posted on 2020-06-12, 12:04authored byAlexey Aleksandrov, Benoît Roux, Alexander D. MacKerell
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 pKa 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 pKa’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 pKa’s differing only by 0.02 pH units from
pKa’s estimated with the exact
approach. Application of the method to predict pKa’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
pKa’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, pKa’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 pKa’s in proteins, shows that the use of a polarizable
model represents a more physically correct model for the treatment
of electrostatic contributions to pKa shifts
in proteins.