Karplus relationship, determination

Slightly more difficult determination of stereochemistry moving from two dimensions to three Revision of the Karplus relationship and of conjugate addition. 

X-ray crystallography for detection of metalloproteins accuracy problems, 66 determination of geometric parameters DFT-the Hohenberg-Kohn theorem approach, 67 QM/S techniques, 67 QSOR approach, Karplus relationship, 67 refinement of, linear-scaling quantum chemical methods, 66-67... 

The observed three-bond coupling constants may be analyzed with a proton-phosphorus Karplus relationship to determine the C4 -C3 -O-P torsional angle c (28). As shown by Dickerson (10) there is a strong correlation (R = -0.92) between torsional angles C4 -C3 -O3 -P (c) and C3 -O3 -P-O5 (C) in the crystal structures of various duplexes. Thus both torsional angles c and ( can often be calculated from the measured P-H3 coupling constant. 

The tj> dihedral angle between the HNCn and the NCaH planes. Values in (a) and (b) are calculated from the amide HN-CaH doublet proton spin-spin splittings (Jnc) in water and in deuterodimethylsulfoxide, respectively, and on the basis of the data reported in (30) and the Karplus relationship of Ramachandran et al. (48). The labelling of the residues at the top refers to an arbitrary PMR classification of the resonances while the data in (c) corresponds to the angles determined by Zalhin et al. (28) for crystalline ferrichrome A, correctly labelled according to the criteria used in Fig. 1. 

Although the determination of both the configuration and the conformation of carbohydrates involves the same general considerations, the quantitative nature of the latter requires a rather more fundamental approach. Accordingly, the following discussion is divided into two main sections the first refers to the development and applications of nuclear magnetic resonance to stereochemical problems, and deals mainly with substituent resonances the second discusses in some detail the Karplus relationship and the determination of carbohydrate conformations. 

The early development of the Karplus relationship has been outlined in Section 1.4 (see p. 60). The significance of this method was soon realized by Jardetzky and by Lemieux, who applied it to the determination of the conformation of the o-ribofuranose and 2-deoxy-D-eri/first time, that furanoid rings are nonplanar in solution. However, it was not realized at that time that the Karplus parameters are subject to a substituent effect, so the original parameters were used hence, the particular values obtained in these investigations may require some slight modification. All of the following empirical modifications of the Karplus parameters were based on the intuitive assumption that allowance must be made for a substituent effect, and this step has only recently been justified by Williamson, and by Laszlo and Schleyer. ... 

The new empirical Karplus relationships for Vccy Vncy proteins have been obtained by Bax and co-workers. ° The couplings required to parametrize these relationships have been measured for ubiquitin and the third IgG-binding domain of protein G. The experimental Karplus curves have been confirmed by the DFT calculations including an unusual phase shift which causes the maximum Vccy - ncy couplings to occur for dihedral angles slightly smaller than 180°. The new Karplus curves permit determination of rotamer populations for the Xi torsion angles. 

C-0-C-1H couplings have been determined in methyl /i-cellobioside after deuterium substitution of all protons on carbon atoms with a free hydroxy group. Assuming a Karplus type relationship between 3JC H and the dihedral angle in 13C-0-C-1H groups, the torsional angles 0 and / of methyl / -cellobioside were determined to be 25 30" [734],... 

Vicinal J-coupling constants provide valuable information for the determination of biomacromolecule conformation. The stmctural information is derived from Karplus equations (12) that provide empirical relationships between dihedral bond angles, and the J-coupling. Karplus equations obey the following general formula ... 

Schaefer et al studied departures from the Karplus-type relationship ( Barfield effect ) to determine the ring pucker in 2-phenyl-1,3-dithiane. The dependence of the 7(H,H) Karplus equation on the internal C—C—H angles was given in mathematical form by Barfield et al., who also recalculated the... 

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