Counterion condensation of a polyelectrolyte

Abstract

Counterion condensation phenomenon of a highly charged polyelectrolyte, which is directly related to DNA condensation and RNA folding, has great importance and potential use in biological science, electrokinetic phenomenon, and medical science. To further understand this fascinating phenomenon, the distribution of the electric potential for a highly charged polyelectrolyte in an electrolyte solution is determined theoretically. The polyelectrolyte is modeled as a charged porous sphere and the full nonlinear Poisson–Boltzmann equation is used to describe the interaction between the counterions in the electrolyte solution and the backbone macroion of the polyelectrolyte itself. The solution is obtained with a pseudo-spectral method based on Chebyshev polynomials. The fraction of total charges condensed is analyzed in particular, with its dependence on the charged condition of the polyelectrolyte as well as the ionic strength of the solution investigated in detail. Comparison with limited experimental data available in the literature for DNA neutralization fraction is excellent in the asymptotic sense, suggesting the reliability of the analysis in this study, as well as the promising possibility of using the charged porous sphere to model a polyelectrolyte. Results presented here provide useful information in biological systems and can be utilized in practical applications such as DNA vaccines and gene delivery.