Deriving Coarse-Grained Charges from All-Atom Systems: An Analytic Solution.

An analytic method to assign optimal coarse-grained charges based on electrostatic potential matching is presented. This solution is the infinite size and density limit of grid-integration charge-fitting and is computationally more efficient by several orders of magnitude. The solution is also minimized with respect to coarse-grained positions which proves to be an extremely important step in reproducing the all-atom electrostatic potential. The joint optimal-charge optimal-position coarse-graining procedure is applied to a number of aggregating proteins using single-site per amino acid resolution. These models provide a good estimate of both the vacuum and Debye-Hückel screened all-atom electrostatic potentials in the vicinity and in the far-field of the protein. Additionally, these coarse-grained models are shown to approximate the all-atom dimerization electrostatic potential energy of 10 aggregating proteins with good accuracy.