Water and backbone dynamics in a hydrated protein

Abstract

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for (1)H and showed that the underlying dynamics driving the protein (1)H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of (1)H(2)O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with (2)H(2)O rather than (1)H(2)O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by (1)H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.

Figure 1

Proton spin-lattice relaxation rate constants as a function of the magnetic field strength plotted as the proton Larmor frequency for dry BSA (open circles) and deuterated 15% BSA gel in D₂O (triangles) at 302 K. The solid line is the best fit to the first term of Eq. 1 with b = 0.782. The second moment, M₂ = 7.98 × 10⁹ s⁻², was measured from the free induction decay and the dipolar coupling strength was calculated as ${\omega }_{\text{dip}}=\sqrt{20M_2/9}$. The peaks in the relaxation profiles are due to ¹⁴N-¹H and ²H-¹H heteronuclear relaxation pathways that become efficient when transition energies at the positions of the gray blocks on the frequency axis. The inset shows one of the ¹⁴N-¹H peaks for dry BSA; it has Gaussian shape centered at 2.86 ± 0.01 MHz and the full width at the half height of 256 ± 20 kHz.

Figure 2

Protein-proton (○) and water-proton (□) relaxation rate constants as a function of proton Larmor frequency for BSA hydrated to the level of 0.32 g water/g protein at −40°C and protein-proton (▵) and water-proton (+) relaxation rate constants at 28°C for the same sample. The gray blocks along the frequency axis identify the ¹⁴N transitions. The inset shows the slow relaxation constant as a function of Larmor frequency computed assuming that the protein protons relax with a power law with slope 0.78 and F = 0.069 appropriate for 10% BSA gel for different values of the transfer rate constant from protein to water spins: from top to bottom 10⁵, 200, 100, 50, 10, with the water rate constant set to 0.33 s⁻¹.

Figure 3

Water-proton relaxation-dispersion profile for bovine serum albumin cross-linked gels at different protein concentrations at 302 K: 40% (g protein/100 g water) (○), 30% (♢), 20% (□), 15% (▾), 10% (+), 7% (▴), and 4.5% (x). (Inset) The water-proton relaxation rate constant as a function of the protein proton fraction, F/(1 + F), where F is the population ratio of protein to water protons at 30 MHz (♦), 1 MHz (•), 0.1 MHz (▾), and 0.01 MHz (▴).

Figure 4

Water-proton 1/T₁ as a function of the magnetic field strength plotted as the proton Larmor frequency for 10% (○) and 20% (^∗) bovine serum albumin gels at 298 K. Solid lines are the best fits to Eq. 2, where the protein-proton-relaxation rate is given by the Eq. 1 and the water proton relaxation rate by Eq. 3. The second moment, M₂ = 4.56 × 10⁹ s⁻², was measured from the free induction decay (54). $1/T_{\mathit{1}}^{\mathit{0}}$ was fixed at 0.33 and $1/T_l^{\text{sur}}$ was calculated as described in Grebenkov et al. (39) with a correlation time of 15 ps. The bound water contribution, $1/T_{\mathit{1}}^{\text{bnd}}$, is given by Eq. 4. The best-fit parameters for the power law exponent and correlation time for bound water stochastic jumps are 0.75 and 41 ns respectively for the 10% gel and 0.74 and 49 ns for the 20% gel. Additional parameters include the magnetization transfer rate, $1/T_{\mathit{1},\text{WP}}$, factor $C\frac{N_{\text{f}}}{N_{\text{H}}}$ (Eq. 4), and a scaling factor associated with the strength of the dipolar coupling for water translational surface diffusion (37). The 5-parameter fit to these data is not unique; however, the values of these last parameters do not affect the value deduced for the motion of protein-bound water molecules. The dashed straight line is for reference. The inset compares the relaxation rate-constants of Fig. 1 with those of the H₂O-hydrated systems in Fig. 4.