Probing side-chain dynamics in proteins by the measurement of nine deuterium relaxation rates per methyl group.

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.