An extrapolation method for computing protein solvation energies based on density fragmentation of a graphical surface tessellation

Modeling chemical events inside proteins often require the incorporation of solvent effects via continuum polarizable models. One of these approaches is based on the assumption that the interface between solute and solvent acts as a conductor. Image charges are added on the molecular surface to satisfy the appropriate conductor boundary conditions in the presence of solute charges. As in the case of other polarizable continuum models that are based on surface tessellation, the simplest implementation of this approach is often limited to several hundred atoms due to a matrix inversion, which scales as the cube of the number or tesserae. For larger systems, approaches that use iterative matrix solvers coupled to fast summation methods must be used. In the present work, we develop a self-consistent approach to obtain conductor-like screening charges suitable for applications in proteins. The approach is based on a density fragmentation of a graphical surface tessellation. This method, although approximate, provides a straightforward scheme of parallelization, which can in principle be added to existing linear scaling implementations of conductor-like models. We implement this method in conjunction with a fixed charge model for the protein, as well as with a moving domain QM/MM description of the protein. In the latter case, the overall result leads to a charge distribution within the protein determined by self-polarization and polarization due to solvent.