Predicting the Blood-Brain Barrier Permeability of New Drug-Like Compounds via HPLC with Various Stationary Phases

The permeation of the blood-brain barrier is a very important consideration for new drug candidate molecules. In this research, the reversed-phase liquid chromatography with different columns (Purosphere RP-18e, IAM.PC.DD2 and Cosmosil Cholester) was used to predict the penetration of the blood-brain barrier by 65 newly-synthesized drug-like compounds. The linear free energy relationships (LFERs) model (log BB = c + eE + sS + aA + bB + vV) was established for a training set of 23 congeneric biologically active azole compounds with known experimental log BB (BB = Cblood/Cbrain) values (R2 = 0.9039). The reliability and predictive potency of the model were confirmed by leave-one-out cross validation as well as leave-50%-out cross validation. Multiple linear regression (MLR) was used to develop the quantitative structure-activity relationships (QSARs) to predict the log BB values of compounds that were tested, taking into account the chromatographic lipophilicity (log kw), polarizability and topological polar surface area. The excellent statistics of the developed MLR equations (R2 > 0.8 for all columns) showed that it is possible to use the HPLC technique and retention data to produce reliable blood-brain barrier permeability models and to predict the log BB values of our pharmaceutically important molecules.


Introduction
The biological activity of drugs depends primarily on their pharmacokinetics. The expected pharmacological effect of a given drug can be observed if the pharmacokinetic processes provide its high concentration within the range of the receptor. The amount of drug in tissue and the time that remains an effective concentration depend on the fundamental processes that make up the pharmacokinetic phase of the drug's action, i.e., liberation (L), absorption (A), distribution (D), metabolism (M) and excretion (E). It is extremely difficult to predict the processes mentioned above because all of them are concentration-dependent and connected with the chemical structure of the agent. Since most drugs must pass through at least one cell membrane to provide the desired effect, for the rational design of drugs, it is vitally important to understand and to be able to predict the solute partitioning in the biomembranes. Drugs can cross membranes by passive or active transport [1][2][3]. While active transport is determined by compounds' affinities for specific transporters and it uses energy, the most Moreover, there is an increasing evidence of the convenience for modelling pharmacokinetic processes chromatographically, especially by reversed-phase liquid chromatography using biomimetic stationary phases. The octadecylsilyl (ODS) stationary phase provides a fast approach, but immobilized artificial membranes (IAMs) are more similar to the membranes of eukaryotic cells and therefore better mimic biological systems [10][11][12]. Artificial membranes are more similar to biological systems because they anchor synthetic phosphatidylcholine analogues to silica [13][14][15][16][17][18]. Cholesterol is one of the major components of many eukaryotic membranes and it seems highly likely that cholesterol immobilized on silica would offer similar possibilities. Currently, the stationary phases with immobilized cholesterol are becoming more and more popular and therefore they are increasingly used to study biological properties of different organic compounds [19,20].
In turn, the confirmed remarkable antiproliferative effects of compounds 12-17 (group III) may be of benefit in the treatment of human multiple myeloma cells that are susceptible and resistant to thalidomide as well as in human tumour cells of cervix and breast [25,26]. Molecules 1, 2, 4, 5, 6, 15, 19, 21, 22, 24, 28, 39, 63 and 64 have been reported as promising anticancer drug candidates, due to not only their proven significant antiproliferative activities in some human cancer cells but also less toxic effects for normal cells [22][23][24][25][26][27]. Furthermore, test compounds proved to be in vivo active when investigated in the central nervous system. Among analgesic active and relatively low toxic molecules (8)(9)(10)(11)32, 34, 39, 42, 48, 51 and 53), the structures 8, 42 and 51 have been shown to produce the strongest antinociceptive effect in mice [19,21,31,33]. been shown to possess the remarkable concentration-dependent potency against Herpes simplex virus type 1, while revealing a low toxicity to normal Vero cells and inhibiting the oxidatively-induced haemolysis of erythrocytes [27]. In turn, the confirmed remarkable antiproliferative effects of compounds 12-17 (group III) may be of benefit in the treatment of human multiple myeloma cells that are susceptible and resistant to thalidomide as well as in human tumour cells of cervix and breast [25,26]. Molecules 1, 2, 4, 5, 6, 15, 19, 21, 22, 24, 28, 39, 63, and 64 have been reported as promising anticancer drug candidates, due to not only their proven significant antiproliferative activities in some human cancer cells but also less toxic effects for normal cells [22][23][24][25][26][27]. Furthermore, test compounds proved to be in vivo active when investigated in the central nervous system. Among analgesic active and relatively low toxic molecules (8-11, 32, 34, 39, 42, 48, 51, and 53), the structures 8, 42, and 51 have been shown to produce the strongest antinociceptive effect in mice [19,21,31,33]. been shown to possess the remarkable concentration-dependent potency against Herpes simplex virus type 1, while revealing a low toxicity to normal Vero cells and inhibiting the oxidatively-induced haemolysis of erythrocytes [27]. In turn, the confirmed remarkable antiproliferative effects of compounds 12-17 (group III) may be of benefit in the treatment of human multiple myeloma cells that are susceptible and resistant to thalidomide as well as in human tumour cells of cervix and breast [25,26]. Molecules 1, 2, 4, 5, 6, 15, 19, 21, 22, 24, 28, 39, 63, and 64 have been reported as promising anticancer drug candidates, due to not only their proven significant antiproliferative activities in some human cancer cells but also less toxic effects for normal cells [22][23][24][25][26][27]. Furthermore, test compounds proved to be in vivo active when investigated in the central nervous system. Among analgesic active and relatively low toxic molecules (8-11, 32, 34, 39, 42, 48, 51, and 53), the structures 8, 42, and 51 have been shown to produce the strongest antinociceptive effect in mice [19,21,31,33]. been shown to possess the remarkable concentration-dependent potency against Herpes simplex virus type 1, while revealing a low toxicity to normal Vero cells and inhibiting the oxidatively-induced haemolysis of erythrocytes [27]. In turn, the confirmed remarkable antiproliferative effects of compounds 12-17 (group III) may be of benefit in the treatment of human multiple myeloma cells that are susceptible and resistant to thalidomide as well as in human tumour cells of cervix and breast [25,26]. Molecules 1, 2, 4, 5, 6, 15, 19, 21, 22, 24, 28, 39, 63, and 64 have been reported as promising anticancer drug candidates, due to not only their proven significant antiproliferative activities in some human cancer cells but also less toxic effects for normal cells [22][23][24][25][26][27]. Furthermore, test compounds proved to be in vivo active when investigated in the central nervous system. Among analgesic active and relatively low toxic molecules (8-11, 32, 34, 39, 42, 48, 51, and 53), the structures 8, 42, and 51 have been shown to produce the strongest antinociceptive effect in mice [19,21,31,33]. been shown to possess the remarkable concentration-dependent potency against Herpes simplex virus type 1, while revealing a low toxicity to normal Vero cells and inhibiting the oxidatively-induced haemolysis of erythrocytes [27]. In turn, the confirmed remarkable antiproliferative effects of compounds 12-17 (group III) may be of benefit in the treatment of human multiple myeloma cells that are susceptible and resistant to thalidomide as well as in human tumour cells of cervix and breast [25,26]. Molecules 1, 2, 4, 5, 6, 15, 19, 21, 22, 24, 28, 39, 63, and 64 have been reported as promising anticancer drug candidates, due to not only their proven significant antiproliferative activities in some human cancer cells but also less toxic effects for normal cells [22][23][24][25][26][27]. Furthermore, test compounds proved to be in vivo active when investigated in the central nervous system. Among analgesic active and relatively low toxic molecules (8-11, 32, 34, 39, 42, 48, 51, and 53), the structures 8, 42, and 51 have been shown to produce the strongest antinociceptive effect in mice [19,21,31,33].

Chromatographic Results
Retention parameters reported as the log k values were calculated by the expression: where tR and t0 are the retention times of the solute and a non-retained compound (citric acid), respectively. They were used to calculate the log kw values, i.e., logarithms of retention parameter in  [19,21] Group VII Molecules 2020, 24, x 4 of 22

Chromatographic Results
Retention parameters reported as the log k values were calculated by the expression: where tR and t0 are the retention times of the solute and a non-retained compound (citric acid), respectively. They were used to calculate the log kw values, i.e., logarithms of retention parameter in [22,23] Molecules 2020, 25, 487 5 of 23

Chromatographic Results
Retention parameters reported as the log k values were calculated by the expression: where t R and t 0 are the retention times of the solute and a non-retained compound (citric acid), respectively. They were used to calculate the log k w values, i.e., logarithms of retention parameter in the buffer as the mobile phase. For this purpose the Soczewiński-Wachtmeister's equation was used [36]: where ϕ is the volume fraction of organic modifier in the mobile phase; k and k w are retention parameters corresponding to mixed effluent and buffer as the mobile phase, respectively. The slope s is characteristic of a given solute and chromatographic system. Strong linear relationships between log k and ϕ values were found for all the compounds in the range of effluent composition examined (R 2 > 0.9). The log k w and s values obtained from particular chromatographic systems are presented in Table 2. The log k w values determined for the ODS (log k w, ODS ), IAM (log k w, IAM ) and Cholester (log k w , Cholester ) columns were intercorrelated and the following linear relationships with a very good statistical quality were obtained:   Moreover highly significant linear relationships were obtained between log k w and s values (intercepts and slopes of Equation (2)

Establishment of the LFER Model
The property of the substance can be predicted on the basis of the linear free-energy relationships (LFER), but to do so, the relationship between the chemical structure and the desired property should be identified [37]. A symbolic representation of LFERs model is the equation originally employed by Abraham et al. [38][39][40][41][42]: Here SP is a set of solute properties in a given system, e.g., log BB values. The independent values are solute descriptors: E is an excess molar refraction, S is the dipolarity/polarizability, A and B are the hydrogen bond acidity (donating ability) and basicity (accepting ability), respectively and V is the solute McGowan volume (cm 3 ·mol −1 /100). Coefficients c, e, s, a, b and v are characteristic for a given biphasic system and solute.
In this study, this equation was established for a training set of 23 azole compounds that were congeneric with those tested in our investigations. For these compounds, we obtained from the literature [43] the experimental log BB (BB = C brain /C plasma ) values for rats ( Table 3 49. This is an important information indicating that there are no significant inter-correlations of structural descriptors, i.e., E, S, A, B and V. On this basis, we can conclude that non-physical factors do not affect the parameters of Equation (10). The reliability and predictive potency of the model expressed by Equation (10) were estimated by leave-one-out (LOO) cross validation and the parameters that were obtained are presented in Table 4. Figure 1 shows the standardized coefficients for particular descriptors and it confirms the well-known qualitative relationships: compound polarity, i.e., dipolarity/polarizability, hydrogen bond acidity and hydrogen bond basicity expressed by S, A and B values, respectively, decreases the BBB permeation, while the compound size measured by the McGovan volume (V) as well as the excess molar refraction E (in a minor degree) contribute to increase of log BB values [41]. The PLS response plot is presented in Figure 2, which shows the linear regression between the predicted (calculated response) and experimental log BB values of the 23 compounds from Table 3. The residual versus leverage plot in Figure 3 proves that the model that was obtained is valid for the domain in which it was developed [44]. The warning leverage limit (h*) was calculated according to: where m is the number of descriptors and n is the number of observations (compounds) in the dataset. Table 4. Statistical parameters of cross-validation of MLR models described by Equations (10), (12), (13) and (14); MSE-mean square error, MSEcv*-mean square error of leave-one-out cross validation, MSEcv**-mean square error of leave-50%-out cross validation, PRESS*-predicted residual sum of squares of leave-one-out cross validation, PRESS**-predicted residual sum of squares of leave-50%-out cross validation.
Equation (10) was used to calculate the log BB values for our 65 pharmaceutically relevant compounds (Table 5).  Equation (10) was used to calculate the log BB values for our 65 pharmaceutically relevant compounds (Table 5).

Establishment of QSARs Models
Efforts to predict the biological activity (including the BBB permeation) based on the properties of substances led to the development of Quantitative Structure Activity Relationships (QSARs) and Quantitative Retention Activity Relationships (QRARs) methodology [37,[44][45][46][47][48]. Various models and approaches have been developed to predict the penetration of the blood-brain barrier based on various physicochemical properties of molecules, including the lipophilicity, molecular size, polarizability, polar surface area and the number of groups that can establish potential hydrogen bonds [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. It is reasonable to assume that the combination of theoretical and experimental data increases the reliability of the anticipated transport of the drug across the blood-brain barrier [64][65][66]. The chromatographic retention parameter is one of the most popular experimental values used to characterize the properties (lipophilicity/hydrophobicity) of compounds used in QRAR and QSAR studies. The solute retention depends on the changes in free energy that are associated with the distribution of the solute between the mobile and stationary phases in a given chromatographic system. Thus, it is possible to use the values obtained on HPLC columns that imitate biomembranes for modelling the blood-brain barrier permeation.
In our investigations in which we modelled the blood-brain permeation of 65 biologically active molecules, the chromatographic lipophilicity (log k w ) ( Table 2), polarizability (α) and topological polar surface area (TPSA) ( Table 5)  The statistics of Equations (12)- (14) were very good, i.e., R 2 > 0.8 for all chromatographic systems and all variance inflation factors (VIF < 5) indicated that the variables were correlated moderately. The reliability of the MLR models, as expressed by Equations (12)-(14), were estimated by leave-one-out as well as leave-50%-out cross validation (Table 4). In each case, the log k w and α values provided positive inputs to the log BB, while TPSA decreased the permeation of the blood-brain barrier (Figure 4). The statistics of Equations (12)- (14) were very good, i.e., R 2 > 0.8 for all chromatographic systems, and all variance inflation factors (VIF < 5) indicated that the variables were correlated moderately. The reliability of the MLR models, as expressed by Equations (12)- (14), were estimated by leave-oneout as well as leave-50%-out cross validation (Table 4). In each case, the log kw and α values provided positive inputs to the log BB, while TPSA decreased the permeation of the blood-brain barrier ( Figure  4).    The relationships showed that molecular polarizability and lipophilicity promote increases in the log BB, while polar surface area decreased the ability of a substance to cross the BBB. The correlations between the log BB values calculated according to the LFER model (Equation (10)) and the optimized QSARs models, i.e., by Equations (12)- (14) are presented in Figures 5-7, which shows the response plots obtained by PLS for particular stationary phases.           Figure 7. PLS response plots obtained for Equation (14).
The relationships showed that molecular polarizability and lipophilicity promote increases in the log BB, while polar surface area decreased the ability of a substance to cross the BBB. The correlations between the log BB values calculated according to the LFER model (Equation (10)) and the optimized QSARs models, i.e., by Equations (12)- (14) are presented in Figures 5-7, which shows the response plots obtained by PLS for particular stationary phases. To assess the significance of chromatographic parameters, the lipophilicity descriptors, log k w were compared with partition coefficients in the n-octanol-water system, i.e., the log P values. The relationships between log P values calculated from molecular structures of the tested compounds and obtained by use of Alog P s algorithm [67,68] and their chromatographic factors (i.e., log k w, ODS , log k w , IAM and log k w, Cholester , respectively) were established. Good linear correlations between these descriptors (R > 0.8), that are observed in Figure 8, confirmed that chromatographic parameters can be used as lipophilicity descriptors in case of the studied compounds ( Figure 8 The statistics of Equation (15) proved to be very good and similar to those obtained for Equations (12)- (14), which confirms their ability in predicting the blood brain barrier permeation.
The relationships showed that molecular polarizability and lipophilicity promote increases in the log BB, while polar surface area decreased the ability of a substance to cross the BBB. The correlations between the log BB values calculated according to the LFER model (Equation (10)) and the optimized QSARs models, i.e., by Equations (12)- (14) are presented in Figures 5-7, which shows the response plots obtained by PLS for particular stationary phases.

Instrumental
Shimadzu Vp (Shimadzu, Izabelin, Poland) liquid chromatographic system equipped with LC 10AT pump, SPD 10A UV-Vis detector, SCL 10A system controller, CTO-10 AS chromatographic oven and Rheodyne injector valve with a 20 µL loop was applied in HPLC measurements. Three stationary phases were employed:

Chromatographic Conditions and Test Substances
As mobile phases buffer-acetonitrile mixtures were used. The buffer was prepared from 0.01 mol L −1 solutions of Na 2 HPO 4 and citric acid and the pH 7.4 value was fixed before mixing with organic modifier. With the ODS column acetonitrile concentration in the effluent, expressed as a volume fraction (ϕ, v/v), was changed in the range 0.3-0.6, with the constant step of 0.1. The flow rate was 1 mL min −1 . With the IAM column acetonitrile concentration was changed in the range 0.2-0.5, also with the constant step of 0.1 and the flow rate was 1.3 mL min −1 . With the Cosmosil Cholester column acetonitrile concentration was changed in the range 0.4-0.6, with the constant step of 0.05 and the flow rate was 0.4 mL min −1 . Samples of test compounds were dissolved in acetonitrile-c.a. 0.005 mg mL −1 . All the compounds proved to be in the neutral form in solution under experimental conditions and had values of peak asymmetry factor in the acceptable range. They were detected under UV light at 210 and 254 nm. All measurements were carried out at 25 • C. The dead time values were measured from non-retained compound (citric acid) peaks. All reported log k w values are the average of at least three independent measurements. The extrapolated retention coefficients (logs k w ) achieved by HPLC on ODS, IAM and Cholester stationary phases were used for modelling the log BB permeation of 65 drug-like compounds employed as a whole test set (Table 1).

Discussion
The usefulness of HPLC with three different reverse-phase columns (including two imitating biosystems) for predicting the blood-brain barrier (BBB) permeability of 65 structurally related drug-like molecules was highlighted in our investigations. QSAR models predicting the BBB permeation were built on the basis of experimentally accessible log k w values of the test molecules together with their important in silico molecular descriptors. The obtained results confirmed that all three stationary phases, i.e., octadecylsilane, immobilized artificial membrane and cholesterol immobilized on silica gel analogously described the lipophilic properties of the studied solutes (Equations (3)- (5)).
In our studies the extrapolated retention parameters (logs k w ) were used as they are preferred in QSARs instead of the isocratic log k values and usually employed in correlation studies with in silico molecular descriptors and drug-likeness properties in case of pharmaceutics and drug-like molecules. It should be noted that chromatographically derived retention parameters are very useful descriptors in QSAR modelling as the partitioning process between the stationary and mobile phase of a solute investigated mimics a membrane penetration process of a pharmaceutic or potential drug candidate [19,21,33,37].
Highly significant linear relationships were obtained between intercepts and slopes of Equation (2), i.e., the log k w and s values, for particular reversed-phase stationary phases. These correlations confirmed not only the congenereity between compounds that were investigated, but also suggested that the log k w and s values may be considered as alternative lipophilicity descriptors [19,21,37] in case of structurally related small molecules that were tested. In our studies compounds bearing more hydrophobic substituents revealed the greater s values. This observation is consistent with other research findings showing that more hydrophobic molecules reveal greater slopes [21]. According to the background retention theory the s values are related to the solute/mobile phase and the solvent/stationary phase net interactions [21,36,37].
The obtained results showed that the chromatographic retention parameters obtained using three stationary phases recruited as well as important in silico molecular descriptors can be recommended to derive the reliable QSAR models for predicting the blood-brain barrier permeability in case of our structurally related small molecules, considered as a test set of potential drug candidates.
The calculated log P values were obtained by using Alog P s algorithm and compared with the experimental log k w, ODS , log k w , IAM and log k w, Cholester values, respectively. This estimation was essential to check the validity of the obtained results through correlation with the log BB values.

Conclusions
Experimental literature data of the log BB (for rats) for a training set of 23 biologically active compounds (including drugs) were correlated against five solute descriptors (E, S, A, B and V) and the established equation (Equation (10)) was validated. The standardized coefficients obtained for particular descriptors confirmed that the compound polarity, i.e., dipolarity/polarizability (S), hydrogen bond acidity (A) and hydrogen bond basicity (B) decreases the blood-brain barrier (BBB) permeation while the compound size measured by the McGovan volume (V) and the excess molar refraction (E) contribute to increase in the log BB values. The Equation (10) was used to calculate the log BB values for 65 newly synthesized compounds being considered as potential drugs.
The blood-brain barrier permeability of the compounds that were tested was modelled by three descriptors, i.e., the chromatographic lipophilicity (log k w ), polarizability (α) and topological polar surface area (TPSA). Using a simple statistical model (i.e., MLR), three structure-activity relationships were obtained for each chromatographic system on endcapped octadecylsilyl, immobilized artificial membrane and cholesteryl stationary phases (Equations (12)- (14)). The log BB values calculated according to Equation (10) and predicted from Equations (12)-(14) were compared and highly significant relationships were obtained between them. The relationships were confirmed by leave-one-out as well as leave-50%-out cross validation, implying that the models are robust and reliable. The results that were obtained showed that, in the case of the compounds that were studied (65 weak organic bases), each of the stationary phases used in the chromatographic measurements was equally useful. From practical and economic perspectives, the Cholester microcolumn is recommended because it allows the acquisition of more data in a shorter time with lower costs. We showed that it is possible to use the HPLC technique to build a reliable model for predicting which our organic compounds (congeneric in structure to the training set of azole molecules) can penetrate the blood-brain barrier in rats. The investigations highlighted the key role of chromatographic techniques and QSARs methods in reducing unethical animal testing.
The presented results will be particularly useful in further more extensive in vivo research, which is planned to be carried out on our small molecules considered as potential drugs.