Predicting skin permeability from complex chemical mixtures: incorporation of an expanded QSAR model

Quantitative structure–activity relationship (QSAR) models have been widely used to study the permeability of chemicals or solutes through skin. Among the various QSAR models, Abraham’s linear free-energy relationship (LFER) model is often employed. However, when the experimental conditions are complex, it is not always appropriate to use Abraham’s LFER model with a single set of regression coefficients. In this paper, we propose an expanded model in which one set of partial slopes is defined for each experimental condition, where conditions are defined according to solvent: water, synthetic oil, semi-synthetic oil, or soluble oil. This model not only accounts for experimental conditions but also improves the ability to conduct rigorous hypothesis testing. To more adequately evaluate the predictive power of the QSAR model, we modified the usual leave-one-out internal validation strategy to employ a leave-one-solute-out strategy and accordingly adjust the Q² _LOO statistic. Skin permeability was shown to have the rank order: water > synthetic > semi-synthetic > soluble oil. In addition, fitted relationships between permeability and solute characteristics differ according to solvents. We demonstrated that the expanded model (r² = 0.70) improved both the model fit and the predictive power when compared with the simple model (r² = 0.21).     

The quality of QSAR models: problems and solutions†

Assessment of the quality of goodness-of-fit and the confidence in predictivity (prediction power) are the main terms used to define the statistical quality of QSAR models. Three parts of this assessment can be defined as:

(1)?Measure of goodness-of-fit.

(2)?Validation of model stability.

(3)?Predictivity analysis.

Currently there are no mandatory requirements for the validation methods to be used and rules for the quantitative confidence estimates. To compare the statistical quality of QSAR models it is necessary to have an overall statistical quality index which will depend on the goodness-of-fit, validation and predictivity results together. To do so it is necessary to define the set of mandatory parameters for all three parts of assessment listed above and develop the approach for overall quality estimates based on these parameters. It is also necessary to include into the overall index the penalty mechanism for parameter absence. The goal of the present study is to analyse parameters for all three parts of the QSAR model statistical quality assessment and investigate the flexible weighting approach for the overall statistical quality index development. Due the different statistical parameters traditionally used for assessment of goodness-of-fit it is necessary to create the mechanism, which allows flexible set of parameters to be used for the overall statistical quality index. Only after approval by scientific community and regulatory boards the final set of mandatory parameters can be selected.     

Structure-Toxicity Relationships for Aminoalkanols: A Comparison with Alkanols and Alkanamines

Abstract

The relative toxicity (logIGC^?1 ₅₀) of 49 selected aliphatic amines and aminoalkanols was evaluated in the static Tetrahymena pyriformis population growth impairment assay. Excess toxicity, indicated by potency greater than predicted for non-polar narcotic alkanols, was associated with both classes of test chemicals. Moreover, the aminoalkanols were found to be more toxic than the corresponding alkanamines. A high quality 1-octanol/water partition coefficient (log K _ow) dependent quantitative structure-activity relationship (QSAR), logIGC^?1 ₅₀ = 0.78 (log K _ow)-1.42; r ² = 0.934, was developed for alkanamines. This QSAR represented the amine narcosis mechanism of toxic action. No quality QSAR was developed for the aminoalkanols. However, several structure-toxicity features were observed for this class of chemicals. Two-amino-1-hydroxy derivatives being more toxic than the corresponding derivatives, where the amino and hydroxy moieties were separated by methylene groups. Hydrocarbon branching next to the amino moiety resulted in decreased toxicity. Aminoalkanol alters lipid metabolism in T. pyriformis.     

Three-dimensional quantitative structure-activity relationships of steroid aromatase inhibitors

Summary Inhibition of aromatase, a cytochrome P450 that converts androgens to estrogens, is relevant in the therapeutic control of breast cancer. We investigate this inhibition using a three-dimensional quantitative structure-activity relationship (3D QSAR) method known as Comparative Molecular Field Analysis, CoMFA [Cramer III, R.D. et al., J. Am. Chem. Soc., 110 (1988) 5959]. We analyzed the data for 50 steroid inhibitors [Numazawa, M. et al., J. Med. Chem., 37 (1994) 2198, and references cited therein] assayed against androstenedione on human placental microsomes. An initial CoMFA resulted in a three-component model for log(1/K_i), with an explained variance r² of 0.885, and a cross-validated q² of 0.673. Chemometric studies were performed using GOLPE [Baroni, M. et al., Quant. Struct.-Act. Relatsh., 12 (1993) 9]. The CoMFA/GOLPE model is discussed in terms of robustness, predictivity, explanatory power and simplicity. After randomized exclusion of 25 or 10 compounds (repeated 25 times), the q² for one component was 0.62 and 0.61, respectively, while r² was 0.674. We demonstrate that the predictive r² based on the mean activity (Y_m) of the training set is misleading, while the test set Y_m-based predictive r² index gives a more accurate estimate of external predictivity. Using CoMFA, the observed differences in aromatase inhibition among C6-substituted steroids are rationalized at the atomic level. The CoMFA fields are consistent with known, potent inhibitors of aromatase, not included in the model. When positioned in the same alignment, these compounds have distinct features that overlap with the steric and electrostatic fields obtained in the CoMFA model. The presence of two hydrophobic binding pockets near the aromatase active site is discussed: a steric bulk tolerant one, common for C4, C6-alpha and C7-alpha substitutents, and a smaller one at the C6-beta region.     

A partial recurrence relation for reduced class coefficients of the symmetric group

An expression for the product of a single-cycle class [(1)^{N - P}(p)]_N and an arbitrary class [(1)^l1(2)^l …? (N)^lN]_N of the symmetric group has recently been conjectured. This expression involves a sum over a relatively small number of reduced class sums, depending on p indices. A further conjecture is formulated and demonstrated, according to which reduced class coefficients (RCCS ) involving cycles whose length is expressed by means of a single index can be related to corresponding coefficients in the product of [(1)^{N - P+1}(p - 1)]_N with an arbitrary class sum. Consequently, the problem of evaluating the general class sum product reduces to that of obtaining a relatively small set of fundamental RCCS containing no single-index cycles. The conjectures mentioned can be used to evaluate the product [(1)^{N - p}(p)]_N · [(1)^{N - q}(q)]_N in terms of fundamental RCCS that can all be obtained from the product [(r)]_r · [(r)]_r, where r = min(p, q). For the latter product, we use a result due to Boccara.     

Some case studies on application of “rm2” metrics for judging quality of quantitative structure–activity relationship predictions: Emphasis on scaling of response data

Quantitative structure–activity relationship (QSAR) techniques have found wide application in the fields of drug design, property modeling, and toxicity prediction of untested chemicals. A rigorous validation of the developed models plays the key role for their successful application in prediction for new compounds. The r_m² metrics introduced by Roy et al. have been extensively used by different research groups for validation of regression‐based QSAR models. This concept has been further advanced here with introduction of scaling of response data prior to computation of r_m². Further, a web application (accessible from http://aptsoftware.co.in/rmsquare/ and http://203.200.173.43:8080/rmsquare/ ) for calculation of the r_m² metrics has been introduced here. The present study reports that the web application can be easily used for computation of r_m² metrics provided observed and QSAR‐predicted data for a set of compounds are available. Further, scaling of response data is recommended prior to r_m² calculation. © 2013 Wiley Periodicals, Inc.     

3-D QSAR for intrinsic activity of 5-HT1A receptor ligands by the method of comparative molecular field analysis

The affinity of a ligand for a receptor is usually expressed in terms of the dissociation constant (K_i) of the drug-receptor complex, conveniently measured by the inhibition of radioligand binding. However, a ligand can be an antagonist, a partial agonist, or a full agonist, a property largely independent of its receptor affinity. This property can be quantitated as intrinsic activity (1A), which can range from 0 for a full antagonist to 1 for a full agonist. Although quantitative structure–activity relationship (QSAR) methods have been applied to the prediction of receptor affinity with considerable success, the prediction of IA, even qualitatively, has rarely been attempted. Because most traditional QSAR methods are limited to congeneric series, and there are often major structural differences between agonists and antagonists, this lack of success in predicting IA is understandable. To overcome this limitation, we used the method of comparative molecular field analysis (CoMFA), which, unlike traditional Hansch analysis, permits the inclusion of structurally dissimilar compounds in a single QSAR model. A structurally diverse set of 5-hydroxytryptamine_1A (5-HT_1A) receptor ligands, with literature IA data (determined by the inhibition of 5-HT sensitive forskolin-stimulated adenylate cyclase), was used to develop a 3-D QSAR model correlating intrinsic activity with molecular structure properties of 5HT_1A receptor ligands. This CoMFA model had a crossvalidated r² of 0.481, five components and final conventional r² of 0.943. The receptor model suggests that agonist and antagonist ligands can share parts of a common binding site on the receptor, with a primary agonist binding region that is also occupied by antagonists and a secondary binding site accommodating the excess bulk present in the sidechains of many antagonists and partial agonists. The CoMFA steric field graph clearly shows that agonists tend to be “flatter” (more coplanar) than antagonists, consistent with the difference between the 5-HT_1A agonist and antagonist pharmacophores proposed by Hibert and coworkers. The CoMFA electrostatic field graph suggests that, in the region surrounding the essential protonated aliphatic amino group, the positive molecular electrostatic potential may be weaker in antagonists as compared to agonists. Together, the steric and electrostatic maps suggest that in the secondary binding site region increased hydrophobic binding may enhance antagonist activity. These results demonstrate that CoMFA is capable of generating a statistically crossvalidated 3-D QSAR model that can successfully distinguish between agonist and antagonist 5-HT_1A ligands. To the best of our knowledge, this is the first time this or any other QSAR method has been successfully applied to the correlation of structure with IA rather than potency or affinity. The analysis has suggested various structural features associated with agonist and antagonist behaviors of 5-HT_1A ligands and thus should assist in the future design of drugs that act via 5-HT_1A receptors. © 1993 John Wiley & Sons, Inc.     

Impact assessment of the rational selection of training and test sets on the predictive ability of QSAR models

This study performed an analysis of the influence of the training and test set rational selection on the quality and predictively of the quantitative structure–activity relationship (QSAR) model. The study was carried out on three different datasets of Influenza Neuraminidase (H1N1) inhibitors. The three datasets were divided into training and test sets using three rational selection methods: based on k-means, Kennard–Stone algorithm and Activity and the results were compared with Random selection. Then, a total of 31,490 mathematical models were developed and those models that presented a determination coefficient higher than: r²_train > 0.8, r²_loo > 0.7, r²_test > 0.5 and minimum standard deviation (SD) and minimum root-mean square error (RMS) were selected. The selected models were validated using the internal leave-one-out method and the predictive capacity was evaluated by the external test set. The results indicate that random selection could lead to erroneous results. In return, a rational selection allows for obtaining more reliable conclusions. The QSAR models with major predictive power were found using the k-means algorithm and selection by activity.     

Grid potential analysis,virtual screening studies and ADME/T profiling on N‐arylsulfonylindoles as anti‐HIV‐1 agents

A grid potential analysis employing a novel approach of 3D quantitative structure–activity relationships (QSAR) as AutoGPA module in MOE2009.10 was performed on a dataset of 42 compounds of N‐arylsulfonylindoles as anti‐HIV‐1 agents. The uniqueness of AutoGPA module is that it automatically builds the 3D‐QSAR model on the pharmacophore‐based molecular alignment. The AutoGPA‐based 3D‐QSAR model obtained in the present study gave the cross‐validated Q² value of 0.588, r²_pred value of 0.701, r²_m statistics of 0.732 and Fisher value of 94.264. The results of 3D‐QSAR analysis indicated that hydrophobic groups at R₁ and R₂ positions and electron releasing groups at R₃ position are favourable for good activity. To find similar analogues, virtual screening on ZINC database was carried out using generated AutoGPA‐based 3D‐QSAR model and showed good prediction. In addition to those mentioned earlier, in‐silico ADME absorption, distribution, metabolism and excretion profiling and toxicity risk assessment test was performed, and results showed that majority of compounds from current dataset and newly virtually screened hits generated were within their standard limit. Copyright © 2013 John Wiley & Sons, Ltd.     

Receptor-based 3D QSAR analysis of estrogen receptor ligands – merging the accuracy of receptor-based alignments with the computational efficiency of ligand-based methods

One of the major challenges in computational approaches to drug design is the accurate prediction of binding affinity of biomolecules. In the present study several prediction methods for a published set of estrogen receptor ligands are investigated and compared. The binding modes of 30 ligands were determined using the docking program AutoDock and were compared with available X-ray structures of estrogen receptor-ligand complexes. On the basis of the docking results an interaction energy-based model, which uses the information of the whole ligand-receptor complex, was generated. Several parameters were modified in order to analyze their influence onto the correlation between binding affinities and calculated ligand-receptor interaction energies. The highest correlation coefficient (r ² = 0.617, q ² _LOO = 0.570) was obtained considering protein flexibility during the interaction energy evaluation. The second prediction method uses a combination of receptor-based and 3D quantitative structure-activity relationships (3D QSAR) methods. The ligand alignment obtained from the docking simulations was taken as basis for a comparative field analysis applying the GRID/GOLPE program. Using the interaction field derived with a water probe and applying the smart region definition (SRD) variable selection, a significant and robust model was obtained (r ² = 0.991, q ² _LOO = 0.921). The predictive ability of the established model was further evaluated by using a test set of six additional compounds. The comparison with the generated interaction energy-based model and with a traditional CoMFA model obtained using a ligand-based alignment (r ² = 0.951, q ² _LOO = 0.796) indicates that the combination of receptor-based and 3D QSAR methods is able to improve the quality of the underlying model.