Waals Lennard-Jones 6–12 potential, an electrostatic potential, and a hydrogen bonding potential), it is evident that variability is introduced via Evdw. It is therefore essential to ensure that the calculated structures display good nonbonded contacts.

The uncertainties associated with the covalent geometry and van der Waals terms can introduce errors of ≈0.3 Å in the coordinates (26). The major determinant of accuracy, however, resides in the number and quality of the experimental NMR restraints that enter into the third term, ENMR, in Eq. 1.

Although a high resolution, carefully refined x-ray structure of a given protein may not be identical to the “true” solution structure, it is likely to be reasonably close in many instances, as evidenced, for example, by the excellent agreement (≤ 1 Hz rms deviation) between the experimentally determined values of the 3JHNα coupling constants in solution and their corresponding calculated values from crystal structures (10, 27, 28). Moreover, it is generally the case that three-bond coupling constants, 13C secondary shifts, and 1H shifts calculated from high resolution crystal structures agree better with the experimentally measured values than those calculated from the corresponding NMR structures (refined in the absence of coupling constant and chemical shift restraints) (1013, 25). It is therefore instructive to examine the dependence of the backbone rms difference between NMR and x-ray structures on the precision of the NMR structures (25). This dependence is shown in Fig. 1 for 14 proteins, for which both NMR and x-ray structures are available and which are representative of some of the different programs used in NMR protein structure

FIG. 1. Correlation between backbone precision of NMR structures and their agreement with x-ray structures. Where the backbone rms difference between the average NMR coordinates (NMR) and the corresponding x-ray structures is available, the values are represented as circles. When only the average backbone rms difference between an ensemble of NMR structures (<NMR>) and the corresponding x-ray structure, is quoted in the literature, squares are used. The straight line represents a linear fit to the data with a slope of 0.70, an intercept of 0.45 Å. and a correlation coefficient of 0.9. The structures are as follows: p53(mon), p53(dim), and p53(tet) are the monomer, dimer, and tetramer, respectively, of the p53 oligomerization domain (51); IL-8, interleukin-8 monomer (52); Hir (new), highly refined structure of hirudin (53); IL-1. interleukin-1β (6, 7); BPTI, bovine pancreatic trypsin inhibitor (54): eglin c (55); PC, French bean plastocyanin (56); tendamistat (57); Hir(old). hirudin (58); Cyp-CsA, cyclophilincyclosporin A complex (59): Mb. carbonmonoxy myoglobin (helices plus heme; ref. 60); CPI, potato carboxypeptidase inhibitor (61); PCP-B, procarboxypeptidase B (62); and BSPI, barley serine proteinase inhibitor 2 (63). The values given exclude conformationally disordered regions as described in the papers cited. Note that the NMR structures of IL-8 and Hir(old) were obtained before the corresponding x-ray structures and that the NMR structure of tendamistat was obtained independently of and at the same time as the x-ray structure. Reproduced from ref. 25.

determination (25). A linear relationship is evident. In addition, in cases in which both low and high precision NMR structures are available for the same protein, the high precision structure is significantly closer to the x-ray structure than the low precision one. The data can be fit to a straight line with a correlation coefficient of 0.9 and a limiting rms difference between NMR and x-ray structures of ≈0.45 Å. Moreover, all of the monomeric NMR structures with a precision of better than 0.5 Å are 0.85 Å or less away from the corresponding crystal structures. Given the fact that the coordinate errors in 1.5- to 2-Å resolution x-ray structures are ≈0.2–0.3 Å (7, 29), these data provide empirical evidence that an accuracy of 0.4–0.8 Å in the backbone coordinates is attainable under appropriate circumstances by using current NMR methodology (25).

The accuracy of NMR structures will be affected by errors in the interproton distance restraints. These errors can arise from two sources: (i) misassignments and (i) errors in distance estimates. Errors due to misassignments may be quite common in low resolution NMR structures. Fortunately, in many cases, these errors are of relatively minor consequence and do not result in the generation of an incorrect fold. Systematic errors in distance estimates may be introduced in attempts to obtain precise distance restraints. For example, interactive relaxation matrix analysis of the NOE intensities (30) and direct refinement against the NOE intensities (31, 32), while accounting for spin diffusion, can result in systematic errors from several sources such as: the presence of internal motions (not only on the picosecond time scale but also on the nanosecond to millisecond time scales); insufficient time for complete relaxation back to equilibrium to occur between successive scans; and differential efficiency of magnetization transfer between protons and their attached heteronucleus in multidimensional heteronuclear NOE experiments (26). For these reasons, it is probably prudent at the present time, at least in cases dealing with proteins, to convert the NOE intensities into loose approximate interproton distance restraints (e.g., 1–8–2.7 Å. 1.8–3.3 Å, 1.8–5.0 Å, and, if appropriate, 1.8–6.0 Å for strong, medium, weak, and very weak NOEs, respectively) with the lower bounds given by the sum of the van der Waals radii of two protons. These distance ranges are sufficiently generous to take into account untoward effects in the conversion of NOE intensities into distances (2, 3, 19, 26). Using this approach, systematic errors in the interproton distance restraints generally will be introduced only at the boundary of two distance ranges.

In the case of experimental structures calculated with an incomplete set of NOE restraints (i.e., comprising <90% of the structurally useful NOEs), there is no doubt that errors, arising both from misassignments as well as from the incorrect classification of NOEs into the various loose approximate distance ranges, will occur, resulting in less accurate structures. This loss in accuracy is due to the fact that, until a significant degree of redundancy is present in the NOE restraints, such errors often can be accommodated readily without unduly comprising the agreement with either the experimental NMR restraints or the restraints for covalent geometry and non-bonded contacts. However, once 90% of the structurally useful NOEs have been assigned and incorporated into the restraints set, corresponding typically to an average of 15 restraints per residue with >60% of the NOEs involving unique proton pairs, two sensitive and complementary techniques can be employed easily to identify and correct such errors.

The first method involves an analysis of the distribution of restraints violations in the ensemble of calculated structures. If a given restraint is systematically violated in more than, for example, 20% of the calculated structures, even by as little as 0.1 Å, it is highly likely that it should either be reclassified into the next looser category (i.e., strong to medium, medium to weak) or that errors in NOE assignments are present (26).

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