On the Dielectric “Constant” of Proteins: Smooth Dielectric Function for Macromolecular Modeling and Its Implementation in DelPhi

Implicit methods for modeling protein electrostatics require dielectric properties of the system to be known, in particular, the value of the dielectric constant of protein. While numerous values of the internal protein dielectric constant were reported in the literature, still there is no consensus of what the optimal value is. Perhaps this is due to the fact that the protein dielectric constant is not a "constant" but is a complex function reflecting the properties of the protein's structure and sequence. Here, we report an implementation of a Gaussian-based approach to deliver the dielectric constant distribution throughout the protein and surrounding water phase by utilizing the 3D structure of the corresponding macromolecule. In contrast to previous reports, we construct a smooth dielectric function throughout the space of the system to be modeled rather than just constructing a "Gaussian surface" or smoothing molecule-water boundary. Analysis on a large set of proteins shows that (a) the average dielectric constant inside the protein is relatively low, about 6-7, and reaches a value of about 20-30 at the protein's surface, and (b) high average local dielectric constant values are associated with charged residues while low dielectric constant values are automatically assigned to the regions occupied by hydrophobic residues. In terms of energetics, a benchmarking test was carried out against the experimental pKa's of 89 residues in staphylococcal nuclease (SNase) and showed that it results in a much better RMSD (= 1.77 pK) than the corresponding calculations done with a homogeneous high dielectric constant with an optimal value of 10 (RMSD = 2.43 pK).