Monte Carlo and Poisson-Boltzmann calculations of the fraction of counterions bound to DNA.

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson-Boltzmann (PB) methods. Two different definitions of the "bound" and "free" components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization--one in which monovalent cations in regions where the average electrostatic potential is less than -kT are considered to be bound--provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B form of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observation is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicted by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylinders of varying linear charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 A hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than -kT is advocated as a more suitable binding or condensation radius than that enclosing the fraction of counterions given by (1 - epsilon-1). A comparison of radii calculated using both of these definitions is presented.