An Analytical Electrostatic Model for Salt Screened Interactions between Multiple Proteins.

We present a new general analytical solution for computing the screened electrostatic interaction between multiple macromolecules of arbitrarily complex charge distributions, assuming they are well described by spherical low dielectric cavities in a higher dielectric medium in the presence of a Debye-Hückel treatment of salt. The benefits to this approach are 3-fold. First, by exploiting multipole expansion theory for the screened Coulomb potential, we can describe direct charge-charge interactions and all significant higher-order cavity polarization effects between low dielectric spherical cavities containing their charges, while treating these higher order terms correctly at all separation distances. Second, our analytical solution is general to arbitrary numbers of macromolecules, is efficient to compute, and can therefore simultaneously provide on-the-fly updates to changes in charge distributions due to protein conformational changes. Third, we can change spatial resolutions of charge description as a function of separation distance without compromising the desired accuracy. While the current formulation describes solutions based on simple spherical geometries, it appears possible to reformulate these electrostatic expressions to smoothly increase spatial resolution back to greater molecular detail of the dielectric boundaries.