Karplus relationship, determination torsional 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],... 

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 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. 

The Karplus-like relationship between HCOP and CCOP dihedral angles and and three-bond coupling constants, respectively, has been used to determine the conformation about the ribose-phosphate backbone of nucleic acids in solution. Torsional angles about both the C3 -03 and C5 -05 bonds in 3, 5 -phosphodiester linkages have been determined from the coupled and P NMR spectra. 

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