Transforming between discrete and continuous angle distribution models: application to protein χ1 torsions.

Two commonly employed angular-mobility models for describing amino-acid side-chain χ(1) torsion conformation, the staggered-rotamer jump and the normal probability density, are discussed and performance differences in applications to scalar-coupling data interpretation highlighted. Both models differ in their distinct statistical concepts, representing discrete and continuous angle distributions, respectively. Circular statistics, introduced for describing torsion-angle distributions by using a universal circular order parameter central to all models, suggest another distribution of the continuous class, here referred to as the elliptic model. Characteristic of the elliptic model is that order parameter and circular variance form complementary moduli. Transformations between the parameter sets that describe the probability density functions underlying the different models are provided. Numerical aspects of parameter optimization are considered. The issues are typified by using a set of χ(1) related (3) J coupling constants available for FK506-binding protein. The discrete staggered-rotamer model is found generally to produce lower order parameters, implying elevated rotatory variability in the amino-acid side chains, whereas continuous models tend to give higher order parameters that suggest comparatively less variation in angle conformations. The differences perceived regarding angular mobility are attributed to conceptually different features inherent to the models.

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/ß-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.

One-bond and two-bond J couplings help annotate protein secondary-structure motifs: J-coupling indexing applied to human endoplasmic reticulum protein ERp18.

NMR coupling constants, both direct one-bond ((1)J) and geminal two-bond ((2)J), are employed to analyze the protein secondary structure of human oxidized ERp18. Coupling constants collected and evaluated for the 18 kDa protein comprise 1268 values of (1)J(CαHα), (1)J(CαCß), (1)J(CαC'), (1)J(C'N'), (1)J(N'Cα), (1)J(N') (HN), (2)J(CαN'), (2)J(HNCα), (2)J(C'HN), and (2)J(HαC'). Comparison with (1)J and (2)J data from reference proteins and pattern analysis on a per-residue basis permitted main-chain ϕ,ψ torsion-angle combinations of many of the 149 amino-acid residues in ERp18 to be narrowed to particular secondary-structure motifs. J-coupling indexing is here being developed on statistical criteria and used to devise a ternary grid for interpreting patterns of relative values of J. To account for the influence of the varying substituent pattern in different amino-acid sidechains, a table of residue-type specific threshold values was compiled for discriminating small, medium, and large categories of J. For the 15-residue insertion that distinguishes the ERp18 fold from that of thioredoxin, the J-coupling data hint at a succession of five isolated Type-I ß turns at progressively shorter sequence intervals, in agreement with the crystal structure.

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.

Solution structure and dynamics of ERp18, a small endoplasmic reticulum resident oxidoreductase .

Here we report the solution structure of oxidized ERp18 as determined using NMR spectroscopy. ERp18 is the smallest member of the protein disulfide isomerase (PDI) family of proteins to contain a Cys-Xxx-Xxx-Cys active site motif. It is an 18 kDa endoplasmic reticulum resident protein with unknown function although sequence similarity to individual domains of the thiol-disulfide oxidoreductase PDI suggests ERp18 may have a similar structure and function. Like the catalytic domains of PDI, ERp18 adopts a thioredoxin fold with a thioredoxin-like active site located at the N-terminus of a long kinked helix that spans the length of the protein. Comparison of backbone chemical shifts for oxidized and reduced ERp18 shows the majority of residues possess the same backbone conformation in both states, with differences limited to the active site and regions in close proximity. S(2) order parameters from NMR backbone dynamics were found to be 0.81 for oxidized and 0.91 for reduced ERp18, and these observations, in combination with amide hydrogen exchange rates, imply a more rigid and compact backbone for the reduced structure. These observations support a putative role for ERp18 within the cell as an oxidase, introducing disulfide bonds to substrate proteins, providing structural confirmation of ERp18's role as a thiol-disulfide oxidoreductase.

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.

Asymmetric Karplus curves for the protein side-chain 3J couplings.

The standard Karplus equation for calculating 3J coupling constants from any given dihedral angle requires three empirical coefficients be determined that relate to the magnitudes of three modes of the angle dependency of 3J. Considering cosine modes only (bimodal, unimodal and baseline component), Karplus curves are generally symmetric with respect to the sign of the angle argument. Typically, their primary and secondary maxima differ in amplitude, whereas the two minima are of equal depth. However, chiral molecular topologies, such as those surrounding the main-chain and side-chain torsions in amino-acid residues, preclude, as regards substituent positioning, exact mirror-image conformations from being formed--for any given torsion-angle value. It is therefore unlikely that 3J couplings assume identical values for the corresponding positive and negative dihedral angles. This suggests that a better empirical fit of the torsion-angle dependency of 3J could be obtained when removing the constraint of symmetrically identical coupling constants. A sine term added to the Karplus equation allows independent modelling of both curve minima typically located near dihedral-angle values of +90 degrees and -90 degrees. Revisiting an extensive 3J coupling dataset previously recorded to determine the side-chain torsions chi1 in the protein flavodoxin, the asymmetric Karplus model accomplishes a more accurate fit to the experimental data. Asymmetries revealed in the angle dependencies exceed the experimental precision in determining 3J. Accounting for these effects helps improve molecular models.

A versatile component-coupling model to account for substituent effects: application to polypeptide phi and chi(1) torsion related (3)J data.

A model is proposed for collating fundamental and incremental component couplings to account for substituent effects on (3)J arising from, for example, amino-acid type variation. The unique topology patterns encountered in each of the common amino acids were modeled by assigning substituents on a (3)J coupling path to four simple categories comprising only relative positions: central (inner) vs. terminal (outer) and first-sphere vs. second-sphere. Associated increment values then reflect the influences on each (3)J coupling accessible for torsion-angle determination. Facility of use of this model, in comparison with previous ones, owes to its strict limitation to no more than three Karplus coefficients for each specific torsion-angle dependency derived. The model was integrated in the concept of self-consistent (3)J analysis and applied to polypeptide fragments X-N-C(alpha)-Y and X-C(alpha)-C(beta)-Y related to torsions phi and chi(1), respectively, yielding quantitative effects of both first- and second-sphere substituents. Regarding the polypeptide backbone, the model predicts first-sphere substituent effects on phi-related (3)J couplings to be within experimental uncertainty because main-chain topologies are identical in most amino-acid types, except for marginal effects in glycine and proline. However, effects in excess of standard errors in (3)J(phi) measurements are anticipated from second-sphere substituent variation. Regarding amino-acid side chains, first-sphere substituent effects on chi(1)-related (3)J couplings were previously found pivotal to accurate torsion-angle interpretation. Taking additional second-sphere effects on (3)J(chi(1)) into account is here demonstrated further to improve biomolecular structure analysis.

Simultaneous measurement of protein one-bond and two-bond nitrogen-carbon coupling constants using an internally referenced quantitative J-correlated [(15)N,(1)H]-TROSY-HNC experiment.

A quantitative J-correlation pulse sequence is described that allows simultaneous determination of one-bond and two-bond nitrogen-carbon coupling constants for protonated or deuterated proteins. Coupling constants are calculated from volume ratios between cross peaks and reference axial peaks observed in a single 3D spectrum. Accurate backbone (1)J(NC'), (1)J(NCalpha), and (2)J(NCalpha) coupling constants are obtained for the two [(15)N;(13)C]-labeled, medium-sized proteins flavodoxin and xylanase and for the [(2)H;(15)N;(13)C]-labeled, large protein DFPase. A dependence of one-bond and two-bond J(NCalpha) values on protein backbone psi torsion angles is readily apparent, in agreement with previously found correlations. In addition, the experiment is performed on isotropic as well as aligned protein to measure associated (15)N-(13)C residual dipolar couplings.