Do salt bridges stabilize proteins? A continuum electrostatic analysis

The electrostatic contribution to the free energy of folding was calculated for 21 salt bridges in 9 protein X-ray crystal structures using a continuum electrostatic approach with the DELPHI computer-program package. The majority (17) were found to be electrostatically destabilizing; the average free energy change, which is analogous to mutation of salt bridging side chains to hydrophobic isosteres, was calculated to be 3.5 kcal/mol. This is fundamentally different from stability measurements using pKa shifts, which effectively measure the strength of a salt bridge relative to 1 or more charged hydrogen bonds. The calculated effect was due to a large, unfavorable desolvation contribution that was not fully compensated by favorable interactions within the salt bridge and between salt-bridge partners and other polar and charged groups in the folded protein. Some of the salt bridges were studied in further detail to determine the effect of the choice of values for atomic radii, internal protein dielectric constant, and ionic strength used in the calculations. Increased ionic strength resulted in little or no change in calculated stability for 3 of 4 salt bridges over a range of 0.1-0.9 M. The results suggest that mutation of salt bridges, particularly those that are buried, to "hydrophobic bridges" (that pack at least as well as wild type) can result in proteins with increased stability. Due to the large penalty for burying uncompensated ionizable groups, salt bridges could help to limit the number of low free energy conformations of a molecule or complex and thus play a role in determining specificity (i.e., the uniqueness of a protein fold or protein-ligand binding geometry).     

Salt bridge stability in monomeric proteins.

Here, we present the results of continuum electrostatic calculations on a dataset of 222 non-equivalent salt bridges derived from 36 non-homologous high-resolution monomeric protein crystal structures. Most of the salt bridges in our dataset are stabilizing, regardless of whether they are buried or exposed, isolated or networked, hydrogen bonded or non-hydrogen bonded. One-third of the salt bridges in our dataset are buried in the protein core, with the remainder exposed to the solvent. The difference in the dielectric properties of water versus the hydrophobic protein interior cost buried salt bridges large desolvation penalties. However, the electrostatic interactions both between the salt-bridging side-chains, and between the salt bridges and charges in their protein surroundings, are also stronger in the interior, due to the absence of solvent screening. Even large desolvation penalties for burying salt bridges are frequently more than compensated for, primarily by the electrostatic interactions between the salt-bridging side-chains. In networked salt bridges both types of electrostatic interactions, those between the salt-bridging side-chains, and those between the salt bridge and its protein environment, are of similar magnitudes. In particular, a major finding of this work is that salt bridge geometry is a critical factor in determining salt bridge stability. Salt bridges with favorable geometrical positioning of the interacting side-chain charged groups are likely to be stabilizing anywhere in the protein structure. We further find that most of the salt bridges are formed between residues that are relatively near each other in the sequence.     

Salt bridges destabilize a leucine zipper designed for maximized ion pairing between helices

Interhelical salt bridges are common in leucine zippers and are thought to stabilize the coiled coil conformation. Here we present a detailed thermodynamic investigation of the designed, disulfide-linked leucine zipper AB(SS) whose high-resolution NMR structure shows six interhelical ion pairs between heptad positions g of one helix and e' of the other helix but no ion pairing within single helices. The average pK(a) value of the Glu side chain carboxyl groups of AB(SS) is slightly higher than the pK(a) of a freely accessible Glu in an unfolded peptide [Marti, D. N., Jelesarov, I., and Bosshard, H. R. (2000) Biochemistry 39, 12804-12818]. This indicates that the salt bridges are destabilizing, a prediction we now have confirmed by determining the pH +/- stability profile of AB(SS). Circular dichroism-monitored unfolding by urea and by heating and differential scanning calorimetry show that the coiled coil conformation is approximately 5 kJ/mol more stable when salt bridges are broken by protonation of the carboxyl side chains. Using guanidinium chloride as the denaturant, the increase in the free energy of unfolding on protonation of the carboxyl side chains is larger, approximately 17 kJ/mol. The discrepancy between urea and guanidinium chloride unfolding can be ascribed to the ionic nature of guanidinium chloride, which screens charge-charge interactions. This work demonstrates the difficulty of predicting the energetic contribution of salt bridges from structural data alone even in a case where the ion pairs are seen in high-resolution NMR structures. The reason is that the contribution to stability results from a fine balance between energetically favorable Coulombic attractions and unfavorable desolvation of charges and conformational constraints of the residues involved in ion pairing. The apparent discrepancy between the results presented here and mutational studies indicating stabilization by salt bridges is discussed and resolved. An explanation is proposed for why interhelical salt bridges are frequently found in natural coiled coils despite evidence that they do not directly contribute to stability.     

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.     

Thermal versus guanidine-induced unfolding of ubiquitin. An analysis in terms of the contributions from charge-charge interactions to protein stability.

We have characterized the guanidine-induced unfolding of both yeast and bovine ubiquitin at 25 degrees C and in the acidic pH range on the basis of fluorescence and circular dichroism measurements. Unfolding Gibbs energy changes calculated by linear extrapolation from high guanidine unfolding data are found to depend very weakly on pH. A simple explanation for this result involves the two following assumptions: (1) charged atoms of ionizable groups are exposed to the solvent in native ubiquitin (as supported by accessible surface area calculations), and Gibbs energy contributions associated with charge desolvation upon folding (a source of pK shifts) are small; (2) charge-charge interactions (another source of pK shifts upon folding) are screened out in concentrated guanidinium chloride solutions. We have also characterized the thermal unfolding of both proteins using differential scanning calorimetry. Unfolding Gibbs energy changes calculated from the calorimetric data do depend strongly on pH, a result that we attribute to the pH dependence of charge-charge interactions (not eliminated in the absence of guanidine). In fact, we find good agreement between the difference between the two series of experimental unfolding Gibbs energy changes (determined from high guanidine unfolding data by linear extrapolation and from thermal denaturation data in the absence of guanidine) and the theoretical estimates of the contribution from charge-charge interactions to the Gibbs energy change for ubiquitin unfolding obtained by using the solvent-accessibility-corrected Tanford-Kirkwood model, together with the Bashford-Karplus (reduced-set-of-sites) approximation. This contribution is found to be stabilizing at neutral pH, because most charged groups on the native protein interact mainly with groups of the opposite charge, a fact that, together with the absence of large charge-desolvation contributions, may explain the high stability of ubiquitin at neutral pH. In general, our analysis suggests the possibility of enhancing protein thermal stability by adequately redesigning the distribution of solvent-exposed, charged residues on the native protein surface.     

Contribution of surface salt bridges to protein stability: guidelines for protein engineering

The small globular protein, ubiquitin, contains a pair of oppositely charged residues, K11 and E34, that according to the three-dimensional structure are located on the surface of this protein with a spatial orientation characteristic of a salt bridge. We investigated the strength of this salt bridge and its contribution to the global stability of the ubiquitin molecule. Using the "double mutant cycle" analysis, the strength of the pairwise interactions between K11 and E34 was estimated to be favorable by 3.6kJ/mol. Further, the salt bridge of the reverse orientation, i.e. E11/K34, can be formed and is found to have a strength (3.8kJ/mol) similar to that of the K11/E34 pair. However, the global stability of the K11/E34 variant of ubiquitin is 2.2kJ/mol higher than that of the E11/K34 variant. The difference in the contribution of the opposing salt bridge orientations to the overall stability of the ubiquitin molecule is attributed to the difference in the charge-charge interactions between residues forming the salt bridge and the rest of the ionizable groups in this protein. On the basis of these results, we concluded that surface salt bridges are stabilizing, but their contribution to the overall protein stability is strongly context-dependent, with charge-charge interactions being the largest determinant. Analysis of 16 salt bridges from six different proteins, for which detailed experimental data on energetics have been reported, support the conclusions made from the analysis of the salt bridge in ubiquitin. Implications of these findings for engineering proteins with enhanced thermostability are discussed.     

Electrostatic interactions in leucine zippers: thermodynamic analysis of the contributions of Glu and His residues and the effect of mutating salt bridges

Electrostatic interactions play a complex role in stabilizing proteins. Here, we present a rigorous thermodynamic analysis of the contribution of individual Glu and His residues to the relative pH-dependent stability of the designed disulfide-linked leucine zipper AB(SS). The contribution of an ionized side-chain to the pH-dependent stability is related to the shift of the pK(a) induced by folding of the coiled coil structure. pK(a)(F) values of ten Glu and two His side-chains in folded AB(SS) and the corresponding pK(a)(U) values in unfolded peptides with partial sequences of AB(SS) were determined by 1H NMR spectroscopy: of four Glu residues not involved in ion pairing, two are destabilizing (-5.6 kJ mol(-1)) and two are interacting with the positive alpha-helix dipoles and are thus stabilizing (+3.8 kJ mol(-1)) in charged form. The two His residues positioned in the C-terminal moiety of AB(SS) interact with the negative alpha-helix dipoles resulting in net stabilization of the coiled coil conformation carrying charged His (-2.6 kJ mol(-1)). Of the six Glu residues involved in inter-helical salt bridges, three are destabilizing and three are stabilizing in charged form, the net contribution of salt-bridged Glu side-chains being destabilizing (-1.1 kJ mol(-1)). The sum of the individual contributions of protonated Glu and His to the higher stability of AB(SS) at acidic pH (-5.4 kJ mol(-1)) agrees with the difference in stability determined by thermal unfolding at pH 8 and pH 2 (-5.3 kJ mol(-1)). To confirm salt bridge formation, the positive charge of the basic partner residue of one stabilizing and one destabilizing Glu was removed by isosteric mutations (Lys-->norleucine, Arg-->norvaline). Both mutations destabilize the coiled coil conformation at neutral pH and increase the pK(a) of the formerly ion-paired Glu side-chain, verifying the formation of a salt bridge even in the case where a charged side-chain is destabilizing. Because removing charges by a double mutation cycle mainly discloses the immediate charge-charge effect, mutational analysis tends to overestimate the overall energetic contribution of salt bridges to protein stability.     

Electrostatic contribution to the thermodynamic and kinetic stability of the homotrimeric coiled coil Lpp-56: A computational study

The protein moiety of the Braun's E. coli outer membrane lipoprotein (Lpp-56) is an attractive object of biophysical investigation in several aspects. It is a homotrimeric, parallel coiled coil, a class of coiled coils whose stability and folding have been studied only occasionally. Lpp-56 possesses unique structural properties and exhibits extremely low rates of folding and unfolding. It is natural to ask how the specificity of the structure determines the extraordinary physical chemical properties of this protein. Recently, a seemingly controversial data on the stability and unfolding rate of Lpp-56 have been published (Dragan et al., Biochemistry 2004;43: 14891-14900; Bjelic et al., Biochemistry 2006;45:8931-8939). The unfolding rate constant measured using GdmCl as the denaturing agent, though extremely low, was substantially higher than that obtained on the basis of thermal unfolding. If this large difference arises from the effect of screening of electrostatic interactions induced by GdmCl, electrostatic interactions would appear to be an important factor determining the unusual properties of Lpp-56. We present here a computational analysis of the electrostatic properties of Lpp-56 combining molecular dynamics simulations and continuum pK calculations. The pH-dependence of the unfolding free energy is predicted in good agreement with the experimental data: the change in DeltaG between pH 3 and pH 7 is approximately 60 kJ mol(-1). The results suggest that the difference in the stability of the protein observed using different experimental methods is mainly because of the effect of the reduction of electrostatic interactions when the salt (GdmCl) concentration increases. We also find that the occupancy of the interhelical salt bridges is unusually high. We hypothesize that electrostatic interactions, and the interhelical salt bridges in particular, are an important factor determining the low unfolding rate of Lpp-56.     

Residual electrostatic effects in the unfolded state of the N-terminal domain of L9 can be attributed to nonspecific nonlocal charge-charge interactions

Residual electrostatic interactions in the unfolded state of the N-terminal domain of L9 (NTL9) were found by Kuhlman et al. [(1999) Biochemistry 38, 4896-4903]. These residual interactions are analyzed here by the Gaussian-chain model [Zhou, H.-X. (2002) Proc. Natl. Acad. Sci. U.S.A. 99, 3569-3574]. The original model is made more realistic by replacing "standard" model-compound pK(a) values for ionizable groups by those measured by Kuhlman et al. in peptide fragments of NTL9. The predicted pH dependence of the unfolding free energy is in agreement with experiment over the pH range of 1-7 at ionic strengths of 100 and 750 mM. This indicates that the residual electrostatic effects in the unfolded state of NTL9 can be attributed to nonspecific nonlocal charge-charge interactions.     

Salt bridge as a gatekeeper against partial unfolding

Salt bridges are frequently observed in protein structures. Because the energetic contribution of salt bridges is strongly dependent on the environmental context, salt bridges are believed to contribute to the structural specificity rather than the stability. To test the role of salt bridges in enhancing structural specificity, we investigated the contribution of a salt bridge to the energetics of native‐state partial unfolding in a cysteine‐free version of Escherichia coli ribonuclease H (RNase H*). Thermolysin cleaves a protruding loop of RNase H^* through transient partial unfolding under native conditions. Lys86 and Asp108 in RNase H^* form a partially buried salt bridge that tethers the protruding loop. Investigation of the global stability of K86Q/D108N RNase H^* showed that the salt bridge does not significantly contribute to the global stability. However, K86Q/D108N RNase H^* is greatly more susceptible to proteolysis by thermolysin than wild‐type RNase H^* is. The free energy for partial unfolding determined by native‐state proteolysis indicates that the salt bridge significantly increases the energy for partial unfolding by destabilizing the partially unfolded form. Double mutant cycles with single and double mutations of the salt bridge suggest that the partially unfolded form is destabilized due to a significant decrease in the interaction energy between Lys86 and Asp108 upon partial unfolding. This study demonstrates that, even in the case that a salt bridge does not contribute to the global stability, the salt bridge may function as a gatekeeper against partial unfolding that disturbs the optimal geometry of the salt bridge.     

Strength and co-operativity of contributions of surface salt bridges to protein stability

Many of the interactions that stabilize proteins are co-operative and cannot be reduced to a sum of pairwise interactions. Such interactions may be analysed by protein engineering methods using multiple thermodynamic cycles comprising wild-type protein and all combinations of mutants in the interacting residues. There is a triad of charged residues on the surface of barnase, comprising residues Asp8, Asp12 and Arg110, that interact by forming two exposed salt bridges. The three residues have been mutated to alanine to give all the single, double and triple mutants. The free energies of unfolding of wild-type and the seven mutant proteins have been determined and the results analysed to give the contributions of the residues in the two salt bridges to protein stability. It is possible to isolate the energies of forming the salt bridges relative to the solvation of the separated ions by water. In the intact triad, the apparent contribution to the stabilization energy of the protein of the salt bridge between Asp12 and Arg110 is -1.25 kcal mol-1, whereas that of the salt bridge between Asp8 with Arg110 is -0.98 kcal mol-1. The strengths of the two salt bridges are coupled: the energy of each is reduced by 0.77 kcal mol-1 when the other is absent. The salt-linked triad, relative to alanine residues at the same positions, does not contribute to the stability of the protein since the favourable interactions of the salt bridges are more than offset by other electrostatic and non-electrostatic energy terms. Salt-linked triads occur in other proteins, for example, haemoglobin, where the energy of only the salt-bridge term is important and so the coupling of salt bridges could be of general importance to the stability and function of proteins.     

Estimating the contribution of engineered surface electrostatic interactions to protein stability by using double-mutant cycles

Coulombic interactions between charges on the surface of proteins contribute to stability. It is difficult, however, to estimate their importance by protein engineering methods because mutation of one residue in an ion pair alters the energetics of many interactions in addition to the coulombic energy between the two components. We have estimated the interaction energy between two charged residues, Asp-12 and Arg-16, in an alpha-helix on the surface of a barnase mutant by invoking a double-mutant cycle involving wild-type enzyme (Asp-12, Thr-16), the single mutants Thr----Arg-16 and Asp----Ala-12, and the double mutant Asp----Ala-12, Thr----Arg-16. The changes in free energy of unfolding of the single mutants are not additive because of the coulombic interaction energy. Additivity is restored at high concentrations of salt that shield electrostatic interactions. The geometry of the ion pair in the mutant was assumed to be the same as that in the highly homologous ribonuclease from Bacillus intermedius, binase, which has Asp-12 and Arg-16 in the native enzyme. The ion pair does not form a hydrogen-bonded salt bridge, but the charges are separated by 5-6 A. The mutant barnase containing the ion pair Asp-12/Arg-16 is more stable than wild type by 0.5 kcal/mol, but only a part of the increased stability is attributable to the electrostatic interaction. We present a formal analysis of how double-mutant cycles can be used to measure the energetics of pairwise interactions.     

Electrostatic contributions to T4 lysozyme stability: solvent-exposed charges versus semi-buried salt bridges

We carried our Poisson-Boltzmann (PB) calculations for the effects of charge reversal at five exposed sites (K16E, R119E, K135E, K147E, and R154E) and charge neutralization and proton titration of the H31-D70 semi-buried salt bridge on the stability of T4 lysozyme. Instead of the widely used solvent-exclusion (SE) surface, we used the van der Waals (vdW) surface as the boundary between the protein and solvent dielectrics (a protocol established in our earlier study on charge mutations in barnase). By including residual charge-charge interactions in the unfolded state, the five charge reversal mutations were found to have DeltaDeltaG(unfold) from -1.6 to 1.3 kcal/mol. This indicates that the variable effects of charge reversal observed by Matthews and co-workers are not unexpected. The H31N, D70N, and H31N/D70N mutations were found to destabilize the protein by 2.9, 1.3, and 1.6 kcal/mol, and the pK(a) values of H31 and D70 were shifted to 9.4 and 0.6, respectively. These results are in good accord with experimental data of Dahlquist and co-workers. In contrast, if the SE surface were used, the H31N/D70N mutant would be more stable than the wild-type protein by 1.3 kcal/mol. From these and additional results for 27 charge mutations on five other proteins, we conclude that 1) the popular view that electrostatic interactions are generally destabilizing may have been based on overestimated desolvation cost as a result of using the SE surface as the dielectric boundary; and 2) while solvent-exposed charges may not reliably contribute to protein stability, semi-buried salt bridges can provide significant stabilization.     

Statistical analysis of protein structures suggests that buried ionizable residues in proteins are hydrogen bonded or form salt bridges

It is well known that nonpolar residues are largely buried in the interior of proteins, whereas polar and ionizable residues tend to be more localized on the protein surface where they are solvent exposed. Such a distribution of residues between surface and interior is well understood from a thermodynamic point: nonpolar side chains are excluded from the contact with the solvent water, whereas polar and ionizable groups have favorable interactions with the water and thus are preferred at the protein surface. However, there is an increasing amount of information suggesting that polar and ionizable residues do occur in the protein core, including at positions that have no known functional importance. This is inconsistent with the observations that dehydration of polar and in particular ionizable groups is very energetically unfavorable. To resolve this, we performed a detailed analysis of the distribution of fractional burial of polar and ionizable residues using a large set of ?2600 nonhomologous protein structures. We show that when ionizable residues are fully buried, the vast majority of them form hydrogen bonds and/or salt bridges with other polar/ionizable groups. This observation resolves an apparent contradiction: the energetic penalty of dehydration of polar/ionizable groups is paid off by favorable energy of hydrogen bonding and/or salt bridge formation in the protein interior. Our conclusion agrees well with the previous findings based on the continuum models for electrostatic interactions in proteins. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

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.     

Empirical parametrization of pK values for carboxylic acids in proteins using a genetic algorithm

Considerable effort has been devoted to the development of theoretical electrostatic methods to predict the pK values of ionizable residues in proteins. However, predictions appear often to be still at the qualitative or semi-quantitative level. We believe that, with the increasing number experimentally available pK values for proteins of known structure, an alternative approach becomes feasible: the empirical parametrization of the experimental protein pK database. Of course, in the long term, this empirical approach is no substitute for rigorous electrostatic analysis but, in the short term, it may prove to have useful predictive power and it may help to pinpoint the main structural determinants of pK values in proteins. Here we demonstrate the feasibility of the parametrization approach by fitting (using a genetic algorithm as fitting tool) the database for carboxylic acid pK values in proteins on the basis of an empirical equation that takes into account the two following kinds of effects: (1) long-range charge-charge interactions; (2) interactions of the given carboxylic acid group with its environment in the protein, which are described in terms of contributions from the different kind of atoms present in the protein (atomic contributions).     

Evaluation of direct and cooperative contributions towards the strength of buried hydrogen bonds and salt bridges

An experimental approach to evaluate the net binding free energy of buried hydrogen bonds and salt bridges is presented. The approach, which involves a modified multiple-mutant cycle protocol, was applied to selected interactions between TEM-1-beta-lactamase and its protein inhibitor, BLIP. The selected interactions (two salt bridges and two hydrogen bonds) all involving BLIP-D49, define a distinct binding unit. The penta mutant, where all side-chains constructing the binding unit were mutated to Ala, was used as a reference state to which combinations of side-chains were introduced. At first, pairs of interacting residues were added allowing the determination of interaction energies in the absence of neighbors, using double mutant cycles. Addition of neighboring residues allowed the evaluation of their cooperative effects on the interaction. The two isolated salt bridges were either neutral or repulsive whereas the two hydrogen bonds contribute 0.3 kcal mol(-1 )each. Conversely, a double mutant cycle analysis of these interactions in their native environment showed that they all stabilize the complex by 1-1.5 kcal mol(-1). Examination of the effects of neighboring residues on each of the interactions revealed that the formation of a salt bridge triad, which involves two connected salt bridges, had a strong cooperative effect on stabilizing the complex independent of the presence or absence of additional neighbors. These results demonstrate the importance of forming net-works of buried salt bridges. We present theoretical electrostatic calculations which predict the observed mode of cooperativity, and suggest that the cooperative networking effect results from the favorable contribution of the protein to the interaction. Furthermore, a good correlation between calculated and experimentally determined interaction energies for the two salt bridges, and to a lesser extent for the two hydrogen bonds, is shown. The data analysis was performed on values of DeltaDeltaG(double dagger)K(d) which reflect the strength of short range interactions, while DeltaDeltaG(o)K(D) values which include the effects of long range electrostatic forces that alter specifically DeltaDeltaG(double dagger)k(a) were treated separately.     

Charge-charge interactions influence the denatured state ensemble and contribute to protein stability

Several recent studies have shown that it is possible to increase protein stability by improving electrostatic interactions among charged groups on the surface of the folded protein. However, the stability increases are considerably smaller than predicted by a simple Coulomb's law calculation, and in some cases, a charge reversal on the surface leads to a decrease in stability when an increase was predicted. These results suggest that favorable charge-charge interactions are important in determining the denatured state ensemble, and that the free energy of the denatured state may be decreased more than that of the native state by reversing the charge of a side chain. We suggest that when the hydrophobic and hydrogen bonding interactions that stabilize the folded state are disrupted, the unfolded polypeptide chain rearranges to compact conformations with favorable long-range electrostatic interactions. These charge-charge interactions in the denatured state will reduce the net contribution of electrostatic interactions to protein stability and will help determine the denatured state ensemble. To support this idea, we show that the denatured state ensemble of ribonuclease Sa is considerably more compact at pH 7 where favorable charge-charge interactions are possible than at pH 3, where unfavorable electrostatic repulsion among the positive charges causes an expansion of the denatured state ensemble. Further support is provided by studies of the ionic strength dependence of the stability of charge-reversal mutants of ribonuclease Sa. These results may have important implications for the mechanism of protein folding.     

Electrostatic calculations of the pKa values of ionizable groups in bacteriorhodopsin.

The effects of solvation and charge-charge interactions on the pKa of ionizable groups in bacteriorhodopsin have been studied using a macroscopic dielectric model with atom-level detail. The calculations are based on the atomic model for bacteriorhodopsin recently proposed by Henderson et al. Even if the structural data are not resolved at the atomic level, such calculations can indicate the quality of the model, outline some general aspects of electrostatic interactions in membrane proteins, and predict some features. The effects of structural uncertainties on the calculations have been investigated by conformational sampling. The results are in reasonable agreement with experimental measurements of several unusually large pKa shifts (e.g. the experimental findings that Asp96 and Asp115 are protonated in the ground state over a wide pH range). In general, we find that the large unfavorable desolvation energies of forming charges in the protein interior must be compensated by strong favorable charge-charge interactions, with the result that the titrations of many ionizable groups are strongly coupled to each other. We find several instances of complex titration behavior due to strong electrostatic interactions between titrating sites, and suggest that such behavior may be common in proton transfer systems. We also propose that they can help to resolve structural ambiguities in the currently available density map. In particular, we find better agreement between theory and experiment when a structural ambiguity in the position of the Arg82 side-chain is resolved in favor of a position near the Schiff base.     

Energetics of charge-charge interactions between residues adjacent in sequence

Statistical analysis of the residue separation between a pair of ionizable side chains within 4 ? of each other was performed on a set of 1560 non-homologous PDB structures. We found that the frequency of pairs of like charges (i.e., pairs consisting of acidic residues Asp and Glu or pairs consisting of basic residues Arg and Lys) is two orders of magnitude lower than the pairs of oppositely charged residues (salt-bridges). We also found that for pairs of like charges the distribution is skewed dramatically towards short residue separation (<3). On the basis of these observations, we hypothesize that at short residue separation the repulsion between charges does not contribute much to the protein stability and the effects are largely dominated by the long range charge-charge interactions with other ionizable groups in the protein molecule. To test this hypothesis, we incorporated various pairs of charged residues at position 63 and 64 of ubiquitin and compared the stabilities of these variants. We also performed calculations of the expected changes in the charge-charge interactions. A very good correlation between experimental changes in the stability of ubiquitin variants, and changes in the energy of charge-charge interactions provides support for the hypothesis that a pair of ionizable residues next to each other in sequence modulates protein stability via long range charge-charge interactions with the rest of the protein.