Partial Least Square and Hierarchical Clustering in ADMET Modeling: Prediction of Blood – Brain Barrier Permeation of α -Adrenergic and Imidazoline Receptor Ligands

- PURPOSE. Rate of brain penetration (logPS), brain/plasma equilibration rate (logPS-brain), and extent of blood-brain barrier permeation (logBB) of 29 α -adrenergic and imidazoline-receptors ligands were examined in Quantitative-Structure-Property Relationship (QSPR) study. METHODS. Experimentally determined chromatographic retention data (logKw at pH 4.4, slope ( S ) at pH 4.4, logKw at pH 7.4, slope ( S ) at pH 7.4, logKw at pH 9.1, and slope ( S ) at pH 9.1) and capillary electrophoresis migration parameters ( μ eff at pH 4.4, μ eff at pH 7.4, and μ eff at pH 9.1), together with calculated molecular descriptors, were used as independent variables in the QSPR study by use of partial least square (PLS) methodology. RESULTS. Predictive potential of the formed QSPR models, QSPR(logPS), QSPR(logPS-brain), QSPR(logBB), was confirmed by cross- and external validation. Hydrophilicity (Hy) and H-indices (H7m) were selected as significant parameters negatively correlated with both logPS and logPS-brain, while topological polar surface area (TPSA(NO)) was chosen as molecular descriptor negatively correlated with both logPS and logBB. The principal component analysis (PCA) and hierarchical clustering analysis (HCA) were applied to cluster examined drugs based on their chromatographic, electrophoretic and molecular properties. Significant positive correlations were obtained between the slope ( S ) at pH 7.4 and logBB in A/B cluster and between the logKw at pH 9.1 and logPS in C/D cluster. CONCLUSIONS . Results of the QSPR, clustering and correlation studies could be used as novel tool for evaluation of blood-brain barrier permeation of related α -adrenergic/imidazoline receptor ligands.

For the active sites of I2-IRs were shown to reside on monoamine oxidase-B (MAO-B) (10), well known drug target for several neurological diseases. Therefore the I2-IRs ligands are examined as novel therapeutic drugs in treatment of various neurological diseases (14). Research on agmatine, an endogenous ligand for all imidazoline receptor(s), has confirmed its implication in mediation of analgesia, stress responses, convulsions, and neuroprotection (15). Since the IRs are involved in many neurophysiologic and pathologic functions the potential for new IRs ligands development is very intriguing (14,15).
Thus, the main goal of the study was to examine brain penetration of the drugs interacting with IRs/α-ARs and to develop Quantitative Structure-Property Relationship (QSPR) models capable to predict and describe rate and extent of the brain penetration for the related IRs/α-ARs ligands. ________________________________________ Initially, we have selected ligands of αadrenergic and imidazoline-receptors for the study.
Because the I-IR ligands exert additional CNS and diuretic effects, we have decided to include few structurally related CNS drugs (clozapine, maprotiline, mianserin, and olanzapine) and diuretics (amiloride, clopamide, indapamide, and triamterene) in the QSPR study.
Rate of brain penetration (logPS), brain/plasma equilibration rate (logPS-brain), and extent of blood-brain barrier permeation (logBB) of the 29 α-adrenergic/imidazoline receptors ligands and related compounds were used as dependent (Y) variables in the QSPR study.
The QSPR (logPS, logPS-brain, logBB) study of the 29 drugs was performed by use of principal component analysis (PCA) and partial least square (PLS) methodologies.
Chromatographic retention parameters (logKw at pH 4.4, slope (S) at pH 4.4, logKw at pH 7.4, slope (S) at pH 7.4, logKw at pH 9.1, and slope (S) at pH 9.1), capillary electrophoresis migration parameters (μeff at pH 4.4, μeff at pH 7.4, and μeff at pH 9.1) and computed molecular parameters of the drugs were used as independent variables (X) for the QSPR modeling. The PLS methodology was applied to select molecular parameters of the drugs with the strongest impact on their brain penetration and to create QSPR (logPS, logPS-brain, logBB) models able to predict blood-brain barrier permeation properties of the related α-adrenergic/imidazoline receptors ligands.
Since the examined drugs are structural very diverse principal component analysis (PCA) and hierarchical clustering analysis (HCA) were applied to cluster examined drugs based on their chromatographic, electrophoretic and molecular properties. The PCA/HCA clusters of the drugs were further examined by the correlation study between chromatographic/electrophoretic parameters, as independent variables, and bloodbrain permeation parameters, as dependant variables.
The performed QSPR, clustering and correlation studies are first reported theoretical investigation of brain penetration process of the αadrenergic/imidazoline receptor ligands.

Chemicals and reagents
All reagents used were of analytical grade purity. Methanol-HPLC gradient grade, glacial acetic acid (J.T. Baker Deventer, Netherlands), ammonium acetate, sodium hydroxide, sodium

Capillary Electrophoresis
Stock solutions of harmane, harmine, clopamide, indapamide, rilmenidine, mianserin, doxazosin, carvedilol, clozapine, olanzapine and triamterene were prepared in methanol and diluted with water to a final concentration of methanol 2 % for triamterene and 1 % for remaining substances. Brimonidine was dissolved in 0.1% formic acid and the other 17 compounds were dissolved in water. Acetone 2% was used as EOF marker. Samples were prepared in different concentrations, from 5.8 to 60 μg mL -1 , depending on their UV response and solubility.

HPLC analysis
Working solutions were prepared by dissolving the substances into the methanol in order to obtain the concentration of 0.7 mg mL -1 for rilmenidine and 0.1 mg mL -1 for the remaining compounds.

CE equipment
All experiments were carried out on SpectraPhoresis 500-capillary electrophoretic system (Spectra Physics Analytical, USA) equipped with UV detector. Data were recorded and analyzed with ChromQuest software version 4.0 (Thermo Finnigan, USA).

Electrophoretic conditions
Separations were performed using an uncoated fused capillary (31,5 cm_50 mm id, effective length 24 cm, Polymicro Technologies, USA) at 25 ºC, 11 kV, and 200 nm. The new capillary was gradually flushed with 0.1 M NaOH (15 min), water (10 min) and running buffer (10 min). Finally, a 10 min application of the high voltage through the capillary filled with background electrolyte were applied in order to equilibrate the inner surface, stabilize electroosmotic flow and to maintain proper reproducibility of run-to-run injections. Background solutions of constant ionic strength (I=25 mmol/L) were prepared at three different pH values (4.4; 7.4 and 9.1). The samples were injected hydrodynamically three times at each pH (4.4; 7.4 and 9.1). Between runs the capillary was rinsed with the background electrolyte for 1 min.
The effective electrophoretic mobility, μeff, of the analyte at three different pH values 4.4; 7.4 and 9.1 (μeff pH 4.4, μeff pH 7.4 and μeff pH 9.1 respectively) were calculated and used for QSPR study.

HPLC equipment
A chromatographic system Agilent Technologies 1200 (Wilmington, DE, USA) equipped with online degasser, binary pump, column oven and photo diode array detector was used for HPLC analysis. Sample injection was performed through Rheodyne injector valve with a 20 μL sample loop. Data were recorded and analyzed with Agilent's ChemStation software.

HPLC conditions
All chromatographic measurements were performed on XTerra ® RP18 column, 4.6 x 100 mm, particle size 3.5 µm (Waters Corporation, Milford, MA, USA). The flow rate was 0.8 ml min -1 with UV detection in the range 200-280 nm. The temperature was set at 25°C. The retention parameters were obtained at the isocratic elution mode using at least six mobile phases methanol/buffer with concentration of methanol varying from 75-2%, depending on compounds retention properties. Buffers solutions of constant ionic strength (I=25 mmol/L) were prepared at three different pH values: 4.4, 7.4 and 9.1. Dead volume was measured with KNO3 as a nonretained marker. The values corresponding to 100% of buffered eluent, log Kw and slope (S), were obtained by extrapolation, following the Snyder-Soczewinski equation (16,17). The logKw and slope (S)of the analyte at three different experimental conditions, methanol/buffer pH 4.4, methanol/buffer pH 7.4 and methanol/buffer pH 9.1 (logKw pH 4.4, slope (S)pH 4.4, logKw pH 7.4, slope (S)pH 7.4, logKw pH 9.1, and slope (S)pH 9.1 respectively) were calculated for all examined compounds and used for QSPR study.
The dominant amino/imino tautomers were selected by use of the B3LYP/6-31G(d, p) level of the Density Functional Theory (DFT) (18,19) incorporated in the Gaussian 98 program (20). The selected basis set was proved to be good choice for examination of the related amidines and guanidines (21). Based on the obtained Self Consistent Field Energy (SCF energy), rilmenidine amine was selected as predominant tautomeric form while moxonidine, clonidine, tizanidine, brimonidine and tramazoline exist as more stable imino tautomers.
Calculation of pKa and selection of dominant molecules/cations species at pH 4.4, 7.4, and 9.1, have been performed for 29 α-adrenergic and imidazoline-receptors ligands using the Marvin 5.5.1.0 ChemAxon program (22). The Marvin program defined nitrogens of the analyzed structures with the highest potential to attract proton at analytical pH.
The geometries of the examined ligands (selected tautomers and molecules/cations species at three different pH values) were completely optimized at B3LYP/3-21(d,p) levels of the Density Functional Theory using the Gaussian 98 program (20).

Molecular descriptors
The molecular descriptors, as numerical parameters representing the chemical structures, were calculated for the optimized molecular models.
The Soft Independent Modeling of Class Analogy SIMCA P+ 12.0 program (29) was used for the PLS analysis and QSPR modeling.
Based on the Principal Component Analysis (PCA) plots (t1 vs. t2 and t1 vs. u1) the data set of 29 compounds is divided on Training Set (22 compounds for QSPR models building) and Verification set (7 compounds for QSPR models validation). Based on the PCA plots were not defined any outlier in the QSPR models.
Partial least square (PLS) regression, recently developed generalization of multiple linear regressions (MLR) (28,29), has been used for calculation of VIP parameter and QSAR models building. In multilinear modeling, a summary of the importance of each variable (xk), for both Y and X matrices, is presented as VIPk parameter. The x-variables with VIP value larger than 1 are the most relevant for explaining the regression model, the x-variables with 1.0>VIP>0.5 are moderately influential, while x-variables with VIP value smaller than 0.5 are not relevant for the model (28,29).  Quality of the obtained QSPR models was examined by use of the R 2 , Q 2 and RMSEE, CV-ANOVA analysis of variance testing of crossvalidated predictive residuals (F-and P-value), and external validation (root mean square error of prediction (RMSEP), R 2 pred, R 2 Obs vs. Pred) (28,30,31).
Predictive power of the model is determined by Q 2 , which is Leave-One-Out Cross-Validated (LOO-CV)/or Leave-n-Out Cross-Validated (LnO-CV) version of R 2 . A model is fitted to the data leaving one/or more compounds out, computing VIP, selecting the best variables, and than predicting Y for the left-out compounds. This procedure is repeated until all compounds have been left out, which result in many parallel models. The difference between observed and the predicted Y values are calculated (e(i)) for each model. In this setting were defined PRESS (Predicted Sum of Squares), RMSE (RMSEE and RMSEP) and Q 2 as: Difference between observed and the predicted Y values -(e(i)) QSPR models with Q 2  0.5 can be considered to have good predictive capability (28,29) Quality of the QSPR models prediction was assessed on test set by use of the RMSEP, R 2 Obs vs.
QSPR models with R 2 pred 0.5 can be considered to have good predictive capability (31).
The response permutation test (Y scrambling) examined the statistical significance of the R 2 and Q 2 and overfitting due to the chance correlation (28,30). In this test the Y-matrix is randomly reordered (100 times in this project) while the Xmatrix is kept intact. Model is fitted to the new Ydata and the new R 2 (Y), Q 2 and VIP parameters are calculated. All model selection steps are repeated on the scrambled Y-response data. Lines are fitted through the R 2 -values and through the Q 2 -values, yielding two separate intercepts. For a valid model, the R 2 -intercept should not exceed the 0.4 while the Q 2 -intercept < 0.05 (28).
The F-test, based on the ratio MS Regression/MS Residual, formally assesses the significance of the model. The P-value indicates the probability level where a model with this Fvalue may be the result of just chance. The common practice is to interpret a P-value lower than 0.05 as pointing to a significant model (28).

Principal component analysis and hierarchical clustering analysis
The Principal component analysis (PCA) (32) is one of the most common methods used in a twoway data analysis. In PCA a two-way matrix, X (m × n), is decomposed into two matrices S (m × fn) and D (n × fn): where m and n denote, respectively, the number of objects and the number of variables, S represents the scores matrix, D represents the loading matrix, E is the residuals matrix, and fn denotes the number of significant factors. Scores and loadings matrices are orthogonal, i.e. S′S = D′D = I. The columns of matrix S are called the Principal Components (PC), or eigenvectors. Each PC is constructed as a linear combination of original variables with weights maximizing description of the data variance (i.e. S = XD). The sum of the squared elements of each eigenvector (PC) is called an eigenvalue. The first PC describes the largest amount of the data variance, so that the associated eigenvalue also has the highest value. The sum of the eigenvalues defines the total variance of the data. Scores vectors (i.e. the columns of matrix S) and loading vectors (i.e. the columns of matrix D) are used to visualize relationships between the objects and the parameters in a matrix X.
Hierarchical clustering analysis (HCA) can be applied to multidimensional data sets, in order to study similarities (or dissimilarities) of objects in the variables space, or similarities of variables in the objects space (33). Final results of hierarchical clustering are presented in a form of a dendrogram. The indices of clustered objects (or variables) are displayed on axis x of the dendrogram, whereas axis y represents the corresponding linkage distances (or an adequate measure of similarity) between the two objects or clusters, which are merged.

Quantitative Structure-Property Relationship (QSPR) study
The pharmacokinetic properties (logPS, logPSbrain, and logBB) of the 29 ligands (Figure 1), calculated by use of ACD/i-Lab program (27), were used as dependent (Y) variables in the QSPR study. Values of the logPS, logPS-brain, and logBB parameters are reflecting rate and extent of blood-brain permeation process, where higher logPS, logPS-brain, and logBB values indicate on higher rate and extent of brain penetration of a ligand.
Based on the obtained Score Plots (t1 vs. t2 and t1 vs. u1) the data set of 29 α-adrenergic and imidazoline-receptors ligands is divided on Training set (22 compounds for QSPR models building) and test set (7 compounds for QSPR models validation) (28,30,31).
The PLS methodology was applied for selection of the most relevant molecular descriptors and QSPR models building.
Descriptors with lowest Variable Importance in the Projection (VIP) value are successively removed from the PLS model, each time new PLS model is created, and the obtained R 2 , Q 2 , F ratio, P-value, RMSEE of new model were compared with the previous one. The procedure is repeated until the best model is created.
The applied PLS methodology has selected sets of significant descriptors during development of each QSPR model. Overfitting of the QSPR models is avoided by continual monitoring of the RMSE for training and test set during the QSPR modeling. The QSPR models were selected when RMSEP of test set begins to increase while RMSEE of training set continues do decrease. Furthermore, the QSPR models with different number of selected significant descriptors were compared and optimal one is chosen by comparing statistical parameters of the training set, such as R 2 , Q 2 (Leave-One-Out Cross Validation (LOO-CV), Leave-n-Out Cross Validation (LnO-CV)), RMSEE, F ratio, and Pvalue, and also statistical parameters of the test set, such as R 2 Obs vs. Pred, R 2 pred, and RMSEP. Apart from the Leave-One-Out Cross Validation, in the QSPR study was performed Leave-2-Out Cross-Validation (L2O-CV) and Leave-3-Out Cross-Validation (L3O-CV).
Optimal QSPR models for each pharmacokinetic parameter (logPS, logPS-brain, and logBB) were selected by use of statistical parameters of the training and test set (Tables 2-4).
In order to investigate the statistical significance of the R 2 and Q 2 and to test the model for overfitting due to the chance correlation the response permutation test (Y scrambling) is applied for all QSPR models. The R 2 -intercepts were less than 0.1 (upper limit is 0.4), while the Q 2 -intercepts were less than -0.1 (upper limit is 0.05) for all developed QSPR models. Thus the response permutation test results have proved good quality of the formed QSPR models.   Since all PLS coefficients of the QSPR (logPS) model are negative numbers (Figure 3a, Table 2) was concluded that all significant descriptors (Mi, H7m, R3s+, Hy, and TPSA(NO)) are in negative correlation with rate of brain penetration -logPS.
Also, decrease in hydrophilicity (Hy), topological polar surface area (TPSA(NO)), mean first ionization potential (Mi), H-indices (H7m), and R-indices (R3s+) of a ligand will lead to increase of rate of brain penetration (logPS). Constitutional descriptors are descriptors reflecting the chemical composition of a compound without any information about its molecular geometry or atom connectivity. The mean first ionization potential (such as Mi) of a molecule is amount of energy required to remove an electron from the molecule in the gaseous state.
Generally, the GETAWAY (GEometry, Topology, and Atom-Weights AssemblY) descriptors (40,41) are chemical structure descriptors derived from the Molecular Influence Matrix. H-indices (such as H7m) are based on the spatial autocorrelation formulas, weighting the molecule atoms by physico-chemical properties w together with 3D information encoded by the elements of the molecular influence matrix H. Rindices (such as R3s+) include some descriptors obtained by applying traditional matrix operators to the influence/distance matrix R and autocorrelations calculated by weighting the molecule atoms by physico-chemical properties w together with 3D information encoded by the elements of the influence/distance matrix. The H, R and maximal R+ indices are molecular descriptors based on spatial autocorrelation, encode information on structural fragments and, therefore, seem to be particularly suitable for describing differences in congeneric series of molecules. Also, GETAWAY descriptors are geometrical descriptors encoding information on the effective position of substituents and fragments in the molecular space and provide information about molecular size, shape, and specific atomic properties (40,41).
The hydrophilic factor (Hy) is a hydrophilicity descriptor defined by Todeschini et al (42).
The topological polar surface area (TPSA) is based on a group contribution method, calculated according to the model proposed by Ertl (43). The TPSA(NO) is topological polar surface area derived only from polar fragments with nitrogen and oxygen. The TPSA(NO) of a molecule is determined by the summation of tabulated surface contributions of the polar atom types. The topological polar surface area descriptors were successfully used in validation studies based on sets of published absorption data, including intestinal absorption, Caco-2 monolayer penetration, and blood-brain barrier penetration (43).

Training Set
Brain/plasma equilibration rate Primary ID Name logPS-brain (27) QSPR-predicted logPS-brain H-indices (such as H7m) are based on the spatial autocorrelation formulas, weighting the molecule atoms by physico-chemical properties w together with 3D information encoded by the elements of the molecular influence matrix H (40,41).
The number of donor atoms for H-bonds (nHDon) is a measure of the hydrogen-bonding ability of a molecule expressed in terms of number of possible hydrogen-bond donors. It is calculated by adding up the hydrogens bonded to any nitrogen and oxygen without negative charge in the molecule.
Weighted topological atom pairs T(X..Y), such as T (N..N), are sums of topological distances between all pairs of type X..Y, where X and Y referring to any heteroatom among N, O, S, P, F, Cl, Br, I.
The hydrophilic factor (Hy) is a hydrophilicity descriptor defined by Todeschini et al (42).
The hydrophilicity (Hy) and H-indices (H7m) are selected by both QSPR (logPS) and QSPR (logPS-brain) study as significant molecular determinant of the rate of brain penetration and brain/plasma equilibration rate of the examined compounds.
The number of heteroatoms (nHet) counts all the atoms that are neither hydrogen nor carbon.
Barysz matrices (Dz(w)) are weighted distance matrices accounting contemporarily for the presence of heteroatoms and multiple bonds in the molecule. They were defined on the basis of a generalization of Barysz weighting scheme in terms of conventional bond orders π* and any atomic property, such as spectral moment of order 1 from Barysz matrix weighted by ionization potential (SM1_Dz(i)) (44).
Burden matrices (B(w)) are augmented adjacency matrices derived from a H-depleted molecular graph as the following: the diagonal elements are atomic carbon-scaled properties (wi/wC); the off-diagonal elements corresponding to pairs of bonded atoms are the square roots of conventional bond orders; entries corresponding to terminal bonds are augmented by 0.1; all other matrix elements are set at 0.001. The AVS_B(s)average vertex sum from Burden matrix is calculated on the basis of the I-State weighting scheme.
The TPSA(NO) is topological polar surface area derived only from polar fragments with nitrogen and oxygen (43). The topological polar surface area (TPSA(NO)) is parameter selected by both QSPR (logPS) and QSPR (logBB) study as significant molecular determinant of the rate of brain penetration and extent of BBB permeation of the examined compounds.
Predictive potential of the QSPR (logBB) model was tested by use of leave-one-out cross validation of the training set (LOO-CV/Q 2 : 0.653, L2O-CV/Q 2 : 0.652, L3O-CV/Q 2 : 0.651, RMSEE:  Table 4). The statistical parameters indicated that the created QSPR (logBB) model has acceptable accuracy for predicting extent of BBB permeation (logBB) of the α-adrenergic and imidazoline receptor ligands. In order to investigate the statistical significance of the R 2 and Q 2 and to test the model for overfitting due to the chance correlation, the response permutation test (Y scrambling) is applied for all three created QSPR models. The R 2 -intercepts were less than 0.4 while the Q 2 -intercepts were less than 0.05 for the three developed QSPR models. Obtained results of the response permutation tests have proved that the formed QSPR models are not overfitted.
An efficient compression of the studied data was not possible with the PCA and obtained results required investigation of many twodimensional plots. Therefore, hierarchical clustering analysis (HCA) was used to explore the studied data set X (29 x 34) and to examine the similarities between the studied compounds. HCA helped to reveal the internal data structure and its clustering tendency.
The HCA results presented in Figure 4 were based on the Euclidean distance and the Ward linkage algorithm.
Because of very high similarity between I-II and III-IV PCA groups with A-B and C-D HCA clusters, respectively, we further examined HCAgroups A and B, as first subset, and HCA-groups C and D, as second subset, in correlation study with rate of brain penetration (logPS), extent of BBB permeation (logBB), and brain/plasma equilibration rate (logPS-brain) of the compounds.
Significant correlations were obtained between the chromatographic retention parameter (S at pH 7.4) and extent of BBB permeation (logBB) in A/B cluster (r(SpH7.4/logBB): 0.677) ( Figure  5a), and also between the chromatographic retention parameter (logKw at pH 9.1) and rate of brain penetration (logPS) in C/D cluster (r(logKwpH 9.1/logPS): 0.684) ( Figure  5b).   Positive sign of correlation coefficient between logKwpH9.1 and logPS (r(logKwpH9.1/logPS): 0.684) in C/D cluster indicate that ligands with lower logKwpH9.1 values will have lower logPS values and therefore decreased rate of brain penetration, while ligands with higher logKwpH9.1 values will have higher logPS values and therefore increased rate of brain penetration.
Results of the clustering and correlation studies could be readily used as time and cost efficient screening method for evaluation of brain penetration process of novel αadrenergic/imidazoline receptor ligands and related compounds.
The QSPR (logPS) study indicated on negative correlation between hydrophilicity (Hy), topological polar surface area (TPSA(NO)), mean first ionization potential (Mi), H7m indices, and R3s+ indices of the α-AR/IR ligands and rate of brain penetration (logPS). Therefore increase in Hy, TPSA(NO), Mi, H7m, and R3s+ values of a ligand will lead to decrease of rate of brain penetration (logPS), and vice versa.
The hydrophilicity (Hy) and H7m indices are selected by both QSPR (logPS) and QSPR (logPS-brain) studies as significant molecular determinant of the compounds for rate of brain penetration and brain/plasma equilibration rate.
The topological polar surface area (TPSA(NO)) is parameter chosen by both QSPR (logPS) and QSPR (logBB) studies as significant molecular determinant of the rate of brain penetration and extent of BBB permeation of the examined compounds.
The hydrophilicity (Hy) and topological polar surface area (TPSA(NO)) are common significant descriptors of QSPR (logPS)/QSPR (logPS-brain) and QSPR (logPS)/QSPR (logBB) models respectively. The observed negative correlations of the hydrophilicity and topological polar surface area on blood-brain penetrations process were in very good agreement with previously reported QSPR studies of brain penetration of other groups of organic compounds (45).
Prognostic capacity of the created QSPR (logPS, logPS-brain, logBB) models was proved by cross-and external validation.
Therefore structures of novel test compounds could be examined by the presented QSPR procedure that includes: molecular modeling, calculation of molecular parameters of the optimized molecular models, and prediction of the logPS, logPS-brain, logBB values by use of the formed QSPR (logPS, logPS-brain, logBB) models.
After PCA and HCA grouping were obtained good correlations between the chromatographic retention parameter (SpH7.4) and logBB in A/B cluster, and between the chromatographic retention parameter (logKwpH9.1) and logPS in C/D cluster.
Structural diversity of the examined drugs provide wide application domain of the QSPR models, which could be used for evaluation of brain penetration of related αadrenergic/imidazoline receptor ligands.