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.     

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.     

Acidity Constant (pKa) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods

pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK_a). Obtaining molecular control over the factors that influence the pK_a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK_a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.     

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.     

Basicity of some aliphatic amines in mixed H2O?CH3CN solvents

The values of pK_a^ms (K_a^ms represents ionization constant of conjugate acid of amine base in mixed water–acetonitrile solvent) for all amines, except for charged amine bases, show a mild decrease (ca. 0.1–0.4 pK units) with the increase in CH₃CN content from 2 to ∼60% v/v. However, the pK_a^ms values at 70% v/v CH₃CN become nearly equal or slightly larger (by ≤0.7 pK units) than the corresponding pK_a^ms at 2% v/v CH₃CN for all neutral and charged amines. The values of pK_a^ms for phenol increase from 10.17 to 13.38 with the increase in the content of CH₃CN from 2 to 70% v/v in mixed aqueous solvent. Taft reaction constants, ρ*, obtained from the plots of pK_a^ms against ∑σ* for primary and secondary amines decrease by ca. 0.8 ρ* units with the increase in the CH₃CN content from 2 to 70% v/v. The values of pK_a^ms show an empirical linear relationship with the corresponding values of pK_a^w (where pK_a^w represents the pK_a obtained in aqueous solvent containing 2% v/v CH₃CN), which allows the estimation of a pK_a in mixed H₂O CH₃CN solvents from that in water. © 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 146–152, 2000     

Prediction of human cytochrome P450 2B6‐substrate interactions using hierarchical support vector regression approach

The human cytochrome P450 2B6 can metabolize a number of clinical drugs. Inhibition of CYP2B6 by coadministered multiple drugs may lead to drug–drug interactions and undesired drug toxicity. The aim of this investigation is to develop an in silico model to predict the interactions between P450 2B6 and novel inhibitors using a novel hierarchical support vector regression (HSVR) approach, which simultaneously takes into account the coverage of applicability domain (AD) and the level of predictivity. Thirty‐seven molecules were deliberately selected and rigorously scrutinized from the literature data, of which 26 and 11 molecules were treated as the training set and the test set to generate the models and to validate the generated models, respectively. The generated HSVR model gave rise to an r² value of 0.97 for observed versus predicted pK_m values for the training set, a q² value of 0.93 by the 10‐fold cross‐validation, and an r² value of 0.82 for the test set. Additionally, the predicted results show that the HSVR model outperformed the individual local models, the global model, and the consensus model. Thus, this HSVR model provides an accurate tool for the prediction of human cytochrome P450 2B6‐substrate interactions and can be utilized as a primary filter to eliminate the potential selective inhibitor of CYP2B6. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

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 ).     

Experimentation with different thermodynamic cycles used for pKa calculations on carboxylic acids using complete basis set and Gaussian‐n models combined with CPCM continuum solvation methods

Complete basis set and Gaussian‐n methods were combined with Barone and Cossi's implementation of the polarizable conductor model (CPCM) continuum solvation methods to calculate pK_a values for six carboxylic acids. Four different thermodynamic cycles were considered in this work. An experimental value of ?264.61 kcal/mol for the free energy of solvation of H⁺, ΔG_s(H⁺), was combined with a value for G_gas(H⁺) of ?6.28 kcal/mol, to calculate pK_a values with cycle 1. The complete basis set gas‐phase methods used to calculate gas‐phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed‐phase free energies are slightly less accurate than the gas‐phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. Thermodynamic cycles that include an explicit water in the cycle are not accurate when the free energy of solvation of a water molecule is used, but appear to become accurate when the experimental free energy of vaporization of water is used. This apparent improvement is an artifact of the standard state used in the calculation. Geometry relaxation in solution does not improve the results when using these later cycles. The use of cycle 1 and the complete basis set models combined with the CPCM solvation methods yielded pK_a values accurate to less than half a pK_a unit. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The SAMPL6 challenge on predicting aqueous p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values from EC-RISM theory

The “embedded cluster reference interaction site model” (EC-RISM) integral equation theory is applied to the problem of predicting aqueous pK_a values for drug-like molecules based on an ensemble of tautomers. EC-RISM is based on self-consistent calculations of a solute’s electronic structure and the distribution function of surrounding water. Following-up on the workflow developed after the SAMPL5 challenge on cyclohexane-water distribution coefficients we extended and improved the methodology by taking into account exact electrostatic solute–solvent interactions taken from the wave function in solution. As before, the model is calibrated against Gibbs energies of hydration from the “Minnesota Solvation Database” and a public dataset of acidity constants of organic acids and bases by adjusting in total 4 parameters, among which only 3 are relevant for predicting pK_a values. While the best-performing training model yields a root-mean-square error (RMSE) of 1 pK unit, the corresponding test set prediction on the full SAMPL6 dataset of macroscopic pK_a values using the same level of theory exhibits slightly larger error (1.7 pK units) than the best test set model submitted (1.7 pK units for corresponding training set vs. test set performance of 1.6). Post-submission analysis revealed a number of physical optimization options regarding the numerical treatment of electrostatic interactions and conformational sampling. While the experimental test set data revealed after submission was not used for reparametrizing the methodology, the best physically optimized models consequentially result in RMSEs of 1.5 if only improved electrostatic interactions are considered and of 1.1 if, in addition, conformational sampling accounts for quantum-chemically derived rankings. We conclude that these numbers are probably near the ultimate accuracy achievable with the simple 3-parameter model using a single or the two best-ranking conformations per tautomer or microstate. Finally, relations of the present macrostate approach to microstate pK_a results are discussed and some illustrative results for microstate populations are presented.     

Experimental and computational study of the pKa of coumaric acid derivatives

The dissociation constant (pK_a) of a drug is a key parameter in drug discovery and pharmaceutical formulation. The hydroxy substituent has a significant effect on the acidity of hydroxycinnamic acid. In this work, the acidic constants of coumaric acids are obtained experimentally by spectrophotometry using the chemometric method and calculated theoretically using ab initio quantum mechanical method at the HF/6‐31G* level of theory in combination with the SMD continuum solvation method. Rank annihilation factor analysis (RAFA) is an efficient chemometric technique based on the elimination of the contribution of one of the chemical components from the data matrix. RAFA cannot be performed because the pure spectrum of HA^? is not available. So, two‐rank annihilation factor analysis (TRAFA) is proposed for the determination of the pK_a OF H₂A. A comparison between the pK_a values obtained previously by TRAFA for the molecules o‐coumaric acid (4.13, 9.58), m‐coumaric acid (4.48, 10.35), and p‐coumaric acid (4.65, 9.92) makes it clear that there is good agreement between the results obtained by TRAFA and ab initio quantum mechanical method.     

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.     

Evaluation of potentiometric acid-base titrations by partial-least-squares calibration

Partial-least-squares calibration is used for the evaluation of acid-base titration curves. The method is advantageous because no physical model is assumed and only information from the titration curves is used. In the procedure, a model is developed from samples of known composition (calibration set) and is then used to predict unknowns (test set). The only assumption is that the two sets are similar. The method was evaluated first by titrating mixtures of two monoprotic acids with a small difference in pK_a values and then by titrating samples containing four or five diprotic acids. The results show that it is possible to determine monoprotic acids having a difference in pK_a of only 0.1, or up to five diprotic acids having pK_a values in the range 1.8–7.2, simultaneously.     

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.     

Efficient Light‐Induced pKa Modulation Coupled to Base‐Catalyzed Photochromism

Photoswitchable acid–base pairs, whose pK_a values can be reversibly altered, are attractive molecular tools to control chemical and biological processes with light. A significant, light‐induced pK_a change of three units in aqueous medium has been realized for two thermally stable states, which can be interconverted using UV and green light. The light‐induced pK_a modulation is based on incorporating a 3‐H‐thiazol‐2‐one moiety into the framework of a diarylethene photoswitch, which loses the heteroaromatic stabilization of the negatively charged conjugate base upon photochemical ring closure, and hence becomes significantly less acidic. In addition, the efficiency of the photoreactions is drastically increased in the deprotonated state, giving rise to catalytically enhanced photochromism. It appears that protonation has a significant influence on the shape of the ground‐ and excited‐state potential energy surfaces, as indicated by quantum‐chemical calculations.     

Effect of Preferential Solvation on the Thermodynamic Properties of Antidepressant Drug Trazodone in Aqueous Ethanol: Linear Free‐Energy Relationships

Dissociation constants (pK_a) of trazodone hydrochloride (TZD⋅HCl) in EtOH/H₂O media containing 0, 10, 20, 30, 40, 50, 60, 70, and 80% (v/v) EtOH at 288.15, 298.15, 308.15, and 318.15 K were determined by potentiometric techniques. At any temperature, pK_a decreased as the solvent was enriched with EtOH. The dissociation and transfer thermodynamic parameters were calculated, and the results showed that a non‐spontaneous free‐energy change (Δ_dissG^o>0) and unfavorable enthalpy (Δ_dissH^o>0) and entropy (Δ_dissS^o<0) changes occurred on dissociation of trazodone hydrochloride. The free‐energy change or pK_a varied nonlinearly with the reciprocal dielectric constant, indicating the inadequacy of the electrostatic approach. The dissociation equilibria are discussed on the basis of the standard thermodynamics of transfer, solvent basicity, and solute‐solvent interactions. The values of Δ_transG^o and Δ_transH^o increased negatively with increasing EtOH content, revealing a favorable transfer of trazodone hydrochloride from H₂O to EtOH/H₂O mixtures and preferential solvation of H⁺ and trazodone (TZD). Also, Δ_transS^o values were negative and reached a minimum, in the H₂O‐rich zone that has frequently been related to the initial promotion and subsequent collapse of the lattice structure of water. The pK_a or Δ_dissG^o values correlated well with the Dimroth‐Reichardt polarity parameter E_T(30), indicating that the physicochemical properties of the solute in binary H₂O/organic solvent mixtures are better correlated with a microscopic parameter than the macroscopic one. Also, it is suggested that preferential solvation plays a significant role in influencing the solvent dependence of dissociation of trazodone hydrochloride. The solute‐solvent interactions were clarified on the basis of the linear free‐energy relationships of Kamlet and Taft. The best multiparametric fit to the Kamlet‐Taft equation was evaluated for each thermodynamic parameter. Therefore, these parameters in any EtOH/H₂O mixture up to 80% were accurately derived by means of the obtained equations.     

Potentiometric and Voltammetric Study of 6‐Benzylaminopurine and Its Derivatives

The protonation‐deprotonation equilibrium of 6‐benzylaminopurine (6‐BAP) and its derivatives was studied by potentiometry and voltammetry. The effect of Cl‐ or OCH₃‐group in position 2′, 3′ and 4′ of the benzene ring of 6‐BAP on both pK_a values was investigated. To determine the enthalpy and entropy, the temperature dependence of pK_a was employed. It was found that with increasing temperature the pK_a decreased. In comparison with 6‐BAP the chloro‐ or methoxy‐ group resulted in pK_a increase. The first pK_a values were also determined by linear sweep (LSV) and elimination voltammetry with linear scan (EVLS). New approaches were shown not only for the determination of pK_a from voltammetric titration curves but also for the evaluation of the reduction processes of benzylaminopurines.     

Determination of Dissociation Constants of Complicated Compounds by Capillary Zone Electrophoresis

In this work, the whole theoretical methods for the determination of pK_a1. and pK_a2. of complicated compounds are proposed by capillary zone electrophoresis. The pK_a values are achieved by non‐linear regression analysis by taking into consideration the effect of activity coefficient. This is the first report on determining the dissociation constants of gastrodin, magnolol, honokiol, quercetin, curcumin, diethylstilbestrol, 4‐acetamidophenol, eugenol and paeonol.     

SAMPL6: calculation of macroscopic p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> values from ab initio quantum mechanical free energies

Macroscopic pK_a values were calculated for all compounds in the SAMPL6 blind prediction challenge, based on quantum chemical calculations with a continuum solvation model and a linear correction derived from a small training set. Microscopic pK_a values were derived from the gas-phase free energy difference between protonated and deprotonated forms together with the Conductor-like Polarizable Continuum Solvation Model and the experimental solvation free energy of the proton. pH-dependent microstate free energies were obtained from the microscopic pK_as with a maximum likelihood estimator and appropriately summed to yield macroscopic pK_a values or microstate populations as function of pH. We assessed the accuracy of three approaches to calculate the microscopic pK_as: direct use of the quantum mechanical free energy differences and correction of the direct values for short-comings in the QM solvation model with two different linear models that we independently derived from a small training set of 38 compounds with known pK_a. The predictions that were corrected with the linear models had much better accuracy [root-mean-square error (RMSE) 2.04 and 1.95 pK_a units] than the direct calculation (RMSE 3.74). Statistical measures indicate that some systematic errors remain, likely due to differences in the SAMPL6 data set and the small training set with respect to their interactions with water. Overall, the current approach provides a viable physics-based route to estimate macroscopic pK_a values for novel compounds with reasonable accuracy.