To refine a coarse-grained model of protein interactions, we seek to conveniently represent how dielectric interface geometry and charge placement affect screened aqueous electrostatic interactions. We study two neighboring low dielectric spheres with near-surface charges, for which we solve the linearized Poisson-Boltzmann equation as a function of sphere-sphere separation. The spheres have ~15Å diameters and internal static dielectric coefficients of 3. The solvent’s Debye length is 6Å. These parameters are consistent with our charge-regulation model of bovine γB-Crystallin and with a wealth of previous experimental data for solutions of this protein. For a fixed on- or off-axis charge in the first sphere, the two-dimensional angular dependence of the near-surface potential in the second sphere is well-fit by a modified, rotated, possibly off-center Student t-distribution at each sphere-sphere distance. We use the full electrostatic solution to fit the parameters of these Student t-distributions as functions of sphere-sphere separation and angular placement of the charge in the first sphere. The approximation developed here is much more accurate than the unmodified Debye-Hückel screened potential and shows the potential for further refinement
