NMR Investigations of Clostridium pasteurianum Rubredoxin. Origin of Hyperfine 1H, 2H, 13C, and 15N NMR Chemical Shifts in Iron−Sulfur Proteins As Determined by Comparison of Experimental Data with Hybrid Density Functional Calculations

High-level, all-electron, density functional calculations on a 104-atom model (B3LYP/6-311G** level) have been used, in conjunction with high-resolution X-ray structural data, to predict the remarkable paramagnetic contact shifts recently measured for 1 H, 2 H, 13 C, and 15 N nuclei in Clostridium pasteurianum rubredoxin. Three published X-ray structures for the Fe(III) rubredoxin from C. pasteurianum were employed to construct a 104-atom model for the iron center that included all atoms shown to have strong electronic interactions with the Fe. Each of these models served as a starting point for quantum mechanical calculations at level B3LYP/6-311G**, which, in turn, yielded calculated values for Fermi contact spin densities. The results indicate that the experimental hyperfine shifts are dominated by Fermi contact interactions: calculated Fermi contact spin densities were found to correlate linearly with isotropic hyperfine 1 H, 2 H, 13 C, and 15 N NMR chemical shifts determined for Fe(III) rubredoxin. At the current level of hyperfine peak assignments (all signals assigned to residue and atom types; some assigned to sequence specifically), comparisons were made between experimental shifts and those calculated from the structural model derived from each of the three X-ray structures. For Fe(III) rubredoxin, the R 2 values for the correlation between the calculated spin densities and experimental chemical shifts ranged, depending on the model, from 0.93 to 0.96 for 12 experimental 2 H signals and from 0.85 to 0.96 for 12 experimental 15 N signals. The correlation with experiment was improved by performing partial geometry optimizations at B3LYP/3-21G* on two of the 104-atom models. In particular, the R 2 correlation with experimental 15 N chemical shifts was improved from 0.85 to 0.94 upon optimizing the positions of the nitrogen bound protons reported for one of the X-ray structures. A small increase in the correlation with experiment was also found after optimizing the positions of the α- and β-protons of the cysteines of another model. The consistent overall agreement between calculation and experiment supports the validity and usefulness of combining quantum chemical methods with NMR spectroscopy and X-ray crystallography for the testing and refinement of molecular structures. Significantly poorer correlations with experiment were obtained when hypothetical Fe(II) models, derived from two of the X-ray structures of Fe(III) rubredoxin, were used as the basis for the spin density calculations; this suggests that the protein undergoes subtle structural changes upon reduction.