2.1 Materials and reagents

Acetonitrile HPLC purity (JT Baker, Deventer, Netherlands), sodium hydrogenphosphate (Sigma Aldrich, Steinheim, Germany), phosphoric acid (Sigma Aldrich, Steinheim, Germany) and deionized water (TKA water purification system, Niederelbert, Germany) were used for the mobile phase preparation. Dimethyl sulfoxide, used for the preparation of stock solutions, was purchased from Fisher (Loughborough, UK).

The design, synthesis and biological evaluation of dual DNA gyrase and topoisomerase IV inhibitors (Fig. 1) tested in this study were previously published [8, 20, 21]. Tested compounds were dissolved in dimethyl sulfoxide to prepare stock solutions (1 mg mL⁻¹), which were then diluted with the mobile phase (see below) to obtain working solutions (0.01 mg mL⁻¹).

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Chemical structures of tested compounds

Citation: Acta Chromatographica 36, 1; 10.1556/1326.2022.01096

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2.2 RP-HPLC analysis

2.3 Calculation of molecular descriptors and logD

Molecular descriptors were calculated using the web-based platform ChemDes [22], which allows the calculation of more than 3,000 molecular descriptors. In this study, 3D Chemopy descriptors were calculated and after deletion of those without variance, 479 molecular descriptors were retained for modeling. ChemDes uses the MOPAC software as default to optimize each molecule. Prior to the descriptor calculation, the dominant form of each molecule at pH 5.5 was determined using MarvinSketch 21.4.0. logD was calculated in MarvinSketch 21.4.0 at two pH values (5.5 and 7.4) by the consensus method, which utilizes ChemAxon and Klopman's models and the PhysProp database. For these calculations, electrolyte concentrations (Na⁺, K⁺ and Cl⁻) were set to the default values [23].

2.4 QSRR modelling

Descriptor selection as well as multiple linear regression (MLR), partial least squares (PLS) and support vector machine (SVM) modelling were performed in Statistica 13.3 [24].

Prior to modelling, the number of descriptors has to be reduced and only the most relevant ones should be retained. Molecular descriptors can be selected using various approaches, such as genetic algorithm [25], principal component analysis [26] or stepwise MLR [27, 28]. In this study, forward stepwise MLR was used for the selection of descriptors prior to model creation. In forward stepwise MLR, descriptors are included in the model sequentially and evaluated at each step. Descriptors are retained or removed according to specified criteria (F to enter and F to remove). In this study, F to enter was 8, whereas F to remove was 3. The following descriptors were selected for SVM and MLR modelling: logP, bcutp3 and bcutm13. For the PLS modelling, nine most influential descriptors were selected following the same procedure (MoRSEU14, RDFC20, DPSA1, E2e, bcutv1, MATSv5, logP, bcutp3 and bcutm13).

The quantitative structure-retention relationship (QSRR) studies were performed to investigate the relationships between φ₀ (dependent variable) of tested compounds and their calculated molecular descriptors (independent variables). In order to perform a relevant comparison between different methodologies used to build QSRR models, the same training and test sets were prepared. For MLR(φ0), PLS(φ0) and SVM (φ0), the test set consisted of six compounds (NDL-20, NHM-80, TAZ-7, TCF-3a, THT-9 and THT-11), while remaining derivatives formed the training set. The test set was formed with the aim to cover structural and physico-chemical diversity of all tested compounds and so the φ₀ of these compounds were evenly distributed over the entire range of φ₀ values.

MLR was applied to assess the linear relationship between selected molecular descriptors and φ0. In this study, the standard MLR model building method was applied.

PLS modeling is useful when analyzing data with collinear, noisy and numerous descriptors. The optimal number of PLS components was selected by analyzing the R²(Y) value and the cumulative R²(Y) value of each component. Scaled regression coefficients were used to evaluate the influence of the descriptors on the created model and for their ranking. The final PLS (φ0) model consisted of three components.

SVM was developed as a binary classification tool [29]. However, in recent years, it has also been used as a nonlinear method in QSAR and QSPR modelling [30, 31]. In this study, the optimal SVM(φ0) model was obtained using radial basis function (RBF) Kernel type and regression type 1. Gamma value was set to 0.25, while optimal capacity (C) and epsilon (Ɛ) values were 8 and 0.1, respectively. The model consisted of 11 support vectors (6 bounded).

3.1 RP-HPLC analysis

The tested compounds contain ionizable groups and therefore, effective lipophilicity (logD) is a more appropriate lipophilicity parameter than logP (logP represents intrinsic lipophilicity, i.e. lipophilicity of unionized form of a compound). The pH values that were chosen in this study were 5.5 and 7.4 because they are the most relevant for the pharmacokinetic (gastrointestinal absorption, distribution and elimination) and pharmacological behavior of drugs. For the initial lipophilicity estimation, logD was calculated at both pH values using MarvinSketch. There are several highly lipophilic compounds with logD > 3 (TEL-28, TAZ-2b, NAS-36, TLK-10, KSK-22 and TCF-3a). Therefore, the shake-flask method might give unreliable results, which justifies the development of HPLC method for the lipophilicity evaluation of these compounds.

Retention parameters (logk_w, S and φ0), as well as calculated logD values of the tested compounds are presented in Table 1. Due to high correlations between logk and φ at both pH values (calculated correlation coefficients were from 0.9837 to 0.9999), logk_w could be calculated by the y-axis extrapolation of these curves.

For the development of HPLC method, C8 column was chosen due to the similarity of its hydrophobicity with the hydrophobicity of octanol alkyl chain (octanol is the most frequently used organic solvent in the shake-flask method). It was also expected that the analysis would be faster than with the C18 column. Phosphate buffer was used for the adjustment of pH values (pH 5.5 and pH 7.4) of the mobile phases because it is present in biological fluids.

Of the three retention parameters presented in Table 1 (logk_w, S and φ₀), φ0 showed the highest correlation with logD at both pH values (r = 0.85 and 0.89 with logD calculated at pH 5.5 and pH 7.4, respectively). Correlation coefficients between logk_w and logD were 0.01 (pH 5.5) and 0.07 (pH 7.4), while correlation coefficients between S and logD were 0.80 (pH 5.5) and 0.79 (pH 7.4). Therefore, φ0 could be considered the most reliable RP-HPLC parameter for logD prediction at both pH values. This retention parameter was introduced by Valko and Slegel [37] and it represents the volume fraction of organic modifier in the mobile phase at which equal partitioning of the solute between the mobile and stationary phases is obtained (k = 1, logk = 0). It relies on the pH, temperature and organic modifier, while it does not rely on column type and length, flow rate and mobile phase composition. It also represents concentration of the organic modifier in the mobile phase resulting in the retention time (t_R) that is double the dead time (t₀). Therefore, it can be accurately estimated which is considered a distinguishable advantage over extrapolating of logk values to pure water mobile phase [38]. This parameter was also proved to be more suitable for the estimation of lipophilicity of sets of structurally unrelated compounds [39, 40]. Although introduced almost thirty years ago, this parameter is still used for the estimation of lipophilicity of various classes of bioactive compounds [38, 41]. Correlations between φ0 and logD at both pH values were presented in Fig. 2.

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a) Correlation between φ0 and logD (pH 5.5) and b) correlation between φ0 and logD (pH 7.4)

Citation: Acta Chromatographica 36, 1; 10.1556/1326.2022.01096

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Compound NDL-20, with an unexpectedly high φ0 at both pH values, was an outlayer. At both pH values, compounds with the highest φ0 values were TEL-28, TAZ-2b and NAS-36, and their calculated logD values were higher than 3.2. TEL-28, TAZ-2b and NAS-36 contain ester groups, halogen atoms (chlorine or bromine) and three or four rings. These moieties increase lipohilicity and consequently increase φ0 values. At pH 5.5, compounds with the lowest φ0 values were NZ97 and THT11, and their logD values were lower than 0.19. At pH 7.4, compounds with the lowest φ0 values were also NZ-97 and THT-11, as well as TAZ-7 and KSK-15, for which calculated logD values were lower than 0.55. NZ-97, THT-11, TAZ-7 and KSK-15 contain carboxylic acid moiety, and as pH increases, the proportion of the ionized form of these compounds also increases, which could explain their low φ0 values determined at pH 7.4.

3.2 QSRR modelling

Due to high correlation between φ0 determined at pH = 5.5 and pH = 7.4 (r = 0.98), only φ0 determined at pH = 5.5 was used for further QSRR modelling.

Results of the validation of created models are presented in Table 2.

PLS (φ0) model cannot be considered reliable due to the high discrepancy between RMSEE and RMSEP. This means that using this model, φ0 values of compounds that are structurally different from those in the training set cannot be reliably predicted. The remaining QSRR models (MLR (φ0) and SVM (φ0)) pass all validation tests. Although RMSEE was higher (2.75 vs 2.48), due to lower RMSEP, lower difference between RMSEE and RMSEP, higher Q², r and R²_pred, MLR (φ0) could be considered more reliable model for the logD prediction. Descriptors which form both MLR (φ0) and SVM (φ0) models were logP, bcutp3 and bcutm13. Cross-correlation between these decscriptors was not higher than 0.41 (logP and bcutp3: r = 0.32; logP and bcutm13: r = 0.07; bcutp3 and bcutm13: r = 0.41). A rule of thumb in regression analysis is that at least 5 observations per descriptor are needed and the more acceptable ratio would be 10:1 [42]. Therefore, the dataset size in this study (twenty-three compounds) allows the use of three descriptors for reliable QSRR modelling. In addition, satisfactory values of validation parameters for the test set (Table 2) show that the model was not overfitted. Statistical data calculated for the MLR (φ0) model are presented in Table 3.

Intrinsic lipophilicity, logP, was calculated by the Crippen method. The relationship between this descriptor and φ0 is linear and positive (Fig. 3) and the increase in lipophilicity results in the increase in φ0. This supports our previous observation that applied RP-HPLC systems can be used for reliable prediction of the lipohilicity of dual DNA gyrase and topoisomerase IV inhibitors.

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Correlation between logP and φ0

Citation: Acta Chromatographica 36, 1; 10.1556/1326.2022.01096

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Descriptors bcutp3 and bcutm13 belong to the Burden descriptors and are based on polarizability and atomic masses, respectively. Descriptors bcut are defined as the eigenvalues of a connectivity matrix which takes into account both connectivity and atomic properties of a molecule, such as atomic weight, partial charge and polarizability. These descriptors are based on a weighted version of the Burden matrix [43, 44] and the weights are a variety of atomic properties placed along the diagonal of the Burden matrix (atomic weight, partial charge (Gasteiger–Marsili) and polarizability weighting schemes are used) [45].

Descriptor bcutp3 represents the highest eigenvalue number 3 of the Burden matrix/weighted by atomic polarizabilities which encode information about the polarizability of the molecules. It was shown that the increase in polarizability increases solubility, i.e. that molecular polarizability, both of the solute and solvent, is a major factor that dictates solubility [46–48]. According to the MLR model, this variable has negative impact on φ0 and the increase in bcutp3 results in the decrease in φ0, which indicates that the water solubility of the molecules is inversely related to φ0. Derivatives with the highest values of this descriptor are NHM-80 and TEL-28, while those with the lowest values are KSK-22 and NDL-20.

Descriptor bcutm13 belongs to the Burden descriptors based on atomic mass. The relationship between bcutm13 and φ0 is positive, according to the positive value of the coefficient in the MLR model. This also means that the molecular weight of tested compounds positively affects their retention in the applied RP-HPLC systems. Compounds with the highest value of this descriptor are LMD-62 and TEL-28 (molecular weights of these compounds are higher than 530), while those with the lowest values are TAZ-7 and KSK-22 (molecular weights of these two compounds are lower than 450). It is difficult to estimate φ0 only on the basis of descriptor values. For example, LMD-62 has low φ0 despite the high value of bcutm13. This could be explained by the high value of bcutp3, which has a negative impact on φ0. TEL-28 also has high bcutm13 value and despite high value of bcutp3 (which has a negative effect on φ0), this compound has high value of φ0. Compound KSK-22 has low values of both bcutm13 and bcutp3 and a high value of logP. Its high φ0 could be explained by the greater influence of bcutp3 and logP on φ0 compared to the influence of bcutm13. Therefore, all selected descriptors have to be taken into account, which underlines the importance of use of the created MLR (φ0) model for valid prediction of φ0.