The dynamical behavior of water around plastocyanin has been investigated in a wide temperature range by molecular dynamics simulation. The mean square displacements of water oxygen atoms show, at long times, a t(alpha) trend for all temperatures. Below 150 K, alpha is constant and equal to 1; at higher temperatures it drops to a value significantly smaller than 1, and thereafter decreases with increasing temperature. The occurrence of such an anomalous diffusion matches the onset of the dynamical transition observed in the protein. The intermediate scattering function of water is characterized, at high temperature, by a stretched exponential decay evolving, at low temperature, toward a two step relaxation behavior, which becomes more evident on increasing the exchanged wave vector q. Both the mean square displacements and the intermediate scattering functions show, beyond the ballistic regime, a plateau, which progressively extends for longer times as long as the temperature is lowered, such behavior reflecting trapping of water molecules within a cage formed by the nearest neighbors. At low temperature, a low frequency broad inelastic peak is observed in the dynamical structure factor of hydration water; such an excess of vibrational modes being reminiscent of the boson peak, characteristic of disordered, amorphous systems. All these features, which are typical of complex systems, can be traced back to the glassy character of the hydration water and suggest a dynamical coupling occurring at the macromolecule-solvent interface.