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

Side-chain dynamics in proteins can be characterized by the NMR measurement of ¹³C and ²H 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^α-C^β bond (χ1 angle) can be derived from ³J_C′-Cγ and ³J_N-Cγ couplings. These couplings can be measured at high accuracy, in particular for Thr, Ile, 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 ¹³C-¹H side-chain dipolar coupling measurements in oriented media, these 3J couplings were used to parametrize empirical Karplus relationships for 3_JC′-Cγ and ³JN-Cγ. These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum ³J_CC and ³J_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 χ1 torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S_J² and S_D², provides a view of side-chain dynamics that is complementary to that obtained from ¹³C and ²H relaxation. On average, results agree well with literature values for ²H-relaxation-derived S_rel² values in ubiquitin and HIV protease, but also identify a fraction of residues for which S_J,D² < S_rel². This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.