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Pharmaceutics 2013, 5(3), 434-444; doi:10.3390/pharmaceutics5030434
Published: 21 August 2013
Abstract: Phenols as a class of molecules have been reported to exhibit higher log maximum fluxes through human stratum corneum, SC, from water, log JMHAQ, than other classes of molecules. This suggests that their corresponding log maximum fluxes through silicone from water, log JMPAQ, may be useful to extend the existing n = 63 log JMPAQ database to include more log JMPAQ values greater than 0.0. The log JMPAQ values for n = 7 phenols predicted to give log JMPAQ values greater than 0.0 based on their log JMHAQ values have been experimentally determined. These n = 7 new log JMPAQ values have been added to the existing n = 63 log JMPAQ database to give a new n = 70 database and the n = 7 literature log JMHAQ values have been added to the existing n = 48 log JMHAQ database (matched to the n = 63 log JMPAQ database) to give a new n = 55 database. The addition of the n = 7 phenols improved the correlations of these flux databases when fitted to the Roberts-Sloan equation, RS, as well as the correlation between the matched experimental (Exp.) log JMPAQ with the Exp. log JMHAQ.
The rate-limiting barrier to diffusion of molecules through human skin is the stratum corneum, SC. The SC is comprised of highly dense, polar, proteinous corneocytes embedded in a lipid matrix. The lipid matrix in turn is comprised of multiple lipid bilayers containing mostly ceramides, fatty acids and cholesterol [1,2,3]. A tortuous pathway through this lipid matrix and around the corneocytes is generally considered to be the route followed by molecules diffusing through the SC. Since the route of molecules diffusing through the SC is lipid-like, the lipid solubility of molecules diffusing through the SC is an important physiochemical determinant of the efficiency of the diffusion process. Similarly, any surrogate for the SC must present with substantially lipid-like properties. Since silicone membranes present with highly lipid-like properties, it has been suggested that silicone membranes could be a surrogate for skin in diffusion cell studies and that those results could be used to predict diffusion through human skin [4,5]. Also, from a theoretical basis it can be assumed that, if the diffusion of unit mass per unit area per unit time, flux, through silicone membranes can be accurately modeled by an equation (Roberts–Sloan, RS, ) that accurately models maximum flux through human skin  exists, a linear relationship exists between the maximum flux of molecules through silicone membranes from water, log JMPAQ, and their maximum flux through human skin in vitro from water, log JMHAQ . Thus experimental (Exp.) log JMPAQ could be used to predict Exp. log JMHAQ.
The flux data for molecules from which the Roberts–Sloan, RS, equation was derived is based on the application of saturated solutions (suspensions of molecules in a solvent) to the membrane being used to give maximum flux, JM. Thus all the molecules are presented to the membrane at their maximum thermodynamic activity in that solvent [6,7,8]. Since the molecules are presented to the membrane at their maximum thermodynamic activity, at equilibrium the molecules are also at their maximum thermodynamic activity in the membrane [8,9], i.e., at their solubility limit or saturated solubility in the first few layers of the membrane, SM1. Thus, JM depends only on the solubility of the molecules in the first layers of the membrane, and unless the solvent changes the solubility limit of the membrane, the solvent/vehicle has no effect on JM. The form of the RS equation for predicting JM derives from an expansion of Fick’s law, Equation 1, so that the dependent variables are molecular weight, MW, solubility in a lipid, SLIPID, and solubility in water, SAQ. SM1 can then be estimated from the product of the partition coefficient between the vehicle (water in this case, AQ) and a surrogate lipid for the membrane (octanol in this case, SOCT), (KOCT:AQ)y∙constant, and the solubility in the vehicle, SAQ: (KOCT:AQ)y∙constant∙SAQ. Expansion of that product into solubilities and taking the logs gives: log SM1 = y log SOCT − y log SAQ + log SAQ + log constant = y log SOCT + (1 − y) log SAQ + log constant.
One problem with determining if the linear relationship between log JMPAQ and log JMHAQ exists is that there are only about n = 63 molecules for which log JMPAQ (output) and the necessary corresponding physicochemical properties (log SAQ and log SOCT, input) literature values exist which can be fitted to RS . Of those n = 63, only 18 molecules exhibit high output values; log JMPAQ values greater than 0.0. Simple phenols present an opportunity to extend the existing n = 63 log JMPAQ database to include more log JMPAQ values greater than 0.0. The log JMHAQ values for n = 18 phenols and their corresponding physicochemical properties that are necessary to determine their fit to RS were published by Roberts, et al. in 1977 . The fit of the n = 18 phenols to RS in the fit of the n = 62 edited Flynn database to RS was published in 2007 . In the edited Flynn database only n = 16 of the n = 62 molecules exhibited log JMHAQ values greater than 0.0 and of those n = 16, n = 11 were from among the n = 18 phenol subset . Thus, phenols as a subset represent molecules that exhibit physicochemical properties (input) that give higher flux (output) than other types of molecules give.
At present, only n = 6 of the n = 18 simple phenol subset from Roberts, et al.  have been included in the n = 63 log JMPAQ database and only n = 2 exhibit log JMPAQ greater than 0.0. In order to improve the correlation of the n = 63 log JMPAQ database with a matched n = 48 log JMHAQ database, the number of log JMPAQ and log JMHAQ greater than 0.0 in each database should be increased. Hence, n = 7 additional phenols have been selected from the n = 18 subset which exhibit physicochemical properties (input) for which RS predicts high log JMPAQ values (output). In addition, the n = 7 phenols exhibit an average log JMHAQ value significantly greater than that of the n = 48 log JMHAQ database: means ± 95% confidence intervals of 0.04 ± 0.42 log units and −1.06 ± 0.31 log units, respectively. Given the increased range and total number of entries resulting from the addition of these n = 7 compounds to the n = 48 log JMHAQ database and the n = 63 log JMPAQ database, the fit of these databases to the RS should improve, and correlation of the log JMPAQ with log JMHAQ values matched in these databases should also improve.
Further, since the addition of the n = 7 new entries to the new n = 63 log JMPAQ database, each potentially exhibiting higher log JMPAQ values than the average of the initial n = 63 log JMPAQ values, will change the relative distribution of flux values in the database, it is imperative to determine if other models would then fit the database better than they did before the addition of the n = 7 new entries. Thus, we will also determine the fit of the new databases to the Kasting–Smith–Cooper (KSC) model  and to the Magnusson–Anissimov–Cross–Roberts (MACR) model  and compare these fits to the fit of RS to the new databases.
2. Materials and Methods
The phenolic compounds used are listed in Table 1. These compounds were obtained from Aldrich and their solubility values were acquired or approximated from literature sources. The phenols were all solids except for 3-methylphenol.
The measurement of maximum flux through silicone was performed according to a literature procedure  at 32 °C, except that the silicone membrane was in contact with the receptor for only 24 h to condition them. The receptor was a 7.1 pH phosphate buffer.
The donor suspensions were prepared by stirring approximately 0.5 g (1 g in the case of 3-methylphenol) of the compounds in 10 mL of water for 24 h. For all compounds, this surpassed the aqueous solubility by a factor of at least 20, which ensured saturation and excess solid/oil present in the donor phase. After the membranes were conditioned, the receptor phases were changed and the donor suspensions (first application, 1 mL) were applied; n = 3. The donor cells were sealed by Parafilm. Samples were taken from the receptor every 2–3 h after application. Following sample collection, the receptor phases were changed to ensure sink conditions, and the donor suspensions were either changed or had more solid/oil added to the existing suspension, depending upon the visible extent of depletion. After 4–5 sampling intervals, the donor suspensions were removed with methanol and the receptors were changed. The membranes were leached with methanol in the donor phase for 48–72 h with samples taken and receptor phases changed every 12–24 h to remove any residual phenol in the membrane.
To ensure that flux data was not altered by possible membrane damage, a standard solute/solvent was applied and its flux determined. A donor suspension was prepared from 400 mg of theophylline suspended with stirring in 6 mL of propylene glycol (PG) for 24 h. This suspension (second application, 0.50 mL) was applied to all the silicone membranes after they were leached with methanol (see above). Samples were taken from the receptor every 24 h after application for at least 72 h so that at least 3 samples were obtained. Following sample collection, the receptor phases were changed and the donor suspensions were changed every other sampling interval. After 3–5 sampling intervals, the diffusion cells were disassembled and the membranes were placed in a methanol bath for maintenance leaching.
The flux values of the first and second application were determined by UV absorption. The wavelengths (λε) and molar absorptivities (ε) used for the phenolic compounds are listed in Table 1. The log flux of theophylline through silicone from PG, log JMPPG, for each membrane was found to be within the standard deviation of the literature value of −2.68 ± 0.12 log units .
Nonlinear regression was performed by SPSS 20.0 (Rel. 20.0.0). The compounds were fitted to the Roberts–Sloan equation for maximum flux, log JMAQ:
3. Results and Discussion
The results are displayed in Table 1. All but 4-chloro-3,5-dimethylphenol exhibited a log JMPAQ greater than 0.0, and even it was very close. As a subset the n = 7 simple phenols had an average log JMPAQ significantly greater than the average log JMPAQ of the n = 63 log JMPAQ database: means ± 95% confidence intervals 1.03 ± 0.45 log units and −0.42 ± 0.29 log units, respectively. The average log JMPAQ in the n = 70 log JMPAQ database has not significantly increased, but is no longer significantly less than 0.0: mean ± 95% confidence interval −0.27 ± 0.29. Unfortunately, the addition of the n = 7 phenols did not significantly increase the average log JMHAQ of the n = 55 log JMHAQ database relative to the n = 48 log JMHAQ database: means ± 95% confidence intervals, −0.918 ± 0.29 log units and −1.058 ± 0.31 log units, respectively.
|Table 1. The relevant measured or literature physicochemical properties for the n = 7 phenolic compounds used in this study.|
|Cmpd. a||MW||Log SAQ b,d||Log KOCT:AQ b||Log SOCT b,d||λε c||ε c,e||Log JMPAQ c,f||Log JMHAQ b,f|
a Substituted phenols. 1, 4-chloro-3-methyl; 2, 4-chloro-3,5-dimethyl; 3, 3,4-dimethyl; 4, 4-methyl; 5, 2,4-dichloro; 6, 2,4,6-trichloro; 7, 3-methyl; b From Roberts et al. 1977  and Majumdar et al. 2007 ; c Measured directly. d Solubility in water (SAQ) or octanol (SOCT) in μmole cm−3; e Molar absorptivity coefficient in L mole−1 cm−1; f Maximum flux through silicone (JMPAQ) or human stratum corneum (JMHAQ) from water in μmole cm−2 h−1.
The addition of these n = 7 phenols to the n = 63 log JMPAQ database and the n = 48 log JMHAQ database improved the fit of these databases to the RS as expected. The fit of the new n = 70 log JMPAQ database gave an r2 of 0.907, an average absolute residual log JMPAQ (Δlog JMPAQ) of 0.300 log units and the coefficients x = −1.606, y = 0.695 and z = 0.00490 were all significant (p < 0.05):
The fit of the n = 70 log JMPAQ database is an improvement over the n = 63 log JMPAQ database, which had r2 = 0.896 and Δlog JMPAQ = 0.310 log units, but had similar coefficient values: x = −1.607, y = 0.701, z = 0.00492. The fit of the new n = 55 log JMHAQ database gave an r2 of 0.883, an average absolute residual log JMHAQ (Δlog JMHAQ) of 0.282 log units and the coefficients x = −3.005 and y = 0.654 were significant (p < 0.05), but the coefficient z = 0.00112 was not significant (p = 0.25):
The lack of statistical significance for the z coefficient indicates a need to further extend the n = 55 log JMHAQ database, since the significance of MW to maximum flux is well-established . The fit of the n = 55 log JMHAQ database to the RS is an improvement over the n = 48 log JMHAQ database, which had r2 = 0.867 and Δlog JMHAQ = 0.331 log units and the coefficients x = −2.763, y = 0.635 and z = 0.00207. The x and y coefficients for the new log JMHAQ database are substantially closer to those coefficients determined for the n = 62 edited Flynn log JMHAQ database: x = −3.008, y = 0.732, z = 0.0048. Relevant results are displayed in Table 2 and Figure 1, Figure 2. Figure 1 shows a plot of experimental (Exp.) log JMPAQ versus log JMPAQ calculated (Calc.) from the coefficients for the fit of the n = 70 database to RS, and Figure 2 shows a plot of Exp. log JMHAQ versus log JMHAQ Calc. from the coefficients for the fit of the n = 55 database to RS.
|Table 2. The calculated (Calc.), predicted (Pred.), and experimental (Exp.) maximum flux values through silicone from water (log JMPAQ) and through human stratum corneum from water (log JMHAQ) for the n = 7 phenolic compounds.|
|Cmpd. a||Exp. log JMPAQ b||Pred. n = 63 log JMPAQ b,c||Calc. n = 70 log JMPAQ b,d||Exp. log JMHAQ b||Pred. n = 48 log JMHAQ b,e||Calc. n = 55 log JMHAQ b,f|
|Δlog JMAQ g||0.200||0.195||0.159||0.162|
a Substituted phenols. 1, 4-chloro-3-methyl; 2, 4-chloro-3,5-dimethyl; 3, 3,4-dimethyl; 4, 4-methyl; 5, 2,4-dichloro; 6, 2,4,6-trichloro; 7, 3-methyl; b Given in units μmole cm−2 h−1; c Using RS coefficients x = −1.607, y = 0.701, z = 0.00492 ; d Using RS coefficients x = −1.606, y = 0.695, z = 0.00490; e Using RS coefficients x = −2.763, y = 0.635 and z = 0.00207 ; f Using RS coefficients x = −3.005, y = 0.654, z = 0.00112; g Average absolute residual log JMPAQ or log JMHAQ for the n = 7 phenols.
Plots of the individual independent variables, log SOCT, log SAQ and MW, against log JMPAQ (n = 70) and against log JMHAQ (n = 55) gave the following r2 values: (a) log JMPAQ versus log SOCT, r2 = 0.677; versus log SAQ, r2 = 0.554; versus MW, r2 = 0.541; (b) log JMHAQ versus log SOCT, r2 = 0.603; versus log SAQ, r2 = 0.526; versus MW, r2 = 0.520. All regression equations had statistically significant (p < 0.05) slope and intercept estimates. In each case, the best regression of the individual independent variables against flux values was by log SOCT. It is worth noting that the n = 7 phenol subset gives the following r2 values and significance profiles when the individual independent variables log SOCT and log SAQ are plotted against log JMPAQ and log JMHAQ: (a) log JMPAQ versus log SOCT, r2 = 0.180, without a statistically significant slope (p = 0.34) or intercept (p = 0.51); versus log SAQ, r2 = 0.949, with a statistically significant slope (p < 0.05), but without a statistically significant intercept (p = 0.50); (b) log JMHAQ versus log SOCT, r2 = 0.335, without a statistically significant slope (p = 0.17) or intercept (p = 0.18); versus log SAQ, r2 = 0.933, with statistically significant (p < 0.05) slope and intercept. The improved dependence of maximum flux from water on the aqueous solubility of highly water-soluble compounds is demonstrated here as a property of both silicone and human stratum corneum, and will be a topic of future investigations. When two individual independent variables, log SOCT and MW, from the n = 70 log JMPAQ database were fitted to the KSC equation (Equation 3) the following x, y and z coefficients to the parameters were obtained along with r2 and Δlog JMPAQ values: x = −0.923, y = 0.794, z = 0.0089, r2 = 0.797 and Δlog JMPAQ = 0.431. All but the y coefficient (p = 0.069) were statistically significant (p < 0.05):
Figure 3 shows a plot of Exp. log JMPAQ versus log JMPAQ values calculated from the coefficients for the fit of the n = 70 database to Equation 7. Although the r2 was substantially improved by including MW with log SOCT as independent variables in the regression against flux, the r2 was poorer than the r2 for the fit of all three independent variables to the Roberts–Sloan Equation (Equation 5). Similarly, when two individual independent variables, log SOCT and MW, from the n = 55 log JMHAQ database were fit to the KSC equation (Equation 8) the following x, y and z coefficients to the parameters were obtained along with r2 and the Δlog JMHAQ values: x = −1.252, y = 0.602, z = 0.0080, r2 = 0.723 and Δlog JMHAQ = 0.441. The estimates for the coefficients were all statistically significant (p < 0.05):
Figure 4 shows a plot of Exp. log JMHAQ versus log JMHAQ values calculated from the coefficients for the fit of the n = 55 database to Equation 8. Again, although a substantial improvement in r2 was obtained by including MW with log SOCT as independent variables in the regression against flux, the r2 was poorer than the r2 for the fit of all three independent variables to the RS equation (Equation 6). The fit of both databases to the MACR equation (Equation 4), which is the remaining model used to predict maximum flux, is simply the regression of MW against log JMPAQ or log JMHAQ shown above to give a somewhat poorer fit than regression of the two individual independent variables, log SOCT or log SAQ, against log JMPAQ or log JMHAQ. Finally, it should be noted the popular Potts–Guy Equation  was not included as a model because its output is permeability coefficient which is not clinically relevant.
The new n = 52 database of compounds contributing to both the n = 70 log JMPAQ database and the n = 55 log JMHAQ database also gives a higher correlation between Exp. log JMPAQ and Exp. log JMHAQ than the previous n = 45 database. A linear regression yielded the expression Exp. log JMHAQ = 0.859 Exp. log JMPAQ − 0.837, r2 = 0.856, which is an improvement over r2 = 0.838 for the n = 45 database. Figure 5 shows the plot of Exp. log JMPAQ versus Exp. log JMHAQ for n = 52.
The addition of the n = 7 phenols improved all aspects of the log JMPAQ database with regards to comparison with the matched log JMHAQ database. Along with strengthening the validity of the assertion that silicone membranes are good surrogates for human stratum corneum, these improvements demonstrate that this surrogate nature holds for a wider range of log JMPAQ and log JMHAQ values than had been previously reported.
Conflicts of Interest
The authors declare no conflict of interest.
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