Numerical Calculations of Electrostatic Potentials of Protein-Solvent Systems by the Self Consistent Boundary Method

A macroscopic dielectric model for a protein-solvent system has been solved by a numerical calculation using a supercomputer. The whole space including a target protein molecule was first divided into lots of cubes, some of which were inside the protein and the others were embedded in the solvent. Poisson equation and Poisson-Boltzmann equation were then numerically solved inside and outside of the protein, respectively. At the artificial boundary far from the protein for the finite difference procedure, neither the potential nor the field was set to be zero, but they were calculated self-consistently from the field and the potential inside the boundary calculated beforehand. The results by this method agreed well with those by the analytical calculations for some simple model cases. The results of actual protein-solvent systems were quantitatively discussed comparing with the experiments.