  Structuring of DNA counterions around the double helix has been studied by
the molecular dynamics method. A DNA dodecamer d(CGCGAATTCGCG) in water
solution with the alkali metal counterions Na$^{+}$, K$^{+}$, and Cs$^{+}$ has
been simulated. The systems have been considered in the regimes without excess
salt and with different salts (0.5 M of NaCl, KCl or CsCl) added. The results
have showed that the Na$^{+}$ counterions interact with the phosphate groups
directly from outside of the double helix and via water molecules at the top
edge of DNA minor groove. The potassium ions are mostly localized in the
grooves of the double helix, and the cesium ions penetrate deeply inside the
minor groove being bonded directly to the atoms of nucleic bases. Due to the
electrostatic repulsion the chlorine ions tend to be localized at large
distances from the DNA polyanion, but some Cl$^{-}$ anions have been detected
near atomic groups of the double helix forming electrically neutral pairs with
counterions already condensed on DNA. The DNA sites, where counterions are
incorporated, are characterized by local changes of double helix structure. The
lifetime of Na$^{+}$ and K$^{+}$ in complex with DNA atomic groups is less than
0.5 ns, while in the case of the cesium ions it may reach several nanoseconds.
In this time scale, the Cs$^{+}$ counterions form a structured system of
charges in the DNA minor groove that can be considered as ionic lattice.
