Karplus equation

Abstract: The relationship between vicinal NMR proton–proton coupling constants and the pseudorotational properties of the sugar ring in nucleosides and nucleotides is reinvestigated. Compared with our earlier study several important improvements are introduced: first, a new empirical generalization of the classical Karplus equation is utilized, which allows an accurate correction for the effects of electronegativity and orientation of substituents on 3J(HH); second, empirical correlations between the parameters governing the conformation of β-D-furanosides (taken from an analysis of 178 crystal structures) were used to define proton–proton torsion angles as a function of the pseudorotation parameters P and Φm; and, third an iterative least-squares computer program was devised to obtain the best fit of the conformational parameters to the experimental coupling constants. NMR data for the sugar ring in the following compounds were taken from the literature and analysed: 3′,5′-cyclic nucleotides, a base-stacked ribonucleotide, 2′-anhydroarabinonucleosides, α-D-2′,2-O-cyclouridine, 2′- and 3′-aminosubstituted ribonucleosides, 2′- and 3′-deoxyribonucleosides. The present results confirm that the conformational properties found in the solid state are, on the whole, preserved in solution.

Abstract: The backbone dihedral angle in polypeptides is characterized by four different J couplings: 3 JHNHR, 3 JHNC', 3 JHNC‚, and 3 JHRC'. E.COSY and quantitative J correlation techniques have been used to measure these couplings in the protein human ubiquitin, uniformly enriched in 13 C and 15 N. Assuming that the dihedral backbone angles in solution are identical to those in the X-ray structure of this protein and that H N is located in the C'-N-C R plane, Karplus relations for 3 JHNHR, 3 JHRC', and 3 JHNC‚, have been reparametrized. The root-mean-square (rms) difference between measured values of 3 JHNHR, 3 JHRC', 3 JHNC‚, and 3 JHNCand their corresponding Karplus curves are 0.53, 0.25, 0.24, and 0.36 Hz, respectively, whereas the precision of these measurements is considerably better. For any given residue, the differences between the four measured J couplings and values predicted by their Karplus curves on the basis of the X-ray structure-derived angle are highly correlated with one another. On average, a root-mean-square change of 5.7° in the X-ray derived angles is needed to obtain optimal agreement with all four measured J couplings. There is no clear correlation between the angle correction needed and the out-of-plane position of the amide proton predicted by ab initio calculations. The small differences in angles therefore presumably result from small uncertainties in the atomic positions of the 1.8 A X-ray structure. However, they may also be caused by genuine differences between the structure of the protein in solution and in the crystalline state or contain a contribution resulting from deviations from the assumption that the H N -N-C R -H R dihedral angle equals - 60°.

Abstract: 13C-31P coupling constants of 10 oligoribonucleoside phosphates, measured at a number of temperatures, are presented. The combination of these data with 1H-31P couplings of the same compounds leads to the derivation of two new and mutually consistent sets of Karplus parameters: J(CCOP) = 6.9cos2 phi--3.4cos phi + 0.7 J(HCOP) = 15.3cos2 phi--6.1cos phi + 1.6 At the same time new values for the base sequence dependent magnitude of the trans conformer of the backbone angle epsilon (C4'-C3'-O3'-P) are calculated. The present results show that the magnitude of epsilon(t) in right-handed ribo helices is confined to the range 214 degrees-226 degrees (average 219 degrees), which is in much better agreement with single crystal X-ray studies (average 218 degrees) than were previous deductions from NMR spectroscopic results (average 208 degrees).