Pharmaceutical Research

, Volume 32, Issue 7, pp 2360–2371 | Cite as

In Silico Predictions of Human Skin Permeability using Nonlinear Quantitative Structure–Property Relationship Models

  • Hiromi Baba
  • Jun-ichi Takahara
  • Hiroshi Mamitsuka
Research Paper



Predicting human skin permeability of chemical compounds accurately and efficiently is useful for developing dermatological medicines and cosmetics. However, previous work have two problems; 1) quality of databases used, and 2) methods for prediction models. In this paper, we attempt to solve these two problems.


We first compile, by carefully screening from the literature, a novel dataset of chemical compounds with permeability coefficients, measured under consistent experimental conditions. We then apply machine learning techniques such as support vector regression (SVR) and random forest (RF) to our database to develop prediction models. Molecular descriptors are fully computationally obtained, and greedy stepwise selection is employed for descriptor selection. Prediction models are internally and externally validated.


We generated an original, new database on human skin permeability of 211 different compounds from aqueous donors. Nonlinear SVR achieved the best performance among linear SVR, nonlinear SVR, and RF. The determination coefficient, root mean square error, and mean absolute error of nonlinear SVR in external validation were 0.910, 0.342, and 0.282, respectively.


We provided one of the largest datasets with purely experimental log k p and developed reliable and accurate prediction models for screening active ingredients and seeking unsynthesized compounds of dermatological medicines and cosmetics.


in silico prediction quantitative structure–property relationship random forest skin permeability support vector regression 



Ghose–Crippen octanol–water partition coefficient


Artificial neural network


Chemical concentration in dose formulation


Steady state flux of the solute


Skin–vehicle partition coefficient


Permeability coefficient


Thickness of the skin

log P

Octanol–water partition coefficient


Mean absolute error


Molecular weight


Principal component analysis


Quantitative structure–property relationship


Determination coefficient


Random forest


Root mean square error


Support vector regression


Support vector regression with Gaussian (radial basis function) kernel


Support vector regression with linear kernel

Supplementary material

11095_2015_1629_MOESM1_ESM.docx (64 kb)
ESM 1 (DOCX 63 kb)


  1. 1.
    Bartek MJ, LaBudde JA, Maibach HI. Skin permeability in vivo: comparison in rat, rabbit, pig and man. J Investig Dermatol. 1972;58(3):114–23.CrossRefPubMedGoogle Scholar
  2. 2.
    Franz TJ. Percutaneous absorption on the relevance of in vitro data. J Investig Dermatol. 1975;64(3):190–5.CrossRefPubMedGoogle Scholar
  3. 3.
    Zhang Q, Grice JE, Li P, Jepps OG, Wang GJ, Roberts MS. Skin solubility determines maximum transepidermal flux for similar size molecules. Pharm Res. 2009;26(8):1974–85.CrossRefPubMedGoogle Scholar
  4. 4.
    Takeuchi H, Ishida M, Furuya A, Todo H, Urano H, Sugibayashi K. Influence of skin thickness on the in vitro permeabilities of drugs through Sprague-Dawley rat or Yucatan micropig skin. Biol Pharm Bull. 2012;35(2):192–202.CrossRefPubMedGoogle Scholar
  5. 5.
    Karadzovska D, Riviere JE. Assessing vehicle effects on skin absorption using artificial membrane assays. Eur J Pharm Sci. 2013;50(5):569–76.CrossRefPubMedGoogle Scholar
  6. 6.
    Blank IH, McAuliffe DJ. Penetration of benzene through human skin. J Investig Dermatol. 1985;85(6):522–6.CrossRefPubMedGoogle Scholar
  7. 7.
    Flynn GL. Physicochemical determinants of skin absorption. In: Gerrity TR, Henry CJ, editors. Principles of route-to-route extrapolation for risk assessment. 1st ed. New York: Elsevier; 1990. p. 93–127.Google Scholar
  8. 8.
    Wilschut A, ten Berge WF, Robinson PJ, McKone TE. Estimating skin permeation. The validation of five mathematical skin permeation models. Chemosphere. 1995;30(7):1275–96.CrossRefPubMedGoogle Scholar
  9. 9.
    Kirchner LA, Moody RP, Doyle E, Bose R, Jeffery J, Chu I. The prediction of skin permeability by using physicochemical data. ATLA. 1997;25:359–70.Google Scholar
  10. 10.
    Patel H, ten Berge W, Cronin MT. Quantitative structure-activity relationships (QSARs) for the prediction of skin permeation of exogenous chemicals. Chemosphere. 2002;48(6):603–13.CrossRefPubMedGoogle Scholar
  11. 11.
    Chauhan P, Shakya M. Role of physicochemical properties in the estimation of skin permeability: in vitro data assessment by partial least-squares regression. SAR QSAR Environ Res. 2010;21(5–6):481–94.CrossRefPubMedGoogle Scholar
  12. 12.
    Khajeh A, Modarress H. Linear and nonlinear quantitative structure-property relationship modelling of skin permeability. SAR QSAR Environ Res. 2014;25(1):35–50.CrossRefPubMedGoogle Scholar
  13. 13.
    Moss GP, Sun Y, Wilkinson SC, Davey N, Adams R, Martin GP, et al. The application and limitations of mathematical modelling in the prediction of permeability across mammalian skin and polydimethylsiloxane membranes. J Pharm Pharmacol. 2011;63(11):1411–27.CrossRefPubMedGoogle Scholar
  14. 14.
    Vecchia BE, Bunge AL. Skin absorption databases and predictive equations. In: Guy R, Hadgraft J, editors. Transdermal drug delivery. 2nd ed. New York: Marcel Dekker; 2003. p. 57–141.Google Scholar
  15. 15.
    Roberts MS, Pugh WJ, Hadgraft J, Watkinson AC. Epidermal permeability-penetrant structure relationships: 1. An analysis of methods of predicting penetration of monofunctional solutes from aqueous solutions. Int J Pharm. 1995;126(1–2):219–33.CrossRefGoogle Scholar
  16. 16.
    Ghafourian T, Fooladi S. The effect of structural QSAR parameters on skin penetration. Int J Pharm. 2001;217(1–2):1–11.CrossRefPubMedGoogle Scholar
  17. 17.
    Panchagnula R, Stemmer K, Ritschel WA. Animal models for transdermal drug delivery. Methods Find Exp Clin Pharmacol. 1997;19(5):335–41.PubMedGoogle Scholar
  18. 18.
    Lehman PA, Raney SG, Franz TJ. Percutaneous absorption in man in vitro-in vivo correlation. Skin Pharmacol Physiol. 2011;24(4):224–30.CrossRefPubMedGoogle Scholar
  19. 19.
    Potts RO, Guy RH. Predicting skin permeability. Pharm Res. 1992;9(5):663–9.CrossRefPubMedGoogle Scholar
  20. 20.
    Lim CW, Fujiwara S, Yamashita F, Hashida M. Prediction of human skin permeability using a combination of molecular orbital calculations and artificial neural network. Biol Pharm Bull. 2002;25(3):361–6.CrossRefPubMedGoogle Scholar
  21. 21.
    Katritzky AR, Dobchev DA, Fara DC, Hür E, Tämm K, Kurunczi L, et al. Skin permeation rate as a function of chemical structure. J Med Chem. 2006;49(11):3305–14.CrossRefPubMedGoogle Scholar
  22. 22.
    Chen LJ, Lian GP, Han LJ. Prediction of human skin permeability using artificial neural network (ANN) modeling. Acta Pharmacol Sin. 2007;28(4):591–600.CrossRefPubMedGoogle Scholar
  23. 23.
    Patel J. Science of the science, drug discovery and artificial neural networks. Curr Drug Discov Technol. 2013;10(1):2–7.PubMedGoogle Scholar
  24. 24.
    Castillo E, Fontenla-Romero O, Guijarro-Berdiñas B, Alonso-Betanzos A. A global optimum approach for one-layer neural networks. Neural Comput. 2002;14(6):1429–49.CrossRefPubMedGoogle Scholar
  25. 25.
    El-Sebakhy EA. Forecasting PVT properties of crude oil systems based on support vector machines modeling scheme. J Petrol Sci Eng. 2009;64(1–4):25–34.CrossRefGoogle Scholar
  26. 26.
    Smola AJ, Schölkopf B. A tutorial on support vector regression. Stat Comput. 2004;14(3):199–222.CrossRefGoogle Scholar
  27. 27.
    Breiman L. Random forests. Mach Learn. 2001;45(1):5–32.CrossRefGoogle Scholar
  28. 28.
    Wang Y, Zheng M, Xiao J, Lu Y, Wang F, Lu J, et al. Using support vector regression coupled with the genetic algorithm for predicting acute toxicity to the fathead minnow. SAR QSAR Environ Res. 2010;21(5–6):559–70.CrossRefPubMedGoogle Scholar
  29. 29.
    Yap CW, Li ZR, Chen YZ. Quantitative structure-pharmacokinetic relationships for drug clearance by using statistical learning methods. J Mol Graph Model. 2006;24(5):383–95.CrossRefPubMedGoogle Scholar
  30. 30.
    Chu A, Ahn H, Halwan B, Kalmin B, Artifon EL, Barkun A, et al. A decision support system to facilitate management of patients with acute gastrointestinal bleeding. Artif Intell Med. 2008;42(3):247–59.CrossRefPubMedGoogle Scholar
  31. 31.
    Monte-Moreno E. Non-invasive estimate of blood glucose and blood pressure from a photoplethysmograph by means of machine learning techniques. Artif Intell Med. 2011;53(2):127–38.CrossRefPubMedGoogle Scholar
  32. 32.
    Hsieh CH, Lu RH, Lee NH, Chiu WT, Hsu MH, Li YC. Novel solutions for an old disease: diagnosis of acute appendicitis with random forest, support vector machines, and artificial neural networks. Surgery. 2011;149(1):87–93.CrossRefPubMedGoogle Scholar
  33. 33.
    Robert GP, Yang W. Density-functional theory of atoms and molecules. Oxford: Oxford University Press; 1989.Google Scholar
  34. 34.
    Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, et al. General atomic and molecular electronic structure system. J Comput Chem. 1993;14(11):1347–63.CrossRefGoogle Scholar
  35. 35.
    Gordon MS, Schmidt MW. Advances in electronic structure theory: GAMESS a decade later. In: Dykstra CE, Frenking G, Kim KS, Scuseria GE, editors. Theory and applications of computational chemistry: the first forty years. Amsterdam: Elsevier; 2005. p. 1167–89.CrossRefGoogle Scholar
  36. 36.
    Lee C, Yang W, Parr RG. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B Condens Matter. 1988;37(2):785–9.CrossRefPubMedGoogle Scholar
  37. 37.
    Beck AD. A new mixing of Hartree-Fock and local density‐functional theories. J Chem Phys. 1993;98:1372–7.CrossRefGoogle Scholar
  38. 38.
    R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, Austria. 2013. Available from
  39. 39.
    Cortes C, Vapnik V. Support-vector networks. Mach Learn. 1995;20(3):273–97.Google Scholar
  40. 40.
    Vapnik V. Statistical learning theory. New York: Wiley; 1998.Google Scholar
  41. 41.
    Meyer D, Dimitriadou E, Hornik K, Weingessel A, Leisch F. e1071: Misc Functions of the Department of Statistics (e1071), TU Wien. R package version 1.6–2. 2014. Available from
  42. 42.
    Svetnik V, Liaw A, Tong C, Culberson JC, Sheridan RP, Feuston BP. Random forest: a classification and regression tool for compound classification and QSAR modeling. J Chem Inf Comput Sci. 2003;43(6):1947–58.CrossRefPubMedGoogle Scholar
  43. 43.
    Liaw A, Wiener M. Classification and regression by randomForest. R News. 2002;2:18–22.Google Scholar
  44. 44.
    Burman P. A Comparative study of ordinary cross-validation, v-fold cross-validation and the repeated learning-testing methods. Biometrika. 1989;76(3):503–14.CrossRefGoogle Scholar
  45. 45.
    Shao J. Linear model selection by cross-validation. J Am Stat Assoc. 1993;88(442):486–94.CrossRefGoogle Scholar
  46. 46.
    Zhang P. Model selection via multifold cross validation. Ann Stat. 1993;21(1):486–94.CrossRefGoogle Scholar
  47. 47.
    Golbraikh A, Tropsha A. Beware of q2! J Mol Graph Model. 2002;20(4):269–76.CrossRefPubMedGoogle Scholar
  48. 48.
    Roy PP, Roy K. On some aspects of variable selection for partial least squares regression models. QSAR Comb Sci. 2008;27(3):302–13.CrossRefGoogle Scholar
  49. 49.
    Abraham MH, Martins F, Mitchell RC. Algorithms for skin permeability using hydrogen bond descriptors: the problem of steroids. J Pharm Pharmacol. 1997;49(9):858–65.CrossRefPubMedGoogle Scholar
  50. 50.
    Neumann D, Kohlbacher O, Merkwirth C, Lengauer T. A fully computational model for predicting percutaneous drug absorption. J Chem Inf Model. 2006;46(1):424–9.CrossRefPubMedGoogle Scholar
  51. 51.
    Neely BJ, Madihally SV, Robinson Jr RL, Gasem KA. Nonlinear quantitative structure-property relationship modeling of skin permeation coefficient. J Pharm Sci. 2009;98(11):4069–84.CrossRefPubMedPubMedCentralGoogle Scholar
  52. 52.
    Law V, Knox C, Djoumbou Y, Jewison T, Guo AC, Liu Y, et al. DrugBank 4.0: shedding new light on drug metabolism. Nucleic Acids Res. 2014;42:D1091–7.CrossRefPubMedPubMedCentralGoogle Scholar
  53. 53.
    We have obtained structures of 6213 compounds in DrugBank:
  54. 54.
    Bos JD, Meinardi MM. The 500 Dalton rule for the skin penetration of chemical compounds and drugs. Exp Dermatol. 2000;9(3):165–9.CrossRefPubMedGoogle Scholar
  55. 55.
    Yano T, Nakagawa A, Tsuji M, Noda K. Skin permeability of various non-steroidal anti-inflammatory drugs in man. Life Sci. 1986;39(12):1043–50.CrossRefPubMedGoogle Scholar
  56. 56.
    Flynn GL, Yalkowsky SH. Correlation and prediction of mass transport across membranes. I. Influence of alkyl chain length on flux-determining properties of barrier and diffusant. J Pharm Sci. 1972;61(6):838–52.CrossRefPubMedGoogle Scholar
  57. 57.
    González MP, Terán C, Teijeira M, Helguera AM. Quantitative structure activity relationships as useful tools for the design of new adenosine receptor ligands. 1. Agonist. Curr Med Chem. 2006;13(19):2253–66.CrossRefPubMedGoogle Scholar
  58. 58.
    Leardi R, Boggia R, Terrile M. Genetic algorithms as a strategy for feature selection. J Chemom. 1992;6(5):267–81.CrossRefGoogle Scholar
  59. 59.
    Shamsipur M, Zare-Shahabadi V, Hemmateenejad B, Akhond M. An efficient variable selection method based on the use of external memory in ant colony optimization. Application to QSAR/QSPR studies. Anal Chim Acta. 2009;646(1–2):39–46.CrossRefPubMedGoogle Scholar
  60. 60.
    Lin WQ, Jiang JH, Shen Q, Shen GL, Yu RQ. Optimized block-wise variable combination by particle swarm optimization for partial least squares modeling in quantitative structure-activity relationship studies. J Chem Inf Model. 2005;45(2):486–93.CrossRefPubMedGoogle Scholar
  61. 61.
    Barratt MD. Quantitative structure-activity relationships for skin permeability. Toxicol in Vitro. 1995;9(1):27–37.CrossRefPubMedGoogle Scholar
  62. 62.
    Kasting GB, Smith RL, Cooper ER. Effect of lipid solubility and molecular size on percutaneous absorption. In: Shroot B, Schaefer H, editors. Skin pharmacokinetics. Basel: Kargar; 1987. p. 138–53.Google Scholar
  63. 63.
    Cronin MT, Dearden JC, Moss GP, Murray-Dickson G. Investigation of the mechanism of flux across human skin in vitro by quantitative structure-permeability relationships. Eur J Pharm Sci. 1999;7(4):325–30.CrossRefPubMedGoogle Scholar
  64. 64.
    Buchwald P, Bodor N. A simple, predictive, structure-based skin permeability model. J Pharm Pharmacol. 2001;53(9):1087–98.CrossRefPubMedGoogle Scholar
  65. 65.
    Basak SC, Mills D, Mumtaz MM. A quantitative structure-activity relationship (QSAR) study of dermal absorption using theoretical molecular descriptors. SAR QSAR Environ Res. 2007;18(1–2):45–55.CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Hiromi Baba
    • 1
  • Jun-ichi Takahara
    • 1
  • Hiroshi Mamitsuka
    • 2
  1. 1.Kyoto R&D Center, Maruho Co., Ltd.Shimogyo-kuJapan
  2. 2.Bioinformatics Center, Institute for Chemical ResearchKyoto UniversityUjiJapan

Personalised recommendations