We have studied picosecond to nanosecond dynamics of hydrated protein powders using dielectric spectroscopy and molecular dynamics (MD) simulations. Our analysis of hydrogen-atom single particle dynamics from MD simulations focused on "main" (tau(main) approximate to tens of picoseconds) and "slow" (tau(slow) approximate to nanosecond) relaxation processes that were observed in dielectric spectra of similar hydrated protein samples. Traditionally, the interpretation of these processes observed in dielectric spectra has been ascribed to the relaxation behavior of hydration water tightly bounded to a protein and not to protein atoms. Detailed analysis of the MD simulations and comparison to dielectric data indicate that the observed relaxation process in the nanosecond time range of hydrated protein spectra is mainly due to protein atoms. The relaxation processes involve the entire structure of protein including atoms in the protein backbone, side chains, and turns. Both surface and buried protein atoms contribute to the slow processes; however, surface atoms demonstrate slightly faster relaxation dynamics. Analysis of the water molecule residence and dipolar relaxation correlation behavior indicates that the hydration water relaxes at much shorter time scales.