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 (H2O)-H-1 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 angstrom(-1) and a temperature range from 4 to 297 K. We used neutrons with a wavelength of lambda = 6 angstrom and an energy resolution of about 65 mu eV 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 Sjolander [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) >> tau(1) or tau(1) >> tau(0). At room temperature, we obtained tau(0) = 104 ps and tau(1) = 37 ps. For the protein bound hydrogen, the dynamics is described by a Brownian oscillator where the protons perform overdamped motions in limited space.