Coarse-grained model of dielectric geometry-modified screened electrostatic protein-protein interactions

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 spheres with near-surface charges, for which we solve the linearized Poisson-Boltzmann equation as a function of sphere-sphere separation. The spheres have 15 Angstrom diameters and internal static dielectric coefficients of 3, and the solvent Debye length is 6 Angstroms; parameters consistent with our charge-regulation model of bovine gamma-B crystallin. The screened electrostatic potential resulting from a single charge can be 4 to 6 times as strong as an unmodified Debye-Huckel screened potential, depending on sphere separation. 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-modeled by a rotated, possibly off-center Student t-distribution at each sphere-sphere distance. We combine these results with dispersion interactions to model the orientation-dependent protein-protein potential for two gamma crystallins with multiple, charge-regulated amino-acid residues sited in accordance with their crystal structures.