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.     

The pH-dependence and group modification of beta-lactamase I.

The pH-dependence of the kinetic parameters for the hydrolysis of the beta-lactam ring by beta-lactamase I (penicillinase, EC 3.5.2.6) was studied. Benzylpenicillin and ampicillin (6-[D(-)-alpha-aminophenylacetamido]penicillanic acid) were used. Both kcat. and kcat./Km for both substrates gave bell-shaped plots of parameter versus pH. The pH-dependence of kcat./Km for the two substrates gave the same value (8.6) for the higher apparent pK, and so this value may characterize a group on the free enzyme; the lower apparent pK values were about 5(4.85 for benzylpenicillin, 5.4 for ampicillin). For benzylpenicillin both kcat. and kcat./Km depended on pH in exactly the same way. The value of Km for benzylpenicillin was thus independent of pH, suggesting that ionization of the enzyme's catalytically important groups does not affect binding of this substrate. The pH-dependence of kcat. for ampicillin differed, however, presumably because of the polar group in the side chain. The hypothesis that the pK5 group is a carboxyl group was tested. Three reagents that normally react preferentially with carboxyl groups inactivated the enzyme: the reagents were Woodward's reagent K, a water-soluble carbodi-imide, and triethyloxonium fluoroborate. These findings tend to support the idea that a carboxylate group plays a part in the action of beta-lactamase I.     

Structural basis of perturbed pKa values of catalytic groups in enzyme active sites

In protein and RNA macromolecules, only a limited number of different side-chain chemical groups are available to function as catalysts. The myriad of enzyme-catalyzed reactions results from the ability of most of these groups to function either as nucleophilic, electrophilic, or general acid-base catalysts, and the key to their adapted chemical function lies in their states of protonation. Ionization is determined by the intrinsic pKa of the group and the microenvironment created around the group by the protein or RNA structure, which perturbs its intrinsic pKa to its functional or apparent pKa. These pKa shifts result from interactions of the catalytic group with other fully or partially charged groups as well as the polarity or dielectric of the medium that surrounds it. The electrostatic interactions between ionizable groups found on the surface of macromolecules are weak and cause only slight pKa perturbations (<2 units). The sum of many of these weak electrostatic interactions helps contribute to the stability of native or folded macromolecules and their ligand complexes. However, the pKa values of catalytic groups that are found in the active sites of numerous enzymes are significantly more perturbed (>2 units) and are the subject of this review. The magnitudes of these pKa perturbations are analyzed with respect to the structural details of the active-site microenvironment and the energetics of the reactions that they catalyze.     

The transient-state kinetics of L-glutamate dehydrogenase. pH-dependence of the burst rate parameters.

The pH dependence of the initial transient velocity of NADPH production during the burst phase of the oxidative deamination of L-glutamate by L-glutamate dehydrogenase (L-glutamate : NAD(P)+ oxidoreductase (deaminating), EC 1.4.1.3) and NADP+ has been measured by stopped-flow spectrophotometry. These studies provide evidence that the entire pH dependence below pH 8.26 arises from reaction steps contributing to V of the burst with an apparent pKa of 8.1 +/- 0.1. The data are consistent with a model in which the formation of the first enzyme-coenzyme-substrate ternary complex on the reaction path equilibrates rapidly and in which the pH-dependent steps are mechanistically close to and may include the catalytic hydrogen transfer itself. At pH 8.87, there is evidence that L-glutamate binds less tightly to the enzyme and to the enzyme-NADP+ complex than at lower pH values.     

The intrinsic pKa values for phosphatidylserine and phosphatidylethanolamine in phosphatidylcholine host bilayers.

Potentiometric titrations and surface potential measurements have been used to determine the intrinsic pKa values of both the carboxyl and amino groups of phosphatidylserine (PS) in mixed vesicles of PS and phosphatidylcholine (PC), and also of the amino group of phosphatidylethanolamine (PE) in mixed PE-PC vesicles. The pKa of the carboxyl group of PS in liposomes with different PS/PC lipid ratios measured by the two different methods is 3.6 +/- 0.1, and the pKa of its amino group is 9.8 +/- 0.1. The pKa of the amino group of PE in PE-PC vesicles, determined solely by surface potential measurements, is 9.6 +/- 0.1. These pKa values are independent of the aqueous phase ionic strength and of the effect of the liposome's surface potential due to the presence of these partially charged lipids.     

Sensitivity to values of the rate constants in a neurochemical metabolic model

Equations were derived for the instantaneous relative sensitivities of reaction rates (controllability indices) and metabolite concentrations (response indices) to perturbations in the values of rate constants and were used to analyze the behavior of a model of in vivo glutamate metabolism in rat brain. Controllabilities of reversible reactions were found to increase as the values of the corresponding rate constants (i.e., the rate of approach to equilibrium) increased. Response indices generally declined with the metabolic distance between the metabolite and the rate constant, but they were unexpectedly high for reversible reactions with high controllabilities. The transient response of a given metabolite is most sensitive to reactions involving metabolites which are changing most rapidly relative to their respective pool sizes. Rapidly reversible reactions are most important for communication between metabolite pools.     

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.     

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.     

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.     

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.     

Calculating reaction rate constants and estimating the efficacy of selective enzyme inhibitors

The dynamic steady state of a pair of forward and backward enzymatic reactions is dependent on the balance between the enzymes catalyzing the reactions. By selectively inhibiting one or more of the enzymes involved, this balance is shifted into a new steady state, making it possible to calculate the reaction rate constants after measurement of the reactants. Ideally, the inhibitors should completely eliminate either reaction, but this is often not the case. Here we present and discuss a method for calculating the reaction rate constants and, thus, for evaluating the efficacy of one or more inhibitors when introduced to a forward-backward pair of enzymatic reactions.     

Progress in the prediction of pKa values in proteins

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

The pH-dependence of amide chemical shift of Asp/Glu reflects its pKa in intrinsically disordered proteins with only local interactions

Detailed knowledge of the pH-dependence of ionizable residues in both folded and unfolded states of proteins is essential to understand the role of electrostatics in protein folding and stability. The reassembly of E. coli Thioredoxin (Trx) by complementation of its two disordered fragments (1-37/38-108) provides a folded heterodimer in equilibrium with its unfolded state which, based on circular dichroism and NMR spectroscopy, consists of two unfolded monomers. To gain insight into the role of electrostatics in protein folding and stability, we compared the pH-dependence of the carboxylate sidechain chemical shift of each Asp/Glu against that of its backbone amide chemical shift in the unfolded heterodimer. We monitored via C(CO)NH experiments four Asp and four Glu in fragments 38 to 108 (C37) of Trx in the pH range from 2.0 to 7.0 and compared them with results from (1)H(15)N HSQC experiments [Pujato et al., Biophys. J., 89 (2005) 3293-3302]. The (1)H(15)N HSQC analysis indicates two segments with quite distinct behavior: (A) a segment from Ala57 to Ala108 in which ionizable residues have up to three contiguous neighbors with pH-dependent backbone amide shifts, and (B) a segment of fifteen contiguous pH-dependent backbone amide shifts (Leu42 to Val56) in which two Asp and two Glu are implicated in medium range interactions. In all cases, the titration curves are simple modified sigmoidals from which a pH-midpoint (pH(m)) can be obtained by fitting. In segment A, the pH(m) of a given backbone amide of Asp/Glu mirrors within 0.15 pH-units that of its carboxylate sidechain (i.e., the pK(a)). In contrast, segment B shows significant differences with absolute values of 0.46 and 0.74 pH-units for Asp and Glu, respectively. The dispersion in the pH(m) of the backbone amide of Asp/Glu is also different in the two segments. Segment A shows a dispersion of 0.31 and 0.17 pH-units for Asp and Glu, respectively. Segment B shows a substantially larger dispersion (0.50 and 1.08 pH-units for Asp and Glu, respectively). In both segments, the dispersion in the pH(m) of its backbone amide is larger than in the pK(a) of the carboxylate sidechain (the latter is only 0.17 and 0.52 pH-units for Asp and Glu, respectively). Our results indicate that the pH(m) of the backbone amide chemical shift of Asp/Glu in a disordered polypeptide segment is a good predictor of its pK(a) whenever there are none or few neighboring backbone amides with similar pH-dependence.