Protein solution structure determination using distances from two-dimensional nuclear Overhauser effect experiments: effect of approximations on the accuracy of derived structures.

Solution structures for many proteins have been determined to date utilizing interproton distance constraints estimated from two-dimensional nuclear Overhauser effect (2D NOE) spectra. Although the simple isolated spin pair approximation (ISPA) generally used can result in systematic errors in distances, the large number of constraints enables protein structure to be defined with reasonably high resolution. Effects of these systematic errors on the resulting protein structure are examined. Iterative relaxation matrix calculations, which account for dipolar interactions between all protons in a molecule, can accurately determine internuclear distances with little or no a priori knowledge of the molecular structure. The value of this additional complexity is also addressed. To assess these distance determination methods, hypothetical "experimental" data, including random noise and peak overlap, are calculated for an arbitrary "true" protein structure. Three methods of obtaining distance constraints from 2D NOE peak intensities are examined: one entails a conservative use of ISPA, one assumes the ISPA to be fairly accurate, and one utilizes an iterative relaxation matrix method called MARDIGRAS (matrix analysis of relaxation for discerning the geometry of an aqueous structure), developed in this laboratory. A distance geometry algorithm was used to generate a family of structures for each distance set. The quality of the average structure from each family was good. The root-mean-square deviation of that average structure from the true structure was improved about 2-5% using the more restrictive rather than the more conservative ISPA approach. Use of MARDIGRAS in a conservative fashion--i.e., with a poor initial model--resulted in improvement in the root-mean-square deviation by 8-15%. With a better initial model, MARDIGRAS obtained even more accurate distances. MARDIGRAS also permits analysis of 2D NOE data at longer mixing times, yielding additional distances. Use of more restrictive ISPA distances did, however, result in a few systematically incorrect structural features in local regions of the protein, producing distortions of 2-3 A. Comparison between experimental data and spectra calculated for the structures correlates with root-mean-square deviation, offering a method of structure evaluation. An R factor for evaluating fit between experimental and calculated 2D NOE intensities is proposed.