From the Institute of Food Research, Reading Laboratory, Earley
Gate, Whiteknights Road, Reading RG6 6BZ, United Kingdom
Accurate prediction of charge interactions in
macromolecules presents a significant challenge for computational
biology. A model for the low Cys30
pKa and oxidizing power of DsbA (Gane, P. J.,
Freedman, R. B., and Warwicker, J. (1995) J. Mol.
Biol. 249, 376-387) has been investigated experimentally
(Hennecke, J., Spleiss, C., and Glockshuber, R. (1997) J. Biol. Chem. 272, 189-195), with substitutions for
Glu37 and Glu38 and with residues 38-40
removed. Measured changes in Cys30 pKa
and redox potential were relatively small and reported to be in
contrast to model predictions. It is now shown, particularly with
calculations of wild-type:mutant differences for a range of salt
concentrations, that the data are consistent with the model and support
the key finding that a number of different factors contribute to the
oxidizing power of DsbA, so that any particular one need not
necessarily be large. A feature of the model is a low protein
dielectric, and higher values (which are becoming popular in
predictions of pH dependence) are inconsistent with both the difference
data and the wild-type Cys30 pKa.
 |
INTRODUCTION |
DsbA from Escherichia coli is a periplasmic protein of
189 amino acids that catalyzes the introduction of disulfide bonds (1,
2). The oxidizing power of DsbA derives from the low Cys30
pKa of about 3.5 (3, 4), exhibiting a
pKa with respect to normal of around
5. DsbA is
a valuable link to theory because models must account for the low
Cys30 pKa and thereby provide a
molecular basis for oxidizing power and physiological function.
Continuum electrostatics has become the most common method for
calculating macromolecular pKas (5), but it is not
yet consistently accurate, with discussion revolving around the choice
of macromolecular relative dielectric,
p (6-8). Variation
in
p reflects the difficulty of reproducing microscopic
solvation effects in a continuum model, particularly where an ionizable
group is buried in the macromolecule, so that part of the high relative
dielectric (
s) solvation shell is swapped for the lower
p environment (see Fig. 1).
A continuum electrostatic model has been presented for the redox
potential difference between E. coli DsbA and E. coli thioredoxin (9), using structural homology and differencing
to circumvent changes in charge burial (see Fig. 1). The low thiolate
pKa and oxidizing power of DsbA were suggested to
arise from several sources including His32 and
Gln97 side chains and summed peptide dipole contributions.
Residues Glu37 and Glu38 were each predicted,
if deprotonated, to move the Cys30 pKa
by about 0.4 in the more reducing direction. The P34H mutation in
thioredoxin supports the model implication for DsbA His32
(10). Redox potential and Cys30 pKa
measurements have been reported for DsbA mutations Glu37
and Glu38 and for the deletion mutant
38-40, which
relates to assessment of the peptide dipoles contribution (11). In
contrast to the reported disparity with the predictions (11), the
current article will demonstrate that data for
38-40 are in line
with the model. The deleted region is just one part of an implicated
section of backbone, and its individual effect, although visible, is
not large. The effects of Glu37 and Glu38
depend on their protonation states, and it will be shown that mutant
measurements (11) and the atomic structure (12) are consistent with an
elevated pKa for one of these residues.
Whereas lower
p gives a reasonable match to experiment in
the Cys30 thiolate difference calculations, it generates
large discrepancies in unmodified full pKa
calculations. A recently introduced modification (8), empirically
accounting for changes in water entropy upon charge burial, is shown to
perform qualitatively well when applied across the ionizable groups of
DsbA.
 |
EXPERIMENTAL PROCEDURES |
Reduced DsbA has been modeled previously (9) from the
crystallographic structure of the oxidized molecule at 2-Å resolution (12) by breaking the Cys30-Cys33 disulfide
bond and torsioning Cys30 to maintain van der Waals contact
with Cys33. The modeled reduced configuration is similar to
that of the homologous Cys32 in the nmr structures of
reduced E. coli and human thioredoxins (13, 14). In the
absence of experimentally determined atomic structures for the DsbA
mutants, E37Q and E38Q were assumed to be isosteric with
WT,1 and the deletion mutant
38-40 could be made with a C
-C
link
between WT residues 37 and 41, accompanied by only minor conformational
rearrangement upon regularization of this region in the program QUANTA,
with the CHARMm force field (Molecular Simulations Inc., Waltham, MA).
Neither the WT nor
38-40 proteins were subjected to extensive
energy minimization, so that the structures would remain close to
experiment and also match each other away from the deletion site.
Calculated differences between WT and the mutants are based on the
assumption of minimal structural alteration, which is consistent with
stereochemical and hydrogen bonding considerations. The efficacy of
such conformational modeling can be assessed when the mutant and
reduced WT structures are determined experimentally.
Charge interactions were calculated with FD solutions to the
Poisson-Boltzmann equation (15, 16), implemented in the program FDCALC,
using
s = 80 and
p ranging from 4 to 80. Calculations of pKa differences between DsbA WT and
mutants (see Fig. 1) used reported ionizable charge assignment (9) for
groups other than Cys30. In addition, calculations of the
electrostatic free energy, differenced between reduced and oxidized
forms and between WT and
38-40 mutant, 

G = (
GWT,RED
GWT,OX)
(
GMUT,RED
GMUT,OX), are compared with ratios of redox
equilibrium measurements (11),
RT
ln(KeqWT/KeqMUT),
from 0 to 1 M added NaCl, with T = 298.15 K. It is assumed that the structural changes associated with both
disulfide bond (Cys30-Cys33) breakage and
mutation are confined to separate localized regions and that these
localized effects will cancel between WT and mutant (for disulfide bond
breakage) and between oxidized and reduced (for the mutation). The
calculated 

G value is therefore the remaining long
range (electrostatic) interaction between the mutation and the
Cys30 thiolate. Ratios of Keq at
each added NaCl concentration will remove any ionic strength dependence
of the glutathione redox potential. Ionic strength dependence was
incorporated into the FD computations without a Stern layer.
Full pKa calculations (Fig.
1) used a statistical treatment of
interacting ionizable groups (17), extended with a Monte Carlo method
for computations with large numbers of such groups (18). This method
used 10,000 Monte Carlo steps and a modification that allows for
multiple site transitions for pairs that are are coupled by an
interaction equivalent to more than 2 pKa units
(18). Partial charges (24) and ionizable group (free amino acid)
pKas (6) were allocated. Ionizable residues included
were Asp, Glu, His, Arg, Lys, Cys, and the amino-terminal group,
whereas the carboxyl-terminal residue (189) is missing from the
coordinates, and tyrosines have been omitted from the pKa calculations. Modification to account
empirically for solvent entropic change upon amino acid transfer to
protein is
Et =
VsEs, where
Vs is the fractional change in first hydration
shell volume (calculated from the FD grids) and Es
is a free energy contribution associated with water ordering for a
complete first hydration shell (8). Fitting to a range of experimental
pKas, with
p = 4, gives values of
Es that correspond to about 6 ordered water
molecules in the hydration shell of a single charge center group and
about 2 for a double charge center group (8). Although there may be
further detailed variation between ionizable group types within the
charge center groupings, these values are starting points for overall
estimates of pH titration curves. Some calculations were made using a
Debye-Hückel model with a uniform dielectric,
eff = 50, in place of the FD procedure. The higher dielectric and the
neglect of counterion exclusion from the protein interior in this
method (19) reduces the size of electrostatic interactions.

View larger version (81K):
[in this window]
[in a new window]
|
Fig. 1.
Full pKa calculations and
charge burial within a macromolecule. The pKa
of a schematically drawn cysteine in the WT protein
(pKaWT, top
left) is derived from the pKa of the free amino acid (pKaAA, top
right) and the electrostatic energy difference between ionization in WT and free amino acid ( GWT:AA = GWT GAA),
pKaWT = pKaAA + pKaWT:AA, with
pKaWT:AA = (1/2.303RT) GWT:AA, where
R is the universal gas constant and T the
absolute temperature. The terms GWT and
GAA contain components from the Born (self)
energy (22) and from charge-charge interactions (17). It is assumed
that electrostatic contributions associated with neutral cysteine are
negligible, focusing on the thiolate interactions in protein and free
amino acid. Cysteine pKa in a mutant
(pKaMUT) is also derived
from differencing with the free amino acid (lower half of the figure).
Significant errors in full pKa calculations may be
associated with modeling charge burial (8), denoted by first hydration
(hyd) shell occlusion between free amino acid and protein in
this figure, because the Born energy is highly dependent on the
difference between p and s. Models with low
p tend to overestimate the cost of charge burial (6). The
figure indicates how differencing between WT and mutant (or related)
proteins with structurally similar thiolate environments,
pKaWT:MUT = pKaWT pKaMUT, circumvents the
hydration shell changes that arise from comparison with the free amino
acid (9, 23). Suggested mechanisms for full pKa
calculations that reduce the cost of charge burial include the use of
relatively high p (6) and the use of lower p
together with an empirical estimate of the favorable entropic
contribution associated with water liberation from the first hydration
shell (8).
|
|
 |
RESULTS AND DISCUSSION |
Difference Calculations between WT and Mutants E37Q, E38Q, and
E37Q/E38Q--
The pKas of these residues in WT
DsbA are currently unknown, and full pKa
calculations are not sufficiently reliable to provide detailed
estimates, largely due to the charge burial term. The more reliable
charge-charge estimates yield interactions of about 2 kJ/mol between a
deprotonated Glu37 or Glu38 and the
Cys30 thiolate. In the WT structure at pH 6.5 (12),
Glu37 and Glu38 carboxylates approach within 3 Å (Fig. 2), strongly suggesting that
they share a proton and that one of the pKas will be
elevated above neutral pH, so that just one carboxylate to thiolate
interaction should be counted for comparison to redox equilibrium
measurements at pH 7. The calculated WT to double mutant difference
would be this single interaction, approximating no conformational
change and limited glutamine side chain charge effects. With regard to
the single mutants, Glu38 lies toward the protein exterior
and Glu37 facing the protein interior (Fig. 2), so that
Glu37 is likely to be buried within the E38Q mutant whereas
Glu38 will be solvent-exposed in the E37Q mutant. These
considerations would be consistent with deprotonation of
Glu38 in the E37Q mutant but neutralization of
Glu37 in the E38Q mutant. The calculated

Gs, WT to (E37Q, E38Q, E37Q/E38Q) mutants, for this
hypothesis with the
p = 4 model are (0,
2,
2) kJ/mol
compared with measured values of (0.6,
2.0,
1.5) in 10 mM sodium phosphate (11). This reasonable agreement, constructed upon a plausible hypothesis for Glu37 and
Glu38 pKas, demonstrates both the
requirement for more accurate full pKa calculations
and the success of the published model (9) in suggesting a route toward
engineering more oxidizing DsbA molecules at neutral pH. Comparisons at
the acidic pH of the Cys30 pKa are
omitted for this set of mutants because it is likely that both
Glu37 and Glu38 will be protonated in this pH
region.

View larger version (161K):
[in this window]
[in a new window]
|
Fig. 2.
Mutated DsbA residues in relation to the
active site. The C backbone is shown for the WT
25-43 region, along with side chains for the active site residues
Cys30 and Cys33 and mutated residues
Glu37 and Glu38. The link between
Glu37 and His41 is shown for the modeled
38-40 mutant, and protein interior and exterior are marked in
relation to Glu37 and Glu38 locations.
|
|
Difference Calculations and Salt Dependence for Redox Equilibria of
WT versus
38-40 Mutant--
The deleted residues 38-40 are within
a larger polypeptide region (Fig. 2), which in total is predicted to
contribute to thiolate stabilization in the low
p model. It
is possible to make the Glu37-His41 link
without substantial disruption to the rest of the protein. Following
the discussion in the previous section, Glu37 becomes
solvent-exposed in the modeled deletion mutant so that, by analogy with
WT Glu38, it is likely to be deprotonated at the neutral pH
of Keq measurements. In difference calculations
between WT and
38-40 it is assumed that the thiolate interactions
to the modeled single negative charge of WT
Glu37/Glu38 and the modeled single negative
charge of Glu37 in
38-40 cancel out. Other ionizable
groups are set at normal neutral pH values except for His32
and Glu24, which are in the vicinity of the active site and
may have pKas around neutral pH (9). These
ionizations were set to +0.5 and
0.5, respectively. For the WT
versus
38-40 mutant calculations, both His32
and Glu24 contributions almost cancel on differencing.
Calculated Cys30 thiolate contributions to


G are compared with experimental values derived
from Keq ratios (11) for WT versus
38-40 over a range of added NaCl concentrations (Table I). The approximations in the
calculations (modeled
38-40 conformation, ionizable charge
assignment, and Keq contribution from
Cys30 thiolate alone included) combined with the small


G values (thermal energy or less) suggest that
qualitative rather than quantitative comparisons should be made. It can
be seen that the
p = 4 model is by far the closest to
experiment, indicating that charge-charge interactions through a low
protein dielectric are important in DsbA and that higher
p
values underestimate these interactions. Within the
p = 4 model, the listing of total and non-ionizable interactions shows the
importance of partial charge stabilization of the Cys30
thiolate. With the modeled
38-40 mutant structurally homologous to
WT DsbA, these partial charge interactions can be attributed to WT
residues 38-40. The measured effects (11) are therefore consistent
with earlier predictions, which estimated interaction energy between
the Cys30 thiolate and cumulative peptide dipoles over
residues 25-43 at about
20 kJ/mol (9). The measured upward
Cys30 pKa shift of 0.5 for the WT to
38-40 mutation (11) compares with a value of 0.3 by
p = 4 calculation, demonstrating that these relatively small shifts are
roughly in line with the prediction that extensive charge interactions
in DsbA play a significant role in generating the low Cys30
pKa and oxidizing power. Residues 38-40 of E. coli DsbA are missing in Vibrio cholerae DsbA, but a
proline causes the same overall kink in the protein backbone (20). The
higher thiolate pKa for V. cholerae
compared with E. coli DsbA (21) is consistent with the
results for the E. coli DsbA
38-40 mutant, but more
detailed assessment must await full difference calculations between the
two WT proteins.
View this table:
[in this window]
[in a new window]
|
Table I
Salt dependence of calculated and measured (using Keq)
  Gs for DsbA WT and 38-40
Calculated Cys30 thiolate stabilization, differenced between WT
and 38-40 (  G) versus RT ln
(KeqWT/KeqMUT),
as added NaCl concentration is varied, with a base level of 10 mM sodium phosphate (11) is shown. Values are in kJ/mol, and the positive sign denotes reduced oxidizing power of 38-40 relative to WT. Calculation methods are listed as ( p,
s) or as eff = 50 for the Debye-Hückel
model. Calculated values are given both as the total and as the
contribution from Cys30 thiolate interactions with
non-ionizable groups (in parentheses).
|
|
Measurements of folding stabilities for oxidized and reduced E. coli DsbA WT and mutants in guanidinium chloride (11) have not
been used for comparison because the key determinant of stability in
these experiments is the folding transition cooperativity (rather than
the transition midpoint) from 1.5-2.5 M guanidinium
chloride. Matching computations would therefore be required to account
for relatively small differences in ionic strength variation at these high denaturing salt concentrations, which is beyond the scope of
current methods. In regard to discussions of the link between redox
potential, Cys30 pKa, and
reduced/oxidized protein stability, the current calculations are
consistent with such a link, with qualitative agreement between the low
p model for Cys30 interactions and
Keq measurements. The remaining discrepancy, such as underestimation of experimental values with
p = 4, could signal the breakdown of the various assumptions and/or modeling
insufficiency. For example, choice of
p within the lower
range (typically 2-4) remains an open question, and
p < 4 would yield higher calculated values. The large difference in scale
between calculated values of 

G (Table I) for
p = 4 and higher
p models is due to the largely
through-protein nature of the (38-40)/thiolate interactions, suggesting that measurements with
38-40 provide a sensitive test of
protein dielectric modeling. Single-site mutations that are predicted
to yield >0.5 pKa shift relative to WT
Cys30 while preserving active site stereochemistry are
removal of the His32 ionizable group or removal of the
Gln97 side chain amide (9).
Full pKa Calculations, pH Titration Curves, and Protein
Dielectric--
The various
p models are now employed in
full pKa calculations for DsbA WT, thereby
introducing the charge burial term (Fig. 1). Extensive studies of
computed versus measured pKas in a range
of proteins have revealed two important factors. There exists a subset
of amino acids with large pKa shifts (often linked
to function) and a much larger set with small pKa
shifts tending toward protein stabilization (6). When
p is
varied to give the best match to experiment, the result tends toward a
higher value (e.g.
p = 20), which yields the
larger set of small pKa shifts (6). The
Cys30 thiolate of DsbA is an excellent example of the
subset of large pKa shifts. Although pH titrations
of the remaining ionizable groups of DsbA have not been measured, it is
appropriate to make a qualitative study of the effect of
p
variation on the overall form of the pH dependence and to ask whether
any of the available models are capable of generating a large and
stabilizing
pKa for Cys30 together
with an overall set of small
pKas that tend toward protein stabilization. Also included is the
p = 4 model with the suggested empirical modification to account for
hydration entropy change upon charge burial in full
pKa calculations (8).
Distributions of
pKa are shown for the various
computational models (Fig. 3). The
Es parameter in the modification for single charge
center groups has been adjusted to match experimental pKa values for the DsbA Cys30 and
thioredoxin Cys32 thiolates (8), so that reproduction of
this match for the DsbA Cys30 pKa in the
modified
p = 4 model is expected. However, application of
the Es modification is much more than a device for
fit to experiment, because it represents a key part of solvation
energetics (solvation entropy), and the derived values fall within the
range of measured ionic hydration numbers. It is important to ask
whether other models can generate the same agreement for
Cys30 and also to analyze the overall distribution of
pKas. Modification of the higher
p
models, with a term accounting for the favorable hydration entropy
contribution on charge burial, would have a much smaller effect than
with a lower
p model, because the magnitude of the
modification must not exceed that of the unfavorable Born term to avoid
a model that favors general charge group burial. In other words, the
higher
p models cannot escape from a general underestimation
of electrostatic interactions that leaves the Cys30
pKa close to zero and in contrast with
experiment.

View larger version (26K):
[in this window]
[in a new window]
|
Fig. 3.
Ranges of calculated
pKa for ionizable groups in DsbA WT, according
to different models. Each panel plots the number of calculated
pKas for intervals over the range from 5 pKa units stabilizing (left side) to 5 units destabilizing (right side). Each panel records the
experimental (3, 11) and calculated Cys30
pKa for comparison and is labeled with the
relevant calculation model.
|
|
With regard to the overall distribution of
pKas,
the unmodified
p = 4 model shows a large spread, with the
extension toward significant destabilization that is characteristic of
charge burial in such a model. Application of the modification gives a
range of
pKas tending toward the moderate overall stabilization that is the basis of success in the higher
p and
eff = 50 models (Fig. 3). One of the largest
pKa shifts upon modification of the
p = 4 model is for Cys30, arising from the significant
thiolate burial within DsbA. Whereas the modified
p = 4 model can target both the overall
pKa
distribution and specific large values, such as that of
Cys30, the cost of reducing all charge interactions in the
higher
p and
eff = 50 models is likely to be
the omission of those larger
pKas that may be of
functional interest. The presence of large calculated
pKas other than that of Cys30 in this
qualitative application of the modified
p = 4 model does not
necessarily indicate model breakdown, because they include residues
which by various indications may have significantly altered
pKas, such as Glu24, Cys33
(3), and Glu37/Glu38.
This article shows that a low
p continuum electrostatic
model is consistent with pKa shifts and redox
equilibrium measurements for DsbA WT versus mutants (11),
reinforcing its value in understanding oxidizing power in this protein
family. In the discussion of methods for full pKa
calculations, DsbA provides a valuable diversion. It is not well
characterized in terms of general pKa measurements,
but the large and functionally significant Cys30
pKa provides a crucial test that higher
p models fail. Because the modified
p = 4 model
recovers a reasonable (moderately stabilizing)
pKa profile as well as the Cys30
pKa, potential clearly exists for detailed model
development against proteins with well characterized
pH-dependent properties.