B4a 170 NMR

NMR relaxation of 170 is free from the complications of cross-relaxation and chemical exchange of protons that influence relaxation of 'H and 2D. Thus, 170 relaxation provides a direct probe of the hydration of proteins

FREQUENCY (MHz)

Figure 8.6 Influence of frequency on the 2D-NMR longitudinal relaxation rate at 18°C for (A) 10% BSA solution in D20; solid line is best fit of the model with two correlation times tCil = 40 ns and tc,2 = 228 ns; (B) 33% BSA solution in D20; solid line is best fit of the model with three correlation times rCil = 48ns,i,i2 = 360 ns, and ic,3 = 4400 ns. Dotted lines show major components of the relaxation. (Reprinted with permission from [7], copyright by Elsevier.)

FREQUENCY (MHz)

Figure 8.6 Influence of frequency on the 2D-NMR longitudinal relaxation rate at 18°C for (A) 10% BSA solution in D20; solid line is best fit of the model with two correlation times tCil = 40 ns and tc,2 = 228 ns; (B) 33% BSA solution in D20; solid line is best fit of the model with three correlation times rCil = 48ns,i,i2 = 360 ns, and ic,3 = 4400 ns. Dotted lines show major components of the relaxation. (Reprinted with permission from [7], copyright by Elsevier.)

[8,13], The NMR relaxation rate of "O in water increases when the water is bound to macromolecules because of the asymmetric electrostatic interactions at the binding site and the longer effective correlation times of bound water. On the other hand, reorientation of water at the binding site and fast exchange between bound and free water tend to decrease the "O NMR relaxation rate.

Starting from the two state model, that is, bound and free water, in eq. (8.6), a linear model was derived for the dependence of the relaxation rates on protein concentration (Cp):

where the m denotes either the longitudinal (/?,) or transverse relaxation rate (R2), Rm,i is the relaxation rate for bound water, RmS) is the relaxation rate for free water, Cp is the concentration of protein in g/g water, and nH is the hydration number in g water bound/g protein. If the correlation time of bound water can be estimated or calculated [13], the Rm>i value can be found. Then, the slope of a plot of Rm_obs vs. Cp can be used to obtain n„.

Inversion-recovery peak heights vs. time for soy protein gave a good fit to the model in Table 8.1 with n = 1. Typical results are shown in Figure

■ 1 i • 1 ■ 1 i ■ ' ■ ■ i 1 1 ■ ■ i 1 1 ■ 1 i 1 1

■ 1 i • 1 ■ 1 i ■ ' ■ ■ i 1 1 ■ ■ i 1 1 ■ 1 i 1 1

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Figure 8.7 Oxygen-17 NMR peak intensities of D20 vs. interpulse delay in an inversion recovery experiment to determined 7",: (Top) Spectra for a 2% (w/w) dispersion of soy protein in D20 at 21°C and effective pH in D20 (pD) = 7.4; (Bottom) Line is the best fit of the peak heights vs. time to model in eq 8.2, ( + ) are experimental data. (Reprinted with permission from [13], copyright by the American Chemical Society.)

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Figure 8.7 Oxygen-17 NMR peak intensities of D20 vs. interpulse delay in an inversion recovery experiment to determined 7",: (Top) Spectra for a 2% (w/w) dispersion of soy protein in D20 at 21°C and effective pH in D20 (pD) = 7.4; (Bottom) Line is the best fit of the peak heights vs. time to model in eq 8.2, ( + ) are experimental data. (Reprinted with permission from [13], copyright by the American Chemical Society.)

8.7. The "O relaxation rates were linear with protein concentration (Figure 8.8), and the slopes of these lines were used to obtain an nH of 0.33 g water/ g protein [13]. This value agrees with estimates from proton NMR at -50°C and from differential scanning calorimetry.

B. 4.b. 1H NMR Relaxation of Soybean Protein

As mentioned in Section B.l, cross-relaxation between protons on water and the protein can cause problems in the analysis of JH NMR relaxation data. In the presence of cross-relaxation, the following equation can be used for the dependence of relaxation rates on protein concentration:

Figure 8.8 Influence of protein concentration the longitudinal (A) and transverse (•) nO NMR relaxation rates for dispersions of soybean protein in D20 at 21°C and neutral pH. (Reprinted with permission from [13], copyright by the American Chemical Society.)

Protein concentration (g/g)

Figure 8.8 Influence of protein concentration the longitudinal (A) and transverse (•) nO NMR relaxation rates for dispersions of soybean protein in D20 at 21°C and neutral pH. (Reprinted with permission from [13], copyright by the American Chemical Society.)

where Rx is the cross-relaxation rate. The influence of cross relaxation can often be neglected for i?2,obs, but its dependence on protein concentration is nonlinear. By neglecting Rx and replacing Cp by the chemical activity of the protein as expressed by a virial expansion [13], the model for R2,0bs becomes

[Cp exp(2B0Cp + 2B05Cp5 + QMIB^C1/ + 1.5B2C2P + . . .)]. (8.11)

The parameters B in eq. (8.11) are called virial coefficients and can be interpreted in terms of various molecular interactions [13].

The dependence of R2obs on soy protein concentration gave good fits to eq. (8.11) (Figure 8.9) [13]. In the range of protein concentrations examined, all the data at pH <9.1 gave best fits to the model using only the B0 virial coefficient. Addition of more terms to the model did not provide a statistically better fit, as was shown by using the extra sum of squares F test. Inclusion of the B0 and the B2 terms was required to give the best fit to the pH 11 data.

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