Vibrations of ordered counterions around left- and right-handed DNA double helixes

The vibrations of ordered counterions around rightand left-handed DNA double helix are studied. To determine the modes of DNA conformational vibrations the structure of the double helix with counterions is considered as ionic lattice (ion-phosphate lattice). Using the developed approach the frequencies and Raman intensities for right-handed B -form and left-handed Z -form of the double helix with Na, K, Rb, Cs, and Mg counterions are calculated. The obtained frequencies of vibrations of internal structure elements of the double helix (<100 cm) weakly depend on counterion type. In contrast, the vibrations of the ion-phosphate lattice are determined by counterion mass and charge. The frequencies of ion-phosphate vibrations of alkali metal counterions decrease from 180 to 100 cm, while their Raman intensities increase as the counterion mass increases for the both B and Z -DNA. In the case of Z -DNA new mode of ion-phosphate vibrations near 150 cm is found. This mode is characterized by vibrations of Mg counterions with respect to the phosphates of different strands of the double helix. Our results explain the experimental Raman spectra of Z -DNA.