Frontispiece: What Are We Missing by Not Measuring the Net Charge of Proteins?

The net electrostatic charge (Z) of a folded protein in solution represents a bird's eye view of its surface potentials—including contributions from tightly bound metal, solvent, buffer, and cosolvent ions—and remains one of its most enigmatic properties. Few tools are available to the average biochemist to rapidly and accurately measure Z at pH≠pI. Tools that have been developed more recently seem to go unnoticed. Most scientists are content with this void and estimate the net charge of a protein from its amino acid sequence, using textbook values of pK_a. Thus, Z remains unmeasured for nearly all folded proteins at pH≠pI. When marveling at all that has been learned from accurately measuring the other fundamental property of a protein—its mass—one wonders: what are we missing by not measuring the net charge of folded, solvated proteins? A few big questions immediately emerge in bioinorganic chemistry. When a single electron is transferred to a metalloprotein, does the net charge of the protein change by approximately one elementary unit of charge or does charge regulation dominate, that is, do the pK_a values of most ionizable residues (or just a few residues) adjust in response to (or in concert with) electron transfer? Would the free energy of charge regulation (ΔΔG_z) account for most of the outer sphere reorganization energy associated with electron transfer? Or would ΔΔG_z contribute more to the redox potential? And what about metal binding itself? When an apo-metalloprotein, bearing minimal net negative charge (e.g., Z=−2.0) binds one or more metal cations, is the net charge abolished or inverted to positive? Or do metalloproteins regulate net charge when coordinating metal ions? The author's group has recently dusted off a relatively obscure tool—the “protein charge ladder”—and used it to begin to answer these basic questions.     

Empirical prediction of protein pKavalues with residue mutation

A fast, empirical method, Mut‐pKa, is presented for predicting the pK_a values of ionizable residues in proteins based on mutation. The method compares the effect of mutating each residue that may act as a hydrogen bond donor or acceptor for the ionizable residue. The energetic effect of each type of mutation, along with a desolvation measure and the overall background charge, is fit against pK_a data for histidine and carboxyl residues. A total of 214 residues from 35 different proteins were used in the dataset. Using 11 parameters for each type of ionizable residue, a root mean squared error (RMSE) of 0.78 and 1.12 pH units were obtained for carboxyl and histidines residues, respectively, using leave one out cross validation (LOOCV). The results were particularly promising for buried residues, which had RMSE values of 0.99 and 1.13 for carboxyl and histidine residues, respectively. A number of desolvation measures were tested. The simplest measure, the number of atoms surrounding the residue, was found to work best. The effect of using dynamics was also studied using short molecular dynamics runs, followed by minimization of the structures. Mut‐pKa has significantly fewer parameters than, but similar performance to, other empirical methods. Because of this and the LOOCV results, we believe the model is robust and that overfitting is not a problem. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

PKA17—A Coarse-Grain Grid-Based Methodology and Web-Based Software for Predicting Protein pK a Shifts

We have developed and tested PKA17, a coarse-grain grid-based model for predicting protein pK _a shifts. Our pK _a predictor is currently deployed via a website interface. We have carried out parameter fitting using 442 Asp, Glu, His, Lys, and Arg residues for which experimental results are available in the literature. PROPKA software has been used for benchmarking. The average unsigned error and root-mean-square deviation (RMSD) have been found to be 0.628 and 0.831 pH units, respectively, for PKA17. The corresponding results with PROPKA are 0.761 and 1.063 units. We have assessed the robustness of the developed PKA17 methodology with a number of tests and have also explored the possibility of using a combination of PROPKA and PKA17 calculations in order to improve the accuracy of predicted pK _a values for protein residues. We have also once again confirmed that protein acidity constants are influenced almost entirely by residues in the immediate spatial proximity of the ionizable amino acids. The resulting PKA17 software has been deployed online with a web-based interface at http://users.wpi.edu/~jpcvitkovic/pka_calc.html . © 2019 Wiley Periodicals, Inc.     

Incorporating solvation effects into density functional theory: Calculation of absolute acidities

An approach to the calculation of molecular electronic structures, solvation energies, and pK_a values in condensed phases is described. The electronic structure of the solute is described by density functional quantum mechanics, and electrostatic features of environmental effects are modeled through external charge distributions and continuum dielectrics. The reaction potential produced by a mode of the molecular charge distribution is computed via finite-difference solutions to the Poisson-Boltzmann equation and incorporated into the self-consistent field procedure. Here we report results on three sets of organic acids, whose pK_a values range over 16 pH units. The first set provides models for ionizable side chains in proteins; the second set considers the effects of substituting one to three chlorine atoms for hydrogens in acetic acid; and the final set consists of 4-substituted-bicyclo-[2.2.2]-octanecarboxylic acids. Successful prediction of “absolute” pK_a values places stringent requirements on the computation of gas-phase proton affinities and on the response to solvation. In some cases the current model shows substantial errors, but overall the results and trends are in good agreement with experiment. Prospects for extending this approach to more complex systems such as proteins are briefly discussed. © 1997 John Wiley & Sons, Inc.     

Physicochemical Profiling of Sartans: A Detailed Study of Ionization Constants and Distribution Coefficients

A detailed investigation of the ionization and lipophilicity profiles of selected sartans (valsartan, losartan, irbesartan, candesartan, candesartan cilexetil), a class of antihypertensives commonly used in therapy, is presented. The pK_a macroconstants were determined by integrated potentiometry, capillary electrophoresis, and UV spectrophotometry. The measured pK_a macroconstants were connected with the ionizable centers present in each molecule with the aid of model compounds. Potentiometric titrations with the GLpKa apparatus were performed to determine the distribution profile (log D vs. pH) of valsartan, while the shake‐flask procedure was used to characterize the distribution profile of the other compounds. Valsartan showed a lipophilicity profile consistent with the presence of two acidic centers. Losartan and irbesartan, which contain one acidic and one basic center, displayed the classical bell‐shaped profile of ordinary ampholytes. By contrast, a more complex situation emerged in the case of candesartan, due to the large number of ionization equilibria involved. The low solubility of candesartan cilexetil, together with the ease of hydrolysis of the ester moiety, prevented a successful investigation of its ionization and lipophilicity profiles.     

Computation of the influence of chemical substitution on the pK a of pyridine using semiempirical and ab initio methods

The physical properties of chemicals are strongly influenced by their protonation state, affecting, for example, solubility or hydrogen-bonding characteristics. The ability to accurately calculate protonation states in the form of pK _as is, therefore, desirable. Calculations of pK _a changes in a series of substituted pyridines are presented. Computations were performed using both ab initio and semiempirical approaches, including free energies of solvation via reaction-field models. The selected methods are readily accessible with respect to both software and computational feasibility. Comparison of calculated and experimental pK _as shows the experimental trends to be reasonably reproduced by the computations with root-mean-square differences ranging from 1.22 to 4.14 pK _a units. Of the theoretical methods applied the best agreement occurred using the second-order M?ller–Plesset/6-31G(d)/isodensity surface polarized continuum solvation model, while the more computationally accessible Austin model 1/Solvent model 2 (SM2) approach yielded results similar to the ab initio methods. Analysis of component contributions to the calculated pK _as indicates the largest source of error to be associated with the free energies of solvation of the protonated species followed by the gas-phase protonation energies; while the latter may be improved via the use of higher levels of theory, enhancements in the former require improvements in the solvation models. The inclusion of alternate minimum in the computation of pK _as is also indicated to contribute to differences between experimental and calculated pK _a values. Received: 27 April 1999 / Accepted: 27 July 1999 / Published online: 2 November 1999     

A reliable and efficient first principles‐based method for predicting pKa values. 4. organic bases

The ionization (dissociation) constant (pK_a) is one of the most important properties of a drug molecule. It is reported that almost 68% of ionized drugs are weak bases. To be able to predict accurately the pK_a value(s) for a drug candidate is very important, especially in the early stages of drug discovery, as calculations are much cheaper than determining pK_a values experimentally. In this study, we derive two linear fitting equations (pK_a = a × ΔE + b; where a and b are constants and ΔE is the energy difference between the cationic and neutral forms, i.e., ΔE = E_neutral?E_cationic) for predicting pK_as for organic bases in aqueous solution based on a training/test set of almost 500 compounds using our previously developed protocol (OLYP/6‐311+G**//3‐21G(d) with the the conductor‐like screening model solvation model, water as solvent; see Zhang, Baker, Pulay, J. Phys. Chem. A 2010 , 114, 432). One equation is for saturated bases such as aliphatic and cyclic amines, anilines, guanidines, imines, and amidines; the other is for unsaturated bases such as heterocyclic aromatic bases and their derivatives. The mean absolute deviations for saturated and unsaturated bases were 0.45 and 0.52 pK_a units, respectively. Over 60% and 86% of the computed pK_a values lie within ±0.5 and ±1.0 pK_a units, respectively, of the corresponding experimental values. The results further demonstrate that our protocol is reliable and can accurately predict pK_a values for organic bases. © 2012 Wiley Periodicals, Inc.     

MCCE2: Improving protein pKa calculations with extensive side chain rotamer sampling

Multiconformation continuum electrostatics (MCCE) explores different conformational degrees of freedom in Monte Carlo calculations of protein residue and ligand pK_as. Explicit changes in side chain conformations throughout a titration create a position dependent, heterogeneous dielectric response giving a more accurate picture of coupled ionization and position changes. The MCCE2 methods for choosing a group of input heavy atom and proton positions are described. The pK_as calculated with different isosteric conformers, heavy atom rotamers and proton positions, with different degrees of optimization are tested against a curated group of 305 experimental pK_as in 33 proteins. QUICK calculations, with rotation around Asn and Gln termini, sampling His tautomers and torsion minimum hydroxyls yield an RMSD of 1.34 with 84% of the errors being <1.5 pH units. FULL calculations adding heavy atom rotamers and side chain optimization yield an RMSD of 0.90 with 90% of the errors <1.5 pH unit. Good results are also found for pK_as in the membrane protein bacteriorhodopsin. The inclusion of extra side chain positions distorts the dielectric boundary and also biases the calculated pK_as by creating more neutral than ionized conformers. Methods for correcting these errors are introduced. Calculations are compared with multiple X‐ray and NMR derived structures in 36 soluble proteins. Calculations with X‐ray structures give significantly better pK_as. Results with the default protein dielectric constant of 4 are as good as those using a value of 8. The MCCE2 program can be downloaded from http://www.sci.ccny.cuny.edu/～mcce . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Direct Measurement of Charge Regulation in Metalloprotein Electron Transfer

Determining whether a protein regulates its net electrostatic charge during electron transfer (ET) will deepen our mechanistic understanding of how polypeptides tune rates and free energies of ET (e.g., by affecting reorganization energy, and/or redox potential). Charge regulation during ET has never been measured for proteins because few tools exist to measure the net charge of a folded protein in solution at different oxidation states. Herein, we used a niche analytical tool (protein charge ladders analyzed with capillary electrophoresis) to determine that the net charges of myoglobin, cytochrome c, and azurin change by 0.62±0.06, 1.19±0.02, and 0.51±0.04 units upon single ET. Computational analysis predicts that these fluctuations in charge arise from changes in the pK_a values of multiple non‐coordinating residues (predominantly histidine) that involve between 0.42–0.90 eV. These results suggest that ionizable residues can tune the reactivity of redox centers by regulating the net charge of the entire protein–cofactor–solvent complex.     

Effect of Phosphorylation on the Structural Behaviour of Peptides Derived from the Intrinsically Disordered C-Terminal Domain of Histone H1.0

To investigate the structural impact of phosphorylation on the human histone H1.0 C-terminal domain, we performed NMR structural studies of model peptides containing a single phosphorylation site: T¹¹⁸-H1.0 (T¹¹⁸PKK motif) and T¹⁴⁰-H1.0 (T¹⁴⁰PVK motif). Both model peptides are mainly disordered in aqueous solution in their non-phosphorylated and phosphorylated forms, but become structured in the presence of trifluoroethanol. The peptides T¹¹⁸-H1.0 and pT¹¹⁸-H1.0 contain two helical regions, a long amphipathic α helix spanning residues 104–115 and a short α/3₁₀ helix (residues 119–123), that are almost perpendicular in T¹¹⁸-H1.0 but have a poorly defined orientation in pT¹¹⁸-H1.0. Peptides T¹⁴⁰-H1.0 and pT¹⁴⁰-H1.0 form very similar α helices between residues 141–147. The TPKK and TPVK motifs show the same backbone conformation, but differ in their side-chain contacts; the Thr and pThr side chains interact with the i+2 Lys side chain in the TPKK motif, and with the i+3 Lys side chain in the TPVK motif. The pT phosphate group in pT¹¹⁸-H1.0 and pT¹⁴⁰-H1.0 has pK_a values below the intrinsic values, which can be explained by non-specific charge–charge interactions with nearby Lys. The non-polar Val in the TPVK motif accounts for the pT¹⁴⁰ pK_a being closer to the intrinsic pK_a value than the pT¹¹⁸ pK_a. Altogether, these results validate that minimalist strategies using model peptides can provide structural details difficult to obtain in short-lived intrinsically disordered proteins and domains.     

A Non‐Invasive NMR Method Based on Histidine Imidazoles to Analyze the pH‐Modulation of Protein–Nucleic Acid Interfaces

A useful ²J(N?H) coupling‐based NMR spectroscopic approach is proposed to unveil, at the molecular level, the contribution of the imidazole groups of histidines from RNA/DNA‐binding proteins on the modulation of binding to nucleic acids by pH. Such protonation/deprotonation events have been monitored on the single His96 located at the second RNA/DNA recognition motif (RRM2) of T‐cell intracellular antigen‐1 (TIA‐1) protein. The pK_a values of the His96 ionizable groups were substantially higher in the complexes with short U‐rich RNA and T‐rich DNA oligonucleotides than those of the isolated TIA‐1 RRM2. Herein, the methodology applied to determine changes in pK_a of histidine side chains upon DNA/RNA binding, gives valuable information to understand the pH effect on multidomain DNA/RNA‐binding proteins that shuttle among different cellular compartments.     

Negative influence of pKa on activation energy barrier: A case study for double proton transfer reaction in inorganic acid dimers

Strength of acid can be determined by means of pK_a value. Attempts have been made to find a relationship between pK_a and activation energy barrier for a double proton transfer (DPT) reaction in inorganic acid dimers. Negative influence of pK_a is observed on activation energy (E_a) which is contrary to the general convention of pK_a. Four different levels of theories with two different basis sets have been used to calculate the activation energy barrier of the DPT reaction in inorganic acid dimers. A model based on first and second order polynomial has been created to find the relationship between activation energy for DPT reaction. © 2018 Wiley Periodicals, Inc.     

Theoretical pKa calculations of proteins; the tyrosine and lysine residues of b-elicitin

Elicitins are small proteins that are secreted by plant pathogenic fungi. In this work we have used a computer program that utilizes the boundary element method for heterogeneous dielectrics with ionic strength to calculate the pK _a of all titrating groups in the 98-residue protein β-cryptogein. Our results are in reasonable agreement with the experimentally determined pK _a values for the Tyr residues in the protein. We find that the functionally important Lys13 residue has a normal pK _a of 10.3. Our work also shows that there is no direct correlation between the exposure of an amino acid sidechain and its pK _a. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 11 November 1998     

Capillary electrokinetic fractionation mass spectrometry (CEkF/MS): Technology setup and application to metabolite fractionation from complex samples coupled at‐line with ultrahigh‐resolution mass spectrometry

Capillary electrokinetic fractionation (CEkF) is investigated as a new, simple, and robust approach for semipreparative and analytical sample analysis based on pK_a‐dependant pH‐driven electrophoretic mobility. CEkF was optimized with contactless conductivity detection and conducted with 10 kV reverse voltage for 10 min, then coupled on/at‐line to ESI/MS. We propose a semi‐empirical model with 14 representative compounds based on the correlation between sample/medium pH regulating the partial charge, the electrokinetic loading of the capillary and intensity (I) of analytes. According to the model, an empirical function (I = f (pH)) could be derived to calculate the acid dissociation constant (pK_a) of various model compounds based on their pH‐dependant MS intensity profiles with the RSD < 4.05. Using the ultrahigh‐resolution of ion cyclotron resonance Fourier transform MS, the pK_a model was further illustrated in real samples into the structure prediction of important compounds in wine over two vintages. The established CEkF was successfully used to selectively fractionate sulfur compounds from the complex wine samples at pH 1.66. The proposed CEkF approach should allow in the future the simultaneous pK_a evaluation of multiple constituents without complicated separation out of a complex mixture in metabolomics or environmental chemistry.     

Imidazoline‐N‐oxyl: A DFT Study of Its Protonation Reaction

Imidazoline‐based nitroxides are developed as pH probes. Their pK_a values vary over a wide range (from 1 to 11), depending on the substituents attached to the five‐membered cyclic nitroxide. Density functional calculations using the PBE1PBE method at the 6‐31+G(d,p) level, combined with natural bond orbital (NBO), frontier molecular orbital (FMO), geometry, Mulliken charge, and thermodynamic analyses, are carried out to disclose the effects involved in the changes in pK_a. The studies show that the decrease of seven pK_a units from pyrrolidine ( 11 ) to imidazoline‐N‐oxyl 8 is due to the inductive electron‐withdrawing capacity of the nitroxyl group. On the other hand, by combining both the inductive and mesomeric electron‐withdrawing capacities of the NO₂ group with delocalization of the lone pair on the amino N atom of the π system of the vinyl linker, the pK_a of 4.5 of 8 was increased by around three units to 7.8 for 1 / 2 .     

Determination of thermodynamic pKa values of pharmaceuticals from five different groups using capillary electrophoresis

A determination of the thermodynamic acid dissociation constants (pK_a) of 22 frequently used pharmaceuticals using capillary electrophoresis in aqueous media is presented in this work. The investigated pharmaceuticals belong to different pharmacological groups: macrolides, fluoroquinolones, sulfonamides, β‐lactams, tetracyclines, and other miscellaneous pharmaceuticals. The electrophoretic mobilities of the investigated analytes were monitored in a pH range from 2.00 to 10.82. The data were fitted with an appropriate mathematical model using a nonlinear regression analysis to obtain pK_a values. Experimentally obtained data were well described by the mathematical model chosen for each analyte that was confirmed by r² values higher than 0.99 for most of the investigated analytes. Extrapolations to zero ionic strength were used to determine the thermodynamic pK_a values. Experimentally obtained acid dissociation constants were interpreted using structural formulae of investigated analytes and the moieties corresponding to specific pK_a were identified.     

Thermodynamic Estimate of pKa Values of the Carboxylic Acids in Aqueous Solution with the Density Functional Theory

The 96 pK_a values of 85 carboxylic acids in aqueous solution were calculated with the density functional theory method at the level of B3LYP/6‐31+G(d,p) and the polarizable continuum model (PCM) was used to describe the solvent. In the calculations of pK_a values, the dissociation Gibbs free energies were directly calculated using carboxylic acid dissociation reactions in aqueous solution, i. e., no thermodynamic cycle was employed, which is different from the previous literatures. A highly significant correlation of R²=0.95 with a standard deviation (SD) of 0.36 between the experimental pK_a values and the calculated dissociation Gibbs free energies [ΔG(calc.)] was found. The slope of pK_a vs. (G(calc.)/(20303RT) is only 47.6% of the theoretically expected value, which implies that the ΔG(calc.) value from the theoretical calculation is larger than the actual one for all 85 carboxylic acids studied. Thus, by adding the 0.476 scaling‐factor into the slope, we can derive a reliably procedure that can reproduce the experimental pK_a values of carboxylic acids. The pK_a values furnished by this procedure are in good agreement with the experimental results for carboxylic acids in aqueous solution.     

Determination of acidity constants of pyridines,imidazoles, and oximes by capillary electrophoresis

The acidity constant in the form of pK_a is one of the most important physicochemical quantities. There are prediction tools available for calculating the pK_a, but they only deliver precise calculated values for a relatively small set of chemicals. For complex structures with multiple functional groups in particular, the error in the predicted pK_a is high due to the application domain of the corresponding models. Thus, we aim to enlarge the dataset of experimentally determined pK_a values using capillary electrophoresis. We, therefore, selected various pyridines, imidazoles, and oximes to determine the pK_a values using the internal standard approach and the classical method. Especially oximes were not investigated in the past, and predictions for them include larger errors. Thus, our experimentally determined values could contribute to an improved understanding of various functional groups impacting the pK_a values and serve as additional datasets to develop improved pK_a prediction tools.     

Effect of charge distribution on electrostatic chromophore—protein interactions in Bacteriorhodopsin

Charge distributions of a protonated and unprotonated Schiff base model compound are determined using different quantum chemical methods. After fitting the model molecule onto the protonated retinal Schiff base in Bacteriorhodopsin, electrostatic interaction energies between the model molecule and protein are calculated. Interaction energies as well as the calculated pK_1/2 values of the model molecule are shown to depend considerably on the chosen charge distribution. Electrostatic potential derived partial charges determined at different ab initio levels reveal interaction energies between the model molecule and nearby residues such as ARG-82, ASP-85, and ASP-212, which are relatively method independent. Consequently, such charge distributions also result in pK_1/2 values for the model molecule that are very similar. Larger deviations in the electrostatic interaction energies, however, are found in the case of charge distributions derived according to the Mulliken population analysis. Nevertheless, some sets of Mulliken derived partial charges predicted pK_1/2 values for the model molecule that are close to those determined with electrostatic potential derived partial charges. This agreement, however, is only achieved because the individual errors of the contributing terms are approximately compensated. The use of the extended atom model is shown to be problematic. Although potential derived charges can correctly describe electrostatic interaction energies, they fail to predict pK_1/2 values. On the basis of the present investigation a new set of partial charges for the protonated and unprotonated retinal Schiff base is proposed to be used in molecular dynamics simulations and electrostatics calculations. © 1997 by John Wiley & Sons, Inc.