  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.
