CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts,residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low‐cost global protein fold determination. Here, we present CABS‐NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C‐Alpha‐Beta‐Side‐group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge‐based force field. Its versatile structure enables a variety of protein‐modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS‐NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low‐energy structures obtained from chemical shifts by CABS‐NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl‐methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post‐experiment processing of various kinds of NMR data or fast and low‐cost structural analysis in the still challenging field of new fold predictions. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Structure determination by restrained molecular dynamics using NMR pseudocontact shifts as experimentally determined constraints

The structure of a DNA octamer d(TTGGCCAA)(2) complexed to chromomycin-A(3) and a single divalent cobalt ion has been solved by using the pseudocontact shifts due to the unpaired electrons on the cobalt. A protocol was developed and critically evaluated for using the pseudocontact shifts in structure determination. The pseudocontact shifts were input as experimental restraints in molecular dynamics simulations with or without NOE constraints. Both the magnitude and orientation of the susceptibility anisotropy tensor required for the shift calculations were determined during the simulations by iterative refinement. The pseudocontact shifts could be used to define the structure to a very high precision and accuracy compared with a corresponding NOE-determined structure. Convergence was obtained from different starting structures and tensors. A structure determination using both NOE's and pseudocontact shifts revealed a general agreement between the two data sets. However, some evidence for a discrepancy between NOE's and pseudocontact shifts was observed in the backbone and terminal base pairs of the DNA. Violations in shift or NOE restraints remaining in the final structures were examined and may be a reflection of motional averaging of the constraints and evidence for flexibility. This work demonstrates that pseudocontact shifts are a powerful tool for NMR structure determination.     

Generalized-ensemble simulations of the human parathyroid hormone fragment PTH(1-34)

A generalized-ensemble technique, multicanonical sampling, is used to study the folding of a 34-residue human parathyroid hormone fragment. An all-atom model of the peptide is employed and the protein-solvent interactions are approximated by an implicit solvent. Our results demonstrate that generalized-ensemble simulations are well suited to sample low-energy structures of such large polypeptides. Configurations with a root-mean-square deviation to the crystal structure of less than 1 A are found. Finally, we discuss limitations of our implicit solvent model.     

Dipolar chemical shift correlation spectroscopy for homonuclear carbon distance measurements in proteins in the solid state: application to structure determination and refinement

High-resolution solid-state NMR spectroscopy has become a promising tool for protein structure determination. Here, we describe a new dipolar-chemical shift correlation experiment for the measurement of homonuclear 13C-13C distances in uniformly 13C,15N-labeled proteins and demonstrate its suitability for protein structure determination and refinement. The experiments were carried out on the beta1 immunoglobulin binding domain of protein G (GB1). Both intraresidue and interresidue distances between carbonyl atoms and atoms in the aliphatic side chains were collected using a three-dimensional chemical shift correlation spectroscopy experiment that uses homogeneously broadened rotational resonance recoupling for carbon mixing. A steady-state approximation for the polarization transfer function was employed in data analysis, and a total of 100 intramolecular distances were determined, all in the range 2.5-5.5 A. An additional 41 dipolar contacts were detected, but the corresponding distances could not be accurately quantified. Additional distance and torsional restraints were derived from the proton-driven spin diffusion measurements and from the chemical shift analysis, respectively. Using all these restraints, it was possible to refine the structure of GB1 to a root-mean square deviation of 0.8 A. The approach is of general applicability for peptides and small proteins and can be easily incorporated into a structure determination and refinement protocol.     

De novo determination of protein backbone structure from residual dipolar couplings using Rosetta

As genome-sequencing projects rapidly increase the database of protein sequences, the gap between known sequences and known structures continues to grow exponentially, increasing the demand to accelerate structure determination methods. Residual dipolar couplings (RDCs) are an attractive source of experimental restraints for NMR structure determination, particularly rapid, high-throughput methods, because they yield both local and long-range orientational information and can be easily measured and assigned once the backbone resonances of a protein have been assigned. While very extensive RDC data sets have been used to determine the structure of ubiquitin, it is unclear to what extent such methods will generalize to larger proteins with less complete data sets. Here we incorporate experimental RDC restraints into Rosetta, an ab initio structure prediction method, and demonstrate that the combined algorithm provides a general method for de novo determination of a variety of protein folds from RDC data. Backbone structures for multiple proteins up to approximately 125 residues in length and spanning a range of topological complexities are rapidly and reproducibly generated using data sets that are insufficient in isolation to uniquely determine the protein fold de novo, although ambiguities and errors are observed for proteins with symmetry about an axis of the alignment tensor. The models generated are not high-resolution structures completely defined by experimental data but are sufficiently accurate to accelerate traditional high-resolution NMR structure determination and provide structure-based functional insights.     

A test on peptide stability of AMBER force fields with implicit solvation

We used replica exchange molecular dynamics (REMD) simulations to evaluate four different AMBER force fields and three different implicit solvent models. Our aim was to determine if these physics-based models captured the correct secondary structures of two alpha-helical and two beta-peptides: the 14-mer EK helix of Baldwin and co-workers, the C-terminal helix of ribonuclease, the 16-mer C-terminal hairpin of protein G, and the trpzip2 miniprotein. The different models gave different results, but generally we found that AMBER ff96 plus the implicit solvent model of Onufriev, Bashford, and Case gave reasonable structures, and is fairly well-balanced between helix and sheet. We also observed differences in the strength of ion pairing in the solvent models, we but found that the native secondary structures were retained even when salt bridges were prevented in the conformational sampling. Overall, this work indicates that some of these all-atom physics-based force fields may be good starting points for protein folding and protein structure prediction.     

Evaluation of DNA Force Fields in Implicit Solvation

DNA structural deformations and dynamics are crucial to its interactions in the cell. Theoretical simulations are essential tools to explore the structure, dynamics, and thermodynamics of biomolecules in a systematic way. Molecular mechanics force fields for DNA have benefited from constant improvements during the last decades. Several studies have evaluated and compared available force fields when the solvent is modeled by explicit molecules. On the other hand, few systematic studies have assessed the quality of duplex DNA models when implicit solvation is employed. The interest of an implicit modeling of the solvent consists in the important gain in the simulation performance and conformational sampling speed. In this study, respective influences of the force field and the implicit solvation model choice on DNA simulation quality are evaluated. To this end, extensive implicit solvent duplex DNA simulations are performed, attempting to reach both conformational and sequence diversity convergence. Structural parameters are extracted from simulations and statistically compared to available experimental and explicit solvation simulation data. Our results quantitatively expose the respective strengths and weaknesses of the different DNA force fields and implicit solvation models studied. This work can lead to the suggestion of improvements to current DNA theoretical models.     

Complete cross-validation and R-factor calculation of a solid-state NMR derived structure

Cross-validation of a solid-state NMR-derived membrane polypeptide structure is demonstrated. An initial structure has been achieved directly from solid-state NMR derived orientational restraints based on a variety of anisotropic nuclear spin interactions. Refining the molecular structure involves setting up a penalty function that incorporates all available solid-state NMR experimental data and an energy function. A validation method is required to choose the optimal weighting factor for the total penalty function to balance the contribution from the experimental restraints and the energy function. Complete cross-validation has been used to avoid over-fitting the orientational restraints. Such cross-validation involves partitioning of the experimental data into a test set and a working set followed by checking the free R-value during the refinement process. This approach is similar to the method used in crystallography and solution NMR. Optimizing the weighting factor on the penalty function by cross-validation will increase the quality of the refined structure from solid-state NMR data. The complete cross-validation and R-factor calculation is demonstrated using experimental solid-state NMR data from gramicidin A, a monovalent cation channel in lipid bilayers.     

Benchmarking implicit solvent folding simulations of the amyloid beta(10-35) fragment

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.     

Ensemble approach for NMR structure refinement against (1)H paramagnetic relaxation enhancement data arising from a flexible paramagnetic group attached to a macromolecule

Paramagnetic relaxation enhancement (PRE) measurements on (1)H nuclei have the potential to play an important role in NMR structure determination of macromolecules by providing unique long-range (10-35 A) distance information. Recent methodological advances for covalently attaching paramagnetic groups at specific sites on both proteins and nucleic acids have permitted the application of the PRE to various biological macromolecules. However, because artificially introduced paramagnetic groups are exposed to solvent and linked to the macromolecule by several freely rotatable bonds, they are intrinsically flexible. This renders conventional back-calculation of the (1)H-PRE using a single-point representation inaccurate, thereby severely limiting the utility of the (1)H-PRE as a tool for structure refinement. To circumvent these limitations, we have developed a theoretical framework and computational strategy with which to accurately back-calculate (1)H-PREs arising from flexible paramagnetic groups attached to macromolecules. In this scheme, the (1)H-PRE is calculated using a modified Solomon-Bloembergen equation incorporating a "model-free" formalism, based on a multiple-structure representation of the paramagnetic group in simulated annealing calculations. The ensemble approach for (1)H-PRE back-calculation was examined using several SRY/DNA complexes incorporating dT-EDTA-Mn(2+) at three distinct sites in the DNA, permitting a large data set comprising 435 experimental backbone and side-chain (1)H-PREs to be obtained in a straightforward manner from 2D through-bond correlation experiments. Calculations employing complete cross-validation demonstrate that the ensemble representation provides a means to accurately utilize backbone and side-chain (1)H-PRE data arising from a flexible paramagnetic group in structure refinement. The results of (1)H-PRE based refinement, in conjunction with previously obtained NMR restraints, indicate that significant gains in accuracy can be readily obtained. This is particularly significant in the case of macromolecular complexes where intermolecular translational restraints derived from nuclear Overhauser enhancement data may be limited.     

Structure determination of protein-protein complexes using NMR chemical shifts: case of an endonuclease colicin-immunity protein complex

Nuclear magnetic resonance (NMR) spectroscopy provides a range of powerful techniques for determining the structures and the dynamics of proteins. The high-resolution determination of the structures of protein-protein complexes, however, is still a challenging problem for this approach, since it can normally provide only a limited amount of structural information at protein-protein interfaces. We present here the determination using NMR chemical shifts of the structure (PDB code 2K5X) of the cytotoxic endonuclease domain from bacterial toxin colicin (E9) in complex with its cognate immunity protein (Im9). In order to achieve this result, we introduce the CamDock method, which combines a flexible docking procedure with a refinement that exploits the structural information provided by chemical shifts. The results that we report thus indicate that chemical shifts can be used as structural restraints for the determination of the conformations of protein complexes that are difficult to obtain by more standard NMR approaches.     

Refinement of multidomain protein structures by combination of solution small-angle X-ray scattering and NMR data

Determination of the 3D structures of multidomain proteins by solution NMR methods presents a number of unique challenges related to their larger molecular size and the usual scarcity of constraints at the interdomain interface, often resulting in a decrease in structural accuracy. In this respect, experimental information from small-angle scattering of X-ray radiation in solution (SAXS) presents a suitable complement to the NMR data, as it provides an independent constraint on the overall molecular shape. A computational procedure is described that allows incorporation of such SAXS data into the mainstream high-resolution macromolecular structure refinement. The method is illustrated for a two-domain 177-amino-acid protein, gammaS crystallin, using an experimental SAXS data set fitted at resolutions from approximately 200 A to approximately 30 A. Inclusion of these data during structure refinement decreases the backbone coordinate root-mean-square difference between the derived model and the high-resolution crystal structure of a 54% homologous gammaB crystallin from 1.96 +/- 0.07 A to 1.31 +/- 0.04 A. Combining SAXS data with NMR restraints can be accomplished at a moderate computational expense and is expected to become useful for multidomain proteins, multimeric assemblies, and tight macromolecular complexes.     

Tri-peptide reference structures for the calculation of relative solvent accessible surface area in protein amino acid residues

Relative amino acid residue solvent accessibility values allow the quantitative comparison of atomic solvent-accessible surface areas in different residue types and physical environments in proteins and in protein structural alignments. Geometry-optimised tri-peptide structures in extended solvent-exposed reference conformations have been obtained for 43 amino acid residue types at a high level of quantum chemical theory. Significant increases in side-chain solvent accessibility, offset by reductions in main-chain atom solvent exposure, were observed for standard residue types in partially geometry-optimised structures when compared to non-minimised models built from identical sets of proper dihedral angles abstracted from the literature. Optimisation of proper dihedral angles led most notably to marked increases of up to 54% in proline main-chain atom solvent accessibility compared to literature values. Similar effects were observed for fully-optimised tri-peptides in implicit solvent. The relief of internal strain energy was associated with systematic variation in N, C^α and C^β atom solvent accessibility across all standard residue types. The results underline the importance of optimisation of ‘hard’ degrees of freedom (bond lengths and valence bond angles) and improper dihedral angle values from force field or other context-independent reference values, and impact on the use of standardised fixed internal co-ordinate geometry in sampling approaches to the determination of absolute values of protein amino acid residue solvent accessibility. Quantum chemical methods provide a useful and accurate alternative to molecular mechanics methods to perform energy minimisation of peptides containing non-standard (chemically modified) amino acid residues frequently present in experimental protein structure data sets, for which force field parameters may not be available. Reference tri-peptide atomic co-ordinate sets including hydrogen atoms are made freely available.     

Coupling constants again: Experimental restraints in structure refinement

Summary Utilization of coupling constants as restraints in computational structure refinement is reviewed. In addition, we address the effect of conformational averaging and examine different approaches to apply the restraints when the experimental observable is obviously a result of averaging. Here, two different computational methods are compared. The simulation of a single structure with time-dependent restraints produces results very similar to those obtained with the calculation of numerous copies of the molecule (an ensemble of structures) and ensemble averaging. The advantages and disadvantages of the two methods are illustrated with simulations of cyclosporin A, for which 117 NOEs and 62 homo- and heteronuclear coupling constants have been measured.     

Prediction of Protein Loop Conformations using the AGBNP Implicit Solvent Model and Torsion Angle Sampling

The OPLS-AA all-atom force field and the Analytical Generalized Born plus Non-Polar (AGBNP) implicit solvent model, in conjunction with torsion angle conformational search protocols based on the Protein Local Optimization Program (PLOP), are shown to be effective in predicting the native conformations of 57 9-residue and 35 13-residue loops of a diverse series of proteins with low sequence identity. The novel nonpolar solvation free energy estimator implemented in AGBNP augmented by correction terms aimed at reducing the occurrence of ion pairing are important to achieve the best prediction accuracy. Extended versions of the previously developed PLOP-based conformational search schemes based on calculations in the crystal environment are reported that are suitable for application to loop homology modeling without the crystal environment. Our results suggest that in general the loop backbone conformation is not strongly influenced by crystal packing. The application of the temperature Replica Exchange Molecular Dynamics (T-REMD) sampling method for a few examples where PLOP sampling is insufficient are also reported. The results reported indicate that the OPLS-AA/AGBNP effective potential is suitable for high-resolution modeling of proteins in the final stages of homology modeling and/or protein crystallographic refinement.     

Stereospecific assignments of protein NMR resonances based on the tertiary structure and 2D/3D NOE data

In many cases of protein structure determination by NMR a high-quality structure is required. An important contribution to structural precision is stereospecific assignment of magnetically nonequivalent prochiral methylene and methyl groups, eliminating the need for introducing pseudoatoms and pseudoatom corrections in distance restraint lists. Here, we introduce the stereospecific assignment program that uses the resonance assignment, a preliminary 3D structure and 2D and/or 3D nuclear Overhauser effect spectroscopy peak lists for stereospecific assignment. For each prochiral group the algorithm automatically calculates a score for the two different stereospecific assignment possibilities, taking into account the presence and intensity of the nuclear Overhauser effect (NOE) peaks that are expected from the local environment of each prochiral group (i.e., the close neighbors). The performance of the algorithm has been tested and used on NMR data of alpha-helical and beta-sheet proteins using homology models and/or X-ray structures. The program produced no erroneous stereospecific assignments provided the NOEs were carefully picked and the 3D model was sufficiently accurate. The set of NOE distance restraints produced by nmr2st using the results of the SSA module was superior in generating good-quality ensembles of NMR structures (low deviations from upper limits in conjunction with low root-mean-square-deviation values) in the first round of structure calculations. The program uses a novel approach that employs the entire 3D structure of the protein to obtain stereospecific assignment; it can be used to speed up the NMR structure refinement and to increase the quality of the final NMR ensemble even when no scalar or residual dipolar coupling information is available.     

Completely automated, highly error-tolerant macromolecular structure determination from multidimensional nuclear overhauser enhancement spectra and chemical shift assignments

The major rate-limiting step in high-throughput NMR protein structure determination involves the calculation of a reliable initial fold, the elimination of incorrect nuclear Overhauser enhancement (NOE) assignments, and the resolution of NOE assignment ambiguities. We present a robust approach to automatically calculate structures with a backbone coordinate accuracy of 1.0-1.5 A from datasets in which as much as 80% of the long-range NOE information (i.e., between residues separated by more than five positions in the sequence) is incorrect. The current algorithm differs from previously published methods in that it has been expressly designed to ensure that the results from successive cycles are not biased by the global fold of structures generated in preceding cycles. Consequently, the method is highly error tolerant and is not easily funnelled down an incorrect path in either three-dimensional structure or NOE assignment space. The algorithm incorporates three main features: a linear energy function representation of the NOE restraints to allow maximization of the number of simultaneously satisfied restraints during the course of simulated annealing; a method for handling the presence of multiple possible assignments for each NOE cross-peak which avoids local minima by treating each possible assignment as if it were an independent restraint; and a probabilistic method to permit both inactivation and reactivation of all NOE restraints on the fly during the course of simulated annealing. NOE restraints are never removed permanently, thereby significantly reducing the likelihood of becoming trapped in a false minimum of NOE assignment space. The effectiveness of the algorithm is demonstrated using completely automatically peak-picked experimental NOE data from two proteins: interleukin-4 (136 residues) and cyanovirin-N (101 residues). The limits of the method are explored using simulated data on the 56-residue B1 domain of Streptococcal protein G.