A combined iterative and boundary-element approach for solution of the nonlinear Poisson-Boltzmann equation

A general numerical method is presented to solve the nonlinear Poisson-Boltzmann (NLPB) equation for an arbitrarily-shaped solute. The essence of the method is the separation of the calculation of the solvent reaction potential from that of the potential due to the ion distribution. The solvent reaction potential is calculated by using an efficient boundary element method. The ion-induced potential is then calculated by means of an efficient volume integration using an iterative solution of the NLPB equation coupled to the fixed molecular and solvent electrostatic potential. At an ionic strength of less-than-or-equal-to 1 M the mobile ion distribution is determined primarily by the solute and the solvent reaction electrostatic potentials; as a consequence, rapid convergence of the iterative procedure is obtained. The accuracy of the results obtained by using the iterative boundary element (IBE) method is tested by comparison with analytical Tanford-Kirkwood results for a model spherical "protein" solute system. Results are also presented for the terminally blocked amino acid N-acetyl-alanyl-N'-methylamide (NANMA) and terminally blocked oligo-lysine peptides. It is found that the IBE method has some computational advantages with respect to the general finite-difference method in applications to large molecules.