Insights into equilibrium dynamics of proteins from comparison of NMR and X-ray data with computational predictions

For a representative set of 64 nonhomologous proteins, each containing a structure solved by NMR and X-ray crystallography, we analyzed the variations in atomic coordinates between NMR models, the temperature (B) factors measured by X-ray crystallography, and the fluctuation dynamics predicted by the Gaussian network model (GNM). The NMR and X-ray data exhibited a correlation of 0.49. The GNM results, on the other hand, yielded a correlation of 0.59 with X-ray data and a distinctively better correlation (0.75) with NMR data. The higher correlation between GNM and NMR data, compared to that between GNM and X-ray B factors, is shown to arise from the differences in the spectrum of modes accessible in solution and in the crystal environment. Mainly, large-amplitude motions sampled in solution are restricted, if not inaccessible, in the crystalline environment of X-rays. Combined GNM and NMR analysis emerges as a useful tool for assessing protein dynamics.     

TASSER-based refinement of NMR structures

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

Linear regression models for solvent accessibility prediction in proteins.

The relative solvent accessibility (RSA) of an amino acid residue in a protein structure is a real number that represents the solvent exposed surface area of this residue in relative terms. The problem of predicting the RSA from the primary amino acid sequence can therefore be cast as a regression problem. Nevertheless, RSA prediction has so far typically been cast as a classification problem. Consequently, various machine learning techniques have been used within the classification framework to predict whether a given amino acid exceeds some (arbitrary) RSA threshold and would thus be predicted to be "exposed," as opposed to "buried." We have recently developed novel methods for RSA prediction using nonlinear regression techniques which provide accurate estimates of the real-valued RSA and outperform classification-based approaches with respect to commonly used two-class projections. However, while their performance seems to provide a significant improvement over previously published approaches, these Neural Network (NN) based methods are computationally expensive to train and involve several thousand parameters. In this work, we develop alternative regression models for RSA prediction which are computationally much less expensive, involve orders-of-magnitude fewer parameters, and are still competitive in terms of prediction quality. In particular, we investigate several regression models for RSA prediction using linear L1-support vector regression (SVR) approaches as well as standard linear least squares (LS) regression. Using rigorously derived validation sets of protein structures and extensive cross-validation analysis, we compare the performance of the SVR with that of LS regression and NN-based methods. In particular, we show that the flexibility of the SVR (as encoded by metaparameters such as the error insensitivity and the error penalization terms) can be very beneficial to optimize the prediction accuracy for buried residues. We conclude that the simple and computationally much more efficient linear SVR performs comparably to nonlinear models and thus can be used in order to facilitate further attempts to design more accurate RSA prediction methods, with applications to fold recognition and de novo protein structure prediction methods.     

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.     

Application of sparse NMR restraints to large-scale protein structure prediction

The protein structure prediction algorithm TOUCHSTONEX that uses sparse distance restraints derived from NMR nuclear Overhauser enhancement (NOE) data to predict protein structures at low-to-medium resolution was evaluated as follows: First, a representative benchmark set of the Protein Data Bank library consisting of 1365 proteins up to 200 residues was employed. Using N/8 simulated long-range restraints, where N is the number of residues, 1023 (75%) proteins were folded to a C(alpha) root-mean-square deviation (RMSD) from native <6.5 A in one of the top five models. The average RMSD of the models for all 1365 proteins is 5.0 A. Using N/4 simulated restraints, 1206 (88%) proteins were folded to a RMSD <6.5 A and the average RMSD improved to 4.1 A. Then, 69 proteins with experimental NMR data were used. Using long-range NOE-derived restraints, 47 proteins were folded to a RMSD <6.5 A with N/8 restraints and 61 proteins were folded to a RMSD <6.5 A with N/4 restraints. Thus, TOUCHSTONEX can be a tool for NMR-based rapid structure determination, as well as used in other experimental methods that can provide tertiary restraint information.     

Comparison of Composer and ORCHESTRAR

Although the number of known protein structures is increasing, the number of protein sequences without determined structures is still much larger. Three-dimensional (3D) protein structure information helps in the understanding of functional mechanisms, but solving structures by X-ray crystallography or NMR is often a lengthy and difficult process. A relatively fast way of determining a protein's 3D structure is to construct a computer model using homologous sequence and structure information. Much work has gone into algorithms that comprise the ORCHESTRAR homology modeling program in the SYBYL software package. This novel homology modeling tool combines algorithms for modeling conserved cores, variable regions, and side chains. The paradigm of using existing knowledge from multiple templates and the underlying protein environment knowledgebase is used in all of these algorithms, and will become even more powerful as the number of experimentally derived protein structures increases. To determine how ORCHESTRAR compares to Composer (a broadly used, but an older tool), homology models of 18 proteins were constructed using each program so that a detailed comparison of each step in the modeling process could be carried out. Proteins modeled include kinases, dihydrofolate reductase, HIV protease, and factor Xa. In almost all cases ORCHESTRAR produces models with lower root-mean-squared deviation (RMSD) values when compared with structures determined by X-ray crystallography or NMR. Moreover, ORCHESTRAR produced a homology model for three target sequences where Composer failed to produce any. Data for RMSD comparisons between structurally conserved cores, structurally variable regions, side-chain conformations are presented, as well as analyses of active site and protein-protein interface configurations.     

On the relation between residue flexibility and residue interactions in proteins

B-factor from X-ray crystal structure can well measure protein structural flexibility, which plays an important role in different biological processes, such as catalysis, binding and molecular recognition. Understanding the essence of flexibility can be helpful for the further study of the protein function. In this study, we attempted to correlate the flexibility of a residue to its interactions with other residues by representing the protein structure as a residue contact network. Here, several well established network topological parameters were employed to feature such interactions. A prediction model was constructed for B-factor of a residue by using support vector regression (SVR). Pearson correlation coefficient (CC) was used as the performance measure. CC values were 0.63 and 0.62 for single amino acid and for the whole sequence, respectively. Our results revealed well correlations between B-factors and network topological parameters. This suggests that the protein structural flexibility could be well characterized by the inter-amino acid interactions in a protein.     

A comparative analysis of the equilibrium dynamics of a designed protein inferred from NMR,X‐ray,and computations

A detailed analysis of high‐resolution structural data and computationally predicted dynamics was carried out for a designed sugar‐binding protein. The mean‐square deviations in the positions of residues derived from nuclear magnetic resonance (NMR) models and those inferred from X‐ray crystallographic B‐factors for two different crystal forms were compared with the predictions based on the Gaussian Network Model (GNM) and the results from molecular dynamics (MD) simulations. GNM systematically yielded a higher correlation than MD, with experimental data, suggesting that the lack of atomistic details in the coarse‐grained GNM is more than compensated for by the mathematically exact evaluation of fluctuations using the native contacts topology. Evidence is provided that particular loop motions are curtailed by intermolecular contacts in the crystal environment causing a discrepancy between theory and experiments. Interestingly, the information conveyed by X‐ray crystallography becomes more consistent with NMR models and computational predictions when ensembles of X‐ray models are considered. Less precise (broadly distributed) ensembles indeed appear to describe the accessible conformational space under native state conditions better than B‐factors. Our results highlight the importance of using multiple conformations obtained by alternative experimental methods, and analyzing results from both coarse‐grained models and atomic simulations, for accurate assessment of motions accessible to proteins under native state conditions. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Prediction of protein continuum secondary structure with probabilistic models based on NMR solved structures

Background  

The structure of proteins may change as a result of the inherent flexibility of some protein regions. We develop and explore probabilistic machine learning methods for predicting a continuum secondary structure, i.e. assigning probabilities to the conformational states of a residue. We train our methods using data derived from high-quality NMR models.     

Structural model of the HIV-1 Tat(46-58)-TAR complex

The trans-activator protein (Tat) of human immunodeficiency virus type 1 (HIV-1) binds to an uridine-rich bulge of an RNA target (TAR; trans-activation responsive element) predominantly via its basic sequence domain. The structure of the Tat(46-58)-TAR complex has been determined by a novel modeling approach relying on structural information about one crucial arginine residue and crosslink data. The strategy described here solely uses this experimental data without additional "modeling" assumptions about the structure of the complex in order to avoid human bias. Model building was performed in a fashion similar to structure calculations from nuclear magnetic resonance (NMR)-spectroscopic data using restrained molecular dynamics. The resulting set of structures of Tat(46-58) in its complex with TAR reveals that all models have converged to a common fold, showing a backbone root mean square deviation (RMSD) of 1.36A. Analysis of the calculated structures suggests that HIV-I Tat forms a hairpin loop in its complex with TAR that shares striking similarity to the hairpin formed by the structure of the bovine immunodeficiency virus Tat protein after TAR binding as determined by NMR studies. The outlined approach is not limited to the Tat-TAR complex modeling, but is also applicable to all molecular complexes with sufficient biochemical and biophysical data available.     

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

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

NMR structure of lung surfactant peptide SP-B(11-25)

Surfactant protein B (SP-B) is a 79-residue essential component of lung surfactant, the film of lipid and protein lining the alveoli, and is the subject of great interest for its role in lung surfactant replacement therapies. Here we report circular dichroism results and the solution NMR structure of SP-B(11-25) (CRALIKRIQAMIPKG) dissolved in CD(3)OH at 5 degrees C. This is the first report of NMR data related to the protein SP-B, whose structure promises to help elucidate the mechanism of its function. Sequence-specific resonance assignments were made for all observable (1)H NMR signals on the basis of standard 2D NMR methods. Structures were determined by the simulated annealing method using restraints derived from 2D NOESY data. The calculations yielded 17 energy-minimized structures, three of which were subjected to 0.95 ns of restrained dynamics to assess the relevance of the static structures to more realistic dynamic behavior. Our CD and NMR data confirm that this segment is an amphiphilic alpha helix from approximately residue L14 through M21. The backbone heavy-atom RMSD for residues L14 through M21 is 0.09 +/- 0.12 A, and the backbone heavy-atom RMSD for the whole peptide is 0.96 +/- 2.45 A, the difference reflecting fraying at the termini. Aside from the disordered termini, the minimized structures represent dynamic structures well. Structural similarity to the homologous regions of related saposin-like proteins and the importance of the distribution of polar residues about the helix axis are discussed.     

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.     

Structure of the coat protein in Pf1 bacteriophage determined by solid-state NMR spectroscopy

The atomic resolution structure of Pf1 coat protein determined by solid-state NMR spectroscopy of magnetically aligned filamentous bacteriophage particles in solution is compared to the structures previously determined by X-ray fiber and neutron diffraction, the structure of its membrane-bound form, and the structure of fd coat protein. These structural comparisons provide insights into several biological properties, differences between class I and class II filamentous bacteriophages, and the assembly process. The six N-terminal amino acid residues adopt an unusual "double hook" conformation on the outside of the bacteriophage particle. The solid-state NMR results indicate that at 30 degrees C, some of the coat protein subunits assume a single, fully structured conformation, and some have a few mobile residues that provide a break between two helical segments, in agreement with structural models from X-ray fiber and neutron diffraction, respectively. The atomic resolution structure determined by solid-state NMR for residues 7-14 and 18-46, which excludes the N-terminal double hook and the break between the helical segments, but encompasses more than 80% of the backbone including the distinct kink at residue 29, agrees with that determined by X-ray fiber diffraction with an RMSD value of 2.0 A. The symmetry and distance constraints determined by X-ray fiber and neutron diffraction enable the construction of an accurate model of the bacteriophage particle from the coordinates of the coat protein monomers.     

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

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

An Insight into Biomolecular Flexibility: Its Measuring,Modeling and Regulating on Function at Single Molecule Level

The protein structure-function paradigm implies that the structure of a protein defines its function. Crystallization techniques such as X-ray, electron microscopy (EM) and nuclear magnetic resonance (NMR) have been applied to resolve the crystal structure of numerous proteins, provided beautiful and informative models of proteins. However, proteins are not intrinsically in static state but in dynamic state, which is lack in crystal models. The protein flexibility, a key mechanical property of proteins, plays important roles in various biological processes, such as ligand-receptor interaction, signaling transduction, substrate recognition and post-translational modifications. Advanced time-resolved crystallography has been developed recent years to visualize and characterize the dynamic of proteins and reviewed in literatures. In the present review, we will focus on the single-molecule based techniques and theoretical methods in determining the flexibility of proteins, exhibit some interest examples of proteins and DNA molecular flexibility to their functions, and provide an insight in molecular flexibility from the biomechanics point of view.     

Structural consequences of metallothionein dimerization: solution structure of the isolated Cd4-alpha-domain and comparison with the holoprotein dimer

The NMR determination of the structure of Cd(7)-metallothionein was done previously using a relatively large protein concentration that favors dimer formation. The reactivity of the protein is also affected under this condition. To examine the influence of protein concentration on metallothionein conformation, the isolated Cd(4)-alpha-domain was prepared from rabbit metallothionein-2 (MT 2), and its three-dimensional structure was determined by heteronuclear, (1)H-(111)Cd, and homonuclear, (1)H-(1)H NMR, correlation experiments. The three-dimensional structure was refined using distance and angle constraints derived from these two-dimensional NMR data sets and a distance geometry/simulated annealing protocol. The backbone superposition of the alpha-domain from rabbit holoprotein Cd(7)-MT 2 and the isolated rabbit Cd(4)-alpha was measured at a RMSD of 2.0 A. Nevertheless, the conformations of the two Cd-thiolate clusters were distinctly different at two of the cadmium centers. In addition, solvent access to the sulfhydryl ligands of the isolated Cd(4)-alpha cluster was 130% larger due to this small change in cluster geometry. To probe whether these differences were an artifact of the structure calculation, the Cd(4)-alpha-domain structure in rabbit Cd(7)-MT 2 was redetermined, using the previously defined set of NOEs and the present calculation protocol. All calculations employed the same ionic radius for Cd(2+) and same cadmium-thiolate bond distance. The newly calculated structure matched the original with an RMSD of 1.24 A. It is hypothesized that differences in the two alpha-domain structures result from a perturbation of the holoprotein structure because of head-to-tail dimerization under the conditions of the NMR experiments.     

Tertiary structure predictions on a comprehensive benchmark of medium to large size proteins

We evaluate tertiary structure predictions on medium to large size proteins by TASSER, a new algorithm that assembles protein structures through rearranging the rigid fragments from threading templates guided by a reduced Calpha and side-chain based potential consistent with threading based tertiary restraints. Predictions were generated for 745 proteins 201-300 residues in length that cover the Protein Data Bank (PDB) at the level of 35% sequence identity. With homologous proteins excluded, in 365 cases, the templates identified by our threading program, PROSPECTOR_3, have a root-mean-square deviation (RMSD) to native < 6.5 angstroms, with >70% alignment coverage. After TASSER assembly, in 408 cases the best of the top five full-length models has a RMSD < 6.5 angstroms. Among the 745 targets are 18 membrane proteins, with one-third having a predicted RMSD < 5.5 A. For all representative proteins less than or equal to 300 residues that have corresponding multiple NMR structures in the Protein Data Bank, approximately 20% of the models generated by TASSER are closer to the NMR structure centroid than the farthest individual NMR model. These results suggest that reasonable structure predictions for nonhomologous large size proteins can be automatically generated on a proteomic scale, and the application of this approach to structural as well as functional genomics represent promising applications of TASSER.     

Structural Model of the HIV-1 Tat(46–58)-TAR Complex

Abstract

The trans-activator protein (Tat) of human immunodeficiency virus type 1 (HIV-1>) binds to an uridine-rich bulge of an RNA target (TAR; trans-activation responsive element) predominantly via its basic sequence domain. The structure of the Tat(46–58)-TAR complex has been determined by a novel modeling approach relying on structural information about one crucial arginine residue and crosslink data. The strategy described here solely uses this experimental data without additional “modeling” assumptions about the structure of the complex in order to avoid human bias. Model building was performed in a fashion similar to structure calculations from nuclear magnetic resonance (NMR)-spectroscopic data using restrained molecular dynamics.

The resulting set of structures of Tat(46–58) in its complex with TAR reveals that all models have converged to a common fold, showing a backbone root mean square deviation (RMSD) of 1.36Å. Analysis of the calculated structures suggests that HIV-1 Tat forms a hairpin loop in its complex with TAR that shares striking similarity to the hairpin formed by the structure of the bovine immunodeficiency virus Tat protein after TAR binding as determined by NMR studies. The outlined approach is not limited to the Tat-TAR complex modeling, but is also applicable to all molecular complexes with sufficient biochemical and biophysical data available.