We show that measurement of the spin-lattice (T1) and spin-spin (T2) relaxation times (or line widths) of irrotationally bound 2H nuclei in macromolecules undergoing isotropic rotational motion outside of the extreme narrowing limit (i.e., for the case ω02τr2 » 1) permits determination of both the rotational correlation time (τr) of the macromolecule and the electric quadrupole coupling constant (e2qQ/h) of the 2H label. The technique has the advantage over 13C nuclear magnetic resonance (NMR) that no assumptions about bond lengths (which appear to the sixth power in 13C relaxation studies) or relaxation mechanisms need to be made, since relaxation will always be quadrupolar, even for aromatic residues at high field. Asymmetry parameter (η) uncertainties are shown to cause negligible effects on τR determinations, and in any case it is shown that both e2qQ/h and η may readily be determined in separate solid-state experiments. By way of example, we report 2H NMR results on aqueous lysozyme (EC 22.214.171.124) at 5.2 and 8.5 T (corresponding to 2H-resonance frequencies of 34 and 55 MHz). Interpretation of the results in terms of the isotropic rigid-rotor model yields e2qQ/h values of ≈170 or ≈190 kHz, respectively, for the imidazolium and free-base forms of [ϵ12H]His-15 lysozyme in solution, in excellent agreement with e2qQ/h values of ∼ 167 and ∼ 190 kHz obtained for the free amino acids in the solid state. In principle, the method may in suitable cases permit comparison between the dynamic structures of proteins in solution and in the crystalline solid state.
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