The mean square displacements (MSD) of a model protein, the maltose binding protein, and its hydration water have been estimated from the elastic neutron scattering intensity measured on the IN5 time-of-flight spectrometer. The availability of the protein in both fully deuterated and hydrogenated form allowed reliable separation of the contribution of the solvent interacting with the biomolecule from that of the hydrated biomolecule. The thermal fluctuations of hydration water and protein activate in the same temperature range between 200-220 K. This result supports a picture where the dynamical coupling between the biomolecule and the solvent is already effective in the picosecond timescale. A quantitative agreement of the MSD, with values from molecular dynamics simulations, is found.