Theoretical prediction of relative and absolute pKa values of aminopyridines

This work presents a study aimed at the theoretical prediction of pK(a) values of aminopyridines, as a factor responsible for the activity of these compounds as blockers of the voltage-dependent K(+) channels. To cover a large range of pK(a) values, a total of seven substituted pyridines is considered as a calibration set: pyridine, 2-aminopyridine, 3-aminopyridine, 4-aminopyridine, 2-chloropyridine, 3-chloropyridine, and 4-methylpirydine. Using ab initio G1, G2 and G3 extrapolation methods, and the CPCM variant of the Polarizable Continuum Model for solvation, we calculate gas phase and solvation free energies. pK(a) values are obtained from these data using a thermodynamic cycle for describing protonation in aqueous and gas phases. The results show that the relatively inexpensive G1 level of theory is the most accurate at predicting pK(a) values in aminopyridines. The highest standard deviation with respect to the experimental data is 0.69 pK(a) units for absolute values calculations. The difference increases slightly to 0.74 pK(a) units when the pK(a) is computed relative to the pyridine molecule. Considering only compounds at least as basic as pyridine (the values of interest for bioactive aminopyridines) the error falls to 0.10 and 0.12 pK(a) units for the absolute and relative computations, respectively. The technique can be used to predict the effect of electronegative substituents in the pK(a) of 4-AP, the most active aminopyridine considered in this work. Thus, 2-chloro and 3-chloro-4-aminopyridine are taken into account. The results show a decrease of the pK(a), suggesting that these compounds are less active than 4-AP at blocking the K(+) channel.     

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.     

Empirical relationships between protein structure and carboxyl pKa values in proteins

Relationships between protein structure and ionization of carboxyl groups were investigated in 24 proteins of known structure and for which 115 aspartate and 97 glutamate pK(a) values are known. Mean pK(a) values for aspartates and glutamates are < or = 3.4 (+/-1.0) and 4.1 (+/-0.8), respectively. For aspartates, mean pK(a) values are 3.9 (+/-1.0) and 3.1 (+/-0.9) in acidic (pI < 5) and basic (pI > 8) proteins, respectively, while mean pK(a) values for glutamates are approximately 4.2 for acidic and basic proteins. Burial of carboxyl groups leads to dispersion in pK(a) values: pK(a) values for solvent-exposed groups show narrow distributions while values for buried groups range from < 2 to 6.7. Calculated electrostatic potentials at the carboxyl groups show modest correlations with experimental pK(a) values and these correlations are not improved by including simple surface-area-based terms to account for the effects of desolvation. Mean aspartate pK(a) values decrease with increasing numbers of hydrogen bonds but this is not observed at glutamates. Only 10 pK(a) values are > 5.5 and most are found in active sites or ligand-binding sites. These carboxyl groups are buried and usually accept no more than one hydrogen bond. Aspartates and glutamates at the N-termini of helices have mean pK(a) values of 2.8 (+/-0.5) and 3.4 (+/-0.6), respectively, about 0.6 units less than the overall mean values.     

Application of the Gaussian dielectric boundary in Zap to the prediction of protein pKa values

The results of two rounds of blind pK(a) predictions for ionizable residues in staphylococcal nuclease using OpenEye's legacy protein pK(a) prediction program based on the Zap Poisson-Boltzmann solver were submitted to the 2009 prediction challenge organized by the Protein pK(a) Cooperative and first round predictions were discussed at the corresponding June 2009 Telluride conference. To better understand these results, 21 additional sets of predictions were performed with the same program, varying the internal dielectric, reference pK(a), partial charge set, and dielectric boundary. The internal dielectric (ε(p)) and dielectric boundary were the two most important factors contributing to the quality of the predictions. Although the lowest overall errors were observed with a molecular dielectric boundary at ε(p) = 8, predictions using a smooth Gaussian dielectric boundary performed almost as well at lower ε(p) values because the Gaussian boundary implicitly accounts for a significant level of solvent penetration. Improved pK(a) predictions with the Gaussian boundary methodology will require better prediction and modeling of structural changes due to changes in ionization state, perhaps without resorting to the more exhaustive sampling of conformational states used by other recent continuum methods.     

The pKa Cooperative: a collaborative effort to advance structure-based calculations of pKa values and electrostatic effects in proteins

The pK(a) Cooperative (http://www.pkacoop.org) was organized to advance development of accurate and useful computational methods for structure-based calculation of pK(a) values and electrostatic energies in proteins. The Cooperative brings together laboratories with expertise and interest in theoretical, computational, and experimental studies of protein electrostatics. To improve structure-based energy calculations, it is necessary to better understand the physical character and molecular determinants of electrostatic effects. Thus, the Cooperative intends to foment experimental research into fundamental aspects of proteins that depend on electrostatic interactions. It will maintain a depository for experimental data useful for critical assessment of methods for structure-based electrostatics calculations. To help guide the development of computational methods, the Cooperative will organize blind prediction exercises. As a first step, computational laboratories were invited to reproduce an unpublished set of experimental pK(a) values of acidic and basic residues introduced in the interior of staphylococcal nuclease by site-directed mutagenesis. The pK(a) values of these groups are unique and challenging to simulate owing to the large magnitude of their shifts relative to normal pK(a) values in water. Many computational methods were tested in this first Blind Prediction Challenge and critical assessment exercise. A workshop was organized in the Telluride Science Research Center to objectively assess the performance of many computational methods tested on this one extensive data set. This volume of Proteins: Structure, Function, and Bioinformatics introduces the pK(a) Cooperative, presents reports submitted by participants in the Blind Prediction Challenge, and highlights some of the problems in structure-based calculations identified during this exercise.     

Redesigning protein pKa values

The ability to re-engineer enzymatic pH-activity profiles is of importance for industrial applications of enzymes. We theoretically explore the feasibility of re-engineering enzymatic pH-activity profiles by changing active site pK(a) values using point mutations. We calculate the maximum achievable DeltapK(a) values for 141 target titratable groups in seven enzymes by introducing conservative net-charge altering point mutations. We examine the importance of the number of mutations introduced, their distance from the target titratable group, and the characteristics of the target group itself. The results show that multiple mutations at 10A can change pK(a) values up to two units, but that the introduction of a requirement to keep other pK(a) values constant reduces the magnitude of the achievable DeltapK(a). The algorithm presented shows a good correlation with existing experimental data and is available for download and via a web server at http://enzyme.ucd.ie/pKD.     

Calculating pKa values in enzyme active sites

The ionization properties of the active-site residues in enzymes are of considerable interest in the study of the catalytic mechanisms of enzymes. Knowledge of these ionization constants (pKa values) often allows the researcher to identify the proton donor and the catalytic nucleophile in the reaction mechanism of the enzyme. Estimates of protein residue pKa values can be obtained by applying pKa calculation algorithms to protein X-ray structures. We show that pKa values accurate enough for identifying the proton donor in an enzyme active site can be calculated by considering in detail only the active-site residues and their immediate electrostatic interaction partners, thus allowing for a large decrease in calculation time. More specifically we omit the calculation of site-site interaction energies, and the calculation of desolvation and background interaction energies for a large number of pairs of titratable groups. The method presented here is well suited to be applied on a genomic scale, and can be implemented in most pKa calculation algorithms to give significant reductions in calculation time with little or no impact on the accuracy of the results. The work presented here has implications for the understanding of enzymes in general and for the design of novel biocatalysts.     

On the NMR analysis of pKa values in the unfolded state of proteins by extrapolation to zero denaturant

Detailed knowledge of the pH-dependence in both folded and unfolded states of proteins is essential to understand the role of electrostatics in protein stability. The increasing number of natively disordered proteins constitutes an excellent source for the NMR analysis of pKa values in the unfolded state of proteins. However, the tendency of many natively disordered proteins to aggregate via intermolecular hydrophobic clusters limits their NMR analysis over a wide pH range. To assess whether the pKa values in natively disordered polypeptides can be extrapolated from NMR measurements in the presence of denaturants, the natively disordered backbone of the C-terminal fragment 75 to 105 of Human Thioredoxin was studied. First, assignments using triple resonance experiments were performed to confirm lack of secondary structure. Then the pH-dependence of the amides and carboxylate side chains of Glu residues (Glu88, Glu95, Glu98, and Glu103) in the pH range from 2.0 to 7.0 was monitored using 2D 1H15N HSQC and 3D C(CO)NH experiments, and the behavior of their amides and corresponding carboxyl groups was compared to confirm the absence of nonlocal interactions. Lastly, the effect of increasing dimethyl urea concentration on the pKa values of these Glu residues was monitored. The results indicate that: (i) the dispersion in the pKa of carboxyl groups and the pH midpoints of amides in Glu residues is about 0.5 pH units and 0.6 pH units, respectively; (ii) the backbone amides of the Glu residues exhibit pH midpoints which are within 0.2 pH units from those of their carboxylates; (iii) the addition of denaturant produces upshifts in the pKa values of Glu residues that are nearly independent of their position in the sequence; and (iv) these upshifts show a nonlinear behavior in denaturant concentration, complicating the extrapolation to zero denaturant. Nevertheless, the relative ordering of the pKa values of Glu residues is preserved over the whole range of denaturant concentrations indicating that measurements at high denaturant concentration (e.g. 4 M dimethyl urea) can yield a qualitatively correct ranking of the pKa of these residues in natively disordered proteins whose pH-dependence cannot be monitored directly by NMR.     

Negatively charged residues and hydrogen bonds tune the ligand histidine pKa values of Rieske iron-sulfur proteins

Rieske proteins carry a redox-active iron-sulfur cluster, which is bound by two histidine and two cysteine side chains. The reduction potential of Rieske proteins depends on pH. This pH dependence can be described by two pK(a) values, which have been assigned to the two iron-coordinating histidines. Rieske proteins are commonly grouped into two major classes: Rieske proteins from quinol-oxidizing cytochrome bc complexes, in which the ligand histidines titrate in the physiological pH range, and bacterial ferredoxin Rieske proteins, in which the ligand histidines are protonated at physiological pH. In the study presented here, we have calculated pK(a) values of the cluster ligand histidines using a combined density functional theory/continuum electrostatics approach. Experimental pK(a) values for a bc-type and a ferredoxin Rieske protein could be reproduced. We could identify functionally important differences between the two proteins: hydrogen bonds toward the cluster, which are present in bc-type Rieske proteins, and negatively charged residues, which are present in ferredoxin Rieske proteins. We removed these differences by mutating the proteins in our calculations. The Rieske centers in the mutated proteins have very similar pK(a) values. We thus conclude that the studied structural differences are the main reason for the different pH-titration behavior of the proteins. Interestingly, the shift caused by neutralizing the negative charges in ferredoxin Rieske proteins is larger than the shift caused by removing the hydrogen bonds toward the cluster in bc-type Rieske proteins.     

Electrostatic effects in highly charged proteins: salt sensitivity of pKa values of histidines in staphylococcal nuclease

The pK(a) values of most histidines in small peptides and in myoglobin increase on average by 0.30 unit between 0.02 and 1.5 M NaCl [Kao et al. (2000) Biophys. J. 79, 1637]. The DeltapK(a) values reflect primarily the ionic strength dependence of the solvation energy; screening of Coulombic interactions contributes only in a minor way. This implies that Coulombic interactions are weak, or that attractive and repulsive contributions to the pK(a) values are balanced. To distinguish experimentally between these two possibilities, and to further characterize the magnitude and salt sensitivity of surface electrostatic interactions in proteins, the salt dependence of pK(a) values of histidines in staphylococcal nuclease was measured by (1)H NMR spectroscopy. Three of the four histidines titrated with significantly depressed pK(a) values, and the salt sensitivity of all histidine pK(a) values was substantial. In three cases, the pK(a) values increased by a full unit between 0.01 and 1.5 M KCl. Anion-specific effects were found; the pK(a) values measured under equivalent ionic strengths in SCN(-) and SO(4)(2-) were higher than in Cl(-); the order of the sensitivity of pK(a) values to anions was SCN(-) > Cl(-) > SO(4)(2-). Structure-based pK(a) calculations with continuum methods were performed to interpret the measured effects structurally and to test their ability to capture the experimental behavior. Calculations in which the protein interior was treated empirically with a dielectric constant of 20 reproduced the pK(a) values and their dependence on the concentration of Cl(-). According to the calculations, the pK(a) values are depressed because of unfavorable self-energies and repulsive Coulombic interactions. Their striking salt sensitivity reflects screening of weak, repulsive, Coulombic interactions among charges separated by more than 10 A. Long-range Coulombic interactions on the surfaces of proteins are weak, but they can add up to produce substantial electrostatic effects when positive and negative charges are not balanced.     

Progress in structure prediction of alpha-helical membrane proteins

Transmembrane (TM) proteins comprise 20-30% of the genome but, because of experimental difficulties, they represent less than 1% of the Protein Data Bank. The dearth of membrane protein structures makes computational prediction a potentially important means of obtaining novel structures. Recent advances in computational methods have been combined with experimental data to constrain the modeling of three-dimensional structures. Furthermore, threading and ab initio modeling approaches that were effective for soluble proteins have been applied to TM domains. Surprisingly, experimental structures, proteomic analyses and bioinformatics have revealed unexpected architectures that counter long-held views on TM protein structure and stability. Future computational and experimental studies aimed at understanding the thermodynamic and evolutionary bases of these architectural details will greatly enhance predictive capabilities.     

Differences in lysine pKa values may be used to improve NMR signal dispersion in reductively methylated proteins

Reductive methylation of lysine residues in proteins offers a way to introduce ¹³C methyl groups into otherwise unlabeled molecules. The ¹³C methyl groups on lysines possess favorable relaxation properties that allow highly sensitive NMR signal detection. One of the major limitations in the use of reductive methylation in NMR is the signal overlap of ¹³C methyl groups in NMR spectra. Here we show that the uniform influence of the solvent on chemical shifts of exposed lysine methyl groups could be overcome by adjusting the pH of the buffering solution closer to the pKa of lysine side chains. Under these conditions, due to variable pKa values of individual lysine side chains in the protein of interest different levels of lysine protonation are observed. These differences are reflected in the chemical shift differences of methyl groups in reductively methylated lysines. We show that this approach is successful in four different proteins including Ca²⁺-bound Calmodulin, Lysozyme, Ca²⁺-bound Troponin C, and Glutathione S-Transferase. In all cases significant improvement in NMR spectral resolution of methyl signals in reductively methylated proteins was obtained. The increased spectral resolution helps with more precise characterization of protein structural rearrangements caused by ligand binding as shown by studying binding of Calmodulin antagonist trifluoperazine to Calmodulin. Thus, this approach may be used to increase resolution in NMR spectra of ¹³C methyl groups on lysine residues in reductively methylated proteins that enhances the accuracy of protein structural assessment. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.     

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.     

A statistical approach to the prediction of pK(a) values in proteins

We propose a simple model for the calculation of pK(a) values of ionizable residues in proteins. It is based on the premise that the pK(a) shift of ionizable residues is linearly correlated to the interaction between a particular residue and the local environment created by the surrounding residues. Despite its simplicity, the model displays good prediction performance. Under the sixfold cross test prediction over a data set of 405 experimental pK(a) values in 73 protein chains with known structures, the root-mean-square deviation (RMSD) between the experimental and calculated pK(a) was found to be 0.77. The accuracy of this model increases with increasing size of the data set: the RMSD is 0.609 for glutamate (the largest data set with 141 sites) and approximately 1 pH unit for lysine, with a data set containing 45 sites.     

Highly perturbed pKa values in the unfolded state of hen egg white lysozyme

The majority of pK_a values in protein unfolded states are close to the amino acid model pK_a values, thus reflecting the weak intramolecular interactions present in the unfolded ensemble of most proteins. We have carried out thermal denaturation measurements on the WT and eight mutants of HEWL from pH 1.5 to pH 11.0 to examine the unfolded state pK_a values and the pH dependence of protein stability for this enzyme. The availability of accurate pK_a values for the folded state of HEWL and separate measurements of mutant-induced effects on the folded state pK_a values, allows us to estimate the pK_a values of seven acidic residues in the unfolded state of HEWL. Asp-48 and Asp-66 display pK_a values of 2.9 and 3.1 in our analysis, thus representing the most depressed unfolded state pK_a values observed to date. We observe a strong correlation between the folded state pK_a values and the unfolded state pK_a values of HEWL, thus suggesting that the unfolded state of HEWL possesses a large degree of native state characteristics.     

pKa values of the 8 alpha-imidazole substituents in selected flavoenzymes containing 8 alpha-histidylflavins

Difference absorption spectroscopy as a function of pH is described as a probe to determine the pKa values of the 8 alpha-imidazole substituent in flavoenzymes containing 8 alpha-histidylflavin coenzymes. Reversible absorption difference spectra are observed in the pH range 5.5 to 8.5 when synthetic 8 alpha-imidazolyl-FMN is bound to the apoflavodoxins from Azotobacter vinelandii and from Clostridium pasterianum. The observed spectral perturbations of these two flavodoxin complexes follow a single proton ionization dependence with respective pKa values of 6.7 and 6.8. No pH-induced spectral perturbations were observed when 8 alpha-(N-CH3)-imidazolium FMN was bound to either flavodoxin. Similar approaches are described to determine the 8 alpha-imidazolyl pKa values of the 8 alpha-histidyl-FAD coenzyme of the cholesterol oxidases from Schizophyllum commune and from Gleocystidium chrysocreas. Previous work has shown the former enzyme contains an 8 alpha-N1-histidyl-FAD (W. C. Kenney et al. (1979) J. Biol. Chem. 254, 4689-4690) while experiments reported here show the latter enzyme also contains one 8 alpha-N1-histidyl-FAD per mole of enzyme. The pKa value for the 8 alpha-imidazole substituent on the flavin of S. commune cholesterol oxidase is 5.4 while that determined for the G. chrysocreas enzyme is 6.2. These results demonstrate that the pKa of the 8 alpha-imidazole substituent can be determined in enzymes containing an 8 alpha-histidylflavin, provided that the enzyme is stable in the pH range required to observe ionization. Furthermore it is shown this the pKa value can differ even on comparison of enzymes from different sources that catalyze the same reaction.     

The determinants of carboxyl pKa values in turkey ovomucoid third domain

A computational methodology for protein pK(a) predictions, based on ab initio quantum mechanical treatment of part of the protein and linear Poisson-Boltzmann equation treatment of the bulk solvent, is presented. The method is used to predict and interpret the pK(a) values of the five carboxyl residues (Asp7, Glu10, Glu19, Asp27, and Glu43) in the serine protease inhibitor turkey ovomucoid third domain. All the predicted pK(a) values are within 0.5 pH units of experiment, with a root-mean-square deviation of 0.31 pH units. We show that the decreased pK(a) values observed for some of the residues are primarily due to hydrogen bonds to the carboxyl oxygens. Hydrogen bonds involving amide protons are shown to be particularly important, and the effect of hydrogen bonding is shown to be nonadditive. Hydrophobic effects are also shown to be important in raising the pK(a). Interactions with charged residues are shown to have relatively little effect on the carboxyl pK(a) values in this protein, in general agreement with experiment.     

pKa values of estrone, 17 beta-estradiol and 2-methoxyestrone

The acid ionization constants of estrone (10.77), 17 beta-estradiol (10.71) and 2-methoxyestrone (10.81) have been determined spectrophotometrically and shown to be consistent with the additivity of substituent effects of the phenol ring. Previously published values for estrone (10.914) and 17 beta-estradiol (10.078) are shown to be incorrect, at variance with the established trend for phenols, and inconcsistent with the similarity of the compounds.