We report results on the structure, local order and dynamics of water surrounding a lysozyme protein. The local order of water molecules is as much tetrahedral as in bulk water already at close vicinity of the protein but the number of hydrogen bonds depends more on the distance from the protein and gradually recovers bulk value upon moving outer. The dynamics of water seems in general to be more affected than its structure by the presence of the protein. An extremely long-relaxation detected in hydration water appears in the first monolayer around the protein, and the slow down is enhanced at low temperature. The dynamics of water within a layer of thickness 6 Å is sub-diffusive up to about ∼1 ns, above 1 ns we observe a crossover toward a hopping regime over a length-scale larger than that of nearest neighbors molecules. This hopping seems connected to transient trapping of water molecules on some specific protein domains
