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 1H ²O 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 1.8Å^-1 and a temperature range from 4 to 297 K. We used neutrons with a wavelength of λ αE 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. In this model, a water molecule stays for a time τ₀ in a bound state performing oscillatory motions. Thereafter, the molecule performs free diffusion for the time τ₁ in a nonbound state followed again by the oscillatory motions for τ₀ and so forth. We used the general formulation with no simplifications as τ₀τ₁ or τ₁τ₀. At room temperature, we obtained τ₀ αE 104 ps and τ₁ αE 37 ps. For the protein bound hydrogen, the dynamics is described by a Brownian oscillator where the protons perform overdamped motions in limited space.