Insights into the mobility of methyl-bearing side chains in proteins from 3JCC and 3JCN couplings

Side-chain dynamics in proteins can be characterized by the NMR measurement of C-13 and 2 H relaxation rates. Evaluation of the corresponding spectral densities limits the slowest motions that can be studied quantitatively to the time scale on which the overall molecular tumbling takes place. A different measure for the degree of side-chain order about the C-alpha-C-beta bond (chi(1) angle) can be derived from (3)J(C'-Cgamma) and (3)J(N-Cgamma) couplings. These couplings can be measured at high accuracy, in particular for Thr, lle, and Val residues. In conjunction with the known backbone structures of ubiquitin and the third IgG-binding domain of protein G, and an extensive set of C-13-H-1 side-chain dipolar coupling measurements in oriented media, these (3)J couplings were used to parametrize empirical Karplus relationships for (3)J(C'-Cgamma) and (3)J(N-Cgamma). These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum (3)J(CC) and (3)J(CN) couplings to occur for dihedral angles slightly smaller than 180, particularly noticeable in Thr residues. The new Karplus curves permit determination of rotamer populations for the X, torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S-J(2) and S-D(2), provides a view of side-chain dynamics that is complementary to that obtained from C-13 and H-2 relaxation. On average, results agree well with literature values for H-2-relaxation-derived S-rel(2) values in ubiquitin and HIV protease, but also identify a fraction of residues for which S-J,D(2) < S-rel(2). This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.