Karplus-type equations

Karplus-type equations have been developed for many other systems of interest, most notably H-C-O-H [242,243], H-C-O-C [387,414,415], H-C-C-C [197,387], and C-O-C-C [416, 417], It should be noted that coupling to hydroxyl protons can be observed in water or water/acetone or water/DMSO mixtures if the NMR tubes are rinsed in phosphate buffers and the carbohydrate derivatives are thoroughly deionized [239,249], If the magnitudes of the coupling constants to carbon are determined on natural abundance material, considerable amounts are required. Alternatively, labeled material can be used [416,417,418,419] and starting materials with varieties of labels are available. 

I. Tvaroska, M. Hricovmi, and E. Petrakova, An attempt to derive a new Karplus-type equation of vicinal proton-carbon coupling constants for C-O-C-H segments of bonded atoms, Carbohydr. Res., 189 (1989) 359-362. 

I. Tvaroska, K. Mazeau, M. Blanc-Muesser, S. Lavaitte, H. Driguez, and F. R. Taravel, Karplus-type equation for vicinal carbon-proton coupling constants for the C-S-C-H pathway in 1-thioglycosides, Carbohydr. Res., 229 (1992) 225-231. 

C. Thibaudeau, J. Plavec, and J. Chattopadhyaya, A new generalized Karplus-type equation relating vicinal proton-fluorine coupling constants to H-C-C-F torsion angles, J. Org. Chem., 63 (1998) 4967 1984. 

Vicinal proton-carbon coupling constants (3.7h65,C4 and J is.v.ci) also provide valuable information about the hydroxymethyl conformation. Theoretical calculations were applied to establish Karplus-type equations that correlate these couplings with lu torsion angle and then these were used to estimate C5—C6 rotamer... 

However, V(N-C) values are observed for 1-propylamine, quinuclidine and their hydrochlorides. (94) In saturated amines it is unlikely that it will be possible to describe calculated 3/(N-C) values in terms of simple Karplus-type equations. Other factors, such as the orientation of the nitrogen lone-pair (important for 3/(N-H)), will undoubtedly be important. (124)... 

Grayson and Sauer computed the coefficients in a Karplus-type equation of the spin-spin coupling constants for a series of rotated ethane geometries. The coupling constants were calculated at the SCF, SOPPA, and SOPPA-CCSD levels and compared with results of previous calculations and experimental data. It was found that the coefficients in the Karplus equation calculated at the SOPPA-CCSD level are in good agreement with coefficients derived from experimental coupling constant data or results of MCSCF calculations. 

Pi, which is related to the main chain conformation, is calculated according to a Karplus-type equation (40-43) from the N<-Cf —Hf ccnipling constant. If... 

To discuss the structure of the DKP rii on an quantitative level, the dihedral angles were calculated from /h c -n-h using two different kinds of Karplus-type equations, which have recently been proposed for cyclic amides. The results of the calculation are shown in Table 4. The experimental data concerning Cyclo-(Gly-His) are in quite good agreement with those reported by Kopple and Ohni i (97). As far as Table 4 is concerned, the main chain structures of the three cyclic dipeptides ate nearly planar in DMSO. The structure in D2O may be planar, although a quantitative consideration cannot be made. 

The methods to determine rotamer populations from NMR homo- and het-eronuclear vicinal couplings have been reviewed by Kraszni et al., who also assessed properties and capacities of the Karplus-type equations. NMR studies of chiral recognition by cyclodextrins which manifests itself in all NMR parameters including couplings have been reviewed by Dodziuk et aV... 

Analysis of the coupling constants according to a Karplus-type equation revealed that the aromatic plane of phenylalanine and tryptophan is parallel to the porphyrin plane, suggesting that the Ti-rc-stacking interactions in water stabilize the complex. ... 

Table 4 shows the results of such an attempt, where the molecular mechanics method was used to estimate the relative population of equilibrating rotamers and to compute population-weighted vicinal H/H coupling constants by means of a Karplus-type equation. The calculated coupling constants are weight-averaged over three C—C rotamers for 4 27 for 5 81 for 6a 27 for 6b and 6c, and 243 for 7. It can be seen that... 

In this work, we critically analyse the use of such Karplus-type equations for the description of the dihedral dependence of d-couplings derived from both experiment and first principles. The use of alternative nonanalytic expressions is also discussed. Finally, we have collected the most accurate d-coupling parameterizations of the recent literature, particularly those that exhibit explicit dependence upon the dihedral angles that govern the backbone and side-chain conformations of polypeptide chains. 

The original Karplus equation has been subjected to continuous modifications and reparameterizations in order to embrace a vast number of different nuclear pairs on diflerent molecular environments [6—23]. The scope of this chapter is to discuss the use of Karplus-type equations for the description of the dihedral dependence of /-couplings and to gather the most relevant data available to date, specifically devoted to the characterization of backbone (secondary structure) and side-chain conformations of proteins, /-couplings over one ( J) and two (/) bond ones are not as highly used as the -couplings for structural determination, but notable exceptions will also be covered. 

Table 5.2 Coefficients of Karplus-type equations for J (l> + S(f>) coupling constants... 

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