Proton Binding to Proteins: A Free-Energy Component Analysis Using a Dielectric Continuum Model

Proton binding plays a critical role in protein structure and function. We report pKa calculations for three aspartates in two proteins, using a linear response approach, as well as a “standard” Poisson-Boltzmann approach. Averaging over conformations from the two endpoints of the proton-binding reaction, the protein’s atomic degrees of freedom are explicitly modeled. Treating macroscopically the protein’s electronic polarizability and the solvent, a meaningful model is obtained, without adjustable parameters. It reproduces qualitatively the electrostatic potentials, proton-binding free energies, Marcus reorganization free energies, and pKa shifts from explicit solvent molecular dynamics simulations, and the pKa shifts from experiment. For thioredoxin Asp-26, which has a large pKa upshift, we correctly capture the balance between unfavorable carboxylate desolvation and favorable interactions with a nearby lysine; similarly for RNase A Asp-14, which has a large pKa downshift. For the unshifted thioredoxin Asp-20, desolvation by the protein cavity is overestimated by 2.9 pKa units; several effects could explain this. “Standard” Poisson-Boltzmann methods sidestep this problem by using a large, ad hoc protein dielectric; but protein charge-charge interactions are then incorrectly downscaled, giving an unbalanced description of the reaction and a large error for the shifted pKa values of Asp-26 and Asp-14.