A boundary element formulation of protein electrostatics with explicit ions

A novel formulation based upon continuum electrostatics to compute the electrostatic potential in and around two biomolecules in a solvent with ionic strength is presented. Many, if not all, current methods rely on the non-linear Poisson–Boltzmann equation to include ionic strength. The present formulation, however, describes ionic strength through the inclusion of explicit ions, which considerably extends its applicability and validity range. The method relies on the boundary element method and results in two very similar coupled integral equations valid on the dielectric boundaries of two molecules, respectively. The method can be employed to estimate the total electrostatic energy of two protein molecules at a given distance and orientation in an electrolyte solution with zero to moderately high ionic strength. The formulation is equally applicable to the case of a single solute in an electrolyte. A number of Monte Carlo simulations of protein-like solutes in NaCl at various concentrations have been performed and demonstrates the method’s usefulness to estimate the electrostatic contribution to the potential of mean force between two biomolecules in an electrolyte.