Calculation of Protein Ionization Equilibria With
Conformational Sampling: pK
a
of a Model
Leucine Zipper, GCN4 and Barnase
Alemayehu A. Gorfe, Philippe Ferrara, Amedeo Caflisch, Daniel N. Marti, Hans Rudolf Bosshard,
and Ilian Jelesarov
*
Department of Biochemistry, University of Zurich, Zurich, Switzerland
ABSTRACT The use of conformational en-
sembles provided by nuclear magnetic resonance
(NMR) experiments or generated by molecular dy-
namics (MD) simulations has been regarded as a
useful approach to account for protein motions in
the context of pK
a
calculations, yet the idea has
been tested occasionally. This is the first report of
systematic comparison of pK
a
estimates computed
from long multiple MD simulations and NMR en-
sembles. As model systems, a synthetic leucine zip-
per, the naturally occurring coiled coil GCN4, and
barnase were used. A variety of conformational
averaging and titration curve-averaging techniques,
or combination thereof, was adopted and/or modi-
fied to investigate the effect of extensive global
conformational sampling on the accuracy of pK
a
calculations. Clustering of coordinates is proposed
as an approach to reduce the vast diversity of MD
ensembles to a few structures representative of the
average electrostatic properties of the system in
solution. Remarkable improvement of the accuracy
of pK
a
predictions was achieved by the use of mul-
tiple MD simulations. By using multiple trajectories
the absolute error in pK
a
predictions for the model
leucine zipper was reduced to as low as approxi-
mately 0.25 pK
a
units. The validity, advantages, and
limitations of explicit conformational sampling by
MD, compared with the use of an average structure
and a high internal protein dielectric value as means
to improve the accuracy of pK
a
calculations, are
discussed. Proteins 2002;46:41– 60.
© 2001 Wiley-Liss, Inc.
Key words: coiled coil; NMR; molecular dynamics;
ensemble; salt bridge; cluster; electro-
statics
INTRODUCTION
Release and uptake of protons are fundamental to a
variety of biological processes such as enzymatic catalysis,
macromolecular stability, and formation of macromolecu-
lar complexes. Determination of the pK
a
values of protein
ionizable groups is key to the understanding of the pH-
dependent properties of proteins. Theoretical studies of
the ionization behavior of protein charged groups are a
vital part of this endeavor. Structure-based predictions of
the electrostatic properties of proteins have motivated
researchers ever since the beginning of modern structural
biology,
1,2
and considerable advances have been made in
the last two decades.
3–8
Quantitative computational pre-
dictions of pK
a
values are still problematic in many
cases.
6,9
The titration behavior of proteins is governed by the
ionization equilibria of their acidic and basic charged
groups. The pK
a
of a group in a folded conformation of a
protein can deviate by several pH units from the pK
a
of a
fully solvated model compound because the electrostatic
environments experienced by a group in the protein and in
solution are very different. Interactions of charged ioniz-
able groups with the charged form of other titratable
groups (site-site interactions) and with permanent dipoles
in the protein (background interactions), as well as the
altered interactions with water (Born energy or desolva-
tion energy) are the main sources of pK
a
shifts.
10
The
change of the ionization equilibrium of charged groups and
the titration behavior of proteins are commonly calculated
by the numerical solution of the linearized form of the
Poisson Boltzmann (FDPB) equation for a group in a
protein relative to an isolated model compound in solu-
tion.
4
In the continuum representation, a dielectric bound-
ary between the bulk solvent and the protein is defined,
usually represented by the solvent accessible surface of the
molecule. The solvent is modeled as a continuum of high
polarizability, whereas a lower dielectric constant is as-
signed to the protein domain, and the protein structure is
treated at atomic level.
4–6
The pH-dependent free ener-
gies are calculated by Boltzmann summation over all
important protonation states in a certain pH interval. As a
result, the average degree of protonation of each ionizable
group as a function of pH is obtained. This methodology
was first applied to titration studies of lysozyme a decade
ago
4
and has since been applied to many proteins.
11–13
The Supplementary Material referred to in this section can be found
at http://www.interscience.wiley.com/jpages/0887-3585/suppmat/46_1/
v46_1.html
Grant sponsor: Bundesamt fu ¨ r Bildung und Wissenschaft; Grant
number: 97.0592; Grant sponsor: Swiss National Science Foundation;
Grant number: 31.55308.98.
*Correspondence to: Ilian Jelesarov, Department of Biochemistry,
University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzer-
land. E-mail: iljel@bioc.unizh.ch
Received 30 March 2001; Accepted 21 August 2001
Published online 00 Month 2001
PROTEINS: Structure, Function, and Genetics 46:41– 60 (2002)
© 2001 WILEY-LISS, INC.
DOI 10.1002/prot.10027