The Flux of Phenolic Compounds through Silicone Membranes

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.


Introduction
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 OPEN ACCESS 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, [6]) that accurately models maximum flux through human skin [7] exists, a linear relationship exists between the maximum flux of molecules through silicone membranes from water, log J MPAQ , and their maximum flux through human skin in vitro from water, log J MHAQ [5]. Thus experimental (Exp.) log J MPAQ could be used to predict Exp. log J MHAQ .
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, J M . 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, S M1 . Thus, J M 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 J M . The form of the RS equation for predicting J M derives from an expansion of Fick's law, Equation 1, so that the dependent variables are molecular weight, MW, solubility in a lipid, S LIPID , and solubility in water, S AQ . S M1 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, S OCT ), (K OCT:AQ ) y •constant, and the solubility in the vehicle, S AQ : (K OCT:AQ ) y •constant•S AQ . Expansion of that product into solubilities and taking the logs gives: log S M1 = y log S OCT − y log S AQ + log S AQ + log constant = y log S OCT + (1 − y) log S AQ + log constant. (1) where D is the diffusion coefficient of the molecule in the membrane, L is the thickness of the membrane, C M1 is the concentration of the molecule in the first few layers of the membrane and C Mn is the concentration in the last few layers of the membrane which is assumed to approach zero. A linear relationship must exist between log D + log S M1 of molecules in a silicone membrane and log D + log S M1 of molecules in human skin in order for a linear relationship between log J MPAQ and log J MHAQ to exist.
One problem with determining if the linear relationship between log J MPAQ and log J MHAQ exists is that there are only about n = 63 molecules for which log J MPAQ (output) and the necessary corresponding physicochemical properties (log S AQ and log S OCT , input) literature values exist which can be fitted to RS [5]. Of those n = 63, only 18 molecules exhibit high output values; log J MPAQ values greater than 0.0. Simple phenols present an opportunity to extend the existing n = 63 log J MPAQ database to include more log J MPAQ values greater than 0.0. The log J MHAQ 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 [10]. 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 [7]. In the edited Flynn database only n = 16 of the n = 62 molecules exhibited log J MHAQ values greater than 0.0 and of those n = 16, n = 11 were from among the n = 18 phenol subset [10]. 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. [10] have been included in the n = 63 log J MPAQ database and only n = 2 exhibit log J MPAQ greater than 0.0. In order to improve the correlation of the n = 63 log J MPAQ database with a matched n = 48 log J MHAQ database, the number of log J MPAQ and log J MHAQ 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 J MPAQ values (output). In addition, the n = 7 phenols exhibit an average log J MHAQ value significantly greater than that of the n = 48 log J MHAQ 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 J MHAQ database and the n = 63 log J MPAQ database, the fit of these databases to the RS should improve, and correlation of the log J MPAQ with log J MHAQ values matched in these databases should also improve.
Further, since the addition of the n = 7 new entries to the new n = 63 log J MPAQ database, each potentially exhibiting higher log J MPAQ values than the average of the initial n = 63 log J MPAQ 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 [11] and to the Magnusson-Anissimov-Cross-Roberts (MACR) model [12] and compare these fits to the fit of RS to the new databases.

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 [13] 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 (λ ε ) and molar absorptivities (ε) used for the phenolic compounds are listed in Table 1. The log flux of theophylline through silicone from PG, log J MPPG , for each membrane was found to be within the standard deviation of the literature value of −2.68 ± 0.12 log units [13].
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 J MAQ : (2) to the KSC Equation: (3) and to the MACR Equation: (4)

Results and Discussion
The results are displayed in Table 1. All but 4-chloro-3,5-dimethylphenol exhibited a log J MPAQ greater than 0.0, and even it was very close. As a subset the n = 7 simple phenols had an average log J MPAQ significantly greater than the average log J MPAQ of the n = 63 log J MPAQ database: means ± 95% confidence intervals 1.03 ± 0.45 log units and −0.42 ± 0.29 log units, respectively. The average log J MPAQ in the n = 70 log J MPAQ 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 J MHAQ of the n = 55 log J MHAQ database relative to the n = 48 log J MHAQ database: means ± 95% confidence intervals, −0.918 ± 0.29 log units and −1.058 ± 0.31 log units, respectively.
The lack of statistical significance for the z coefficient indicates a need to further extend the n = 55 log J MHAQ database, since the significance of MW to maximum flux is well-established [12]. The fit of the n = 55 log J MHAQ database to the RS is an improvement over the n = 48 log J MHAQ database, which had r 2 = 0.867 and Δlog J MHAQ = 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 J MHAQ database are substantially closer to those coefficients determined for the n = 62 edited Flynn log J MHAQ database: x = −3.008, y = 0.732, z = 0.0048. Relevant results are displayed in Table 2 and Figures 1 and 2. Figure 1 shows a plot of experimental (Exp.) log J MPAQ versus log J MPAQ calculated (Calc.) from the coefficients for the fit of the n = 70 database to RS, and Figure 2 shows a plot of Exp. log J MHAQ versus log J MHAQ Calc. from the coefficients for the fit of the n = 55 database to RS.    Plots of the individual independent variables, log S OCT , log S AQ and MW, against log J MPAQ (n = 70) and against log J MHAQ (n = 55) gave the following r 2 values: (a) log J MPAQ versus log S OCT , r 2 = 0.677; versus log S AQ , r 2 = 0.554; versus MW, r 2 = 0.541; (b) log J MHAQ versus log S OCT , r 2 = 0.603; versus log S AQ , r 2 = 0.526; versus MW, r 2 = 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 S OCT . It is worth noting that the n = 7 phenol subset gives the following r 2 values and significance profiles when the individual independent variables log S OCT and log S AQ are plotted against log J MPAQ and log J MHAQ : (a) log J MPAQ versus log S OCT , r 2 = 0.180, without a statistically significant slope (p = 0.34) or intercept (p = 0.51); versus log S AQ , r 2 = 0.949, with a statistically significant slope (p < 0.05), but without a statistically significant intercept (p = 0.50); (b) log J MHAQ versus log S OCT , r 2 = 0.335, without a statistically significant slope (p = 0.17) or intercept (p = 0.18); versus log S AQ , r 2 = 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 S OCT and MW, from the n = 70 log J MPAQ database were fitted to the KSC equation (Equation 3) the following x, y and z coefficients to the parameters were obtained along with r 2 and Δlog J MPAQ values: x = −0.923, y = 0.794, z = 0.0089, r 2 = 0.797 and Δlog J MPAQ = 0.431. All but the y coefficient (p = 0.069) were statistically significant (p < 0.05): (7) Figure 3 shows a plot of Exp. log J MPAQ versus log J MPAQ values calculated from the coefficients for the fit of the n = 70 database to Equation 7. Although the r 2 was substantially improved by including MW with log S OCT as independent variables in the regression against flux, the r 2 was poorer than the r 2 for the fit of all three independent variables to the Roberts-Sloan Equation   . Again, although a substantial improvement in r 2 was obtained by including MW with log S OCT as independent variables in the regression against flux, the r 2 was poorer than the r 2 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 J MPAQ or log J MHAQ shown above to give a somewhat poorer fit than regression of the two individual independent variables, log S OCT or log S AQ , against log J MPAQ or log J MHAQ . Finally, it should be noted the popular Potts-Guy Equation [14] 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 J MPAQ database and the n = 55 log J MHAQ database also gives a higher correlation between Exp. log J MPAQ and Exp. log J MHAQ than the previous n = 45 database. A linear regression yielded the expression Exp. log J MHAQ = 0.859 Exp. log J MPAQ − 0.837, r 2 = 0.856, which is an improvement over r 2 = 0.838 for the n = 45 database. Figure 5 shows the plot of Exp. log J MPAQ versus Exp. log J MHAQ for n = 52.

Conclusions
The addition of the n = 7 phenols improved all aspects of the log J MPAQ database with regards to comparison with the matched log J MHAQ 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 J MPAQ and log J MHAQ values than had been previously reported.