Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, ≥90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed (?, ψ) torsion angles of ca 12º. TALOS-N also reports sidechain χ¹ rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.     

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.     

Protein backbone angle restraints from searching a database for chemical shift and sequence homology

Chemical shifts of backbone atoms in proteins are exquisitely sensitive to local conformation, and homologous proteins show quite similar patterns of secondary chemical shifts. The inverse of this relation is used to search a database for triplets of adjacent residues with secondary chemical shifts and sequence similarity which provide the best match to the query triplet of interest. The database contains 13C, 13C, 13C, 1H and 15N chemical shifts for 20 proteins for which a high resolution X-ray structure is available. The computer program TALOS was developed to search this database for strings of residues with chemical shift and residue type homology. The relative importance of the weighting factors attached to the secondary chemical shifts of the five types of resonances relative to that of sequence similarity was optimized empirically. TALOS yields the 10 triplets which have the closest similarity in secondary chemical shift and amino acid sequence to those of the query sequence. If the central residues in these 10 triplets exhibit similar and backbone angles, their averages can reliably be used as angular restraints for the protein whose structure is being studied. Tests carried out for proteins of known structure indicate that the root-mean-square difference (rmsd) between the output of TALOS and the X-ray derived backbone angles is about 15°. Approximately 3% of the predictions made by TALOS are found to be in error.     

Sequential nearest-neighbor effects on computed <Superscript>13</Superscript>C<Superscript>α</Superscript> chemical shifts

To evaluate sequential nearest-neighbor effects on quantum-chemical calculations of ¹³C^α chemical shifts, we selected the structure of the nucleic acid binding (NAB) protein from the SARS coronavirus determined by NMR in solution (PDB id 2K87). NAB is a 116-residue α/β protein, which contains 9 prolines and has 50% of its residues located in loops and turns. Overall, the results presented here show that sizeable nearest-neighbor effects are seen only for residues preceding proline, where Pro introduces an overestimation, on average, of 1.73 ppm in the computed ¹³C^α chemical shifts. A new ensemble of 20 conformers representing the NMR structure of the NAB, which was calculated with an input containing backbone torsion angle constraints derived from the theoretical ¹³C^α chemical shifts as supplementary data to the NOE distance constraints, exhibits very similar topology and comparable agreement with the NOE constraints as the published NMR structure. However, the two structures differ in the patterns of differences between observed and computed ¹³C^α chemical shifts, Δ _ca,i , for the individual residues along the sequence. This indicates that the Δ _ca,i -values for the NAB protein are primarily a consequence of the limited sampling by the bundles of 20 conformers used, as in common practice, to represent the two NMR structures, rather than of local flaws in the structures.     

Prediction of Xaa-Pro peptide bond conformation from sequence and chemical shifts

We present a program, named Promega, to predict the Xaa-Pro peptide bond conformation on the basis of backbone chemical shifts and the amino acid sequence. Using a chemical shift database of proteins of known structure together with the PDB-extracted amino acid preference of cis Xaa-Pro peptide bonds, a cis/trans probability score is calculated from the backbone and ¹³C^β chemical shifts of the proline and its neighboring residues. For an arbitrary number of input chemical shifts, which may include Pro-¹³C^γ, Promega calculates the statistical probability that a Xaa-Pro peptide bond is cis. Besides its potential as a validation tool, Promega is particularly useful for studies of larger proteins where Pro-¹³C^γ assignments can be challenging, and for on-going efforts to determine protein structures exclusively on the basis of backbone and ¹³C^β chemical shifts.     

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the α and β regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.     

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and ¹³C^β chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and ¹³C^β atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for δ¹⁵N, δ¹³C’, δ¹³C^α, δ¹³C^β, δ¹H^α and δ¹H^N, respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2–10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts.     

Predicting <Superscript>13</Superscript>C<Superscript>α</Superscript> chemical shifts for validation of protein structures

The ¹³C^α chemical shifts for 16,299 residues from 213 conformations of four proteins (experimentally determined by X-ray crystallography and Nuclear Magnetic Resonance methods) were computed by using a combination of approaches that includes, but is not limited to, the use of density functional theory. Initially, a validation test of this methodology was carried out by a detailed examination of the correlation between computed and observed ¹³C^α chemical shifts of 10,564 (of the 16,299) residues from 139 conformations of the human protein ubiquitin. The results of this validation test on ubiquitin show agreement with conclusions derived from computation of the chemical shifts at the ab initio Hartree–Fock level. Further, application of this methodology to 5,735 residues from 74 conformations of the three remaining proteins that differ in their number of amino acid residues, sequence and three-dimensional structure, together with a new scoring function, namely the conformationally averaged root-mean-square-deviation, enables us to: (a) offer a criterion for an accurate assessment of the quality of NMR-derived protein conformations; (b) examine whether X-ray or NMR-solved structures are better representations of the observed ¹³C^α chemical shifts in solution; (c) provide evidence indicating that the proposed methodology is more accurate than automated predictors for validation of protein structures; (d) shed light as to whether the agreement between computed and observed ¹³C^α chemical shifts is influenced by the identity of an amino acid residue or its location in the sequence; and (e) provide evidence confirming the presence of dynamics for proteins in solution, and hence showing that an ensemble of conformations is a better representation of the structure in solution than any single conformation. Electronic Supplementary Material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

Detection of closed influenza virus hemagglutinin fusion peptide structures in membranes by backbone 13CO-15N rotational-echo double-resonance solid-state NMR

The influenza virus fusion peptide is the N-terminal ~20 residues of the HA2 subunit of the hemagglutinin protein and this peptide plays a key role in the fusion of the viral and endosomal membranes during initial infection of a cell. The fusion peptide adopts N-helix/turn/C-helix structure in both detergent and membranes with reports of both open and closed interhelical topologies. In the present study, backbone ¹³CO-¹⁵N REDOR solid-state NMR was applied to the membrane-associated fusion peptide to detect the distribution of interhelical distances. The data clearly showed a large fraction of closed and semi-closed topologies and were best-fitted to a mixture of two structures that do not exchange. One of the earlier open structural models may have incorrect G13 dihedral angles derived from TALOS analysis of experimentally correct ¹³C shifts.     

Identification of helix capping and β-turn motifs from NMR chemical shifts

We present an empirical method for identification of distinct structural motifs in proteins on the basis of experimentally determined backbone and ¹³C^β chemical shifts. Elements identified include the N-terminal and C-terminal helix capping motifs and five types of β-turns: I, II, I′, II′ and VIII. Using a database of proteins of known structure, the NMR chemical shifts, together with the PDB-extracted amino acid preference of the helix capping and β-turn motifs are used as input data for training an artificial neural network algorithm, which outputs the statistical probability of finding each motif at any given position in the protein. The trained neural networks, contained in the MICS (motif identification from chemical shifts) program, also provide a confidence level for each of their predictions, and values ranging from ca 0.7–0.9 for the Matthews correlation coefficient of its predictions far exceed those attainable by sequence analysis. MICS is anticipated to be useful both in the conventional NMR structure determination process and for enhancing on-going efforts to determine protein structures solely on the basis of chemical shift information, where it can aid in identifying protein database fragments suitable for use in building such structures.     

SHIFTX2: significantly improved protein chemical shift prediction

A new computer program, called SHIFTX2, is described which is capable of rapidly and accurately calculating diamagnetic ¹H, ¹³C and ¹⁵N chemical shifts from protein coordinate data. Compared to its predecessor (SHIFTX) and to other existing protein chemical shift prediction programs, SHIFTX2 is substantially more accurate (up to 26% better by correlation coefficient with an RMS error that is up to 3.3× smaller) than the next best performing program. It also provides significantly more coverage (up to 10% more), is significantly faster (up to 8.5×) and capable of calculating a wider variety of backbone and side chain chemical shifts (up to 6×) than many other shift predictors. In particular, SHIFTX2 is able to attain correlation coefficients between experimentally observed and predicted backbone chemical shifts of 0.9800 (¹⁵N), 0.9959 (¹³Cα), 0.9992 (¹³Cβ), 0.9676 (¹³C′), 0.9714 (¹HN), 0.9744 (¹Hα) and RMS errors of 1.1169, 0.4412, 0.5163, 0.5330, 0.1711, and 0.1231 ppm, respectively. The correlation between SHIFTX2’s predicted and observed side chain chemical shifts is 0.9787 (¹³C) and 0.9482 (¹H) with RMS errors of 0.9754 and 0.1723 ppm, respectively. SHIFTX2 is able to achieve such a high level of accuracy by using a large, high quality database of training proteins (>190), by utilizing advanced machine learning techniques, by incorporating many more features (χ₂ and χ₃ angles, solvent accessibility, H-bond geometry, pH, temperature), and by combining sequence-based with structure-based chemical shift prediction techniques. With this substantial improvement in accuracy we believe that SHIFTX2 will open the door to many long-anticipated applications of chemical shift prediction to protein structure determination, refinement and validation. SHIFTX2 is available both as a standalone program and as a web server ().     

Backbone and side-chain resonance assignments of the membrane localization domain from Pasteurella multocida toxin

¹H, ¹³C, and ¹⁵N chemical shift assignments are presented for the isolated four-helical bundle membrane localization domain (MLD) from Pasteurella multocida toxin (PMT) in its solution state. We have assigned 99 % of all backbone and side-chain carbon atoms, including 99 % of all backbone residues excluding proline amide nitrogens. Secondary chemical shift analysis using TALOS+ demonstrates four helices, which align with those observed within the MLD in the crystal structure of the C-terminus of PMT (PDB 2EBF) and confirm the use of the available crystal structures as templates for the isolated MLDs.     

Molecular and crystal structure of Nα-(9-fluorenyl)- methoxycarbonyl-L-ornithine hydrochloride diethyl ether solvate

Summary The solid-state conformation of the first N-protected ornithine derivative has been established by X-ray analysis. The hydrochloride of N^α-(9-fluorenyl)methoxycarbonyl-l-ornithine crystallises as diethyl ether solvate. The backbone (ω₀ ϕ, ψ χ¹) torsion angles are (174.9°,–84.0°, 145.9°,–171.0°). The conformation of the urethane amide bonds istrans. The ornithine aliphatic side chain adopts preferred fully extended conformation which is stabilised by the hydrogen bonding of the-NH ₃ ⁺ group to the diethyl ether molecule, carboxyl group and Cl⁻ anions.     

Deuterium isotope effects on <Superscript>15</Superscript>N backbone chemical shifts in proteins

Quantum mechanical calculations are presented that predict that one-bond deuterium isotope effects on the ¹⁵N chemical shift of backbone amides of proteins, ¹Δ¹⁵N(D), are sensitive to backbone conformation and hydrogen bonding. A quantitative empirical model for ¹Δ¹⁵N(D) including the backbone dihedral angles, Φ and Ψ, and the hydrogen bonding geometry is presented for glycine and amino acid residues with aliphatic side chains. The effect of hydrogen bonding is rationalized in part as an electric-field effect on the first derivative of the nuclear shielding with respect to N–H bond length. Another contributing factor is the effect of increased anharmonicity of the N–H stretching vibrational state upon hydrogen bonding, which results in an altered N–H/N–D equilibrium bond length ratio. The N–H stretching anharmonicity contribution falls off with the cosine of the N–H···O bond angle. For residues with uncharged side chains a very good prediction of isotope effects can be made. Thus, for proteins with known secondary structures, ¹Δ¹⁵N(D) can provide insights into hydrogen bonding geometries. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Empirical correlation between protein backbone <Superscript>15</Superscript>N and <Superscript>13</Superscript>C secondary chemical shifts and its application to nitrogen chemical shift re-referencing

The linear analysis of chemical shifts (LACS) has provided a robust method for identifying and correcting ¹³C chemical shift referencing problems in data from protein NMR spectroscopy. Unlike other approaches, LACS does not require prior knowledge of the three-dimensional structure or inference of the secondary structure of the protein. It also does not require extensive assignment of the NMR data. We report here a way of extending the LACS approach to ¹⁵N NMR data from proteins, so as to enable the detection and correction of inconsistencies in chemical shift referencing for this nucleus. The approach is based on our finding that the secondary ¹⁵N chemical shift of the backbone nitrogen atom of residue i is strongly correlated with the secondary chemical shift difference (experimental minus random coil) between the alpha and beta carbons of residue i − 1. Thus once alpha and beta ¹³C chemical shifts are available (their difference is referencing error-free), the ¹⁵N referencing can be validated, and an appropriate offset correction can be derived. This approach can be implemented prior to a structure determination and can be used to analyze potential referencing problems in database data not associated with three-dimensional structure. Application of the LACS algorithm to the current BMRB protein chemical shift database, revealed that nearly 35% of the BMRB entries have δ ¹⁵N values mis-referenced by over 0.7 ppm and over 25% of them have δ ¹H^N values mis-referenced by over 0.12 ppm. One implication of the findings reported here is that a backbone ¹⁵N chemical shift provides a better indicator of the conformation of the preceding residue than of the residue itself. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein ¹H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6–17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for ¹Hα, ¹HN, ¹³Cα, ¹³Cβ, ¹³CO and backbone ¹⁵N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at .     

Practical use of chemical shift databases for protein solid-state NMR: 2D chemical shift maps and amino-acid assignment with secondary-structure information

We introduce a Python-based program that utilizes the large database of ¹³C and ¹⁵N chemical shifts in the Biological Magnetic Resonance Bank to rapidly predict the amino acid type and secondary structure from correlated chemical shifts. The program, called PACSYlite Unified Query (PLUQ), is designed to help assign peaks obtained from 2D ¹³C–¹³C, ¹⁵N–¹³C, or 3D ¹⁵N–¹³C–¹³C magic-angle-spinning correlation spectra. We show secondary-structure specific 2D ¹³C–¹³C correlation maps of all twenty amino acids, constructed from a chemical shift database of 262,209 residues. The maps reveal interesting conformation-dependent chemical shift distributions and facilitate searching of correlation peaks during amino-acid type assignment. Based on these correlations, PLUQ outputs the most likely amino acid types and the associated secondary structures from inputs of experimental chemical shifts. We test the assignment accuracy using four high-quality protein structures. Based on only the Cα and Cβ chemical shifts, the highest-ranked PLUQ assignments were 40–60 % correct in both the amino-acid type and the secondary structure. For three input chemical shifts (CO–Cα–Cβ or N–Cα–Cβ), the first-ranked assignments were correct for 60 % of the residues, while within the top three predictions, the correct assignments were found for 80 % of the residues. PLUQ and the chemical shift maps are expected to be useful at the first stage of sequential assignment, for combination with automated sequential assignment programs, and for highly disordered proteins for which secondary structure analysis is the main goal of structure determination.     

Quantification of protein backbone hydrogen-deuterium exchange rates by solid state NMR spectroscopy

We present the quantification of backbone amide hydrogen-deuterium exchange rates (HDX) for immobilized proteins. The experiments make use of the deuterium isotope effect on the amide nitrogen chemical shift, as well as on proton dilution by deuteration. We find that backbone amides in the microcrystalline α-spectrin SH3 domain exchange rather slowly with the solvent (with exchange rates negligible within the individual ¹⁵N–T ₁ timescales). We observed chemical exchange for 6 residues with HDX exchange rates in the range from 0.2 to 5 s⁻¹. Backbone amide ¹⁵N longitudinal relaxation times that we determined previously are not significantly affected for most residues, yielding no systematic artifacts upon quantification of backbone dynamics (Chevelkov et al. 2008b). Significant exchange was observed for the backbone amides of R21, S36 and K60, as well as for the sidechain amides of N38, N35 and for W41ε. These residues could not be fit in our previous motional analysis, demonstrating that amide proton chemical exchange needs to be considered in the analysis of protein dynamics in the solid-state, in case D₂O is employed as a solvent for sample preparation. Due to the intrinsically long ¹⁵N relaxation times in the solid-state, the approach proposed here can expand the range of accessible HDX rates in the intermediate regime that is not accessible so far with exchange quench and MEXICO type experiments.     

Spectral fitting for signal assignment and structural analysis of uniformly <Superscript>13</Superscript>C-labeled solid proteins by simulated annealing based on chemical shifts and spin dynamics

We describe an approach for the signal assignment and structural analysis with a suite of two-dimensional (13)C-(13)C magic-angle-spinning solid-state NMR spectra of uniformly (13)C-labeled peptides and proteins. We directly fit the calculated spectra to experimental ones by simulated annealing in restrained molecular dynamics program CNS as a function of atomic coordinates. The spectra are calculated from the conformation dependent chemical shift obtained with SHIFTX and the cross-peak intensities computed for recoupled dipolar interactions. This method was applied to a membrane-bound 14-residue peptide, mastoparan-X. The obtained C', C(alpha) and C(beta) chemical shifts agreed with those reported previously at the precisions of 0.2, 0.7 and 0.4 ppm, respectively. This spectral fitting program also provides backbone dihedral angles with a precision of about 50 degrees from the spectra even with resonance overlaps. The restraints on the angles were improved by applying protein database program TALOS to the obtained chemical shifts. The peptide structure provided by these restraints was consistent with the reported structure at the backbone RMSD of about 1 A.     

Rapid protein fold determination using secondary chemical shifts and cross-hydrogen bond 15N-13C′ scalar couplings (3hbJNC′)

The possibility of generating protein folds at the stage of backbone assignment using structural restraints derived from experimentally measured cross-hydrogen bond scalar couplings and secondary chemical shift information is investigated using as a test case the small / protein chymotrypsin inhibitor 2. Dihedral angle restraints for the and angles of 32 out of 64 residues could be obtained from secondary chemical shift analysis with the TALOS program (Corneliscu et al., 1999a). This information was supplemented by 18 hydrogen-bond restraints derived from experimentally measured cross-hydrogen bond ^3hbJ_NC coupling constants. These experimental data were sufficient to generate structures that are as close as 1.0 Å backbone rmsd from the crystal structure. The fold is, however, not uniquely defined and several solutions are generated that cannot be distinguished on the basis of violations or energetic considerations. Correct folds could be identified by combining clustering methods with knowledge-based potentials derived from structural databases.