A theoretical study of distance determinations from NMR. Two-dimensional nuclear overhauser effect spectra

Abstract

In principle, two-dimensional nuclear Overhauser effect NMR experiments can be used to establish internuclear distances and thus to determine molecular structure in solution. Theoretical calculations have been carried out for the 2D NOE experiment addressing the questions of (l) how sensitive 2D NOE cross-peak intensities are to spatial location of nuclear spins, and (2) how well the motional characteristics (and, therefore, spectral densities) of the molecule must be known in order to determine accurate distances. Theoretical values for cross-peak intensities obtained in 2D NOE spectra were calculated for a set of three-proton spins and a set of four-proton spins. The relaxation rate matrix whose elements establish the cross-peak intensities was diagonalized using a numerical procedure which enables accurate calculations of cross-peak intensities in large spin systems at any mixing time. Several calculations were performed; each calculation entailed a different set of circumstances. Specifically, the transformation of cross-peak intensities into proton-proton distances was examined for 21 configurations of the three-proton system and 7 configurations of the four-proton spin system. Additionally the influence of specific types of overall and internal motion on the calculated cross-peak intensities and the distances determined from them was tested. The conclusions from these calculations are as follows. With the experimental signal-to-noise ratio usually attained for biomolecular concentrations < 10 m M, interproton distances up to 5 Å should lead to detectable cross-peaks in the 2D NOE spectrum with mixing times within a few hundred milliseconds. Recording cross-peak intensities at several mixing times is important for obtaining accurate distances from them. Simple motional models assuming only a single isotropic motion with an effective correlation time may be used to obtain the spectral densities needed to calculate cross-peak intensities even though the actual motional dynamics of the molecule may be more complicated. Using the simplified models introduces approximately 10% error in the distance determination. Finally, it is shown how the cross-peak between a proton and each of its neighbors may increase the accuracy of the determination and help in locating the position of the proton. Our calculations indicate that distances with an accuracy of ±0.5 Å should be attainable with knowledge of the overall molecular reorientation rate or individual proton relaxation times.