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     

Laws of complex formation in a series of azo-substituted pyrocatechol derivatives and their tin(II) complexes

Physicochemical properties of new reagents, azo-substituted pyrocatechol derivatives and their tin(II) complexes, are studied. The acid-base properties of the hydroxy groups (pK′_i, pK″_i), parameters of complex formation reactions (pH, temperature, time), and instability constants of the complexes formed (pK _i) are determined. Quantitative correlations between the dissociation constants (pK′_a) of the functional analytical group, and the electronic Hammett constant σ for a substituent (pK′_a-pH₅₀ of the complex formation reaction), as well as between pK′_a and instability constants of the complexes (pK _a), are established. The quantitative correlations established allow the prediction of the physicochemical properties of the reagents and tin(II) complexes with new reagents of this class with the same functional analytical group (FAG) but other substituents.     

Benchmarking and validating algorithms that estimate p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values of drugs based on their molecular structures

The REGDIA regression diagnostics algorithm in S-Plus is introduced in order to examine the accuracy of pK _a predictions made with four updated programs: PALLAS, MARVIN, ACD/pKa and SPARC. This report reviews the current status of computational tools for predicting the pK _a values of organic drug-like compounds. Outlier predicted pK _a values correspond to molecules that are poorly characterized by the pK _a prediction program concerned. The statistical detection of outliers can fail because of masking and swamping effects. The Williams graph was selected to give the most reliable detection of outliers. Six statistical characteristics (F _exp, R ², , MEP, AIC, and s(e) in pK _a units) of the results obtained when four selected pK _a prediction algorithms were applied to three datasets were examined. The highest values of F _exp, R ², , the lowest values of MEP and s(e), and the most negative AIC were found using the ACD/pK _a algorithm for pK _a prediction, so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test performed by the REGDIA program can also be applied to test the accuracy of other predicted values, such as log P, log D, aqueous solubility or certain physicochemical properties of drug molecules.     

Determination of the pKa of Benzophenones by Capillary Zone Electrophoresis

Electrophoretic behavior of seven benzophenones as a function of the buffer pH was investigated, and their pK_a values were determined by capillary zone electrophoresis. The determination of pK_a allows us to rationalize the influence of the buffer pH on the migration behavior of benzophenones. The results reveal that both the presence of intramolecular hydrogen bond and the favorable π‐electronic delocalization decrease the degree of the acid dissociation of the hydroxyl groups of hydroxybenzophenones. However, the introduction of a hydroxyl group at the 4‐position or at the 2′‐position of the aromatic ring of hydroxybenzophenones would decrease greatly their pK_a1 values. Thus the presence of this type of hydrogen bonding also plays an important role in the acid dissociation of these hydroxybenzophenones.     

Determination of acid dissociation constants of flavin analogues by capillary zone electrophoresis

Acid dissociation constants (pK_a) of nine kinds of flavin analogues as molecular catalyst candidates were determined by CZE. Although some of the analogues are instable and degradable under the light exposure or in alkaline aqueous solutions, the effective electrophoretic mobility of the flavin analogue of interest has been measured with the residual substance. The pK_a values of the flavin analogues were analyzed through the changes in the effective electrophoretic mobility with varying pH of the separation buffer. One or two steps pK_a values were determined by the analysis. One of the degraded species from the flavin analogues, lumichrome, was also detected in the CZE analysis, and its pK_a values were also determined. While coexisting impurities generated over the storage conditions were found in some analogues, the pK_a values of the target analogues were successfully determined with the help of the CZE separations. A pressure-assisted CZE was utilized for the determination or the estimation of the pK_a values of such analogues as possessing carboxylic acid moiety.     

Avoiding gas-phase calculations in theoretical p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> predictions

CBS-QB3, two simplified and less computationally demanding versions of CBS-QB3, DFT-B3LYP, and HF quantum chemistry methods have been used in conjunction with the CPCM continuum solvent model to calculate the free energies of proton exchange reactions in water solution following an isodesmic reaction approach. According to our results, the precision of the predicted pK _a values when compared to experiment is equivalent to that of the thermodynamic cycles that combine gas-phase and solution-phase calculations. However, in the aqueous isodesmic reaction schema, the accuracy of the results is less sensitive to the presence of explicit water molecules and to the global charges of the involved species since the free energies of solvation are not required. In addition, this procedure makes easier the prediction of pK _a values for molecules that undergo large conformational changes in solvation process and makes possible the pK _a prediction of unstable species in gas-phase such as some zwitterionic tautomers. The successive pK _a values of few amino acids corresponding to the ionization of the α-carboxylic acid and α-amine groups, which is one of the problematic cases for thermodynamic cycles, were successfully calculated by employing the aqueous isodesmic reaction yielding mean absolute deviations of 0.22 and 0.19 pK _a units for the first and second ionization processes, respectively.     

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.     

Accurate pKa Calculation of the Conjugate Acids of Alkanolamines,Alkaloids and Nucleotide Bases by Quantum Chemical Methods

The pK_a of the conjugate acids of alkanolamines, neurotransmitters, alkaloid drugs and nucleotide bases are calculated with density functional methods (B3LYP, M08‐HX and M11‐L) and ab initio methods (SCS‐MP2, G3). Implicit solvent effects are included with a conductor‐like polarizable continuum model (CPCM) and universal solvation models (SMD, SM8). G3, SCS‐MP2 and M11‐L methods coupled with SMD and SM8 solvation models perform well for alkanolamines with mean unsigned errors below 0.20 pK_a units, in all cases. Extending this method to the pK_a calculation of 35 nitrogen‐containing compounds spanning 12 pK_a units showed an excellent correlation between experimental and computational pK_a values of these 35 amines with the computationally low‐cost SM8/M11‐L density functional approach.     

Direct determination of pKa values of cationic acids conjugated to heterocyclic amine N-oxides in polar aprotic and amphiprotic solvents

The applicability of the direct method of pK_a determination in the case of protonated heterocyclic amine N-oxides in a series of polar non-aqueous (aprotic and amphiprotic) solvents has been tested. The method is based on the pH determination of the non-aqueous solution of complex salt (the semiperchlorate in this case) formed by the N-oxides studied. The direct method not only provides for quick (one data point per each pK_a determined), but also relatively accurate estimates of acidic dissociation constants. It has been experimentally shown on the example of substituted pyridine N-oxides that this method is precise enough in all studied non-aqueous solvents when applied to compounds of not too low basicity (the pK_a being of the order of 5 or higher). To prove this, the pK_a values of protonated monocyclic N-oxides obtained by the direct method have been compared with those resulting from the potentiometric titration curve. The agreement between the results found by using both methods is very good in most cases, the differences being within standard deviations. Based upon this observation it can be inferred that the pK_a values of protonated bicyclic N-oxides in solvents studied determined by using the direct method can be also considered reliable, especially in the case of polar aprotic solvents.     

Acidity of Several Anilinium Derivatives in Pure Tetrahydrofuran

The acidity constant (pK _a) of eleven substituted anilinium ions and the dissociation constants of their perchlorate salts (pK _salt) were determined in pure tetrahydrofuran by potentiometry and conductometry. The pK _a values of the studied aniliniums extend downward the range of previously determined pK _a values. The resolution of acid strength for cationic acids in tetrahydrofuran was compared with those obtained in other amphiprotic and aprotic solvents. It is shown that the resolution in tetrahydrofuran is higher than the ones in water and methanol, similar to those in acetone, dimethyl sulfoxide and isobutylmethylketone, but lower than those in acetonitrile and nitromethane.     

Determination of thermodynamic pKa values of benzimidazole and benzimidazole derivatives by capillary electrophoresis

Thermodynamic pK_a values for benzimidazole and several substituted benzimidazoles were determined by CE. Electrophoretic mobilities of benzimidazoles were determined by CE at different pH levels and ionic strengths. The dependence of electrophoretic mobilities on pH was used to obtain pK_a values at different ionic strengths. Extrapolations to zero ionic strength were used to determine the thermodynamic pK_a values. Using this method the thermodynamic pK_a values of 15 benzimidazoles were determined and found to range from 4.48 to 7.38. Results from the CE measurements were compared with spectrophotometric measurements which were evaluated at wavelengths where the highest absorbance difference for varying pH was recorded. The two analytical techniques were in good agreement.     

Determination of acidity constants,ionic mobilities,and hydrodynamic radii of carborane-based inhibitors of carbonic anhydrases by capillary electrophoresis

Capillary electrophoresis (CE) has been applied for determination of the thermodynamic acidity constants (pK_a) of the sulfamidoalkyl and sulfonamidoalkyl groups, the actual and limiting ionic mobilities and hydrodynamic radii of important compounds, eight carborane-based inhibitors of carbonic anhydrases, which are potential new anticancer drugs. Two types of carboranes were investigated, (i) icosahedral cobalt bis(dicarbollide)(1-) ion with sulfamidoalkyl moieties, and (ii) 7,8-nido-dicarbaundecaborate with sulfonamidoalkyl side chains. First, the mixed acidity constants, pK_a^mix, of the sulfamidoalkyl and sulfonamidoalkyl groups of the above carboranes and their actual ionic mobilities were determined by nonlinear regression analysis of the pH dependences of their effective electrophoretic mobility measured by capillary electrophoresis in the pH range 8.00−12.25, at constant ionic strength (25 mM), and constant temperature (25°C). Second, the pK_a^mix were recalculated to the thermodynamic pK_as using the Debye–Hückel theory. The sulfamidoalkyl and sulfonamidoalkyl groups were found to be very weakly acidic with the pK_as in the range 10.78−11.45 depending on the type of carborane cluster and on the position and length of the alkyl chain on the carborane scaffold. These pK_as were in a good agreement with the pK_as (10.67−11.27) obtained by new program AnglerFish (freeware at https://echmet.natur.cuni.cz ), which provides thermodynamic pK_as and limiting ionic mobilities directly from the raw CE data. The absolute values of the limiting ionic mobilities of univalent and divalent carborane anions were in the range 18.3−27.8 TU (Tiselius unit, 1 × 10⁻⁹ m²/Vs), and 36.4−45.9 TU, respectively. The Stokes hydrodynamic radii of univalent and divalent carborane anions varied in the range 0.34−0.52 and 0.42−0.52 nm, respectively.     

Linear Free‐Energy Relationships between a Single Gas‐Phase Ab Initio Equilibrium Bond Length and Experimental pKa Values in Aqueous Solution

Remarkably simple yet effective linear free energy relationships were discovered between a single ab initio computed bond length in the gas phase and experimental pK_a values in aqueous solution. The formation of these relationships is driven by chemical features such as functional groups, meta/para substitution and tautomerism. The high structural content of the ab initio bond length makes a given data set essentially divide itself into high correlation subsets (HCSs). Surprisingly, all molecules in a given high correlation subset share the same conformation in the gas phase. Here we show that accurate pK_a values can be predicted from such HCSs. This is achieved within an accuracy of 0.2 pK_a units for 5 drug molecules.     

Influence of pH and organic modifiers on the dissociation constants of selected drugs using reversed‐phase thin‐layer chromatography: Comparison with other techniques and computational tools

Knowledge of the acid–base dissociation constants of drugs is the key to understanding their biopharmaceutical characteristics. In the present work, the effect of pH and organic modifiers (acetonitrile and methanol) was investigated in the determination of dissociation constants (pK_a) of nine representative drugs (atenolol, betahistine, clarithromycin, deferiprone, diclofenac, ibuprofen, metoprolol, naproxen and propranolol) using reversed‐phase thin‐layer chromatography. Mobile phase consisting of various buffers and methanol–acetonitrile (10, 20, 30, 40, 50 and 60%, v/v) was used to evaluate the retention pattern on reversed‐phase plates. Compared with methanol, acetonitrile gave better results for the experimentally determined pK_a values by extrapolation to zero organic modifier volume fractions. To assess the effectiveness of the developed method the results were correlated using principal component analysis and hierarchical cluster analysis. The calculated values of the aqueous dissociation constant were compared with those reported previously using potentiometry and capillary electrophoresis and also with different computational platforms like ACD/Lab, ChemAxon and Jchem calculator. The results obtained by the RPTLC method were in good agreement with potentiometric methods for pK_a determination.     

Protolytic equilibria of picric acid in a mixture of protophobic and protophilic polar solvents non-donors of H-bonds

A new differentiating medium for the study of prototropic equilibria is proposed: acetonitrile with a small addition of DMSO. From the dependence of the picric acid pK _a on the content of DMSO in this medium the optimum composition of the mixture was found ensuring the stability of the pK _a values with minimal addition of DSMO: 4 wt %. It was experimentally confirmed that the addition of water in an amount up to 0.1 wt % has virtually no effect on the measured pK _a value in a mixture with the optimum composition.     

CE determination of the thermodynamic pKa values and limiting ionic mobilities of 14 low molecular mass UV absorbing ampholytes for accurate characterization of the pH gradient in carrier ampholytes-based IEF and its numeric simulation

Fourteen low molecular mass UV absorbing ampholytes containing 1 or 2 weakly acidic and 1 or 2 weakly basic functional groups that best satisfy Rilbe's requirement for being good carrier ampholytes (ΔpK_a = pKa_monoanion ‒ pKa_monocation < 2) were selected from a large group of commercially readily available ampholytes in a computational study using two software packages (ChemSketch and SPARC). Their electrophoretic mobilities were measured in 10 mM ionic strength BGEs covering the 2 < pH < 12 range. Using our Debye-Hückel and Onsager-Fuoss laws-based new software, AnglerFish (freeware, https://echmet.natur.cuni.cz/software/download ), the effective mobilities were recalculated to zero ionic strength from which the thermodynamic pK_a values and limiting ionic mobilities of the ampholytes were directly calculated by Henderson-Hasselbalch equation-type nonlinear regression. The tabulated thermodynamic pK_a values and limiting ionic mobilities of these ampholytes (pI markers) facilitate both the overall and the narrow-segment characterization of the pH gradients obtained in IEF in order to mitigate the errors of analyte ampholyte pI assignments caused by the usual (but rarely proven) assumption of pH gradient linearity. These thermodynamic pK_a and limiting mobility values also enable the reality-based numeric simulation of the IEF process using, for example, Simul (freeware, https://echmet.natur.cuni.cz/software/download ).     

EFFECT OF THE BROMINE ATOM UPON THE DISSOCIATION CONSTANTS OF BROMOPYRIDINES,BROMOQUINOLINES AND 4-BROMOISOQUINOLINE IN THEIR LOWEST EXCITED SINGLET AND TRIPLET STATES*

Abstract— The lowest excited singlet-state dissociation constants (pK^S_a) of bromosubstituted pyridines, quinolines, and isoquinolines were determined from the pH-dependent shifts in their electronic absorption spectra. The lowest excited triplet-state dissociation constants (pK^T_a) of bromosubstituted quinolines and 4-bromoisoquinoline were obtained from the shifts of the 0–0 phosphorescence bands measured in rigid aqueous solution at 77 K. The pK^S_a values indicate that the basicity of these brominated nitrogen heterocycles is increased in the lowest excited singlet state by 2 to 10 orders of magnitude as compared with the ground state. The pK^T_a values are found to be significantly different from the corresponding ground-state pK_a values, indicating that the basicity of bromoquinolines is increased in the lowest excited triplet state by 1.7 to 3.0 pK units. The enhancement of the excited singlet-and triplet-state basicity of brominated nitrogen heterocycle derivatives as compared with the unsuhstituted parent compounds is attributed to the increased electron-donor conjugative interactions of the bromine atom pπ orbitals with π orbitals in the lowest excited singlet and triplet state.     

Capillary zone electrophoresis of basic drugs in non-aqueous acetonitrile with buffers based on a conventional pH scale

Summary The pK _a ^* values of 10 nitrogen-containing basic drugs in non-aqueous acetonitrile were determined from the pH^* dependence of their electrophoretic mobilities. The pH^* scale in the organic solvent was established using background electrolytes with known conventional pK _a ^* values, making further calibration with reference pH electrodes unnecessary. In acetonitrile the pK _a ^* values of analytes (or their conjugated cation acids, BH⁺, respectively) were 5.2±8.9 pK units>those in water. The observed change in pK _a ^* values of cationic analytes was, however, much less than the known respective change for neutral acids type HA. From the pK _a ^* values and the actual mobilities, it is possible to predict pH^* conditions to enable separation of analytes, and this was demonstrated for two pairs of common drugs.     

What are the pKa values of organophosphorus compounds?

A first-principle theoretical protocol was developed, which could successfully predict the pK_a values of a number of amines and thiols in DMSO with a precision of about 1.1 pK_a unit. Using this protocol we calculated the pK_a values of diverse types of organophosphorus compounds in DMSO. The accuracy of these predicted values was estimated to be about 1.1 pK_a because phosphorus is in the same group as nitrogen and in the same period as sulfur. The theoretical predictions were also consistent with all the available experimental data. Thus, a scale of reliable pK_a values was constructed for the first time for organophosphorus. These pK_a values would be helpful to synthetic chemists who need to design the experimental conditions for handling deprotonated organophosphorus. On the basis of these pK_a values we also studied, for the first time, some interesting topics such as the substituent effects on the pK_a values of various types of organophosphorus, and the differences between the pK_a values of organophosphorus and organic amines.