Numerical solution of the nonlinear Poisson-Boltzmann equation for a macroion modeled as an array of non overlapping beads.

In this work, an approximate numerical procedure, AB, is developed to solve the nonlinear Poisson-Boltzmann equation around a macroion modeled as an array of non overlapping beads containing charges placed at their centers. The bead radii, their charges, and the relative bead configuration are arbitrary. In the limit of a single bead of arbitrary charge, the AB procedure is exact. For dimers and other bead arrays, it is possible to compare the approximate potentials derived using the AB procedure with exact potentials obtained by a boundary element, BE, procedure. Average surface or "zeta" potentials are examined for dimers, trimers, and tetramers. The bead size and charges are chosen to ensure that nonlinear charge effects are significant. In these test cases, the AB procedure is accurate to better than 5% over a wide range of ionic strength. Finally, the electrostatics of short duplex DNA (≤100 base pairs) are examined using both "smooth cylinder" and "touching bead" models. It is concluded that the modeling DNA as a string of touching beads using the AB procedure yields "zeta" potentials that are accurate to better than 10%.