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Phenols as a class of molecules have been reported to exhibit higher log maximum fluxes through human stratum corneum, SC, from water, log _{MHAQ}, than other classes of molecules. This suggests that their corresponding log maximum fluxes through silicone from water, log _{MPAQ}, may be useful to extend the existing _{MPAQ} database to include more log _{MPAQ} values greater than 0.0. The log _{MPAQ} values for _{MPAQ} values greater than 0.0 based on their log _{MHAQ} values have been experimentally determined. These _{MPAQ} values have been added to the existing _{MPAQ} database to give a new _{MHAQ} values have been added to the existing _{MHAQ} database (matched to the _{MPAQ} database) to give a new _{MPAQ} with the Exp. log _{MHAQ}.

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 [_{MPAQ}, and their maximum flux through human skin _{MHAQ} [_{MPAQ} could be used to predict Exp. log _{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, _{M}. Thus all the molecules are presented to the membrane at their maximum thermodynamic activity in that solvent [_{M1}. Thus, _{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 _{M}. The form of the RS equation for predicting _{M} derives from an expansion of Fick’s law, Equation 1, so that the dependent variables are molecular weight, MW, solubility in a lipid, _{LIPID}, and solubility in water, _{AQ}. _{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, _{OCT}), (_{OCT:AQ})^{y}_{AQ}: (_{OCT:AQ})^{y}_{AQ}. Expansion of that product into solubilities and taking the logs gives: log _{M1} = _{OCT} − _{AQ} + log _{AQ} + log constant = _{OCT} + (1 − _{AQ} + log constant.
_{M1} - _{Mn} ): _{M} = _{M1} - _{Mn}) _{M1} is the concentration of the molecule in the first few layers of the membrane and _{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 _{M1} of molecules in a silicone membrane and log _{M1} of molecules in human skin in order for a linear relationship between log _{MPAQ} and log _{MHAQ} to exist.

One problem with determining if the linear relationship between log _{MPAQ} and log _{MHAQ} exists is that there are only about _{MPAQ} (output) and the necessary corresponding physicochemical properties (log _{AQ} and log _{OCT}, input) literature values exist which can be fitted to RS [_{MPAQ} values greater than 0.0. Simple phenols present an opportunity to extend the existing _{MPAQ} database to include more log _{MPAQ} values greater than 0.0. The log _{MHAQ} values for _{MHAQ} values greater than 0.0 and of those

At present, only _{MPAQ} database and only _{MPAQ} greater than 0.0. In order to improve the correlation of the _{MPAQ} database with a matched _{MHAQ} database, the number of log _{MPAQ} and log _{MHAQ} greater than 0.0 in each database should be increased. Hence, _{MPAQ} values (output). In addition, the _{MHAQ} value significantly greater than that of the _{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 _{MHAQ} database and the _{MPAQ} database, the fit of these databases to the RS should improve, and correlation of the log _{MPAQ} with log _{MHAQ} values matched in these databases should also improve.

Further, since the addition of the _{MPAQ} database, each potentially exhibiting higher log _{MPAQ} values than the average of the initial _{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

The phenolic compounds used are listed in

The measurement of maximum flux through silicone was performed according to a literature procedure [

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;

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 _{MPPG}, 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 _{MAQ}:
_{MAQ} = _{OCT} + (1 − _{AQ} − _{MAQ} = _{OCT} − _{MAQ} =

The results are displayed in _{MPAQ} greater than 0.0, and even it was very close. As a subset the _{MPAQ} significantly greater than the average log _{MPAQ} of the _{MPAQ} database: means ± 95% confidence intervals 1.03 ± 0.45 log units and −0.42 ± 0.29 log units, respectively. The average log _{MPAQ} in the _{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 _{MHAQ} of the _{MHAQ} database relative to the _{MHAQ} database: means ± 95% confidence intervals, −0.918 ± 0.29 log units and −1.058 ± 0.31 log units, respectively.

The relevant measured or literature physicochemical properties for the

Cmpd. ^{a} |
MW | Log _{AQ} ^{b,d} |
Log _{OCT:AQ} ^{b} |
Log _{OCT} ^{b,d} |
λ_{ε} ^{c} |
ε ^{c,e} |
Log _{MPAQ} ^{c,f} |
Log _{MHAQ} ^{b,f} |
---|---|---|---|---|---|---|---|---|

1 | 143 | 1.55 | 3.10 | 4.65 | 283 | 1241 | 1.01 | 0.29 |

2 | 157 | 0.28 | 3.39 | 3.67 | 285 | 1041 | −0.027 | −0.95 |

3 | 122 | 1.61 | 2.35 | 3.96 | 277 | 1668 | 1.37 | 0.17 |

4 | 108 | 2.29 | 1.95 | 4.24 | 276 | 1614 | 1.62 | 0.53 |

5 | 163 | 1.49 | 3.08 | 4.57 | 285 | 1791 | 1.16 | 0.27 |

6 | 197 | 0.66 | 3.69 | 4.35 | 312 | 4518 | 0.49 | −0.57 |

7 | 108 | 2.36 | 1.96 | 4.32 | 271 | 1468 | 1.61 | 0.54 |

^{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 ^{c} Measured directly. ^{d} Solubility in water (_{AQ}) or octanol (_{OCT}) in μmole cm^{−3}; ^{e} Molar absorptivity coefficient in L mole^{−1} cm^{−1}; ^{f} Maximum flux through silicone (_{MPAQ}) or human stratum corneum (_{MHAQ}) from water in μmole cm^{−2} h^{−1}.

The addition of these _{MPAQ} database and the _{MHAQ} database improved the fit of these databases to the RS as expected. The fit of the new _{MPAQ} database gave an ^{2} of 0.907, an average absolute residual log _{MPAQ} (Δlog _{MPAQ}) of 0.300 log units and the coefficients _{MPAQ} = −1.606 + 0.695 log _{OCT} + 0.305 log _{AQ} − 0.00490 MW

The fit of the _{MPAQ} database is an improvement over the _{MPAQ} database, which had ^{2} = 0.896 and Δlog _{MPAQ} = 0.310 log units, but had similar coefficient values: _{MHAQ} database gave an ^{2} of 0.883, an average absolute residual log _{MHAQ} (Δlog _{MHAQ}) of 0.282 log units and the coefficients _{MHAQ} = −3.005 + 0.645 log _{OCT} + 0.346 log _{AQ} − 0.00112 MW

The lack of statistical significance for the _{MHAQ} database, since the significance of MW to maximum flux is well-established [_{MHAQ} database to the RS is an improvement over the _{MHAQ} database, which had ^{2} = 0.867 and Δlog _{MHAQ} = 0.331 log units and the coefficients _{MHAQ} database are substantially closer to those coefficients determined for the _{MHAQ} database: _{MPAQ}_{MPAQ} calculated (Calc.) from the coefficients for the fit of the _{MHAQ}_{MHAQ} Calc. from the coefficients for the fit of the

The calculated (Calc.), predicted (Pred.), and experimental (Exp.) maximum flux values through silicone from water (log _{MPAQ}) and through human stratum corneum from water (log _{MHAQ}) for the

Cmpd. ^{a} |
Exp. log _{MPAQ} ^{b} |
Pred. _{MPAQ} ^{b,c} |
Calc. _{MPAQ} ^{b,d} |
Exp. log _{MHAQ} ^{b} |
Pred. _{MHAQ} ^{b,e} |
Calc. _{MHAQ} ^{b,f} |
---|---|---|---|---|---|---|

1 | 1.01 | 1.41 | 1.40 | 0.29 | 0.46 | 0.41 |

2 | −0.027 | 0.28 | 0.26 | −0.95 | −0.66 | −0.68 |

3 | 1.37 | 1.05 | 1.04 | 0.17 | 0.087 | 0.0053 |

4 | 1.62 | 1.52 | 1.51 | 0.53 | 0.54 | 0.44 |

5 | 1.16 | 1.24 | 1.23 | 0.27 | 0.35 | 0.32 |

6 | 0.49 | 0.67 | 0.65 | −0.57 | −0.17 | −0.15 |

7 | 1.61 | 1.60 | 1.59 | 0.54 | 0.62 | 0.52 |

Δlog
_{MAQ} ^{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 ^{d} Using RS coefficients ^{e} Using RS coefficients ^{f} Using RS coefficients ^{g} Average absolute residual log _{MPAQ} or log _{MHAQ} for the

The correlation of the calculated (Calc.) log _{MPAQ} from the fit of _{MPAQ}. The dashed lines represent the boundaries for residual log _{MPAQ} greater than 1.0, the solid line indicates points where the Calc. log _{MPAQ} is equivalent to the Exp. log _{MPAQ}. The filled circles indicate the _{MPAQ} values were determined with Equation 5: log _{MPAQ} = −1.606 + 0.695 log _{OCT} + 0.305 log _{AQ} − 0.00490MW. ^{2} = 0.907, average absolute residual log _{MPAQ} = 0.300.

The correlation of the calculated (Calc.) log _{MHAQ} from the fit of _{MHAQ}. The dashed lines represent the boundaries for residual Exp. log _{MHAQ} greater than 1.0, and the solid line indicates points where the Calc. log _{MHAQ} is equivalent to the Exp. log _{MHAQ}. The filled circles indicate the _{MHAQ} values were determined with Equation 6: log _{MHAQ} = −3.005 + 0.654 log _{OCT} + 0.346 log _{AQ} − 0.00112 MW, ^{2} = 0.883, average absolute residual log _{MHAQ} = 0.282.

Plots of the individual independent variables, log _{OCT}, log _{AQ} and MW, against log _{MPAQ} (_{MHAQ} (^{2} values: (a) log _{MPAQ}_{OCT}, ^{2} = 0.677; _{AQ}, ^{2} = 0.554; ^{2} = 0.541; (b) log _{MHAQ}_{OCT}, ^{2} = 0.603; _{AQ}, ^{2} = 0.526; ^{2} = 0.520. All regression equations had statistically significant (_{OCT}. It is worth noting that the ^{2} values and significance profiles when the individual independent variables log _{OCT} and log _{AQ} are plotted against log _{MPAQ} and log _{MHAQ}: (a) log _{MPAQ}_{OCT}, ^{2} = 0.180, without a statistically significant slope (_{AQ}, ^{2} = 0.949, with a statistically significant slope (_{MHAQ}_{OCT}, ^{2} = 0.335, without a statistically significant slope (_{AQ}, ^{2} = 0.933, with statistically significant (_{OCT} and MW, from the _{MPAQ} database were fitted to the KSC equation (Equation 3) the following ^{2} and Δlog _{MPAQ} values: ^{2} = 0.797 and Δlog _{MPAQ} = 0.431. All but the _{MPAQ} = −0.923 + 0.794 log S_{OCT} − 0.0089 MW

_{MPAQ}_{MPAQ} values calculated from the coefficients for the fit of the ^{2} was substantially improved by including MW with log _{OCT} as independent variables in the regression against flux, the ^{2} was poorer than the ^{2} for the fit of all three independent variables to the Roberts–Sloan Equation (Equation 5). Similarly, when two individual independent variables, log _{OCT} and MW, from the _{MHAQ} database were fit to the KSC equation (Equation 8) the following ^{2} and the Δlog _{MHAQ} values: ^{2} = 0.723 and Δlog _{MHAQ} = 0.441. The estimates for the coefficients were all statistically significant (

_{MHAQ}= −1.252 + 0.602 log

_{OCT}− 0.0080 MW

The correlation of the calculated (Calc.) log _{MPAQ} from the fit of _{MPAQ}. The dashed lines represent the boundaries for residual Exp. log _{MPAQ} greater than 1.0, the solid line indicates points where the Calc. log _{MPAQ} is equivalent to the Exp. log _{MPAQ}. The filled circles indicate the _{MPAQ} values were determined with Equation 7: log _{MPAQ} = −0.923 + 0.794 log _{OCT} − 0.0089 MW, ^{2} = 0.797, average absolute residual log _{MPAQ} = 0.431.

_{MHAQ}_{MHAQ} values calculated from the coefficients for the fit of the ^{2} was obtained by including MW with log _{OCT} as independent variables in the regression against flux, the ^{2} was poorer than the ^{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 _{MPAQ} or log _{MHAQ} shown above to give a somewhat poorer fit than regression of the two individual independent variables, log _{OCT} or log _{AQ}, against log _{MPAQ} or log _{MHAQ}. Finally, it should be noted the popular Potts–Guy Equation [

The correlation of the calculated (Calc.) log _{MHAQ} from the fit of _{MHAQ}. The dashed lines represent the boundaries for residual Exp. log _{MHAQ} greater than 1.0, and the solid line indicates points where the Calc. log _{MHAQ} is equivalent to the Exp. log _{MHAQ}. The filled circles indicate the _{MHAQ} values were determined with Equation 8: log _{MHAQ} = −1.252 + 0.602 log _{OCT} − 0.0080 MW, ^{2} = 0.723, average absolute residual log _{MHAQ} = 0.441.

The new _{MPAQ} database and the _{MHAQ} database also gives a higher correlation between Exp. log _{MPAQ} and Exp. log _{MHAQ} than the previous _{MHAQ} = 0.859 Exp. log _{MPAQ} − 0.837, ^{2} = 0.856, which is an improvement over ^{2} = 0.838 for the _{MPAQ}_{MHAQ} for

The correlation of the _{MHAQ} with log _{MPAQ} database. The dashed lines represent the boundaries for residual Exp. log _{MHAQ} greater than 1.0, and the solid line is the regression equation. The filled circles indicate the

The addition of the _{MPAQ} database with regards to comparison with the matched log _{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 _{MPAQ} and log _{MHAQ} values than had been previously reported.

The authors declare no conflict of interest.