Solubility properties in polymers and biological media: 6. An equation for correlation and prediction of solubilities of liquid organic nonelectrolytes in blood

Gas/blood partition coefficients, Kgb, and molar solubilities in blood, Sb, of 27 liquid aliphatic nonelectrolyte solutes are described by the equation: log Sb congruent to log (Sg/Kgb) = 1.35-3.05V/100-0.28 pi* + 3.58 beta (at 37 degrees C) r = 0.9870 and SD = 0.144 where Sg is the solute concentration in its saturated vapor at 37 degrees C, given by Sg = Patm/25.4; V is the solute molar volume; and pi* and beta are parameters that are measures of solute dipolarity/polarizability and hydrogen bond acceptor basicity, respectively. The above equation applies to compounds with calculated log solubilities greater than -1.5. A nondipolar solubility reservoir provided by hydrophobic pockets in hemoglobin leads to greater than predicted solubilities for the less soluble alkanes, alkylbenzenes, and chlorobenzenes. It is suggested that equations similar to the one above can be constructed to describe and predict gas-lipid and gas-homogenized tissue, and hence blood-lipid, blood-tissue, tissue-lipid, and tissue-tissue partition coefficients of pharmacologically and toxicologically active solutes.     

Intrinsic molecular volume as a measure of the cavity term in linear solvation energy relationships: octanol-water partition coefficients and aqueous solubilities

A new, calculated value of the van der Waals or intrinsic molecular volume VI is shown to be at least as effective as molar volume, V (the molecular weight divided by the liquid density), as a measure of the cavity term in linear solvation energy relationships for octanol-water partition coefficients and aqueous solubilities. Use of VI obviates the need for the empirical 10-mL/mol correction factor for aromatic and alicyclic solutes which was previously required, and which is shown here to arise from an underestimate of the cavity term due to reduced free volume in the pure liquid. In addition, since VI is a calculated quantity, equations which contain this term can be extended to compounds that are solids or gases in the pure state. Octanol-water partition coefficients, log P, of gases and solids are predicted accurately by the equation: log P = 0.41 + 5.14 VI/100 - 0.29 mu - 3.58 beta, where mu is the dipole moment and beta is the hydrogen bond acceptor basicity. Aqueous solubilities of some solids are reasonably well predicted by the equation: log Sw = 0.19 - 5.79 VI/100 + 0.24 mu + 4.95 beta - 0.01 (mp - 25), where mp is the melting point. The same equation without the melting point term gives good estimates of the comparable solubility of some gases.     

Solubility properties in polymers and biological media 5: an analysis of the physicochemical properties which influence octanol-water partition coefficients of aliphatic and aromatic solutes

Octanol-water partition coefficients of 102 aliphatic, polychloro aliphatic, and aromatic non-hydrogen-bond donor and hydrogen-bond donor solutes are well correlated (r = 0.989, SD = 0.175) by the equation: log Kow = 0.20 + 2.74 V/100 - 0.92 pi - 3.49 beta, where V is the molar volume (taken as the molecular weight divided by the liquid density) and pi and beta are the solvatochromic parameters that measure solute dipolarity/polarizability and hydrogen-bond acceptor basicity. A set of "ground rules" (modifications of the input parameters) are described which allow the inclusion of both aliphatic and aromatic solutes in the same correlation equation. Monomer beta values (betam) are used for alcohol solutes.     

Linear solvation energy relationships: 36. Molecular properties governing solubilities of organic nonelectrolytes in water

Molar solubilities of non-hydrogen bond donor and weak hydrogen bond donor liquid aliphatic solutes in water, or the nearly equivalent quantities, Sg/Kgw, where Kgw is the gas-water partition coefficient and Sg is the solute concentration in the solute saturated vapor (Sg = Patm/24.5) are well correlated by the equation: log Sw congruent to log (Sg/Kgw) = 0.54 - 3.32V/100 + 0.46 pi* + 5.17 (beta or beta m) (at 25 degrees C) n = 105, r = 0.9954, SD = 0.137 V is the solute molar volume (the molecular weight divided by the liquid density at 20 degrees C), and pi* and beta are the solvatochromic parameters that are measures of solute dipolarity-polarizability and hydrogen bond acceptor basicity. The equation, which applies to liquid monofunctional aliphatic solutes is used to calculate additional new beta and beta m values. The beta m values, which are intended to apply to self-associated compounds when acting as "monomer" solutes, are: methanol, 0.42; all primary alkanols, 0.45; all secondary alkanols, 0.51; and all tertiary alkanols, 0.57.     

Estimation of the effect of NaCl on the solubility of organic compounds in aqueous solutions

The Setschenow constant, K(salt), of a nonelectrolyte in a NaCl solution is shown to be related to the logarithm of its octanol-water partition coefficient, log K(ow), determined by K(salt) = A log K(ow) + B, where K(ow) is the octanol-water partition coefficient of the solute and the coefficients A and B are constants. The values of A and B were empirically determined from literature data for 62 organic compounds and validated for a test set of 15 compounds including several drugs.     

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

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 cm³/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.     

蒙花苷溶解度及油水分配系数的研究

目的测定蒙花苷的溶解度及油水分配系数,为药物成药性评价及剂型设计提供依据。方法采用HPLC法测定蒙花苷在不同有机溶剂及不同pH值缓冲盐溶液中的平衡溶解度,并测定蒙花苷在高分子材料和表面活性剂中的溶解度;利用Molinspiration软件对蒙花苷的油水分配系数进行预测,并采用摇瓶-HPLC法测定药物在正辛醇-水、正辛醇-缓冲液体系中的表观油水分配系数。结果蒙花苷在水中的平衡溶解度为0.059μg/mL,在碱性溶液中的溶解度有所增加;高分子材料和表面活性剂均可增加蒙花苷的溶解度,其中HP-β-CD的增溶作用最强,可增加214.6倍;lg蒙花苷在正辛醇-水、正辛醇-缓冲盐溶液中的P值在0.50～1.04,与计算机预测值0.513一致。结论蒙花苷不溶于水,脂溶性差,通过添加辅料,其溶解性有所提高。     

Comparison of models for the estimation of biological partition coefficients

Several models have been published for calculating blood-air, tissue-air, or tissue-blood partition coefficients of volatile organic chemicals in human or rat tissues, from functions of their octanol-water partition coefficients or solubilities in vegetable oil and water. In this work, the relative accuracy, strengths, and limitations of the various models are examined. Comparison of predicted human tissue-air and tissue-blood partition coefficients with experimental values has been made for 12 chemicals, covering a wide range of lipophilicity (acetone, isopropanol, diethylether, methylene dichloride, benzene, toluene, trichloroethylene, trichloroethane, n-pentane, cyclohexane, n-hexane, and n-heptane). Seven published models for human tissue-air and 10 models for tissue-blood partition coefficients have been compared. Fewer models are available for predicting rat tissue-air and rat tissue-blood partition coefficients, but a similar comparison has been made. The ratio of predicted to experimental partition coefficients and their mean, R(mean), and the mean magnitude of the difference between predicted and experimental values of log(10) P, E, were used to assess the accuracy of each model. For the test set the most accurate for human blood-air partition coefficients were the empirical equations of Meulenberg and Vijverberg (R(mean) = 1.1 +/- 0.46, E = 0.156) and the empirical solvation equation of Abraham and Weathersby (1994) (R(mean) = 0.93 +/- 0.38, E = 0.166). For rat blood, predictions are much less accurate due to difficulties in modeling the effects of protein binding, which are much larger. Overall, for rat blood-air partition coefficients the equation of Meulenberg and Vijverberg (1999) (R(mean) = 0.74 +/- 0.50, E = 0.236) was the most accurate. The tissue-composition-based equations of Poulin and Krishnan, using solubilities in vegetable oil, performed well for human liver-air partition coefficients (R(mean) = 1.21 +/- 0.28, E = 0.079) for log(octanol-water partition coefficients) > 0.7 and for fat-air partition coefficients, but overestimated solubilities in human kidney and brain tissues (e.g., for kidney tissue, R = 1.88 +/- 0.58, E = 0.255). The equations of Meulenberg and Vijverberg (2000a), Abraham and Weathersby (1994), and Paterson and Mackay (1989) also performed moderately well for human tissue-air partition coefficients. For rat muscle-air, liver-air, and fat-air partition coefficients the model of Poulin and Krishnan (1996a) gave the most accurate predictions. For tissue-blood partition coefficients, generally good agreement with experimental values is obtained by the empirical model of Balaz and Lukacova (1999) (e.g., for human kidney, R(mean) = 1.15 +/- 0.38, E = 0.085) and, if solubility in fat is known, by the equations of Fiserova-Bergerova and Diaz (1986) (e.g., for human muscle, R(mean) = 1.10 +/- 0.39, E = 0.107). The equations of DeJongh et al. (1997) gave the most accurate predictions for rat muscle-blood, liver-blood and fat-blood partition coefficients (e.g., for rat muscle R(mean) = 1.03 +/- 0.39, E = 0.149), but predictions were less accurate than for human tissue-blood partition coefficients, attributable to difficulties in modeling the effect of protein binding. The choice of equation for use in physiologically based pharmacokinetic (PBPK) models depends on the species, tissue, and chemical lipophilicity.     

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.     

Partitioning of solutes in different solvent systems: the contribution of hydrogen-bonding capacity and polarity

Published partition coefficient values of 121 solutes in five solvent systems (1-octanol-water, n-heptane-water, chloroform-water, diethyl ether-water, and n-butyl acetate-water) were correlated with solute properties, namely intrinsic molecular volume (indicator of cavity formation) and the solvatochromic parameters pi* (dipolarity/polarizability), beta (H-bond acceptor basicity), and alpha (H-bond donor acidity). While the cavity term and the H-bond accepting capacity played a comparable role in all solvent systems, the H-bond donor acidity was significant only in the alkane-water and chloroform-water systems. Comparison of the regression coefficients of pi*, beta, and alpha demonstrated the important role that water content at saturation in the organic solvents plays in the partitioning of solutes. Analysis of the differences between 1-octanol-water and n-heptane-water partition coefficients (delta log Poct-hep) and between 1-octanol-water and chloroform-water partition coefficients (delta log Poct-chf) showed that these values mainly quantitate the capacity of solute to donate hydrogen bonds. In contrast, the differences between 1-octanol-water and diethyl ether-water or n-butylacetate-water partition coefficients, (delta log Poct-dee and delta log Poct-ba, respectively) contain no structural information.     

Physical parameters and biological activity of sulfonamides

The activity coefficients "gamma" aqueous solution and the diffusion rate constants (Kd) from artificial gastric and intestinal juices were measured for eleven sulfonamides; the corresponding absorption rate constants (Ki) were then calculated. The activity coefficient was correlated with various parameters, such as the n-octanol/water and isoamyl acetate/water partition coefficients, and the absorption constant. The activity coefficient "gamma" plays an important role on the global biological activity, even if partly depending upon chemical interactions. Constant ratios (about 10%) referred to solubility of the sulfonamidic compounds in the "amorphous state" were regarded as available in blood for biological activity, regardless of the respective binding with plasma proteins.     

In vitro studies of intestinal drug absorption. Determination of partition and distribution coefficients with brush border membrane vesicles.

Brush border membrane vesicles (BBMV) were isolated from rat small intestine and characterized in terms of relative enrichment of specific organelle marker enzymes (20-fold enrichment; 20% yield), contamination by other subcellular organelles (less than 1%) and functional integrity (Na(+)-dependent glucose uptake). Using these vesicles, techniques were developed for the determination of partition and distribution coefficients for the model solutes, nitrobenzene, toluene and benzoic acid. No gender, age or regional variation along the small intestine in partition coefficient (log P) values was detected. There was no temperature (10-40 degrees) or pH (4.5-8.0) dependence in partition coefficients of nitrobenzene and toluene. Fair agreement was obtained for log P and log D values for these two solutes determined with BBMV and those reported with octanol and propylene glycol dipelargonate. Selective removal of proteins, both ecto-brush border and micro-villus core proteins, did not alter the partition coefficients of the three model solutes. In contrast, depletion of the BBMV of non-esterified fatty acids significantly decreased the partition coefficients. Liposomes prepared from BBMV lipid extracts were also used for partition coefficient determinations and gave similar values to intact BBMV; addition of increasing amounts of cholesterol to the lipid extract caused small increases in the partition coefficients of the model solutes in the liposomes. It was concluded that the partition coefficients of the BBMV were related to the lipid and not to the protein composition of the vesicles. The method offers a rapid and reliable means of measuring the partition coefficient of non-protein bound drugs and nutrients in isolated intestinal BBMV and should assist in the subsequent modelling and prediction of intestinal absorption in vivo.     

Solubility of drugs in aqueous solutions. Part 2: binary nonideal mixed solvent

As in a previous paper [Int. J. Pharm. 258 (2003) 193–201], the Kirkwood–Buff theory of solutions was employed to calculate the solubility of a solid in mixed solvents. Whereas in the former paper the binary solvent was assumed ideal, in the present one it was considered nonideal. A rigorous expression for the activity coefficient of a solute at infinite dilution in a mixed solvent [Int. J. Pharm. 258 (2003) 193–201] was used to obtain an equation for the solubility of a poorly soluble solid in a nonideal mixed solvent in terms of the solubilities of the solute in the individual solvents, the molar volumes of those solvents, and the activity coefficients of the components of the mixed solvent.

The Flory–Huggins and Wilson equations for the activity coefficients of the components of the mixed solvent were employed to correlate 32 experimental data sets regarding the solubility of drugs in aqueous mixed solvents. The results were compared with the models available in literature. It was found that the suggested equation can be used for an accurate and reliable correlation of the solubilities of drugs in aqueous mixed binary solvents. It provided slightly better results than the best literature models but has also the advantage of a theoretical basis.     

Solubility of drugs in aqueous solutions. Part 4. Drug solubility by the dilute approximation

As in our previous publications in this journal [Int. J. Pharm. 258 (2003a) 193; Int. J. Pharm. 260 (2003b) 283; Int. J. Pharm. 267 (2003c) 121], this paper is concerned with the solubility of poorly soluble drugs in aqueous mixed solvents. In the previous publications, the solubilities of drugs were assumed to be low enough for the so-called infinite dilution approximation to be applicable. In contrast, in the present paper, the solubilities are considered to be finite and the dilute solution approximation is employed. As before, the fluctuation theory of solutions is used to express the derivatives of the activity coefficient of a solute in a ternary solution (dilute solute concentrations in a binary solvent) with respect to the concentrations of the solvent and cosolvent. The expressions obtained are combined with a theoretical equation for the activity coefficient of the solute. As a result, the activity coefficient of the solute was expressed through the activity coefficients of the solute at infinite dilution, solute mole fraction, some properties of the binary solvent (composition, molar volume and activity coefficients of the components) and parameters reflecting the nonidealities of binary species. The expression thus obtained was used to derive an equation for the solubility of poorly soluble drugs in aqueous binary solvents which was applied in two different ways. First, the nonideality parameters were considered as adjustable parameters, determined from experimental solubility data. Second, the obtained equation was used to correct the solubilities of drugs calculated via the infinite dilution approximation. It was shown that both procedures provide accurate correlations for the drug solubility.     

HPLC法测定叶黄素的平衡溶解度及表观油水分配系数

目的 测定叶黄素在不同溶剂中的平衡溶解度及表观油水分配系数。方法 建立高效液相色谱法用于测定叶黄素含量,采用摇瓶法考察叶黄素在多种有机溶剂及不同pH值缓冲液中的平衡溶解度,并测定其表观油水分配系数。结果 叶黄素几乎不溶于水及缓冲液,在有机溶剂中溶解度有不同程度提高,其中在四氢呋喃中的溶解度最高（66 mg·mL^-1）;其表观油水分配系数为1.03。结论 叶黄素在多数溶剂中的溶解度均较低,可通过提高溶解度改善溶出和吸收。     

Solubility of drugs in aqueous solutions. Part 5. Thermodynamic consistency test for the solubility data

This paper is devoted to the verification of the quality of experimental data regarding the solubility of sparingly soluble solids, such as drugs, environmentally important substances, etc. in mixed solvents. A thermodynamic consistency test based on the Gibbs-Duhem equation for ternary mixtures is suggested. This test has the form of an equation, which connects the solubilities of the solid, and the activity coefficients of the constituents of the solute-free mixed solvent in two mixed solvents of close compositions. The experimental data regarding the solubility of sparingly soluble substances can be verified with the suggested test if accurate data for the activity coefficients of the constituents of the solute-free mixed solvent are available. The test was applied to a number of systems representing the solubilities of sparingly soluble substances in mixed solvents. First, the test was scrutinized for four nonaqueous systems for which accurate solubility data were available. Second, the suggested test was applied to a number of systems representing experimental data regarding the solubility of sparingly soluble substances in aqueous mixed solvents.     

Skin Solubility Determines Maximum Transepidermal Flux for Similar Size Molecules

Purpose  The maximum flux of solutes penetrating the epidermis has been known to depend predominantly on solute molecular weight. Here we sought to establish the mechanistic dependence of maximum flux on other solute physicochemical parameters. Methods  Maximum fluxes, stratum corneum solubilities and estimated diffusivities through human epidermis were therefore determined for 10 phenols with similar molecular weights and hydrogen bonding but varying in lipophilicity. Results  Maximum flux and stratum corneum solubilities of the phenolic compounds both showed a bilinear dependence on octanol-water partition coefficient (P), with solutes having a maximum solubility in the stratum corneum when 2.7<log P<3.1. In contrast, lag times and diffusivities were relatively independent of P. Stratum corneum-water partition coefficients and epidermal permeability coefficients were consistent with previously reported data. Conclusion  A key finding is that the convex dependence of maximum flux on lipophilicity arises primarily from variations in stratum corneum solubility, and not from diffusional or partitioning barrier effects at the stratum corneum–viable epidermis interface for the more lipophilic phenols. Our data support a solute structure-skin transport model for aqueous solutions in which permeation rates depend on both partitioning and diffusivity: partitioning is related to P, and diffusivity to solute size and hydrogen bonding. (199 words)     

Correlation and estimation of gas-chloroform and water-chloroform partition coefficients by a linear free energy relationship method.

A linear free energy relationship, LFER, has been used to correlate 150 values of gas-chloroform partition coefficients, as log Lchl with a standard deviation, sd, of 0.23 log units, a correlation coefficient r2 of 0.985, and an F-statistic of 1919. The equation reveals that bulk chloroform is dipolar/polarizable, of little hydrogen-bond basicity, but as strong a hydrogen-bond acid as bulk methanol or bulk ethanol. However, the main influence on gaseous solubility in chloroform is due to solute-solvent London dispersion interactions. A slightly modified LFER has been used to correlate 302 values of water-chloroform partition coefficients, as log Pchl. The correlation equation predicts log Pchl for a further 34 compounds not used in the equation with sd = 0.17 log units. When the LFER is applied to all 335 log Pchl values, the resulting equation has sd = 0.25, r2 = 0.971, and F = 2218.     

The influence of drug partition coefficient on follicular penetration: in vitro human skin studies.

The aim of this study was to employ the novel skin sandwich system in order to quantify the influence of the octanol-water partition coefficient on follicular drug absorption in human skin. To this end, seven different drugs - estradiol, corticosterone, hydrocortisone, aldosterone, cimetidine, deoxyadenosine and adenosine - exhibiting a wide range of log octanol-water partition coefficients (logK(o/w)) but relatively similar molecular weights were selected as candidate solutes. Application of the skin sandwich technique yielded an interesting relationship between % follicular contribution and logK(o/w). The follicular contribution to total flux was small (4 and 2%) for the two most lipophilic drugs but varied between 34 and 60% for the remaining drugs of intermediate and low logK(o/w) values. Lipophilicity seems to be an important modulator of drug absorption into follicular orifices only above a critical logK(o/w) threshold. Below this critical logK(o/w) value, lipophilicity does not apparently influence the follicular contribution in an obvious way and the process is probably governed by other molecular properties. Identification of these other active properties would require performing this kind of a study on a much larger set of candidate drugs.