A general methodology is presented for analyzing dipolar shifts induced by paramagnetic ions in the nuclear magnetic resonance (NMR) spectra of ligand molecules. The method is applied to the shift perturbations induced by Co2+ in the spectrum of hen egg white lysozyme. A hypothesis testing scheme is employed to evaluate statistically the relative precision with which the axially symmetric and non-axially symmetric forms of the dipolar shift equation fit the observed data. The assumption of axial symmetry for the magnetic susceptibility tensor of Co2+ is rejected at the confidence level of 99%. Since the results presented here are similar to those reached in our analysis of lanthanide-induced shifts, we suggest that the assumption of axial symmetry may, in general, not hold. Similar conclusions have been reached by other investigators in studies of paramagnetic metal binding to model systems. We have included the three Co2+ coordinates in an eight-parameter fit of the Co2+ shift data. The Co2+ position obtained from this fit is in statistical agreement with the position inferred from x-ray data. Thus, the analysis of shift data may furnish a means for determining the site of metal complexation in macromolecules whose structure has been determined by x-ray crystallography.
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