Dependencies of J-Couplings upon Dihedral Angles on Proteins

Indirect spin–spin coupling constants, or simply J-couplings, are one of the most useful and widely used NMR parameters for structure determination. Accurate analytic representation of their structural dependence is crucial for quantitative analysis. The dependence of vicinal J-coupling constants upon the dihedral angle of the coupled nuclei was first established by Karplus more than 50 years ago. Since then, Karplus original equations have been extensively modified and generalized in order to account for different effects upon the J-coupling values. In this work, we critically analyse the use of such Karplus-type equations for the description of the dihedral dependence of J-couplings derived from both experiment and first principles. The use of alternative nonanalytic expressions is also discussed. Finally, we have collected the most accurate J-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.