Exploring the limits of precision and accuracy of protein structures determined by nuclear magnetic resonance spectroscopy.

Abstract The effects of the number, precision and accuracy of interproton distance restraints, of direct refinement against nuclear Overhauser enhancement (NOE) intensities and of the description of the non-bonded contacts on the precision and accuracy of a nuclear magnetic resonance (NMR) protein structure determination have been investigated. The model system employed is the 56 residue immunoglobulin G binding domain of streptococcal protein G. This choice was based on the availability of a very high resolution NMR structure (atomic root-mean-square distribution of the ensemble of 60 calculated structures about the mean co-ordinate positions of 0·25 A for the backbone atoms, 0·65 A for all atoms and 0·39 A for all atoms excluding disordered surface side-chains). The experimental NMR data set for this structure determination comprised a total of 1058 experimental restraints of which 854 were approximate interproton distance restraints corresponding to all the structurally useful NOEs observable for this protein. The calculations presented in this paper reveal the following. (1) The number of interproton distance restraints constitutes the single most important determinant of both precision and accuracy. The ensemble precision and accuracy improves significantly as the number of interproton distance restraints is increased to an average of ∼15 per residue, of which ∼60% involve unique proton pairs; subsequent additions of interproton distance restraints, however, lead to less dramatic improvements as information redundancy sets in. (2) The ratio of ensemble precision to ensemble accuracy (which ranges from 0·5 to 0·7 for the backbone atoms) is approximately independent both of the number, precision and accuracy of the interproton distance restraints, and of whether the structures are refined against interproton distance restraints or directly against NOE intensities. (3) In an ensemble of structures generated from a large number of loose approximate interproton distance restraints (an average of ∼15 restraints per reside with ∼60% involving unique proton pairs), the interproton distances vectors corresponding to the restraints are very well defined with ∼80% of vectors between unique proton pairs having a standard deviation of ≤0·1 A. (4) The accuracy of the mean co-ordinates of an ensemble of structures is significantly higher than the average accuracy of the individual structures comprising the ensemble. For an average ensemble precision of ≥0·6 A, the dependence of the accuracy of the mean co-ordinates on ensemble precision is approximately linear. As the ensemble precision, however, increases beyond ∼0·6 A, the dependence is asymptotic and the accuracy of the mean co-ordinates reaches a limiting value of ∼0·1 A. (5) There is no significant difference in the results obtained with precise interproton distance restraints versus those with loose approximate interproton distance restraints. (6) The ensemble precision of a structure determination can potentially be improved by the use of either accurate (as opposed to simply precise) interproton distance restraints or by direct refinement against NOE intensities; the former, however, cannot be obtained experimentally, while the latter can potentially introduce systematic errors unless effects of internal motions are taken into account approximately. This increase in precision, however, is not necessarily reflected by a corresponding increase in the accuracy of the mean co-ordinates. Hence, in practice, direct refinement against NOE intensities is unlikely to have a significant impact in terms of attainable accuracy over the use of the much simpler and computationally much more efficient loose approximate interproton distance restraints for all but a very exceptional cases. (7) Neglecting the effects of the non-bonded contacts, the maximum ensemble accuracy that can be achieved in practice is ∼0·25 to 0·30 A for the backbone atoms. (8) The discription of the non-bonded contacts can have a profound effects on both the precision and accurancy of the resulting structures, and when these effects are taken into account, the likely practical limit on the attainable ensemble accurancy is 0·4 to 0·6 A for the backbone atoms, 0·8 to 1·1 A for the atoms and 0·5 to 0·8 A for all ordered atoms, with the corresponding accurancy of the mean co-ordinates being 0·1 to 0·2 A better.