MCCE analysis of the pKas of introduced buried acids and bases in staphylococcal nuclease

The pK(a)s of 96 acids and bases introduced into buried sites in the staphylococcal nuclease protein (SNase) were calculated using the multiconformation continuum electrostatics (MCCE) program and the results compared with experimental values. The pK(a)s are obtained by Monte Carlo sampling of coupled side chain protonation and position as a function of pH. The dependence of the results on the protein dielectric constant (ε(prot)) in the continuum electrostatics analysis and on the Lennard-Jones non-electrostatics parameters was evaluated. The pK(a)s of the introduced residues have a clear dependence on ε(prot,) whereas native ionizable residues do not. The native residues have electrostatic interactions with other residues in the protein favoring ionization, which are larger than the desolvation penalty favoring the neutral state. Increasing ε(prot) scales both terms, which for these residues leads to small changes in pK(a). The introduced residues have a larger desolvation penalty and negligible interactions with residues in the protein. For these residues, changing ε(prot) has a large influence on the calculated pK(a). An ε(prot) of 8-10 and a Lennard-Jones scaling of 0.25 is best here. The X-ray crystal structures of the mutated proteins are found to provide somewhat better results than calculations carried out on mutations made in silico. Initial relaxation of the in silico mutations by Gromacs and extensive side chain rotamer sampling within MCCE can significantly improve the match with experiment.     

Toward accurate prediction of pKa values for internal protein residues: the importance of conformational relaxation and desolvation energy

Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pK(a) prediction informs about proton pathways, thereby revealing detailed acid-base mechanisms. Physics-based methods in the framework of molecular dynamics simulations not only offer pK(a) predictions but also inform about the physical origins of pK(a) shifts and provide details of ionization-induced conformational relaxation and large-scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pK(a) prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pK(a) values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root-mean-square deviation of 1.69 pK units from experiment, and there were only two pK(a)'s with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side-chains in the context of the errors of calculated pK(a) values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pK(a) predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit-solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit-solvent representation may offer improvement of accuracy.     

Progress in the prediction of pKa values in proteins

The pK(a) -cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pK(a) values and protein electrostatics in general. The first round of the pK(a) -cooperative, which challenged computational labs to carry out blind predictions against pK(a) s experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6-10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pK(a) calculations, emphasizing methods that were used by the participants in calculating the blind pK(a) values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pK(a) calculations.     

Calculation of pK(a) in proteins with the microenvironment modulated-screened coulomb potential

The MM-SCP has been applied to predict pK(a) values of titratable residues in wild type and mutants of staphylococcal nuclease (SNase). The calculations were based on crystal structures made available by the Garcia-Moreno Laboratory. In the mutants, mostly deeply buried hydrophobic residues were replaced with ionizable residues, and thus their pK(a) values could be measured and calculated using various methods. The data set used here consisted of a set of WT SNase for which His pK(a) at several ionic strengths had been measured, a set of mutants for which measured pK(a) were available and a set of 11 mutants for which the measured pK(a) were not known at the time of calculation. For this latter set, blind predictions were submitted to the protein pK(a) cooperative, 2009 workshop at Telluride, where the results of the blind predictions were discussed (the RMSD of the submitted set was 1.10 pH units). The calculations on the structures with known pK(a) indicated that in addition to weaknesses of the method, structural issues were observed that led to larger errors (>1) in pK(a) predictions. For example, different crystallographic conditions or steric clashes can lead to differences in the local environment around the titratable residue, which can produce large differences in the calculated pK(a) . To gain further insight into the reliability of the MM-SCP, pK(a) of an extended set of 54 proteins belonging to several structural classes were carried out. Here some initial results from this study are reported to help place the SNase results in the appropriate context.     

pK(a) calculations of calbindin D(9k): effects of Ca(2+) binding, protein dielectric constant, and ionic strength

Calbindin is a small (75 residues) helix-loop-helix ("EF-hand") calcium-binding protein belonging to the calmodulin superfamily. It binds two Ca(2+) ions. Continuum electrostatics in combination with the boundary element method was employed for the calculation of the acid-dissociation constants K(a) (pK(a) = -log K(a)) values of all titratable residues in the protein. The objectives were to determine quantitatively the effects of divalent ion binding and small ion-induced structural changes on predicted pK(a)'s. Computations were carried out for the apo and holo form of calbindin, for which both X-ray and NMR structures were available. Comparison was made with several sets of experimental pK(a) values determined by NMR spectroscopy. Different choices of the dielectric constant (ranging from 4 to 78.5) for calbindin and variations in ionic strength (from 0 to 0.3 M) were investigated in a systematic fashion. Removal of the two bound Ca(2+) ions increases the pK(a) values of all residues if no conformational changes were allowed. If conformational differences between the apo and holo were accounted for, shifts in either direction were observed. Titrating groups that are directly involved in Ca(2+) binding (Asp and Glu) required a dielectric constant of 78.5 for the holo structure to obtain a reasonable estimate of their pK(a)'s. For the apo structure, passable values for the pK(a)'s of these ligating groups could be determined if the structure was allowed to relax upon ion removal.     

Acidic range titration of HEWL using a constant-pH molecular dynamics method

In this work, we present the first application to a protein of the stochastic constant-pH molecular dynamics (MD) method with the inclusion of proton tautomerism. The acidic titration of HEWL was performed under different conditions. Both generalized reaction field (GRF) and particle mesh Ewald (PME) methods were used in the treatment of the long range electrostatics and, even though the PME simulations revealed to be more stable, the better results were obtained using GRF (pK(a) RMSD of 0.82 for GRF and 1.13 for PME). The results using PME at different dielectric constants (2, 4, and 8) also revealed that there was no significant improvement in pK(a)'s prediction upon increasing the dielectric constant. The secondary structure analysis of HEWL revealed a remarkably stable protein in the acidic pH range. The beta-sheet strands (unlike the alpha-helices) seem to be destabilized upon pH decrease, suggesting that the beta-domain is less stable than the alpha-domain. The four principal alpha-helices were also ordered according to their stability in the acidic pH range and the results (4 < 1 < 2 approximately = 3) were consistent with the ones obtained in thermal denaturation studies.     

Spatial distribution of dielectric shielding in the interior of Pyrococcus furiosus rubredoxin as sampled in the subnanosecond timeframe by hydrogen exchange

Experimental pK values of ionizable sidechains provide the most direct test for models representing dielectric shielding within the interior of a protein. However, only the strongly shifted pK values are particularly useful for discriminating among models. NMR titration studies have usually found only one or two such shifted pK values in each protein, so that the fitting of the experimental data to a uniform internal dielectric (epsilon(int)) model is not well constrained. The observed variation among proteins for such epsilon(int) estimates may reflect nonuniformity of dielectric shielding within each protein interior or qualitative differences between individual proteins. The differential amide kinetic acidities for a series of metal-substituted rubredoxins are shown to be consistent with Poisson-Boltzmann predictions of dielectric shielding that is relatively uniform for all of the amides that are sensitive to the metal charge, a region which corresponds to roughly 1/3 of the internal volume. The effective epsilon(int) values near 6 that are found in this study are significantly lower than many such estimates derived from sidechain pK measurements. The differing timeframes in which dielectric relaxation can respond to the highly transient peptide anion as compared to the longer lived states of the charged sidechains offers an explanation for the lower apparent dielectric constant deduced from these measurements.     

Is the prediction of pKa values by constant-pH molecular dynamics being hindered by inherited problems?

In this study, we investigate two factors that can hinder the performance of constant-pH molecular dynamics methods in predicting protein pK(a) values, using hen egg white lysozyme as a test system. The first factor is related to the molecular definition and pK(a) value of model compounds in the Poisson-Boltzmann framework. We address this by defining the model compound as a molecular fragment with an associated pK(a) value that is calibrated against experimental data, which results in a decrease of 0.12 units in pK(a) errors. The second addressed factor is the possibility that detrimental structural distortions are being introduced in the simulations by the underlying molecular mechanics force field. This issue is investigated by analyzing how the gradual structural rearrangements affect the predicted pK(a) values. The two GROMOS force fields studied here (43A1 and 53A6) yield good pK(a) predictions, although a time-dependent performance is observed: 43A1 performs better after a few nanoseconds of structural reorganization (pK(a) errors of ~0.45), while 53A6 gives the best prediction right at the first nanosecond (pK(a) errors of 0.42). These results suggest that the good performance of constant-pH molecular dynamics methods could be further improved if these force field limitations were overcome.     

Hydrogen bonding is the prime determinant of carboxyl pKa values at the N-termini of alpha-helices

Experimentally determined mean pK(a) values of carboxyl residues located at the N-termini of alpha-helices are lower than their overall mean values. Here, we perform three types of analyses to account for this phenomenon. We estimate the magnitude of the helix macrodipole to determine its potential role in lowering carboxyl pK(a) values at the N-termini. No correlation between the magnitude of the macrodipole and the pK(a) values is observed. Using the pK(a) program propKa we compare the molecular surroundings of 18 N-termini carboxyl residues versus 233 protein carboxyl groups from a previously studied database. Although pK(a) lowering interactions at the N-termini are similar in nature to those encountered in other protein regions, pK(a) lowering backbone and side-chain hydrogen bonds appear in greater number at the N-termini. For both Asp and Glu, there are about 0.5 more hydrogen bonds per residue at the N-termini than in other protein regions, which can be used to explain their lower than average pK(a) values. Using a QM-based pK(a) prediction model, we investigate the chemical environment of the two lowest Asp and the two lowest Glu pK(a) values at the N-termini so as to quantify the effect of various pK(a) determinants. We show that local interactions suffice to account for the acidity of carboxyl residues at the N-termini. The effect of the helix dipole on carboxyl pK(a) values, if any, is marginal. Backbone amide hydrogen bonds constitute the single biggest contributor to the lowest carboxyl pK(a) values at the N-termini. Their estimated pK(a) lowering effects range from about 1.0 to 1.9 pK(a) units.     

Exploring conformational changes coupled to ionization states using a hybrid Rosetta-MCCE protocol

A hybrid protocol combining Rosetta fullatom refinement and Multi-Conformation Continuum Electrostatics (MCCE) to estimate pK(a) is applied to the blind prediction of 94 mutated residues in Staphylococcal nuclease (SNase), as part of the pK(a)-cooperative benchmark test. The standard MCCE method is limited to sidechain conformational changes. The Rosetta refinement protocol is used to add the backbone conformational changes in pK(a) calculations. The non-electrostatic energy component from Rosetta and the electrostatic energy from MCCE are combined to weight the calculated ionization states. Of 63 measured pK(a)s, the root mean squared deviation (RMSD) between the calculated pK(a)s and the measured values is 4.3, showing an improvement compared to the RMSD of 6.6 in the standard MCCE calculations, using a low protein dielectric constant of 4. The breakdown of pK(a) shift from the solution values (ΔpK(a)) shows that the desolvation energy contributes the most in the standard MCCE calculations. Lowering desolvation penalties and optimizing electrostatic interactions with the Rosetta/MCCE protocol reduces the ΔpK(a) to favor the charged states. Analysis also showed that the Rosetta/MCCE protocol samples conformations with pK(a)s close to the solution values. The question remains whether the correct conformational changes coupled to the ionization changes are found here. Nevertheless, a challenge emerges to accurately estimate the reorganization energy, which is not directly measured from the electrostatic environment of the site of interest. Possible improvements to the protocol are also discussed.     

An empirical model for electrostatic interactions in proteins incorporating multiple geometry-dependent dielectric constants

Here we introduce an electrostatic model that treats the complexity of electrostatic interactions in a heterogeneous protein environment by using multiple parameters that take into account variations in protein geometry, local structure, and the type of interacting residues. The optimal values for these parameters were obtained by fitting the model to a large dataset of 260 experimentally determined pK(a) values distributed over 41 proteins. We obtain fits between the calculated and observed values that are significantly better than the null model. The model performs well on the groups that exhibit large pK(a) shifts from solution values in response to the protein environment and compares favorably with other, successful continuum models. The empirically determined values of the parameters correlate well with experimentally observed contributions of hydrogen bonds and ion pairs as well as theoretically predicted magnitudes of charge-charge and charge-polar interactions. The magnitudes of the dielectric constants assigned to different regions of the protein rank according to the strength of the relaxation effects expected for the core, boundary, and surface. The electrostatic interactions in this model are pairwise decomposable and can be calculated rapidly. This model is therefore well suited for the large computations required for simulating protein properties and especially for prediction of mutations for protein design.     

Prediction of protein structural class for the twilight zone sequences

Structural class characterizes the overall folding type of a protein or its domain. This paper develops an accurate method for in silico prediction of structural classes from low homology (twilight zone) protein sequences. The proposed LLSC-PRED method applies linear logistic regression classifier and a custom-designed, feature-based sequence representation to provide predictions. The main advantages of the LLSC-PRED are the comprehensive representation that includes 58 features describing composition and physicochemical properties of the sequences and transparency of the prediction model. The representation also includes predicted secondary structure content, thus for the first time exploring synergy between these two related predictions. Based on tests performed with a large set of 1673 twilight zone domains, the LLSC-PRED's prediction accuracy, which equals over 62%, is shown to be better than accuracy of over a dozen recently published competing in silico methods and similar to accuracy of other, non-transparent classifiers that use the proposed representation.     

Prediction of short loops in intrinsically disordered proteins

A new possibility of predicting short disordered regions (loops) at a small window size (three amino acid residues) by the FoldUnfold program is described. As demonstrated with the example of three G proteins, FoldUnfold predicted almost all existing loops at the positions fitting well the X-ray structural data. The loops predicted in the Ras p21 structure were classified into two types. The loops of the first type display high Debye-Waller factor values, characteristic of the so-called functional loops (flexible loops). The second-type loops had lower Debye-Waller factor values and, consequently, were regarded as the loops connecting secondary structure elements (rigid loops). Comparison of the results predicted by FoldUnfold with the predictions of other programs (PONDR, RONN, DisEMBL, PreLINK, IUPred, GlobPlot 2, and FoldIndex) demonstrated that the first program was much better in predicting the positions of short loops. FoldUnfold made it possible to solve the problem difficult for the other programs, that is, to determine the boundary between the ordered and disordered regions in proteins with a large fraction of disordered regions, exemplified by the ubiquitin-like domain. In particular, FoldUnfold predicted a boundary between the ordered and disordered regions at residues 30 and 31, whereas the other programs predicted the boundary in the range of 28–70 amino acid residues.     

Blind, one-eyed, or eagle-eyed? pKa calculations during blind predictions with staphylococcal nuclease

In the current contribution, the performance of Poisson-Boltzmann-based pK(a) calculations of SNase mutants as part of a blind prediction exercise facilitated by the pK(a) cooperative ("pK(a) _coop") is described. A one parameter setting ("quick&dirty" approach) is used to provide an industry perspective where strong time constraints are frequently encountered. On the one hand, results are analyzed in terms of root mean square deviation performance. Furthermore, the pK(a) calculations are assessed for their ability to properly assign protonation state. For this purpose, a new measure called BIPS (binary protonation state at physiological pH) is introduced. Significant differences were found with both comparison measures based on the class of residues examined. In addition, the performance of PROPKA3 as well as the NULL model is examined on the same data set. Finally, pK(a) calculations on SNase mutants with available structural information have been performed and provide support for our calculation methods. The performance on this subset is better than on the pK(a) cooperative mutation data. In the pK(a) _coop data, no structural information on the generated mutants is available. This suggests the occurrence of a substantial structural rearrangement on the insertion of additional charged groups into SNase, which leads to improved prediction quality.     

Prediction of pKa and redox properties in the thioredoxin superfamily

Electrostatic interactions play important roles in diverse biological phenomena controlling the function of many proteins. Polar molecules can be studied with the FDPB method solving the Poisson-Boltzmann equation on a finite difference grid. A method for the prediction of pK(a)s and redox potentials in the thioredoxin superfamily is introduced. The results are compared with experimental pK(a) data where available, and predictions are made for members lacking such data. Studying CxxC motif variation in the context of different background structures permits analysis of contributions to cysteine DeltapK(a)s. The motif itself and the overall framework regulate pK(a) variation. The reported method includes generation of multiple side-chain rotamers for the CxxC motif and is an effective predictive tool for functional pK(a) variation across the superfamily. Redox potential follows the trend in cysteine pK(a) variation, but some residual discrepancy indicates that a pH-independent factor plays a role in determining redox potentials for at least some members of the superfamily. A possible molecular basis for this feature is discussed.     

Calculation of protein ionization equilibria with conformational sampling: pK(a) of a model leucine zipper, GCN4 and barnase.

The use of conformational ensembles provided by nuclear magnetic resonance (NMR) experiments or generated by molecular dynamics (MD) simulations has been regarded as a useful approach to account for protein motions in the context of pK(a) calculations, yet the idea has been tested occasionally. This is the first report of systematic comparison of pK(a) estimates computed from long multiple MD simulations and NMR ensembles. As model systems, a synthetic leucine zipper, the naturally occurring coiled coil GCN4, and barnase were used. A variety of conformational averaging and titration curve-averaging techniques, or combination thereof, was adopted and/or modified to investigate the effect of extensive global conformational sampling on the accuracy of pK(a) calculations. Clustering of coordinates is proposed as an approach to reduce the vast diversity of MD ensembles to a few structures representative of the average electrostatic properties of the system in solution. Remarkable improvement of the accuracy of pK(a) predictions was achieved by the use of multiple MD simulations. By using multiple trajectories the absolute error in pK(a) predictions for the model leucine zipper was reduced to as low as approximately 0.25 pK(a) units. The validity, advantages, and limitations of explicit conformational sampling by MD, compared with the use of an average structure and a high internal protein dielectric value as means to improve the accuracy of pK(a) calculations, are discussed.     

Direct proton magnetic resonance determination of the pKa of the active center histidine in thiolsubtilisin

The serine proteases constitute a group of endopeptidases whose members owe their catalytic activity to the presence of a catalytic triad of amino acids consisting of a serine, a histidine and an aspartate. The pK(a) values for this histidine have been determined for several cases in which there is a negative charge installed at the serine to mimic the oxyanionic intermediate and related transition state for the catalytic pathway. Instances from this laboratory include (1) replacement of the serine by a cysteine in subtilisin to create a thiolate; (2) formation of monoisopropylphosphoryl-Ser 195 monoanionic phosphodiesters (in trypsin and chymotrypsin, Ser 221 in subtilisins); and (3) tetrahedral boronates formed with peptide boronic acids. The nuclear magnetic resonance (NMR) signals pertinent to this histidine, or signals indirectly reflecting the state of ionization of this histidine, have been used effectively to monitor changes in the active center ionization state. In every case studied, there is elevation of the pK(a) at the histidine when the negative charge is installed at the serine position. Herein is reported the first NMR measurement of the active center His 63 pK(a) in thiolsubtilisin Carlsberg; it is elevated by 3 units compared with the parent enzyme. Using a numerical solution (finite difference) of the Poisson-Boltzmann equation, a protein dielectric constant of 4 provides a good estimate of the experimentally observed pK(a) elevations. Very significantly, a very low protein dielectric constant (epsilon(p) = 3-5) is required in all of the comparisons, and for all three enzymes used (chymotrypsin, trypsin, and subtilisin). Finally, we discuss why the electrostatic perturbation sensed at His of the active center is more amplified by a negative charge on the Ser side than the same charge on the Asp side. A plausible explanation is that the positive charge on the imidazolium ring of the His is localized, with the N(delta 1) carrying a smaller fraction, the N(epsilon 2) carrying the bulk of the positive charge.     

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.     

Optimizing pKa computation in proteins with pH adapted conformations

pK(A) in proteins are determined by electrostatic energy computations using a small number of optimized protein conformations derived from crystal structures. In these protein conformations hydrogen positions and geometries of salt bridges on the protein surface were determined self-consistently with the protonation pattern at three pHs (low, ambient, and high). Considering salt bridges at protein surfaces is most relevant, since they open at low and high pH. In the absence of these conformational changes, computed pK(A)(comp) of acidic (basic) groups in salt bridges underestimate (overestimate) experimental pK(A)(exp), dramatically. The pK(A)(comp) for 15 different proteins with 185 known pK(A)(exp) yield an RMSD of 1.12, comparable with two other methods. One of these methods is fully empirical with many adjustable parameters. The other is also based on electrostatic energy computations using many non-optimized side chain conformers but employs larger dielectric constants at short distances of charge pairs that diminish their electrostatic interactions. These empirical corrections that account implicitly for additional conformational flexibility were needed to describe the energetics of salt bridges appropriately. This is not needed in the present approach. The RMSD of the present approach improves if one considers only strongly shifted pK(A)(exp) in contrast to the other methods under these conditions. Our method allows interpreting pK(A)(comp) in terms of pH dependent hydrogen bonding pattern and salt bridge geometries. A web service is provided to perform pK(A) computations.     

Salt effects on ionization equilibria of histidines in myoglobin

The salt dependence of histidine pK(a) values in sperm whale and horse myoglobin and in histidine-containing peptides was measured by (1)H-NMR spectroscopy. Structure-based pK(a) calculations were performed with continuum methods to test their ability to capture the effects of solution conditions on pK(a) values. The measured pK(a) of most histidines, whether in the protein or in model compounds, increased by 0.3 pH units or more between 0.02 M and 1.5 M NaCl. In myoglobin two histidines (His(48) and His(36)) exhibited a shallower dependence than the average, and one (His(113)) showed a steeper dependence. The (1)H-NMR data suggested that the salt dependence of histidine pK(a) values in the protein was determined primarily by the preferential stabilization of the charged form of histidine with increasing salt concentrations rather than by screening of electrostatic interactions. The magnitude and salt dependence of interactions between ionizable groups were exaggerated in pK(a) calculations with the finite-difference Poisson-Boltzmann method applied to a static structure, even when the protein interior was treated with arbitrarily high dielectric constants. Improvements in continuum methods for calculating salt effects on pK(a) values will require explicit consideration of the salt dependence of model compound pK(a) values used for reference in the calculations.