Model of inversion of DNA charge by a positive polymer: fractionalization of the polymer charge.

We model one strand of DNA by a one-dimensional lattice (ODL) of negative charges and consider the problem of inversion of its charge by a positive polyelectrolyte (PE). In the neutral state of the ODL-PE complex, each of the ODL charges is locally compensated by a PE charge. When an additional PE molecule is adsorbed by ODL, its charge gets fractionalized into monomer charges of defects (tails and arches) on the background of the perfectly neutralized ODL. Defects spread all over the ODL, eliminating the self-energy of PE. For DNA this fractionalization mechanism leads to a substantial inversion of charge, a phenomenon which is widely used for gene delivery.