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We tested the dependence of the accuracy and precision of calculated NMR structures on the errors of the distance constraints using sequential simulated annealing and found that: (1) the accuracy of the family of structures depends mainly on the quality of the data, but is no better than about 1 A even if the errors in distance constraints are smaller than ± 1 A. (2) The precision of the calculated structures, on the other hand, is nearly insensitive to the quality of the data. With present methods, the accuracy of NMR structures is at best of the order of 1 to 2 A, although a precision of 0·4 to 0·7 A is readily attainable. Comparisons with recent studies of this problem also brought out the importance of distinguishing between correct and incorrect definitions of accuracy when reporting numerical estimates. Using an incorrect definition of the term accuracy can lead to an artificially favorable estimate of its numerical value.

Dynamic averaging effects from internal motions on interproton distances estimated from nuclear Overhauser effects (NOE) are determined by using a molecular dynamics simulation of lysozyme. Generalized order parameters measuring angular averaging and radial averaging parameters are calculated. The product of these two parameters describes the full averaging effects on cross-relaxation. Analysis of 2778 non-methyl NOE interactions from the protein interior and surface indicates that distances estimated by assuming a rigid molecule have less than 10% error for 89% of the NOE interactions. However, analysis of 1854 methyl interactions found that only 68% of the distances estimated from cross-relaxation rates would have less than 10% error. Qualitative evaluation of distances according to strong, medium and weak NOE intensities, when used to define only the upper bound for interproton separation, would misassign less than 1% of the distance constraints because of motional averaging. Internal motions do not obscure the identification of secondary structure, although some instances of significant averaging effects were found for interactions in α-helical regions. Interresidue NOEs for amino acids more than three residues apart in the primary sequence are more extensively averaged than intraresidue or shortrange interresidue NOEs. Intraresidue interactions exhibit a greater degree of angular averaging than those involving interresidue proton pairs. An internal motion does not equally affect all NOE interactions for a particular proton. Thus, incorporation of averaging parameters in nuclear magnetic resonance structure determination procedures must be made on a proton-pair-wise basis. On the basis of the motional averaging results, particular fixed-distance proton pairs in proteins are suggested for use as distance references. A small percentage of NOE pairs localized to three regions of the protein exhibit extreme averaging effects from internal motions. The regions and types of motions involved are described.

Stereo-specific 1H nuclear magnetic resonance assignments can be obtained following distance geometry structure calculations. The key to this method is to allow stereo-related atoms or methyls to float between pro-R and pro-S configurations, the final configuration being determined by the experimental constraints. Resonances from stereo-related pairs are given initial random assignments (either pro-R or pro-S) for identifying nuclear Overhauser effects (NOEs). A list of distance constraints using these assignments is compiled and a series of structures calculated where the chirality of non-Cα chiral centers is not constrained; no pseudoatom corrections are required. Calculated structures are both locally and globally well-determined since the assignments rely upon the structure determination rather than the structure quality relying upon stereo-specific assignments. The method represents a global approach to determining stereo-specific assignments versus previously reported methods where only intraresidue NOEs and J-coupling information are used.

Chemical techniques have been applied to proteins to determine the spatial proximity of certain sequentially distant amino acid residues. We present a specific example of how chemical information can aid in the prediction of the structure of myoglobin. The algorithm of Cohen et al. (1979a) for predicting the myoglobin fold produced a list of 20 possible structures from 108 alternatives by introducing two filters. We added a third filter by exploiting non-crystallographically derived chemical data to constrain the distal-proximal histidine separation. Of the 20 possible structures, only two very similar structures satisfied this additional filter. The two remaining structures have root-mean-square deviations of 4.48 and 4.53 A from the crystal structure. The relative effects of the various constraints used to reduce the number of candidates for the myoglobin fold from 1032 in a random structure to two are explained.

An evaluation of the potential of nuclear magnetic resonance (n.m.r.) as a means of determining polypeptide conformation in solution is performed with the aid of a new distance geometry program which is capable of computing complete spatial structures for small proteins from n.m.r. data. Ten sets of geometric constraints which simulate the results available from n.m.r. experiments of varying precision and completeness were extracted from the crystal structure of the basic pancreatic trypsin inhibitor, and conformers consistent with these constraints were computed. Comparison of these computed structures with each other and with the original crystal structure shows that it is possible to determine the global conformation of a polypeptide chain from the distance constraints which are available from n.m.r. experiments. The results obtained with the different data sets also provide a standard by which the quality of protein structures computed from n.m.r. data can be evaluated when no crystal structure is available, and indicate directions in which n.m.r. experiments for protein structure determination could be further improved.