Intrinsically disordered inhibitor of glutamine synthetase is a functional protein with random‐coil‐like pKa values

The sequential action of glutamine synthetase (GS) and glutamate synthase (GOGAT) in cyanobacteria allows the incorporation of ammonium into carbon skeletons. In the cyanobacterium Synechocystis sp. PCC 6803, the activity of GS is modulated by the interaction with proteins, which include a 65‐residue‐long intrinsically disordered protein (IDP), the inactivating factor IF7. This interaction is regulated by the presence of charged residues in both IF7 and GS. To understand how charged amino acids can affect the binding of an IDP with its target and to provide clues on electrostatic interactions in disordered states of proteins, we measured the pK_a values of all IF7 acidic groups (Glu32, Glu36, Glu38, Asp40, Asp58, and Ser65, the backbone C‐terminus) at 100 mM NaCl concentration, by using NMR spectroscopy. We also obtained solution structures of IF7 through molecular dynamics simulation, validated them on the basis of previous experiments, and used them to obtain theoretical estimates of the pK_a values. Titration values for the two Asp and three Glu residues of IF7 were similar to those reported for random‐coil models, suggesting the lack of electrostatic interactions around these residues. Furthermore, our results suggest the presence of helical structure at the N‐terminus of the protein and of conformational changes at acidic pH values. The overall experimental and in silico findings suggest that local interactions and conformational equilibria do not play a role in determining the electrostatic features of the acidic residues of IF7.     

Potentiometric titration curves of oxidized and reduced horse heart cytochrome c

Potentiometric titration curves of oxidized and reduced horse heart cytochrome c in 0.15M KCl at 20°C have been obtained by timed titration (0.125–0.500 μmol/sec) from the isoionic points (pH 10.2–10.4) to pH 3 and back to the isoionic point. Computer-assisted (PROPHET) data acquisition and blank corrections give curves with good precision with a maximum standard deviation of 0.3 groups for an average error of 1%. The potentiometric titration curve of reduced cytochrome c is reversible within the precision of the method and for the pH range studied. The potentiometric curves for oxidized cytochrome c titrated upscale (pH 3–10) and downscale (pH 10–3) are not reversible. However, they show the same ionization behavior after the initial downscale titration. This is probably the result of a conformational change. Comparison of the data herein reported with the titration curves of oxidized cytochrome c already published by others indicates good agreement on the basis of a normalization of the concentration of protein or on the basis of 25 titrable groups between the acid end point and the isoionic pH. Titration of the 2 μmol imidazole in the upscale or downscale direction gives the correct analytical concentration and pK′ after correction for the solvent titration. Titration of reduced cytochrome c in the presence and absence of an additional equivalent of imidazole gave a difference titration curve, which indicates that a group on the protein shifts from pK′ 5.8 to pK′ 5.3 in the presence of imidazole. The pK′ of imidazole, in the presence of the protein, remains at a nearly normal value of 7.34.     

1H-Nuclear magnetic resonance study on imidazole–imidazole interaction in L-histidyl-L-histidine and D-histidyl-L-histidine: Analysis including microscopic dissociation series

The ¹H-nmr titration curves of chemical shifts versus pH were observed for the protons of _D,L-histidyl-_D,L-histidine as representative of cases with two or more ionizable groups with similar pK_a values. The titration curves of L -histidyl-L -histidine and D -histidyl-L -histidine were individually analyzed according to two mathematical models: one of a macroscopic dissociation series and one of a microscopic dissociation series. Most-probable values and standard deviations were obtained for pK_a values and intrinsic chemical shifts. An analysis including the microscopic dissociation series yielded an electrostatic interaction between twoimidazole rings of about 0.3 pH units for L -histidyl-L -histidine and about 0.7 pH units for D -histidyl-L -histidine. The difference of the magnitude of imidazole-imidazole interactions between L -histidyl-L -histidyne and D -histidyl-L -histidine was interpreted in terms of the spatial arrangement of two imidazole rings in each molecule based on the solution conformation estimated from Gd(III)-induced relaxation enhancements.     

Functional tuning of the catalytic residue pKa in a de novo designed esterase

AlleyCatE is a de novo designed esterase that can be allosterically regulated by calcium ions. This artificial enzyme has been shown to hydrolyze p‐nitrophenyl acetate (pNPA) and 4‐nitrophenyl‐(2‐phenyl)‐propanoate (pNPP) with high catalytic efficiency. AlleyCatE was created by introducing a single‐histidine residue (His¹⁴⁴) into a hydrophobic pocket of calmodulin. In this work, we explore the determinants of catalytic properties of AlleyCatE. We obtained the pK_a value of the catalytic histidine using experimental measurements by NMR and pH rate profile and compared these values to those predicted from electrostatics pK_a calculations (from both empirical and continuum electrostatics calculations). Surprisingly, the pK_a value of the catalytic histidine inside the hydrophobic pocket of calmodulin is elevated as compared to the model compound pK_a value of this residue in water. We determined that a short‐range favorable interaction with Glu¹²⁷ contributes to the elevated pK_a of His¹⁴⁴. We have rationally modulated local electrostatic potential in AlleyCatE to decrease the pK_a of its active nucleophile, His¹⁴⁴, by 0.7 units. As a direct result of the decrease in the His¹⁴⁴ pK_a value, catalytic efficiency of the enzyme increased by 45% at pH 6. This work shows that a series of simple NMR experiments that can be performed using low field spectrometers, combined with straightforward computational analysis, provide rapid and accurate guidance to rationally improve catalytic efficiency of histidine‐promoted catalysis. Proteins 2017; 85:1656–1665. © 2017 Wiley Periodicals, Inc.     

On the Hill plot of NMR data for titration of protein residues

The Hill plots of NMR titration data for protein residues disclose more clearly than the usual titration curves the presence of multiple weak perturbations originating from other titratable groups, and should be used whenever the conventional curve fitting is poor. For a quantitative interpretation, we derive here expressions for the Hill equation and the Hill coefficient when the titration of the observed group is perturbed by more than one titratable group. When the generalized Hill equation is fitted to the data, values of the interaction parameters between the observed group and the others are extracted provided that there are no mutual interactions between the latter groups. The method is applied to the titration data of two histidyl residues of l-arginine phosphotransferase (E.C. 2.7.3.3.) in the transition state analogue complex (enzyme-Mg²⁺-ADP-NOsk3/–l-Arg). From the Hill plots, interactions with three titratable groups are disclosed for both residues, and the fitting with the Hill equation reveals that they experience perturbations from the same three groups. Microscopic pK values are obtained for all the involved groups, indicating large changes (up to 3 pH units) upon protonation of the interacting groups. As compared to the conventional fitting procedure, the use and fitting of Hill plots yields from NMR data more information on the neighbourhood of enzyme residues and on the changes intervening therein through the steps involved in the catalysis.     

Reactions of the amino groups in ribonuclease A: I. Kinetic studies

A kinetic analysis has been made of the reaction of the amino groups of ribonuclease A with trinitrobenzene-sulfonic acid. The number of reactive groups and the number of subsets were markedly dependent on the nature and concentrations of the buffer and the pH. Apparent values of pK_a, calculated from the variation of the velocity constants with pH, could, in general, be obtained only for pH values above 7.4. Below this pH the velocity constants were greater than the values calculated from the intrinsic constants. The values of pK_a were in the range of 7.9 – 9.0, which are somewhat smaller than those derived from titration data.The change of behavior of the amino groups with pH is confirmed by a study of the effects of ionic strength on the reactions.The velocity constants generally appear to decrease with increasing concentration of protein.It is shown that there is a close correlation between the pH region in which large changes occur of the reactivities of the amino groups of RNase and the kinetics of the enzyme reaction.     

Ionization behavior of proteins. II. Chymotrypsinogen and its group-modified derivatives: Study of their ionization characteristics by potentiometric and calorimetric titration

Chymotrypsinogen, nitrated chymotrypsinogen (two of the four tyrosyls nitrated), acetylated chymotrypsinogen (all amino groups blocked), and nitrated-acetylated chymotrypsinogen were titrated as f(pH) in an isoperibolic calorimeter at 20°C. After appropriate correction and reduction of both the potentiometric and thermal titration data, the parameters N (ionizable groups per group-set), pK′, and ΔH_i (heat of ionization) were evaluated using the iterative curve-fitting algorithm of the MLAB computer program. The pK′ parameters so obtained for the two normally ionizing tyrosyl groups in chymotrypsinogen and the two nitrated tyrosyl groups in the nitrated proteins essentially agreed with the results of spectral titration. Excellent fits to all data could be obtained using evaluated parameter sets of N and pK′ for the potentiometric titration data (groups vs pH plots) and N, pK′, and ΔH_i sets for the calorimetric data (total heat vs pH plots). The invocation of electrostatic interaction effects was not required to explain the data satisfactorily, despite the differences in charge number and type among the four proteins. Rather, the data can be represented by series expressions of the mass-action law. Using all information, viz., the consequences of functional group modification, the downscale shift in tyrosyl group pK's on nitration, and the numerical values of the evaluated N, pK′, and ΔH_i parameter sets for all proteins, the chemical identity of the various classes of group sets can be assigned with reasonable assurance.     

pH dependence of conformational fluctuations of the protein backbone

Proton binding equilibria (pK_a values) of ionizable groups in proteins are exquisitely sensitive to their microenvironments. Apparent pK_a values measured for individual ionizable residues with NMR spectroscopy are actually population‐weighted averages of the pK_a in different conformational microstates. NMR spectroscopy experiments with staphylococcal nuclease were used to test the hypothesis that pK_a values of surface Glu and Asp residues are affected by pH‐sensitive fluctuations of the backbone between folded and locally unfolded conformations. ¹⁵N spin relaxation studies showed that as the pH decreases from the neutral into the acidic range the amplitudes of backbone fluctuations in the ps‐ns timescale increase near carboxylic residues. Hydrogen exchange experiments suggested that backbone conformational fluctuations promoted by decreasing pH also reflect slower local or sub‐global unfolding near carboxylic groups. This study has implications for structure‐based pK_a calculations: (1) The timescale of the backbone's response to ionization events in proteins can range from ps to ms, and even longer; (2) pH‐sensitive fluctuations of the backbone can be localized to both the segment the ionizable residue is attached to or the one that occludes the ionizable group; (3) Structural perturbations are not necessarily propagated through Coulomb interactions; instead, local fluctuations appear to be coupled through the co‐operativity inherent to elements of secondary structure and to networks of hydrogen bonds. These results are consistent with the idea that local conformational fluctuations and stabilities are important determinants of apparent pK_a values of ionizable residues in proteins. Proteins 2014; 82:3132–3143. © 2014 Wiley Periodicals, Inc.     

Combined computational and biochemical study reveals the importance of electrostatic interactions between the “pH sensor” and the cation binding site of the sodium/proton antiporter NhaA of Escherichia coli

Sodium proton antiporters are essential enzymes that catalyze the exchange of sodium ions for protons across biological membranes. The crystal structure of NhaA has provided a basis to explore the mechanism of ion exchange and its unique regulation by pH. Here, the mechanism of the pH activation of the antiporter is investigated through functional and computational studies of several variants with mutations in the ion‐binding site (D163, D164). The most significant difference found computationally between the wild type antiporter and the active site variants, D163E and D164N, are low pK_a values of Glu78 making them insensitive to pH. Although in the variant D163N the pK_a of Glu78 is comparable to the physiological one, this variant cannot demonstrate the long‐range electrostatic effect of Glu78 on the pH‐dependent structural reorganization of trans‐membrane helix X and, hence, is proposed to be inactive. In marked contrast, variant D164E remains sensitive to pH and can be activated by alkaline pH shift. Remarkably, as expected computationally and discovered here biochemically, D164E is viable and active in Na⁺/H⁺ exchange albeit with increased apparent K_M. Our results unravel the unique electrostatic network of NhaA that connect the coupled clusters of the “pH sensor” with the binding site, which is crucial for pH activation of NhaA. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Bayesian model aggregation for ensemble‐based estimates of protein pKa values

This article investigates an ensemble‐based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pK_a predictions. Structure‐based pK_a calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pK_a prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pK_a prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pK_a values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pK_a Cooperative and the pK_a measurements are based on experimental work conducted by the García‐Moreno lab. Our cross‐validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble‐based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pK_a prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy. Proteins 2014; 82:354–363. © 2013 Wiley Periodicals, Inc.     

A thermodynamic characterization of the interaction of 8‐anilino‐1‐naphthalenesulfonic acid with native globular proteins: the effect of the ligand dimerization in the analysis of the binding isotherms

8‐Anilino‐1‐naphthalenesulfonic acid (ANS) is a popular fluorescence probe, broadly used for the analysis of proteins, but the nature of its interaction with proteins and the high increase in the fluorescence intensity that takes place upon such process are still unclear. In the last few years, isothermal titration calorimetry has been used to characterize the nature of the interaction of this dye with proteins. The analysis of the binding isotherms of these studies has not considered the dimerization equilibrium of ANS, which is pH dependent, and it can result in serious errors in the data analysis. In the present work we have developed a suitable data analysis by which this process is taken into account. To study the binding of the dye to proteins at different pH values, we have used the Abl‐SH3 domain. Our results suggest that at pH 3 and 5, where the dimerization of the ANS is important, electrostatic interactions are significant for the binding of ANS to the Abl‐SH3 domain. However, at pH 7, ANS behaves mostly as monomer and the interaction with the protein is mainly hydrophobic. The pH dependent behavior of the ANS binding to proteins can be explained in terms of ionization states of both, the protein and the ANS. Copyright © 2010 John Wiley & Sons, Ltd.     

Predicting protein pKa by environment similarity

A statistical method to predict protein pK_a has been developed by using the 3D structure of a protein and a database of 434 experimental protein pK_a values. Each pK_a in the database is associated with a fingerprint that describes the chemical environment around an ionizable residue. A computational tool, MoKaBio, has been developed to identify automatically ionizable residues in a protein, generate fingerprints that describe the chemical environment around such residues, and predict pK_a from the experimental pK_a values in the database by using a similarity metric. The method, which retrieved the pK_a of 429 of the 434 ionizable sites in the database correctly, was crossvalidated by leave‐one‐out and yielded root mean square error (RMSE) = 0.95, a result that is superior to that obtained by using the Null Model (RMSE 1.07) and other well‐established protein pK_a prediction tools. This novel approach is suitable to rationalize protein pK_a by comparing the region around the ionizable site with similar regions whose ionizable site pK_a is known. The pK_a of residues that have a unique environment not represented in the training set cannot be predicted accurately, however, the method offers the advantage of being trainable to increase its predictive power. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Electrostatic interactions in the acid denaturation of alpha-lactalbumin determined by NMR.

alpha-Lactalbumin (alpha-LA) undergoes a pH-dependent unfolding from the native state to a partially unfolded state (the molten globule state). To understand the role of electrostatic interactions in protein denaturation, NMR and CD pH titration experiments are performed on guinea pig alpha-LA. Variation of pH over the range of 7.0 to 2.0 simultaneously leads to the acid denaturation of the protein and the titration of individual ionizable groups. The pH titrations are interpreted in the context of these coupled events, and indicate that acid denaturation in alpha-LA is a cooperative event that is triggered by the protonation of two ionizable residues. Our NMR results suggest that the critical electrostatic interactions that contribute to the denaturation of alpha-LA are concentrated in the calcium binding region of the protein.     

Calorimetric determination of the enthalpy of ionization of oxidized and reduced horse heart cytochrome c

The heats of ionization of protons, ΔH_i, of oxidized and reduced horse heart cytochrome c in 0.15M KCl at 20°C were determined using a titration calorimeter which simultaneously afforded the potentiometric titration curve. Reproducibility of the thermal titrations is within 2%, and evaluation of the heats observed after the heat loss corrections is estimated to be within 5%. A single titration of oxidized cytochrome c from pH 11 to 3 is in excellent agreement with the thermal titration of this protein obtained with flow calorimetry. The thermal titration, however, is not reversible, due in part to the loss of titratable group(s) in this pH region and to the heat contribution of the acid and alkaline conformational changes which occur. Although of lesser magnitude, the reduced form also indicates similar thermal transitions. These differences are due solely to conformational contributions to the thermal process, since the potentiometric curves are reversible. The nature of the irreversibility for oxidized cytochrome c appears to involve the loss of a group with pK′ 8.9 and the shift of two groups from pK′ 5.6 to 4.8. Thermal difference curves for this process indicate that heats of ?7.8 and ?24.1 kcal/mol are liberated which are centered at pH 9.3 and 3.9, respectively.     

Improving the analysis of NMR spectra tracking pH‐induced conformational changes: Removing artefacts of the electric field on the NMR chemical shift

pH‐induced chemical shift perturbations (CSPs) can be used to study pH‐dependent conformational transitions in proteins. Recently, an elegant principal component analysis (PCA) algorithm was developed and used to study the pH‐dependent structural transitions in bovine β‐lactoglobulin (βLG) by analyzing its NMR pH‐titration spectra. Here, we augment this analysis method by filtering out changes in the NMR chemical shift that stem from effects that are electrostatic in nature. Specifically, we examine how many CSPs can be explained by purely electrostatic effects arising from titrational events in βLG. The results show that around 20% of the amide nuclei CSPs in βLG originate exclusively from “through‐space” electric field effects. A PCA of NMR data where electric field artefacts have been removed gives a different picture of the pH‐dependent structural transitions in βLG. The method implemented here is well suited to be applied on a whole range of proteins, which experience at least one pH‐dependent conformational change. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

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.     

Effect of methylation on the side‐chain pKa value of arginine

Arginine methylation is important in biological systems. Recent studies link the deregulation of protein arginine methyltransferases with certain cancers. To assess the impact of methylation on interaction with other biomolecules, the pK_a values of methylated arginine variants were determined using NMR data. The pK_a values of monomethylated, symmetrically dimethylated, and asymmetrically dimethylated arginine are similar to the unmodified arginine (14.2 ± 0.4). Although the pK_a value has not been significantly affected by methylation, consequences of methylation include changes in charge distribution and steric effects, suggesting alternative mechanisms for recognition.     

Electrostatic contributions to the stability of the GCN4 leucine zipper structure

Ion pairs are ubiquitous in X-ray structures of coiled coils, and mutagenesis of charged residues can result in large stability losses. By contrast, pK_a values determined by NMR in solution often predict only small contributions to stability from charge interactions. To help reconcile these results we used triple-resonance NMR to determine pK_a values for all groups that ionize between pH 1 and 13 in the 33 residue leucine zipper fragment, GCN4p. In addition to the native state we also determined comprehensive pK_a values for two models of the GCN4p denatured state: the protein in 6 M urea, and unfolded peptide fragments of the protein in water. Only residues that form ion pairs in multiple X-ray structures of GCN4p gave large pK_a differences between the native and denatured states. Moreover, electrostatic contributions to stability were not equivalent for oppositely charged partners in ion pairs, suggesting that the interactions between a charge and its environment are as important as those within the ion pair. The pH dependence of protein stability calculated from NMR-derived pK_a values agreed with the stability profile measured from equilibrium urea-unfolding experiments as a function of pH. The stability profile was also reproduced with structure-based continuum electrostatic calculations, although contributions to stability were overestimated at the extremes of pH. We consider potential sources of errors in the calculations, and how pK_a predictions could be improved. Our results show that although hydrophobic packing and hydrogen bonding have dominant roles, electrostatic interactions also make significant contributions to the stability of the coiled coil.     

Constant pH molecular dynamics of proteins in explicit solvent with proton tautomerism

pH is a ubiquitous regulator of biological activity, including protein‐folding, protein‐protein interactions, and enzymatic activity. Existing constant pH molecular dynamics (CPHMD) models that were developed to address questions related to the pH‐dependent properties of proteins are largely based on implicit solvent models. However, implicit solvent models are known to underestimate the desolvation energy of buried charged residues, increasing the error associated with predictions that involve internal ionizable residue that are important in processes like hydrogen transport and electron transfer. Furthermore, discrete water and ions cannot be modeled in implicit solvent, which are important in systems like membrane proteins and ion channels. We report on an explicit solvent constant pH molecular dynamics framework based on multi‐site λ‐dynamics (CPHMD^MSλD). In the CPHMD^MSλD framework, we performed seamless alchemical transitions between protonation and tautomeric states using multi‐site λ‐dynamics, and designed novel biasing potentials to ensure that the physical end‐states are predominantly sampled. We show that explicit solvent CPHMD^MSλD simulations model realistic pH‐dependent properties of proteins such as the Hen‐Egg White Lysozyme (HEWL), binding domain of 2‐oxoglutarate dehydrogenase (BBL) and N‐terminal domain of ribosomal protein L9 (NTL9), and the pK_a predictions are in excellent agreement with experimental values, with a RMSE ranging from 0.72 to 0.84 pK_a units. With the recent development of the explicit solvent CPHMD^MSλD framework for nucleic acids, accurate modeling of pH‐dependent properties of both major class of biomolecules—proteins and nucleic acids is now possible. Proteins 2014; 82:1319–1331. © 2013 Wiley Periodicals, Inc.