Ulrich W. Kesselring

A New Predictive Equation for the Solubility of Drugs Based on the Thermodynamics of Mobile Disorder

The thermodynamics of mobile disorder rejects the static model of the quasi-lattice for liquids. Because of the perpetual change of neighbors, during the observation time of thermodynamics of the order of seconds, each molecule of a given kind in a solution has experienced the same environment and had at its disposal the same mobile volume. This domain is not localizable and not orientable. Each molecular group perpetually “visits” successively all parts of this domain. The highest entropy is obtained when the groups visit all the parts of the domain without preference. H-bonds are preferential contacts with given sites of the neighbors that cause deviations with respect to such “random” visiting, thereby decreasing the entropy. The quantitative development of these ideas leads to equations describing the effect of solvent–solvent, solute–solvent, and solute–solute hydrogen bonds on the chemical potential of the solute. A universal equation predicting the solubility of drugs in a given solvent is derived. The effect of H-bonds is governed not by “solubility parameters” but by stability constants from which the order of magnitude can be estimated. From the sole knowledge of the solubility of methylparaben in pentane, the method predicts correctly the order of magnitude of its solubility in 26 other solvents, including alcohols and water.

Aqueous solubility prediction of environmentally important chemicals from the mobile order thermodynamics

Applied to the aqueous solubility of only-sligthly polar compounds with no hydrogen bond donor capacity, the quantitative development of the thermodynamics of mobile order results in a very simple nearly linear predictive solubility equation requiring only the molar volume of the solute and its melting properties in the case of solids. Enhancement of the solubility by weak solvation effects associated to the proton-acceptor ability of the solute towards water is taken into account through standard stability constants reflecting the functionality, the degree of unsaturation and cyclization of the molecule. Accordingly, the molar aqueous solubility of a diverse set of 531 chemicals of environmental relevance is predicted with an average absolute error of 0.37 log units though the solubilities span over more than 12 orders of magnitude. The analysis of the relative importance of the terms contributing to the solubility demonstrates that the poor solubility of low-polarity compounds in water is merely the result of the hydrophobic effect and of its extremely rapid increase with the size of the solute. The mobile order thermodynamics also provides explanations for the empirically deduced solubility-volume linear relationships.

Comparison of the solubility of polycyclic aromatic hydrocarbons in non-associated and associated solvents: The hydrophobic effect

Abstract A remarkable improvement of the predictions of the solubility, Φ B , of a solute B in a solvent S is achieved by the theory of the mobile order of Huyskens. In this theory, the hydrophobic effect of the associated solvents like alcohols against inert substances is no longer considered as a result from a change in the energy of the molecular interactions, but as a decrease of the entropy due to temporary correlated displacements of two or more hydroxylic groups of solvent molecules. Such correlated displacements create a kind of mobile order. Quantitatively, the hydrophobic effect reduces ln Φ B by an amount of r S Φ S V B / V S . A direct consequence of this effect is that an increase in the ratio V B / V S of the molar volumes, which in non-H-bonded solvents is favourable for the solubility, becomes unfavourable in alcohols. For polycyclic aromatic hydrocarbons, the prediction of the solubilities in apolar, polar and associated solvents by the mobile order theory necessitates the knowledge of a single parameter only which can be deduced from one experimental solubility.

Prediction of carbazole solubility and its dependence upon the solvent nature

Abstract On the basis of at most three parameters, the solubility of carbazole is predicted in 33 nonelectrolyte solvents by means of the general solubility equation derived from the thermodynamics of mobile order. Particular attention is focussed on the influence of the formation of solute-solvent stoechiometrical hydrogen bonds on the treatment of the non-specific dipole-dipole and dispersion interactions. Three classes of solvents can be distinguished according to their solubilizing potential towards carbazole: non-complexing solvents, complexing non-associated solvents and complexing amphiphilic solvents. The analysis of the relative importance of the different terms contributing to the solubility allows one to quantitatively understand its variation between the different classes as well as within each class of solvents.

Validation of an HPLC method for the determination of urinary and plasma levels of N1-methylnicotinamide, an endogenous marker of renal cationic transport and plasma flow.

N1-Methylnicotinamide (NMN) is an endogenous cationic metabolite of nicotinamide (niacine, vitamine PP) whose renal clearance reflects both the capacity of the renal tubular transport system to secrete organic cations and renal plasma flow. NMN is present in human plasma and urine at the 1-117-ng ml(-1) and 0.5-25-microg ml(-1) concentration range, respectively, and its level depends notably on pathophysiological (age, renal or hepatic diseases) conditions. We report the optimization and validation of an HPLC method for the measurement of endogenous NMN in biological fluids after derivatization into a fluorescent compound. Plasma is first deproteinized with TCA 20% and the urine diluted 1:10 with HCI 10(-4) M prior to the derivatization procedure, which includes a condensation reaction of NMN with acetophenone in NaOH at 0 degrees C, followed by dehydration in formic acid and subsequent formation of the fluorescent 1,6-naphthyridine derivatives after heating samples in a boiling water bath. The synthetic homologous derivative N1-ethylnicotinamide (NEN) reacts similarly and is added as internal standard into the biological fluid. The reaction mixture is subjected to reverse phase high performance liquid chromatography on a Nucleosil 100-C18 column using a mobile phase (acetonitrile 22%, triethylamine 0.5%, 0.01 M sodium heptanesulfonate adjusted to pH 3.2), delivered isocratically at a flow rate of 1 ml min(-1), NMN and NEN are detected at 7.8 and 10 min by spectrofluorimetry with excitation and emission wavelengths set at 366 and 418 nm, respectively. The addition-calibration method is used with plasma and urine pools. Calibration curves (using the internal standard method) are linear (r2 > 0.997) at concentrations up to 109 ng ml(-1) and 15.7 microg ml(-1) in plasma and urine, respectively. Both intra- and inter-assay precision of plasma control samples at 10, 50 and 90 ng ml(-1) were lower than 3.3% and concentrations not deviating more than 2.7% from their nominal values. In urine intra- and inter-assay CVs of control samples at 1, 5 and 9 microg ml(-1) are lower than 8.3%, with concentrations not deviating more than -9.0 to +11.8% from their nominal values. This analytical method has therefore the required sensitivity and selectivity to measure NMN in plasma and urine, enabling the non-invasive determination of the tubular secretory capacity of the kidney and the renal plasma flow.

The effect of proton-acceptor sites of the solute on its solubility in proton-donor solvents

Abstract The solubilities of five solid ketones and two esters are predicted in common organic nonelectrolyte solvents using the solubility equation derived from the mobile order theory. In the framework of this theory, the formation of solute-solvent hydrogen bonds is treated on the basis of standard stability constants. Two different values characterizing the ketone-alcohol and the ester-alcohol hydrogen bonds, respectively 170 and 110 cm 3 /mol, have been determined. The formation of specific molecular interactions brings about a net increasing of the solubility without modifying the values of the other contributions relevant to the solution process. Using the predetermined values of the stability constants, the solubility equation is then successfully applied to predict the solubility of testosterone propionate in 28 solvents including alcohols and water from the sole knowledge of its solubility in hexane.

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

SummaryThe thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the π electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant Ko which can be derived from solubility data. At 25°C, this constant amounts to 80 cm3/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.

Solubility Predictions for Solid Nitriles and Tertiary Amides Based on the Mobile Order Theory

The solubilities of hexadecanenitrile, octadecanenitrile, N,N-diphenyl capramide, and N.N-diphenyl lauramide are predicted in common organic nonelectrolyte solvents using the solubility equation derived from the mobile order theory. In the framework of this theory, the formation of hydrogen bonds is treated on the basis of stability constants. Two values characterizing the nitrile–alcohol and the tertiary amide–alcohol hydrogen bonds, 175 and 600 cm3 mol−1, respectively, are determined. Although the formation of solute–solvent specific molecular interactions brings about a net increase in the solubility, the solubilities of the nitriles and amides in alcohols remain lower than those measured in nonassociated solvents because of the large negative hydrophobic effect of the alcohol molecules.

Experimentally optimized determination of the partial and total cohesion parameters of an insoluble polymer (microcrystalline cellulose) by gas-solid chromatography

Abstract The partial solubility parameters of microcrystalline cellulose ( δ d = 9.5 ± 0.5, δ p = 6.2 ± 1.0, δ h = 15.3 ± 0.7 δ t = 19.2 ± 0.4) were obtained, on the basis of the Snyder/Karger-Hansen interaction model, where Δ E A = V i ( δ d i d d i + δ p i δ p j + δ h i d h j ). They were deduced from the internal adsorption energy of n -decane, carbon tetrachloride, benzene, acetonitrile, methanol and ethanol, determined by gas-solid chromatography. In order to get the highest accuracy and precision possible with minimal experimental work and the most appropriate solutes, the planification of the experiments was achieved by optimization of the experimental matrix. This revealed that the best results are obtained when 6 out of the 14 solutes were chosen.

Extractionless method for the simultaneous high-performance liquid chromatographic determination of urinary caffeine metabolites for N-acetyltransferase 2, cytochrome P450 1A2 and xanthine oxidase activity assessment

Urinary metabolic ratios of caffeine are used in humans to assess the enzymatic activities of cytochrome P450 isoenzyme 1A2 (CYP1A2), xanthine oxidase (XO) and for phenotyping individuals for the bimodal N-acetyltransferase 2 (NAT2), all of them involved in the activation or detoxification of various xenobiotic compounds. Most reported analytical procedures for the measurement of the urinary metabolites of caffeine include a liquid-liquid extraction of urine samples prior to their analysis by reversed-phase HPLC. At neutral to basic pH however, 5-acetylamino-6-formylamino-3-methyluracil (AFMU), a metabolite of caffeine, spontaneously decomposes to 5-acetylamino-6-amino-3-methyluracil (AAMU). Since AAMU is not extracted in most organic solvents, the extent of AFMU decomposition cannot be precisely assessed. Although the decomposition reaction can be minimized by immediate acidification of the urine, accurate results can only be obtained when both AAMU and AFMU are monitored, or alternatively, if AAMU is measured after complete transformation of AFMU into AAMU in basic conditions. We report a liquid chromatographic method for the simultaneous quantitative analysis of the five urinary metabolites of caffeine used for the CYP1A2, XO and NAT2 phenotyping studies: AAMU, AFMU, 1-methylxanthine, 1-methyluric acid and 1,7-dimethyluric acid. These metabolites are satisfactory separated from all other known caffeine metabolites as well as endogenous urinary constituents. Sample treatment does not require any liquid-liquid extraction procedure. Urine samples are diluted and centrifuged before being injected (10 microl) onto a YMC-Pack Polyamine II (250x4.6 mm) column. A step-wise gradient elution program is applied using acetonitrile-0.75% (v/v) formic acid: (91:9) at 0 min-->(75:25) at 25 min-->(65:35) at 35 min-->(65:35) at 45 min, followed by a re-equilibration step to the initial solvent composition. The flow-rate is 1.0 ml/min and the separations are monitored by UV absorbance at 260 and 280 nm. The procedure described here represents a substantial improvement over previous methods: a single analysis and a minimal urine sample treatment enables the simultaneous quantitation of five caffeine metabolites, notably AFMU and AAMU, used for the determination of CYP450 1A2, XO and NAT2 enzyme activity. Importantly enough, phenotyping individuals for the bimodal NAT2 is made possible without the uncertainty associated with the deformylation of AFMU, which is likely to happen at all steps prior to the analysis, during sample storage and even in the bladder of the subjects.