Calculations of one-, two- and three-bond nuclear spin-spin couplings in a model peptide and correlations with experimental data

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

Assessing the One-Bond Cα-H Spin-Spin Coupling Constants in Proteins: Pros and Cons of Different Approaches

In the present work, we explore three different approaches for the computation of the one-bond spin-spin coupling constants (SSCC) 1JCαH in proteins: density functional theory (DFT) calculations, a Karplus-like equation, and Gaussian process regression. The main motivation of this work is to select the best method for fast and accurate computation of the 1JCαH SSCC, for its use in everyday applications in protein structure validation, refinement, and/or determination. Our initial results showed a poor agreement between the DFT-computed and observed 1JCαH SSCC values. Further analysis leads us to the understanding that the model chosen for the DFT computations is inappropriate and that more complex models will require a higher, if not prohibitively, computational cost. Finally, we show that the Karplus-like equation and Gaussian Process regression provide faster and more accurate results than DFT-based calculations.

Biomolecular NMR: Past and future

The editors of this special volume suggested this topic, presumably because of the perspective lent by our combined >90-year association with biomolecular NMR. What follows is our personal experience with the evolution of the field, which we hope will illustrate the trajectory of change over the years. As for the future, one can confidently predict that it will involve unexpected advances. Our narrative is colored by our experience in using the NMR Facility for Biomedical Studies at Carnegie-Mellon University (Pittsburgh) and in developing similar facilities at Purdue (1977-1984) and the University of Wisconsin-Madison (1984-). We have enjoyed developing NMR technology and making it available to collaborators and users of these facilities. Our group's association with the Biological Magnetic Resonance data Bank (BMRB) and with the Worldwide Protein Data Bank (wwPDB) has also been rewarding. Of course, many groups contributed to the early growth and development of biomolecular NMR, and our brief personal account certainly omits many important milestones.

Improved validation of IDP ensembles by one-bond Cα-Hα scalar couplings

Intrinsically disordered proteins (IDPs) are best described by ensembles of conformations and a variety of approaches have been developed to determine IDP ensembles. Because of the large number of conformations, however, cross-validation of the determined ensembles by independent experimental data is crucial. The (1)JCαHα coupling constant is particularly suited for cross-validation, because it has a large magnitude and mostly depends on the often less accessible dihedral angle ψ. Here, we reinvestigated the connection between (1)JCαHα values and protein backbone dihedral angles. We show that accurate amino-acid specific random coil values of the (1)JCαHα coupling constant, in combination with a reparameterized empirical Karplus-type equation, allow for reliable cross-validation of molecular ensembles of IDPs.

How uniform is the peptide plane geometry? A high-accuracy NMR study of dipolar Cα-C'/H N-N cross-correlated relaxation

Highly precise and accurate measurements of very small NMR cross-correlated relaxation rates, namely those between protein H (i) (N) -N(i) and C (i-1) (α) -C(i-1)' dipoles, are demonstrated with an error of 0.03 s(-1) for GB3. Because the projection angles between the two dipole vectors are very close to the magic angle the rates range only from -0.2 to +0.2 s(-1). Small changes of the average vector orientations have a dramatic impact on the relative values. The rates suggest deviation from idealized peptide plane geometry caused by twists around the C'-N bonds and/or pyramidalization of the nitrogen atoms. A clear alternating pattern along the sequence is observed in β strands 1, 3 and 4 of GB3, where the side chains of almost all residues with large positive rates are solvent exposed. In the α helix all rates are relatively large and positive. Some of the currently most accurate structures of GB3 determined by both high resolution X-ray crystallography and NMR are in satisfactory agreement with the experimental rates in the helix and β strand 3, but not in the loops and the two central strands of the sheet for which no alternating pattern is predicted.

Improved accuracy in measuring one-bond and two-bond (15)N, (13)C (α) coupling constants in proteins by double-inphase/antiphase (DIPAP) spectroscopy

An extension to HN(CO-α/β-N,C(α)-J)-TROSY (Permi and Annila in J Biomol NMR 16:221-227, 2000) is proposed that permits the simultaneous determination of the four coupling constants (1) J (N'(i)Cα(i)), (2) J (HN(i)Cα(i)), (2) J (Cα(i-1)N'(i)), and (3) J (Cα(i-1)HN(i)) in (15)N,(13)C-labeled proteins. Contrasting the original scheme, in which two separate subspectra exhibit the (2) J (CαN') coupling as inphase and antiphase splitting (IPAP), we here record four subspectra that exhibit all combinations of inphase and antiphase splittings possible with respect to both (2) J (CαN') and (1) J (N'Cα) (DIPAP). Complementary sign patterns in the different spectrum constituents overdetermine the coupling constants which can thus be extracted at higher accuracy than is possible with the original experiment. Fully exploiting data redundance, simultaneous 2D lineshape fitting of the E.COSY multiplet tilts in all four subspectra provides all coupling constants at ultimate precision. Cross-correlation and differential-relaxation effects were taken into account in the evaluation procedure. By applying a four-point Fourier transform, the set of spectra is reversibly interconverted between DIPAP and spin-state representations. Methods are exemplified using proteins of various size.

Correlation of (2)J couplings with protein secondary structure

Geminal two-bond couplings ((2)J) in proteins were analyzed in terms of correlation with protein secondary structure. NMR coupling constants measured and evaluated for a total six proteins comprise 3999 values of (2)J(CalphaN'), (2)J(C'HN), (2)J(HNCalpha), (2)J(C'Calpha), (2)J(HalphaC'), (2)J(HalphaCalpha), (2)J(CbetaC'), (2)J(N'Halpha), (2)J(N'Cbeta), and (2)J(N'C'), encompassing an aggregate 969 amino-acid residues. A seamless chain of pattern comparisons across the spectrum datasets recorded allowed the absolute signs of all (2)J coupling constants studied to be retrieved. Grouped by their mediating nucleus, C', N' or C(alpha), (2)J couplings related to C' and N' depend significantly on phi,psi torsion-angle combinations. beta turn types I, I', II and II', especially, can be distinguished on the basis of relative-value patterns of (2)J(CalphaN'), (2)J(HNCalpha), (2)J(C'HN), and (2)J(HalphaC'). These coupling types also depend on planar or tetrahedral bond angles, whereas such dependences seem insignificant for other types. (2)J(HalphaCbeta) appears to depend on amino-acid type only, showing negligible correlation with torsion-angle geometry. Owing to its unusual properties, (2)J(CalphaN') can be considered a "one-bond" rather than two-bond interaction, the allylic analog of (1)J(N'Calpha), as it were. Of all protein J coupling types, (2)J(CalphaN') exhibits the strongest dependence on molecular conformation, and among the (2)J types, (2)J(HNCalpha) comes second in terms of significance, yet was hitherto barely attended to in protein structure work.

Variation in protein C(alpha)-related one-bond J couplings

Four types of polypeptide (1)J(C alpha X) couplings are examined, involving the main-chain carbon C(alpha) and either of four possible substituents. A total 3105 values of (1)J(C alpha H alpha), (1)J(C alpha C beta), (1)J(C alpha C'), and (1)J(C alpha N') were collected from six proteins, averaging 143.4 +/- 3.3, 34.9 +/- 2.5, 52.6 +/- 0.9, and 10.7 +/- 1.2 Hz, respectively. Analysis of variances (ANOVA) reveals a variety of factors impacting on (1)J and ranks their relative statistical significance and importance to biomolecular NMR structure refinement. Accordingly, the spread in the (1)J values is attributed, in equal proportions, to amino-acid specific substituent patterns and to polypeptide-chain geometry, specifically torsions phi, psi, and chi(1) circumjacent to C(alpha). The (1)J coupling constants correlate with protein secondary structure. For alpha-helical phi, psi combinations, (1)J(C alpha H alpha) is elevated by more than one standard deviation (147.8 Hz), while both (1)J(C alpha N') and (1)J(C alpha C beta) fall short of their grand means (9.5 and 33.7 Hz). Rare positive phi torsion angles in proteins exhibit concomitant small (1)J(C alpha H alpha) and (1)J(C alpha N') (138.4 and 9.6 Hz) and large (1)J(C alpha C beta) (39.9 Hz) values. The (1)J(C alpha N') coupling varies monotonously over the phi torsion range typical of beta-sheet secondary structure and is largest (13.3 Hz) for phi around -160 degrees. All four coupling types depend on psi and thus help determine a torsion that is notoriously difficult to assess by traditional approaches using (3)J. Influences on (1)J stemming from protein secondary structure and other factors, such as amino-acid composition, are largely independent.

Edge-to-face CH/pi aromatic interaction and molecular self-recognition in epi-cinchona-based bifunctional thiourea organocatalysis

The impact of cooperativity between intermolecular interactions is demonstrated by the molecular self-recognition properties of highly enantioselective epi-cinchona bifunctional thiourea organocatalysts. Low-temperature NMR experiments in inert solvents have revealed two sets of nonequivalent resonances in equal population for thiourea-modified members of the epi-quinine and epi-quinidine families. In solution, the predominance of an asymmetric (C1) dimeric self-assembly with noteworthy structural motifs became evident: simultaneous intra- and intermolecular thiourea hydrogen bonding and a CH/pi interaction were observed. Both the stereochemical and the diverse conformational features of the system favor the observed quinoline T-shaped aromatic pi-pi stacking interaction. The structure findings are supported by quantitative proton-proton distance data that were available from NOE buildup curves. The 3D structure of the dimeric assembly has been modeled in agreement with the H-H distance restraints. Owing to the geometrical preference associated with the dimerization process, the self-assembled bifunctional system is interpreted as a charge-transfer complex with the potential for catalyst self-activation.

Study of nonplanarity of peptide bond using theoretical calculations

The conformational dependence of nonplanarity of the peptide bond of formylglycinamide has been studied using ab initio and density functional theory methods. Hartree-Fock self-consistent field theory (HF), Møller-Plesset perturbation theory (MP2) of ab initio and B3LYP level of theory of dft method have been used employing 6-31++G** basis set. The MP2 method predicts better results than HF and B3LYP levels of theory for conformational stability dependence of nonplanarity. Systematic dependence of planarity deviation has been observed in MP2 theory. The chemical hardness values successfully predict the conformational region, but fail to obey maximum hardness principle. It is concluded that the most reliable dft method could not successfully predict the planarity of peptide bond in comparison with electron correlated method of ab initio method.

Measurement of 1J(Ni,Calpha(i)), 1J(Ni,C'i-1), 2J(Ni,Calpha(i-1)), 2J(H(N)i,C'i-1) and 2J(H(N)i,Calpha(i)) values in 13C/15N-labeled proteins

Use of partial or selective (13)C/(15)N labeling of specific amino acid residues in a given protein to measure the values of (1)J((15)N(i),(13)C(alpha) (i)), (2)J((1)H(N),(13)C(alpha) (i)), (2)J((15)N(i),(13)C(alpha) (i-1)), (1)J((15)N(i),(13)C'(i-1)) and (2)J((1)H(N),(13)C'(i-1)) is described. This was achieved by recording a sensitivity-enhanced 2D [(15)N-(1)H] HSQC experiment, without mixing the spin states of C(alpha) and C' during the course of entire experiment.

A protein backbone psi and phi angle dependence of 2J(N(i),C alpha(i-1)): the new NMR experiment and quantum chemical calculations

A new pulse sequence exploiting double- and zero-quantum evolution of two-spin 15N-13C' coherence is proposed for the accurate measurements of 2J(N(i),C alpha(i-1)) coupling constants. Application of the new experiment is presented for 13C,15N-labeled ubiquitin sample. The density functional theory calculations of 2J(N(i),C alpha(i-1)) coupling constants have been performed to study their dependence on both psi(i - 1) and phi(i - 1) angle in model peptides, and the results exhibit a good correlation with experimental data.

Efficient and precise measurement of H(alpha)-C(alpha), C(alpha)-C', C(alpha)-C(beta) and H(N)-N residual dipolar couplings from 2D H(N)-N correlation spectra

A suite of experiments are presented for the measurement of H(alpha)-C(alpha), C(alpha)-C', C(alpha)-C(beta) and H(N)-N couplings from uniformly 15N, 13C labeled proteins. Couplings are obtained from a series of intensity modulated two-dimensional H(N)-N spectra equivalent to the common 1H-15N-HSQC spectra, alleviating many overlap and assignment issues associated with other techniques. To illustrate the efficiency of this method, H(alpha)-C(alpha), C(alpha)-C', and H(N)-N isotropic scalar couplings were determined for ubiquitin from data collected in less than 4.5 h, C(alpha)-C(beta) data collection required 10 h. The resulting couplings were measured with an average error of +/-0.06, +/-0.05, +/-0.04 and +/-0.10 Hz, respectively. This study also shows H(alpha)-C(alpha) and C(alpha)-C(beta) couplings, valuable because they provide orientation of bond vectors outside the peptide plane, can be measured in a uniform and precise way. Superior accuracy and precision to existing 3D measurements for C(alpha)-C' couplings and increased precision compared to IPAP measurements for H(N)-N couplings are demonstrated. Minor modifications allow for acquisition of modulated H(N)-C' 2D spectra, which can yield additional well resolved peaks and significantly increase the number of measured RDCs for proteins with crowded 1H-15N resonances.

Application of HN(C)N to rapid estimation of 1J(N-C(alpha)) coupling constants correlated to psi torsion angles in proteins: implication to structural genomics

We recently described a triple resonance experiment, HN(C)N, for sequential correlation of H(N) and 15N atoms in (15N, 13C) labeled proteins [J. Biomol. NMR. 20 (2001) 135]. Here, we describe an approach based on this experiment for estimation of one bond N-C(alpha) J-couplings in medium size labeled proteins, which seem to show good correlations with psi torsion angles along the protein backbone. The approach uses the ratio of the intensities of the sequential and diagonal peaks in the F(2)-F(3) planes of the HN(C)N spectrum. The reliability of the approach has been demonstrated using a short peptide wherein the coupling constants have been measured by the present method and also independently from peak splittings in HSQC spectra. The two results agree within 10%. The applicability of the procedure to proteins has been demonstrated using doubly labeled FK506 binding protein (FKBP, molecular mass approximately 12 kDa). Coupling constant estimates have been obtained for 62 out of 100 non-proline residues and they show a correlation with psi torsion angles, as has been reported before. This semi-quantitative application of HN(C)N extends the significance of the experiment especially, in the context of structural genomics, since the single experiment, not only provides a great enhancement in the speed of resonance assignment, but also provides quantitative structural information.

Deviations from planarity of the peptide bond in peptides and proteins

The work described here is the result of a survey of the peptide omega angles in the Cambridge Structural Database of small molecules, which was carried out to establish "ideal" or "target" values for their distribution. We have shown that substantial deviations from planarity can be tolerated with a standard deviation in the angle of up to 6 degrees about a mean value for the trans peptide that is less than 180 degrees . The distortion can arise from pyramidalization at the amino nitrogen atom as well as simple twist about the peptide bond. We include an analysis of omega angles in the existing database of protein structure (PDB) and show that their distributions can depend on the refinement method used, but no correlation with resolution is evident. A surprising finding was a systematic variation of omega in phi,psi space in proteins as well as in the linear and cyclic peptides. This is particularly manifest as a consistent difference between the mean omega values in chains of left and right-hand chirality. This dichotomy is observed for all the standard amino acids and is especially striking in the absence of secondary structure. The phenomenon is discussed in the context of theoretical work on peptide analogues, and the implications for protein conformation and structure are briefly considered.

Estimates of phi and psi torsion angles in proteins from one-, two- and three-bond nuclear spin-spin couplings: application to staphylococcal nuclease

Calculated coupling constants (3JHNH alpha, 1JC alpha H alpha, 2JC'H alpha, 1JC alpha N and 2JC alpha N) from our accompanying paper [Edison, A.S. et al. (1994) J. Biomol. NMR, 4, 519-542] have been used to generate error surfaces that can provide estimates of the phi and psi angles in proteins. We have used experimental coupling data [3JHNH alpha: Kay, L.E. et al. (1989) J. Am. Chem. Soc., 111, 5488-5490; 1JC alpha H alpha: Vuister, G. W. et al. (1993) J. Biomol. NMR, 3, 67-80; 2JC'H alpha: Vuister, G.W. and Bax, A. (1992) J. Biomol. NMR, 2, 401-405; 1JC alpha N and 2JC alpha N: Delaglio, F. et al. (1991) J. Biomol. NMR, 1, 439-446] to create error surfaces for selected residues of the protein staphylococcal nuclease. The residues were chosen to include all those with five experimental couplings, as well as some with four experimental couplings, to demonstrate the relative importance of 3JHNH alpha and 1JC alpha H alpha. For most of the cases, we obtained good agreement between the X-ray structure [Loll, P.J. and Lattman, E.E. (1989) Protein Struct. Funct. Genet., 5, 183-201] and the NMR data.