The hydrogen peroxide is present in the living cell at small concentrations that increase under the action of the heavy ion beams in the process of anticancer therapy. The interactions of hydrogen peroxide with DNA, proteins and other biological molecules are poorly understood. In the present work the competitive binding of the hydrogen peroxide and water molecules with the DNA double helix backbone has been studied using the molecular dynamics method. The simulations have been carried out for the DNA double helix in a water solution with hydrogen peroxide molecules and Na$^{+}$ counterions. The obtained radial distribution functions of counterions, H$_2$O$_2$ and H$_2$O molecules with respect to the oxygen atoms of DNA phosphate groups have been used for the analysis of the formation of different complexes. The calculated mean residence times show that a hydrogen peroxide molecule stays at least twice as long near the phosphate group (up to 7 ps) than a water molecule (about 3 ps). The hydrogen peroxide molecules form more stable complexes with the phosphate groups of the DNA backbone than water molecules do.
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