Interproton distances calculation

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 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. 

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. 

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,... 

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. 

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. 

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... 

NMR using liquid crystal solvents is now a well-established tool for the investigation of molecular structure. Selenophene was studied in a liquid crystal composed of sodium sulfate, decanol, deuterium oxide, and sodium decylsulfate.12 The refined direct couplings were obtained iteratively with the help of a computer. The ratios of the interproton distances were calculated from the direct couplings and found to be in good agreement with corresponding values calculated from the microwave data. 

A combined approach is to use interproton distances determined by simulation and experimental NOE intensities to calculate the dynamic behavior of specific linkages in an oligosaccharide. The MM force field was employed for the computer simulation of calonyctin Ai (40) where interglycosidic NOEs served as experimental distance restraints for the molecular dynamics 104). 

Interproton distances were calculated from the formula Vij = rijirij2/(xi tji where r,ji... 

Besides the advantage of the high-temperature measurements for quantitative interpretation of NOESY spectra, fig. 6 also indicates a special role of the high temperature maximum (note that positive cross-relaxation rates increase downward) of u". If the NOESY spectrum can be recorded at several temperatures around the cr" maximum, than calculated cross-relaxation rates can be used to obtain simultaneously the correlation time and the interproton distances without the necessity of any other knowledge. A typical problem in the cross-relaxation experiments is that cross-relaxation rate depends on two parameters, Tc and r (eq. (la)), and to calculate one of them the other must be independently known. However, the position of the maximum uniquely determines correlation time, and its height uniquely determines interproton distances. 

Fig. 6. Normalized cross-peak volumes of five representative spin pairs from NOESY spectra of cyclo(Pro-Gly) at different temperatures, recorded with Tm = 300 ms. Circles, crossrelaxation rates calculated from eq. (27a) using only the linear term. Dashed lines were drawn according to eqs (la) and (2a) using uiol2n = 500 MHz (actual resonance frequency) and interproton distances, r, from the model (table 1). Solid lines connect the points of one spin pair at different temperatures. Experimental temperatures indicated at the top are superimposed on the correlation time axis according to eq. (5) logTc 1/T. Reciprocal temperature axis is scaled and shifted to produce the best visual overlap of the theoretical curves and experimental data points. Inset represents the indicated region around the crossrelaxation rate maximum in the extreme-narrowing regime, magnified 14 times.

Structure calculations for the bound conformation of the ligand can be done in the absence of any knowledge on the actual structure of the receptor protein, as they involve only interproton distances of the ligand molecule. However, if the 3D structure of the protein is known, a model of the complex can be generated by using the tr-NOE distances as restraints to lock the otherwise flexible ligand in the bound conformation, which reduces the number of docking calculations considerably. 

The only model available for direct quantum-mechanical study of interatomic interaction is the hydrogen molecular ion Hj. If the two protons are considered clamped in position at a fixed distance apart, the single electron is represented by a Schrodinger equation, which can be separated in confo-cal elliptic coordinates. On varying the interproton distance for a series of calculations a complete mapping of the interaction for all possible configurations is presumably achieved. This is not the case. Despite its reasonable appearance the model is by no means unbiased. 

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