FINGAR: A new genetic algorithm-based method for fitting NMR data

Summary A new NMR refinement method, FINGAR (FIt NMR using a Genetic AlgoRithm), has been developed, which allows one to determine a weighted set of structures that best fits measured NMR-derived data. This method shows appreciable advantages over commonly used refinement methods. FINGAR generates an ensemble of conformations whose average reproduces the experimental NMR-derived restraints. In addition, a statistical importance weight is assigned to each of the conformations in the ensemble. As a result, one is not limited to simply presenting an envelope of sampled conformers. Instead, one can subsequently focus on a select few conformers of high weight. This is critical, because many structural analyses depend on using discrete conformations, not simply averages or ensembles. The genetic algorithm used by FINGAR allows one to simultaneously and reliably fit against many restraints, and to generate solutions which include as many conformations with non-zero weights as are necessary to generate the best fit. An added benefit of FINGAR is that because the time-consuming step in this method needs only to be performed once, in the beginning of the first run, numerous FINGAR simulations can be performed rapidly.     

TOUCHSTONEX: protein structure prediction with sparse NMR data

TOUCHSTONEX, a new method for folding proteins that uses a small number of long-range contact restraints derived from NMR experimental NOE (nuclear Overhauser enhancement) data, is described. The method employs a new lattice-based, reduced model of proteins that explicitly represents C(alpha), C(beta), and the sidechain centers of mass. The force field consists of knowledge-based terms to produce protein-like behavior, including various short-range interactions, hydrogen bonding, and one-body, pairwise, and multibody long-range interactions. Contact restraints were incorporated into the force field as an NOE-specific pairwise potential. We evaluated the algorithm using a set of 125 proteins of various secondary structure types and lengths up to 174 residues. Using N/8 simulated, long-range sidechain contact restraints, where N is the number of residues, 108 proteins were folded to a C(alpha)-root-mean-square deviation (RMSD) from native below 6.5 A. The average RMSD of the lowest RMSD structures for all 125 proteins (folded and unfolded) was 4.4 A. The algorithm was also applied to limited experimental NOE data generated for three proteins. Using very few experimental sidechain contact restraints, and a small number of sidechain-main chain and main chain-main chain contact restraints, we folded all three proteins to low-to-medium resolution structures. The algorithm can be applied to the NMR structure determination process or other experimental methods that can provide tertiary restraint information, especially in the early stage of structure determination, when only limited data are available.     

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.     

Strategy for supplementing structure calculations using limited data with hydrophobic distance restraints

Introductory biochemistry texts often note that the fold of a protein is completely defined when the dihedral angles phi and psi are known for each amino acid. This assertion was examined with torsion angle dynamics and simulated annealing (TAD/SA) calculations of protein G using only dihedral angle restraints. When all dihedral angles were restrained to within 1 degrees of the values of the X-ray structure, the TAD/SA structures gave a backbone root mean square deviation to the target of 4 A. Factors that contributed to divergence from the correct solution include deviations of peptide bonds from planarity, internal conflicts resulting from the nonuniform energies of different phi, psi combinations, and relaxation to extended conformations in the absence of long-range constraints. Simulations including hydrogen-bond restraints showed that even a few long-range contacts constrain the fold better than a complete set of accurate dihedral restraints. A procedure is described for TAD/SA calculations using hydrogen-bond restraints, idealized dihedral restraints for residues in regular secondary structures, and "hydrophobic distance restraints" derived from the positions of hydrophobic residues in the amino acid sequence. The hydrogen-bond restraints are treated as inviolable, whereas violated hydrophobic restraints are removed following reduction of restraint upper bounds from 2 to 1 times the predicted radius of gyration. The strategy was tested with simulated restraints from X-ray structures of proteins from different fold classes and NMR data for cold shock protein A that included only backbone chemical shifts and hydrogen bonds obtained from a long-range HNCO experiment.     

NMR spectroscopy, molecular dynamics, and conformation of a synthetic octasaccharide fragment of the O-specific polysaccharide of Shigella dysenteriae type 1

A synthetic octasaccharide fragment (2) of the O-specific polysaccharide (1) of Shigella dysenteriae type 1 has been studied as its methyl glycoside by one- and two-dimensional homo- and heteronuclear NMR spectroscopy. Complete 1H and 13C NMR assignments have been generated, and the 13C spin-lattice relaxation times have been measured for the octasaccharide 2. A congener (6) of this octasaccharide containing one D-galactose residue with a specific 13C label at C-1 has been synthesized and used to measure interglycosidic 13C-1H coupling by the 2D J-resolved 1H NMR method. From the NMR data, three types of conformational restraints were developed: (a) 29 inter-residue, distance restraints; (b) 48 intra-residue, ring atom dihedral angle restraints, and (c) one heteronuclear, inter-residue dihedral angle restraint. The use of these restraints in a restrained molecular dynamics computation with simulated annealing yielded a conformation resembling a short, irregular spiral, with methyl substituents on the exterior.     

Protein structure calculation with data imputation: the use of substitute restraints

The amount of experimental restraints e.g., NOEs is often too small for calculating high quality three-dimensional structures by restrained molecular dynamics. Considering this as a typical missing value problem we propose here a model based data imputation technique that should lead to an improved estimation of the correct structure. The novel automated method implemented in AUREMOL makes a more efficient use of the experimental information to obtain NMR structures with higher accuracy. It creates a large set of substitute restraints that are used either alone or together with the experimental restraints. The new approach was successfully tested on three examples: firstly, the Ras-binding domain of Byr2 from Schizosaccharomyces pombe, the mutant HPr (H15A) from Staphylococcus aureus, and a X-ray structure of human ubiquitin. In all three examples, the quality of the resulting final bundles was improved considerably by the use of additional substitute restraints, as assessed quantitatively by the calculation of RMSD values to the “true” structure and NMR R-factors directly calculated from the original NOESY spectra or the published diffraction data.     

Evaluation of the utility of NMR structures determined from minimal NOE-based restraints for structure-based drug design, using MMP-1 as an example

The application of deuterium labeling and residual dipolar coupling constants in combination with other structural information has demonstrated the potential for significantly expanding the range of viable protein targets for structural analysis by NMR. A previous study by Clore et al. [(1999) J. Am. Chem. Soc. 121, 6513-6514] demonstrated that a significant improvement in the overall protein structure occurs with the combination of residual dipolar coupling constants and minimal tertiary long-range distance restraints. The analysis of NMR protein structures determined with minimal structural information is extended with a particular interest in the utility of these structures for a structure-based drug design program. As an example, the catalytic fragment of human fibroblast collagenase (MMP-1) was used to follow the effect of minimal restraint sets on the protein structure and its utility in drug design with a particular interest in the effect on the active site conformation. An MMP-1 structure that was calculated with the maximal number of restraints attainable with the constraint of a deuterated protein was shown to be very similar to a high-quality MMP-1 structure that was calculated from a complete set of restraints. The superposition of the active site backbone atoms for the high-quality and minimal restraint MMP-1 structures yielded an rmsd of 0.68 A where the size and shape of the S1' pocket are nearly identical. Additionally, an MMP-1-CGS-27023A complex based on a minimal set of NOE-based restraints reliably reproduced the structure of the complex, establishing the usefulness of the structures for drug design.     

Molecular dynamics simulation using weak-coupling NOE distance restraining

Summary Application of the weak-coupling scheme to restrain the configurations of a molecular system to a set of NOE distance restraints is investigated using two test systems: (i) a 15-atom chain molecule with one distance restraint; and (ii) a protein molecule with hundreds of NOE distance restraints. Atom-atom distance restraining by the weak-coupling technique is possible, but this method does not produce as good results as the penalty function method normally used to maintain NOE distance restraints.Abbreviations NOE nuclear Overhauser effect - MD molecular dynamics - PDB protein data bank     

A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

High-resolution structure determination of homo-oligomeric protein complexes remains a daunting task for NMR spectroscopists. Although isotope-filtered experiments allow separation of intermolecular NOEs from intramolecular NOEs and determination of the structure of each subunit within the oligomeric state, degenerate chemical shifts of equivalent nuclei from different subunits make it difficult to assign intermolecular NOEs to nuclei from specific pairs of subunits with certainty, hindering structural analysis of the oligomeric state. Here, we introduce a graphical method, DISCO, for the analysis of intermolecular distance restraints and structure determination of symmetric homo-oligomers using residual dipolar couplings. Based on knowledge that the symmetry axis of an oligomeric complex must be parallel to an eigenvector of the alignment tensor of residual dipolar couplings, we can represent distance restraints as annuli in a plane encoding the parameters of the symmetry axis. Oligomeric protein structures with the best restraint satisfaction correspond to regions of this plane with the greatest number of overlapping annuli. This graphical analysis yields a technique to characterize the complete set of oligomeric structures satisfying the distance restraints and to quantitatively evaluate the contribution of each distance restraint. We demonstrate our method for the trimeric E. coli diacylglycerol kinase, addressing the challenges in obtaining subunit assignments for distance restraints. We also demonstrate our method on a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G to show the resilience of our method to ambiguous atom assignments. In both studies, DISCO computed oligomer structures with high accuracy despite using ambiguously assigned distance restraints.     

Validation of a new restraint docking method for solution structure determinations of protein–ligand complexes

A new method is proposed for docking ligands into proteins in cases where an NMR-determined solution structure of a related complex is available. The method uses a set of experimentally determined values for protein–ligand, ligand–ligand, and protein–protein restraints for residues in or near to the binding site, combined with a set of protein–protein restraints involving all the other residues which is taken from the list of restraints previously used to generate the reference structure of a related complex. This approach differs from ordinary docking methods where the calculation uses fixed atomic coordinates from the reference structure rather than the restraints used to determine the reference structure. The binding site residues influenced by replacing the reference ligand by the new ligand were determined by monitoring differences in ¹H chemical shifts. The method has been validated by showing the excellent agreement between structures of L. casei dihydrofolate reductase.trimetrexate calculated by conventional methods using a full experimentally determined set of restraints and those using this new restraint docking method based on an L. casei dihydrofolate reductase.methotrexate reference structure.     

The influence of stereospecific assignments on the determination of three-dimensional structures of proteins by nuclear magnetic resonance spectroscopy. Application to the sea anemone protein BDS-I

The influence of the stereospecific assignments of beta-methylene protons and the classification of chi 1 torsion angles on the definition of the three-dimensional structures of proteins determined from NMR data is investigated using the sea anemone protein BDS-I (43 residues) as a model system. Two sets of structures are computed. The first set comprises 42 converged structures (denoted STEREO structures) calculated on the basis of the complete list of restraints derived from the NMR data, consisting of 489 interproton and 24 hydrogen bonding distance restraints, supplemented by 23 phi backbone and 21 chi 1 side chain torsion angle restraints. The second set comprises 31 converged structures (denoted NOSTEREO structures) calculated from a reduced data set in which those restraints arising from stereospecific assignments, and the corresponding chi 1 torsion angle restraints, are explicitly omitted. The results show that the inclusion of the stereospecific restraints leads to a significant improvement in the definition of the structure of BDS-I, both with respect to the backbone and the detailed arrangement of the side chains. Average atomic rms differences between the individual structures and the mean structures for the backbone atoms are 0.67 +/- 0.12 A and 0.93 +/- 0.16 A for the STEREO and NOSTEREO structures, respectively; the corresponding values for all atoms are 0.90 +/- 0.17 A and 1.17 +/- 0.17 A, respectively. In addition, while the overall fold remains unchanged, there is a small but significant atomic displacement between the two sets of structures.     

Relaxation data in NMR structure determination: model calculations for the lysozyme-Gd3+ complex

The effect of including paramagnetic relaxation data as additional restraints in the determination of protein tertiary structures from NMR data has been explored by a systematic series of model calculations. The system used for testing the method was the 2.0 A resolution tetragonal crystal structure of hen egg white lysozyme (129 amino acid residues) and structures were generated using a version of the hybrid "distance geometry-dynamic simulated annealing" procedure. A limited set of 769 NOEs was used as restraints in all the calculations; the strengths of these were categorized into three classes on the basis of distances observed in the crystal structure. The values of 50 phi angles were also restrained on the basis of amide-alpha coupling constants calculated from the X-ray structure. Five sets of 12 structures were determined using differing sets of paramagnetic relaxation data as restraints additional to those involving the NOE and coupling constant data. The paramagnetic relaxation data were modeled on the basis of the distances of defined protons from the crystallographic binding site of Gd3+ in lysozyme. Analysis of the results showed that the relaxation data significantly improved the correspondence between the set of generated structures and the crystal structure, and that the more well defined the relaxation data, the more significant the improvement in the quality of the structures. The results suggest that the inclusion of paramagnetic relaxation restraints could be of significant value for the experimental determination of protein structures from NMR data.     

Simultaneous determination of disulphide bridge topology and three-dimensional structure using ambiguous intersulphur distance restraints: Possibilities and limitations

Knowledge of the native disulphide bridge topology allows the introduction of conformational restraints between remote parts of the peptide chain. This information is therefore of great importance for the successful determination of the three-dimensional structure of cysteine-rich proteins by NMR spectroscopy. In this paper we investigate the limitations of using ambiguous intersulphur restraints [Nilges, M. (1995) J. Mol. Biol., 245, 645–660] associated with NMR experimental information to determine the native disulphide bridge pattern. Using these restraints in a simulated annealing protocol we have determined the correct topology of numerous examples, including a protein with seven disulphide bridges (phospholipase A₂) and a protein in which 25% of the total number of residues are cysteines (-conotoxin GIIIB). We have also characterised the behaviour of the method when only limited experimental data is available, and find that the proposed protocol permits disulphide bridge determination even with a small number of restraints (around 5 NOEs – including a long-range restraint – per residue). In addition, we have shown that under these conditions the use of a reduced penalty function allows the identification of misassigned NOE restraints. These results indicate that the use of ambiguous intersulphur distances with the proposed simulated annealing protocol is a general method for the determination of disulphide bridge topology, particularly interesting in the first steps of NMR study of cysteine-rich proteins. Comparison with previously proposed protocols indicates that the presented method is more reliable and the interpretation of results is straightforward.     

Distributed torsion angle grid search in high dimensions: A systematic approach to NMR structure determination

Two complementary approaches for systematic search in torsion angle space are described for the generation of all conformations of polypeptides which satisfy experimental NMR restraints, hard-sphere van der Waals radii, and rigid covalent geometry. The first procedure is based on a recursive, tree search algorithm for the examination of linear chains of torsion angles, and uses a novel treatment to propagate the search results to neighboring regions so that the structural consequences of the restraints are fully realized. The second procedure is based on a binary combination of torsion vector spaces for connected submolecules, and produces intermediate results in Cartesian space for a more robust restraint analysis. Restraints for NMR applications include bounds on torsion angles and internuclear distances, including relational and degenerate restraints involving equivalent and nonstereoassigned protons. To illustrate these methods, conformation search results are given for the tetrapeptide APGA restrained to an idealized -turn conformation, an alanine octapeptide restrained to a right-handed helical conformation, and the structured region of the peptide SYPFDV.     

MMM: Integrative ensemble modeling and ensemble analysis

Proteins and their complexes can be heterogeneously disordered. In ensemble modeling of such systems with restraints from several experimental techniques the following problems arise: (a) integration of diverse restraints obtained on different samples under different conditions; (b) estimation of a realistic ensemble width; (c) sufficient sampling of conformational space; (d) representation of the ensemble by an interpretable number of conformers; (e) recognition of weak order with site resolution. Here, I introduce several tools that address these problems, focusing on utilization of distance distribution information for estimating ensemble width. The RigiFlex approach integrates such information with high‐resolution structures of ordered domains and small‐angle scattering data. The EnsembleFit module provides moderately sized ensembles by fitting conformer populations and discarding conformers with low population. EnsembleFit balances the loss in fit quality upon combining restraint subsets from different techniques. Pair correlation analysis for residues and local compaction analysis help in feature detection. The RigiFlex pipeline is tested on data simulated from the structure 70 kDa protein‐RNA complex RsmE/RsmZ. It recovers this structure with ensemble width and difference from ground truth both being on the order of 4.2 Å. EnsembleFit reduces the ensemble of the proliferating‐cell‐nuclear‐antigen‐associated factor p15^PAF from 4,939 to 75 conformers while maintaining good fit quality of restraints. Local compaction analysis for the PaaA2 antitoxin from E. coli O157 revealed correlations between compactness and enhanced residual dipolar couplings in the original NMR restraint set.     

Time- and ensemble-averaged direct NOE restraints

Summary NMR data are collected as time- and ensemble-averaged quantities. Yet, in commonly used methods for structure determination of biomolecules, structures are required to satisfy simultaneously a large number of constrainsts. Recently, however, methods have been developed that allow a better fit of the experimental data by the use of time- or ensemble-averaged restraints. Thus far, these methods have been applied to structure refinement using distance and J-coupling restraints. In this paper, time and ensemble averaging is extended to the direct refinement with experimental NOE data. The implementation of time- and ensemble-averaged NOE restraints in DINOSAUR is described and illustrated with experimental NMR data for crambin, a 46-residue protein. Structure refinement with both time- and ensemble-averaged NOE restraints results in lower R-factors, indicating a better fit of the experimental NOE data.     

Molecular dynamics re-refinement of two different small RNA loop structures using the original NMR data suggest a common structure

Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility-using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions-by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to "update" older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias (such as small angle deviations with the current AMBER force fields), and a proper balance between the various restraint weights.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

Methods of NMR structure refinement: molecular dynamics simulations improve the agreement with measured NMR data of a C-terminal peptide of GCN4-p1

The C-terminal trigger sequence is essential in the coiled-coil formation of GCN4-p1; its conformational properties are thus of importance for understanding this process at the atomic level. A solution NMR model structure of a peptide, GCN4p16–31, encompassing the GCN4-p1 trigger sequence was proposed a few years ago. Derived using a standard single-structure refinement protocol based on 172 nuclear Overhauser effect (NOE) distance restraints, 14 hydrogen-bond and 11 ϕ torsional-angle restraints, the resulting set of 20 NMR model structures exhibits regular α-helical structure. However, the set slightly violates some measured NOE bounds and does not reproduce all 15 measured ³J(H_N-H_Cα)-coupling constants, indicating that different conformers of GCN4p16–31 might be present in solution. With the aim to resolve structures compatible with all NOE upper distance bounds and ³J-coupling constants, we executed several structure refinement protocols employing unrestrained and restrained molecular dynamics (MD) simulations with two force fields. We find that only configurational ensembles obtained by applying simultaneously time-averaged NOE distance and ³J-coupling constant restraining with either force field reproduce all the experimental data. Additionally, analyses of the simulated ensembles show that the conformational variability of GCN4p16–31 in solution admitted by the available set of 187 measured NMR data is larger than represented by the set of the NMR model structures. The conformations of GCN4p16–31 in solution differ in the orientation not only of the side-chains but also of the backbone. The inconsistencies between the NMR model structures and the measured NMR data are due to the neglect of averaging effects and the inclusion of hydrogen-bond and torsional-angle restraints that have little basis in the primary, i.e. measured NMR data.