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).

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Introduction
Modeling the electrostatic potential and energies in systems comprised of biological macromolecules is an essential step for each study aimed at understanding the macromolecules’ function, STABILITY, and interactions. However, this is not a trivial task, especially for huge systems made of large biomolecules and their assemblages and for modeling phenomena occurring in microseconds and longer timeframes. Continuum electrostatics offers an advantage over explicit methods in such cases since (a) the atomic details of the water phase are reduced and (b) continuum electrostatics intrinsically provides equilibrium solutions. Typically, the macromolecule is considered to be a low dielectric medium while the water phase is modeled as a homogeneous medium with a dielectric constant of 80. While there is a consensus in the community that a dielectric constant of about 80 is appropriate for describing dielectric properties of bulk water in modeling equilibrated systems, the optimal value of the protein (macromolecular) dielectric constant is still an ongoing debate in the literature.1 This INCONSISTENCY is indicated by the use of numerous “optimal” dielectric constant values in various studies. Investigations modeling the macromolecule as a rigid object or using snap-shots obtained from molecular dynamics (MD) simulations to deliver the energies via Molecular Mechanics Poisson–Boltzmann (MMPB) or Generalized Born (MMGB) methods typically use a low dielectric constant of ε = 1 or ε = 2 (to account for electronic polarizability),2,3 although larger values were reported as well.4 In works devoted to modeling protein stability, numerous dielectric constant values were used, from as low as ε = 1 or 25 to as high as ε = 40,6 including multidielectric regions.7 Similarly, in the field of modeling macromolecular interactions, researchers were using various values for the protein