Interproton distances

The secondary stmcture elements are then identified, and finally, the three-dimensional protein stmcture is obtained from the measured interproton distances and torsion angle parameters. This procedure requites a minimum of two days of nmr instmment time per sample, because two pulse delays are requited in the 3-D experiment. In addition, approximately 20 hours of computing time, using a supercomputer, is necessary for the calculations. Nevertheless, protein stmcture can be assigned using 3-D nmr and a resolution of 0.2 nanometers is achievable. The largest protein characterized by nmr at this writing contained 43 amino acid units (51). However, attempts ate underway to characterize the stmcture of interleukin 2 [85898-30-2] which has over 150 amino acid units. 

Usually, simplified representations of the data are used to obtain preliminary structures. Thus, lower and upper bounds on the interproton distances are estimated from the NOE intensity [10], using appropriate reference distances for calibration. The bounds should include the estimates of the cumulative error due to all sources such as peak integration errors, spin diffusion, and internal dynamics. 

To put the errors in comparative models into perspective, we list the differences among strucmres of the same protein that have been detennined experimentally (Fig. 9). The 1 A accuracy of main chain atom positions corresponds to X-ray structures defined at a low resolution of about 2.5 A and with an / -factor of about 25% [192], as well as to medium resolution NMR structures determined from 10 interproton distance restraints per residue [193]. Similarly, differences between the highly refined X-ray and NMR structures of the same protein also tend to be about 1 A [193]. Changes in the environment... 

This simple theoryis based on the expectation that, to a reasonable degree of approximation, proton-proton, dipolar contributions to the measured spin-lattice relaxation-rate are pairwise additive and decrease as a simple sixth power of the interproton distance. The simplified version of the dipole-dipole mechanism is summarized in the following two equations for spin i coupled intramolecularly with a group of spins j... 

Thus, identification of all pairwise, interproton relaxation-contribution terms, py (in s ), for a molecule by factorization from the experimentally measured / , values can provide a unique method for calculating interproton distances, which are readily related to molecular structure and conformation. When the concept of pairwise additivity of the relaxation contributions seems to break down, as with a complex molecule having many interconnecting, relaxation pathways, there are reliable separation techniques, such as deuterium substitution in key positions, and a combination of nonselective and selective relaxation-rates, that may be used to distinguish between pairwise, dipolar interactions. Moreover, with the development of the Fourier-transform technique, and the availability of highly sophisticated, n.m.r. spectrometers, it has become possible to measure, routinely, nonselective and selective relaxation-rates of any resonance that can be clearly resolved in a n.m.r. spectrum. 

This simple relaxation theory becomes invalid, however, if motional anisotropy, or internal motions, or both, are involved. Then, the rotational correlation-time in Eq. 30 is an effective correlation-time, containing contributions from reorientation about the principal axes of the rotational-diffusion tensor. In order to separate these contributions, a physical model to describe the manner by which a molecule tumbles is required. Complete expressions for intramolecular, dipolar relaxation-rates for the three classes of spherical, axially symmetric, and asymmetric top molecules have been evaluated by Werbelow and Grant, in order to incorporate into the relaxation theory the appropriate rotational-diffusion model developed by Woess-ner. Methyl internal motion has been treated in a few instances, by using the equations of Woessner and coworkers to describe internal rotation superimposed on the overall, molecular tumbling. Nevertheless, if motional anisotropy is present, it is wiser not to attempt a quantitative determination of interproton distances from measured, proton relaxation-rates, although semiquantitative conclusions are probably justified by neglecting motional anisotropy, as will be seen in the following Section. 

A final caution concerns the error introduced into the calculated interproton distances. As this depends on the errors of the measured quantities, it is propagated through the calculations according to Eq. for independent and random errors, namely,... 

From these studies of sugars and related molecules, it is possible to derive empirical rules whereby Ri(ns) values can be used as the basis for configurational assignments. These rules are illustrated graphically in Fig. 5, where the relative relaxation-efficiency between two protons is plotted as a function of the interproton distance. 

Interproton Distances (A) for 2, 4,6>2 >3 -Hexa-0-acetyl-l,6-anhydro-4-0- -glucopyranosyI- 8-D-glucopyranose (3)... 

Interproton distances of 0-ceIIobiose (see Ref. 49) error 0.01 A. Interproton distances of 1,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.01 A. Interproton distances of -cellobiose octaacetate (see Ref. 49) error 0.05 A. Interproton distances of 2,3,4-tri-0-acetyl-l,6-anhydro- -D-glucopyranose (see Ref. 49) error 0.05 A. Error calculations based on the errors of the measured quantities in Eqs. 18 and 21. Interproton distances calculated from the relaxation parameters of the methylene protons. 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

R,1S isomer. However, this proposal is tentative, because X-ray diffraction has shown that another specimen of asperlin, possessing a different crystalline form, has structure 49b. It should be noted that 1 tumbles somewhat anisotropically, with D /D = 1.3, as deduced from C relaxation measurements. If, however, the anisotropic motion of 1 were not properly corrected for, the largest error in the measurement of its interproton distances would not exceed 4%. 

From the previous discussion, it is clear that relaxation experiments constitute a very powerful tool for investigation of the structure and conformation of carbohydrate molecules in solution. However, the nature of the individual problem may determine which relaxation experiment should be chosen in order to extract interproton distances to the desired accuracy of < 0.2 A. Although the limitations and relative merits of all of the various relaxation methods have not yet been systematically studied, accumulated experience provides some direct knowledge about the range of errors associated with relaxation experiments. 

Combinations of non-selective and/or single-selective relaxation-rates, or both, with n.0.e. values may conveniently be performed with reliable results, especially when other methods seem impractical. However, these experiments are time-consuming, as they entail the determination of a rather large number of experimental values. Moreover, the n.O.e. parameters carry their own systematic and random errors, which are magnified in the calculation of interproton distances. The deuterium-substitution method requires specific deuteration at a strategic position, which, in many cases, may be inconvenient or impractical. Also, this technique is valid only when the relaxation rates obtained after deuterium substitution are at least 5% enhanced, relative to the relaxation rates of the unsubstituted compound, and it requires that, for a meaningful experiment, the following condition " be satisfied. 

Fig. 8.—Plot of the Ratio of Interproton Distances, as a Function of the Inverse...

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

The significance of n.m.r. spectroscopy for structural elucidation of carbohydrates can scarcely be underestimated, and the field has become vast with ramifications of specialized techniques. Although chemical shifts and spin couplings of individual nuclei constitute the primary data for most n.m.r.-spectral analyses, other n.m.r. parameters may provide important additional data. P. Dais and A. S. Perlin (Montreal) here discuss the measurement of proton spin-lattice relaxation rates. The authors present the basic theory concerning spin-lattice relaxation, explain how reliable data may be determined, and demonstrate how these rates can be correlated with stereospecific dependencies, especially regarding the estimation of interproton distances and the implications of these values in the interpretation of sugar conformations. 

In compound 1, all interproton distances lie in a range which would be expected to give rise to an NOE, as the experiment confirmed. In 3, although the structural formula is very similar, only the distance between the CH proton and the neighbouring ortho protons lies clearly in the NOE range . The others are close to or above 5 A, so that only very small NOEs or none at all could be expected. 

---