Theory of the Poisson Green’s function for discontinuous dielectric media with an application to protein biophysics

A theory of the Poisson Green’s function is given for the case of an interior region of dielectric constant ${\epsilon }_i$ separated by an arbitrary closed interface from an exterior region of dielectric constant ${\epsilon }_e$. A convergent multiple induction expansion is developed as the basis of an approximation scheme for the Green’s function. In a sense, this expansion effectively extends the method of images to surfaces of arbitrary shape. As an application of the general theory, a protein in an aqueous electrolyte is modeled as a charge-bearing region of low dielectric constant surrounded by a region of high dielectric constant.