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PROTEINS: Structure, Function, and Genetics 37:106–115 (1999)
Ionization Behavior of Acidic Residues in Calbindin D9k
Tõnu Kesvatera,1,2 Bo Jönsson,1* Eva Thulin,1and Sara Linse1
of Physical Chemistry 2, Lund University, Center for Chemistry and Chemical Engineering, Lund, Sweden
2National Institute of Chemical Physics and Biophysics, Akadeemia 23, Tallinn, Estonia
The ionization state of seven glutamate residues, one aspartate, and the C-terminal
␣-COOH group in bovine apo calbindin D9k has been
studied by measurement and modeling of the pH
titration curves and apparent pKa values. The observed pKa ranged from 3.0 to 6.5. Most of the
observed acidic groups were half-ionized at lower
pH values than those in unstructured proteins. As a
rule, the ionization equilibria extended over a wider
pH range than in the case of unperturbed single
titrations, indicating a complex influence of protein
charges on the charge state of each individual residue. Glu17, which is a backbone Ca2ⴙ-ligand in the
N-terminal binding loop of calbindin D9k, was halfprotonated at pH 3.6 but manifested biphasic titration with apparent pKa values of 3.2 and 6.5. Complementary Monte Carlo simulations of the titration
process and pKa values of the acidic groups in
calbindin D9k reproduce the experimentally observed titration features, except for the pronounced
double titration of Glu17. Discrepancies between
the results from direct measurement and from modeling may be partly caused by changes in the protein
structure when the net charge changes from ⴚ8 to
ⴙ11 over the isoelectric point at pH 5. Proteins
1999;37:106–115. r 1999 Wiley-Liss, Inc.
As a consequence of protein folding, the pKa values of
titratable groups shift relative to their values in small
model compounds or denatured proteins. In a folded
protein, the specific arrangement of charged residues may
cause a significant variation of the electrostatic potential
throughout the protein. The electrostatic potential can be
probed locally at many points of a protein by measuring
the titration behavior of acidic and basic groups and
provide rigorous tests of theoretical predictions of electrostatic effects in proteins.
Computational algorithms for prediction of pKa values of
titratable groups have been the focus of theoretical studies
over the years. Traditionally, the protein is treated as a
low-dielectric cavity in a high-dielectric environment. Recent theoretical studies have demonstrated that better
results in accounting for the ionization behavior of proteins can be obtained by using a high-dielectric constant
for the protein interior.1–5 Further studies about the state
of ionic residues in proteins are thus highly motivated, and
reliable determination of pKa values for individual titratable groups is necessary for developing the theoretical
models for electrostatic interactions in proteins.
A common feature of the ubiquitous calmodulin-like
proteins is the accumulation of negative charges on the
protein surface, especially in the Ca2⫹ binding area. These
proteins are of particular interest for theoretical structurebased modeling of long-range electrostatic interactions in
proteins, because the pKa values of some of these acidic
groups are expected to be strongly shifted toward high pH
compared with the corresponding model compounds where
the pKa perturbations due to ionic interactions are insignificant. The knowledge of pKa values of acidic residues is also
helpful in understanding the function of EF-hand Ca2⫹
binding sites in a large number of regulatory or Ca2⫹
buffering proteins. However, the ionization behavior of
acidic groups has not been reported yet for any of the
ubiquitous calcium-dependent proteins belonging to the
calmodulin superfamily.
Bovine calbindin D9k is a small (75 residues, Mr 8,500)
and well-characterized representative of the EF-hand
proteins, which efficiently binds two Ca2⫹ ions.6 The excess
negative charge in the binding area causes large upward
pKa shifts for lysine residues2 located in the vicinity of
Ca2⫹ binding sites, implying that the ionization equilibria
of some carboxylate groups can be also shifted close to the
physiologically relevant neutral pH values. Calbindin D9k
is an excellent model or target for the experimental pKa
measurements via nuclear magnetic resonance (NMR)
spectroscopy because of its moderate size and remarkable
stability in a variety of solvent conditions. In variance with
the regulatory proteins of the calmodulin family, which
undergo a significant conformational change on calcium
binding, calbindin D9k has essentially the same structure
in the absence and presence of metal ions in the binding
sites. This is an advantage for theoretical calculations that
can be sensitive to the variations in protein structure. In
this study, we describe pKa measurements of nine acidic
groups in calbindin D9k using 13C isotope labeling and
two-dimensional heteronuclear NMR spectroscopy.
Protein Preparation
Calbindin D9k was expressed in Escherichia coli from a
synthetic gene yielding a protein with bovine minor A
Grant sponsor: Swedish Natural Science Council; Grant sponsor:
The Royal Swedish Academy of Sciences; Grant sponsor: Estonian
Science Foundation.
*Correspondence to: Bo Jönsson, Physical Chemistry 2, Lund University, Center for Chemistry and Chemical Engineering, S-221 00 Lund,
Sweden. E-mail:
Received 21 December 1998; Accepted 30 April 1999
sequence except that residue 43 was changed to a glycine
instead of a proline. The Pro43=Gly mutation was introduced to avoid the appearance of two sets of resonances in
the NMR spectrum due to cis-trans isomerization of the
Gly42-Pro43 peptide bond.7 The cells were first grown
overnight in Luria-Bertani Medium (LB) medium, and 10
mL of the overnight culture was used to inoculate 250 mL
of minimal medium. When the absorbance at 600 nm was
0.5, 60 mL of this middle culture was transferred into 500
mL of minimal medium, and cells were harvested 2–3 h
after this final culture reached the lag phase, at which
point the yield was at maximum.The minimal medium was
made in the local tap water and 1 L contained: 6 g of
Na2HPO4, 3 g of KH2PO4, 0.5 g of NaCl, 1 mM of MgSO4,
0.1 mM of CaCl2, 1 mg of Vitamin B1, and 18 µM of FeCl3.
To prepare the medium, a mix of Na2HPO4, KH2PO4, and
NaCl was autoclaved and supplemented by MgSO4 and
CaCl2 from separately autoclaved stock solutions and
Vitamin B1 and FeCl3 from separately sterile filtered stock
solutions. All amino acids were added to the minimal
media as sterile filtered free L-amino acids in relative
amounts according to their frequencies of occurrence in
proteins. The total amount of amino acids was 1.0 g/L in
the middle culture and 0.5 g/L in the final growth medium.
Carbon-13 labeled L-[␤-13C]aspartic and L-[␥-13C]glutamic
acids were purchased from Cambridge Isotope Laboratories (Andover, MA), whereas unlabeled amino acids were
purchased from Sigma.
Purification of the protein and removal of calcium was
performed as described by Johansson et al. (1990),8 and
the purity was confirmed by agarose gel electrophoresis,
sodium dodecyl sulfate (SDS) polyacrylamide gel electrophoresis, isoelectric focusing, and 1H NMR. The residual
Ca2⫹ concentration after chelex 100 treatment was below
0.1 equivalents as judged from 1H NMR spectra and
titrations in the presence of the chromophoric chelator
quin 2. The total yield of purified Ca2⫹-free protein was 15
mg from 2 L of culture. Protein samples for titration
experiments were made 0.5 mM in a 0.5-mL final volume
containing 90% H2O and 10% 2H2O.
NMR Spectroscopy
Two-dimensional 13C-1H HSQC-TOCSY NMR spectra9–12 were recorded at 300 K on a Varian Unity Plus
spectrometer operating at 599.89 MHz for 1H and 150.85
MHz for 13C. The spectral width was 8,000 Hz for protons
and 4,300 Hz for carbon, and the digital resolution was
4,096 complex points in ␻2 and 128 real points in ␻1 and
128–256 FIDs were collected for each t1 point. Decoupling
of the 13C nuclei during the acquisition period was achieved
by using Garp-1 phase modulation.13 The DIPSI-2 mixing
sequence14 with a mixing time of 80 ms was used. The
water signal was suppressed by using pulsed field gradients.15,16 1H chemical shifts were referenced to the water
signal at 4.75 ppm, and the 13C chemical shifts were
measured relative to the spectrometer frequency. NMR
spectra were processed on Sun or SiliconGraphics workstations using Felix95 (Biosym Technologies, San Diego, CA).
pH-Dependent Chemical Shift Measurements
The pH titrations of calbindin D9k were performed
starting at pH 6.0. The pH was adjusted by adding 0.2–1
µL amounts of concentrated HCl or NaOH with a Hamilton syringe to obtain accurate estimates of the added Na⫹
or Cl⫺ ions at each titration point. The pH of a sample was
measured, and the adjustments were made in an NMR
tube with use of the Radiometer PHM63 Digital pH meter
with an Ingold U402-M3–57/200 electrode. The pH readings taken before and after the acquiring of NMR spectra
were similar within 0.1 pH units, and the latter reading
was used in data processing, uncorrected for isotope effects
caused by the presence of 10% 2H2O. The pH of a 0.5 mM
calbindin D9k sample from the current preparations, made
in 10% 2H2O, 90% H2O, was always 6.0 ⫾ 0.1. After
addition of a certain amount of 1 M of HCl to obtain a
required pH of a sample, we observed the tendency that
the pH of the sample was increasing by up to 0.1 pH units
(probably because of some process related to a protein)
during the 10–15 h of acquiring the NMR spectrum. It has
been checked that most of this increase took place within
2–3 h after the pH adjustment. For this reason the pH
reading of a sample after the acquiring NMR spectra was
taken as a more correct value for the pH in a sample for
which the spectrum was obtained. 1H-13C HSQC-TOCSY
spectra were acquired at about 0.3 pH unit intervals
between pH 2.4 and 7.6. Figure 1 shows the spectra at pH
7.0 and 2.4. The resonances in these spectra were identified by using proton resonance assignments for the P43G
mutant of apo calbindin D9k at pH 5.25.17 In the test for
reversibility of the titration the pH of a sample used for
acquiring data at pH 2.4 was adjusted back to 5.25, and the
spectrum obtained was essentially the same as at the start
of titration.
Determination of Titration Parameters
Titration parameters were obtained by fitting the chemical shifts for ␤- or ␥-13C nuclei of aspartic acid, asparagine,
glutamic acid ,or glutamine residues at different pH values
by nonlinear least-squares analysis according to the equation for one-step titration:
␦obs ⫽ [␦HA ⫹ ␦A 10n(pH⫺pKa) ]/[1 ⫹ 10n(pH⫺pKa) ].
Here, ␦obsis the observed chemical shift at a given pH
value, ␦HA and ␦A are the asymptotes corresponding to
chemical shift values for the protonated and unprotonated
forms of a given residue, pKa is the negative logarithm of
the apparent equilibrium constant for the observed protonation equilibrium, and n is the Hill parameter that accounts for the deviations from the unperturbed titration,
caused by the influence of other titrating residues in the
protein over the observed pH range. Four parameters, the
apparent pKa value, n, and the chemical shifts at limiting
pH values were optimized. Titration shift, ⌬␦, the change
in the observed chemical shift upon titration from high to
Fig. 1. 13C-1H HSQC-TOCSY spectra of 0.5 mM apo calbindin D9k at 300 K and pH 2.4 and 7.0.
Assignments of ␣-protons are indicated. The 13C chemical shifts are given relative to spectrometer
frequency 150.85 MHz for 13C.
low pH, was calculated as ⌬␦ ⫽ ␦A⫺␦HA. The biphasic
titration curve for Glu17 was analyzed according to the
␦obs ⫽ 5[␦1 ⫹ ␦2 10(pH⫺pK1) ]/[1 ⫹ 10(pH⫺pK1) ] ⫹ ␦3 10(pH⫺pK2) 6
/[1 ⫹ 10(pH⫺pK2) ]
The reported standard errors characterize the precision of
the data fitting, but not other possible errors, e.g., the
accuracy of pH measurements or chemical shift readings.
Theoretical Model and Monte Carlo Simulations
The protein coordinates PDB3ICB from the Brookhaven
Data Bank obtained from an X-ray diffraction study of the
crystalline Ca2⫹-loaded protein18 were used. Each protein
atom was represented as a hard sphere, impenetrable to
any solvent ions unit charge on the ␨-nitrogen.
Carboxylic oxygens were given a charge of ⫺0.5, and
lysine residues carried a positive unit charge on the
␨-nitrogen, whereas all other protein atoms were kept
neutral. The charges of all carboxyl groups were allowed to
change according to the solution pH. The protein coordinates were kept fixed during the simulation, and the
protein was placed in the center of a spherical cell to which
counterions and salt ions were added in accordance with
experimental conditions at each pH value. These ions were
treated as mobile charged hard spheres confined to the
cell, whose radius was determined by the protein concentration. This is in contrast to most other theoretical
studies in which the protein usually is assumed to be at
infinite dilution. Changing the protein concentration by a
factor of 3 leads to pKa shifts of approximately 0.2 units for
the lysine residues in calbindin D9k.2 The cell, including
protein, counterions, and salt is always electroneutral.
The number of counterions is given by the protein net
charge, and increasing the cell radius (i.e., lowering the
protein concentration) consequently leads to a reduced
counterion concentration. This, of course, affects the electrostatic screening and in the limit of zero protein concentration all the screening is caused by the added salt. The
interaction energy between charged species i and j is
given by,
u(ri j ) ⫽ qiq je 2/4␲⑀0⑀ri j
u(ri j ) ⫽ ⬁
ri j ⱖ (␴i ⫹ ␴j )/2
ri j ⬍ (␴i ⫹ ␴j )/2
where q is a partial charge, e is the elementary charge, ⑀o is
the permittivity of free space, ␴i is the hard core diameter
of particle i, and rij is the distance between the particles i
and j. Only interactions between particles within the cell
are taken into account. The dielectric constant, ⑀, was
chosen as 77.8 at the experimental temperature of 300 K
and was assumed to be uniform throughout the cell.
The simulations were performed in the canonical ensemble with respect to salt ions and counterions with use
of the traditional Metropolis Monte Carlo procedure.19 One
million moves per mobile particle was attempted in each
MC run. Half of that number was considered to be
equilibration, and the second half was used for calculation
of averages. The calculated fractional charges on the
titrating residues were determined with an accuracy of
⫾0.001. In addition, the simulation cell was coupled to a
proton bath to establish a constant pH in the system. After
every tenth attempted move of the mobile charges, an
attempt was also made to delete or insert a proton on a
titrating residue. The proton is not explicitly inserted, but
only the charges on the two carboxylic oxygens are neutralized. The opposite procedure takes place on a ‘‘proton
deletion.’’ In reality, an addition of a proton to a carboxylate group means that acid (HCl) has been added to the
solution. Hence in the simulation, a proton addition to a
carboxylate group was always accompanied by the addition of a negative mobile charge to the cell to keep the
system electroneutral. The acceptance or rejection of an
attempt to change the ionization state of a particular
carboxylate group was based on the trial energy,
⌬E ⫽ ⌬Ec ⫾ kT ln 10 (pH ⫺ pK0 )
where ⌬Ec is the change in Coulomb energy due to the
protonation or deprotonation, and K0 is the dissociation
constant for the model compound.20 The plus sign is used
when a residue is to be protonated, and the minus sign
when it is to be deprotonated. In the theoretical analysis,
the pKa of an ionizable group is taken as the pH value at
which the group is half-protonated. The calculated pKa
were corrected for the deviations of the activity coefficient
for H⫹ from unity at low pH using a modified Widom
technique.21,22 The main part of the correction originates
from the increasing net positive charge on the protein,
which gives rise to a significant electrostatic potential
throughout the simulation cell. The calbindin preparation
includes contaminant salt above the necessary counterions, about 10 times the concentration of protein, as
estimated by atomic absorption spectroscopy measurements. This residual salt as well as the stepwise increase
in salt concentration, resulting from addition of acid in the
experimental determination of the titration curve, was
taken into account in the simulations.
The calcium-binding loop of the ubiquitous EF-hand
proteins usually contains four acidic residues, which participate in coordination of the Ca2⫹ion. The free energy of
calcium binding to this type of site is largely of electro-
static origin.23 Therefore, it is important to know the
charge state and titration behavior of ionizable groups to
understand the impact of overall electrostatic interactions
on the structure and function of these proteins. The pKa
values for lysine residues have been estimated for apo and
holo forms of both calmodulin24 and calbindin
D9k.2,25However, the individual pKa values of acidic groups
have not been determined for any of the calcium-binding
proteins belonging to the EF-hand family. This study
describes an attempt to measure the pKa values of acidic
residues in Ca2⫹-free calbindin D9kusing 13C labeling and
heteronuclear NMR spectroscopy.
Electrostatic interactions, known as determinants of the
individual pKa values in proteins, are highly dependent on
the presence of screening factors. To minimize the screening, no buffer or salt was added to the protein sample,
except for controlled amounts of acid (HCl) or alkaline
(NaOH), which were taken into account in Monte Carlo
simulations of the titration process.Because the protein
itself, an amphoteric polyelectrolyte, is a screening factor
for ionic interactions,26 it was important to keep the
concentration of calbindin D9k as low as possible. It was
also established, that below the isoelectric point at about
pH 5, the solubility of calbindin D9k abruptly decreases to
⬍1 mM, and well-resolved homonuclear TOCSY NMR
spectra could not be acquired within a time period of 24 h.
13C labeling of acidic residues was therefore used to
increase the sensitivity of NMR experiments and to facilitate the use of 0.5 mM protein concentration in the present
titration experiments.
Selective 13C-labeling of acidic residues in a protein via
expression in E. coli is complicated because of transamination reactions. E. coli strains exist with lesions to prevent
metabolic conversion of aspartic acid to asparagine,27 but
not those to prevent interconversion of glutamate and
glutamine. The use of the general transaminase-deficient
E. coli strain did not prevent the conversion of 13C-labeled
glutamate to glutamine in Bacillus circulans xylanase.28
Because calbindin D9k contains 13 glutamates and only 4
aspartates, our protocol for the production of calbindin D9k
in the presence of 13C-labeled aspartic and glutamic acid
did not include any protective means against their metabolic conversion to respective amines during the expression in E. coli. As a result, the 13C label was also found in
asparagine and glutamine residues of calbindin D9k, but
eight acidic amino acids were 13C-enriched enough to be
identified in NMR spectra and followed throughout the
titration. It is conspicuous that all the acidic residues that
were significantly labeled are half-ionized at pH values
below the isoelectric point of approximately 5. The acidic
groups with low apparent pKa values can be considered as
those of primarily structural importance for a protein.29
Chemical Shift Assignments
The 1H-13C HSQC-TOCSY experiments were used in pH
titration to provide correlations between the ␥-13C (Glu,
TABLE I. Experimentala and Simulatedb Titration Parameters of Acidic Residues and the C-Terminal ␣-Carboxyl Group
in the Apo Form of Bovine Calbindin D9k at 0.5 mM Protein Concentration and 300 Kc
⌬␦(13C), ppm
4.01 ⫾ 0.06
4.50 ⫾ 0.09
3.92 ⫾ 0.08
2.09 ⫾ 0.12
0.76 ⫾ 0.10
3.02 ⫾ 0.14
3.62 ⫾ 0.03
4.04 ⫾ 0.24
4.04 ⫾ 0.07
0.44 ⫾ 0.02
0.80 ⫾ 0.02
0.77 ⫾ 0.02
0.70 ⫾ 0.03
0.98 ⫾ 0.07
0.68 ⫾ 0.05
0.58 ⫾ 0.06
0.78 ⫾ 0.02
1.17 ⫾ 0.10
3.77 ⫾ 0.02
3.40 ⫾ 0.02
4.74 ⫾ 0.02
3.21 ⫾ 0.06
6.46 ⫾ 0.16
4.08 ⫾ 0.04
3.04 ⫾ 0.09
4.62 ⫾ 0.06
3.84 ⫾ 0.02
3.20 ⫾ 0.05
pKa shiftd
pKa shiftd
pKaexp ⫺ pKasim
experimental titration parameters, including pKa values, n values, and titration shifts, were determined from the titration behavior of
chemical shifts for aspartate ␤-13C, glutamate ␥-13C, and of the ␥-13C NMR resonances of the C-terminal Gln75 residue (␣-COOH).
bThe protein coordinates with accession number 3ICB from the Brookhaven Data Bank for the crystalline Ca2⫹-loaded calbindin D18 were used.
cThe estimated initial salt concentration in a protein sample for titration experiments was 0.5 mM at pH 6.0 due to residual salt in a purified
protein. An increase in ionic strength due to added HCl or NaOH during the titration was taken into account in Monte Carlo simulations.
dpK shift from the model compound pK values, pK –pK : pK is 4.0 for Asp, 4.4 for Glu, and 3.8 for ␣-COOH.20
eIn simulations the pK of an ionizable group is defined as the pH value at which the group is half-protonated.
fThe Hill parameter (n) values for simulated titration curves were determined using Equation 1.
gResidues located in calcium-binding loops of calbindin D : Glu64 in the C-terminal loop, Glu26 and Glu17 in the N-terminal loop; the backbone
carbonyl oxygen of Glu17 provides a calcium ligand in the Ca2⫹-loaded form of calbindin D9k .
hThe experimentally observed pH value corresponding to a half-protonated state of Glu17.
Gln) or ␤-13C (Asp, Asn) and the main-chain ␣-protons, as
well as side-chain protons of respective residues. Because
of the dilution of the carbon-13 label by transamination
reactions and the overlap of resonances in the recorded
NMR spectra, only 8 of 17 acidic amino acid residues
present in calbindin D9k could be identified by using the
proton resonance assignments for the apo calbindin D9k at
pH 5.25.17 Thus, it was possible to unambiguously identify
and follow the titration behavior of residues Glu4, Glu5,
Glu11, Glu17, Glu26, Asp47, Glu48, Glu64 and the Cterminal ␣-carboxyl group of Gln75. In addition, the
chemical shift changes of residues Gln22, Gln33, and
Gln67 with changing pH were followed. The side-chain
proton resonances, although helpful in making positive
identification of 13C resonances, did not provide titration
curves for reliable pKa determination for all the observed
residues because of the overlap of resonances in NMR
spectra at several pH values. The titration parameters for
individual residues reported in this work were therefore
determined from the pH dependence of their carbon-13
chemical shifts. The experimental measurements were
complemented by Monte Carlo simulations of the titration
process and pKa values. The results are summarized in
Table I.
Titration Shifts
The chemical shifts of the 13C nuclei, located next to the
ionizing carboxyl groups in the side chains of aspartates
and glutamates, decrease with decreasing pH. Titration
shifts were observed in the range from 2.85 to 4.50 ppm.
These upfield titration shifts with decreasing pH are
consistent with those observed for the chemical shifts of ␤and ␥-13C resonances of aspartates and glutamates in
other proteins, e.g., human immunodeficiency virus protease30 or bovine pancreatic trypsin inhibitor.31 The titration
shift of 3.62 ppm for Asp47 may be underestimated (and
the experimental pKa value overestimated) because the
low pH limit of the titration curve was not observed in the
pH range under the study. All the titration curves in
Figure 2 are better described at their high-pH ends.
Therefore, all the reported experimental pKa values, to a
different extent, should be considered as ‘‘upper estimates.’’ Apart from Asp47, this particularly concerns residues Glu5, Glu17, and the C-terminal ␣-COOH, which are
characterized by low pKa values and ‘‘uncompletely covered’’ low-pH ends of their titration curves.
The upfield titration shift of 0.45 ppm with decreasing
pH, characterized by an apparent pKa of 3.20 ⫾0.05, was
registered for the ␥-13C nucleus of the Gln75 side chain and
assigned as resulting from the change in the ionization
state of the C-terminal ␣carboxyl group of Gln75. This
titration shift may include conformation-mediated influences resulting from the titration of the relatively distant
␣-carboxyl group. Similar titration shift of 0.58 ppm with
an apparent pKa of 3.17 ⫾ 0.10 for the ␥-13C resonance of
Gln67, is probably dominated by conformational consequences of the change in ionization state of ␣-carboxyl
group of Gln75. The ␥-13C resonance frequency of the
Gln33 residue was independent of pH in the observed
Multiple-Site Titration
Figure 2 shows theoretical unperturbed titration curves
for each ionizable group with its model compound pK0
value. The shape of experimental titration curve for the
side-chain carboxyl group of Glu26 and the C-terminal
Fig. 2. Experimental (circles, thick line) and simulated (dashed line) titration curves and pKa
(experimental values underlined) for acidic groups in apo calbindin D9k at 300 K. Unperturbed
titrations with corresponding model compound pK0 values (Asp 4.0, Glu 4.4, and ␣-COOH 3.8), and
the n equal to 1 are given by thin curves.
␣-COOH group is close to the ideal single-proton titration.
The experimental titration curves for the rest of the
observed ionizing residues, however, extend over a significantly wider pH range than those for unperturbed model
compounds and display Hill coefficient values less than
unity. The titration range is even larger for the simulated
titration curves and can be clearly seen for all the studied
ionizable groups in Figure 2. The Hill coefficient values for
simulated titrations, as a rule, are lower than for experimental titration curves (Table I). The negative cooperativity, as manifested by the Hill parameter, both in theory
and experiment, can be explained as an effect due to other
acidic residues that undergo a change in their ionization
state in the observed pH range, resulting in modulation of
the Coulomb interaction over the long distances. Because
of the monotonically delayed titration behavior, it is not
possible, by analyzing the experimental titration curves in
terms of limited number of strongly interacting ionizable
groups,32,33 to unambiguously identify particular ionizing
groups affecting the titration of each individual residue.
In contrast to the titration of other residues, the pH
dependence of [␥-13C] chemical shift of Glu17 shows a
distinguished biphasic titration curve, pointing to the
strongly coupled titration of two acidic groups. Theoretical
structure-based modeling of the titration of this residue
does not explicitly reproduce the pronounced two-step
titration observed in the experiment, and significant differences in predicted and determined ionization step are
observed from pH 2.5 to 6. However, the Hill parameter for
the simulated titration curve of Glu17, equal to 0.30, is
significantly lower than for other residues observed in this
work. This confirms that, to some extent, the theoretical
model is still capable of reproducing electrostatic effects
arising from structural features of calbindin D9k that cause
the titration of Glu17 to take place under the strong
influence of the electrostatic field created by nearby resi-
dues. Another explanation for the biphasic titration behavior of Glu 17 could be a conformational change taking place
at pH 4.5–5. This would also explain the discrepancy
observed between experimental and theoretical results.
Apparent pKa Values of Acidic Groups in Apo
Calbindin D9k
The protonation-deprotonation equilibria of ionizable
groups in unstructured peptides are largely determined by
their intrinsic properties and are usually not significantly
affected by specific influences from other residues. The pKa
values normally observed in such peptides are 4.0 for an
aspartic acid side chain, 4.4 for glutamic acid side chain,
and 3.8 for a C-terminal ␣-carboxyl group. Individual
ionizable groups in folded proteins are usually characterized by apparent pKa that are significantly different from
their intrinsic values in unstructured model peptides, the
shifts from intrinsic pK0 values being largely caused by
site-specific electrostatic interactions. The ionization constants for acidic groups observed in apo calbindin D9k were
found to deviate from their model compound values as
illustrated in Figure 3. Experimental pKa for Glu11 and
Glu48 are shifted toward high pH by 0.34 and 0.22 pK
units, respectively. Local electrostatic environment of the
remaining observed ionizable groups favors their deprotonated state in a folded protein, thus causing their apparent
pKa values to be shifted toward low pH, with the shifts
ranging from 0.32 to 1.0 pK units. Reduced pKa values of
these carboxyl groups can be explained as resulting from
global electrostatic effects due to protein charges. Most of
these ionizable groups are distant from the calciumbinding sites, and they titrate under conditions in which
the protein carries a net positive charge dominated by
cationic lysine side chains. It should then be expected that
among the acidic residues that were not accessible through
13C-labeling are residues titrating under the influence of
net negative charge of the protein, and some of them
probably display pKa values significantly shifted toward
high pH.
The data obtained in this work do not allow the discussion about involvement of hydrogen-bonding effects. Some
information about hydrogen bonds could be obtained by
inspection of the pH effects on backbone amide proton
chemical shifts, which we do not possess here. Obtaining
these data is a part of ongoing studies. The pKa shifts of
ionizable residues, whether acidic groups or lysines, from
their model compound values are interpreted as resulting
from the cumulative effect of ionic charges from all over
the protein molecule. Partial charges and dipoles are not
included. The theoretical model also neglects H-bonds and
conformational changes. However, lysines and acidic residues ionize in different electrostatic environments. The
onset of a proton uptake by lysines at strongly alkaline pH
occurs under the influence of 18 negatively charged acidic
groups. When all the lysines are protonated at about pH 9,
the net charge of the protein is still ⫺8, assuming that the
N-terminal ␣-NH2 uptakes a proton between pH 7 and 8.
The ionization of acidic groups, on the other hand, involves
Fig. 3. Experimental (filled bars) and simulated (empty bars) pKa shifts
from corresponding model compound values for Asp and Glu residues
and the C-terminal ␣-COOH group in apo calbindin D9k at 300 K.
the change of protein net charge from ⫺7 to ⫹10, with
isoelectric pH around 5.
The measured and modeled pKa shifts, as illustrated in
Figure 3, are in fair agreement. For residues Glu5, Glu26,
and Glu64, the observed and predicted pKa values agree
within 0.3 pK units and for residues Glu4, Asp47, Glu48,
and ␣-COOH the agreement is within 0.4–0.5 pK units.
For Glu11 the predicted pKa shift is in opposite direction to
what was observed in experiment, with the difference of
0.64 units in pKa values. The major disagreement between
the measured and predicted titration behavior is observed
for Glu17, which is a backbone Ca2⫹-ligand in the Nterminal calcium binding loop. According to the measurements, this residue is half-protonated at pH 3.6 but
manifests a biphasic titration with apparent pKa values of
3.2 and 6.5 (Table I). In Figure 2 the comparison is made
between the pH values corresponding to the half-protonated state in experiment and simulation. Analogously,
the pH dependence of the chemical shift of ␥-13C resonance
of Gln22 can be also described as a two-step titration with
apparent pKa values of 4.13 ⫾ 0.18 and 6.20 ⫾ 0.16 and the
total titration shift of 0.51 ppm. It is not possible, however,
from the present data to decide whether the apparent pKa
of 6.2 for Gln 22 manifests the titration of the Glu 17
residue. Neither is it possible to tell whether the apparent
pKa of 6.5 is a characteristic of only Glu17 or reports the
change in ionization state of some other nearby acidic
residue. In either case the events resulting in 20% neutralization with apparent pKa of about 6.5 of a Ca2⫹-ligating
residue Glu17 in the N-terminal calcium-binding loop are
most probably significant for the physiological activity of
calbindin D9k.
Impact of pH Change on Protein Structure
Computational approaches to the calculation of pKa
values in a protein usually rely on the assumption that the
structure of the protein is well established ,and it does not
change over the pH range used in titration experiments.
Calbindin D9k has been reported to have similar structure
both in crystal and solution, which does not respond
significantly to the specific binding of two calcium ions34or
changes in solvent and temperature.35 In agreement with
Fig. 4. A diagram showing side chain carboxyl groups for aspartate
and glutamate residues in a set of 33 structures of apo calbindin D9k at pH
5.3 by NMR spectroscopy. The backbone is shown for one of the
structures. The pKa values were measured for residues shown by dashed
this, no significant changes in calbindin D9k structure were
observed at pH values up to 12.2,25The Hill coefficient for
lysine titrations did not significantly deviate from unity,
and the theoretical pKa values for lysine residues in
calbindin D9k, calculated for the structure of protein
crystals that were obtained at neutral pH, were found to be
in good agreement with experimental data.2
The solution structure of apo calbindin D9k is not a single
well-defined protein configuration but a set of 33 structures (1clb.pdb), whose statistical weights are unknown.
Figure 4 shows the side chain carboxyl groups of acidic
residues in these structures. Except for Glu11,Glu35, and
Glu60, configurations of side chains of acidic groups are
not well defined. In many cases, their configurations occur
in two to four groups, and for Glu17 and Asp58 the side
chain carboxyl groups are more or less uniformly spread
over the sphere with a diameter of 10–12 Å. This may
indicate the conformational lability of these side chains in
the solution. Because the overall charge state of a protein
as well as the charge states of individual residues are
gradually changing with changing the pH, the configuration of side chains can also vary with pH, particularly in
the calcium-binding area. At present, we can see no
reliable way of accounting for these structural changes in
theoretical calculations. The use of a rigid structure of a
calcium-loaded calbindin in theoretical pKa calculations is
an approximation that neglects structural changes due to
calcium binding and changing pH. The failure to exactly
reproduce the biphasic titration curve for Glu17 in theoretical calculations may be intrinsic to a model but may also
result from this neglect. The side chain of Glu17 seems to
be the least well-defined in the apo calbindin D9k structures.
The results of the present study indicate that calculations based on the crystal structure of the calcium-loaded
protein can reproduce the main features of titration behavior of acidic residues, including apparent pKa values and
broadened titration curves. Differences in measured and
modeled titration behavior of acidic residues may arise
partly from shortcomings of the theoretical model for
electrostatic interactions in proteins. However, it is also
highly possible that some changes in protein structure
take place with decreasing pH. It is relevant that neutralization of all the acidic groups in calbindin D9k, while pH is
changing from neutral to strongly acidic values, causes the
change in the overall charge of the protein by 18 units,
from ⫺7 to ⫹11, assuming the N-terminal ␣-NH2 group
(pKa ⱖ 7.5) protonated at pH 7. The change includes
reversal of the net charge from negative to positive values
over the isoelectric point at about pH 5. It may not be
reasonable to expect that the structure of a protein will
remain resistant to such a large change in the net charge.
An indication of possible structural change is that the
experimental titration curves for acidic residues in calbindin D9k are characterized by distinctly higher Hill parameter values than simulated titrations, obtained under the
assumption of protein structure being constant at variable
pH. It is reasonable to expect that while the change in the
overall charge takes place during the titration, the protein
structure will respond to this change to maintain optimal
interaction between the groups still remaining ionized in a
new electrostatic environment. On the basis of the comparison of solution structures of apo and calcium-loaded calbindin D9k, it has been suggested that such changes in the
spatial arrangement of the side chains of some acidic
residues occur on calcium binding.36It is also possible that
changes in configuration of side chains of ionizable residues take place with changing pH to compensate the
changes in the charge state of their own or other titratable
groups. This may be the case for Glu17, the backbone
carbonyl group of which is a calcium ligand in the Nterminal binding site, highly populated by acidic residues.
The biphasic titration observed for this residue in experiment, but not explicitly reproduced in the theoretical
calculations, may well be a manifestation of the change in
side-chain configuration around pH 5. At similar overall
three-dimensional structure of a protein, differences in
positions of particular ionizable side chains can cause
significant differences in their pKa values.5 It is important
that the onset of titration of Glu17 at near-neutral pH,
down to the pH where this residue is protonated in 20% of
the protein, is remarkably well reproduced in simulations
(Fig. 2). This observation suggests that at high pH limit of
titration the side chain of Glu17 is in a configuration given
by crystal structure. When 20% of Glu17 is protonated, the
change in side-chain configuration takes place, resulting
in a charge distribution of the protein molecule that favors
the ionization step of this residue being unchanged between pH 5 and 4 while further titration takes place with a
different pKa value at lower pH values.
However, because the simulations, in general, fairly
agree with the experimental data, the changes in the net
charge of calbindin D9k, either resulting from calcium
binding or caused by changes in pH, are apparently
balanced not to result in large fluctuations of the overall
charge distribution or the global structure of the protein.
This assumption is supported by a recent remarkable
observation that the overall charge distribution of a protein catalyst acetylcholinesterase remained stable despite
the change in its net charge by a factor of 2.37
The Dielectric Constant
In pKa simulations according to the electrostatic continuum model we use a high dielectric constant throughout the system, including the protein interior. This may
appear a rather drastic approximation, but previous Monte
Carlo simulations of this model accurately reproduce
experimentally observed shifts in the calcium-binding
affinity on mutations of the protein as well as changes in
salt and protein concentration.22,23,26,38 Recent studies1–5 of
the titration behavior of proteins support the use of a high
dielectric permittivity for the protein interior. Molecular
simulations also support the notion of a high dielectric
permittivity of the protein interior.39 These results are in
agreement with the ideas advocated by Warshel and
co-workers40–42 emphasizing that protein charges have to
be stabilized one way or another. One possibility is that the
charges are located on the surface of the protein and
stabilized by the aqueous solvent. An ‘‘interior’’ charge, on
the other hand, has to be stabilized by other nearby
charges or polar groups. To describe the latter type of
stabilization in a macroscopic model is difficult, if not
impossible, but one possible way to approximate the effect
is to assume a high dielectric response also from the
protein interior. The detailed microscopic information concerning hydrogen bonds, partial solvation, etc. will be lost,
and the ‘‘interior’’ dielectric permittivity becomes in this
case just an additional fitting parameter. An easy and
accurate way out of this dilemma is to assume a uniform
dielectric permittivity equal to the value of pure water for
the whole solution.
A second aspect of this problem is at what separation
between two charges can we expect the macroscopic theory
to be valid? Previous experimental and theoretical results
for the calcium- binding properties of calbindin seem to
indicate that the macroscopic theory is valid down to
separations below one nanometer.23 This notion is also
supported by titration data for diamines and dicarboxylic
acids.43 The effective dielectric screening between the two
nitrogens (3.4 Å apart) in 1,2-diaminoethane is 26, whereas
for 1,5-diaminopentane it is already close to 70. The
separation between the charged nitrogens in the latter
molecule is about 6 Å. Similar results are also observed for
polycarboxylic acids. It turns out that the titration pattern
for polyacrylic acid is well reproduced in a continuum
model44 while it fails completely for more highly charged
chains such as polyfumaric acid and polymaleic acid (M.
Borkovec and G. Koper, personal communication). From
the X-ray structure of Ca2⫹-loaded calbindin D9k we find
that of the acidic residues studied in this work it is only
Glu17 and Asp47 that have any additional charged groups
within 5 Å distance. The carboxylic oxygens of Glu27 are
approximately 4.5 Å from those of Glu17 and the positively
charged nitrogen of Lys25 is only 3.5 Å away from the
carboxylate group of Asp47. In the latter case we should
expect a significant upward shift of Lys25 and a downward
shift of Asp47. This is indeed born out in the experiments.2
It is interesting to note that despite the short separations
between Lys25 and Asp47 in the X-ray structure both
shifts are reasonably well reproduced in the theoretical
modeling. A possible explanation for the good agreement is
that their separation is increased by a few Ångströms
compared with the X-ray structure. Thus, we might conclude that a macroscopic continuum model assuming a
high dielectric response from the protein interior adequately describes the ionic interactions in calbindin D9k.
Prospects of pKa Determination
The agreement between theory and experiment is not
perfect; for some residues even the sign of the predicted
pKa shift is wrong. Overall, the comparison is of the same
quality as obtained from other macroscopic models.1 The
pKa values of six residues at the binding sites of calbindin
D9k have been recently calculated by using Debye-Hückel
theory.45 A reasonable prediction was made for Asp 19 to
have a pKa of 4.22 in the apo form. The rest of predicted
pKa values, in the range from 9 to 22, seem to be far too
unrealistic. Unfortunately, none of these residues could be
followed in our present study. However, all titratable acidic
groups in calbindin D9k were included in calculations.
Simulated pKa values span the range from 2.5 (Asp47) to
6.0 (Glu60). The ongoing work has shown that the pKa
values can be determined for all the acidic residues in
calbindin D9k.
The agreement between the measurement and modeling
in the present study would of course improve slightly by
using the interior dielectric permittivity as a fitting parameter. No further information should, however, be gained by
such an attempt. Structural changes in the protein on pH
change are not taken into account in our model and neither
are nonelectrostatic effects on the intrinsic dissociation
constant, pK0. That is, we assume that the pK0 values of
glutamic acid and aspartic acid are the same in folded
calbindin D9k as in small model peptides. These are
theoretical or modeling problems that should be discussed
together with the experimental difficulties of identifying
and following every single titrating group in a protein.
Note that this has to be done over a wide pH range actually
passing through the pI.
Previously2 we were successful in determining the apparent pKa values for all 10 lysine residues in calbindin D9k
using 13C enrichment. In the present work we were able to
identify nine apparent pKa values for acidic groups, but
nine escaped our efforts. The correctness of the assignment
of both the acidic groups and the lysines has been verified
by using homonuclear 1H TOCSY NMR experiments. The
remaining nine glutamic and aspartic acid residues will be
studied by using a different labeling strategy, e.g., 15N
labeling. Depending on the method in use the number of
peaks in NMR spectra can be huge, and the risk of making
errors in assignments of resonances at variable pH is not
negligible. For larger proteins, the problem will escalate.
Thus, a question of paramount importance to be answered
is how reliable a pKa determination is whether it is
experimental or theoretical.
We thank Dr. Göran Carlström for help with NMR
spectroscopy and Dr. Bryan Finn for support in computer
related issues.
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