## Abstract

This contribution presents the first results of an application of high-resolution quasielastic neutron scattering to the dynamics of protein hydration. Using two samples (film stacks and `fluffy' powders) of biosynthetically fully deuterated C-phycocyanin extracted from blue-green algae, we have studied the Doppler-like broadening of the quasi-elastic line as a function of scattering angle 2<latex>$\theta$</latex> at several sub-monolayer H<latex>$_2$</latex>O hydration levels. The backscattering spectrometer IN 10 at the Institut Laue-Langevin (I.L.L.), Grenoble, was employed to measure wet-minus-dry difference broadenings <latex>$\Delta E$</latex> of up to 5 10<latex>$^{-3}$</latex> cm<latex>$^{-1}$</latex>, or 0.4 <latex>$\mu eV$</latex>, for momentum transfers k = (4<latex>$\pi$</latex>/<latex>$\lambda_0$</latex>) sin <latex>$\theta$</latex> between 0.15 and 1.7 A<latex>$^{-1}$</latex> (incident wavelength <latex>$\lambda_0$</latex> = 6 A). The results show that <latex>$\Delta E$</latex>(k) possesses an oscillatory structure with a first maximum between k<latex>$_{max}$</latex> = 0.4 and 0.8 A<latex>$^{-1}$</latex>. The position of this maximum shifts to higher k with increasing hydration, while its intensity increases and the following minimum at k<latex>$_{min}$</latex> = 0.7-1.3 A<latex>$^{-1}$</latex> becomes progressively more shallow. Structure factor measurements indicate that line narrowing due to structure in S(k) is not the dominant mechanism in determining this oscillatory behaviour of <latex>$\Delta E$</latex>(k). A Chudley-Elliott jump diffusion model was adopted as a working hypothesis to extract a characteristic length (water migration distance a) and a characteristic time (residence time <latex>$\tau_0$</latex> at a hydration site) from the <latex>$\Delta E$</latex>(k) data. Values of a = 6-9 A and <latex>$\tau_0$</latex> = 5-30 ns were obtained for the powder sample and are shown to agree well with the average jump distances derived from topographical considerations in conjunction with hydration number estimates.