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

Charge inversion of a DNA double helix by an oppositely charged flexible polyelectrolyte (PE) is widely used for gene delivery. It is considered here taking into account the discreteness of the 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 of charge inversion works also for non-linear 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.