NMR continues to expand, along with the list of applications for these techniques. Recent advances in covariance NMR include the utilization of covariance to reconstruct pure shift NMR spectra, and the growing use of covariance NMR in processing non-uniformly sampled data, especially in solid state NMR and metabolomics. This review describes theoretical and practical considerations for direct and indirect covariance NMR techniques, and summarizes recent additions to the covariance NMR family. The review also outlines some of the applications of covariance NMR, and places covariance NMR in the larger context of methods that use statistical and algebraic approaches to enhance and combine various kinds of spectroscopic data, including tensor-based approaches for multidimensional NMR and heterocovariance spectroscopy.

Protein structure prediction assisted with sparse NMR data in CASP13.

CASP13 has investigated the impact of sparse NMR data on the accuracy of protein structure prediction. NOESY and 15 N-1 H residual dipolar coupling data, typical of that obtained for 15 N,13 C-enriched, perdeuterated proteins up to about 40 kDa, were simulated for 11 CASP13 targets ranging in size from 80 to 326 residues. For several targets, two prediction groups generated models that are more accurate than those produced using baseline methods. Real NMR data collected for a de novo designed protein were also provided to predictors, including one data set in which only backbone resonance assignments were available. Some NMR-assisted prediction groups also did very well with these data. CASP13 also assessed whether incorporation of sparse NMR data improves the accuracy of protein structure prediction relative to nonassisted regular methods. In most cases, incorporation of sparse, noisy NMR data results in models with higher accuracy. The best NMR-assisted models were also compared with the best regular predictions of any CASP13 group for the same target. For six of 13 targets, the most accurate model provided by any NMR-assisted prediction group was more accurate than the most accurate model provided by any regular prediction group; however, for the remaining seven targets, one or more regular prediction method provided a more accurate model than even the best NMR-assisted model. These results suggest a novel approach for protein structure determination, in which advanced prediction methods are first used to generate structural models, and sparse NMR data is then used to validate and/or refine these models.

Prediction of protein flexibility using a conformationally restrained contact map.

Knowledge of protein flexibility is crucial to understanding protein function. However, probing protein flexibility by either experiment or computational simulations is a difficult process. In particular, many computational approaches to understanding protein flexibility require an experimentally determined protein structure. The Conformationally Restrained Contact Map (CoRe-CMap) approach reported here couples protein disorder predictions with protein structure predictions and only requires sequence data to predict protein flexibility. This paper reports the application of the CoRe-CMap model to predicting Lipari-Szabo order parameters of all proteins for which experimentally derived Lipari-Szabo order parameters are available in the BioMagResBank: the median root mean square deviation between a protein's predicted and experimentally derived order parameters is 0.124. Additionally, application of the CoRe-CMap model to predict Lipari-Szabo order parameters for the 10th Type III Domain in Fibronectin and a homologous domain from Tenascin demonstrates the ability of CoRe-CMap to predict functionally important differences in protein flexibility.

Cohort-Controlled Comparison of Umbilical Cord Blood Transplantation Using Carlecortemcel-L, a Single Progenitor-Enriched Cord Blood, to Double Cord Blood Unit Transplantation.

Umbilical cord blood (UCB) transplantation has a high early mortality rate primarily related to transplanted stem cell dose. To decrease early mortality and enhance engraftment, a portion of selected cord blood units (20% to 50%) was expanded with cytokines and the copper chelator tetraethylenepentamine (carlecortemcel-L) and transplanted with the unmanipulated fraction after myeloablative conditioning. The primary endpoint was 100-day survival, which was compared with a contemporaneous double-unit cord blood transplantation (DUCBT) group. We enrolled 101 patients at 25 sites; the DUCBT comparison (n = 295) was selected from international registries using study eligibility criteria. Baseline carlecortemcel-L study group unit nucleated cell (NC) and CD34+ were 3.06 × 107 cell dose/kg and 1.64 × 105 cell dose/kg. Median NC and CD34+ fold expansion were 400 and 77, with a mean total CD34 infused of 9.7 × 105/kg. The 100-day survival was 84.2% for the carlecortemcel-L study group versus 74.6% for the DUCBT group (odds ratio, .50; 95% CI, .26 to .95; P = .035). Survival at day 180 was similar for the 2 groups; the major cause of death after day 100 was opportunistic infections. Faster median neutrophil (21 days versus 28 days; P < .0001), and platelet (54 days versus 105 days; P = .008) engraftment was seen in the carlecortemcel-L study group; acute and chronic graft-versus-host disease rates were similar. In this multinational comparative study, transplanting expanded CD34+ stem cells from a portion of a single UCB unit, with the remaining unmanipulated fraction improved 100-day survival compared with DUCBT control patients while facilitating myeloid and platelet engraftment. This trial was registered at www.clinicaltrials.gov as #NCT00469729.

Analysis of ligand-protein exchange by Clustering of Ligand Diffusion Coefficient Pairs (CoLD-CoP).

NMR spectroscopy is a powerful tool in describing protein structures and protein activity for pharmaceutical and biochemical development. This study describes a method to determine weak binding ligands in biological systems by using hierarchic diffusion coefficient clustering of multidimensional data obtained with a 400 MHz Bruker NMR. Comparison of DOSY spectrums of ligands of the chemical library in the presence and absence of target proteins show translational diffusion rates for small molecules upon interaction with macromolecules. For weak binders such as compounds found in fragment libraries, changes in diffusion rates upon macromolecular binding are on the order of the precision of DOSY diffusion measurements, and identifying such subtle shifts in diffusion requires careful statistical analysis. The "CoLD-CoP" (Clustering of Ligand Diffusion Coefficient Pairs) method presented here uses SAHN clustering to identify protein-binders in a chemical library or even a not fully characterized metabolite mixture. We will show how DOSY NMR and the "CoLD-CoP" method complement each other in identifying the most suitable candidates for lysozyme and wheat germ acid phosphatase.

The expanded FindCore method for identification of a core atom set for assessment of protein structure prediction.

Maximizing the scientific impact of NMR-based structure determination requires robust and statistically sound methods for assessing the precision of NMR-derived structures. In particular, a method to define a core atom set for calculating superimpositions and validating structure predictions is critical to the use of NMR-derived structures as targets in the CASP competition. FindCore (Snyder and Montelione, Proteins 2005;59:673-686) is a superimposition independent method for identifying a core atom set and partitioning that set into domains. However, as FindCore optimizes superimposition by sensitively excluding not-well-defined atoms, the FindCore core may not comprise all atoms suitable for use in certain applications of NMR structures, including the CASP assessment process. Adapting the FindCore approach to assess predicted models against experimental NMR structures in CASP10 required modification of the FindCore method. This paper describes conventions and a standard protocol to calculate an "Expanded FindCore" atom set suitable for validation and application in biological and biophysical contexts. A key application of the Expanded FindCore method is to identify a core set of atoms in the experimental NMR structure for which it makes sense to validate predicted protein structure models. We demonstrate the application of this Expanded FindCore method in characterizing well-defined regions of 18 NMR-derived CASP10 target structures. The Expanded FindCore protocol defines "expanded core atom sets" that match an expert's intuition of which parts of the structure are sufficiently well defined to use in assessing CASP model predictions. We also illustrate the impact of this analysis on the CASP GDT assessment scores.

Solution NMR structure of the ribosomal protein RP-L35Ae from Pyrococcus furiosus.

The ribosome consists of small and large subunits each composed of dozens of proteins and RNA molecules. However, the functions of many of the individual protomers within the ribosome are still unknown. In this article, we describe the solution NMR structure of the ribosomal protein RP-L35Ae from the archaeon Pyrococcus furiosus. RP-L35Ae is buried within the large subunit of the ribosome and belongs to Pfam protein domain family PF01247, which is highly conserved in eukaryotes, present in a few archaeal genomes, but absent in bacteria. The protein adopts a six-stranded anti-parallel ß-barrel analogous to the "tRNA binding motif" fold. The structure of the P. furiosus RP-L35Ae presented in this article constitutes the first structural representative from this protein domain family.

Generalized indirect covariance NMR formalism for establishment of multidimensional spin correlations.

Multidimensional nuclear magnetic resonance (NMR) experiments measure spin-spin correlations, which provide important information about bond connectivities and molecular structure. However, direct observation of certain kinds of correlations can be very time-consuming due to limitations in sensitivity and resolution. Covariance NMR derives correlations between spins via the calculation of a (symmetric) covariance matrix, from which a matrix-square root produces a spectrum with enhanced resolution. Recently, the covariance concept has been adopted to the reconstruction of nonsymmetric spectra from pairs of 2D spectra that have a frequency dimension in common. Since the unsymmetric covariance NMR procedure lacks the matrix-square root step, it does not suppress relay effects and thereby may generate false positive signals due to chemical shift degeneracy. A generalized covariance formalism is presented here that embeds unsymmetric covariance processing within the context of the regular covariance transform. It permits the construction of unsymmetric covariance NMR spectra subjected to arbitrary matrix functions, such as the square root, with improved spectral properties. This formalism extends the domain of covariance NMR to include the reconstruction of nonsymmetric NMR spectra at resolutions or sensitivities that are superior to the ones achievable by direct measurements.

Z-matrix formalism for quantitative noise assessment of covariance nuclear magnetic resonance spectra.

Due to the limited sensitivity of many nuclear magnetic resonance (NMR) applications, careful consideration must be given to the effect of NMR data processing on spectral noise. This work presents analytical relationships as well as simulated and experimental results characterizing the propagation of noise by unsymmetric covariance NMR processing, which concatenates two NMR spectra along a common dimension, resulting in a new spectrum showing spin correlations as cross peaks that are not directly measured in either of the two input spectra. It is shown how the unsymmetric covariance spectrum possesses an inhomogeneous noise distribution across the spectrum with the least amount of noise in regions whose rows and columns do not contain any cross or diagonal peaks and with the largest amount of noise on top of signal peaks. Therefore, methods of noise estimation commonly used in Fourier transform spectroscopy underestimate the amount of uncertainty in unsymmetric covariance spectra. Different data processing procedures, including the Z-matrix formalism, thresholding, and maxima ratio scaling, are described to assess noise contributions and to reduce noise inhomogeneity. In particular, determination of a Z score, which measures the difference in standard deviations of a statistic from its mean, for each spectral point yields a Z matrix, which indicates whether a given peak intensity above a threshold arises from the covariance of signals in the input spectra or whether it is likely to be caused by noise. Application to an unsymmetric covariance spectrum, obtained by concatenating two 2D (13)C-(1)H heteronuclear, single quantum coherence (HSQC) and (13)C-(1)H heteronuclear, multiple bond correlation (HMBC) spectra of a metabolite mixture along their common proton dimension, reveals that for sufficiently sensitive input spectra the reduction in sensitivity due to covariance processing is modest.

Non-negative matrix factorization of two-dimensional NMR spectra: application to complex mixture analysis.

A central problem in the emerging field of metabolomics is how to identify the compounds comprising a chemical mixture of biological origin. NMR spectroscopy can greatly assist in this identification process, by means of multi-dimensional correlation spectroscopy, particularly total correlation spectroscopy (TOCSY). This Communication demonstrates how non-negative matrix factorization (NMF) provides an efficient means of data reduction and clustering of TOCSY spectra for the identification of unique traces representing the NMR spectra of individual compounds. The method is applied to a metabolic mixture whose compounds could be unambiguously identified by peak matching of NMF components against the BMRB metabolomics database.

Covariance NMR in higher dimensions: application to 4D NOESY spectroscopy of proteins.

Elucidation of high-resolution protein structures by NMR spectroscopy requires a large number of distance constraints that are derived from nuclear Overhauser effects between protons (NOEs). Due to the high level of spectral overlap encountered in 2D NMR spectra of proteins, the measurement of high quality distance constraints requires higher dimensional NMR experiments. Although four-dimensional Fourier transform (FT) NMR experiments can provide the necessary kind of spectral information, the associated measurement times are often prohibitively long. Covariance NMR spectroscopy yields 2D spectra that exhibit along the indirect frequency dimension the same high resolution as along the direct dimension using minimal measurement time. The generalization of covariance NMR to 4D NMR spectroscopy presented here exploits the inherent symmetry of certain 4D NMR experiments and utilizes the trace metric between donor planes for the construction of a high-resolution spectral covariance matrix. The approach is demonstrated for a 4D (13)C-edited NOESY experiment of ubiquitin. The 4D covariance spectrum narrows the line-widths of peaks strongly broadened in the FT spectrum due to the necessarily short number of increments collected, and it resolves otherwise overlapped cross peaks allowing for an increase in the number of NOE assignments to be made from a given dataset. At the same time there is no significant decrease in the positive predictive value of observing a peak as compared to the corresponding 4D Fourier transform spectrum. These properties make the 4D covariance method a potentially valuable tool for the structure determination of larger proteins and for high-throughput applications in structural biology.

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.

Comparisons of NMR spectral quality and success in crystallization demonstrate that NMR and X-ray crystallography are complementary methods for small protein structure determination.

X-ray crystallography and NMR spectroscopy provide the only sources of experimental data from which protein structures can be analyzed at high or even atomic resolution. The degree to which these methods complement each other as sources of structural knowledge is a matter of debate; it is often proposed that small proteins yielding high quality, readily analyzed NMR spectra are a subset of those that readily yield strongly diffracting crystals. We have examined the correlation between NMR spectral quality and success in structure determination by X-ray crystallography for 159 prokaryotic and eukaryotic proteins, prescreened to avoid proteins providing polydisperse and/or aggregated samples. This study demonstrates that, across this protein sample set, the quality of a protein's [15N-1H]-heteronuclear correlation (HSQC) spectrum recorded under conditions generally suitable for 3D structure determination by NMR, a key predictor of the ability to determine a structure by NMR, is not correlated with successful crystallization and structure determination by X-ray crystallography. These results, together with similar results of an independent study presented in the accompanying paper (Yee, et al., J. Am. Chem. Soc., accompanying paper), demonstrate that X-ray crystallography and NMR often provide complementary sources of structural data and that both methods are required in order to optimize success for as many targets as possible in large-scale structural proteomics efforts.

Clustering algorithms for identifying core atom sets and for assessing the precision of protein structure ensembles.

An important open question in the field of NMR-based biomolecular structure determination is how best to characterize the precision of the resulting ensemble of structures. Typically, the RMSD, as minimized in superimposing the ensemble of structures, is the preferred measure of precision. However, the presence of poorly determined atomic coordinates and multiple "RMSD-stable domains"--locally well-defined regions that are not aligned in global superimpositions--complicate RMSD calculations. In this paper, we present a method, based on a novel, structurally defined order parameter, for identifying a set of core atoms to use in determining superimpositions for RMSD calculations. In addition we present a method for deciding whether to partition that core atom set into "RMSD-stable domains" and, if so, how to determine partitioning of the core atom set. We demonstrate our algorithm and its application in calculating statistically sound RMSD values by applying it to a set of NMR-derived structural ensembles, superimposing each RMSD-stable domain (or the entire core atom set, where appropriate) found in each protein structure under consideration. A parameter calculated by our algorithm using a novel, kurtosis-based criterion, the epsilon-value, is a measure of precision of the superimposition that complements the RMSD. In addition, we compare our algorithm with previously described algorithms for determining core atom sets. The methods presented in this paper for biomolecular structure superimposition are quite general, and have application in many areas of structural bioinformatics and structural biology.