Can a simple function for the dielectric response model electrostatic effects in globular proteins?

The relationship between the effective dielectric constant that models the electrostatic effect from a charged side chain in a protein was evaluated both experimentally and theoretically. Experimental values were obtained from the shifts in pKa that resulted from point mutations of side chains in subtilisin. Theoretical values were obtained from an iterative solution to Poisson's equation that considers the dielectric response of the protein and the solvent together with charge positions. There is no simple relationship between the effective dielectric constant and the distance from the charge responsible for the interactions. For some charge positions a linear but not a direct proportional relationship of the effective dielectric with distance of separation was observed. Thus, simple models such as a linear distance-dependence for the dielectric response are not suitable to evaluate electrostatic effects in proteins.