Balanced Permeability Index: A Multiparameter Index for Improved In Vitro Permeability

Abstract

The optimization of passive permeability is a key objective for orally available small molecule drug candidates. For drugs targeting the central nervous system (CNS), minimizing P-gp-mediated efflux is an additional important target for optimization. The physicochemical properties most strongly associated with high passive permeability and lower P-gp efflux are size, polarity, and lipophilicity. In this study, a new metric called the Balanced Permeability Index (BPI) was developed that combines these three properties. The BPI was found to be more effective than any single property in classifying molecules based on their permeability and efflux across a diverse range of chemicals and assays. BPI is easy to understand, allowing researchers to make decisions about which properties to prioritize during the drug development process.

Human effective permeability across the jejunum membrane has been quantitatively linked to the extent of absorption in human oral experiments for highly soluble drugs.¹ This relationship has enabled the use of certain cell lines, such as Cancer coli (Caco-2) cells, as suitable tools to rank order marketed drugs based on their jejunum permeability.^2,3 Madin–Darby canine kidney (MDCK) cell lines have also been increasingly used in the pharmacokinetics (PK) field over the last two decades to assess passive permeability in a high-throughput assay.^4,5 Similar to Caco-2 cells, measurements of passive permeability in MDCK cells are well-correlated with human jejunum permeability and bioavailability.⁶ Additionally, MDCK cells can be transfected with P-glycoprotein (P-gp/MDR1) and/or breast cancer resistance protein (BCRP) to assess the risk of efflux mediated by specific membrane transporters that impairs central nervous system (CNS) disposition.⁷

The availability of well-validated and robust in vitro assays provides drug discovery scientists with tools to build rational structure–activity relationships with respect to oral and CNS absorption. Importantly, the resulting in vitro permeability data sets have allowed linking passive permeability and P-gp-mediated efflux to a small number of physicochemical properties, such as molecular weight (MW), heavy atom count (HAC), polarity, number of hydrogen bond donors/acceptors, lipophilicity (e.g., LogD), charge, and rigidity.⁸⁻¹² These physicochemical properties have also been used alongside molecular descriptors in machine learning (ML) models. While ML models have shown promising accuracy at predicting permeability and efflux, these models are not readily interpretable. Additionally, it can be challenging to assess the applicability domain of the predictions.¹³ To recover interpretability while maintaining predictive power, one strategy is to combine physicochemical properties and well-validated cutoffs into simpler rules. This approach was popularized by Pfizer’s CNS multiparameter optimization model (CNS-MPO). MPOs remain a powerful and intuitive tool for guiding chemistry design.^14,15

An analysis of the Genentech compound collection demonstrated that physicochemical properties associated with poor permeability (such as large size, high polarity, and low lipophilicity) were also often correlated with P-gp recognition.¹² A similar analysis of 20,000 compounds in the Bayer collection found that permeable compounds are most likely to have a calculated LogD (cLogD) value within the preferred range of 3 to 3.5. However, compounds with lower molecular weight were more likely to be permeable even if their cLogD value fell outside of that range.¹⁶

In this study, we present a new metric, the Balanced Permeability Index (BPI), that combines three physicochemical properties associated with permeability: size, polarity, and lipophilicity. In an analysis of the Bristol-Myers Squibb (BMS) compound collection, we show that this simple and interpretable metric classifies molecules by permeability and efflux classes better than any one of its individual components alone. The guidelines resulting from the interpretation of BPI are in line with previously published work: molecules that are smaller, less polar, and more lipophilic lead to better permeability. An additional learning from BPI is that high polarity (typically linked to low permeability and high efflux) can be balanced by the addition of lipophilic moieties as long as the molecule size is kept in check. This can inform nontraditional small molecule projects, for which the starting point for compound optimization may lie outside of the boundaries traditionally employed in MPO scores and medicinal chemistry rules of thumb. The property distributions for the BMS compounds included in this analysis are shown in Figure 1A.

Figure 1.

Comparison of the ability of BPI against other parameters to distinguish permeable compounds. (A) Distributions of the heavy atom count (HAC), HPLC LogD_7.4, and measured exposed polar surface area (EPSA) for the 2393 compounds included in this analysis. (B) Enrichment of permeable Genentech (GNE) compounds gMDCK Papp A-to-B > 10 × 10^–6 cm/sec² and gMDCK-MDR1 ER < 3 reported in ref (12) using the calculated TPSA (green), reported LogD at pH 7.4 (blue), and BPI (red) calculated from those values. (C) Enrichment of highly permeable BMS compounds Caco-2 Papp A-to-B > 10 × 10^–6 cm/sec² and Caco-2 ER < 3 using the measured EPSA (green), HPLC LogD_7.4 (blue), and BPI (red) calculated from those values, and compared to the Pfizer CNS MPO (yellow) described in ref (15).

We define the experimental Balanced Permeability Index (BPI) as

where LogD is the partition coefficient characterizing lipophilicity (measured or calculated, at the pH of interest), PSA is polar surface area, and HAC is heavy atom count.

To investigate the effectiveness of BPI in classifying compounds with high in vitro permeability, we first turned to the Genetech compound data set.¹² Although the chemical structures were not available as part of the released data set, the authors reported topological polar surface area (TPSA), HAC, and experimentally determined LogD at pH 7.4, and measured permeability in two engineered MDCK cell lines: gMDCKI in which endogenous P-gp transporters were knocked out and gMDCKI-MDR in which the MDR transporter was knocked into the gMDCKI cell line background. We were able to validate the ability of the BPI to enrich high-permeability compounds, defined as gMDCKI A-to-B Papp > 10 × 10^–6 cm/s, and compounds that are not P-gp efflux substrates, defined as gMDCKI-MDR1 Efflux Ratio < 3. Our initial analysis compared the ability of BPI, TPSA, and LogD at pH 7.4 to distinguish those compounds using receiver operating characteristic (ROC) plots (Figure 1B). In this data set, BPI is better able to enrich the low-efflux compounds when P-gp-mediated efflux is considered. On the other hand, the added utility of BPI in enriching passive permeability (in the absence of P-gp transporters) when compared to TPSA is limited in this data set.

Next, we analyzed the BMS chemical compound collection. We did not rely on calculated LogD, instead measuring lipophilicity with a high-throughput chromatographic LogD assay at pH 7.4 (HPLC LogD_7.4). This chromatographic assay was similar to what has been previously reported.¹⁷ It utilized a retention-time-based approach where compounds, along with a set of calibration standards with known LogD values, were analyzed with an isocratic HPLC-UV/MS method with a mobile phase of 60% methanol and 40% ammonium acetate (5 mM) on a YMC C18 ODS-A column (2.1 × 50 mm, 5 μm) at a flow rate of 0.5 mL/min. The LogD values of the compounds were then derived from comparison of their retention times to those of the standards (p-methoxyphenol, p-cresol, 1-naphthol, thymol, diphenyl ether, and hexachlorobenzene). No unexpected or unusually high safety hazards were encountered.

TPSA is calculated solely based on the 2-dimensional structure of the molecule, which may not accurately represent the true 3-dimensional polar surface area of a molecule in solution. In our analysis, we utilized the experimentally determined exposed polar surface area (EPSA). The original EPSA assay was described by Goetz et al., and the data in this work was measured by using our in-house EPSA assay that was modified for higher throughput.¹⁸ For small compounds with few rotatable bonds, TPSA is a reliable indicator of compound polarity in solution and, in those cases, may be a useful tool for assessing passive permeability, as demonstrated in the Genentech data set. However, for larger, more flexible drug-like molecules that have the potential for intramolecular hydrogen bonds, TPSA is not an accurate reflection of the EPSA measured in solution. In fact, a study of more than 11,450 EPSA data points in the BMS compound collection found no correlation to the calculated TPSA value, with an R² value of 0.07 (not shown, manuscript in preparation).

We evaluated a total of 2393 compounds with available data for both EPSA and HPLC LogD_7.4. To ensure the reliability of our analysis, we applied strict cutoffs to the permeability assay data, limiting the recovery between 80% and 120%. Compounds failing to satisfy the set criteria could be trapped in the membrane, degraded, or metabolized at rates competing with the intrinsic membrane permeability rate. These mechanisms have the potential to compromise the estimate of the intrinsic permeability of the test compound. Our analysis included 690 compounds with measured passive permeability data in a MDCK cell line with knocked-out endogenous canine MDR1 P-gp efflux transporter (MDCK-KO), and 481 molecules with permeability data in the Caco-2 cell line.¹⁹ We excluded compounds for which efflux could not be accurately quantified due to low permeability outside the quantifiable range. Highly permeable molecules were defined as those with Caco-2 Papp A-to-B permeability > 10 × 10^–6 cm/sec², Caco-2 Efflux Ratio < 3, and MDCK-KO Papp A-to-B permeability > 10 × 10^–6 cm/sec², and low permeability is defined as Caco-2 Papp A-to-B permeability < 1.5 × 10^–6 cm/sec (the lowest level of detection), Caco-2 Efflux Ratio > 10, and MDCK KO Papp A-to-B permeability < 10^–6 cm/sec².

The analysis of BMS compounds revealed that the use of the BPI metric provides an advantage over relying solely on EPSA or HPLC LogD_7.4 alone to classify compounds in the Caco-2 high permeability and low efflux bin (Figure 1C). While each parameter alone can aid in identifying permeable compounds, BPI leads to better enrichment and higher early enrichment. We also compared our results to those of the Pfizer CNS MPO, which did not enrich the permeable compounds in the Caco-2 cell line in this collection. It is important to note that most compounds in the collection were not specifically designed to be brain-penetrant. To evaluate the predictive ability of each classifier, we used the area under the ROC curve, a common metric used to characterize the predictive ability of a given classifier. Our results demonstrated that BPI is more predictive than EPSA and HPLC LogD_7.4 alone across all the permeability and efflux assays (Table 1).

Table 1. ROC-AUC for Enrichment of Highly Permeable and Low Efflux Compounds^a.

	gMDCKI AB > 10	gMDCK-MDR1 ER < 3	Caco-2 AB > 10	Caco-2 ER < 3	MDCK-KO AB > 10
Dataset size	135	135	481	390	690
BPI	0.90	0.84	0.91	0.88	0.93
TPSA/EPSA	0.88	0.70	0.84	0.73	0.74
LogD7.4	0.60	0.70	0.66	0.74	0.89
CNS MPO	Na	NA	0.45	0.3	0.53

^aThe gMDCKI and gMDCK-MDR1 datasets in the white columns are reported in ref (12), while the highlighted Caco-2 and MDCK-KO columns represent data from proprietary BMS datasets.

The distributions of BPI, EPSA, HPLC LogD_7.4, and HAC for the high-, medium-, and low-permeability/efflux bins in the BMS collection are shown in Figure 2. The distributions were found to be statistically different (Kruskal–Wallis one-way ANOVA test, p < 0.05) in most cases. One exception is the MDCK-KO Papp A-to-B permeability, where the difference with the HPLC LogD_7.4 distribution was not statistically significant (p > 0.05). These findings further support the idea that BPI is more predictive of passive permeability and low efflux than relying solely on the physicochemical properties included in the index. It is important to note that we did not filter the molecules based on size, pK_a, or chemical class, and our analysis included molecules with different sizes, polarities, and lipophilicities, with ranges of HAC between 15 and 80, EPSA between 40 and 350, and HPLC LogD_7.4 between −1 and 6.5. The lack of compound-related exclusion criteria, in addition to the translatability across chemical spaces, cell lines, and data sets from different companies, strongly suggests that the BPI metric can generalize beyond the data used in the analysis.

Figure 2.

Distribution of BPI and other physicochemical properties across different permeability and efflux ranges. The distribution of (A) BPI, (B) EPSA, (C) HPLC LogD_7.4, and (D) HAC split by permeability bins as measured by the Caco-2 A-to-B forward permeability (blue boxes), the Caco-2 efflux ratio (pink boxes), and the MDCK-KO A-to-B forward permeability (yellow boxes). Compounds are binned according to permeability as follows: highly permeable molecules are defined as Caco-2 Papp A-to-B permeability > 10 × 10^–6 cm/sec², Caco-2 Efflux Ratio < 3, and MDCK-KO Papp A-to-B permeability > 10 × 10^–6 cm/sec², and low permeability is defined as Caco-2 Papp A-to-B permeability < 1.5 × 10^–6 cm/sec² (the lowest level of detection), Caco-2 Efflux Ratio > 10, and MDCK KO AB permeability < 10^–6 cm/sec², and the middle bin falls between those two ranges.

It is suggested that cut-offs be associated with BPI to provide tangible objectives during compound optimization. The recommended BPI cutoff may vary based on the experimental assays and therapeutic indication. However, based on the available data, tentative guidelines have been provided (as shown in Figure 3). The BPI bins are colored by measured Caco-2 Papp A-to-B permeability and efflux ratio, which supports a guidance of BPI > 1 for programs looking for orally dosed small molecule compounds, and BPI > 1.5 for programs looking for exposure in the central nervous system, which requires a higher permeability and lower efflux. Conversely, the desired candidate profile may require limiting permeability and absorption (e.g., intestinally restricted therapeutics), and in those cases the available data suggests a BPI < 0.5.

Figure 3.

Caco-2 permeability binned by BPI in the BMS collection data set. Binning of BPI provides some guidelines to enrich compounds with high permeability and low efflux (green boxes in both panels): BPI > 1 for orally dosed small molecules, and BPI > 1.5 for molecules targeting central nervous system exposure, which requires high permeability and low efflux.

To further validate the guidelines and utility of BPI, a correlation between BPI and free brain-to-plasma partition from rodent experiments was investigated.²⁰ The brain and plasma protein binding was derived from either equilibrium dialysis or Transil binding assays selected by PK experts based on the scaffold-specific characteristics. In the analysis, free brain-to-plasma ratio (Kpu,u) and calculated BPI (based on measured EPSA and internal machine learning models for LogD_7.4) showed a high degree of correlation with R² = 0.7 (Figure 4a). For this specific analysis, the choice of using calculated LogD_7.4 was a function of the data availability, not a preference toward calculated parameters. Notably, the Kpu,u data set includes compounds from 3 different therapeutic projects and six distinct chemotypes. The correlation between Kpu,u and calculated BPI further suggests that this new metric can generalize across different chemotypes, as previously mentioned in the analysis of data sets from different companies. In this analysis, the calculated BPI differentiates between brain penetration classes (low, moderate, high based on Kpu,u cut-offs of 0.1 and 0.3) with minimal overlap, as shown in Figure 4b.

Figure 4.

BPI is highly indicative of compound ability to partition into the CNS. (A) The Log(Kpu,u) is highly correlated to BPI (R² = 0.7, N = 44). Compounds originated from three programs and six chemotypes across the BMS portfolio, all with an aim to achieve CNS penetrance. (B) The BPI distribution across low, medium, and high Kpu,u bins can be used to classify compounds. In this case, a BPI > 1 is recommended to increase the likelihood of finding medium and high permeability compounds, while BPI > 1.5 enriches highly permeable compounds.

In conclusion, BPI is a new metric that combines size, polarity, and lipophilicity. It is better able to distinguish highly permeable, low-efflux compounds than any of the constituent properties alone in both a published data set and across the proprietary compound collection. The BPI is easily understood and can guide compound design toward smaller, less polar, and more lipophilic compounds. This versatile metric can be applied to a wide range of chemical spaces, including small molecules that lie outside the typical physicochemical property space. Adoption of BPI as a multiparameter score can guide chemistry into a better in vitro permeability space, raising the likelihood that compounds will show desirable oral and CNS availability in vivo.

Glossary

ABBREVIATIONS

BPI

Balanced Permeability Index

CNS

central nervous system

P-gp

P-glycoprotein

Caco-2

Cancer coli

PK

pharmacokinetics

MDCK

Madin–Darby canine kidney

MDCK-KO

MDCK knock out

BCRP

breast cancer resistance protein

MW

molecular weight

ML

machine learning

MPO

multiparameter optimization

BMS

Bristol-Myers Squibb Company

HAC

heavy atom count

TPSA

Topological polar surface area

EPSA

exposed polar surface area

ROC

receiver operating characteristic

AUC

area under curve

ER

efflux ratio

Kpu,u

unbound brain-to-plasma drug partition coefficient

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

The authors gratefully acknowledge financial support from Bristol-Myers Squibb.

The authors are currently or were previously employees of Bristol-Myers Squibb and have received Bristol-Myers Squibb stock.

The authors declare no competing financial interest.