B 3 a Field Dispersion in Protein Solutions

NMR relaxation provides additional molecular information if it can be done at a series of frequencies. The general observation in NMR frequency dependence experiments in solutions of proteins is that the longitudinal NMR relaxation rates (R, = l/7\) of 2D nuclei are independent of the field at very low NMR frequencies. As NMR frequency (and magnetic field strength) increases, Ri gradually decreases in a sigmoid-shaped curve until finally it becomes independent of the frequency and field strength [7], An example, shown in Figure 8.5 illustrates the field dispersion of the NMR relaxation.

Figure 8.5 Influence of frequency on the 2D-NMR longitudinal relaxation rate for a 30.6 mg mL-1 solution of a-hemocyanin in 80% D20/20% H20. The solid curve represents the best fit of the model in Table 8.3 with two correlation times (i.e., k = 2), with tCil = 180 ns and tc 2 = 1070 ns. (Reprinted with permission from [7], copyright by Elsevier.)

Frequency (MHz)

Figure 8.5 Influence of frequency on the 2D-NMR longitudinal relaxation rate for a 30.6 mg mL-1 solution of a-hemocyanin in 80% D20/20% H20. The solid curve represents the best fit of the model in Table 8.3 with two correlation times (i.e., k = 2), with tCil = 180 ns and tc 2 = 1070 ns. (Reprinted with permission from [7], copyright by Elsevier.)

The limiting high-frequency value for R2 of water bound to proteins is larger than the frequency-independent relaxation rate of pure water. The inflection point of the sigmoid curve, that is, the midpoint between the high and low frequency plateaus, is related to the protein rotational correlation time [8-10], Field dispersion data fully describe the spectral density function(s) that characterize the various dynamic processes in the system responsible for NMR relaxation.

In interpreting NMR relaxation data for protein solutions, it is instructive to have an idea of the time scale of the dynamic processes involving water. For a globular protein, water molecules are generally thought to exchange between a "free" (bulk water) state and a "bound" state with a approximate lifetime of 10~5-10"6 [11], Water molecules bound to the protein reorient with the protein, with correlation times on the order of 10~8-10~9s, and diffuse along the surface of the protein on a time scale of 10"7 s [11]. Other possible dynamic processes that involve "bound" water molecules include the motion of hydrated protein side chains (10" "MO 11 s), rotation of water molecules around their bonding axis to the protein surface (10"n s), and the chemical exchanges of hydrogen between water molecules and ionizable protein side chains as well as between "bound" and "free" water molecules (10-4 s) [7-11].

These time scales can be compared to the translation/rotation of "free" water (10~12 s) and proton exchange between 'free' water molecules with a lifetime on the order of 10 4 s [11], The contribution of NMR relaxation due to motions faster than 10~10 s is frequency independent in the experimentally accessible frequency range. Motions involving water that are slower than this limit give rise to the frequency dependence of NMR relaxation in protein solutions.

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