Overcharging of DNA in the presence of salt: Theory and simulation

A study of a model rodlike polyelectrolyte molecule immersed in a monovalent or divalent electrolyte is presented. Results for the local concentration profile, mean electrostatic potential, charge distribution function, and ζ-potential are obtained from hypernetted-chain/mean spherical approximation (HNC/MSA) theory and compared with molecular dynamics (MD) simulations. As a particular case, the parameters of the polyelectrolyte molecule are mapped to those of a DNA molecule. Both HNC/MSA and MD predict the occurrence of overcharging, which is not present in the Poisson-Boltzmann theory. Further an excellent qualitative, and in some cases quantitative, agreement between HNC/MSA and MD is found. Oscillations observed in the mean electrostatic potential, local concentration profiles, and the curvature of the ζ-potential are discussed in terms of the observed overcharging effect. Particularly interesting results are a very nonmonotonic behavior of the ζ-potential, as a function of the rod charge density, and the overcharging by monovalent counterions.