Energetics of charge–charge interactions in proteins

Electrostatic interactions between pairs of atoms in proteins are calculated with a model based on the linearized Poisson-Boltzmann equation. The equation is solved accurately by a method that takes into account the detailed shape of the protein. This paper presents applications to several systems. Experimental data for the interaction of ionized residues with an active site histidine in subtilisin BPN' allow the model to be tested, using various assumptions for the electrical properties of the protein and solvent. The electrostatic stabilization of the active site thiolate of rhodanese is analyzed, with attention to the influence of alpha-helices. Finally, relationships between electrostatic potential and charge-charge distance are reported for large and small globular proteins. The above results are compared with those of simpler electrostatic models, including Coulomb's law with both a distance-dependent dielectric constant (epsilon = R) and a fixed dielectric constant (epsilon = 2), and Tanford-Kirkwood theory. The primary conclusions are as follows: 1) The Poisson-Boltzmann model agrees with the subtilisin data over a range of ionic strengths; 2) two alpha-helices generate a large potential in the active site of rhodanese; 3) epsilon = R overestimates weak electrostatic interactions but yields relatively good results for strong ones; 4) Tanford-Kirkwood theory is a useful approximation to detailed solutions of the linearized Poisson-Boltzmann equation in globular proteins; and 5) the modified Tanford-Kirkwood theory over-screens the measured electrostatic interactions in subtilisin.