Development of a Gaussian Process - feature selection model to characterise (poly)dimethylsiloxane (Silastic® ) membrane permeation

OBJECTIVES

The current study aims to determine the effect of physicochemical descriptor selection on models of polydimethylsiloxane permeation.

METHODS

A total of 2942 descriptors were calculated for a data set of 77 chemicals. Data were processed to remove redundancy, single values, imbalanced and highly correlated data, yielding 1363 relevant descriptors. For four independent test sets, feature selection methods were applied and modelled via a variety of Machine Learning methods.

KEY FINDINGS

Two sets of molecular descriptors which can provide improved predictions, compared to existing models, have been identified. Best permeation predictions were found with Gaussian Process methods. The molecular descriptors describe lipophilicity, partial charge and hydrogen bonding as key determinants of PDMS permeation.

CONCLUSIONS

This study highlights important considerations in the development of relevant models and in the construction and use of the data sets used in such studies, particularly that highly correlated descriptors should be removed from data sets. Predictive models are improved by the methodology adopted in this study, notably the systematic evaluation of descriptors, rather than simply using any and all available descriptors, often based empirically on in vitro experiments. Such findings also have clear relevance to a number of other fields.

The influence of diffusion cell type and experimental temperature on machine learning models of skin permeability

OBJECTIVES

The aim of this study was to use Gaussian process regression (GPR) methods to quantify the effect of experimental temperature (T_exp ) and choice of diffusion cell on model quality and performance.

METHODS

Data were collated from the literature. Static and flow-through diffusion cell data were separated, and a series of GPR experiments was conducted. The effect of T_exp was assessed by comparing a range of datasets where T_exp either remained constant or was varied from 22 to 45 °C.

KEY FINDINGS

Using data from flow-through diffusion cells results in poor model performance. Data from static diffusion cells resulted in significantly greater performance. Inclusion of data from flow-through cell experiments reduces overall model quality. Consideration of T_exp improves model quality when the dataset used exhibits a wide range of experimental temperatures.

CONCLUSIONS

This study highlights the problem of collating literature data into datasets from which models are constructed without consideration of the nature of those data. In order to optimise model quality data from only static, Franz-type, experiments should be used to construct the model and T_exp should either be incorporated as a descriptor in the model if data are collated from a range of studies conducted at different temperatures.

Endocytosis and Lack of Cytotoxicity of Alkyl-Capped Silicon Quantum Dots Prepared from Porous Silicon

Freely-dissolved silicon quantum dots were prepared by thermal hydrosilation of 1-undecene at high-porosity porous silicon under reflux in toluene. This reaction produces a suspension of alkyl-capped silicon quantum dots (alkyl SiQDs) with bright orange luminescence, a core Si nanocrystal diameter of about 2.5 nm and a total particle diameter of about 5 nm. Previous work has shown that these particles are rapidly endocytosed by malignant cell lines and have little or no acute toxicity as judged by the standard 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay for viability and the Terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) assay for apoptosis. We have extended this work to the CACO-2 cell line, an established model for the human small intestinal mucosa, and demonstrate that neither acute nor chronic (14 days) toxicity is observed as judged by cell morphology, viability, ATP production, ROS production and DNA damage (single cell gel electrophoresis) at doses of 50–200 μg mL−1. Quantitative assessment of the extent of uptake of alkyl SiQDs by CACO-2, HeLa, HepG2, and Huh7 cell lines by flow cytometry showed a wide variation. The liver cell lines (HepG2 and Huh7) were the most active and HeLa and CACO-2 showed comparable activity. Previous work has reported a cholesterol-sensitivity of the endocytosis (HeLa), which suggests a caveolin-mediated pathway. However, gene expression analysis by quantitative real–time polymerase chain reaction (RT-PCR) indicates very low levels of caveolins 1 and 2 in HepG2 and much higher levels in HeLa. The data suggest that the mechanism of endocytosis of the alkyl SiQDs is cell-line dependent.

Model fitting for small skin permeability data sets: hyperparameter optimisation in Gaussian Process Regression

OBJECTIVES

The aim of this study was to investigate how to improve predictions from Gaussian Process models by optimising the model hyperparameters.

METHODS

Optimisation methods, including Grid Search, Conjugate Gradient, Random Search, Evolutionary Algorithm and Hyper-prior, were evaluated and applied to previously published data. Data sets were also altered in a structured manner to reduce their size, which retained the range, or 'chemical space' of the key descriptors to assess the effect of the data range on model quality.

KEY FINDINGS

The Hyper-prior Smoothbox kernel results in the best models for the majority of data sets, and they exhibited significantly better performance than benchmark quantitative structure-permeability relationship (QSPR) models. When the data sets were systematically reduced in size, the different optimisation methods generally retained their statistical quality, whereas benchmark QSPR models performed poorly.

CONCLUSIONS

The design of the data set, and possibly also the approach to validation of the model, is critical in the development of improved models. The size of the data set, if carefully controlled, was not generally a significant factor for these models and that models of excellent statistical quality could be produced from substantially smaller data sets.

Support vector regression to estimate the permeability enhancement of potential transdermal enhancers

Objectives

Searching for chemicals that will safely enhance transdermal drug delivery is a significant challenge. This study applies support vector regression (SVR) for the first time to estimating the optimal formulation design of transdermal hydrocortisone formulations.

Methods

The aim of this study was to apply SVR methods with two different kernels in order to estimate the enhancement ratio of chemical enhancers of permeability.

Key findings

A statistically significant regression SVR model was developed. It was found that SVR with a nonlinear kernel provided the best estimate of the enhancement ratio for a chemical enhancer.

Conclusions

Support vector regression is a viable method to develop predictive models of biological processes, demonstrating improvements over other methods. In addition, the results of this study suggest that a global approach to modelling a biological process may not necessarily be the best method and that a ‘mixed-methods’ approach may be best in optimising predictive models.

The application of machine learning to the modelling of percutaneous absorption: an overview and guide

Machine learning (ML) methods have been applied to the analysis of a range of biological systems. This paper reviews the application of these methods to the problem domain of skin permeability and addresses critically some of the key issues. Specifically, ML methods offer great potential in both predictive ability and their ability to provide mechanistic insight to, in this case, the phenomena of skin permeation. However, they are beset by perceptions of a lack of transparency and, often, once a ML or related method has been published there is little impetus from other researchers to adopt such methods. This is usually due to the lack of transparency in some methods and the lack of availability of specific coding for running advanced ML methods. This paper reviews critically the application of ML methods to percutaneous absorption and addresses the key issue of transparency by describing in detail - and providing the detailed coding for - the process of running a ML method (in this case, a Gaussian process regression method). Although this method is applied here to the field of percutaneous absorption, it may be applied more broadly to any biological system.

The application of Gaussian processes in the predictions of permeability across mammalian and polydimethylsiloxane membranes

The problem of predicting the rate of percutaneous absorption of a drug is an important issue, particular with the increasing use of the skin as a means of moderating and controlling drug delivery. One key feature of this problem domain is that human skin permeability to penetrants (often characterised by Kp, the permeability coefficient) has been shown to be inherently non-linear when mathematically related to the key physicochemical parameters of penetrants. The aims of the current study were to apply and validate Gaussian process regression methods to datasets for membranes other than human skin, and to explore how the nature of the dataset may influence its analysis. Permeability data for absorption across rodent and pig skin, and polydimethylsiloxane Silastic® membranes was collected from the literature. Two QSPR methods were applied to compare to the Gaussian process models. The results demonstrated that Gaussian process models with different covariance functions outperform the QSPR model for human, pig and rodent datasets, but in general are not good for Silastic® membranes. These results suggest that the physicochemical parameters employed in this study might not be appropriate for developing models that represent this membrane. In addition, the results show the size of the datasets, in both absolute and comparative senses, appears to influence model quality.

The application and limitations of mathematical modelling in the prediction of permeability across mammalian skin and polydimethylsiloxane membranes

OBJECTIVES

Predicting the rate of percutaneous absorption of a drug is an important issue with the increasing use of the skin as a means of moderating and controlling drug delivery. One key feature of this problem domain is that human skin permeability (as K(p)) has been shown to be inherently non-linear when mathematically related to the physicochemical parameters of penetrants. As such, the aims of this study were to apply and evaluate Gaussian process (GP) regression methods to datasets for membranes other than human skin, and to explore how the nature of the dataset may influence its analysis.

METHODS

Permeability data for absorption across rodent and pig skin, and artificial membranes (polydimethylsiloxane, PDMS, i.e. Silastic) membranes was collected from the literature. Two quantitative structure-permeability relationship (QSPR) models were used to compare with the GP models. Further performance metrics were computed in terms of all predictions, and a range of covariance functions were examined: the squared exponential (SE), neural network (NNone) and rational quadratic (QR) covariance functions, along with two simple cases of Matern covariance function (Matern3 and Matern5) where the polynomial order is set to 1 and 2, respectively. As measures of performance, the correlation coefficient (CORR), negative log estimated predictive density (NLL, or negative log loss) and mean squared error (MSE) were employed.

KEY FINDINGS

The results demonstrated that GP models with different covariance functions outperform QSPR models for human, pig and rodent datasets. For the artificial membranes, GPs perform better in one instance, and give similar results in other experiments (where different covariance parameters produce similar results). In some cases, the GP predictions for some of the artificial membrane dataset are poorly correlated, suggesting that the physicochemical parameters employed in this study might not be appropriate for developing models that represent this membrane.

CONCLUSIONS

While the results of this study indicate that permeation across rodent (mouse and rat) and pig skin is, in a statistical sense, similar, and that the artificial membranes are poor replacements of human or animal skin, the overriding issue raised in this study is the nature of the dataset and how it can influence the results, and subsequent interpretation, of any model produced for particular membranes. The size of the datasets, in both absolute and comparative senses, appears to influence model quality. Ideally, to generate viable cross-comparisons the datasets for different mammalian membranes should, wherever possible, exhibit as much commonality as possible.

Attitudes of community optometrists to smoking cessation: an untapped opportunity overlooked?

AIM

To assess community optometrists' attitudes and current behaviour regarding provision of smoking cessation advice in their practice.

METHODS

A self-completion postal questionnaire was sent to community optometrists in north-west England identified from the General Optical Council's practice lists.

RESULTS

Of 709 optometrists identified, 71.8% (509/709) returned the completed questionnaire. Few community optometrists routinely asked about smoking habits: only 6.2% (95% CI: 4.1-8.3) (n = 31) at new patient consultations, and 2.2% (95% CI: 0.9-3.5) (n=11) at follow-up visits. Reasons for optometrists not routinely providing smoking cessation advice included: not their role (35.4%, n=180), lack of time (22.0%, n=112) and forgetting to ask (21.4%, n=109). Overall 67.6% (95% CI: 63.5-71.7) (n=344) of community optometrists wanted to improve their knowledge of smoking and visual impairment with 56.2% (95% CI: 51.9-60.5) (n=286) requesting further training.

CONCLUSION

Despite low levels of current involvement, many optometrists were keen to receive training on smoking cessation topics. We suggest that there are untapped opportunities to develop brief interventions to promote smoking cessation services in community optometry settings.

The influence of water mixtures on the dermal absorption of glycol ethers

Glycol ethers are solvents widely used alone and as mixtures in industrial and household products. Some glycol ethers have been shown to have a range of toxic effects in humans following absorption and metabolism to their aldehyde and acid metabolites. This study assessed the influence of water mixtures on the dermal absorption of butoxyethanol and ethoxyethanol in vitro through human skin. Butoxyethanol penetrated human skin up to sixfold more rapidly from aqueous solution (50%, 450 mg/ml) than from the neat solvent. Similarly penetration of ethoxyethanol was increased threefold in the presence of water (50%, 697 mg/ml). There was a corresponding increase in apparent permeability coefficient as the glycol ether concentration in water decreased. The maximum penetration rate of water also increased in the presence of both glycol ethers. Absorption through a synthetic membrane obeyed Fick's Law and absorption through rat skin showed a similar profile to human skin but with a lesser effect. The mechanisms for this phenomenon involves disruption of the stratum corneum lipid bilayer by desiccation by neat glycol ether micelles, hydration with water mixtures and the physicochemical properties of the glycol ether-water mixtures. Full elucidation of the profile of absorption of glycol ethers from mixtures is required for risk assessment of dermal exposure. This work supports the view that risk assessments for dermal contact scenarios should ideally be based on absorption data obtained for the relevant formulation or mixture and exposure scenario and that absorption derived from permeability coefficients may be inappropriate for water-miscible solvents.

Interactions of skin thickness and physicochemical properties of test compounds in percutaneous penetration studies

OBJECTIVES

To determine the effect of skin thickness on the percutaneous penetration and distribution of test compounds with varying physicochemical properties using in vitro systems. Studies were carried out in accordance with OECD guidelines on skin absorption tests.

METHODS

Percutaneous penetration of caffeine (log P -0.01), testosterone (log P 3.32), propoxur (log P 1.52) (finite dose in ethanol to water vehicle ratio) and butoxyethanol (log P 0.83) (undiluted finite dose or as an infinite dose 50% [v/v] aqueous solution) through skin of varying thicknesses under occluded conditions was measured using flow through cells for 8-24 h. Saline (adjusted to pH 7.4) was used as receptor fluid, with BSA added for studies with testosterone and propoxur. Following exposure, the remaining surface dose was removed by swabbing and the skin digested prior to scintillation counting.

RESULTS

The maximum flux of caffeine was increased with decreasing skin thickness, although these differences were found to be non-significant. The presence of caffeine in the skin membrane was not altered by skin thickness. Maximum flux and cumulative dose absorbed of testosterone and butoxyethanol (in both finite and infinite doses) were markedly reduced with full thickness (about 1 mm thick) skin compared with split thickness skin (about 0.5 mm). Maximum flux of propoxur (dissolved in 60% ethanol) was clearly higher through skin of 0.71 mm than through skin of 1.36 mm, but no difference was found between 0.56 and 0.71 mm. The proportion of propoxur present in the membrane after 24 h increased significantly over the complete range of thicknesses tested (0.56-1.36 mm).

CONCLUSIONS

A complex relationship exists between skin thickness, lipophilicity and percutaneous penetration and distribution. This has implications for risk assessment studies and for the validation of models with data from different sources.

Inter‐ and intralaboratory variation of in vitro diffusion cell measurements: An international multicenter study using quasi‐standardized methods and materials

In vitro measurements of skin absorption are an increasingly important aspect of regulatory studies, product support claims, and formulation screening. However, such measurements are significantly affected by skin variability. The purpose of this study was to determine inter- and intralaboratory variation in diffusion cell measurements caused by factors other than skin. This was attained through the use of an artificial (silicone rubber) rate-limiting membrane and the provision of materials including a standard penetrant, methyl paraben (MP), and a minimally prescriptive protocol to each of the 18 participating laboratories. "Standardized" calculations of MP flux were determined from the data submitted by each laboratory by applying a predefined mathematical model. This was deemed necessary to eliminate any interlaboratory variation caused by different methods of flux calculations. Average fluxes of MP calculated and reported by each laboratory (60 +/- 27 microg cm(-2) h(-1), n = 25, range 27-101) were in agreement with the standardized calculations of MP flux (60 +/- 21 microg cm(-2) h(-1), range 19-120). The coefficient of variation between laboratories was approximately 35% and was manifest as a fourfold difference between the lowest and highest average flux values and a sixfold difference between the lowest and highest individual flux values. Intralaboratory variation was lower, averaging 10% for five individuals using the same equipment within a single laboratory. Further studies should be performed to clarify the exact components responsible for nonskin-related variability in diffusion cell measurements. It is clear that further developments of in vitro methodologies for measuring skin absorption are required.

In vitro predictions of skin absorption of caffeine, testosterone, and benzoic acid: a multi-centre comparison study

To obtain better insight into the robustness of in vitro percutaneous absorption methodology, the intra- and inter-laboratory variation in this type of study was investigated in 10 European laboratories. To this purpose, the in vitro absorption of three compounds through human skin (9 laboratories) and rat skin (1 laboratory) was determined. The test materials were benzoic acid, caffeine, and testosterone, representing a range of different physico-chemical properties. All laboratories performed their studies according to a detailed protocol in which all experimental details were described and each laboratory performed at least three independent experiments for each test chemical. All laboratories assigned the absorption of benzoic acid through human skin, the highest ranking of the three compounds (overall mean flux of 16.54+/-11.87 microg/cm(2)/h). The absorption of caffeine and testosterone through human skin was similar, having overall mean maximum absorption rates of 2.24+/-1.43 microg/cm(2)/h and 1.63+/-1.94 microg/cm(2)/h, respectively. In 7 out of 9 laboratories, the maximum absorption rates of caffeine were ranked higher than testosterone. No differences were observed between the mean absorption through human skin and the one rat study for benzoic acid and testosterone. For caffeine the maximum absorption rate and the total penetration through rat skin were clearly higher than the mean value for human skin. When evaluating all data, it appeared that no consistent relation existed between the diffusion cell type and the absorption of the test compounds. Skin thickness only slightly influenced the absorption of benzoic acid and caffeine. In contrast, the maximum absorption rate of testosterone was clearly higher in the laboratories using thin, dermatomed skin membranes. Testosterone is the most lipophilic compound and showed also a higher presence in the skin membrane after 24 h than the two other compounds. The results of this study indicate that the in vitro methodology for assessing skin absorption is relatively robust. A major effort was made to standardize the study performance, but, unlike in a formal validation study, not all variables were controlled. The variation observed may be largely attributed to human variability in dermal absorption and the skin source. For the most lipophilic compound, testosterone, skin thickness proved to be a critical variable.

Effects of experimental conditions on absorption of glycol ethers through human skin in vitro

OBJECTIVES

To determine effects of experimental variables on the dermal absorption of 2-ethoxyethanol (EE), 2-butoxyethanol (BE) and 1-methoxy-2-propanol (M2P) through human skin in vitro.

METHODS

Percutaneous absorption of EE, BE and M2P, in aqueous solution (3 mg ml(-1), 200 microl) or undiluted (10.5 microl), though full thickness or dermatomed human breast skin (0.64 cm(2) exposed area) was measured for 24 h using flow-through diffusion cells. Tissue culture medium was used as receptor fluid, with 2% (w/v) bovine serum albumin (BSA) or 2%-6% (w/v) polyethylene glycol 20 oleyl ether (PEG 20) added for some studies. Volatilised test compounds were trapped on charcoal filters placed above cells.

RESULTS

In aqueous solution, steady-state flux of BE (544+/-64 nmol cm(-2) h(-1)) exceeded that of EE (143+/-19 nmol cm(-2) h(-1)) and M2P (48+/-6 nmol cm(-2) h(-1)). Reducing the dose volume to 100 microl decreased the steady-state flux of BE by about 55%, though the flux of EE was approximately doubled. Doubling the dose concentration of EE increased the flux by about eight-fold. Using full thickness skin increased tau of both EE and BE and reduced the steady-state flux of BE. Absorption rates of undiluted solvents in finite doses exceeded those measured with aqueous solutions, though the apparent permeability coefficient was higher with aqueous doses. Addition of BSA or PEG 20 to receptor fluid markedly increased absorption in both aqueous and undiluted doses.

CONCLUSIONS

The dermal absorption potential of M2P from a liquid application was markedly lower than from EE or BE in all but infinite undiluted doses. The influence of receptor fluid on dermal absorption of glycol ethers could be relevant to prediction of absorption in vivo.

Visualization of root caries lesions by means of a diazonium dye

A diazonium dye was used to visualize caries lesions in root tissue. Root caries lesions were created in vitro according to a variety of protocols based on methylcellulose gel (6% w/v) and/or lactic acid buffer (0.05 M, pH 4.5). Teeth containing lesions were soaked overnight in an alkaline solution of 2% (w/v) 2-naphthol or resorcinol, rinsed with distilled water, and immersed in a diazonium solution (prepared by titration of aniline with sodium nitrite in 1 M HCl at 5 degrees C) for up to 10 min, prior to being thoroughly rinsed with distilled water. The area of the caries lesion on the anatomical surface was clearly marked with a red/orange color following 5 minutes' incubation in the diazonium solution. The diazonium complex formed with 2-naphthol was found to be more resistant to leaching during rinsing and sectioning than that formed with resorcinol. Microscopic examination of sections taken in the apicalcoronal plane showed that the depth of area of the lesion was also marked by the red/orange coloration. Chemical changes in root mineral monitored during lesion formation showed some degree of correlation between lesion area and mineral dissolution. Visualization of coronal caries by this technique is currently under investigation. The visualization technique provides a simple means of determining the extent and severity of root caries lesions and may be a useful first step in their classification.