Comparison of dielectric response models for simulating electrostatic effects in proteins

Two recent approaches for calculating pK shifts in proteins are compared. The first of these uses Coulomb's law with a distance-dependent dielectric permittivity, epsilon (r), to model the screening effects of the environment, and the second uses a finite difference approach to solve Poisson's equation. It is shown that an explicit form of epsilon (r) which has been fitted to experimentally determined values of the dielectric permittivity in a range from 1 to 21 A can be approximated by a linear form in the functionally significant range of charge separations of approximately 3-10 A, but for distances greater than 10 A the effective permittivity is strongly nonlinear. A statistical analysis of the errors in calculated pK shifts due to electrostatic interactions between charges with separations greater than 10 A shows that there are only marginal differences in reliability between using Coulomb's law with an appropriate form of epsilon (r) or the finite difference approach for solving Poisson's equation. Thus it is concluded that pK shifts can be calculated just as well, and with considerably less effort, using Coulomb's law.