Nuclear Magnetic Resonance Studies of Amino Acids and Proteins. Rotational Correlation Times of Proteins by Deuterium Nuclear Magnetic Resonance Spectroscopy

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 ω₀²τ_r² » 1) permits determination of both the rotational correlation time (τ_r) 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 τ_R 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 3.2.1.17) 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.