One hundred ten compounds of diverse structures (actives and excipients used in pharmaceutical preparations) were studied by RP-18 HPLC with acetonitrile-pH 7.4 phosphate buffer 1 : 1 (v/v) as the mobile phase. The relationships between the BBB permeation coefficients and the chromatographic parameters log _{f} and _{f}/PSA known from our earlier studies. It was found that the correlations between the BBB permeability and the HPLC data are slightly worse than those achieved for the thin-layer chromatographic data. MLR analysis based upon the physicochemical data confirmed the value of the molecular descriptors, related to the CNS bioavailability. These variables, combined with the HPLC data, made it possible to generate computational models, explaining 70–96% of the total variance of the CNS bioavailability. Contrary to TLC _{f}, the advantage of the modification of HPLC log

The blood-brain barrier (BBB) is a static anatomic barrier but also a dynamic barrier in which protein transporters of efflux and influx are active. The most important transporters are glycoprotein P (P-gp) and organic anions transporting polypeptides (OATP family) [

The compounds that reach the CNS are defined as BBB+ and the molecules of the limited CNS availability as BBB−. Classification of the BBB+/BBB− type may be based upon the values of log

The parameter based on kinetic studies of the BBB penetration ^{−1}) is the measure of the observed BBB permeability and ^{2}/g) is the surface area of vascular endothelium. PS in the physical meaning is the constant of one-way flux level (_{in}), corrected with the brain flux value [

Threshold values of the log

Over the last 20 years, several different methods to determine the CNS bioavailability have been proposed based upon log

The practical approach by the “

Another group of analyses are

Passive diffusion through the BBB is one of the most frequently investigated pharmacokinetic processes. One can say that a low passive diffusion level through the BBB (constant log

Although many types of descriptors are used to model the BBB permeation, four are preferred and appear in many acceptable models. The key molecular descriptors are PSA (polar surface area), log

In 1994, the so-called solvation parameters were introduced to the BBBp analysis [

At some earlier stage, the same variables made it possible to successfully distinguish between benzodiazepine derivatives (211 compounds) belonging to 4 groups differing in their site of action. Biological targets within the CNS or outside of it were the basis for full discrimination of these groups [

The BBB permeability may be reflected by column and thin-layer chromatographic data (retention factors _{f}, and _{M}, retention time _{k}, and retention volume _{k}) [_{f} and a novel parameter _{f}/PSA, supported by a set of physicochemical data. It was confirmed that the generated models may be successfully applied to compounds of different structures and increasing the number of cases did not diminish the predictive ability of the models, but on the contrary, in some situations, it increased it. In total, a group of 154 structurally diverse molecules was investigated; this group included the set of 110 currently investigated structures.

The log _{f}/PSA) exhibited a significant stability of the threshold limit between the CNS+ and CNS− compounds in all our experiments, involving a group of CNS+ drugs [

Having obtained such favorable results of the investigations involving the simple RP-18 TLC stationary phase, we wished to test the applicability of the RP-18 HPLC data obtained using the phase system as described earlier for the TLC models [

Our current HPLC analysis has involved 110 compounds used in pharmaceutical preparations (actives or excipients). It was our objective to select the model of the greatest predictive ability and, at the same time, as rapid, low-cost, and resistant to the structural diversity of analytes as possible. The number of cases in our current study has been reduced to 110 because of the limited availability of information on the CNS activity of some analytes (in our previous report [

One hundred ten drugs analyzed during these investigations (Figure

HPLC was performed with the Perkin-Elmer series 200 HPLC apparatus equipped with a UV detector (210 nm) and the LiChospher 100 RP-18 (5 ^{−1}. All compounds were injected as 0.1 mg·mL^{−1} solutions in methanol (injection volume–1

The physicochemical properties of compounds

The molecular descriptors for the compounds investigated during this study were calculated with HyperChem 7.0 [^{3})), energy of the highest occupied molecular orbital (eH (eV)), and energy of the lowest unoccupied molecular orbital (eL (eL × 10) (eV))). The distribution coefficient (log ^{2}), the number of H-bond donors (HD), and the number of H-bond acceptors (HA) were calculated using ACD/Labs 8.0 software [

One hundred ten compounds analyzed during these investigations were divided into two subsets: the training set (compounds with the known experimental BBB permeability (BBvivo), cases

The physicochemical parameters related to the compounds’ BBB permeability were previously determined [

The statistical significance (^{2} > 0.4, one of them was removed.

Validation of the correlation models was carried out by the general internal cross-validation procedures: “leave-one-out” (LOO) and “leave-many-out” (LMO). In the LOO approach, one element is removed from the whole data set and used to verify the model generated with the remaining _{PRESS}), and standard deviation of error of prediction (SDEP). The LMO cross-validation was applied by deleting 25% of the compounds in four cycles and predicting the BBB permeability of compounds deleted in each cycle from the corresponding equations derived from the reduced data set. Some criteria for the reliability prediction and robustness of the models are suggested in References [

Investigations of the CNS activity of the drugs analyzed throughout this study were based on the discriminant function analysis (DFA) using the physicochemical and chromatographic data connected with the BBB permeability and selected by MLR analysis. All results were compared with the models obtained and tested in the previous investigations [

Discriminant function analysis is a multivariate technique that has two purposes: to separate cases from distinct populations and to allocate new cases into previously defined populations [^{2} tests of subsequent roots. Using statistically significant discriminant functions as the basis, canonical values were determined for the particular grouping variables. The scatter diagrams of the canonical values of the subsequent cases for the first two roots determined in the course of the analysis cannot be drawn to evaluate the discriminant power of the obtained models because there are only two discriminated groups. The final phase of the qualitative analysis of the compounds was to determine the classification functions for each activity group. After calculation of the classification scores for a case, it is easy to decide how to classify it: in general, we assign a case to a group for which it has the highest classification score. The tool used to determine how well the classification functions predict the group membership of cases is a classification matrix. The classification matrix shows the number of cases that were correctly classified (on the diagonal of the matrix) and those that were incorrectly classified.

The obtained discriminant models were evaluated by classification of 61 cases not included in the model (test set

In our previous investigations [

At first, the correlations of the BBB permeability parameters with the chromatographic data log ^{2} = 0.17, and ^{2} = 0.17, and _{f} and _{f}/PSA parameters (^{2} = 0.15;

The correlation of the same chromatographic data with the computed permeability parameter B2 used in our earlier investigations has also been considered. This part of our study involved only the cases with the established BBvivo value (^{2} = 0.11, and ^{2} = 0.10; _{f} and _{f}/PSA parameters (^{2} = 0.44;

In our earlier research [^{2} = 0.19; ^{2} = 0.18, and _{f} and _{f}/PSA has once again proved the advantage of the TLC model [^{2} = 0.30;

Studying the group of compounds

The compounds _{LOO} and _{LMO}. We have therefore considered it unnecessary to process the MLR analysis of all physicochemical data collected earlier [

In the group of 46 compounds with the established BBB bioavailability, the significance of the following parameters was presented [^{3})), correlated with the dependent variable BBvivo (^{2} = 0.59;

The strongest correlations with the calculated measure of the BBB permeability B2 were for DM, HA, and HD. The parameters of the equation proposed earlier [

The same variables (HD, HA, and DM) were efficient in the group of 154 compounds [

Even if the results change following the reduction of a group of studied cases, this comparison may be considered the confirmation of the significance of all molecular descriptors in studies of the BBB permeation.

Our further investigations concentrated on the possibility of using RP-18 HPLC to partially mimic the physiological conditions of crossing the BBB. It was assumed that the results of biochromatographic experiments should improve the predictive capabilities of purely computational models.

RP-18 HPLC data alone gave statistically significant correlations neither with BBvivo (

In the next MR analysis, these physicochemical data were combined with HPLC chromatographic parameters (log

The model (Figures

Plot of observed vs. predicted values (equation (

Plot of residues vs. predicted values (equation (

The improvement in the result of BBvivo variation studies after the chromatographic data have been introduced suggests the possibility of using these data in modeling of the variation of the computed BBB permeation descriptor B2. Multiple regression analysis was performed first for the group of compounds

In the case of

Plot of observed vs. predicted values (equation (

Plot of residues vs. predicted values (equation (

Analysis of all the cases

Plot of observed vs. predicted values (equation (

Plot of residues vs. predicted values (equation (

All the models presented above point to a leading role of the physicochemical parameters. Introduction of the chromatographic data to the stepwise MR analysis confirms their relationship with BBvivo and B2, increasing the correlation coefficient or improving other models’ parameters.

In all our previous experiments based on thin-layer chromatography, the parameter _{f}/PSA played a visibly important role [_{f} values studied for the same group of 110 cases varied across a very broad range (0.1–0.9 for CNS+ and 0.5–0.9 for CNS−) [_{f}/PSA parameter in predictions of the BBB permeation turned our attention to the (log

In discriminant function analysis (DFA), a qualitative parameter CNS was used as a grouping variable. The compounds described in the literature and the database [

At first, the stepwise DFA analysis was performed for 40 cases with known CNS bioavailability (compounds

The classification functions for each group of activity CNS

The outcome of the last DFA was verified demonstrating the high classification power of the model (Wilks’ lambda parameter = 0.337195; ^{2} = 38.59180;

The reliability of the model derived from the DFA was determined by a cross-validation test based on the leave-one-out methodology. All cases with measured BBB permeability (BBvivo) (

Classification matrix for the model with discriminating variables (HD, eH,

Observed | Percentage of correctly classified cases | CNS− | CNS+ |
---|---|---|---|

CNS− | 100.0000 | 6 | 0 |

CNS+ | 100.0000 | 0 | 34 |

Total | 100.0000 | 6 | 34 |

In order to validate the methods and confirm the discriminating value of the descriptors selected in the course of this study, a group of 61 cases without measured BBvivo but with the BBB permeability known from the database [

The classification functions (

On the basis of the DFA classification function, obtained for 40 cases with the established BBvivo values, 5 out of 20 CNS

Just like in the case of the training set (

Classification matrix for the model with discriminating variables HD, log

Observed | Percentage of correctly classified cases | CNS− | CNS+ |
---|---|---|---|

CNS− | 84.61539 | 22 | 4 |

CNS+ | 98.66666 | 1 | 74 |

Total | 95.04951 | 23 | 78 |

The classification functions for each group of CNS− and CNS+ activity were calculated:

The outcome of the last DFA was verified demonstrating the high classification power of the model (Wilks’ lambda parameter = 0.429066, ^{2} = 81.65287,

Only 5 cases in the group of 101 compounds were incorrectly classified.

Both of the chromatographic parameters are discriminating variables.

The predictive values of the determined classification functions (equations (

Summarizing the results of the discriminant analysis, we have concluded that all the variables in the model are statistically significant.

Application of the RP-18 TLC analysis for the prediction of the CNS bioavailability of solutes has been a starting point of our RP-18 HPLC model. The mobile phase consisting of phosphate buffer with pH 7.4 and acetonitrile was used, and a novel strategy to predict the BBB permeation was developed using the RP-18 HPLC-derived chromatographic data [

The correlation of the BBB permeation coefficient and chromatographic parameters log _{f} and _{f}/PSA descriptors, explaining

The correlation of the same chromatographic data with the calculated and previously used permeability coefficient B2 has also been studied [_{f} and _{f}/PSA descriptors (^{2} = 0.44) [_{f} and _{f}/PSA variables has once again pointed to the advantages of the TLC model that explains the total variance in the group of 154 cases in over 30%. The level of correlation BBvivo/B2 does not change in both experiments.

MLR analysis based upon the physicochemical data confirms the value of the molecular descriptors, related to the CNS bioavailability. These variables, combined with the chromatographic data, make it possible to generate computational models, explaining 70–96% of the total variance of the CNS bioavailability. All of our models of the BBB permeability point to a leading role of the physicochemical parameters. Introduction of the chromatographic data to the stepwise MR analysis confirms their relationship with BBvivo and B2, increasing the correlation coefficient or improving other model parameters. Contrary to the previous experiments [

DFA for all the 101 cases with the known CNS± parameter resulted in 95% correct classification. On the basis of this result, we have concluded that the RP-18 HPLC analytical model is entirely successful in studies and predictions of the BBB permeability.

The final comparison of the RP-18 TLC and RP-18 HPLC analytical models points to a small predictive advantage of TLC. The stability of _{f}/PSA with the repetitive threshold limit for compounds that cross the BBB (CNS+ ≥ 0.009) and those that do not enter the brain (CNS− < 0.009) [

The selection of a better chromatographic model to predict the CNS bioavailability is facilitated by the comparison of timing, simplicity, and costs of both experiments.

The molecular descriptors and chromatographic data used to support the findings of this study are included within the supplementary information file.

The authors declare that there are no conflicts of interest related to the publication of this manuscript.

This work was supported by an internal grant of the Medical University of Lodz (no. 503/3-016-03/503-31-001).

Figure 1: structures of compounds

Table 1: calculated descriptors for compounds

Table 2: statistics for Equations (

Table 4: calculated probability classification for compounds