We were attracted to the recent article by Sandberg and Edholm 1 (SE) in which the authors describe a fast way to calculate protonation states in proteins by using a distance-and position-dependent screening of the Coulomb potential. Because this article embodies some common misconceptions regarding electrostatic effects that are particularly crucial for the calculation of protonation states in macromolecules, we address these issues by using the results obtained by SE as an illustrative example. To show how these deficient treatments may lead to erroneous results, we expand on recent studies from the Mehler and Warshel laboratories.
Sandberg and Edholm start their work by deriving a relationship between their Coulombic screening function [(r) in Eq. 5] and the dielectric permittivity, ⑀(r) (their Eq. 6). We note that their result is in exact agreement with results presented earlier by one of us (ELM), using identical assumptions 2 and prior to that by Toulouse and Fritsch 3 in the context of calculating electrostatic forces for use in molecular dynamics simulations. The authors then recast their Eq. ( 6) in the form of a nonlinear differential equation [to calculate (r) from ⑀(r)] stating that its solution would be less straightforward. Although this observation is correct, this equation has been integrated 2,4 and used to evaluate screening functions from analytic forms of ⑀(r) that were derived from the classical dielectric theory of polar solvation. [5][6][7][8] The authors then formulate their distance-and positiondependent dielectric function, starting from a distancedependent function proposed by one of us, Warshel et al. 9 (hereafter referred to as WRC), for the treatment of charge-charge interactions. They neglect, however, the contribution from the self-energy terms, stating that these terms are omitted because they are usually small. In many crucial cases, however, this assumption is invalid, and it is puzzling because the main theme of Warshel et al. 9 , published in 1984, from which SE took the starting point of their treatment, was the importance of including the self-energy in calculations of electrostatic energies in proteins. Sadly, the authors have overlooked a large body of literature that has appeared since 1984 10 -21 , including several reviews [22][23][24][25][26][27] , that has discussed this problem and the calculation of solvation energies.