Inelastic neutron scattering experiments and molecular dynamics simulations have been used to investigate the low frequency modes, in the region between 0 and 100 meV, of hydration water in selected hydrophilic and hydrophobic biomolecules. The results show changes in the plasticity of the hydrogen-bond network of hydration water molecules depending on the biomolecular site. At 200 K, the measured low frequency density of states of hydration water molecules of hydrophilic peptides is remarkably similar to that of high density amorphous ice, whereas, for hydrophobic biomolecules, it is comparable to that of low density amorphous ice behavior. In both hydrophilic and hydrophobic biomolecules, the high frequency modes show a blue shift of the libration mode as compared to the room temperature data. These results can be related to the density of water molecules around the biological interface, suggesting that the apparent local density of water is larger in a hydrophilic environment