  Charge inversion of a DNA double helix by an oppositely charged flexible
polyelectrolyte (PE) is widely used for gene delivery. It is considered here in
terms of discrete charges of DNA. We concentrate on the worst scenario case
when in the neutral state of the DNA-PE complex, each of the DNA charges is
locally compensated by a PE charge and show that charge inversion exists even
in this case. When an additional PE molecule is adsorbed by DNA, its charge
gets fractionalized into monomer charges of defects (tails and arches) on the
background of the perfectly neutralized DNA. These charges spread all over the
DNA eliminating the self-energy of PE. Fractionalization leads to a substantial
charge inversion of DNA. We show that fractionalization mechanism charge
inversion works also for nonlinear polymers such as dendrimers. Remarkably,
such fractionalization happens for adsorption of both PE or dendrimers on a
two-dimensional charged lattice, as well. Relation of fractionalization to
other mechanisms of charge inversion is discussed.
