Complete relaxation matrix refinement of NMR structures of proteins using analytically calculated dihedral angle derivatives of NOE intensities

Summary A new method for refining three-dimensional (3D) NMR structures of proteins is described, which takes account of the complete relaxation pathways. Derivatives of the NOE intensities with respect to the dihedral angles are analytically calculated, and efficiently evaluated with the use of a filter technique for identifying the dominant terms of these derivatives. This new method was implemented in the distance geometry program DIANA. As an initial test, we refined 30 rigid distorted helical structures, using a simulated data set of NOE distance constraints for a rigid standard -helix. The final root-mean-square deviations of the refined structures relative to the standard helix were less than 0.1 Å, and the R-factors dropped from values between 7% and 32% to values of less than 0.5% in all cases, which compares favorably with the results from distance geometry calculations. In particular, because spin diffusion was not explicitly considered in the evaluation of exact¹H–¹H distances corresponding to the simulated NOE intensities, a group of nearly identical distance geometry structures was obtained which had about 0.5 Å root-mean-square deviation from the standard -helix. Further test calculations using an experimental NOE data set recorded for the protein trypsin inhibitor K showed that the complete relaxation matrix refinement procedure in the DIANA program is functional also with systems of practical interest.Abbreviations RMSD root-mean-square deviation - NOE nuclear Overhauser enhancement - NOESY 2-dimensional nuclear Overhauser enhancement spectroscopy - CPU central processing unit     

Determination of the conformation of Lewis blood group oligosaccharides by simulation of two-dimensional nuclear Overhauser data

Through control of both the nmr probe temperature and of the solvent viscosity, phase-sensitive two-dimensional 1H nuclear Overhauser data (NOESY) at 300 and 500 MHz are obtained with excellent signal-to-noise ratios for Lewis blood group penta- and hexasaccharides isolated from human milk. Relatively long mixing times are required to produce measurable NOE intensities in these oligosaccharides, which makes a full relaxation matrix analysis necessary. By measurements of selective T1 for a few isolated 1H resonances, it was possible to generate a simulation of the complete NOESY spectrum at arbitrary mixing time for comparison with the experimental data. From an exhaustive search of the conformational space, it was found that only a small range of glycosidic dihedral angles of the nonreducing terminal Lewis blood group determinant fragments of the milk oligosaccharides LNF-2 and LND-1 produce simulated spectra agreeing within experimental error to the data. Conformational energy calculations reveal that each of these conformations is also one of minimum energy. It is concluded that the Lewis(a) and Lewis(b) oligosaccharides adopt relatively compact rigid structures in solution, as shown by the observation of cross peaks between protons in nonadjacent residues. Like the blood group A and H oligosaccharides, there exists only a small dependence of the conformation for Lewis(a) and Lewis(b) oligosaccharides on solvent. The apparent lack of dependence of conformation of these oligosaccharides on DMSO in D2O suggests that modification of solvent viscosity with mixtures of DMSO:D2O may provide a useful general strategy of NOESY studies of oligosaccharides.     

The program ASNO for computer-supported collection of NOE upper distance constraints as input for protein structure determination

Summary A new program, ASNO (ASsign NOes), for computer-supported NOE cross-peak assignments is described. ASNO is used for structure refinement in several rounds of NOESY cross-peak assignments and 3D structure calculations, where the preliminary structures are used as a reference to resolve ambiguities in NOE assignments which are otherwise based on the chemical shifts available from the sequence-specific resonance assignments. The practical use of ASNO for proteins is illustrated with the structure determination of Dendrotoxin K from Dendroaspis polylepis polylepis.Abbreviations Toxin K dendrotoxin K (or trypsin inhibitor homologue K) from the venom of the black mamba Dendroaspis polylepis polylepis - NOE nuclear Overhauser effect - NOESY NOE spectroscopy - REDAC use of redundant dihedral angle constraints - RMSD root-mean-square deviation To whom correspondence should be addressed.     

High-resolution solution structure of siamycin II: Novel amphipathic character of a 21-residue peptide that inhibits HIV fusion

Summary The 21-amino acid peptides siamycin II (BMY-29303) and siamycin I (BMY-29304), derived from Streptomyces strains AA3891 and AA6532, respectively, have been found to inhibit HIV-1 fusion and viral replication in cell culture. The primary sequence of siamycin II is CLGIGSCNDFAGCGYAIVCFW. Siamycin I differs by only one amino acid; it has a valine residue at position 4. In both peptides, disulfide bonds link Cys¹ with Cys¹³ and Cys⁷ with Cys¹⁹, and the side chain of Asp⁹ forms an amide bond with the N-terminus. Siamycin II, when dissolved in a 50:50 mixture of DMSO and H₂O, yields NOESY spectra with exceptional numbers of cross peaks for a peptide of this size. We have used 335 NOE distance constraints and 13 dihedral angle constraints to generate an ensemble of 30 siamycin II structures; these have average backbone atom and all heavy atom rmsd values to the mean coordinates of 0.24 and 0.52 Å, respectively. The peptide displays an unusual wedge-shaped structure, with one face being predominantly hydrophobic and the other being predominantly hydrophilic. Chemical shift and NOE data show that the siamycin I structure is essentially identical to siamycin II. These peptides may act by preventing oligomerization of the HIV transmembrane glycoprotein gp41, or by interfering with interactions between gp41 and the envelope glycoprotein gp120, the cell membrane or membrane-bound proteins [Frèchet, D. et al. (1994) Biochemistry, 33, 42–50]. The amphipathic nature of siamycin II and siamycin I suggests that a polar (or apolar) site on the target protein may be masked by the apolar (or polar) face of the peptide upon peptide/protein complexation.Abbreviations ABNR adopted basis Newton Raphson - AIDS acquired immunodeficiency syndrome - CW continuous wave - DMSO dimethylsulfoxide - DQF-COSY two-dimensional double-quantum-filtered correlation spectroscopy - HIV human immunodeficiency virus - HSQC heteronuclear single-quantum coherence - NOE nuclear Overhauser enhancement - NOESY two-dimensional nuclear Overhauser enhancement spectroscopy - ppm parts per million - P.E.-COSY two-dimensional primitive exclusive correlation spectroscopy - REDAC redundant dihedral angle constraint - rf radio frequency - rmsd root-mean-square difference - SIV simian immunodeficiency virus - sw spectral width - _m mixing time - TOCSY two-dimensional total correlation spectroscopy - TSP trimethylsilyl-2,2,3,3-²H₄-propionate - 2D two-dimensional     

RFAC,a program for automated NMR R-factor estimation

A computer program (RFAC) has been developed, which allows the automated estimation of residual indices (R-factors) for protein NMR structures and gives a reliable measure for the quality of the structures. The R-factor calculation is based on the comparison of experimental and simulated ¹H NOESY NMR spectra. The approach comprises an automatic peak picking and a Bayesian analysis of the data, followed by an automated structure based assignment of the NOESY spectra and the calculation of the R-factor. The major difference to previously published R-factor definitions is that we take the non-assigned experimental peaks into account as well. The number and the intensities of the non-assigned signals are an important measure for the quality of an NMR structure. It turns out that for different problems optimally adapted R-factors should be used which are defined in the paper. The program allows to compute a global R-factor, different R-factors for the intra residual NOEs, the inter residual NOEs, sequential NOEs, medium range NOEs and long range NOEs. Furthermore, R-factors can be calculated for various user defined parts of the molecule or it is possible to obtain a residue-by-residue R-factor. Another possibility is to sort the R-factors according to their corresponding distances. The summary of all these different R-factors should allow the user to judge the structure in detail. The new program has been successfully tested on two medium sized proteins, the cold shock protein (TmCsp) from Termotoga maritima and the histidine containing protein (HPr) from Staphylococcus carnosus. A comparison with a previously published R-factor definition shows that our approach is more sensitive to errors in the calculated structure.     

AUREMOL-RFAC-3D,combination of R-factors and their use for automated quality assessment of protein solution structures

We present here the computer program AUREMOL-RFAC-3D that is a generalization of the previously published program RFAC for the fully automated estimation of residual indices (R-factors) from 2D NOESY spectra. It is part of the larger AUREMOL software package (www.auremol.de). RFAC-3D calculates R-factors directly from two-dimensional homonuclear NOESY spectra as well as from three-dimensional ¹⁵N or ¹³C edited NOESY-HSQC spectra and thus extends the application range to larger proteins. The fully automated method includes automated peak picking and integration, a Bayesian noise and artifact recognition and the use of the complete relaxation matrix formalism. To enhance the reliability of the calculated R-factors the method is also generalized to calculate combined R-factors from a set of 2D and 3D-spectra. For an optimal combination of the information derived from different sources a plausible formalism had to be derived. In addition, we present a novel direct R-factors based measure that correlates an R-factors as defined in this paper to the root mean square deviation of the actual structure from the optimal structure. The new program has been successfully tested on the histidine containing phosphocarrier protein (HPr) from Staphylococcus carnosus and on the Ras-binding domain (RBD) of the Ral guanine-nucleotide dissociation stimulation factor (RalGDS).     

Solution structures of human transforming growth factor alpha derived from 1H NMR data

The 600-MHz 1H NMR spectrum of the des-Val-Val mutant of human transforming growth factor alpha (TGF-alpha) was reassigned at pH = 6.3. The conformation space of des-Val-Val TGF-alpha was explored by distance geometry embedding followed by restrained molecular dynamics refinement using NOE distance constraints and some torsion angle constraints derived from J-couplings. Over 80 long-range NOE constraints were found by completely assigning all resolved cross-peaks in the NOESY spectra. Low NOE constraint violations were observed in structures obtained with the following three different refinement procedures: interactive annealing in DSPACE, AMBER 3.0 restrained molecular dynamics, and dynamic simulated annealing in XPLOR. The segment from Phe15 to Asp47 was found to be conformationally well-defined. Back-calculations of NOESY spectra were used to evaluate the quality of the structures. Our calculated structures resemble the ribbon diagram presentations that were recently reported by other groups. Several side-chain conformations appear to be well-defined as does the relative orientation of the C loop to the N-terminal half of the protein.     

Protein NMR structure determination with automated NOE-identification in the NOESY spectra using the new software ATNOS

Novel algorithms are presented for automated NOESY peak picking and NOE signal identification in homonuclear 2D and heteronuclear-resolved 3D [¹H,¹H]-NOESY spectra during de novoprotein structure determination by NMR, which have been implemented in the new software ATNOS (automated NOESY peak picking). The input for ATNOS consists of the amino acid sequence of the protein, chemical shift lists from the sequence-specific resonance assignment, and one or several 2D or 3D NOESY spectra. In the present implementation, ATNOS performs multiple cycles of NOE peak identification in concert with automated NOE assignment with the software CANDID and protein structure calculation with the program DYANA. In the second and subsequent cycles, the intermediate protein structures are used as an additional guide for the interpretation of the NOESY spectra. By incorporating the analysis of the raw NMR data into the process of automated de novoprotein NMR structure determination, ATNOS enables direct feedback between the protein structure, the NOE assignments and the experimental NOESY spectra. The main elements of the algorithms for NOESY spectral analysis are techniques for local baseline correction and evaluation of local noise level amplitudes, automated determination of spectrum-specific threshold parameters, the use of symmetry relations, and the inclusion of the chemical shift information and the intermediate protein structures in the process of distinguishing between NOE peaks and artifacts. The ATNOS procedure has been validated with experimental NMR data sets of three proteins, for which high-quality NMR structures had previously been obtained by interactive interpretation of the NOESY spectra. The ATNOS-based structures coincide closely with those obtained with interactive peak picking. Overall, we present the algorithms used in this paper as a further important step towards objective and efficient de novoprotein structure determination by NMR.     

How accurately can oligonucleotide structures be determined from the hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics approach?

The accuracy and precision of structures derived from a combined hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics methodology were examined with simulations that included typical experimental errors. NOESY data were simulated for a DNA dodecamer duplex, d-(CGCGAATTCGCG)2, with added volume error of approximately 20% and low-level thermal noise. Distances derived from a hybrid relaxation matrix analysis of the NOE data were used as constraints in molecular dynamics driven structural refinements of several initial model geometries. The final structures were compared against results obtained from the traditional isolated two-spin approximation treatment of these NOESY volumes and also against refined structures that employed error-free data. Results show that the structures derived from the relaxation rate matrix analysis of the NOESY data are more accurate than those derived from a simple two-spin approximation analysis and it is possible to achieve refinement to the level of simulated experimental error. Results may be significantly improved with the use of either more accurately measured NOESY volumes or additional matrix-derived constraints. Many of the helical parameters and backbone torsional angles may be accurately reproduced by the hybrid matrix methodology.     

Exploration of disorder in protein structures by X-ray restrained molecular dynamics

Conformational disorder in crystal structures of ribonuclease-A and crambin is studied by including two independent structures in least-squares optimizations against X-ray data. The optimizations are carried out by X-ray restrained molecular dynamics (simulated annealing refinement) and by conventional least-squares optimization. Starting from two identical structures, the optimizations against X-ray data lead to significant deviations between the two, with rms backbone displacements of 0.45 A for refinement of ribonuclease at 1.53 A resolution, and 0.31 A for crambin at 0.945 A. More than 15 independent X-ray restrained molecular dynamics runs have been carried out for ribonuclease, and the displacements between the resulting structures are highly reproducible for most atoms. These include residues with two or more conformations with significant dihedral angle differences and alternative hydrogen bonding, as well as groups of residues that undergo displacements that are suggestive of rigid-body librations. The crystallographic R-values obtained are approximately 13%, as compared to 15.3% for a comparable refinement with a single structure. Least-squares optimization without an intervening restrained molecular dynamics stage is sufficient to reproduce most of the observed displacements. Similar results are obtained for crambin, where the higher resolution of the X-ray data allows for refinement of unconstrained individual anisotropic temperature factors. These are shown to be correlated with the displacements in the two-structure refinements.     

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.     

Application of automated NOE assignment to three-dimensional structure refinement of a 28 kDa single-chain T cell receptor

An automated procedure for NOE assignment and three-dimensional structure refinement is presented. The input to the procedure consists of (1) an ensemble of preliminary protein NMR structures, (2) partial sequence-specific assignments for the protein and (3) the positions and volumes of unassigned NOESY cross peaks. Chemical shifts for unassigned side chain protons are predicted from the preliminary structures. The chemical shifts and unassigned NOESY cross peaks are input to an automated procedure for NOE assignment and structure calculation (ARIA) [Nilges et al. (1997) J. Mol. Biol., 269, 408–422]. ARIA is optimized for the task of structure refinement of larger proteins. Errors are filtered to ensure that sequence-specific assignments are reliable. The procedure is applied to the 27.8 kDa single-chain T cell receptor (scTCR). Preliminary NMR structures, nearly complete backbone assignments, partial assignments of side chain protons and more than 1300 unassigned NOESY cross peaks are input. Using the procedure, the resonant frequencies of more than 40 additional side chain protons are assigned. Over 400 new NOE cross peaks are assigned unambiguously. Distances derived from the automatically assigned NOEs improve the precision and quality of calculated scTCR structures. In the refined structures, a hydrophobic cluster of side chains on the scTCR surface that binds major histocompatibility complex (MHC)/antigen is revealed. It is composed of the side chains of residues from three loops and stabilizes the conformation of residues that interact with MHC.     

A NOESY-HSQC simulation program, SPIRIT

A program SPIRIT (Simulation Program considering Incomplete Recovery of z magnetization and INEPT Transfer efficiency) has been developed to simulate three-dimensional NOESY-HSQC spectra. This program takes into account (1) different transfer efficiency during INEPT and reverse INEPT durations due to differential relaxation rates and¹ J coupling constants; (2) the different effect of the sensitivity-enhancement scheme on CH, CH₂ and CH₃ systems; and (3) incomplete recovery of longitudinal magnetization between scans. The simulation program incorporates anisotropic tumbling mode for symmetric tops, and allows for differential external relaxation rates for protons. Some well-defined internal motions, such as the fast rotation of methyl groups, are taken into account. The simulation program also allows for input of multiple conformations and their relative populations to calculate the average relaxation matrix to account for slow internal motions. With the SPIRIT program, the sensitivity-enhanced NOESY-HSQC experiment can be used directly in the evaluation of the accuracy of structures, which can potentially be improved by direct refinement against the primary data. Abbreviations: NOESY, nuclear Overhauser enhancement spectroscopy; HSQC, heteronuclear single quantum correlation; INEPT, insensitive nuclei enhanced by polarization transfer.     

Sucrose in aqueous solution revisited, Part 2: adaptively biased molecular dynamics simulations and computational analysis of NMR relaxation

We report 100 ns molecular dynamics simulations, at various temperatures, of sucrose in water (with concentrations of sucrose ranging from 0.02 to 4M), and in a 7:3 water‐DMSO mixture. Convergence of the resulting conformational ensembles was checked using adaptive‐biased simulations along the glycosidic Φ and ψ torsion angles. NMR relaxation parameters, including longitudinal (R₁) and transverse (R₂) relaxation rates, nuclear Overhauser enhancements (NOE), and generalized order parameter (S²) were computed from the resulting time‐correlation functions. The amplitude and time scales of molecular motions change with temperature and concentration in ways that track closely with experimental results, and are consistent with a model in which sucrose conformational fluctuations are limited (with 80–90% of the conformations having ??ψ values within 20° of an average conformation), but with some important differences in conformation between pure water and DMSO‐water mixtures. © 2011 Wiley Periodicals, Inc. Biopolymers 97: 289–302, 2012.     

Multiple helical conformations of the helix‐turn‐helix region revealed by NOE‐restrained MD simulations of tryptophan aporepressor,TrpR

The nature of flexibility in the helix‐turn‐helix region of E. coli trp aporepressor has been unexplained for many years. The original ensemble of nuclear magnetic resonance (NMR structures showed apparent disorder, but chemical shift and relaxation measurements indicated a helical region. Nuclear Overhauser effect (NOE) data for a temperature‐sensitive mutant showed more helical character in its helix‐turn‐helix region, but nevertheless also led to an apparently disordered ensemble. However, conventional NMR structure determination methods require all structures in the ensemble to be consistent with every NOE simultaneously. This work uses an alternative approach in which some structures of the ensemble are allowed to violate some NOEs to permit modeling of multiple conformational states that are in dynamic equilibrium. Newly measured NOE data for wild‐type aporepressor are used as time‐averaged distance restraints in molecular dynamics simulations to generate an ensemble of helical conformations that is more consistent with the observed NMR data than the apparent disorder in the previously reported NMR structures. The results indicate the presence of alternating helical conformations that provide a better explanation for the flexibility of the helix‐turn‐helix region of trp aporepressor. Structures representing these conformations have been deposited with PDB ID: 5TM0. Proteins 2017; 85:731–740. © 2016 Wiley Periodicals, Inc.     

Solution conformation study of substance P methyl ester and [Nle10]-neurokinin A (4–10) by nmr spectroscopy

High-resolution proton spectra at 500 MHz of two tachykinin peptides, substance P methyl ester (SPOMe) and [Nle¹⁰]-neurokinin A (4–10), have been obtained in dimethylsulfoxide (DMSO), and for SPOMe, also in 2, 2, 2-trifluoroethanol (TFE)/water mixtures. Complete chemical shift assignments for these peptides were made based on two-dimensional (2D) nmr techniques, correlated spectroscopy and total COSY. J coupling measurement and nuclear Overhauser effect spectroscopy (NOESY) were then used to determine the conformation of these peptides in the various solvents. Based on the J coupling, NOE correlations, and temperature coefficients of the NH resonances, it is concluded that these two peptides exist in DMSO at room temperature as a mixture of conformers that are primarily extended. For SPOMe in TFE/water with high TFE content, however, helical structures are found to be present, and they become quite clear at temperatures between 270 and 280 K. The variation of the ¹³C chemical shifts of the C_α (the secondary shift) with TFE contents corroborates this conclusion. The NOE and C_α shifts show that the main helical region for SPOMe lies between ⁴P and ⁹G. The C-terminus segment L? M? NH₂ is found to be quite flexible, which appears to be quite common for neurokinin-1 selective peptides. © 1993 John Wiley & Sons, Inc.     

Crystallographic Refinement and Structure-Factor Time-Averaging by Molecular Dynamics in the Absence of a Physical Force Field

Abstract

The application of Molecular-Dynamics simulation in protein-crystallographic structure refinement has become common practice. In this paper, structure optimizations are described where the driving force is derived only from the crystallographic data and not from any physical potential energy function. Under this extreme condition ab initio structure refinement and the application of structure-factor time averaging was investigated using a small 9 atom test system. Success in ab initio refinement, where the starting atomic positions are randomly distributed, depends on the resolution of the crystallographic data used in the optimization. The presence of high resolution data introduces false minima in the X-ray energy profile, enhancing the search problem significantly. On the same system, we also tested the method of time-averaged crystallographically restrained Molecular Dynamics, again in the absence of a physical force field. In this method, the diffraction data is modelled by an ensemble of structures instead of one single structure. In comparison to conventional single-structure refinement, more reflections were required to determine a correct atomic distribution. A time-averaging simulation at 0.2 nm resolution (40 reflections) yielded an incorrect distribution, although a low R-factor was obtained. Simulations at 0.1 nm resolution (248 reflections) gave both low R-factors, 3 to 4%, and correct atomic distributions. The scale factor between the observed and time-averaged calculated structure factor amplitudes appeared to be unstable, when optimized during a time-averaging simulation. Tests of time-averaged restrained simulations with noise added to the observed structure-factor amplitudes, indicated that noise is modelled when no information in the form of constraints or restraints is available to distinguish it from real data.     

Comparison of multiple crystal structures with NMR data for engrailed homeodomain

Two methods are currently available to solve high resolution protein structures—X-ray crystallography and nuclear magnetic resonance (NMR). Both methods usually produce highly similar structures, but small differences between both solutions are always observed. Here the raw NMR data as well as the solved NMR structure were compared to the multiple crystal structures solved for the WT 60 residue three helix bundle engrailed homeodomain (EnHD) and single point mutants. There was excellent agreement between TALOS-predicted and crystal structure-observed dihedral angles and a good agreement for the ³ J(H ^N H ^α ) couplings for the multiple crystal structures. Around 1% of NOEs were violated for any crystal structure, but no NOE was inconsistent with all of the crystal structures. Violations usually occurred for surface residues or for residues for which multiple discreet conformations were observed between the crystal structures. Comparison of the disorder shown in the multiple crystal structures shows little correlation with dynamics under native conditions for this protein.     

Predicting the preferred conformations of luteolin-4′-O-β-D-glucoside in gas phase: a comparison of two computational approaches

A tree-step computational approach has been applied to determine the lowest-energy conformers of luteolin-4′-O-β-D-glucoside (L4′G). Fifty-seven starting structures of the L4′G have been built, and then by performing with density functional theory (DFT) optimizations and second-order Møller-Plesset (MP2) calculations, the preferred conformations of L4′G are predicted. In order to test the accuracy of the computational approach, a hybrid Monte-Carlo multiple minimum (MCMM)/quantum mechanical (QM) approach is applied to determine the favorable conformers of L4′G. The alternative classification is employed to put similar conformations into the same catalogue according to the dihedral angles among the luteolin rings, glycosidic dihedral angles, and the orientations of hydroxyl and hydroxymethyl groups. The low-energy conformations are located after the optimizations at the HF/6-31G(d) and B3LYP/6-311+G(d) levels. Compared with the hybrid MCMM/QM approach, the tree-step computational approach not only remains accurate but also saves a lot of computing resources.