## B1 NMR Relaxation of aD and 1H in Aqueous Solutions of 3Lactoglobulin

Proton, deuterium, and oxygen-17 NMR relaxation can be used to investigate the amount and mobility of water bound to proteins. In this example, we illustrate the analysis of pulsed NMR relaxation data for 2D and 'H nuclei of water in a protein solution for such a system.

Figure 8.2 shows typical proton relaxation results for an aqueous solution of the protein /3-lactoglobulin A. The transverse relaxation data gave a

Figure 8.2 Proton NMR peak intensities vs. delay time r for 0.061 g /3-lactoglobulin A/g H20 at pH 6.2,30°C. Longitudinal relaxation data (T¡, o) from inversion recovery experiment with line representing best fit to single exponential model in eq. (8.2) and transverse relaxation data (7"2, •) from spin-locking measurements with line representing best fit to sum of two exponentials in eq. (8.4). (Reprinted with permission from [3], copyright by Academic Press.)

Figure 8.2 Proton NMR peak intensities vs. delay time r for 0.061 g /3-lactoglobulin A/g H20 at pH 6.2,30°C. Longitudinal relaxation data (T¡, o) from inversion recovery experiment with line representing best fit to single exponential model in eq. (8.2) and transverse relaxation data (7"2, •) from spin-locking measurements with line representing best fit to sum of two exponentials in eq. (8.4). (Reprinted with permission from [3], copyright by Academic Press.)

good fit to a single exponential (eq. (8.4)), indicating a single relaxation rate with decay time T2. However, the longitudinal relaxation data gave a best fit to the sum of two exponential terms (n = 2, Figure 8.2). This behavior is consistent with the finding that cross-relaxation between protons of water bound to the protein and protons on the protein itself contributes [4, 5] to the longitudinal relaxation rate.

Cross-relaxation is not significant for the deuterium NMR relaxation in solutions of proteins in D20. Models with a single time constant gave excellent fits for both longitudinal (Table 8.1, n = 1) and transverse relaxation (eq. (8.4)) of 2D in solutions of /3-lactoglobulin A in D20 (Figure 8.3) [3],

Plots of relaxation rates in the D20 solutions as = 1ITX and R2 = II T2 vs. concentration were linear up to 0.04 g /3-lactoglobulin A per g D20.

Table 8.1 Model for the NMR Longitudinal Relaxation Rate

Assumptions: Inversion-recovery pulse sequence [l] Regression equation:

Regression parameters: Data:

Special instructions: Begin testing models with n = 1. Test for best fit by comparing residual plots and using the extra sum of squares F test (Section 3.C.1)

Figure 8.3 Deuterium NMR peak intensities vs. delay time r for 0.029 g /3-lactoglobulin A/g D20 at pH 6.2, 30°C. Longitudinal relaxation data (T,, o) from inversion recovery experiment with line representing best fit to single exponential model in eq. (8.2) and transverse relaxation data (T2, •) from spin-locking measurements with line representing best fit to single exponential in eq. (8.4). Results indicate no cross-relation with protein (Reprinted with permission from [3], copyright by Academic Press.)

Figure 8.3 Deuterium NMR peak intensities vs. delay time r for 0.029 g /3-lactoglobulin A/g D20 at pH 6.2, 30°C. Longitudinal relaxation data (T,, o) from inversion recovery experiment with line representing best fit to single exponential model in eq. (8.2) and transverse relaxation data (T2, •) from spin-locking measurements with line representing best fit to single exponential in eq. (8.4). Results indicate no cross-relation with protein (Reprinted with permission from [3], copyright by Academic Press.)

These results were used to obtain the correlation time of D20 bound to the protein [3]. At 30°C and pH 6.2, this correlation time was 10 ns, which was used to obtain a hydrodynamic radius of the protein of 23 A at this pH.^At pH 4.65, a correlation time of 22.5 ns translates into a radius of 30 A indicative of association of the protein. Thermodynamic parameters were also obtained by methods outlined in the original paper [3].

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