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 εᵢ separated by an arbitrary closed interface from an exterior region of dielectric constant εₑ. 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.