  The dynamics of the structured water molecules in the hydration shell of the
DNA double helix is of paramount importance for the understanding of many
biological mechanisms. In particular, the vibrational dynamics of a water spine
that is formed in the DNA minor groove is the aim of the present study. Within
the framework of the developed phenomenological model, based on the approach of
DNA conformational vibrations, the modes of H-bond stretching, backbone
vibrations, and water translational vibrations have been established. The
calculated frequencies of translation vibrations of water molecules vary from
167 to 205 cm$^{-1}$ depending on the nucleotide sequence. The mode of water
vibrations higher than the modes of internal conformational vibrations of DNA.
The calculated frequencies of water vibrations have shown a sufficient
agreement with the experimental low-frequency vibrational spectra of DNA. The
obtained modes of water vibrations are observed in the same region of the
vibrational spectra of DNA as translation vibrations of water molecules in the
bulk phase. To distinguish the vibrations of water molecules in the DNA minor
groove from those in the bulk water, the dynamics of DNA with heavy water was
also considered. The results have shown that in the case of heavy water the
frequencies of vibrations decrease for about 10 cm$^{-1}$ that may be used in
the experiment to identify the mode of water vibrations in the spine of
hydration in DNA minor groove.
