posted on 2015-06-09, 00:00authored byTim Meyer, Ernst-Walter Knapp
For
a benchmark set of 194 measured pKa values
in 13 proteins, electrostatic energy computations are performed
in which pKa values are computed by solving
the Poisson–Boltzmann equation. In contrast to the previous
approach of Karlsberg+ (KB+) that essentially
used protein crystal structures with variations in their side chain
conformations, the present approach (KB2+MD) uses protein
conformations from four molecular dynamics (MD) simulations of 10
ns each. These MD simulations are performed with different specific
but fixed protonation patterns, selected to sample the conformational
space for the different protonation patterns faithfully. The root-mean-square
deviation between computed and measured pKa values (pKa RMSD) is shown to be reduced
from 1.17 pH units using KB+ to 0.96 pH units using KB2+MD. The pKa RMSD can be further
reduced to 0.79 pH units, if each conformation is energy-minimized
with a dielectric constant of εmin = 4 prior to calculating
the electrostatic energy. The electrostatic energy expressions upon
which the computations are based have been reformulated such that
they do not involve terms that mix protein and solvent environment
contributions and no thermodynamic cycle is needed. As a consequence,
conformations of the titratable residues can be treated independently
in the protein and solvent environments. In addition, the energy terms
used here avoid the so-called intrinsic pKa and can therefore be interpreted without reference to arbitrary
protonation states and conformations.