Reparametrization of the Karplus Relation for 3 J ( HaN ) and 3 J ( HNC ’ ) in Peptides from Uniformly 13 C / 15 N-Enriched Human Ubiquitin

The Karplus relations for vicinal J couplings, which relate the peptide backbone angles # and q to 3J(HaN) and 3J(HN-C’), have been reparametrized on the basis of measurements made on uniformly 13C/’5N-enriched human ubiquitin and backbone angles derived from the 1.8 8, X-ray structure of this protein (Vijay-Kumar, S.; Bugg, C. E.; Cook, W. J. J. Mol. Biol. 1987, 194, 531-544). For 3J(Ha-N), values measured using an ECOSYtype HCACO experiment fall in the -1.9 to 0.1 Hz range and are described by the following: 3J(Ha-N) = -0.88 cos2(q + 60”) 0.61 cos(q + 60”) 0.27. The root-mean-square difference (rmsd) between measured values and the Karplus relation is 0.16 Hz. Values measured for 3J(HN-C’) using an E.COSY-type HNCA experiment fall in the -0.4 to 3.6 Hz range, are described by 4.0 cos2(&) f 1.1 cos(#) + 0.1, and fit the observed J couplings with an rmsd of 0.45 Hz. The importance of three-bond J couplings for determining three-dimensional molecular conformation by NMR methods is well-established. For peptides and proteins a wide variety of different J couplings is readily accessible and is commonly being used in the structure determination process. For most common types of three-bond J couplings the K q l u s equation,’ which correlates J with the intervening torsion angle, has been parametrized on the basis of conformationally constrained small molecules with similar patterns of substituents as the molecule of interest.2 A more direct approach was used by Pardi et who parametrized the Karplus relation for 3J(HN-Ha) by relating the J values measured for peptide amides in pancreatic trypsin inhibitor to the dihedral angles available from highresolution crystallographic studies. Very similar values for the Karplus coefficients describing 3J(HN-Ha) were also derived using a range of other protein^. ^,^ The present paper describes use of the same approach to parametrize Karplus equations for 3J(HN-C’) and 3J(Ha-N), which are related to the peptide backbone angles 41 and q, respectively. Our study uses a sample of human ubiquitin, a protein which commercially can be obtained uniformly enriched with I3C and I5N (VLI Research, Southeastern, PA) and for which a high-resolution crystal structure is available.6 In peptides and proteins the most common ways to measure heteronuclear J couplings are E.COSY-based techniques’ and quantitative J correlation,8 a method in which the strength of a long-range correlation is related in a simple manner to the intensity of the corresponding cross peak. For measurement @Abstract published in Advance ACS Abstracts, February 1, 1995. (1) Karplus, M. J. Chem. Phys. 1959, 30, 11-15. (2) Bystrov, V. F. Prog. NMR. Spectrosc. 1976, 10, 41-81. (3) Pardi, A,; Billeter, M. ; Wiithrich, K. J. Mol. Biol. 1984, 180, 741(4) Ludvigsen, S . ; Andersen, K. V. ; Poulsen, F. M . J. Mol. Biol. 1991, ( 5 ) Vuister, G. W. ; Bax, A. J. Am. Chem. SOC. 1993, 115, 7772-7777. (6) Vijay-Kumar, S. ; Bugg, C. E. ; Cook, W. J. J. Mol. Biol. 1987, 194, (7) Griesinger, C. ; S@rensen, 0. W; Emst, R. R. J . Chem. Phys. 1986, ( 8 ) Bax, A. ; Vuister, G. W. ; Grzesiek, S . ; Delaglio, F. ; Wang, A. C. ; 751.