PhysChem Forum: Closing the loop – measuring, modelling and predicting PhysChem properties

Andrius Sazonovas ^{1, 2} , Kiril Lanevskij ^{1, 2}, Remigijus Didziapetris ^{1, 2}

¹ UAB ACD/Labs Vilnius, J. Savickio g. 4, LT-01108 Vilnius, Lithuania
² ACD/Labs, Inc., 8 King Street East, Suite 107, Toronto, Ontario, M5C 1B5, Canada

In silico studies of P-glycoprotein (P-gp) mediated efflux of pharmaceuticals usually treat it as a binary endpoint and only attempt to classify molecules as P-gp substrates or non-substrates. However, recently we have proposed a QSAR model that can circumvent the lack of accurate quantitative data by employing censored regression-based machine learning approach that can make use of experimental measurements recorded as open-ended intervals, or so called censored data points [1]. This model, parameterized using a minimal set of relevant physicochemical descriptors (lipophilicity, ionization, molecular size and topology), is capable of producing predictions in the form of numerical Efflux Ratio (ER) values, i.e. the ratios of bidirectional permeation rates observed in polarized transport assays.

In the current study we extend this approach by applying an estimate of passive permeability in Caco-2 cells [2] to split measured ER values into the contributions of passive and active transport routes, and subsequently fitting the model to represent pure P-gp efflux effect. The new approach achieves similar predictive power on the qualitative classification task (> 75% overall accuracy at a threshold of ER > 2 for substrates), while being more readily interpretable compared to the previous model. Practical utility of quantitative predictions is demonstrated by incorporating predicted ER values into a previously described CNS Access classifier [3]. The respective model augmented with P-gp efflux estimates was able to predict one of the key brain penetration characteristics, the unbound brain/blood partitioning ratio (Kp,uu) with R squared > 0.5.

[1] Lanevskij K, Didziapetris R, Sazonovas A. Toxicol Lett. 2023;384:S118.
[2] Lanevskij K, Didziapetris R. J Pharm Sci. 2019;108(1):78-86.
[3] Lanevskij K, Japertas P, Didziapetris R, Petrauskas A. Chem Biodivers. 2009;6(11):2050-4.

Kiril Lanevskij ^1,2, Alexander Proskura ³, Andrey Vazhentsev ⁴, Andrius Sazonovas ^1,2 , Eduard
Kolovanov ²

¹ UAB ACD/Labs Vilnius, J. Savickio g. 4, LT-01108 Vilnius, Lithuania
² ACD/Labs, Inc., 8 King Street East, Suite 107, Toronto, Ontario, M5C 1B5, Canada
³ ACD Development Unipessoal Lda, Rua Eng. Ferreira Dias 728, 4100-246 Porto, Portugal
⁴ Advanced Chemistry Development Germany GmbH, Hahnstrasse 70, 60528 Frankfurt am Main, Germany

Compounds with multiple ionization centers exhibit complex behaviors that are important for scientists to understand in many sectors of R&D. For more than 25 years, ACD/Labs has been supporting researchers with prediction algorithms to help with this. The latest improvements in Percepta’s pKa algorithm directly impact predictions of logD, pH-dependent aqueous solubility, and the distribution of ionic species.

The logD at given pH depends on logP of molecule as well as on percentage of different ionic species of
molecule existing at this pH. Ionic species distribution directly depends on all pKa micro-constants of the
molecule. To calculate the distribution of ionic forms from pH, it is necessary to solve a non-linear system of equations for concentration values where pKa micro-constants are used as coefficients. Due to the excessive number of pKa micro-constants, the system of equations turns out to be overprovisioned and therefore has to be solved by the least squares method. Since the micro constants pKa are predicted by the algorithm with some error, the solution found by the traditional method quite often leads to the situation where the distribution of ionic species, and subsequently the logD curve (or solubility, or any other properties depending on pKa), deviates significantly from the initially predicted “defining” micro-constants. This raises questions among observers regarding the accuracy of the logD curve prediction itself.

This problem has been resolved in the new version. Now the solution to the overprovisioned system is sought by
minimizing the total error of all equations, taking into account the relative importance of a particular micro-constant. For this purpose, instead of the usual Euclidean norm, a weighted norm is used. The procedure for selecting the weighting coefficients of the norm is non-trivial, since the system of equations being solved is nonlinear, and it is also not always obvious which micro-constants should be considered less important or more important.