COMMUNICATION
Modeling Charge Interactions and Redox Properties in DsbA*

Jim WarwickerDagger

From the Institute of Food Research, Reading Laboratory, Earley Gate, Whiteknights Road, Reading RG6 6BZ, United Kingdom

    ABSTRACT
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Abstract
Introduction
Procedures
Results & Discussion
References

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
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Abstract
Introduction
Procedures
Results & Discussion
References

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 Delta 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, epsilon p (6-8). Variation in epsilon 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 (epsilon s) solvation shell is swapped for the lower epsilon 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 Delta 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 Delta 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 epsilon 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
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Abstract
Introduction
Procedures
Results & Discussion
References

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 Delta 38-40 could be made with a Calpha -Calpha 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 Delta 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 epsilon s = 80 and epsilon 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 Delta 38-40 mutant, Delta Delta Delta G = (Delta GWT,RED - Delta GWT,OX- (Delta GMUT,RED - Delta 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 Delta Delta Delta 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 Delta Et = Delta VsEs, where Delta 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 epsilon 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, epsilon 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.


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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 (Delta Delta GWT:AA = Delta GWT - Delta GAA), pKaWT = pKaAA + Delta pKaWT:AA, with Delta pKaWT:AA = (1/2.303RT)Delta Delta GWT:AA, where R is the universal gas constant and T the absolute temperature. The terms Delta GWT and Delta 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 epsilon p and epsilon s. Models with low epsilon 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, Delta 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 epsilon p (6) and the use of lower epsilon p together with an empirical estimate of the favorable entropic contribution associated with water liberation from the first hydration shell (8).

    RESULTS AND DISCUSSION
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Abstract
Introduction
Procedures
Results & Discussion
References

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 Delta Delta Gs, WT to (E37Q, E38Q, E37Q/E38Q) mutants, for this hypothesis with the epsilon 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.


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Fig. 2.   Mutated DsbA residues in relation to the active site. The Calpha 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 Delta 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 Delta 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 epsilon 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 Delta 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 Delta 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 Delta 38-40 mutant calculations, both His32 and Glu24 contributions almost cancel on differencing.

Calculated Cys30 thiolate contributions to Delta Delta Delta G are compared with experimental values derived from Keq ratios (11) for WT versus Delta 38-40 over a range of added NaCl concentrations (Table I). The approximations in the calculations (modeled Delta 38-40 conformation, ionizable charge assignment, and Keq contribution from Cys30 thiolate alone included) combined with the small Delta Delta Delta G values (thermal energy or less) suggest that qualitative rather than quantitative comparisons should be made. It can be seen that the epsilon 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 epsilon p values underestimate these interactions. Within the epsilon 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 Delta 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 Delta 38-40 mutation (11) compares with a value of 0.3 by epsilon 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 Delta 38-40 mutant, but more detailed assessment must await full difference calculations between the two WT proteins.

                              
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Table I
Salt dependence of calculated and measured (using Keq) Delta Delta Delta Gs for DsbA WT and Delta 38-40
Calculated Cys30 thiolate stabilization, differenced between WT and Delta 38-40 (Delta Delta Delta 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 Delta 38-40 relative to WT. Calculation methods are listed as (varepsilon p, varepsilon s) or as varepsilon 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 epsilon p model for Cys30 interactions and Keq measurements. The remaining discrepancy, such as underestimation of experimental values with epsilon p = 4, could signal the breakdown of the various assumptions and/or modeling insufficiency. For example, choice of epsilon p within the lower range (typically 2-4) remains an open question, and epsilon p < 4 would yield higher calculated values. The large difference in scale between calculated values of Delta Delta Delta G (Table I) for epsilon p = 4 and higher epsilon p models is due to the largely through-protein nature of the (38-40)/thiolate interactions, suggesting that measurements with Delta 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 epsilon 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 epsilon p is varied to give the best match to experiment, the result tends toward a higher value (e.g. epsilon 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 epsilon 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 Delta pKa for Cys30 together with an overall set of small Delta pKas that tend toward protein stabilization. Also included is the epsilon p = 4 model with the suggested empirical modification to account for hydration entropy change upon charge burial in full pKa calculations (8).

Distributions of Delta 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 epsilon 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 Delta pKas. Modification of the higher epsilon 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 epsilon 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 epsilon p models cannot escape from a general underestimation of electrostatic interactions that leaves the Cys30 Delta pKa close to zero and in contrast with experiment.


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Fig. 3.   Ranges of calculated Delta pKa for ionizable groups in DsbA WT, according to different models. Each panel plots the number of calculated Delta pKas for intervals over the range from 5 Delta pKa units stabilizing (left side) to 5 units destabilizing (right side). Each panel records the experimental (3, 11) and calculated Cys30 Delta pKa for comparison and is labeled with the relevant calculation model.

With regard to the overall distribution of Delta pKas, the unmodified epsilon 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 Delta pKas tending toward the moderate overall stabilization that is the basis of success in the higher epsilon p and epsilon eff = 50 models (Fig. 3). One of the largest Delta pKa shifts upon modification of the epsilon p = 4 model is for Cys30, arising from the significant thiolate burial within DsbA. Whereas the modified epsilon p = 4 model can target both the overall Delta pKa distribution and specific large values, such as that of Cys30, the cost of reducing all charge interactions in the higher epsilon p and epsilon eff = 50 models is likely to be the omission of those larger Delta pKas that may be of functional interest. The presence of large calculated Delta pKas other than that of Cys30 in this qualitative application of the modified epsilon 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 epsilon 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 Delta pKa provides a crucial test that higher epsilon p models fail. Because the modified epsilon p = 4 model recovers a reasonable (moderately stabilizing) Delta pKa profile as well as the Cys30 Delta pKa, potential clearly exists for detailed model development against proteins with well characterized pH-dependent properties.

    FOOTNOTES

* This work was supported by Biotechnology and Biological Sciences Research Council of the United Kingdom.The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Dagger To whom correspondence should be addressed. Tel.: 44-0-118-935-7142; Fax: 44-0-118-926-7917.

1 The abbreviations used are: WT, wild type; FD, finite difference.

    REFERENCES
Top
Abstract
Introduction
Procedures
Results & Discussion
References

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