The influence of spin diffusion and internal motions on NOE intensities in proteins

An algorithm has been coded for calculating NOE time courses for an arbitrary number of protons. Simulations were made on three proteins: myoglobin, bovine pancreatic trypsin inhibitor, and the toxic domain of Escherichia coli heat-stable enterotoxin. The calculations were carried out to simulate several conditions under which NOE measurements are commonly made, namely variation of the overall tumbling time and solvent (¹H₂O, and ²H₂O). The influence of spin diffusion and internal motions on NOE intensities in secondary structures was studied. It was found that spin diffusion is unlikely to lead to false identification of secondary structure elements, but does lead to considerable underestimation of distances longer than about 4 Å, which are used for determination of tertiary structures. Internal motions were simulated using truncated, anisotropic three-dimensional harmonic oscillation. For motions slower than the Larmor frequency, the oscillation has significant effects on the long-range NOEs, whereas faster motions tend to yield distance estimates similar to those of the rigid body calculation, because of counteracting effects of the motion on the correlation time and the average distance. These considerations have significance for the refinement of structures generated by distance geometry or other algorithms.