Karplus parameters

Structural properties of two macrocyclic derivatives 42 (R = H, Ts) have been studied by molecular mechanics and 111 NMR spectroscopy, and new sets of Karplus parameters for calculation of the vicinal coupling constants of the butyrolactone moieties have been determined <2002EJ0351>. 

In his calculations, Karplus assumed that both of the carbon atoms to which the hydrogen atoms are attached are sp -hybridized, and he pointed out that evidence was available to show that the actual value of the relationship was dependent on the other substituents attached to the carbon atoms. The empirical modifications of the Karplus parameters which were developed to obtain meaningful results from carbohydrates are discussed in detail in Section 11,2 (p. 71). Williamson has since obtained some rather elegant results which largely justify these empirical assumptions. From derivatives of hexachloronorbornene, he obtained a linear relationship between 1,3-coupling constants and substituent electronegativities which show unequivocally that allowance has to be made for substituent effects in the Karplus relationship. 

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 essential fragments encountered in carbohydrate proton magnetic resonance are shown in (13) and (14), where (14) represents the situation at the anomeric center of a sugar. The first attempt to check the validity of the original Karplus parameters when they are applied to the fragment... 

Determination of Karplus Parameters From Static to Self-Consistent Fittings 187... 

DETERMINATION OF KARPLUS PARAMETERS FROM STATIC TO SELF-CONSISTENT FITTINGS... 

Hence, the set of incremental coefficients ACq is included in the fitting process. The authors used this formulation within a self-consistent fitting approach [81] to obtain very accurate amino acid-specific Karplus parameters for the six vicinal -couplings that probe the side-chain torsion angle x by making use of six additional AC parameters. In a subsequent study, the results were further improved by introducing an additional sine term to account for asymmetry effects. 

Hruska (12) developed a procedure to determine the rotamer populations of the 3 GH20H-group from the coupling constants between H(3 A), H0 B) and H(A ). With the Karplus parameters given in eq. (1) the equations used are ... 

Karplus parameters were devized for analysis of magnitudes... 

M Schlenkrich, J Bnckmann, AD MacKerell Jr, M Karplus. In KM Merz, B Roux, eds. Empirical Potential Energy Eunction for Phospholipids Criteria for Parameter Optimization and Applications. Boston Birkhaiiser, 1996, pp 31-81. 

HWT van Vlijmen, M Karplus. PDB-based protein loop prediction Parameters for selection and methods for optimization. I Mol Biol 267 975-1001, 1997. 

Schlenkrich, M., Brickmann, J., MacKerell Jr., A. D., and Karplus, M. (1996) An empirical potential energy function for phospholipids criteria for parameter optimization and application. In Biological membranes a molecular perspective from computational and experiment, Merz Jr., K. M. and Roux, B. (eds.), Birkhauser, Boston, 31-81. 

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