Conformation and hydrogen ion titration of proteins: a continuum electrostatic model with conformational flexibility.

A new method for including local conformational flexibility in calculations of the hydrogen ion titration of proteins using macroscopic electrostatic models is presented. Intrinsic pKa values and electrostatic interactions between titrating sites are calculated from an ensemble of conformers in which the positions of titrating side chains are systematically varied. The method is applied to the Asp, Glu, and Tyr residues of hen lysozyme. The effects of different minimization and/or sampling protocols for both single-conformer and multi-conformer calculations are studied. For single-conformer calculations it is found that the results are sensitive to the choice of all-hydrogen versus polar-hydrogen-only atomic models and to the minimization protocol chosen. The best overall agreement of single-conformer calculations with experiment is obtained with an all-hydrogen model and either a two-step minimization process or minimization using a high dielectric constant. Multi-conformational calculations give significantly improved agreement with experiment, slightly smaller shifts between model compound pKa values and calculated intrinsic pKa values, and reduced sensitivity of the intrinsic pKa calculations to the initial details of the structure compared to single-conformer calculations. The extent of these improvements depends on the type of minimization used during the generation of conformers, with more extensive minimization giving greater improvements. The ordering of the titrations of the active-site residues, Glu-35 and Asp-52, is particularly sensitive to the minimization and sampling protocols used. The balance of strong site-site interactions in the active site suggests a need for including site-site conformational correlations.     

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.     

Molecular mechanisms of pH-driven conformational transitions of proteins: insights from continuum electrostatics calculations of acid unfolding

The acid unfolding of staphylococcal nuclease (SNase) is very cooperative (Whitten and García-Moreno, Biochemistry 2000;39:14292-14304). As many as seven hydrogen ions (H+) are bound preferentially by the acid-unfolded state relative to the native (N) state in the pH range 3.2-3.9. To investigate the mechanism of acid unfolding, structure-based pKa calculations were performed with a variety of continuum electrostatic methods. The calculations reproduced successfully the H+ binding properties of the N state between pH 5 and 9, but they systematically overestimated the number of H+ bound upon acid unfolding. The calculated pKa values of all carboxylic residues in the N state were more depressed than they should be. The discrepancy between the observed and the calculated H+ uptake upon acid unfolding was not improved by using high protein dielectric constants, structures relaxed with molecular dynamics, or other empirical modifications implemented previously by others to maximize agreement between measured and calculated pKa values. This suggests an important role for conformational fluctuations of the backbone as important determinants of pKa values of carboxylic groups. Because no global or subglobal conformational changes have been observed previously for SNase under acidic conditions above the acid-unfolding region, these fluctuations must be local. The acid unfolding of SNase does not seem to involve the disruption of the N state by accruement of intramolecular repulsive interactions, nor the protonation of key ion paired carboxylic residues. It is more consistent with modest contributions from many H+ binding groups, with an important role for local conformational fluctuations in the coupling between H+ binding and the global structural transition.     

Proton nuclear magnetic resonance study of cobrotoxin.

Cobrotoxin (Mr 6949), which binds tightly to the acetylcholine receptors, contains no phenylalanines and only two histidines, two tyrosines, and one tryptophan that result in well-resolved aromatic proton resonances in D2O at 360 MHz. His-32, Tyr-25, and the Trp are essential for toxicity and may interact with the acetylcholine receptor. We assign two titratable resonances (pKa = 5.1) at delta = 9.0 and 7.5 ppm at pH 2.5 and at 7.7 and 7.1 ppm at pH 9.5 to the C-2 and C-4 ring protons, respectively, of His-4. Two other titratable resonances (pKa = 5.7) at delta = 8.8 and 6.9 ppm at pH 2.5 and at 7.8 and 6.7 ppm at pH 9.5 are assigned to the C-2 and C-4 ring protons of His-32, respectively. The differences in delta values of the two histidines reflect chemically different microenvironments while their low pKa values could arise from nearby positive charges. A methyl resonance gradually shifts upfield to delta approximately 0.4 ppm as His-4 is deprotonated and is tentatively assigned to the methyl group of Thr-14 or Thr-15 which, from published X-ray studies of neurotoxins, are located in the vicinity of His-4. Further, we have identified the aromatic resonances of the invariant tryptophan and individual tyrosines and the methyl resonance of one of the two isoleucines in the molecule. Several broad nontitrating resonances of labile protons which disappear at pH greater than 9 may arise from amide groups of the beta sheet in cobrotoxin.     

Electrostatic interactions in ubiquitin: stabilization of carboxylates by lysine amino groups

To explore electrostatic interactions in ubiquitin, pK(a) values have been determined by NMR for all 12 carboxyl groups in wild-type ubiquitin and in variants where single lysines have been replaced by neutral residues. Aspartate pK(a) values in ubiquitin range from 3.1 to 3.8 and are generally less than model compound values. Most aspartate pK(a) values are within 0.2 pH unit of those predicted with a simple Tanford-Kirkwood model. Glutamate pK(a) values range from 3.8 to 4.5, close to model compound values and differing by 0.1-0.8 pH unit from calculated values. To determine the role of positive charges in modulating carboxyl pK(a) values, we mutated lysines at positions 11, 29, and 33 to glutamine and threonine. NMR studies with these six single-site mutants reveal significant interactions of Lys 11 and Lys 29 with Glu 34 and Asp 21, respectively: pK(a) values for Glu 34 and Asp 21 increase by approximately 0.5-0.8 pH unit, similar to predicted values, when the lysines are replaced by neutral residues. In contrast, the predicted interaction between Lys 33 and Glu 34 is not observed experimentally. In some instances, substitution of lysine by glutamine and threonine did not lead to the same changes in carboxyl pK(a) values. These may reflect new short-range interactions between the mutated residues and the carboxyl groups. Carboxyl pK(a) shifts > 0.5 pH unit result from mutations at groups that are <5 A from the carboxyl group. No interactions are observed at >10 A.     

pK(a) values for the unfolded state under native conditions explain the pH-dependent stability of PGB1

Understanding the role of electrostatics in protein stability requires knowledge of these interactions in both the folded and unfolded states. Electrostatic interactions can be probed experimentally by characterizing ionization equilibria of titrating groups, parameterized as pK_a values. However, pK_a values of the unfolded state are rarely accessible under native conditions, where the unfolded state has a very low population. Here, we report pK_a values under nondenaturing conditions for two unfolded fragments of the protein G B1 domain that mimic the unfolded state of the intact protein. pK_a values were determined for carboxyl groups by monitoring their pH-dependent ¹³C chemical shifts. Monte Carlo simulations using a Gaussian chain model provide corrections for changes in electrostatic interactions that arise from fragmentation of the protein. Most pK_a values for the unfolded state agree well with model values, but some residues show significant perturbations that can be rationalized by local electrostatic interactions. The pH-dependent stability was calculated from the experimental pK_a values of the folded and unfolded states and compared to experimental stability data. The use of experimental pK_a values for the unfolded state results in significantly improved agreement with experimental data, as compared to calculations based on model data alone.     

Probing electrostatic interactions along the reaction pathway of a glycoside hydrolase: histidine characterization by NMR spectroscopy

We have characterized by NMR spectroscopy the three active site (His80, His85, and His205) and two non-active site (His107 and His114) histidines in the 34 kDa catalytic domain of Cellulomonas fimi xylanase Cex in its apo, noncovalently aza-sugar-inhibited, and trapped glycosyl-enzyme intermediate states. Due to protection from hydrogen exchange, the level of which increased upon inhibition, the labile 1Hdelta1 and 1H epsilon1 atoms of four histidines (t1/2 approximately 0.1-300 s at 30 degrees C and pH approximately 7), as well as the nitrogen-bonded protons in the xylobio-imidazole and -isofagomine inhibitors, could be observed with chemical shifts between 10.2 and 17.6 ppm. The histidine pKa values and neutral tautomeric forms were determined from their pH-dependent 13C epsilon1-1H epsilon1 chemical shifts, combined with multiple-bond 1H delta2/epsilon1-15N delta1/epsilon2 scalar coupling patterns. Remarkably, these pKa values span more than 8 log units such that at the pH optimum of approximately 6 for Cex activity, His107 and His205 are positively charged (pKa > 10.4), His85 is neutral (pKa < 2.8), and both His80 (pKa = 7.9) and His114 (pKa = 8.1) are titrating between charged and neutral states. Furthermore, upon formation of the glycosyl-enzyme intermediate, the pKa value of His80 drops from 7.9 to <2.8, becoming neutral and accepting a hydrogen bond from an exocyclic oxygen of the bound sugar moiety. Changes in the pH-dependent activity of Cex due to mutation of His80 to an alanine confirm the importance of this interaction. The diverse ionization behaviors of the histidine residues are discussed in terms of their structural and functional roles in this model glycoside hydrolase.     

Very fast empirical prediction and rationalization of protein pKa values

A very fast empirical method is presented for structure-based protein pKa prediction and rationalization. The desolvation effects and intra-protein interactions, which cause variations in pKa values of protein ionizable groups, are empirically related to the positions and chemical nature of the groups proximate to the pKa sites. A computer program is written to automatically predict pKa values based on these empirical relationships within a couple of seconds. Unusual pKa values at buried active sites, which are among the most interesting protein pKa values, are predicted very well with the empirical method. A test on 233 carboxyl, 12 cysteine, 45 histidine, and 24 lysine pKa values in various proteins shows a root-mean-square deviation (RMSD) of 0.89 from experimental values. Removal of the 29 pKa values that are upper or lower limits results in an RMSD = 0.79 for the remaining 285 pKa values.     

Nuclear magnetic resonance titration curves of histidine ring protons. Human metmyoglobin and the effects of azide on human, horse, and sperm whale metmyoglobins.

Four titrating histidine ring C2 and C4 proton resonances are observed in 220 MHz proton NMR spectra of human metmyoglobin as a function of pH. Values of ionization constants determined from the NMR titration data using an equation describing a simple proton association-dissociation equilibrium are curves (1) 6.6, (2) 7.0, (3) 5.8, and (4) 7.4. Four histidine residues have also been found to be solvent-accessible in human metmyoglobin by carboxymethylation studies (Harris, C.M., and Hill, R.L. (1969) J. Biol. Chem. 244, 2195-2203). Two of the titration curves (3 and 4) deviate significantly from the chemical shift values normally observed for histidine C2 proton resonances. Curve 3, with a low pKa, is shifted downfield at high values of pH and also exhibits a second minor inflection with a pKa value of 8.8. On the other hand, the high pKa curve, 4, is shifted upfield at all values of pH. The characteristics of the NMR titration curves with the lowest and highest pKa values (3 and4) are very similar to curves observed previously with sperm whale and horse metmyoglobins (Cohen, J.S., Hagenmaier, H., Pollard, H., and Schechter, A.N. (1972) J. Mol. Biol. 71, 513-519). These results indicate that the histidine residues from which these curves are derived have unusual and characteristic environments in this series of homologous proteins. The NMR spectra of all three metmyoglobins are changed extensively as a result of azide ion binding, indicating conformational changes affecting the environments of several imidazole side chains. The presence of azide ion causes a selective downfield chemical shift for the low pKa curve and a selective upfield chemical shift for the high pKa curve in all three proteins. Azide also abolishes the second inflection seen in the low pKa curve at high pH. In addition to these effects, the presence of azide ion permits the observation of two additional titrating proton resonances for all three metmyoglobins. Increasing the azide to protein ratio at several fixed values of pH yields results which show that a slow exchange process is occurring with each of the metmyoglobins. In the azide titration studies the maximum changes in the NMR spectra occurred at approximately equimolar concentrations. The NMR results for these proteins in the absence and presence of azide ion are related to x-ray crystallographic studies of sperm whale metmyoglobin and the known alkylation properties of the histidine residues. Tentative assignments of the titrating resonances observed are suggested.     

Electrostatic contributions to residue-specific protonation equilibria and proton binding capacitance for a small protein

Charge-charge interactions in proteins are important in a host of biological processes. Here we use 13C NMR chemical shift data for individual aspartate and glutamate side chain carboxylate groups to accurately detect site-specific protonation equilibria in a variant of the B1 domain of protein G (PGB1-QDD). Carbon chemical shifts are dominated by changes in the electron distribution within the side chain and therefore excellent reporters of the charge state of individual groups, and the data are of high precision. We demonstrate that it is possible to detect local charge interactions within this small protein domain that stretch and skew the chemical shift titration curves away from "ideal" behavior and introduce a framework for the analysis of such convoluted data to study local charge-charge interactions and electrostatic coupling. It is found that, due to changes in electrostatic potential, the proton binding affinity, Ka, of each carboxyl group changes throughout the titration process and results in a linearly pH dependent pKa value. This result could be readily explained by calculations of direct charge-charge interactions based on Coulomb's law. In addition, the slope of pKa versus pH was dependent on screening by salt, and this dependence allowed the selective study of charge-charge interactions. For PGB1-QDD, it was established that mainly differences in self-energy, and not direct charge-charge interactions, are responsible for shifted pKa values within the protein environment.     

Electrostatic properties of protein-protein complexes

Statistical electrostatic analysis of 37 protein-protein complexes extracted from the previously developed database of protein complexes (ProtCom, http://www.ces.clemson.edu/compbio/protcom) is presented. It is shown that small interfaces have a higher content of charged and polar groups compared to large interfaces. In a vast majority of the cases the average pKa shifts for acidic residues induced by the complex formation are negative, indicating that complex formation stabilizes their ionizable states, whereas the histidines are predicted to destabilize the complex. The individual pKa shifts show the same tendency since 80% of the interfacial acidic groups were found to lower their pKas, whereas only 25% of histidines raise their pKa upon the complex formation. The interfacial groups have been divided into three sets according to the mechanism of their pKa shift, and statistical analysis of each set was performed. It was shown that the optimum pH values (pH of maximal stability) of the complex tend to be the same as the optimum pH values of the complex components. This finding can be used in the homology-based prediction of the 3D structures of protein complexes, especially when one needs to evaluate and rank putative models. It is more likely for a model to be correct if both components of the model complex and the entire complex have the same or at least similar values of the optimum pH.     

Electrostatic calculations of amino acid titration and electron transfer, Q-AQB-->QAQ-B, in the reaction center.

The titration of amino acids and the energetics of electron transfer from the primary electron acceptor (QA) to the secondary electron acceptor (QB) in the photosynthetic reaction center of Rhodobacter sphaeroides are calculated using a continuum electrostatic model. Strong electrostatic interactions between titrating sites give rise to complex titration curves. Glu L212 is calculated to have an anomalously broad titration curve, which explains the seemingly contradictory experimental results concerning its pKa. The electrostatic field following electron transfer shifts the average protonation of amino acids near the quinones. The pH dependence of the free energy between Q-AQB and QAQ-B calculated from these shifts is in good agreement with experiment. However, the calculated absolute free energy difference is in severe disagreement (by approximately 230 meV) with the observed experimental value, i.e., electron transfer from Q-A to QB is calculated to be unfavorable. The large stabilization energy of the Q-A state arises from the predominantly positively charged residues in the vicinity of QA in contrast to the predominantly negatively charged residues near QB. The discrepancy between calculated and experimental values for delta G(Q-AQB-->QAQ-B) points to limitations of the continuum electrostatic model. Inclusion of other contributions to the energetics (e.g., protein motion following quinone reduction) that may improve the agreement between theory and experiment are discussed.     

Developing hybrid approaches to predict pKa values of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.     

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.     

Electrostatic pKa computations in proteins: role of internal cavities

The solvent accessible surface area (SASA) algorithm is conventionally used to characterize protein surfaces in electrostatic energy computations of proteins. Unfortunately, it often fails to find narrow cavities inside a protein. As a consequence pK(a) computations based on this algorithm perform badly. In this study a new cavity-algorithm is introduced, which solves this problem and provides improved pK(a) values. The procedure is applied to 20 pK(a) values of titratable groups introduced as point mutations in SNase variants, where crystal structures are available. The computations of these pK(a)s are particular challenging, since they are placed in a rather hydrophobic environment. For nine mutants, where the titratable residue is in contact with a large cavity, the RMSD(pKa) between computed and measured pK(a) values is 2.04, which is a considerable improvement as compared to the original results obtained with Karlsberg(+) (http://agknapp.chemie.fu-berlin.de/karlsberg/) that yielded an RMSD(pKa) of 8.8. However, for 11 titratable residues the agreement with experiments remains poor (RMSD(pKa) = 6.01). Considering 15 pK(a)s of SNase, which are in a more conventional less hydrophobic protein environment, the RMSD(pKa) is 2.1 using the SASA-algorithm and 1.7 using the new cavity-algorithm. The agreement is reasonable but less good than what one would expect from the general performance of Karlsberg(+) indicating that SNase belongs to the more difficult proteins with respect to pK(a) computations. We discuss the possible reasons for the remaining discrepancies between computed and measured pK(a)s.     

Assessing the quality of the homology-modeled 3D structures from electrostatic standpoint: test on bacterial nucleoside monophosphate kinase families

In this study, we address the issue of performing meaningful pK(a) calculations using homology modeled three-dimensional (3D) structures and analyze the possibility of using the calculated pK(a) values to detect structural defects in the models. For this purpose, the 3D structure of each member of five large protein families of a bacterial nucleoside monophosphate kinases (NMPK) have been modeled by means of homology-based approach. Further, we performed pK(a) calculations for the each model and for the template X-ray structures. Each bacterial NMPK family used in the study comprised on average 100 members providing a pool of sequences and 3D models large enough for reliable statistical analysis. It was shown that pK(a) values of titratable groups, which are highly conserved within a family, tend to be conserved among the models too. We demonstrated that homology modeled structures with sequence identity larger than 35% and gap percentile smaller than 10% can be used for meaningful pK(a) calculations. In addition, it was found that some highly conserved titratable groups either exhibit large pK(a) fluctuations among the models or have pK(a) values shifted by several pH units with respect to the pK(a) calculated for the X-ray structure. We demonstrated that such case usually indicates structural errors associated with the model. Thus, we argue that pK(a) calculations can be used for assessing the quality of the 3D models by monitoring fluctuations of the pK(a) values for highly conserved titratable residues within large sets of homologous proteins.     

Role of the C-terminal chain in human interferongamma stability: an electrostatic study

Electrostatic interactions in two structures of human interferon gamma (hIFNgamma), corresponding to interferon molecule alone and bound to its receptor, were analyzed on the basis of a continuum dielectric model. It was found that a number of titratable groups, mainly basic, show large pK shifts and remain in their neutral forms at physiologically relevant pH. The fact that these groups are largely common to both structures and that most of them belong to the set of most conserved sites suggests that this is a property inherent to the hIFNgamma molecule rather than an artifact of the crystal packing. His111 was also found deprotonated at neutral pH. It was concluded that receptor recognition involving His111 is driven by aromatic coupling of His111 and Tyr52 from the receptor rather than by electrostatic interactions. The structure corresponding to hIFNgamma in complex with its receptor shows a reduction in number and in degree of desolvation of the buried titratable sites. This finding suggested that on receptor binding, hIFNgamma adopts energetically more favorable, relaxed, conformation. It was experimentally shown that in contrast to the full-size hIFNgamma, the construct having 21 amino acid residues deleted from the C-terminus is soluble. The hydrophobicity profile analysis suggested that factors other than the exposure of hydrophobic parts of the molecule are responsible for the low stability and propensity for aggregation. On the basis of these results, it was assumed that the electrostatic influence of the C-terminal part contributes particularly to the low solvent exposure of the titratable groups, and hence to the low structural stability and propensity for aggregation of the recombinant hIFNgamma. Proteins 2001;43:125-133.     

On the calculation of electrostatic interactions in proteins

In this paper we present a classical treatment of electrostatic interactions in proteins. The protein is treated as a region of low dielectric constant with spherical charges embedded within it, surrounded by an aqueous solvent of high dielectric constant, which may contain a simple electrolyte. The complete analysis includes the effects of solvent screening, polarization forces, and self energies, which are related to solvation energies. Formulae, and sample calculations of forces and energies, are given for the special case of a spherical protein. Our analysis and model calculations point out that any consistent treatment of electrostatic interactions in proteins should account for the following. Solvent polarization is an important factor in the calculation of pairwise electrostatic interactions. Solvent polarization substantially affects both electrostatic energies and forces acting upon charges. No simple expression for the effective dielectric constant, Deff, can generally be valid, since Deff is a sensitive function of position. Solvent screening of pairwise interactions involving dipolar groups is less effective than the screening of charges. In fact for many interactions involving dipoles, solvent screening can be essentially ignored. The self energy of charges makes a large contribution to the total electrostatic energy of a protein. This must be compensated by specific interactions with other groups in the protein. Strategies for applying our analysis to proteins whose structures are known are discussed.