Improving the Continuum Dielectric Approach to Calculating pK_as of Ionizable Groups in Proteins

Abstract

The pH-dependent characteristics of a protein are determined by the pK a s of its titratable residues. Continuum electrostatic approaches provide a fast means of calculating the pK a s of the titratable residues in proteins immersed in aqueous ionic solution. Here, we show how optimization of the parameters used in continuum electrostatic calculations can lead to significant improvements in the accuracy of pK a predictions. Dependence on the protein dielectric constant is studied, and two classes of ionizable sites are identified: (1) a large number of mostly solvent exposed residues for which the best pK a is calculated if the protein dielectric constant is set close to that of the aqueous solvent; and (2) a small number of mostly buried residues for which the best pK a is calculated with a lower site-specific protein dielectric constant. These two classes of ionizable sites can be distinguished using a criterion based on desolvation energy. A priori determination of the optimum protein dielectric constant for the second class is not easy, but satisfactory results are obtained if it is assigned in the range 10-20. The accuracy of the calculated pK a s is influenced by the assignment of proton positions and we suggest modifications to the OPLS parameter set that eliminate the need to construct hypothetical, and therefore error prone, proton positions during the calculation procedure. For the test set of proteins studied, the final recommended protocol enables the tautomers of histidine residues to be assigned automatically, the pK a s of residues in the "high dielectric constant" class to be calculated to within 0.7 pK a units, and the pK a s of residues in the "low dielectric constant" class to be calculated to within 1.6 pK a units.

Very fast prediction and rationalization of pKa values for protein–ligand complexes

“…Similar algorithms to those used to determine the positions of NÀ ÀH protons of backbone amides, Asn, Gln, Trp, His, and Arg residues that may be involved in hydrogen bonding have been implemented to determine the positions of the NÀ ÀH protons for amide, aromatic, trigonal planar and sp 3 nitrogen as well as the position of a ghost atom for the N1 atom-type in order to include the orientation effect in the hydrogen bonding term.…”

“…For sp 3 nitrogen, the number of protons assigned will depend on the number of non-hydrogen atoms linked to the nitrogen: If 0 or 1 atoms are linked to the nitrogen atom; we do not assign any proton due to the spherical symmetry of the group.…”

“…(10). There are four possible interactions between charged residues (Asp/Glu, His, Cys, Tyr, Lys and Arg) and ligand groups (carboxylate, aromatic N, sp 3 hybridized N, and trigonal planar N): negative with negative, positive with positive, negative with positive, and positive with negative. For the negative with negative and positive with positive interactions, the pK a shift is applied to the group with the higher and the lower temporary pK a , respectively.…”

“…[3][4][5][6][7][8][9]11,13 In the LPBE approaches the protein is described by the partial charges from a classical force field and embedded within a dielectric continuum with dielectric constants (e) of 80 for the solvent and between 4 and 20 for the interior of the protein. pK a shifts are obtained by computing the difference in electrostatic energy of a charged residue with that of its neutral form; the resulting shift is added to a model pK a value.…”

Development of constant-pH simulation methods in implicit solvent and applications in biomolecular systems

“…This sphere is immersed in a medium with high dielectric permittivity ( s ), the electrolyte solution. At this point, proposing a dielectric interface, they introduced a rather polemical and controversial model choice under intense debate in the literature (Demchuk and Wade 1996;Penfold et al 1998;Warshel andÅqvist 1991;King et al 1991;Antonsiewicz et al 1994Antonsiewicz et al , 1996Simonson and Perahia 1995;Simonson and Brooks 1996;Löffler et al 1997;Sham et al 1997;Warwicker 1999 A dielectric constant is a macroscopic parameter related to the movement of microscopic charges. It describes the reorientation of the electronic cloud around a nucleus and/or the reorientation of permanent dipoles in the presence of an electric field (Böttcher 1973).…”