The Metropolis Monte Carlo (MC) method when applied to part of the degrees of freedom of a system is shown to turn into a Brownian dynamics simulation by solving the master equation which describes the sampling process in the Metropolis MC by the Omega-expansion approximation. Using the method, Brownian dynamics simulations are carried out on model DNA solutions to determine relaxation times of the ion atmosphere polarization. The MC approach to the problem eliminates the distinction between "free" and "bound" counterions often assumed in analytical studies. Molecular interpretation of the relaxation of the counterion cloud based on a simple model is attempted. In the absence of a complete theory, computer simulation is a promising method to assist in the interpretation of the experimental data.