NMR chemical shifts and structure refinement in proteins

Summary Computation of the ¹³C chemical shifts (or shieldings) of glycine, alanine and valine residues in bovine and Drosophila calmodulins and Staphylococcal nuclease, and comparison with experimental values, is reported using a gauge-including atomic orbital quantum-chemical approach. The full 24 ppm shielding range is reproduced (overall r.m.s.d.=1.4 ppm) using optimized protein structures, corrected for bond-length/bond-angle errors, and rovibrational effects.To whom correspondence should be addressed.     

Factors affecting the use of 13C(alpha) chemical shifts to determine, refine, and validate protein structures

Interest centers here on the analysis of two different, but related, phenomena that affect side-chain conformations and consequently 13C(alpha) chemical shifts and their applications to determine, refine, and validate protein structures. The first is whether 13C(alpha) chemical shifts, computed at the DFT level of approximation with charged residues is a better approximation of observed 13C(alpha) chemical shifts than those computed with neutral residues for proteins in solution. Accurate computation of 13C(alpha) chemical shifts requires a proper representation of the charges, which might not take on integral values. For this analysis, the charges for 139 conformations of the protein ubiquitin were determined by explicit consideration of protein binding equilibria, at a given pH, that is, by exploring the 2(xi) possible ionization states of the whole molecule, with xi being the number of ionizable groups. The results of this analysis, as revealed by the shielding/deshielding of the 13C(alpha) nucleus, indicated that: (i) there is a significant difference in the computed 13C(alpha) chemical shifts, between basic and acidic groups, as a function of the degree of charge of the side chain; (ii) this difference is attributed to the distance between the ionizable groups and the 13C(alpha) nucleus, which is shorter for the acidic Asp and Glu groups as compared with that for the basic Lys and Arg groups; and (iii) the use of neutral, rather than charged, basic and acidic groups is a better approximation of the observed 13C(alpha) chemical shifts of a protein in solution. The second is how side-chain flexibility influences computed 13C(alpha) chemical shifts in an additional set of ubiquitin conformations, in which the side chains are generated from an NMR-derived structure with the backbone conformation assumed to be fixed. The 13C(alpha) chemical shift of a given amino acid residue in a protein is determined, mainly, by its own backbone and side-chain torsional angles, independent of the neighboring residues; the conformation of a given residue itself, however, depends on the environment of this residue and, hence, on the whole protein structure. As a consequence, this analysis reveals the role and impact of an accurate side-chain computation in the determination and refinement of protein conformation. The results of this analysis are: (i) a lower error between computed and observed 13C(alpha) chemical shifts (by up to 3.7 ppm), was found for approximately 68% and approximately 63% of all ionizable residues and all non-Ala/Pro/Gly residues, respectively, in the additional set of conformations, compared with results for the model from which the set was derived; and (ii) all the additional conformations exhibit a lower root-mean-square-deviation (1.97 ppm < or = rmsd < or = 2.13 ppm), between computed and observed 13C(alpha) chemical shifts, than the rmsd (2.32 ppm) computed for the starting conformation from which this additional set was derived. As a validation test, an analysis of the additional set of ubiquitin conformations, comparing computed and observed values of both 13C(alpha) chemical shifts and chi(1) torsional angles (given by the vicinal coupling constants, 3J(N-Cgamma) and 3J(C'-Cgamma), is discussed.     

Effects of side-chain orientation on the <Superscript>13</Superscript>C chemical shifts of antiparallel β-sheet model peptides

The dependence of the ¹³C chemical shift on side-chain orientation was investigated at the density functional level for a two-strand antiparallel β-sheet model peptide represented by the amino acid sequence Ac-(Ala)₃-X-(Ala)₁₂-NH₂ where X represents any of the 17 naturally occurring amino acids, i.e., not including alanine, glycine and proline. The dihedral angles adopted for the backbone were taken from, and fixed at, observed experimental values of an antiparallel β-sheet. We carried out a cluster analysis of the ensembles of conformations generated by considering the side-chain dihedral angles for each residue X as variables, and use them to compute the ¹³C chemical shifts at the density functional theory level. It is shown that the adoption of the locally-dense basis set approach for the quantum chemical calculations enabled us to reduce the length of the chemical-shift calculations while maintaining good accuracy of the results. For the 17 naturally occurring amino acids in an antiparallel β-sheet, there is (i) good agreement between computed and observed ¹³C^α and ¹³C^β chemical shifts, with correlation coefficients of 0.95 and 0.99, respectively; (ii) significant variability of the computed ¹³C^α and ¹³C^β chemical shifts as a function of χ¹ for all amino acid residues except Ser; and (iii) a smaller, although significant, dependence of the computed ¹³C^α chemical shifts on χ^ξ (with ξ ≥ 2) compared to χ¹ for eleven out of seventeen residues. Our results suggest that predicted ¹³C^α and ¹³C^β chemical shifts, based only on backbone (φ,ψ) dihedral angles from high-resolution X-ray structure data or from NMR-derived models, may differ significantly from those observed in solution if the dihedral-angle preferences for the side chains are not taken into account. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users.     

On the existence of MHn species with M=Al, Ga and n=4, 5, 6. Computational study of structures, stabilities and bonding

Based on second-order perturbation theory (MP2) predictions with large 6-311++G(3df, 3pd) basis set we have reviewed the possible structures and stabilities of a series of neutral MH_n(M=Al, Ga; n=4, 5, 6) species. For AlH₄ and AlH₅, our results confirm the previous theoretical findings, which indicate the dihydrogen C_s complexes (²A′) AlH₂(H₂) and (¹A′) AlH₃(H₂), respectively, as the lowest energy isomers. We found, similarly, C_s (²A′) GaH₂(H₂) and (¹A′) GaH₃(H₂) van der Waals complexes as the most stable species of the gallium analogues GaH₄ and GaH₅. The calculated H₂ dissociation energies (D_e) for AlH₂(H₂) and AlH₃(H₂) are of the order 1.8–2.5 kcalmol¹, whereas this range of values for GaH₂(H₂) and GaH₃(H₂) is 1.4–1.8 kcalmol¹ . Symmetry-adapted perturbation theory (SAPT) was used to analyze the interaction energies of these dihydrogen complexes (for n=5) to determine why the Ga species show a smaller binding energy than the Al species. The SAPT partitioning of the interaction energy showed significant differences between AlH₃(H₂) and GaH₃(H₂), resulting from the much stronger “hydride” character of the aluminum species. The experimental observation of AlH₂(H₂) and AlH₃(H₂), and likely GaH₃(H₂), via low-temperature matrix isolation has been reported recently by Pullumbi et al. and Andrews et al., supporting the theoretical predictions. For n=6, we found the degenerate C₂(²A) and C_s(²A′) MH₂(H₂)₂ “double H₂” type van der Waals complexes as the lowest energy species for both M=Al and Ga.Electronic Supplementary Material Supplementary material is available for this article at     

Analysis of 1H chemical shifts in DNA: Assessment of the reliability of 1H chemical shift calculations for use in structure refinement

The reliability of ¹H chemical shift calculations for DNA is assessed by comparing the experimentally and calculated chemical shifts of a reasonably large number of independently determined DNA structures. The calculated chemical shifts are based on semiempirical relations derived by Giessner-Prettre and Pullman [(1987) Q. Rev. Biophys., 20, 113–172]. The standard deviation between calculated and observed chemical shifts is found to be quite small, i.e. 0.17 ppm. This high accuracy, which is achieved without parameter adjustment, makes it possible to analyze the structural dependencies of chemical shifts in a reliable fashion. The conformation-dependent ¹H chemical shift is mainly determined by the ring current effect and the local magnetic anisotropy, while the third possible effect, that of the electric field, is surprisingly small. It was further found that for a double helical environment, the chemical shift of the sugar protons, H2 to H5, is mainly affected by the ring current and magnetic anisotropy of their own base. Consequently, the chemical shift of these sugar protons is determined by two factors, namely the type of base to which the sugar ring is attached, C, T, A, or G, and secondly by the -angle. In particular, the H2 shift varies strongly with the -angle, and strong upfield H2 shifts directly indicate that the -angle is in the syn domain. The H1 shift is not only strongly affected by its own base, but also by its 3-neighboring base. On the other hand, base protons, in particular H5 of cytosine and methyl protons of thymine, are affected mainly by the 5-neighboring bases, although some effect (0.2 ppm) stems from the 3-neighboring base. The H2 protons are mainly affected by the 3-neighboring base. As a result of these findings a simple scheme is proposed for sequential assignment of resonances from B-helices based on chemical shifts.     

Secondary structural effects on protein NMR chemical shifts

For an amino acid in protein, its chemical shift, (, )_s, is expressed as a function of its backbone torsion angles ( and ) and secondary state (s): (, )_{s=, )_coil+(, )_s}, where (, )_coil represents its chemical shift at coil state (s=coil); (, )_s (s=sheet or helix) is herein defined as secondary structural effect correction factor, which are quantitatively determined from Residue-specific Secondary Structure Shielding Surface (RSS) for ¹³CO, ¹³C, ¹³C,¹H, ¹⁵N, and ¹HN nuclei. The secondary structural effect correction factors defined in this study differ from those in earlier investigations by separating out the backbone conformational effects. As a consequence, their magnitudes are significantly smaller than those earlier reported. The present (, )_sheet and (, )_helix were found varying little with backbone conformation and the 20 amino acids, specifically for ¹³CO, ¹³C, and ¹H nuclei. This study also carries out some useful investigations on other chemical shift prediction approaches – the traditional shielding surfaces, SHIFTS, SHIFTX, PROSHIFT, and identifies some unexpected shortcomings with these methods. It provides some useful insights into understanding protein chemical shifts and suggests a new route to improving chemical shifts prediction. The RSS surfaces were incorporated into the program PRSI [Wang and Jardetzky, J. Biomol. NMR, 28: 327–340 (2004)], which is available for academic users at http://www.pronmr.com or by sending email to the author (yunjunwang@yahoo.com).     

Pseudocontact shifts as constraints for energy minimization and molecular dynamics calculations on solution structures of paramagnetic metalloproteins

The pseudocontact shifts of NMR signals, which arise from the magnetic susceptibility anisotropy of paramagnetic molecules, have been used as structural constraints under the form of a pseudopotential in the SANDER module of the AMBER 4.1 molecular dynamics software package. With this procedure, restrained energy minimization (REM) and restrained molecular dynamics (RMD) calculations can be performed on structural models by using pseudocontact shifts. The structure of the cyanide adduct of the Met80Ala mutant of the yeast iso-1-cytochrome c has been used for successfully testing the calculations. For this protein, a family of structures is available, which was obtained by using NOE and pseudocontact shifts as constraints in a distance geometry program. The structures obtained by REM and RMD calculations with the inclusion of pseudocontact shifts are analyzed. Proteins 29:68–76, 1997. © 1997 Wiley-Liss, Inc.     

Determination of the three-dimensional structure of oligosaccharides in the solid state from experimental 13C NMR data and ab initio chemical shift surfaces

A novel method for the determination of the three-dimensional (3D) structure of oligosaccharides in the solid state using experimental 13C NMR data is presented. The approach employs this information, combined with 13C chemical shift surfaces (CSSs) for the glycosidic bond carbons in the generation of NMR pseudopotential energy functions suitable for use as constraints in molecular modeling simulations. Application of the method to trehalose, cellobiose, and cellotetraose produces 3D models that agree remarkably well with the reported X-ray structures, with phi and psi dihedral angles that are within 10 degrees from the ones observed in the crystals. The usefulness of the approach is further demonstrated in the determination of the 3D structure of the cellohexaose, an hexasaccharide for which no X-ray data has been reported, as well as in the generation of accurate structural models for cellulose II and amylose V6.     

First principle calculations of <Superscript>113</Superscript>Cd chemical shifts for proteins and model systems

¹¹³Cd isotropic NMR shieldings are calculated for a number of metal ion binding sites in proteins, using the GIAO-B3LYP and GIAO-HF methods with the uncontracted (19s15p9d4f) polarized basis set of Kellö and Sadlej on cadmium and 6-31G(d) on the ligands. The results compare favorably with experimental data, indicating that first principle calculations are a useful tool for structural interpretation of ¹¹³Cd chemical shift data from metal ion containing proteins. The effect of different ligand types (thiolate, imidazole, water, and monodentate carboxylate), coordination number, and deviations of the coordination geometry from ideal structures is evaluated. In particular, the ligand type and coordination number are important factors, but also changes in cadmium–ligand bond lengths may cause significant changes of the chemical shift.     

H-bonded complexes between acetylacetone and two molecules of methanol: HF and DFT level study

Five stable H-bonded complexes (supersystems) between acetylacetone and two methanol molecules were investigated at the B3LYP and HF levels of theory using the 6-311G** and 6-11++G** basis sets. The most stable complex was found as the one with the highest relative bonding and interaction energies. All vibrational frequencies resulting from calculations with the 6-311++G** basis set were compared with the recorded IR spectrum of acetylacetone/methanol mixture in a molar ratio 1:2.     

Assembly of protein tertiary structures from secondary structures using optimized potentials

We present a simulated annealing-based method for the prediction of the tertiary structures of proteins given knowledge of the secondary structure associated with each amino acid in the sequence. The backbone is represented in a detailed fashion whereas the sidechains and pairwise interactions are modeled in a simplified way, following the LINUS model of Srinivasan and Rose. A perceptron-based technique is used to optimize the interaction potentials for a training set of three proteins. For these proteins, the procedure is able to reproduce the tertiary structures to below 3 A in root mean square deviation (rmsd) from the PDB targets. We present the results of tests on twelve other proteins. For half of these, the lowest energy decoy has a rmsd from the native state below 6 A and, in 9 out of 12 cases, we obtain decoys whose rmsd from the native states are also well below 5 A.     

蛋白质结构从头预测方法研究进展

蛋白质结构从头预测是不依赖模板仅从氨基酸序列信息得到天然结构。它的关键是正确定义能量函数、精确选用计算机搜索算法来寻找能量最低值。基于此,本文系统介绍了能量函数和构象搜索策略,并列举了几种比较成功的从头预测方法,通过比较得出结论:基于统计学知识的能量函数是近年来从头预测发展的主要方向,现有从头预测的构象搜索都用到Monte Carlo法。这表明随着蛋白质结构预测研究的深入,能量函数的构建、构象搜索方法的选择、大分子蛋白质结构的从头预测等关键性问题都取得了突破性进展。     

3-Silaoxetane and 3-silathietane: structure and reactivity studies on the basis of spectroscopic data and theoretical calculations

The ab initio and DFT calculations (structural parameters, electron localization function (ELF)) on 3-silaoxetane 3,3-dimethyl-2,2,4,4-tetraphenyl-1-oxa-3-silacyclobutane (1) and 3-silathietane 3,3-dimethyl-2,2,4,4-tetraphenyl-1-sila-3-thiacyclobutane (2) show the cyclobutane ring in 2 as being non-planar with a C-Si-C angle of 89.2° and a C-S-C angle of 93.3°, whereas the cyclobutane ring in 1 is planar with an unusual small bond angle at the silicon atom of 74.7°, which can only be explained by bent bonds. Since the synthesis was performed in water, small bent angles cannot be indicative for high reactivity. The Raman spectra of 1 and 2 were then recorded and analyzed in the 1800-200 cm⁻¹ spectral region at various temperatures (300-10 K) with the help of the DFT calculation results (harmonic vibrational wavenumbers, Raman scattering activities). Although the wavenumber shifts are quite small, the subtle changes in the spectral features of the 3-silaoxetane and phenyl rings vibrational modes may indicate a loss of symmetry in 1 (between 200 and 150 K) and a possible phase transition in 2 (at about 200 K). Furthermore, the Raman spectra of 1 and 2 confirmed the ELF calculation results, excluding any bond interaction between the silicon and the oxygen or sulfur atom.     

Influence of N-H...O and O-H...O hydrogen bonds on the (17)O, (15)N and (13)C chemical shielding tensors in crystalline acetaminophen: a density functional theory study

A computational investigation was carried out to characterize the (17)O, (15)N and (13)C chemical shielding tensors in crystalline acetaminophen. We found that N-H...O and O-H...O hydrogen bonds around the acetaminophen molecule in the crystal lattice have different influences on the calculated (17)O, (15)N and (13)C chemical shielding eigenvalues and their orientations in the molecular frame of axes. The calculations were performed with the B3LYP method and 6-311++G(d, p) and 6-311+G(d) standard basis sets using the Gaussian 98 suite of programs. Calculated chemical shielding tensors were used to evaluate the (17)O, (15)N, and (13)C NMR chemical shift tensors in crystalline acetaminophen, which are in reasonable agreement with available experimental data. The difference between the calculated NMR parameters of the monomer and molecular clusters shows how much hydrogen-bonding interactions affect the chemical shielding tensors of each nucleus. The computed (17)O chemical shielding tensor on O(1), which is involved in two intermolecular hydrogen bonds, shows remarkable sensitivity toward the choice of the cluster model, whereas the (17)O chemical shielding tensor on O(2) involved in one N-H...O hydrogen bond, shows smaller improvement toward the hydrogen-bonding interactions. Also, a reasonably good agreement between the experimentally obtained solid-state (15)N and (13)C NMR chemical shifts and B3LYP/6-311++G(d, p) calculations is achievable only in molecular cluster model where a complete hydrogen-bonding network is considered. Moreover, at the B3LYP/6-311++G(d, p) level of theory, the calculated (17)O, (15)N and (13)C chemical shielding tensor orientations are able to reproduce the experimental values to a reasonably good degree of accuracy.     

Regression formulae for ab initio and density functional calculated chemical shifts

Linear regression formulae are given for converting ¹H and ¹³C magnetic shielding constants calculated at common ab initio and density functional theory levels of calculation into chemical shifts relative to tetramethylsilane. Accuracies of roughly ±2.2 ppm (¹³C) and ±0.15 ppm (¹H) or better are found for the training set for most levels. The highest level calculations do not always give better results than economical standard calculations.Electronic Supplementary Material Supplementary material is available for this article at     

Synthesis, structure, and antimycobacterial activity of 6-[1(3H)-isobenzofuranylidenemethyl]purines and analogs

6-Benzofuryl-, styryl, benzyl, and furfurylpurines as well as 6-[1(3H)-isobenzofuranylidenemethyl]purines have been synthesized and their activities against Mycobacterium tuberculosis (Mtb) determined. Several compounds displayed profound antimycobacterial activity in combination with low toxicity towards mammalian cells. NMR and X-ray crystallography were employed to determine the detailed structures and the results were supported by quantum chemical calculations.     

High-accuracy protein structures by combining machine-learning with physics-based refinement

Protein structure prediction has long been available as an alternative to experimental structure determination, especially via homology modeling based on templates from related sequences. Recently, models based on distance restraints from coevolutionary analysis via machine learning to have significantly expanded the ability to predict structures for sequences without templates. One such method, AlphaFold, also performs well on sequences where templates are available but without using such information directly. Here we show that combining machine-learning based models from AlphaFold with state-of-the-art physics-based refinement via molecular dynamics simulations further improves predictions to outperform any other prediction method tested during the latest round of CASP. The resulting models have highly accurate global and local structures, including high accuracy at functionally important interface residues, and they are highly suitable as initial models for crystal structure determination via molecular replacement.     

Refinement of homology-based protein structures by molecular dynamics simulation techniques

The use of classical molecular dynamics simulations, performed in explicit water, for the refinement of structural models of proteins generated ab initio or based on homology has been investigated. The study involved a test set of 15 proteins that were previously used by Baker and coworkers to assess the efficiency of the ROSETTA method for ab initio protein structure prediction. For each protein, four models generated using the ROSETTA procedure were simulated for periods of between 5 and 400 nsec in explicit solvent, under identical conditions. In addition, the experimentally determined structure and the experimentally derived structure in which the side chains of all residues had been deleted and then regenerated using the WHATIF program were simulated and used as controls. A significant improvement in the deviation of the model structures from the experimentally determined structures was observed in several cases. In addition, it was found that in certain cases in which the experimental structure deviated rapidly from the initial structure in the simulations, indicating internal strain, the structures were more stable after regenerating the side-chain positions. Overall, the results indicate that molecular dynamics simulations on a tens to hundreds of nanoseconds time scale are useful for the refinement of homology or ab initio models of small to medium-size proteins.     

ORB, a homology-based program for the prediction of protein NMR chemical shifts

A computer program (ORB) has been developed to predict ¹H,¹³C and ¹⁵N NMR chemical shifts of previouslyunassigned proteins. The program makes use of the information contained in achemical shift database of previously assigned proteins supplemented by astatistically derived averaged chemical shift database in which the shifts arecategorized according to their residue, atom and secondary structure type[Wishart et al. (1991) J. Mol. Biol., 222, 311–333]. The predictionprocess starts with a multiple alignment of all previously assigned proteinswith the unassigned query protein. ORB uses the sequence and secondarystructure alignment program XALIGN for this task [Wishart et al. (1994)CABIOS, 10, 121–132; 687–688]. The prediction algorithm in ORB isbased on a scoring of the known shifts for each sequence. The scores dependon global sequence similarity, local sequence similarity, structuralsimilarity and residue similarity and determine how much weight one particularshift is given in the prediction process. In situations where no applicablepreviously assigned chemical shifts are available, the shifts derived from theaveraged database are used. In addition to supplying the user with predictedchemical shifts, ORB calculates a confidence value for every prediction. Theseconfidence values enable the user to judge which predictions are the mostaccurate and they are particularly useful when ORB is incorporated into acomplete autoassignment package. The usefulness of ORB was tested on threemedium-sized proteins: an interleukin-8 analog, a troponin C synthetic peptideheterodimer and cardiac troponin C. Excellent results are obtained if ORB isable to use the chemical shifts of at least one highly homologous sequence.ORB performs well as long as the sequence identity between proteins with knownchemical shifts and the new sequence is not less than 30%.     

2DCSi: identification of protein secondary structure and redox state using 2D cluster analysis of NMR chemical shifts

Chemical shifts of amino acids in proteins are the most sensitive and easily obtainable NMR parameters that reflect the primary, secondary, and tertiary structures of the protein. In recent years, chemical shifts have been used to identify secondary structure in peptides and proteins, and it has been confirmed that ¹H^α, ¹³C^α, ¹³C^β, and ¹³C′ NMR chemical shifts for all 20 amino acids are sensitive to their secondary structure. Currently, most of the methods are purely based on one-dimensional statistical analyses of various chemical shifts for each residue to identify protein secondary structure. However, it is possible to achieve an increased accuracy from the two-dimensional analyses of these chemical shifts. The 2DCSi approach performs two-dimension cluster analyses of ¹H^α, ¹H^N, ¹³C^α, ¹³C^β, ¹³C′, and ¹⁵N^H chemical shifts to identify protein secondary structure and the redox state of cysteine residue. For the analysis of paired chemical shifts of 6 data sets, each of the 20 amino acids has its own 15 two-dimension cluster scattering diagrams. Accordingly, the probabilities for identifying helix and extended structure were calculated by using our scoring matrix. Compared with existing the chemical shift-based methods, it appears to improve the prediction accuracy of secondary structure identification, particularly in the extended structure. In addition, the probability of the given residue to be helix or extended structure is displayed, allows the users to make decisions by themselves. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Grant sponsor: National Science Council of ROC; Grant numbers: NSC-94-2323-B006- 001, NSC-93-2212-E-006.