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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 chargesof DNA. We concentrate on the worst scenario case when in the neutral state of the DNA-PEcomplex, each of the DNA charges is locally compensated by a PE charge and show that chargeinversion exists even in this case. When an additional PE molecule is adsorbed by DNA, itscharge gets fractionalized into monomer charges of defects (tails and arches) on the backgroundof 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.

Inversion of DNA charge by a positive polymer via fractionalization of the polymer charge