pK_a Calculations with the Polarizable Drude Force Field and Poisson-Boltzmann Solvation Model

Electronic polarization effects have been suggested to play an important role in proton binding to titratable residues in proteins. In this work, we describe a new computational method for pK_a calculations, using Monte Carlo (MC) simulations to sample protein protonation states with the Drude polarizable force field and Poisson-Boltzmann (PB) continuum electrostatic solvent model. While the most populated protonation states at the selected pH, corresponding to residues that are half-protonated at that pH, are sampled using the exact relative free energies computed with Drude particles optimized in the field of the PB implicit solvation model, we introduce an approximation for the protein polarization of low-populated protonation states to reduce the computational cost. The highly populated protonation states used to compute the polarization and pK_a's are then iteratively improved until convergence. It is shown that for lysozyme, when considering 9 of the 18 titratable residues, the new method converged within two iterations with computed pK_a's differing only by 0.02 pH units from pK_a's estimated with the exact approach. Application of the method to predict pK_a's of 94 titratable side chains in 8 proteins shows the Drude-PB model to produce physically more correct results as compared to the additive CHARMM36 (C36) force field (FF). With a dielectric constant of two assigned to the protein interior the Root Mean Square (RMS) deviation between computed and experimental pK_a's is 2.07 and 3.19 pH units with the Drude and C36 models, respectively, and the RMS deviation using the Drude-PB model is relatively insensitive to the choice of the internal dielectric constant in contrast to the additive C36 model. At the higher internal dielectric constant of 20, pK_a's computed with the additive C36 model converge to the results obtained with the Drude polarizable force field, indicating the need to artificially overestimate electrostatic screening in a nonphysical way with the additive FF. In addition, inclusion of both syn and anti orientations of the proton in the neutral state of acidic groups is shown to yield improved agreement with experiment. The present work, which is the first example of the use of a polarizable model for the prediction of pK_a's in proteins, shows that the use of a polarizable model represents a more physically correct model for the treatment of electrostatic contributions to pK_a shifts in proteins.