The application of feature selection to the development of Gaussian process models for percutaneous absorption

Multivariate Analytical Approaches to Identify Key Molecular Properties of Vehicles, Permeants and Membranes That Affect Permeation through Membranes

There has been considerable recent interest in employing computer models to investigate the relationship between the structure of a molecule and its dermal penetration. Molecular permeation across the epidermis has previously been demonstrated to be determined by a number of physicochemical properties, for example, the lipophilicity, molecular weight and hydrogen bonding ability of the permeant. However little attention has been paid to modeling the combined effects of permeant properties in tandem with the properties of vehicles used to deliver those permeants or to whether data obtained using synthetic membranes can be correlated with those obtained using human epidermis. This work uses Principal Components Analysis (PCA) to demonstrate that, for studies of the diffusion of three model permeants (caffeine, methyl paraben and butyl paraben) through synthetic membranes, it is the properties of the oily vehicle in which they are applied that dominated the rates of permeation and flux. Simple robust and predictive descriptor-based quantitative structure-permeability relationship (QSPR) models have been developed to support these findings by utilizing physicochemical descriptors of the oily vehicles to quantify the differences in flux and permeation of the model compounds. Interestingly, PCA showed that, for the flux of co-applied model permeants through human epidermis, the permeation of the model permeants was better described by a balance between the physicochemical properties of the vehicle and the permeant rather than being dominated solely by the vehicle properties as in the case of synthetic model membranes. The important influence of permeant solubility in the vehicle along with the solvent uptake on overall permeant diffusion into the membrane was substantiated. These results confirm that care must be taken in interpreting permeation data when synthetic membranes are employed as surrogates for human epidermis; they also demonstrate the importance of considering not only the permeant properties but also those of both vehicle and membrane when arriving at any conclusions relating to permeation data.

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.

Predicting Skin Permeability by Means of Computational Approaches: Reliability and Caveats in Pharmaceutical Studies

The skin is the main barrier between the internal body environment and the external one. The characteristics of this barrier and its properties are able to modify and affect drug delivery and chemical toxicity parameters. Therefore, it is not surprising that permeability of many different compounds has been measured through several in vitro and in vivo techniques. Moreover, many different in silico approaches have been used to identify the correlation between the structure of the permeants and their permeability, to reproduce the skin behavior, and to predict the ability of specific chemicals to permeate this barrier. A significant number of issues, like interlaboratory variability, experimental conditions, data set building rationales, and skin site of origin and hydration, still prevent us from obtaining a definitive predictive skin permeability model. This review wants to show the main advances and the principal approaches in computational methods used to predict this property, to enlighten the main issues that have arisen, and to address the challenges to develop in future research.

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.

Surging footprints of mathematical modeling for prediction of transdermal permeability

In vivo skin permeation studies are considered gold standard but are difficult to perform and evaluate due to ethical issues and complexity of process involved. In recent past, a useful tool has been developed by combining the computational modeling and experimental data for expounding biological complexity. Modeling of percutaneous permeation studies provides an ethical and viable alternative to laboratory experimentation. Scientists are exploring complex models in magnificent details with advancement in computational power and technology. Mathematical models of skin permeability are highly relevant with respect to transdermal drug delivery, assessment of dermal exposure to industrial and environmental hazards as well as in developing fundamental understanding of biotransport processes. Present review focuses on various mathematical models developed till now for the transdermal drug delivery along with their applications.

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.

An evaluation of the potential of linear and nonlinear skin permeation models for the prediction of experimentally measured percutaneous drug absorption

Objectives

The developments in combinatorial chemistry have led to a rapid increase in drug design and discovery and, ultimately, the production of many potential molecules that require evaluation. Hence, there has been much interest in the use of mathematical models to predict dermal absorption. Therefore, the aim of this study was to test the performance of both linear and nonlinear models to predict the skin permeation of a series of 11 compounds.

Methods

The modelling in this study was carried out by the application of both quantitative structure permeability relationships and Gaussian process-based machine learning methods to predict the flux and permeability coefficient of the 11 compounds. The actual permeation of these compounds across human skin was measured using Franz cells and a standard protocol with high performance liquid chromatography analysis. Statistical comparison between the predicted and experimentally-derived values was performed using mean squared error and the Pearson sample correlation coefficient.

Key findings

The findings of this study would suggest that the models failed to accurately predict permeation and in some cases were not within two- or three-orders of magnitude of the experimentally-derived values. However, with this set of compounds the models were able to effectively rank the permeants.

Conclusions

Although not suitable for accurately predicting permeation the models may be suitable for determining a rank order of permeation, which may help to select candidate molecules for in-vitro screening. However, it is important to note that such predictions need to take into account actual relative drug candidate potencies.

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.