©Liverpool John Moores University

Determination of the optimal physico-chemical parameters to use in a QSAR-approach to predict skin permeation rate

Mark Cronin ¹

1. QSAR and Modelling Research Group, School of Pharmacy and Chemistry, Liverpool John Moores University, Byrom Street, Liverpool, L3 3AF, England.

Executive Summary

This report describes the development of quantitative structure-activity relationships (QSARs) for the prediction of the ability of a chemical to cross human skin. It represents the final report of a one year project undertaken by the QSAR and Modelling Group in the School of Pharmacy and Chemistry at Liverpool John Moores University, England. The project was funded by the European Chemical Industry Council Long-range Research Initiative. The report is available from the web site of the QASR and Modelling Research Group web site.

The report summarises the findings of an extensive literature review, firstly into the methods available for the assessment of skin permeability, and secondly the use of QSARs to predict skin permeability. A large number of studies have been performed to assess the ability of chemicals to cross the skin of a number of animals. Some of the data have been used to develop QSARs, of which there are many examples. Many of these studies were performed on small data sets (typically less than twenty compounds), with varying methodologies for the assessment of skin permeability. Many of the human in vitro data were brought together by Flynn (1990), and have been subjected to a variety of QSAR analyses. The results of the QSAR analyses have demonstrated that many physico-chemical properties may be important for the prediction of skin permeability. Further, certain chemicals within the data set (notably the steroids) were consistently found to be outliers, some of these data have more recently been shown to be erroneous.

The report goes on to describe the prediction and interpretation of the L-a-dimyristoyl phosphatidyl choline- water partition coefficient (K_DMPC-W). Log K_DMPC-W has been suggested as a replacement for the octanol-water solvent pair, as DMPC represents more accurately lipid bilayers. The disadvantage of its use for QSAR is that few measured data are available, and no reliable prediction method has been developed. A total of 49 log K_DMPC-W values were obtained from the literature and a total of 81 physico-chemical descriptors calculated for each compound. The log K_DMPC-W data were highly correlated with the data using the octanol-water solvent pair (log K_OW). In order to predict log K_DMPC-W accurately, a three parameter model was proposed, following the removal of two outliers:

log K_DMPC-W = 0.936 log K_OW – 0.0281 ⁹X + 0.319 E_HOMO + 3.40

n = 47 r² = 0.98 s = 0.26 F = 669

Where ⁹X is the ninth order molecular connectivity; E_HOMO is the energy of the highest occupied molecular orbital; n is the number of observations; r² is the coefficient of determination; s is the standard error; F is the Fisher statistic.

The above equation was shown to predict log K_DMPC-W very well, and was utilised for the prediction of skin permeability.

The report also describes the development of a novel descriptor for molecular linearity. The parameterisation of the steric attributes of molecules was identified as a key aspect to this project. However, the description of the shape of molecules has never been addressed adequately. In this chapter, a novel descriptor was developed that was able quantify molecular linearity i.e. the difference between a linear molecular, as opposed to a spherical molecule. To achieve this, a data set of 200 chemical structures, varying from long unbranched alkyl chains (i.e. linear molecules), to highly branched chemicals (i.e. spherical molecules) was constructed. It was demonstrated that a combination of the moments of inertia of the molecules, factored by molecular weight, was able to quantify molecular linearity:

Where L_i is the novel ‘linearity index’; IM1(L), IM2(L), IM3(L) are the first, second, and third order moments of inertia for length; MW is molecular weight.

This equation was shown to describe molecular linearity very well, and was utilised for the prediction of skin permeability.

The development of QSARs for the prediction of the permeation through human skin in vitro of a large number of chemicals is described. To achieve this, permeability data for 158 chemicals were obtained. For each of the chemicals, 169 physico-chemical descriptors were calculated. Confirming previous findings, the steroids and other large complex structures were observed to be outliers. These outliers, fifteen in total, significantly reduced the quality of the QSARs and were removed. Stepwise regression analysis on the data set revealed the following as the most significant QSAR:

log K_p = 0.652 log K_OW – 0.00603 MW – 0.623 ABSQon – 0.313 SsssCH – 2.30

n = 143 r² = 0.90 s = 0.35 F = 312

Where K_p is the permeability coefficient; ABSQon is the sum of absolute charges on oxygen and nitrogen atoms; SsssCH is the sum of E-state indices for all methyl groups.

The above equation predicts skin permeability very well and indicates that skin permeability is a function of the hydrophobicity of a molecular, as well as its size and hydrogen bonding characteristics. Further investigation of the description of molecular size in QSARs for skin permeability revealed that models based on log K_OW and any of the molecular weight, molecular volume or zero order molecular connectivity were statistically significant, with r² greater than 0.8 in all cases.

The report draws together the conclusions from the study, and makes formal recommendations for the use of QSARs to predict skin permeability.

References

First published on www.herox.org on 29th August 2001.

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This report summary has not been peer-reviewed and the publisher takes no responsibility for the scientific quality of the work.

© Liverpool John Moores University

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