Analysis of a model of biomolecular interaction for small separations at the Debye-Hückel level

The cellular environment, which in fact is a dense collection of biomolecules in a high dielectric constant solvent (water) containing various ions, can in certain respects be modeled as a colloidal system. Previous work has focused on rigorously examining at the Debye-Hückel level an arbitrary collection of dielectric spheres in a high dielectric solvent containing ions. However, when a pair of biomolecules are in close proximity — about to form a complex or reject forming a complex — the molecular surfaces can be approximated as planar. Therefore a system of two charged semi-infinite half spaces separated by a layer of solvent containing ions is here examined at the Debye-Hückel level with the same mathematical rigor as was developed previously for spheres. Interesting and counterintuitive behavior is found when the charges are of very different magnitude.