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Towards better understanding of lipophilicity: Assessment of in silico and chromatographic logP measures for pharmaceutically important compounds by nonparametric rankings
Journal of Pharmaceutical and Biomedical Analysis 115 (2015) 183–191
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Towards better understanding of lipophilicity: Assessment of in silico and chromatographic logP measures for pharmaceutically important compounds by nonparametric rankings Filip Andric´ a , Károly Héberger b,∗ a b
Faculty of Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia Research Centre for Natural Sciences, Hungarian Academy of Sciences, H-1117 Budapest XI., Magyar Tudósok krt 2, Hungary
a r t i c l e
i n f o
Article history: Received 10 April 2015 Received in revised form 6 July 2015 Accepted 7 July 2015 Available online 17 July 2015 Keywords: Lipophilicity Natural toxins Antifungal drugs Thin-layer chromatography Sum of ranking differences Generalized pairwise-correlation method Multivariate data analysis
a b s t r a c t Lipophilicity is one of the most frequently used physicochemical properties that affects compound solubility, determines its passive transport through biological membranes, influences biodistribution, metabolism and pharmacokinetics. We compared, ranked and grouped chromatographic lipophilicity indices and computationally estimated logP–s by sensitive and robust non-parametric approaches: sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM). Chromatographic indices of fourteen neurotoxins and twenty one 1,2,4-triazole compounds have been derived from typical reversed-phase thin-layer chromatography and micellar chromatography. They were compared with in silico estimated logP–s. Under typical reversed-phase conditions, octadecyl-, octyl-, and cyanopropyl-modified silica have clear advantage over ethyl-, aminopropyl, and diol-modified beds, i.e., the preferable choice of the stationary phase follows this order: octadecyl > octyl > cyanopropyl > ethyl > octadecyl wettable > aminopropyl > diol. Many of these indices outperform the majority of computationally estimated logP–s. Clear distinction can be made based on cross-validation and statistical tests. Oppositely, micellar chromatography may not be successfully used for the lipophilicity assessment, since retention parameters obtained from the typical reversed-phase conditions outperform the parameters obtained by micellar chromatography. Both ranking approaches, SRD and GPCM, although based on different background, provide highly similar variable ordering and grouping leading to the same, above mentioned conclusions. However, GPCM results in more degeneracy, i.e., in some cases it cannot distinguish the lipophilicity parameters whereas SRD and its cross-validated version can. On the other hand GPCM produces a more characteristic grouping. Both methods can be successfully used for selection of the most and least appropriate lipophilicity measures. © 2015 Published by Elsevier B.V.
1. Introduction Lipophilicity is one of the major physical–chemical properties used in pharmaceutical and environmental sciences. Its role is of utmost importance in drug discovery [1] and modeling of the fate
Abbrevaitions: C18, octadecyl; C18W, octadecyl wettable; C2, ethyl; C8, octyl; CE-PW, conditional exact Fisher test & probability weighted ranking; CMC, critical micellar concentration; CN, cyanopropyl; CRRN, validation of the SRD procedure: comparison of ranks by random numbers; CV, cross-validation; GPCM, generalized pair correlation method; HCA, hierarchical cluster analysis; HPLC, high performance liquid chromatography; IAM, immobilized artificial membrane chromatography; MLC, micellar liquid chromatography; NH2 , aminopropyl; OPLC, overpressured layer chromatography; PC, principal component; PCA, principal component analysis; RP, reversed-phase; RP-TLC, reversed-phase thin-layer chromatography; SRD, sum of ranking (absolute) differences; TLC, thin-layer chromatography. ∗ Corresponding author. E-mail address: [email protected] (K. Héberger). http://dx.doi.org/10.1016/j.jpba.2015.07.006 0731-7085/© 2015 Published by Elsevier B.V.
of a compound in the environment. It strongly affects compound solubility, and determines passive transport through biological membranes such as gastrointestinal tract or blood to brain barrier [2]. It also influences biodistribution, metabolism and pharmacokinetics [3]. It significantly impacts the protein binding, modeling of drug-receptor interactions, compound-related toxicity or adverse effects [4]. Among other parameters, such as solubility, stability, acid-base character, etc., lipophilicity is determined at the early stages of drug development, and included in identification of starting points, viable chemical leads, and developing candidates [5]. Bioavailability and bioconcentration in the food chain through sorption from water, and soil or sediment, is also affected by lipophilicity [6], which makes it an important factor in risk assessment and management of hazardous materials. The octanol–water partition coefficient (logPO/W, or more often written as logP) is generally accepted as the golden standard for lipophilicity measurement (assessment) [6]. The experimental
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measurement of logP is described in the guidelines of the Organization for Economic Cooperation and Development (OECD): Test No. 107, Shake flask method [7], and Test No. 123, slow stirring method [8]. However, both methods are time and reagent consuming and they are unsuitable for analysis of impure or degraded compounds or compounds of extremely low or high logP values (logP < −3 or logP > 4). Therefore, in the past decade they have been often replaced by more elegant, far simpler, and more versatile chromatographic methods that give similar and coherent results in the close logP range, (the OECD Test No. 117 [9]), which are able to efficiently analyze contaminated compounds and products of their degradation, the latter being of the particular interest in drug analysis. Among all chromatographic techniques, thin-layer chromatography (TLC) takes specific place because of its simplicity, low costs, and reduced consumptions of solvents and reagents (green analytical technique). The most frequently employed TLC modality for lipophilicity assessment of drugs and compounds of pharmaceutical importance is a typical reversed-phase one [10–13]. Non-polar stationary phases such as various hydrocarbon modified silica gels (octadecyl, octyl, ethyl, and phenyl, commonly denoted as: C18, C8, C2 and Ph, respectively), [14] or amphiphilic sorbents such as cyanopropyl-, aminopropyl- or diol-modified silica [14,15] in combination with polar mobile phase (binary mixtures of water and miscible organic solvents) are used. Different stationary phases that imitate biosystems, such as immobilized artificial membranes (IAMs) [16,17], immobilized proteins [18], and cholesterol [19], or other techniques like micellar liquid chromatography (MLC), have also been proposed for studying the lipophilicity of different compounds [20–24]. Micellar chromatography, as a variety of reversed-phase modality, is of particular interest. Addition of surfactants to the mobile phase in the concentration above the critical micelle concentration (CMC) leads to the constellation of specific molecular interactions that form an intricate retention mechanism: solute association with the polar head of the surfactant, solute penetration into the micelle core, adsorption of surfactant monomers on the alkyl-bounded stationary phases, and solute interactions with adsorbed surfactant and alkyl chains [25]. Regardless to the modality used, all lipophilicity indices are derived either directly from retention data or extrapolated from linear or bilinear relationships between retention parameters and mobile phase composition. Most frequently applied lipophilicity indices derived from TLC experiments are: mean RM , RM 0 (RM values extrapolated to the zero content of organic modifier), b (slope in the linear dependence of RM against the volume fraction of organic modifier), C0 (volume fraction of organic modifier in a mobile phase that provides equal distribution of analyte between mobile and stationary phase; RM = 0), and PC1/RM (score values of the first principal component defined as the linear combination of RM values) [26]. In the case of micellar chromatography the retention factor extrapolated to the zero micellar concentration of surfactant, i.e., the CMC in the mobile phase, logkm , is used [20,25]. All chromatographically derived lipophilicity measures used in the scope of this work are summarized in the Table S1 (Supplementary material), accompanied with simple explanations. Alongside the chromatographic methods, computational approaches for lipophilicity estimation have been extensively utilized. In silico predicted logP–s, either based on fragmentation approaches, or property-based are often compared with chromatographic lipophilicity indices [27,28]. However many of them exhibit significant differences in predicted logP values [29,30], which might question the reliability of these methods.
The computationally estimated logP scales used in the scope of the present work are summarized in the Table S2 (Supplementary material), alongside with the short description provided. Considering the importance of properly selected lipophilicity measure, the primary goal of this study was to compare, rank and group lipophilicity measures using sensitive non-parametric approaches. Therefore, comparison of TLC derived lipophilicity indices were in the main focus of this research. Such indices were obtained under typical reversed-phase conditions and under micellar chromatography, using stationary phases of different polarities. Further comparison of in silico estimation approaches, and chromatographic indices based on direct retention measures vs. the extrapolated ones was the subject of particular importance, as well. Many lipophilicity measures are derived from chromatographic experiments. For some compounds the chromatographic approaches are the only solutions for experimental lipophilicity determination (e.g., charged, polar molecules resolved under hydrophilic interaction liquid chromatography). To present no systematic, sensitive, and reliable approach for comparison and selection of the most suitable lipophilicity scales is enforced or widely accepted. The lack of systematic solution is especially harmful when it comes to testing of novel or emerging methods for lipophilicity estimation, such as micellar chromatography. Present work is a natural continuation of our previous research regarding the use of the sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM) for selection of the best lipophilicity measures [31].
2. Materials and methods (calculations) 2.1. Lipophilicity data Lipophilicity data have been taken from the literature [32,33] and are presented in Sections 3.1 and 3.2. We have selected cases providing they cover typical reversed-phase chromatography that combines stationary phases of different polarity [32]. Also, micellar chromatographic indices are studied alongside with typical RP-TLC derived descriptors. [33]. We paid attention to secure significant diversity of studied compounds and target their pharmacological importance (natural toxins and 1,2,4-triazoles as potent fungicides). A special care was taken in order to ensure the wide range of chromatographically derived lipophilicity indices and logP computational approaches.
2.2. Data pretreatment and multivariate exploratory statistical analysis In order to compare different lipophilicity measures all variables were rescaled. Three data transformation approaches have been tested: (a) standardization to unit standard deviation (also called autoscaling), (b) interval scaling between the lowest and the highest computationally estimated logP value and (c) rank transformation. Standardized data were further used for the exploratory data analysis employing HCA and PCA, while the sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM) have been performed on all three sets of transformed data separately. In the case of HCA the Euclidian distance was selected as measure of dissimilarity among the variables while the Ward’s method was used to define the distances among clusters. PCA has been performed using PCA and multivariate/Batch SPC module as a part of Statistica v.10 (Statsoft Inc., Tulsa, Oklahoma, USA). The number of principal components has been determined using visual evaluation of screen plot.
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2.3. Sum of ranking differences (SRD) and comparison with random numbers (CRRN) The method with all theoretical details has been already described elsewhere [34–36], however some simplified description will be provided here. The data are arranged in a form of a matrix. In our case compounds are organized in rows, and lipophilicity scales in columns. Then for each variable (lipophilicity scale), every object (compound) is ranked, and ranks are subtracted from the ranked benchmark variable. All (absolute) rank differences are then summed and the SRD values are scaled to the interval 0–100. Variables are then sorted in ascending order of the SRD values. The closer the SRD value is to zero, the better might be considered that particular variable, i.e., the closer to the benchmark. Usage of a benchmark or a reference ranking makes this method supervised. Depending on the specific features of a task the benchmark variable can be maximum, minimum, average, or a priori known ranking. In the present work, we have decided to use the arithmetic means of rows as benchmarks for two reasons. First of all, according to the maximum likelihood principle, the most probable ranking should be achieved in case of using the arithmetic mean. Second of all, it is expected that random and systematic errors of each lipophilicity estimation method cancel each other to some degree, by averaging. The SRD values were further compared with simulated random numbers or theoretical distribution of the random SRD values as described in Ref. [35], so called comparison of ranks by random numbers (CRRN). Those SRD-s that fall away from each side of the theoretical or fitted Gaussian curve at the probability level p = 0.05, are considered to be statistically significant. The variables that overlap with the random distribution curve may be considered to be ranked by chance (not statistically significant). In addition, in order to validate grouping and ranking of variables, the portion of uncertainty was assigned to each SRD value using sevenfold cross-validation approach. Approximately 1/7 of objects are removed and the ranking is performed on the remaining data set. Procedure is repeated seven times producing seven SRD values for each lipophilicity measure. Since the number of compounds was smaller only for 1/7 portion, the variance in obtained SRD values is slightly overestimated. Statistical difference among each pair of variables is then tested by applying Wilcoxon’s matched pair test, as well as sign test. Graphical presentation of uncertainties and distribution of variables is done by plotting the box and whisker plot according to the following criteria: (1) increasing median values, if the median values are the same, then (2) the quartiles and interquartile range is taken into account. In that sense the first and third quartiles have the same “power”: if the two first quartiles are the same then, the smaller 3rd quartile should be the first. If the two 3rd quartiles are the same then, the smaller 1st quartile should be the first. If they are contradictory, then and only then the larger interquartile range counts. If they are equal, then (3) the maximum and minimum values are checked. If the two minimums are the same, then, the smaller maximum should be the first. If the two maximums are the same then, the smaller maximum should be the first. If they are contradictory, then and only then the larger range between minimum and maximum counts. If they are all equal, no decision can be made. Box and whisker plots provide additional insight into grouping of variables and their statistical significance. 2.4. Generalized pairwise correlation method (GPCM) The data are arranged in the same matrix as for SRD. Also, a benchmark variable is required. However, the GPCM approach resides on completely different philosophy from SRD. Basically, the method compares two variables at a time with the reference and decides, which one is superior, inferior, or no decision can be
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made. Few statistical tests are usually used to determine statistical significance of decision: Conditional exact Fisher test (CE), McNemar test, Chi-square test and Williams’ t-test, but in this work only conditional exact Fisher test has been employed. In addition, all variables are ranked according to the number of wins, number of wins minus losses, or probability weighted wins minus losses (PW), i.e. p(wins)–p(losses). In this particular case the probability weighted ranking was used and the values have been further reversely scaled and rescaled in order to be comparable with the SRD values. For the benchmark arithmetic means of all rows were chosen. Details of the GPCM procedure may be found elsewhere [37,38]. 3. Results and discussion 3.1. Assessment of lipophilicity measures obtained by typical reversed phase TLC experiments and in silico approaches Nascu-Briciu and Sarbu provided a well comprised data set (Supplementary material of the Ref. [32]). Data included assessments of lipophilicity indices by RP-TLC using seven stationary phases of different polarity, namely C2-, C8-, C18-, C18W- (octadecyl wettable), cyanopropyl-, aminopropyl-, and diol-modified silica plates, and 16 computational logP methods for 14 neurotoxins. They used three simple chromatographic descriptors: RM 0 (an extrapolated one), and those derived on direct chromatographic measurements: mRM, and PC1/RM . Majority of computational logP estimation approaches were based on fragmentation methods: logD, Hy, MlogP, logPc, logP, logPC , logPV , ClogP, AlogPs, AClogP, ABlogP, miLogP, KOWWIN, XlogP2 and XlogP3. The data matrix provided by the authors was consisting of 14 objects and ×37 lipophilicity measures. Because of the presence of missing data logPC and logPV have been excluded from further analysis. The final data matrix used for data analysis consisted of 14 objects (compounds) and 35 variables (lipophilicity measures) (see Supplementary material, Tables S3a and b). 3.1.1. Exploratory multivariate data analysis and clustering The authors performed PCA only on the set of computationally estimated lipophilicity scales to get an insight into the data structure, to reveal the presence of outliers, and possible groupings of objects. In order to compare both in silico and chromatographic measures, we have performed multivariate explanatory analysis on the overall data (computationally assessed plus chromatographic lipophilicity indices). PCA resulted in two principal components describing 85.0 % of the overall data variability (PC1 71.9 %, and PC2 13.1 %). All studied compounds have been grouped into two clusters; the first one consisted of compounds 1–8, 13 and 14, and the second one accounting compounds 9–12 (Fig. 1A). Two major groups of variables are separated along the PC2 direction, accompanied with one outlier variable (logPC ) (loading plot of PC1 vs. PC2, Fig. 1B). The first group, located in the upper part of the graph, is consisted mainly of descriptors derived directly from retention data, i.e., PC1/RM and mRM , obtained under various chromatographic conditions, together with hydrophobicity (Hy) and logP (parameter estimated by Alchemy 2000 software package). The second group gathers mainly extrapolated chromatographic descriptors, RM 0 , obtained on different stationary phases, as well as most of the computationally assessed logP values. Clustering obtained by HCA (Fig. 2) provides similar variable groupings. There are two clusters (A and B) at the linkage distance of around ten units and above. Most of computationally estimated logP measures and chromatographically extrapolated lipophilicity indices can be found in the cluster B followed by outliers: logPC and RM 0 (C2). The cluster A is mainly consisted of chromatographic
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Fig. 1. PCA score plot (PC1 vs. PC2) showing characteristic grouping (A) and loading plot (B) of RP-TLC lipophilicity indices and computationally estimated logP values. For original numeration of compounds see Ref. [32].
Fig. 2. Hierarchical cluster analysis: a dendrogram showing grouping pattern (similarities) of different RP-TLC chromatographic lipophilicity indices in combination with computationally estimated logP scales. Cluster A is mainly consisted of lipophilicity indices derived from direct retention parameters. Computationally estimated and chromatographic indices based on extrapolated measures are gathered in the cluster B.
descriptors (PC1/RM and mRM ). Direct retention derived parameter such as PC1/RM is equally efficient or even superior lipophilicity estimates than RM 0 which is affected by extrapolation [39,40]. This can, to a certain degree, explain division of lipophilicity parameters on these two groups. The major data variation, 71.9 %, is due to inherent, crude ability of the variables to grasp the lipophilic character of the studied compounds, but only 13.1 % of variance accounts for slight, refined differences in this ability. However, if the similarity with computationally estimated logP scales is chosen as a rule to find the best lipophilicity measure, than the opposite conclusion might stand: the best lipophilicity measures should be the extrapolated RM 0 values on various stationary phases. This is exactly the same conclusion that the authors of the original paper reached comparing chromatographic lipophilicity measures with computationally assessed ones. They observed that the highest correlation between the chromatographically determined indices and the computed logP–s is achieved for RM 0 , obtained on C18-, C18W, C8- and cyanopropyl-silica, which is closely followed by PC1/RM and mRM . 3.1.2. Comparison of lipophilicity scales by SRD and GPCM Inspection of PCA and HCA plots leads to several conclusions about similarities and possible grouping among lipophilicity
scales, but it is difficult to choose, which one represents the best lipophilicity measure. On that point the two approaches are limited, especially HCA. Both methods provide no reference for comparison. Even if the reference is available; both approaches do not give any information about statistical significance of such comparison, at least not straightforwardly. Also, logP data are not always normally distributed. Therefore non-parametric, sensitive and robust methods such as SRD and GPCM are used for comparison, grouping and ranking of variables according to the best chosen reference measure (in this particular case, the average). SRD provided information regarding statistical significance of ranking. According to the SRD–CRRN ranking, in the case of standardized data, the lowest scores (the closest to the benchmark values, and in that sense the best lipophilicity estimations) are obtained for mRM and PC1/RM on C18-modified silica, followed closely by the same descriptors on C8-modified silica (Fig. 3). In addition, majority of chromatographically derived indices have lower SRD values, lying approximately in the range 8–20 % of scaled units, compared with most of the computationally estimated measures (SRD values in the range 25–40 % of scaled units). Only two variables (RM 0 (C2) and logPC ) are overlapped with the population of random numbers (p = 0.05). Therefore they can be considered as non-significant, i.e., the worst lipophilicity estimates. The ranking of lipophilicity
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Fig. 3. Comparison of chromatographically derived and computationally assessed lipophilicity measures (autoscaled data) using sum of ranking differences; x axis and left y axis represent SRD values scaled between 0 and 100; right y axis display relative frequencies of the theoretical distribution for ranking random numbers.
scales is slightly altered depending on the data pretreatment (Table S5, Supplementary material); however, similarities in ranking are obvious. Obviously, mRM and PC1/RM have advantage over RM 0 (Fig. 3), which is in agreement with the claims [39,40], but not with the findings of original work [32]. Lipophilicity measures obtained on C18-, C8-, cyanopropyl-, and C2-modified silica layers outperform the same ones using diol- and especially aminopropyl-modified sorbents. It is evident that characteristics of the stationary phase exhibit strong influence on separation process, which has indirect impact on measuring lipophilic character of particular compounds and will be discussed later. Additional validation of the SRD ranking was done by a sevenfold cross-validation procedure (Fig. 4). All lipophilicity measures are arranged in increasing trend of medians of SRD values. Grouping of similar variables is done by applying Wilcoxon’s matched pair test and sign test. Variables that are statistically significantly different from the rest (p = 0.05) are separated with dashed lines. Here, PC1/RM (C18) and mRM (C18) are clearly superior, while RM 0 (C2) and logPC are apparently the worst. The trend of increased interquartile ranges (variability) among computationally estimated logP–s compared to chromatographic measures is apparent, and suggests that these lipophilicity measures are not as reliable as the rest of the lipophilicity indices. GPCM method provides similar lipophilicity scale ordering (Fig. 5), with some differences in variable degeneration. ”Degeneration” means the methodology cannot distinguish variables. However, all the milestones variables are the same, such as the best (PC1/RM (C18), mRM (C18), mRM (C8), PC1/RM (C8)), and the worst lipophilicity measures (RM 0 (C2), logPC ). A more characteristic grouping can be observed than in Fig. 4. A gap can be seen between PC1/RM (CN) or mRM (C2) and miLogP. This separates chromatographic indices obtained on C18-, C8-, cyanopropyl-, and C2-modified sorbents in the left part of the graph, from those derived from amino-propyl and diol modified-beds. The first group is closer to the benchmark and includes mostly chromatographic indices and minority of in silico estimates (14 % of the total number), while the second one is positioned farther from the reference and includes majority (86 % of the total number) of computationally estimated logP–s. Therefore, chromatographic indices obtained on aminopropyl- and diol-modified sorbents do not estimate lipophilicity better than computational approaches. The stationary phases that provide chromatographic most suitable for lipophilicity estimation conditions could be then roughly arranged in the following order: C18 > C8 > cyanopropyl > C2 > C18W > aminopropyl > diol. Apart from the lipophilic interactions that are more dominant in the group of C18-, C8-, cyanopropyl-, and C2-modified silica gels,
diol- and especially aminopropyl-modified layers provide significant amount of specific interactions, mostly through the hydrogen bonding, that alter retention behavior of the studied compounds. Significant involvement of specific interactions makes these two sorbents less suitable for lipophilicity measurements. In addition, according to both SRD and GPCM ranking, C18W sorbents are overlapped mostly with computationally estimated lipophilicity scales, and are closer to the diol- and aminopropyl-modified ones than to the first group (C18, C8, cyanopropyl, and C2). This can be explained by lower degree of surface modification of silica particles by hydrophobic hydrocarbon chains, and the uncovered silanol active centers that lead to more complex retention behavior. More or less the same conclusion was provided by the authors themselves [32]. If the mRM (C18) and PC1/RM (C18) are selected as the best lipophilicity measures based on both SRD and GPCM, then the choice of the most lipophilic compound is quite straightforward, i.e., compound No. 12 ((DHQ) 2 AQN, a quinine derivative). However, the authors themselves cannot reach decision easily, since the data do not offer the apparent choice. C18, C18W, and C8 are suggesting compound 11, while C2, cyanopropyl, and aminopropyl suggest compound 12, and finally retention profile on diol-modified plates indicates compound 8 as the most lipophilic one. After additional analysis they still could not clearly differentiate between compounds 12 and 11, since the differences in ordering strongly depend on the selected lipophilicity index. According to SRD and GPCM, the compound 13 (etoposide, a mycotoxine) presents the lowest lipophilicity. Both findings are in agreement with final conclusions of the authors. Compared with the methodology of Nascu-Briciu and Sarbu [32], which is based on Pearson’s correlations between computationally and chromatographically estimated lipophilicity measures (correlation matrices), lipophilicity charts and graphical profiles of principal component loadings, SRD and GPCM are simple and straightforward in ranking and selection of significant variables.
3.2. Assessment of lipophilicity measures obtained by micellar chromatography and typical reversed phase TLC experiments combined with in silico approaches Janicka et al. investigated retention behavior of 21 newly synthesized 1,2,4-triazole compounds with antifungal properties and potential importance in medicine and agriculture, under typical reversed-phase and micellar chromatographic conditions [33]. They used thin-layer chromatography, overpressured-layer chromatography (OPLC), as well as high performance liquid chromatography to separate compounds and derive chromatographic lipophilicity indices.
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Fig. 4. Ranking of chromatographic lipophilicity indices obtained under typical reversed-phase conditions and computationally estimated logP measures by means of the sevenfold cross-validation SRD procedure—box and whisker plot, y-axis represent SRD values; Dashed lines separate variables statistically significantly different from the rest of them (p = 0.05).
Fig. 5. GPCM comparison of chromatographically derived and computationally assessed lipophilicity measures (autoscaled data); x and y axis represent probability weighted wins minus losses p (wins)–p(losses), reversely scaled in order to be comparable with SRD values.
The authors compared micellar chromatographic parameters, logkm , obtained by all three chromatographic techniques, with RM 0 values determined by means of reversed-phase TLC using acetonitrile (RM 0 (1)) and tetrahydrofuran (RM 0 (2)) as a mobile phase constituents. The authors also selected seven computational methods for logP assessment (AlogPs, AlogP, AClogP, MlogP, XlogP2, XlogP3, and KOWWIN). The selection of the best lipophilicity measure was done by analyzing the correlations between in silico estimated logP–s and chromatographically proposed lipophilicity indices. The data have been obtained from the Tables 1 and 3 of the Ref. [33], and are provided as a part of the Supplementary material of the present work (Table S4). 3.2.1. Exploratory multivariate data analysis and clustering Similarities and groupings, as well as potential outlying effect among lipophilicity measures were revealed by PCA and HCA. Principal component analysis performed on the overall lipophilicity data, resulted in two principal components taking into account 77.7 % (PC1) and 19.0 % (PC2) of the overall data variability. According to the score plot all studied compounds could be sorted out into two major groups (I—1, 2, 4–7, 10–13, 18; II—3, 8, 9, 14–17, 19–21) (Fig 6A). Loading plot of PC1 vs. PC2 reveals the presence of a single group of variables (RM 0 (1), RM 0 (2), logkm (TLC), mixed with AClogP, AlogP, KOWWIN, AlogPs, XlogP2, and XlogP3) and
three outliers MlogP, logkm (OPLC) and logkm (HPLC) (Fig. 6B). The loadings of logkm (OPLC) and logkm (HPLC) on the PC1 direction are significantly lower (around 0.45 and 0.15) compared to the rest of the variables ranging between 0.8 and 1.0. Since thePC1 direction might be considered as the latent variable directly proportional to the lipophilicity measure, low loading values might imply that the last two indices might not represent suitable lipophilicity estimates. Similar grouping of variables was obtained by HCA (Fig. 7). All lipophilicity scales are grouped into two clusters at the linkage distance of four units and above. The first one consisting of: KOWWIN, RM 0 (1), RM 0 (2), AlogPs, XlogP3, AlogP, AClogP, XlogP2, and logkw (TLC) (Fig. 7), and the second one is comprised of logkm (OPLC), logkm (HPLC) and MlogP as an outlier. 3.2.2. Comparison of lipophilicity scales by SRD and GPCM Although some grouping of lipophilicity indices might be derived from PCA and HCA, selection of the best lipophilicity measure might be a difficult task. If the PC1 is considered as a direction of the major variability of lipophilicity data, i.e., lipophilicity measures (77.74 %), then variables with high loading values might be considered as the most suitable. A more refined way is at our disposal: SRD approach has chosen AClogP as the best lipophilicity measure for standardized data, i.e., the closest to the zero SRD, and furthest from the random number distribution. It is closely
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Fig. 6. PCA score plot of PC1 vs. PC2 (A) depicting separation of two main groups, and loading plot (B) revealing similarities among typical reversed-phase micellar chromatographic retention data and computationally estimated logP measures.
Fig. 7. Hierarchical cluster analysis: a dendrogram showing grouping pattern of reversed-phase and micellar chromatographic retention data in combination with computationally estimated logP values.
Fig. 8. SRD ranking of chromatographic lipophilicity measures obtained by means of micellar and typical reversed-phase chromatography modalities in combination with computationally estimated logP scales; x axis and left y axis represent SRD values scaled between 0 and 100; right y axis display relative frequencies of the theoretical distribution for ranking random numbers.
followed in order: RM 0 (2), XlogP2, KOWWIN, logkm (TLC), RM 0 (1), AlogPs, and AlogP (Fig. 8). The worst, farthest from the zero SRD value, and not significantly different from the random number distribution are logkm (OPLC) and logkm (HPLC). All three thin-layer chromatographic descriptors are superior lipophilicity measures compared to the OPLC or HPLC techniques. There is some similarity with the ordering of the PC1 loadings. The SRD scaled values differ slightly depending on the data pretreatment, but the main milestones such as the best and the worst variables are preserved (Table S6, Supplementary material).
In addition, SRD ranking combined with sevenfold crossvalidation confirmed the same order of lipophilicity measures (Fig. 9). The medians of SRD values of logkm (OPLC) and logkm (HPLC) are statistically significantly different from the rest of lipophilicity parameters (Wilcoxon’s match paired test and sign test, p = 0.05), and exhibit significantly higher variability (interquartile ranges) imposed by the cross-validation procedure, which implies that these two lipophilicity measures are not as reliable as the rest of the lipophilicity indices. GPCM comparison gave astonishingly the same rankings as SRD and SRD sevenfold cross-validation (Fig. 10), which is quite surpris-
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Fig. 9. Ranking of chromatographic lipophilicity scales obtained under typical reversed-phase and micellar chromatographic conditions in combination with computationally estimated logP values by means of the sevenfold cross-validation procedure (SRD)—box and whisker plot y-axis represent SRD values; Dashed lines separate variables statistically significantly different from the rest of them (p = 0.05).
Fig. 10. GPCM ranking of chromatographically estimated lipophilicity scales from micellar and typical reversed-phase conditions in combination with computationally calculated logP values; x and y axis represent probability weighted wins minus losses, p(wins)–p(losses), reversely scaled in order to be comparable with SRD values.
ing, since these two approaches derived from completely different philosophy and computations. This is an additional confirmation of the SRD–CRRN and SRD–CV findings. However, Janicka et al. [33] concluded, after detailed evaluation of micellar logk parameters, which was based on linear regression with computationally estimated logP–s and RM 0 values, that “The best linearity was observed between micellar parameters and XlogP2, XlogP3 and logP average values, as for HPLC, OPLC and TLC techniques. Analogous relationships corresponding to RM 0 values characterized by much lower coefficients of determination, demonstrate that extrapolated RM 0 parameters rather poorly correlate with partitioning lipophilicity descriptors”. They further suggest that “micellar chromatography is an excellent technique for studying lipophilicity of triazoles”. This is a good example that using simple univariate linear correlation/regression models might lead to erroneous conclusion(s). PC loading plot clearly demonstrates that OPLC and HPLC micellar data are outliers from the rest of the lipophilicity parameters; therefore, they cannot “outperform” lipophilicity measures obtained from the typical reversed-phase systems (RM 0 (1), and RM 0 (2)) as well as computationally assessed logP values. However, this is not the case with the thin-layer chromatographic data. The same conclusion was obtained by two distinct approaches: SRD and GPCM. Therefore, in this particular case, multivariate methods and rankings (by SRD and GPCM) suggest that micellar chromatography is not the optimal way to determine lipophilicity of the particular set of triazole derivatives. This can be partially explained by the intricate retention mechanism of the micellar chromatography involving solute association
with the polar part of the surfactant, solute penetration into the micelle, adsorption of surfactant monomers on the alkyl-bounded stationary phases, and solute interactions with adsorbed surfactant and alkyl chains. Such mechanism can be altered to a certain degree by adding higher amounts of organic modifier and produce lower logkm values [33]. If the AClogP is chosen as the best lipophilicity estimator, then the most lipophilic candidate would be compound No. 10, i.e. p-bromo-phenyl derivate of structure A [33]. Fortunately the same conclusion would be reached for any of the studied variables. The least lipophilic compound is No. 11, i.e., n-propyl derivative of structure B [33]. This is valid for all variables except for MlogP, which assigns n-propyl derivative to the group of structure A as the least lipophilic one.
4. Conclusions Both non-parametric procedures, sum of ranking differences and generalized pairwise correlation method, gave very similar results. In the case of the typical reversed-phase thinlayer chromatography applied on different stationary phases, lipophilicity indices based on direct retention measures, mRM and PC1/RM , have advantage over extrapolated ones, RM 0 . Also, octadecyl-, octyl-, and cyanopropyl-modified silica have advantage over ethyl-, diol- and especially aminopropyl-modified silica, i.e., the preferable choice of the stationary phases follows this order: octadecyl > octyl > cyanopropyl > ethyl > octadecylwettable > aminopropyl > diol. Many chromatographic lipophilicity
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measures outperform computational methods, but no clear distinction based on cross-validation and Wilcoxon’s test or sign test (p = 0.05) can be made. The most and least lipophilic compounds are Nos. 12 and 13, respectively, which is in accordance with original findings by Nascu-Briciu and Sarbu [32]. Micellar chromatography may not be apparent choice for lipophilicity assessment, since both retention par ameters obtained from the typical reversed-phase conditions outperforms the parameters obtained by micellar chromatography, but neither one is better than the computationally estimated logP scales. Comparing generalized pairwise correlation method with sum of ranking differences, the first one result in more degeneracy, i.e., in some cases it cannot distinguish the lipophilicity parameters, whereas sum of ranking differences and its cross-validated version can. On the other hand it provides more characteristic groupings. The proposed approaches can be successfully used for selection of the most appropriate lipophilicity measures as well as the ranking and selection of the most and the least lipophilic (promising) candidates. Acknowledgments This work has been supported by the Ministry of Education, Science and Technological development, of the Republic of Serbia, grant No. 172017. KH is indebted to the support from OTKA (Hungary), contract No. K112547. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jpba.2015.07.006 References [1] M.J. Waring, Lipophilicity in drug discovery, Expert Opin. Drug Discov. 5 (2010) 235–248. [2] M.J. Waring, Defining optimum lipophilicity and molecular weight ranges for drug candidates—molecular weight dependent lower logD limits based on permeability, Bioorg. Med. Chem. Lett. 19 (2009) 2844–2851. [3] M.P. Gleeson, Generation of a set of simple, interpretable AMDET rules of thumb, J. Med. Chem. 51 (2008) 817–834. [4] D.A. Price, J. Blagg, L. Jones, N. Greene, T. Wager, Physicochemical drug properties associated with in vivo toxicological outcomes: a review, Expert Opin. Drug Metab. Toxicol. 5 (2009) 921–931. ˝ G.M. Makara, The influence of lead discovery strategies on the [5] G.M. Keseru, properties of drug candidates, Nat. Rev. Drug Discov. 8 (2009) 203–212. [6] S.K. Poole, C.F. Poole, Separation methods for estimating octanol–water partition coefficients, J. Chromatogr. B 797 (2003) 3–19. [7] OECD Guideline for the testing of chemicals, Test No. 107, Partition coefficient (n-octanol/water), Shake flask method (1995) OECD, Paris,
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Zachariasz, A comparison of theoretical methods of calculation of partition coefficients for selected drugs, Acta Pol. Pharm. 63 (2006) 159–167. [30] R. Estrada-Tejedor, N. Sabate, F. Broto, S. Nonell, I.Q. De Sarria, U.R. Llull, V. Augusta, Octano–water partition coefficients of highly hydrophobic photodynamic therapy drugs: a computational study, Afinidad LXX 564 (2013) 250–256. [31] F. Andric, K. Heberger, Chromatographic and computational assessment of lipophilicity using sum of ranking differences and generalized pair-correlation, J. Chromatogr. A 1380 (2015) 130–138. [32] R.D. Nascu-Briciu, C. Sarbu, A comparative study concerning the chromatographic behaviour and lipophilicity of certain natural toxins, J. Sep. Sci. 35 (2012) 1059–1067. [33] M. Janicka, K. Stepnik, A. Pachuta-Stec, Quantification of lipophilicity of 1,2,4-triazoles using micellar chromatography, Chromatographia 75 (2012) 449–456. [34] K. 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Journal of Pharmaceutical and Biomedical Analysis journal homepage: www.elsevier.com/locate/jpba
Towards better understanding of lipophilicity: Assessment of in silico and chromatographic logP measures for pharmaceutically important compounds by nonparametric rankings Filip Andric´ a , Károly Héberger b,∗ a b
Faculty of Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia Research Centre for Natural Sciences, Hungarian Academy of Sciences, H-1117 Budapest XI., Magyar Tudósok krt 2, Hungary
a r t i c l e
i n f o
Article history: Received 10 April 2015 Received in revised form 6 July 2015 Accepted 7 July 2015 Available online 17 July 2015 Keywords: Lipophilicity Natural toxins Antifungal drugs Thin-layer chromatography Sum of ranking differences Generalized pairwise-correlation method Multivariate data analysis
a b s t r a c t Lipophilicity is one of the most frequently used physicochemical properties that affects compound solubility, determines its passive transport through biological membranes, influences biodistribution, metabolism and pharmacokinetics. We compared, ranked and grouped chromatographic lipophilicity indices and computationally estimated logP–s by sensitive and robust non-parametric approaches: sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM). Chromatographic indices of fourteen neurotoxins and twenty one 1,2,4-triazole compounds have been derived from typical reversed-phase thin-layer chromatography and micellar chromatography. They were compared with in silico estimated logP–s. Under typical reversed-phase conditions, octadecyl-, octyl-, and cyanopropyl-modified silica have clear advantage over ethyl-, aminopropyl, and diol-modified beds, i.e., the preferable choice of the stationary phase follows this order: octadecyl > octyl > cyanopropyl > ethyl > octadecyl wettable > aminopropyl > diol. Many of these indices outperform the majority of computationally estimated logP–s. Clear distinction can be made based on cross-validation and statistical tests. Oppositely, micellar chromatography may not be successfully used for the lipophilicity assessment, since retention parameters obtained from the typical reversed-phase conditions outperform the parameters obtained by micellar chromatography. Both ranking approaches, SRD and GPCM, although based on different background, provide highly similar variable ordering and grouping leading to the same, above mentioned conclusions. However, GPCM results in more degeneracy, i.e., in some cases it cannot distinguish the lipophilicity parameters whereas SRD and its cross-validated version can. On the other hand GPCM produces a more characteristic grouping. Both methods can be successfully used for selection of the most and least appropriate lipophilicity measures. © 2015 Published by Elsevier B.V.
1. Introduction Lipophilicity is one of the major physical–chemical properties used in pharmaceutical and environmental sciences. Its role is of utmost importance in drug discovery [1] and modeling of the fate
Abbrevaitions: C18, octadecyl; C18W, octadecyl wettable; C2, ethyl; C8, octyl; CE-PW, conditional exact Fisher test & probability weighted ranking; CMC, critical micellar concentration; CN, cyanopropyl; CRRN, validation of the SRD procedure: comparison of ranks by random numbers; CV, cross-validation; GPCM, generalized pair correlation method; HCA, hierarchical cluster analysis; HPLC, high performance liquid chromatography; IAM, immobilized artificial membrane chromatography; MLC, micellar liquid chromatography; NH2 , aminopropyl; OPLC, overpressured layer chromatography; PC, principal component; PCA, principal component analysis; RP, reversed-phase; RP-TLC, reversed-phase thin-layer chromatography; SRD, sum of ranking (absolute) differences; TLC, thin-layer chromatography. ∗ Corresponding author. E-mail address: [email protected] (K. Héberger). http://dx.doi.org/10.1016/j.jpba.2015.07.006 0731-7085/© 2015 Published by Elsevier B.V.
of a compound in the environment. It strongly affects compound solubility, and determines passive transport through biological membranes such as gastrointestinal tract or blood to brain barrier [2]. It also influences biodistribution, metabolism and pharmacokinetics [3]. It significantly impacts the protein binding, modeling of drug-receptor interactions, compound-related toxicity or adverse effects [4]. Among other parameters, such as solubility, stability, acid-base character, etc., lipophilicity is determined at the early stages of drug development, and included in identification of starting points, viable chemical leads, and developing candidates [5]. Bioavailability and bioconcentration in the food chain through sorption from water, and soil or sediment, is also affected by lipophilicity [6], which makes it an important factor in risk assessment and management of hazardous materials. The octanol–water partition coefficient (logPO/W, or more often written as logP) is generally accepted as the golden standard for lipophilicity measurement (assessment) [6]. The experimental
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measurement of logP is described in the guidelines of the Organization for Economic Cooperation and Development (OECD): Test No. 107, Shake flask method [7], and Test No. 123, slow stirring method [8]. However, both methods are time and reagent consuming and they are unsuitable for analysis of impure or degraded compounds or compounds of extremely low or high logP values (logP < −3 or logP > 4). Therefore, in the past decade they have been often replaced by more elegant, far simpler, and more versatile chromatographic methods that give similar and coherent results in the close logP range, (the OECD Test No. 117 [9]), which are able to efficiently analyze contaminated compounds and products of their degradation, the latter being of the particular interest in drug analysis. Among all chromatographic techniques, thin-layer chromatography (TLC) takes specific place because of its simplicity, low costs, and reduced consumptions of solvents and reagents (green analytical technique). The most frequently employed TLC modality for lipophilicity assessment of drugs and compounds of pharmaceutical importance is a typical reversed-phase one [10–13]. Non-polar stationary phases such as various hydrocarbon modified silica gels (octadecyl, octyl, ethyl, and phenyl, commonly denoted as: C18, C8, C2 and Ph, respectively), [14] or amphiphilic sorbents such as cyanopropyl-, aminopropyl- or diol-modified silica [14,15] in combination with polar mobile phase (binary mixtures of water and miscible organic solvents) are used. Different stationary phases that imitate biosystems, such as immobilized artificial membranes (IAMs) [16,17], immobilized proteins [18], and cholesterol [19], or other techniques like micellar liquid chromatography (MLC), have also been proposed for studying the lipophilicity of different compounds [20–24]. Micellar chromatography, as a variety of reversed-phase modality, is of particular interest. Addition of surfactants to the mobile phase in the concentration above the critical micelle concentration (CMC) leads to the constellation of specific molecular interactions that form an intricate retention mechanism: solute association with the polar head of the surfactant, solute penetration into the micelle core, adsorption of surfactant monomers on the alkyl-bounded stationary phases, and solute interactions with adsorbed surfactant and alkyl chains [25]. Regardless to the modality used, all lipophilicity indices are derived either directly from retention data or extrapolated from linear or bilinear relationships between retention parameters and mobile phase composition. Most frequently applied lipophilicity indices derived from TLC experiments are: mean RM , RM 0 (RM values extrapolated to the zero content of organic modifier), b (slope in the linear dependence of RM against the volume fraction of organic modifier), C0 (volume fraction of organic modifier in a mobile phase that provides equal distribution of analyte between mobile and stationary phase; RM = 0), and PC1/RM (score values of the first principal component defined as the linear combination of RM values) [26]. In the case of micellar chromatography the retention factor extrapolated to the zero micellar concentration of surfactant, i.e., the CMC in the mobile phase, logkm , is used [20,25]. All chromatographically derived lipophilicity measures used in the scope of this work are summarized in the Table S1 (Supplementary material), accompanied with simple explanations. Alongside the chromatographic methods, computational approaches for lipophilicity estimation have been extensively utilized. In silico predicted logP–s, either based on fragmentation approaches, or property-based are often compared with chromatographic lipophilicity indices [27,28]. However many of them exhibit significant differences in predicted logP values [29,30], which might question the reliability of these methods.
The computationally estimated logP scales used in the scope of the present work are summarized in the Table S2 (Supplementary material), alongside with the short description provided. Considering the importance of properly selected lipophilicity measure, the primary goal of this study was to compare, rank and group lipophilicity measures using sensitive non-parametric approaches. Therefore, comparison of TLC derived lipophilicity indices were in the main focus of this research. Such indices were obtained under typical reversed-phase conditions and under micellar chromatography, using stationary phases of different polarities. Further comparison of in silico estimation approaches, and chromatographic indices based on direct retention measures vs. the extrapolated ones was the subject of particular importance, as well. Many lipophilicity measures are derived from chromatographic experiments. For some compounds the chromatographic approaches are the only solutions for experimental lipophilicity determination (e.g., charged, polar molecules resolved under hydrophilic interaction liquid chromatography). To present no systematic, sensitive, and reliable approach for comparison and selection of the most suitable lipophilicity scales is enforced or widely accepted. The lack of systematic solution is especially harmful when it comes to testing of novel or emerging methods for lipophilicity estimation, such as micellar chromatography. Present work is a natural continuation of our previous research regarding the use of the sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM) for selection of the best lipophilicity measures [31].
2. Materials and methods (calculations) 2.1. Lipophilicity data Lipophilicity data have been taken from the literature [32,33] and are presented in Sections 3.1 and 3.2. We have selected cases providing they cover typical reversed-phase chromatography that combines stationary phases of different polarity [32]. Also, micellar chromatographic indices are studied alongside with typical RP-TLC derived descriptors. [33]. We paid attention to secure significant diversity of studied compounds and target their pharmacological importance (natural toxins and 1,2,4-triazoles as potent fungicides). A special care was taken in order to ensure the wide range of chromatographically derived lipophilicity indices and logP computational approaches.
2.2. Data pretreatment and multivariate exploratory statistical analysis In order to compare different lipophilicity measures all variables were rescaled. Three data transformation approaches have been tested: (a) standardization to unit standard deviation (also called autoscaling), (b) interval scaling between the lowest and the highest computationally estimated logP value and (c) rank transformation. Standardized data were further used for the exploratory data analysis employing HCA and PCA, while the sum of ranking differences (SRD) and generalized pairwise correlation method (GPCM) have been performed on all three sets of transformed data separately. In the case of HCA the Euclidian distance was selected as measure of dissimilarity among the variables while the Ward’s method was used to define the distances among clusters. PCA has been performed using PCA and multivariate/Batch SPC module as a part of Statistica v.10 (Statsoft Inc., Tulsa, Oklahoma, USA). The number of principal components has been determined using visual evaluation of screen plot.
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2.3. Sum of ranking differences (SRD) and comparison with random numbers (CRRN) The method with all theoretical details has been already described elsewhere [34–36], however some simplified description will be provided here. The data are arranged in a form of a matrix. In our case compounds are organized in rows, and lipophilicity scales in columns. Then for each variable (lipophilicity scale), every object (compound) is ranked, and ranks are subtracted from the ranked benchmark variable. All (absolute) rank differences are then summed and the SRD values are scaled to the interval 0–100. Variables are then sorted in ascending order of the SRD values. The closer the SRD value is to zero, the better might be considered that particular variable, i.e., the closer to the benchmark. Usage of a benchmark or a reference ranking makes this method supervised. Depending on the specific features of a task the benchmark variable can be maximum, minimum, average, or a priori known ranking. In the present work, we have decided to use the arithmetic means of rows as benchmarks for two reasons. First of all, according to the maximum likelihood principle, the most probable ranking should be achieved in case of using the arithmetic mean. Second of all, it is expected that random and systematic errors of each lipophilicity estimation method cancel each other to some degree, by averaging. The SRD values were further compared with simulated random numbers or theoretical distribution of the random SRD values as described in Ref. [35], so called comparison of ranks by random numbers (CRRN). Those SRD-s that fall away from each side of the theoretical or fitted Gaussian curve at the probability level p = 0.05, are considered to be statistically significant. The variables that overlap with the random distribution curve may be considered to be ranked by chance (not statistically significant). In addition, in order to validate grouping and ranking of variables, the portion of uncertainty was assigned to each SRD value using sevenfold cross-validation approach. Approximately 1/7 of objects are removed and the ranking is performed on the remaining data set. Procedure is repeated seven times producing seven SRD values for each lipophilicity measure. Since the number of compounds was smaller only for 1/7 portion, the variance in obtained SRD values is slightly overestimated. Statistical difference among each pair of variables is then tested by applying Wilcoxon’s matched pair test, as well as sign test. Graphical presentation of uncertainties and distribution of variables is done by plotting the box and whisker plot according to the following criteria: (1) increasing median values, if the median values are the same, then (2) the quartiles and interquartile range is taken into account. In that sense the first and third quartiles have the same “power”: if the two first quartiles are the same then, the smaller 3rd quartile should be the first. If the two 3rd quartiles are the same then, the smaller 1st quartile should be the first. If they are contradictory, then and only then the larger interquartile range counts. If they are equal, then (3) the maximum and minimum values are checked. If the two minimums are the same, then, the smaller maximum should be the first. If the two maximums are the same then, the smaller maximum should be the first. If they are contradictory, then and only then the larger range between minimum and maximum counts. If they are all equal, no decision can be made. Box and whisker plots provide additional insight into grouping of variables and their statistical significance. 2.4. Generalized pairwise correlation method (GPCM) The data are arranged in the same matrix as for SRD. Also, a benchmark variable is required. However, the GPCM approach resides on completely different philosophy from SRD. Basically, the method compares two variables at a time with the reference and decides, which one is superior, inferior, or no decision can be
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made. Few statistical tests are usually used to determine statistical significance of decision: Conditional exact Fisher test (CE), McNemar test, Chi-square test and Williams’ t-test, but in this work only conditional exact Fisher test has been employed. In addition, all variables are ranked according to the number of wins, number of wins minus losses, or probability weighted wins minus losses (PW), i.e. p(wins)–p(losses). In this particular case the probability weighted ranking was used and the values have been further reversely scaled and rescaled in order to be comparable with the SRD values. For the benchmark arithmetic means of all rows were chosen. Details of the GPCM procedure may be found elsewhere [37,38]. 3. Results and discussion 3.1. Assessment of lipophilicity measures obtained by typical reversed phase TLC experiments and in silico approaches Nascu-Briciu and Sarbu provided a well comprised data set (Supplementary material of the Ref. [32]). Data included assessments of lipophilicity indices by RP-TLC using seven stationary phases of different polarity, namely C2-, C8-, C18-, C18W- (octadecyl wettable), cyanopropyl-, aminopropyl-, and diol-modified silica plates, and 16 computational logP methods for 14 neurotoxins. They used three simple chromatographic descriptors: RM 0 (an extrapolated one), and those derived on direct chromatographic measurements: mRM, and PC1/RM . Majority of computational logP estimation approaches were based on fragmentation methods: logD, Hy, MlogP, logPc, logP, logPC , logPV , ClogP, AlogPs, AClogP, ABlogP, miLogP, KOWWIN, XlogP2 and XlogP3. The data matrix provided by the authors was consisting of 14 objects and ×37 lipophilicity measures. Because of the presence of missing data logPC and logPV have been excluded from further analysis. The final data matrix used for data analysis consisted of 14 objects (compounds) and 35 variables (lipophilicity measures) (see Supplementary material, Tables S3a and b). 3.1.1. Exploratory multivariate data analysis and clustering The authors performed PCA only on the set of computationally estimated lipophilicity scales to get an insight into the data structure, to reveal the presence of outliers, and possible groupings of objects. In order to compare both in silico and chromatographic measures, we have performed multivariate explanatory analysis on the overall data (computationally assessed plus chromatographic lipophilicity indices). PCA resulted in two principal components describing 85.0 % of the overall data variability (PC1 71.9 %, and PC2 13.1 %). All studied compounds have been grouped into two clusters; the first one consisted of compounds 1–8, 13 and 14, and the second one accounting compounds 9–12 (Fig. 1A). Two major groups of variables are separated along the PC2 direction, accompanied with one outlier variable (logPC ) (loading plot of PC1 vs. PC2, Fig. 1B). The first group, located in the upper part of the graph, is consisted mainly of descriptors derived directly from retention data, i.e., PC1/RM and mRM , obtained under various chromatographic conditions, together with hydrophobicity (Hy) and logP (parameter estimated by Alchemy 2000 software package). The second group gathers mainly extrapolated chromatographic descriptors, RM 0 , obtained on different stationary phases, as well as most of the computationally assessed logP values. Clustering obtained by HCA (Fig. 2) provides similar variable groupings. There are two clusters (A and B) at the linkage distance of around ten units and above. Most of computationally estimated logP measures and chromatographically extrapolated lipophilicity indices can be found in the cluster B followed by outliers: logPC and RM 0 (C2). The cluster A is mainly consisted of chromatographic
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Fig. 1. PCA score plot (PC1 vs. PC2) showing characteristic grouping (A) and loading plot (B) of RP-TLC lipophilicity indices and computationally estimated logP values. For original numeration of compounds see Ref. [32].
Fig. 2. Hierarchical cluster analysis: a dendrogram showing grouping pattern (similarities) of different RP-TLC chromatographic lipophilicity indices in combination with computationally estimated logP scales. Cluster A is mainly consisted of lipophilicity indices derived from direct retention parameters. Computationally estimated and chromatographic indices based on extrapolated measures are gathered in the cluster B.
descriptors (PC1/RM and mRM ). Direct retention derived parameter such as PC1/RM is equally efficient or even superior lipophilicity estimates than RM 0 which is affected by extrapolation [39,40]. This can, to a certain degree, explain division of lipophilicity parameters on these two groups. The major data variation, 71.9 %, is due to inherent, crude ability of the variables to grasp the lipophilic character of the studied compounds, but only 13.1 % of variance accounts for slight, refined differences in this ability. However, if the similarity with computationally estimated logP scales is chosen as a rule to find the best lipophilicity measure, than the opposite conclusion might stand: the best lipophilicity measures should be the extrapolated RM 0 values on various stationary phases. This is exactly the same conclusion that the authors of the original paper reached comparing chromatographic lipophilicity measures with computationally assessed ones. They observed that the highest correlation between the chromatographically determined indices and the computed logP–s is achieved for RM 0 , obtained on C18-, C18W, C8- and cyanopropyl-silica, which is closely followed by PC1/RM and mRM . 3.1.2. Comparison of lipophilicity scales by SRD and GPCM Inspection of PCA and HCA plots leads to several conclusions about similarities and possible grouping among lipophilicity
scales, but it is difficult to choose, which one represents the best lipophilicity measure. On that point the two approaches are limited, especially HCA. Both methods provide no reference for comparison. Even if the reference is available; both approaches do not give any information about statistical significance of such comparison, at least not straightforwardly. Also, logP data are not always normally distributed. Therefore non-parametric, sensitive and robust methods such as SRD and GPCM are used for comparison, grouping and ranking of variables according to the best chosen reference measure (in this particular case, the average). SRD provided information regarding statistical significance of ranking. According to the SRD–CRRN ranking, in the case of standardized data, the lowest scores (the closest to the benchmark values, and in that sense the best lipophilicity estimations) are obtained for mRM and PC1/RM on C18-modified silica, followed closely by the same descriptors on C8-modified silica (Fig. 3). In addition, majority of chromatographically derived indices have lower SRD values, lying approximately in the range 8–20 % of scaled units, compared with most of the computationally estimated measures (SRD values in the range 25–40 % of scaled units). Only two variables (RM 0 (C2) and logPC ) are overlapped with the population of random numbers (p = 0.05). Therefore they can be considered as non-significant, i.e., the worst lipophilicity estimates. The ranking of lipophilicity
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Fig. 3. Comparison of chromatographically derived and computationally assessed lipophilicity measures (autoscaled data) using sum of ranking differences; x axis and left y axis represent SRD values scaled between 0 and 100; right y axis display relative frequencies of the theoretical distribution for ranking random numbers.
scales is slightly altered depending on the data pretreatment (Table S5, Supplementary material); however, similarities in ranking are obvious. Obviously, mRM and PC1/RM have advantage over RM 0 (Fig. 3), which is in agreement with the claims [39,40], but not with the findings of original work [32]. Lipophilicity measures obtained on C18-, C8-, cyanopropyl-, and C2-modified silica layers outperform the same ones using diol- and especially aminopropyl-modified sorbents. It is evident that characteristics of the stationary phase exhibit strong influence on separation process, which has indirect impact on measuring lipophilic character of particular compounds and will be discussed later. Additional validation of the SRD ranking was done by a sevenfold cross-validation procedure (Fig. 4). All lipophilicity measures are arranged in increasing trend of medians of SRD values. Grouping of similar variables is done by applying Wilcoxon’s matched pair test and sign test. Variables that are statistically significantly different from the rest (p = 0.05) are separated with dashed lines. Here, PC1/RM (C18) and mRM (C18) are clearly superior, while RM 0 (C2) and logPC are apparently the worst. The trend of increased interquartile ranges (variability) among computationally estimated logP–s compared to chromatographic measures is apparent, and suggests that these lipophilicity measures are not as reliable as the rest of the lipophilicity indices. GPCM method provides similar lipophilicity scale ordering (Fig. 5), with some differences in variable degeneration. ”Degeneration” means the methodology cannot distinguish variables. However, all the milestones variables are the same, such as the best (PC1/RM (C18), mRM (C18), mRM (C8), PC1/RM (C8)), and the worst lipophilicity measures (RM 0 (C2), logPC ). A more characteristic grouping can be observed than in Fig. 4. A gap can be seen between PC1/RM (CN) or mRM (C2) and miLogP. This separates chromatographic indices obtained on C18-, C8-, cyanopropyl-, and C2-modified sorbents in the left part of the graph, from those derived from amino-propyl and diol modified-beds. The first group is closer to the benchmark and includes mostly chromatographic indices and minority of in silico estimates (14 % of the total number), while the second one is positioned farther from the reference and includes majority (86 % of the total number) of computationally estimated logP–s. Therefore, chromatographic indices obtained on aminopropyl- and diol-modified sorbents do not estimate lipophilicity better than computational approaches. The stationary phases that provide chromatographic most suitable for lipophilicity estimation conditions could be then roughly arranged in the following order: C18 > C8 > cyanopropyl > C2 > C18W > aminopropyl > diol. Apart from the lipophilic interactions that are more dominant in the group of C18-, C8-, cyanopropyl-, and C2-modified silica gels,
diol- and especially aminopropyl-modified layers provide significant amount of specific interactions, mostly through the hydrogen bonding, that alter retention behavior of the studied compounds. Significant involvement of specific interactions makes these two sorbents less suitable for lipophilicity measurements. In addition, according to both SRD and GPCM ranking, C18W sorbents are overlapped mostly with computationally estimated lipophilicity scales, and are closer to the diol- and aminopropyl-modified ones than to the first group (C18, C8, cyanopropyl, and C2). This can be explained by lower degree of surface modification of silica particles by hydrophobic hydrocarbon chains, and the uncovered silanol active centers that lead to more complex retention behavior. More or less the same conclusion was provided by the authors themselves [32]. If the mRM (C18) and PC1/RM (C18) are selected as the best lipophilicity measures based on both SRD and GPCM, then the choice of the most lipophilic compound is quite straightforward, i.e., compound No. 12 ((DHQ) 2 AQN, a quinine derivative). However, the authors themselves cannot reach decision easily, since the data do not offer the apparent choice. C18, C18W, and C8 are suggesting compound 11, while C2, cyanopropyl, and aminopropyl suggest compound 12, and finally retention profile on diol-modified plates indicates compound 8 as the most lipophilic one. After additional analysis they still could not clearly differentiate between compounds 12 and 11, since the differences in ordering strongly depend on the selected lipophilicity index. According to SRD and GPCM, the compound 13 (etoposide, a mycotoxine) presents the lowest lipophilicity. Both findings are in agreement with final conclusions of the authors. Compared with the methodology of Nascu-Briciu and Sarbu [32], which is based on Pearson’s correlations between computationally and chromatographically estimated lipophilicity measures (correlation matrices), lipophilicity charts and graphical profiles of principal component loadings, SRD and GPCM are simple and straightforward in ranking and selection of significant variables.
3.2. Assessment of lipophilicity measures obtained by micellar chromatography and typical reversed phase TLC experiments combined with in silico approaches Janicka et al. investigated retention behavior of 21 newly synthesized 1,2,4-triazole compounds with antifungal properties and potential importance in medicine and agriculture, under typical reversed-phase and micellar chromatographic conditions [33]. They used thin-layer chromatography, overpressured-layer chromatography (OPLC), as well as high performance liquid chromatography to separate compounds and derive chromatographic lipophilicity indices.
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Fig. 4. Ranking of chromatographic lipophilicity indices obtained under typical reversed-phase conditions and computationally estimated logP measures by means of the sevenfold cross-validation SRD procedure—box and whisker plot, y-axis represent SRD values; Dashed lines separate variables statistically significantly different from the rest of them (p = 0.05).
Fig. 5. GPCM comparison of chromatographically derived and computationally assessed lipophilicity measures (autoscaled data); x and y axis represent probability weighted wins minus losses p (wins)–p(losses), reversely scaled in order to be comparable with SRD values.
The authors compared micellar chromatographic parameters, logkm , obtained by all three chromatographic techniques, with RM 0 values determined by means of reversed-phase TLC using acetonitrile (RM 0 (1)) and tetrahydrofuran (RM 0 (2)) as a mobile phase constituents. The authors also selected seven computational methods for logP assessment (AlogPs, AlogP, AClogP, MlogP, XlogP2, XlogP3, and KOWWIN). The selection of the best lipophilicity measure was done by analyzing the correlations between in silico estimated logP–s and chromatographically proposed lipophilicity indices. The data have been obtained from the Tables 1 and 3 of the Ref. [33], and are provided as a part of the Supplementary material of the present work (Table S4). 3.2.1. Exploratory multivariate data analysis and clustering Similarities and groupings, as well as potential outlying effect among lipophilicity measures were revealed by PCA and HCA. Principal component analysis performed on the overall lipophilicity data, resulted in two principal components taking into account 77.7 % (PC1) and 19.0 % (PC2) of the overall data variability. According to the score plot all studied compounds could be sorted out into two major groups (I—1, 2, 4–7, 10–13, 18; II—3, 8, 9, 14–17, 19–21) (Fig 6A). Loading plot of PC1 vs. PC2 reveals the presence of a single group of variables (RM 0 (1), RM 0 (2), logkm (TLC), mixed with AClogP, AlogP, KOWWIN, AlogPs, XlogP2, and XlogP3) and
three outliers MlogP, logkm (OPLC) and logkm (HPLC) (Fig. 6B). The loadings of logkm (OPLC) and logkm (HPLC) on the PC1 direction are significantly lower (around 0.45 and 0.15) compared to the rest of the variables ranging between 0.8 and 1.0. Since thePC1 direction might be considered as the latent variable directly proportional to the lipophilicity measure, low loading values might imply that the last two indices might not represent suitable lipophilicity estimates. Similar grouping of variables was obtained by HCA (Fig. 7). All lipophilicity scales are grouped into two clusters at the linkage distance of four units and above. The first one consisting of: KOWWIN, RM 0 (1), RM 0 (2), AlogPs, XlogP3, AlogP, AClogP, XlogP2, and logkw (TLC) (Fig. 7), and the second one is comprised of logkm (OPLC), logkm (HPLC) and MlogP as an outlier. 3.2.2. Comparison of lipophilicity scales by SRD and GPCM Although some grouping of lipophilicity indices might be derived from PCA and HCA, selection of the best lipophilicity measure might be a difficult task. If the PC1 is considered as a direction of the major variability of lipophilicity data, i.e., lipophilicity measures (77.74 %), then variables with high loading values might be considered as the most suitable. A more refined way is at our disposal: SRD approach has chosen AClogP as the best lipophilicity measure for standardized data, i.e., the closest to the zero SRD, and furthest from the random number distribution. It is closely
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Fig. 6. PCA score plot of PC1 vs. PC2 (A) depicting separation of two main groups, and loading plot (B) revealing similarities among typical reversed-phase micellar chromatographic retention data and computationally estimated logP measures.
Fig. 7. Hierarchical cluster analysis: a dendrogram showing grouping pattern of reversed-phase and micellar chromatographic retention data in combination with computationally estimated logP values.
Fig. 8. SRD ranking of chromatographic lipophilicity measures obtained by means of micellar and typical reversed-phase chromatography modalities in combination with computationally estimated logP scales; x axis and left y axis represent SRD values scaled between 0 and 100; right y axis display relative frequencies of the theoretical distribution for ranking random numbers.
followed in order: RM 0 (2), XlogP2, KOWWIN, logkm (TLC), RM 0 (1), AlogPs, and AlogP (Fig. 8). The worst, farthest from the zero SRD value, and not significantly different from the random number distribution are logkm (OPLC) and logkm (HPLC). All three thin-layer chromatographic descriptors are superior lipophilicity measures compared to the OPLC or HPLC techniques. There is some similarity with the ordering of the PC1 loadings. The SRD scaled values differ slightly depending on the data pretreatment, but the main milestones such as the best and the worst variables are preserved (Table S6, Supplementary material).
In addition, SRD ranking combined with sevenfold crossvalidation confirmed the same order of lipophilicity measures (Fig. 9). The medians of SRD values of logkm (OPLC) and logkm (HPLC) are statistically significantly different from the rest of lipophilicity parameters (Wilcoxon’s match paired test and sign test, p = 0.05), and exhibit significantly higher variability (interquartile ranges) imposed by the cross-validation procedure, which implies that these two lipophilicity measures are not as reliable as the rest of the lipophilicity indices. GPCM comparison gave astonishingly the same rankings as SRD and SRD sevenfold cross-validation (Fig. 10), which is quite surpris-
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Fig. 9. Ranking of chromatographic lipophilicity scales obtained under typical reversed-phase and micellar chromatographic conditions in combination with computationally estimated logP values by means of the sevenfold cross-validation procedure (SRD)—box and whisker plot y-axis represent SRD values; Dashed lines separate variables statistically significantly different from the rest of them (p = 0.05).
Fig. 10. GPCM ranking of chromatographically estimated lipophilicity scales from micellar and typical reversed-phase conditions in combination with computationally calculated logP values; x and y axis represent probability weighted wins minus losses, p(wins)–p(losses), reversely scaled in order to be comparable with SRD values.
ing, since these two approaches derived from completely different philosophy and computations. This is an additional confirmation of the SRD–CRRN and SRD–CV findings. However, Janicka et al. [33] concluded, after detailed evaluation of micellar logk parameters, which was based on linear regression with computationally estimated logP–s and RM 0 values, that “The best linearity was observed between micellar parameters and XlogP2, XlogP3 and logP average values, as for HPLC, OPLC and TLC techniques. Analogous relationships corresponding to RM 0 values characterized by much lower coefficients of determination, demonstrate that extrapolated RM 0 parameters rather poorly correlate with partitioning lipophilicity descriptors”. They further suggest that “micellar chromatography is an excellent technique for studying lipophilicity of triazoles”. This is a good example that using simple univariate linear correlation/regression models might lead to erroneous conclusion(s). PC loading plot clearly demonstrates that OPLC and HPLC micellar data are outliers from the rest of the lipophilicity parameters; therefore, they cannot “outperform” lipophilicity measures obtained from the typical reversed-phase systems (RM 0 (1), and RM 0 (2)) as well as computationally assessed logP values. However, this is not the case with the thin-layer chromatographic data. The same conclusion was obtained by two distinct approaches: SRD and GPCM. Therefore, in this particular case, multivariate methods and rankings (by SRD and GPCM) suggest that micellar chromatography is not the optimal way to determine lipophilicity of the particular set of triazole derivatives. This can be partially explained by the intricate retention mechanism of the micellar chromatography involving solute association
with the polar part of the surfactant, solute penetration into the micelle, adsorption of surfactant monomers on the alkyl-bounded stationary phases, and solute interactions with adsorbed surfactant and alkyl chains. Such mechanism can be altered to a certain degree by adding higher amounts of organic modifier and produce lower logkm values [33]. If the AClogP is chosen as the best lipophilicity estimator, then the most lipophilic candidate would be compound No. 10, i.e. p-bromo-phenyl derivate of structure A [33]. Fortunately the same conclusion would be reached for any of the studied variables. The least lipophilic compound is No. 11, i.e., n-propyl derivative of structure B [33]. This is valid for all variables except for MlogP, which assigns n-propyl derivative to the group of structure A as the least lipophilic one.
4. Conclusions Both non-parametric procedures, sum of ranking differences and generalized pairwise correlation method, gave very similar results. In the case of the typical reversed-phase thinlayer chromatography applied on different stationary phases, lipophilicity indices based on direct retention measures, mRM and PC1/RM , have advantage over extrapolated ones, RM 0 . Also, octadecyl-, octyl-, and cyanopropyl-modified silica have advantage over ethyl-, diol- and especially aminopropyl-modified silica, i.e., the preferable choice of the stationary phases follows this order: octadecyl > octyl > cyanopropyl > ethyl > octadecylwettable > aminopropyl > diol. Many chromatographic lipophilicity
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measures outperform computational methods, but no clear distinction based on cross-validation and Wilcoxon’s test or sign test (p = 0.05) can be made. The most and least lipophilic compounds are Nos. 12 and 13, respectively, which is in accordance with original findings by Nascu-Briciu and Sarbu [32]. Micellar chromatography may not be apparent choice for lipophilicity assessment, since both retention par ameters obtained from the typical reversed-phase conditions outperforms the parameters obtained by micellar chromatography, but neither one is better than the computationally estimated logP scales. Comparing generalized pairwise correlation method with sum of ranking differences, the first one result in more degeneracy, i.e., in some cases it cannot distinguish the lipophilicity parameters, whereas sum of ranking differences and its cross-validated version can. On the other hand it provides more characteristic groupings. The proposed approaches can be successfully used for selection of the most appropriate lipophilicity measures as well as the ranking and selection of the most and the least lipophilic (promising) candidates. Acknowledgments This work has been supported by the Ministry of Education, Science and Technological development, of the Republic of Serbia, grant No. 172017. KH is indebted to the support from OTKA (Hungary), contract No. K112547. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.jpba.2015.07.006 References [1] M.J. Waring, Lipophilicity in drug discovery, Expert Opin. Drug Discov. 5 (2010) 235–248. [2] M.J. Waring, Defining optimum lipophilicity and molecular weight ranges for drug candidates—molecular weight dependent lower logD limits based on permeability, Bioorg. Med. Chem. Lett. 19 (2009) 2844–2851. [3] M.P. Gleeson, Generation of a set of simple, interpretable AMDET rules of thumb, J. Med. Chem. 51 (2008) 817–834. [4] D.A. Price, J. Blagg, L. Jones, N. Greene, T. Wager, Physicochemical drug properties associated with in vivo toxicological outcomes: a review, Expert Opin. Drug Metab. Toxicol. 5 (2009) 921–931. ˝ G.M. Makara, The influence of lead discovery strategies on the [5] G.M. Keseru, properties of drug candidates, Nat. Rev. Drug Discov. 8 (2009) 203–212. [6] S.K. Poole, C.F. Poole, Separation methods for estimating octanol–water partition coefficients, J. Chromatogr. B 797 (2003) 3–19. [7] OECD Guideline for the testing of chemicals, Test No. 107, Partition coefficient (n-octanol/water), Shake flask method (1995) OECD, Paris,
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