An equation for the prediction of human skin permeability of neutral molecules, ions and ionic species

Machine learning for skin permeability prediction: random forest and XG boost regression

Background: Machine learning algorithms that can quickly and easily estimate skin permeability (Kp) are increasingly being used in drug delivery research. The linear free energy relationship (LFER) developed by Abraham is a practical technique for predicting Kp. The permeability coefficients and Abraham solute descriptor values for 175 organic compounds have been documented in the scientific literature.Purpose: The purpose of this project was to use a publicly available dataset to make skin permeability predictions using the random forest and XBoost regression techniques.Methods: We employed Pandas-based methods in JupyterLab to predict permeability coefficient (Kp) from solute descriptors (excess molar refraction [E], combined dipolarity/polarizability [S], overall solute hydrogen bond acidity and basicity [A and B], and the McGowan's characteristic molecular volume [V]).Results: The random forest and XG Boost regression models established statistically significant association between the descriptors and the skin permeability coefficient.

Simulating the Skin Permeation Process of Ionizable Molecules

It is commonly assumed that ionizable molecules, such as drugs, permeate through the skin barrier in their neutral form. By using molecular dynamics simulations of the charged and neutral states separately, we can study the dynamic protonation behavior during the permeation process. We have studied three weak acids and three weak bases and conclude that the acids are ionized to a larger extent than the bases, when passing through the headgroup region of the lipid barrier structure, at pH values close to their pKa. It can also be observed that even if these dynamic protonation simulations are informative, in the cases studied herein they are not necessary for the calculation of permeability coefficients. It is sufficient to base the calculations only on the neutral form, as is commonly done.

Penetration pathways, influencing factors and predictive models for dermal absorption of exobiotic molecules: A critical review

This review provides a comprehensive summary of the skin penetration pathways of xenobiotics, including metals, organic pollutants, and nanoparticles (NPs), with a particular focus on the methodologies employed to elucidate these penetration routes. The impacts of the physicochemical properties of exogenous substances and the properties of solvent carriers on the penetration efficiencies were discussed. Furthermore, the review outlines the steady-state and transient models for predicting the skin permeability of xenobiotics, emphasizing the models which enable realistic visualization of pharmaco-kinetic phenomena via detailed geometric representations of the skin microstructure, such as stratum corneum (SC) (bricks and mortar) and skin appendages (hair follicles and sebaceous gland units). Limitations of published research, gaps in current knowledge, and recommendations for future research are highlighted, providing insight for a better understanding of the skin penetration behavior of xenobiotics and associated health risks in practical application contexts.

Ability of biomimetic chromatography and physicochemical systems to predict the skin permeation of neutral compounds. A comparison study

Five in vitro physicochemical systems have been evaluated in terms of its ability to emulate the skin permeation of neutral compounds: the permeation in two different PAMPA membranes, the classical octanol-water partition coefficient, and two biomimetic chromatography systems, one based in cerasome electrokinetic chromatography and another based in reversed-phase liquid chromatography measurements. The coefficients of the solvation parameter model equation of the mentioned systems have been compared to the ones of the skin permeation process through different comparison parameters. Moreover, a method to predict whether a physicochemical system is able to emulate satisfactorily a biological one, just by the analysis of the equation coefficients has been developed. Results reveal that the two PAMPA systems are a good choice to emulate directly the skin permeation of neutral compounds. Instead, the other three systems need a volume correction term to provide a satisfactory emulation. However, after the correction, all the evaluated systems show a similar ability to emulate well skin permeation, as predicted.

Determination of descriptors for the principal flavor compounds of the cinnamons of commerce by gas chromatography and liquid-liquid partition

Descriptors for fourteen semivolatile organic compounds associated with the authenticity, botanical origin, and flavor potential of the cinnamons of commerce were determined using the Solver method and experimental retention factors determined by gas chromatography at several temperatures on a minimum of seven selectivity-selected, open-tubular columns and liquid-liquid partition constants in up to twenty totally organic biphasic systems. The six descriptors that encode the solvation properties of the compounds were used to predict water-gas, octanol-gas, and octanol-water partition constants commonly employed to assess environmental distribution properties. For octanol-water partition constants, log KOW, the predicted partition constants exhibited an average absolute deviation of 0.12 for log KOW experimental - log KOW predicted (n = 14). Soil-water, soil-air, urban aerosol-air, skin-water permeation, and non-specific toxicity to the fathead minnow were predicted for the same compounds to assess their potential environmental impact. The product terms of the solvation parameter model provide a useful insight into the contribution of individual intermolecular interactions to the distribution properties of the cinnamon compounds and their environmental impact.

Novel Models for Accurate Estimation of Air-Blood Partitioning: Applications to Individual Compounds and Complex Mixtures of Neutral Organic Compounds

The air-blood partition coefficient (Kab) is extensively employed in human health risk assessment for chemical exposure. However, current Kab estimation approaches either require an extensive number of parameters or lack precision. In this study, we present two novel and parsimonious models to accurately estimate Kab values for individual neutral organic compounds, as well as their complex mixtures. The first model, termed the GC×GC model, was developed based on the retention times of nonpolar chemical analytes on comprehensive two-dimensional gas chromatography (GC×GC). This model is unique in its ability to estimate the Kab values for complex mixtures of nonpolar organic chemicals. The GC×GC model successfully accounted for the Kab variance (R2 = 0.97) and demonstrated strong prediction power (RMSE = 0.31 log unit) for an independent set of nonpolar chemical analytes. Overall, the GC×GC model can be used to estimate Kab values for complex mixtures of neutral organic compounds. The second model, termed the partition model (PM), is based on two types of partition coefficients: octanol to water (Kow) and air to water (Kaw). The PM was able to effectively account for the variability in Kab data (n = 344), yielding an R2 value of 0.93 and root-mean-square error (RMSE) of 0.34 log unit. The predictive power and explanatory performance of the PM were found to be comparable to those of the parameter-intensive Abraham solvation models (ASMs). Additionally, the PM can be integrated into the software EPI Suite, which is widely used in chemical risk assessment for initial screening. The PM provides quick and reliable estimation of Kab compared to ASMs, while the GC×GC model is uniquely suited for estimating Kab values for complex mixtures of neutral organic compounds. In summary, our study introduces two novel and parsimonious models for the accurate estimation of Kab values for both individual compounds and complex mixtures.

Characterization of solute-solvent interactions in liquid chromatography systems: A fast method based on Abraham's linear solvation energy relationships

The Abraham's solvation parameter model, based on linear solvation energy relationships (LSER), allows the accurate characterization of the selectivity of chromatographic systems according to solute-solvent interactions (polarizability, dipolarity, hydrogen bonding, and cavity formation). However, this method, based on multilinear regression analysis, requires the measurement of the retention factors of a considerably high number of compounds, turning it into a time-consuming low throughput method. Simpler methods such as Tanaka's scheme are preferred. In the present work, the Abraham's model is revisited to develop a fast and reliable method, similar to the one proposed by Tanaka, for the characterization of columns employed in reversed-phase liquid chromatography and particularly in hydrophilic interaction liquid chromatography. For this purpose, pairs of compounds are carefully selected in order to have in common all molecular descriptors except for a specific one (for instance, similar molecular volume, dipolarity, polarizability, and hydrogen bonding basicity features, but different hydrogen bonding acidity). Thus, the selectivity factor of a single pair of test compounds can provide information regarding the extent of the dissimilar solute-solvent interactions and their influence on chromatographic retention. The proposed characterization method includes the determination of the column hold-up volume and Abraham's cavity term by means of the injection of four alkyl ketone homologues. Therefore, five chromatographic runs in a reversed-phase column (four pairs of test solutes and a mixture of four homologues) are enough to characterize the selectivity of a chromatographic system. Tanaka's method is also analyzed from the LSER point of view.

Evaluation of the Ability of PAMPA Membranes to Emulate Biological Processes through the Abraham Solvation Parameter Model

Two parallel artificial membrane permeability assay (PAMPA) systems intended for emulating skin permeability have been characterized through the solvation parameter model of Abraham using multilinear regression analysis. The coefficients of the obtained equations have been compared to the ones already established for other PAMPA membranes using statistical tools. The results indicate that both skin membranes are similar to each other in their physicochemical properties. However, they are different from other PAMPA membranes (e.g., intestinal absorption and blood-brain PAMPAs), mainly in terms of hydrophobicity and hydrogen bonding properties. Next, all PAMPA membranes have been compared to relevant biological processes also characterized through the solvation parameter model. The results highlight that skin-PAMPA membranes are a very good choice to emulate skin permeability.

Recent advances for estimating environmental properties for small molecules from chromatographic measurements and the solvation parameter model

The transfer of neutral compounds between immiscible phases in chromatographic or environmental systems can be described by six solute properties (solute descriptors) using the solvation parameter model. The solute descriptors are size (McGowan's characteristic volume), V, excess molar refraction, E, dipolarity/polarizability, S, hydrogen-bond acidity and basicity, A and B, and the gas-liquid partition constant on n-hexadecane at 298.15 K, L. V and E for liquids are accessible by calculation but the other descriptors and E for solids are determined experimentally by chromatographic, liquid-liquid partition, and solubility measurements. These solute descriptors are available for several thousand compounds in the Abraham solute descriptor databases and for several hundred compounds in the WSU experimental solute descriptor database. In the first part of this review, we highlight features important in defining each descriptor, their experimental determination, compare descriptor quality for the two organized descriptor databases, and methods for estimating Abraham solute descriptors. In the second part we focus on recent applications of the solvation parameter model to characterize environmental systems and its use for the identification of surrogate chromatographic models for estimating environmental properties.

Thermodynamics-Based Model Construction for the Accurate Prediction of Molecular Properties From Partition Coefficients

Developing models for predicting molecular properties of organic compounds is imperative for drug development and environmental safety; however, development of such models that have high predictive power and are independent of the compounds used is challenging. To overcome the challenges, we used a thermodynamics-based theoretical derivation to construct models for accurately predicting molecular properties. The free energy change that determines a property equals the sum of the free energy changes (ΔG_Fs) caused by the factors affecting the property. By developing or selecting molecular descriptors that are directly proportional to ΔG_Fs, we built a general linear free energy relationship (LFER) for predicting the property with the molecular descriptors as predictive variables. The LFER can be used to construct models for predicting various specific properties from partition coefficients. Validations show that the models constructed according to the LFER have high predictive power and their performance is independent of the compounds used, including the models for the properties having little correlation with partition coefficients. The findings in this study are highly useful for applications in drug development and environmental safety.

Development and evaluation of two-parameter linear free energy models for the prediction of human skin permeability coefficient of neutral organic chemicals

The experimental values of skin permeability coefficients, required for dermal exposure assessment, are not readily available for many chemicals. The existing estimation approaches are either less accurate or require many parameters that are not readily available. Furthermore, current estimation methods are not easy to apply to complex environmental mixtures. We present two models to estimate the skin permeability coefficients of neutral organic chemicals. The first model, referred to here as the 2-parameter partitioning model (PPM), exploits a linear free energy relationship (LFER) of skin permeability coefficient with a linear combination of partition coefficients for octanol–water and air–water systems. The second model is based on the retention time information of nonpolar analytes on comprehensive two-dimensional gas chromatography (GC × GC). The PPM successfully explained variability in the skin permeability data (n = 175) with R² = 0.82 and root mean square error (RMSE) = 0.47 log unit. In comparison, the US-EPA’s model DERMWIN™ exhibited an RMSE of 0.78 log unit. The Zhang model—a 5-parameter LFER equation based on experimental Abraham solute descriptors (ASDs)—performed slightly better with an RMSE value of 0.44 log unit. However, the Zhang model is limited by the scarcity of experimental ASDs. The GC × GC model successfully explained the variance in skin permeability data of nonpolar chemicals (n = 79) with R² = 0.90 and RMSE = 0.23 log unit. The PPM can easily be implemented in US-EPA’s Estimation Program Interface Suite (EPI Suite™). The GC × GC model can be applied to the complex mixtures of nonpolar chemicals.

Permeability coefficients and vapour pressure determination for fragrance materials

OBJECTIVE

This study aims to correlate new experimental data relevant to the description of the combined evaporation/permeation process of a perfume applied onto the skin.

METHODS

The vapour pressure data were measured by thermogravimetric analysis (TG-DTA). The Antoine constants and the Clarke and Glew parameters were determined for the same set of fragrance molecules to describe its low vapour pressures at new temperature ranges. The permeability coefficient of a set of 14 fragrance molecules in ethanolic solution was determined by Franz diffusion cell experiments, using porcine skin. The samples were analysed by gas chromatography with a flame ionization detector (GC/FID) and high-performance liquid chromatography with UV visible detector (HPLC/UV). A QSAR model was proposed to correlate the experimental data.

RESULTS

The Antoine constants were determined and presented low standard deviations. The Clarke and Glew physically significant parameters were obtained along with its statistical analysis. The fitting is good since the magnitude order is in accordance with the literature, associated with the low correlation between the estimated parameters and low standard deviations. The presented correlation, based on a mixture using only ethanol as solvent, showed better results than previous QSAR models with a standard relative deviation ( σ r ) of 0.190, a standard error (SE) of 0.397 and a determination coefficient (R² ) of 0.7786.

CONCLUSION

The dataset is still small compared to larger and more general QSAR models; however, it is much more specific as to the type of solvent and class of materials studied. This work represents an advance for the modelling of the perfume diffusion process since it specifies important properties that until then had been treated in a more general way.

Linear free energy relationship models for the retention of partially ionized acid-base compounds in reversed-phase liquid chromatography

The LFER model of Abraham is applied to the retention of the neutral and ionic forms of 94 solutes in a C18 column and 40% v/v acetonitrile/water mobile phase. The results show that polarizability and cavity formation interactions increase retention, whereas dipole and hydrogen bonding interactions favours partition to the mobile phase and thus, they decrease retention. The coefficients of the ionic descriptors measure the effect of the electrostatic interactions and their contribution to partition of the cation or anion between the two mobile and stationary chromatographic phases. A new LFER model for application to the retention of partially dissociated acids and bases is derived averaging the descriptors of the neutral and ionic forms according to their degrees of ionization in the mobile phase. This new LFER model is satisfactorily compared to other literature modified Abraham models for a set of 498 retention data of partially dissociated acids and bases. All tested models require the calculation of the ionization degrees of the compounds at the measuring pH. Calculation of the ionization degrees in the chromatographic mobile phase (i.e. from pH and pK_a in the eluent) give good correlations for all tested models. However, estimation of these ionization degrees from pH - pK_a data in pure water gives biased estimations of the retention of the partially ionized solutes.

Optimization of experimental conditions for skin-PAMPA measurements

In recent years, the parallel artificial membrane permeability assay (PAMPA) has been extended for prediction of skin permeation by developing an artificial membrane which mimics the stratum corneum structure, skin-PAMPA. In the present work, the different parameters affecting skin-PAMPA permeability, such as incubation time and stirring, have been studied to establish ideal assay conditions to generate quality data for a screening of active pharmaceutical ingredients (API) in early stage drug discovery. Another important parameter is membrane retention, which shows dependence on lipophilicity when compounds are in their neutral form. Furthermore, the stability of the membrane has been investigated at different pH values, especially at basic pHs. Finally, a good correlation between human skin permeability and skin-PAMPA permeability, with a large dataset (n = 46), has been established. The optimized assay conditions were an incubation time of 4 hours with stirring in a pH below 8. With all these considerations the thickness of the aqueous boundary layer is decreased as much as possible and the membrane stability is guaranteed.

Solvation Descriptors for Zwitterionic α-Aminoacids; Estimation of Water-Solvent Partition Coefficients, Solubilities, and Hydrogen-Bond Acidity and Hydrogen-Bond Basicity

The literature data on solubilities and water-solvent partition coefficients have been used to obtain properties or "Absolv descriptors" for zwitterionic α-aminoacids: glycine, α-alanine (α-aminopropanoic acid), α-aminobutanoic acid, norvaline (α-aminopentanoic acid), norleucine (α-aminohexanoic acid), valine (α-amino-3-methylbutanoic acid), leucine (α-amino-4-methylpentanoic acid), and α-phenylalanine. Together with equations that we have previously constructed, these descriptors can be used to estimate further solubilities and partition coefficients in a variety of organic solvents and in water-methanol and water-ethanol mixtures. It is shown that equations for neutral solutes are inadequate for the description of solubilities and partition coefficients for these α-aminoacids, and our equations developed for use with both neutral and ionic solutes must be used. The Absolv descriptors include those for hydrogen-bond acidity, A, and hydrogen-bond basicity, B. We find that both of these descriptors are far smaller in value than those for compounds that contain the corresponding ionic groups. Thus, A for α-alanine is 0.28, but A for the ethylammonium cation is 1.31; B for α-alanine is 0.83, and yet B for the acetate anion is no less than 2.93. The additional descriptors that we developed for equations that involve ions, J ⁺ and J ^-, are very significant for the α-aminoacids, although numerically smaller than for ionic species such as EtNH₃ ⁺ and CH₃CO₂ ^-.

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.

Evaluating Molecular Properties Involved in Transport of Small Molecules in Stratum Corneum: A Quantitative Structure-Activity Relationship for Skin Permeability

The skin permeability (Kp) defines the rate of a chemical penetrating across the stratum corneum. This value is widely used to quantitatively describe the transport of molecules in the outermost layer of epidermal skin and indicate the significance of skin absorption. This study defined a Kp quantitative structure-activity relationship (QSAR) based on 106 chemical substances of Kp measured using human skin and interpreted the molecular interactions underlying transport behavior of small molecules in the stratum corneum. The Kp QSAR developed in this study identified four molecular descriptors that described the molecular cyclicity in the molecule reflecting local geometrical environments, topological distances between pairs of oxygen and chlorine atoms, lipophilicity, and similarity to antineoplastics in molecular properties. This Kp QSAR considered the octanol-water partition coefficient to be a direct influence on transdermal movement of molecules. Moreover, the Kp QSAR identified a sub-domain of molecular properties initially defined to describe the antineoplastic resemblance of a compound as a significant factor in affecting transdermal permeation of solutes. This finding suggests that the influence of molecular size on the chemical’s skin-permeating capability should be interpreted with other relevant physicochemical properties rather than being represented by molecular weight alone.

Partition of Neutral Molecules and Ions from Water to o-Nitrophenyl Octyl Ether and of Neutral Molecules from the Gas Phase to o-Nitrophenyl Octyl Ether

We have set out an equation for partition of 87 neutral molecules from water to o-nitrophenyl octyl ether, NPOE, an equation for partition of the 87 neutral molecules and 21 ionic species from water to NPOE, and an equation for partition of 87 neutral molecules from the gas phase to NPOE. Comparison with equations for partition into other solvents shows that, as regards partition of neutral (nonelectrolyte) compounds, NPOE would be a good model for 1,2-dichloroethane and for nitrobenzene. In terms of partition of ions and ionic species, NPOE is quite similar to 1,2-dichloroethane and not far away from other aprotic solvents such as nitrobenzene.