Inadequacies of the point-dipole approximation for describing electron-nuclear interactions in paramagnetic proteins: Hybrid density functional calculations and the analysis of NMR relaxation of high-spin iron(III) rubredoxin

High-level, all-electron, density functional calculations have been used, in conjunction with high-resolution X-ray structural data, to predict, and to compare with experiment, the contribution of unpaired electrons to the relaxation times for N-15 nuclei in oxidized Clostridium pasteurianum rubredosin. Published X-ray structures for the iron(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 unpaired iron electrons. The remainder of the amide nitrogen resonances in the protein, which show no apparent Fermi contact contribution to the chemical shift, are represented in the model by ghost atoms (atoms with no charge or basis functions). This model served as a starting point for quantum mechanical calculations at the B3LYP/6-311G** level, which, in turn, yielded calculated values for eigenvalues of the spin-differential field gradient tensor, which finally yielded expectation values for effective distances between nuclei and the delocalized spin-density. We report here that using effective distances, which are calculated from the spin-differential field gradient tensor, in the Solomon-Bloembergen equation in place of distances measured from the crystal structures greatly improves the correlation for a plot of experimental relaxation rates versus r(-6) for N-15 resonances in C. pasteurianum iron(III) rubredoxin. With increases in the speed of computers and algorithms, iterative quantum chemical optimization of paramagnetic center geometries based on NMR-derived distance and angular constraints from paramagnetic interactions should lead to significant improvements in the determination of the structures of paramagnetic centers in proteins by NMR spectroscopy.