Dynamical properties of the hydration shell of fully deuterated myoglobin

Freeze-dried perdeuterated sperm whale myoglobin was kept in a water-saturated atmosphere in order to obtain a hydration degree of 335 ${}^1$H${}_2$O molecules per one myoglobin molecule. Incoherent neutron scattering was performed at the neutron spectrometer TOFTOF at the FRM II in an angular range of $q$ from 0.6 to 1.8 Å${}^{-1}$ and a temperature range from 4 to 297 K. We used neutrons with a wavelength of λ $\alpha E$ 6 Å and an energy resolution of about 65 μeV corresponding to motions faster than 10 ps. At temperatures above 225 K, broad lines appear in the spectra caused by quasielastic scattering. For an explanation of these lines, we assumed that there are only two types of protons, those that are part of the hydration water (72$\%$) and those that belong to the protein (28$\%$). The protons of the hydration water were analyzed with the diffusion model of Singwi and Sjölander [Phys. Rev. 119, 863 (1960)]. In this model, a water molecule stays for a time ${\tau }_0$ in a bound state performing oscillatory motions. Thereafter, the molecule performs free diffusion for the time ${\tau }_1$ in a nonbound state followed again by the oscillatory motions for ${\tau }_0$ and so forth. We used the general formulation with no simplifications as ${\tau }_0\gg {\tau }_1$ or ${\tau }_1\gg {\tau }_0$. At room temperature, we obtained ${\tau }_0$ $\alpha E$ 104 ps and ${\tau }_1$ $\alpha E$ 37 ps. For the protein bound hydrogen, the dynamics is described by a Brownian oscillator where the protons perform overdamped motions in limited space.

Figure 1

Incoherent neutron scattering on perdeuterated myoglobin with a hydration shell of light water. $T$ $\alpha E$ 297 K, $q$ $\alpha E$ 1.7 Å${}^{-1}$. Squares, experimental data; solid line, least-squares fit; dashed line, contribution of the water protons; dotted line, contributions of the protein protons; thin solid line, resolution function of the instrument.

Figure 2

Some typical spectra covering the temperature and the $q$ range. Only the experimental data and the results of the fitting procedure (solid line) are given.

Figure 3

Influence of a variation of ${\tau }_0$ on the spectrum. Solid line $b$: Spectrum according to Singwi-Sjölander with the obtained fit parameters at room temperature, no convolution with the resolution of the spectrometer, ${\tau }_0$ $\alpha E$ 104 ps. For curves $a$ and $c$: ${\tau }_0$ is changed by ±20$\%$. Note the logarithmic scale. The full width at half-height is indicated by arrows. Although the three spectra cannot be distinguished at full width at half-height, their wings are separated.