Modeling of small molecule's affinity to phospholipids using IAM-HPLC andQSRR approach enhanced by similarity-based machine algorithms

https://doi.org/10.1016/j.chroma.2023.464549 1 2 Modeling of small molecule's affinity to phospholipids using IAM-HPLC and QSRR 3 approach enhanced by similarity-based machine algorithms 4 5 Krzesimir Ciura 1,2* 6 7 1 Department of Physical Chemistry, Faculty of Pharmacy, Medical University of Gdańsk, Al. 8 Gen. J. Hallera 107, 80-416, Gdańsk, Poland 9 2 QSAR Lab Ltd., Trzy Lipy 3 St., 80-172 Gdańsk, Poland 10 11 12 13 14 Abstract: 15 Immobilized artificial membrane chromatography (IAM) has been proposed as a more 16 biosimilar alternative to classical lipophilicity measurement. Determination of small molecule's 17 affinity to phospholipids can be supported for predicting their behavior in the human body. 18 Therefore, a better understanding of the molecular interaction mechanism between small 19 xenobiotics and phospholipids can accelerate drug discovery. Here, the quantitative structure20 retention relationships (QSRR) approach was integrated with mechanistic descriptors 21 calculated using Chemicalize software to propose an easy-to-interpretation QSRR model. 22 Considering the heterogeneous character of the data set, locally weighted least squares kernel 23 regression belonging to similarity-based machine learning methods have been applied. The 24 results showed that lipophilicity, charge, and maximum projection area determine molecule 25 binding to phospholipids. Full validation of the obtained model based on OECD 26 recommendations has been performed and the applicability domain was defined using the 27 probability-oriented distance-based approach. The high values of predictive squared correlation 28 coefficient (Q2), and small root mean square error of prediction (RMSEP), 0.812 and 6.739, 29 respectively, confirmed that the obtained QSRR model is not well-fitted to the training data but 30 also showed prediction power. Additionally, only 1.5% of molecules from the training set and 31 2.8% from the validation test are outside the applicability domain, confirming great predictive 32 abilities. 33 34 Key words: Immobilized artificial membrane chromatography; quantitative structure35 retention relationships; similarity-based machine learning; QSRR 36 37 List of abbreviations 38 39 IAM - immobilized artificial membrane 40 QSRR - quantitative structure-property relationships 41 ML - machine learning 42 SBM - similarity-based machine learning methods 43 CHIIAM - chromatographic hydrophobicity index with an immobilized artificial membrane 44 MLR - multiple linear regression 45 GA - genetic algorithm 46 KwLPR - locally weighted least squares kernel regression 47 PCA - principal component analysis 48 t-SNE - t-distributed Stochastic Neighbor Embedding 49 R2 - coefficient of determination 50 Q2loo - correlation coefficient of leave-one-out cross-validation 51 RMSEloo - root-mean-square error of leave-one-out cross-validation 52 RMSEC - root mean square error of calibration 53 RMSEP - root mean square error of prediction 54 Q2 - predictive squared correlation coefficient 55 CCC - concordance correlation coefficient 56 57 1. Introduction 58 Discovering and developing new drugs is an expensive, demanding, and time59 consuming process with uncertain outcomes in clinical trials[1]. Nowadays, chemical synthesis 60 and biological screening possibilities in the drug discovery pipeline have significantly 61 increased. However, poor pharmacokinetic properties and high toxicity have been considered 62 major limitations of drug candidates. Therefore, lipophilicity assessment is an essential process 63 in drug discovery since it noticeably affects the diffusion of molecules through a biological 64 membrane[2], determining the molecule’s pharmacokinetic properties and toxicity[3]. The 65 detailed experimental protocols proposed by OECD (test no 107 and 117) and several 66 procedures developed for academic and industrial institutions describe methods for lipophilicity 67 assessment based on the shake flask method or reversed-phase liquid chromatography (RP68 LC)[4–10]. Nevertheless, currently, more biosimilar alternatives to classical lipophilicity are 69 available. One of the alternatives is immobilized artificial membrane (IAM) chromatography. 70 The IAM stationary phase shows superior biomimetic properties compared to classical 71 lipophilicity measurement since phosphatidylcholine molecules (the primary phospholipid of 72 cell membranes) are covalently bound to silica, mimicking the phospholipid membrane 73 monolayer[11]. 74 The first HPLC columns with an immobilized artificial membrane were developed by 75 Pidgeon et al. in 1989[12]. IAM high-performance liquid chromatography (IAM-HPLC) allows 76 for assessing the affinity to phospholipids while maintaining all the advantages of HPLC. It is 77 worth emphasizing that chromatographic approaches hold great promise for high-throughput 78 screening among non-cell-based methods. Modern HPLC systems are highly automated and 79 very popular in academia and the pharmaceutical industry. [13]. 80 The relationship between retention and the chemical structure of analytes has attracted 81 attention from the beginning of chromatographic research. Kaliszan initiated and introduced a 82 particular type of quantitative structure-property relationships (QSPR) analysis, namely the 83 quantitative structure-retention relationships (QSRR), in 1987[14]. Since then, QSRR has been 84 a powerful tool in chromatographic research and has also been applied to study the retention 85 mechanism of IAM-HPLC[15–21]. 86 In the past decades, machine learning (ML) and data sciences have made remarkable 87 progress and are being applied in every scientific discipline, including QSPR/QSRR. Among 88 available algorithms, similarity-based machine learning methods (SBM) showed significant 89 advantages in dealing with heterogeneous noisy toxicological data[22,23]. Nonetheless, the use 90 of SBM in the case of chromatographic data is still in its infancy, although some studies showed 91 its high potential[24]. 92 This study's purpose was to understand better the molecular mechanism of interaction 93 between small xenobiotics and phospholipids. IAM-HPLC data was integrated with molecular 94 descriptors via the QSRR approach to realize this goal. A chromatographic hydrophobicity 95 index with an immobilized artificial membrane (CHIIAM) was used as an endpoint in QSRR 96 modeling. Based on a heterogeneous set of 402 molecules, primarily of pharmaceutical or 97 toxicological significance, the QSRR model was developed. The proposed model was validated 98 using retention factors of potential drug candidates, 106 molecules belonging to 5 different 99 chemical classes, analyzed in our laboratory. Using Chemicalize software, mechanistic 100 molecular descriptors were calculated; therefore, the straightforward interpretation of obtained 101 QSRR models can be described. Initial descriptor selection was performed by applying multiple 102 linear regression (MLR) coupled with a genetic algorithm (GA). Additionally, inspired by 103 recent developments of SBM, especially locally weighted least squares kernel regression 104 (KwLPR), we checked that KwLPR can increase model performances. 105 2. Materials and methods 106 2.1 Data collection 107 In this study, we collected data expressing molecules' affinity to phospholipids determined 108 based on fast gradient methods established by Valko and co-workers[25]. The experimental 109 protocol is based on fast acetonitrile gradient elution; in such conditions, the CHIIAM refers to 110 the acetonitrile concentration necessary for the elution of analytes from IAM columns and 111 consequently expresses the binding to phospholipids. CHIIAM values were collected from 112 literature for molecules included in the training set[26–30] and for drug candidates used as the 113 validation set[31–35]. Drug candidates represented five chemical classes; isoxazoles, 114 fluoroquinolones, arylpiperazines, sulfonamides and oleanolic acid derivatives. 115 Although Regis Technologies Inc. (Morton Grove, IL, USA) is the only manufacturer of the 116 IAM stationary phase, some changes in the column manufacturing process occurred. Since 117 "type A" silica was no longer available, the IAM column introduced "type B" silica in 2018, 118 causing slight changes to the surface and properties of the silica beds. Considering reports 119 published by Valko and co-workers [36], we decided to combine data coming from "new" and 120 "old" IAM columns since they proved that, in general, the CHIIAM values from the “new” IAM 121 column were comparable with the values obtained from the previous batches of IAM columns 122 and differences occurred only for small polar basic compounds. Therefore, to maximize the size 123 of the training set, we decided not to limit data only to one type of IAM column. In most studies, 124 ammonium acetate was used as water-mobile phases; in two research, the phosphate buffer was 125 applied[34,35], but in both cases, pH was 7.4 to mimic physiological conditions. A high 126 correlation between CHIIAM of reference substances and the fact that investigated isoxazoles 127 and oleanolic acid derivatives are mostly presented as the neutral forms under applied 128 conditions indicated that the data are comparable. 129 Molecular weight has been used as a criterion for including or excluding molecules. Since the 130 developing model will be dedicated to low-molecular substances, the cutoff was set at 650 131 g/mol level. Following the FAIRness recommendation on how to share the (meta)data[37], all 132 data collected during this study (CHIIAM) and calculated (molecular descriptors) together with 133 molecular identification (SMILES notation) are available as supplementary materials and in the 134 author’s GitHub as machine-readable form making it interoperability. 135 2.2 Calculation of molecular descriptors 136 For the calculation of molecular descriptors, Chemicalize software (https://chemicalize.com/) 137 was applied. The basic version of subscriptions is free of cost and allows for the calculation of 138 molecular properties of up to 12 non-hydrogen atoms molecules. During this study, several 139 classes of theoretical descriptors were calculated, referring to molecules' geometrical, 140 topological, and bulkiness-related properties. Also, descriptors were obtained to code the 141 molecule's lipophilicity, including logP and logD7.4, charge, and ability to form H-bonds. All 142 calculated descriptors were collected in supplementary materials together with 2D molecule 143 structures and information about chemical character established based on the most dominant 144 form in experimental pH (7.4). 145 2.3 Data analysis 146 Principal component analysis (PCA) and t-distributed Stochastic Neighbor Embedding (t-SNE) 147 were performed to explore similarities and dissimilarities of observed structures. PCA and 148 t-SNE were calculated for databases of calculated descriptors. Before analysis, data were 149 standardized to eliminate the impact of different scales by using the Z-score scaling algorithm 150 (V = mean of V/δ, where V is the value of variables and δ is the standard deviation). In the 151 case of t-SNE, perplexity was 5, whereas the maximum number of interactions was 1000. Both 152 analyses were performed in the R environment. 153 2.4 QSRR modeling 154 The first step of QSRR modeling includes multiple linear regression algorithms supported by 155 GA. For the calculation of GA-MLR, QSARINS software was used[38]. The set of parameters 156 applied to control GA was the size of the population—200 and the mutation rate—20%. Priori 157 to analyze data were divided into two groups, the training group (n = 408, ≈ 80%) and the 158 testing group (n = 106, ≈ 20%) included 5 following chemical classes of drug candidates: 159 oleanolic acid derivatives, sulfonamide derivatives, arylpiperazine derivatives, isoxazolo 160 derivatives, and fluoroquinolone derivatives. Next, based on the selected descriptors, KwLPR 161 was calculated using the protocol proposed by Gajewicz-Skrętna and all [23]. 162 The model fitting, robustness, and predictive abilities were assessed by using the 163 following statistical figures: coefficient of determination (R2), correlation coefficient of leave164 one-out cross-validation (Q2loo), root-mean-square error of leave-one-out cross-validation 165 (RMSEloo), root mean square error of calibration (RMSEC), root mean square error of prediction 166 (RMSEP), predictive squared correlation coefficient (Q2), and concordance correlation 167 coefficient (CCC). Detailed descriptions and formulas of all investigated statistical parameters 168 are described in supplementary material. 169 For the final model the applicability domain was defined using the probability-oriented 170 distance-based approach proposed by Gajewicz-Skrętna[39]. Data analysis and results 171 visualization have been performed using RStudio software (R version 4.1.1) with “carat” and 172 “ggplot2” packages[40]. 173 3. Results and discussion 174 3.1 Data distribution in datasets 175 176 In this study, the data set of 508 molecules, mostly with therapeutic or toxicological potency, 177 has been collected from studies published by Valko[26–29] and for our in-house data from 178 previously published research[30–33,35]. Since some molecules were analyzed in both 179 laboratories, we checked differences in the CHIIAM indices (Figure S1). Generally, the CHIIAM 180 values did not vary by more than five units[41], which can be considered a typical method 181 deviation; only for seven molecules, this difference was slightly large but still less than seven 182 units. Based on these results, it can be concluded that Valko’s protocol demonstrates high 183 reproducibility. 184 Then using Chemicalize software, the ionization state of molecules under experimental 185 conditions was determined (Figure 1A). Most molecules are present predominantly in neutral 186 form (46%), while the numbers of cations and anions are at similar levels, 26% and 19%, 187 respectively. The smallest group (9%) included zwitterions. The distribution of CHIIAM among 188 chemical classes is presented in Figure 1B. Usually, we observed normal distribution in each 189 group, with the p-value of the Shapiro-Wilk test > 0.05, except for cations where compounds 190 with high CHIIAM values are in the majority. 191 Figure 1. A) Distribution of chemical classes. B) Distribution of CHIIAM among chemical 192 classes 193 After calculating theoretical descriptors, PCA and t-SNE analysis was performed to verify the 194 data structure and remove potential outliers, which can negatively affect the performance of the 195 regression model. PCA is a linear technique that reorients the data into a new coordinate system 196 by identifying the principal components. These principal components are linear combinations 197 of the original features. On the other hand, t-SNE is a non-linear technique that concentrates on 198 preserving pairwise similarities between data points in the high-dimensional space and then 199 represents them in a lower-dimensional space, usually 2D. Both methods allow for the 200 assessment of the similarities or dissimilarities of data points, in the case of this study 201 similarities between drug candidates and model substances were investigated. As can be 202 observed in Figure 2, most drug candidates are mixed with model substances. Only a few 203 oleanolic acid derivatives are outside the circle indicating the 0.95 level of group membership. 204 351 [1] Danishuddin, V. Kumar, M. Faheem, K.W. Lee, A decade of machine learning-based 352 predictive models for human pharmacokinetics: advances and challenges, Drug Discov 353 Today. 27 (2021) 529–537. https://doi.org/10.1016/j.drudis.2021.09.013. 354 [2] H. van de Waterbeemd, E. Gifford, ADMET in silico modelling: towards prediction 355 paradise?, Nat Rev Drug Discov. 2 (2003) 192–204. https://doi.org/10.1038/nrd1032. 356 [3] T. Hou, J. Wang, Structure – ADME relationship: still a long way to go?, Expert Opin 357 Drug Met. 4 (2008) 759–770. https://doi.org/10.1517/17425255.4.6.759. 358 [4] K. Ciura, J. Nowakowska, P. Pikul, W. Struck-Lewicka, M.J. Markuszewski, A 359 Comparative Quantitative Structure-Retention Relationships Study for Lipophilicity 360 Determination of Compounds with a Phenanthrene Skeleton on Cyano-, Reversed Phase-, and 361 Normal Phase-Thin Layer Chromatography Stationary Phases, J Aoac Int. 98 (2015) 345– 362 353. https://doi.org/10.5740/jaoacint.14-187. 363 [5] K. Ciura, M. Belka, P. Kawczak, T. Bączek, J. Nowakowska, The comparative study of 364 micellar TLC and RP-TLC as potential tools for lipophilicity assessment based on QSRR 365 approach, J Pharmaceut Biomed. 149 (2018) 70–79. 366 https://doi.org/10.1016/j.jpba.2017.10.034. 367 [6] K. Ciura, P. Kawczak, K.E. Greber, H. Kapica, J. Nowakowska, T. Bączek, Application of 368 reversed-phase thin layer chromatography and QSRR modelling for prediction of protein 369 binding of selected β-blockers, J Pharmaceut Biomed. 176 (2019) 112767. 370 https://doi.org/10.1016/j.jpba.2019.07.015. 371 [7] M.-L. Jeličić, D.A. Klarić, J. Kovačić, D. Verbanac, A. Mornar, Accessing Lipophilicity 372 and Biomimetic Chromatography Profile of Biologically Active Ingredients of Botanicals 373 Used in the Treatment of Inflammatory Bowel Disease, Pharm. 15 (2022) 965. 374 https://doi.org/10.3390/ph15080965. 375 [8] M. Dąbrowska, M. Starek, G. Chłoń-Rzepa, A. Zagórska, Ł. Komsta, A. Jankowska, M. 376 Ślusarczyk, M. Pawłowski, Estimation of the lipophilicity of purine-2,6-dione-based TRPA1 377 antagonists and PDE4/7 inhibitors with analgesic activity, Bioorg Med Chem Lett. 49 (2021) 378 128318. https://doi.org/10.1016/j.bmcl.2021.128318. 379 [9] A. Fernández-Pumarega, S. Amézqueta, E. Fuguet, M. Rosés, Tadpole toxicity prediction 380 using chromatographic systems, J Chromatogr A. 1418 (2015) 167–176. 381 https://doi.org/10.1016/j.chroma.2015.09.056. 382 [10] C. Stergiopoulos, F. Tsopelas, K. Valko, M. Ochsenkühn-Petropoulou, The use of 383 biomimetic chromatography to predict acute aquatic toxicity of pharmaceutical compounds, 384 Toxicol Environ Chem. 104 (2022) 1–19. https://doi.org/10.1080/02772248.2021.2005065. 385 [11] A.W. Sobańska, Affinity of Compounds for Phosphatydylcholine-Based Immobilized 386 Artificial Membrane—A Measure of Their Bioconcentration in Aquatic Organisms, Membr. 387 12 (2022) 1130. https://doi.org/10.3390/membranes12111130. 388 [12] C. Pidgeon, U.V. Venkataram, Immobilized artificial membrane chromatography: 389 Supports composed of membrane lipids, Analytical Biochemistry. 176 (1989) 36–47. 390 https://doi.org/10.1016/0003-2697(89)90269-8. 391 [13] K.L. Valko, Biomimetic chromatography—A novel application of the chromatographic 392 principles, Anal Sci Adv. (2022). https://doi.org/10.1002/ansa.202200004. 393 [14] R. Kaliszan, QSRR: Quantitative Structure-(Chromatographic) Retention Relationships, 394 Chem Rev. 107 (2007) 3212–3246. https://doi.org/10.1021/cr068412z. 395 [15] L. Grumetto, C. Carpentiero, P.D. Vaio, F. Frecentese, F. Barbato, Lipophilic and polar 396 interaction forces between acidic drugs and membrane phospholipids encoded in IAM-HPLC 397 indexes: Their role in membrane partition and relationships with BBB permeation data, J. 398 Pharm. Biomed. Anal. 75 (2013) 165–172. https://doi.org/10.1016/j.jpba.2012.11.034. 399 [16] L. Grumetto, C. Carpentiero, F. Barbato, Lipophilic and electrostatic forces encoded in 400 IAM-HPLC indexes of basic drugs: Their role in membrane partition and their relationships 401 with BBB passage data, Eur. J. Pharm. Sci. 45 (2012) 685–692. 402 https://doi.org/10.1016/j.ejps.2012.01.008. 403 [17] J. Li, J. Sun, S. Cui, Z. He, Quantitative structure-retention relationship studies using 404 immobilized artificial membrane chromatography I: Amended linear solvation energy 405 relationships with the introduction of a molecular electronic factor, J. Chromatogr. A. 1132 406 (2006) 174–182. https://doi.org/10.1016/j.chroma.2006.07.073. 407 [18] J. Li, J. Sun, Z. He, Quantitative structure–retention relationship studies with 408 immobilized artificial membrane chromatography: II: Partial least squares regression, Journal 409 of Chromatography A. 1140 (2007) 174–179. https://doi.org/10.1016/j.chroma.2006.11.091. 410 [19] H. Du, J. Watzl, J. Wang, X. Zhang, X. Yao, Z. Hu, Prediction of retention indices of 411 drugs based on immobilized artificial membrane chromatography using Projection Pursuit 412 Regression and Local Lazy Regression, J. Sep. Sci. 31 (2008) 2325–2333. 413 https://doi.org/10.1002/jssc.200700665. 414 [20] E. Daghir-Wojtkowiak, S. Studzińska, B. Buszewski, R. Kaliszan, M.J. Markuszewski, 415 Quantitative structure–retention relationships of ionic liquid cations in characterization of 416 stationary phases for HPLC, Anal. Methods. 6 (2013) 1189–1196. 417 https://doi.org/10.1039/c3ay41805g. 418 [21] G. Russo, L. Grumetto, F. Barbato, G. Vistoli, A. Pedretti, Prediction and mechanism 419 elucidation of analyte retention on phospholipid stationary phases (IAM-HPLC) by in silico 420 calculated physico-chemical descriptors, Eur. J. Pharm. Sci. 99 (2017) 173–184. 421 https://doi.org/10.1016/j.ejps.2016.11.026. 422 [22] A. Gajewicz-Skretna, E. Wyrzykowska, M. Gromelski, Quantitative multi-species 423 toxicity modeling: Does a multi-species, machine learning model provide better performance 424 than a single-species model for the evaluation of acute aquatic toxicity by organic pollutants?, 425 Science of The Total Environment. 861 (2023) 160590. 426 https://doi.org/10.1016/j.scitotenv.2022.160590. 427 [23] A. Gajewicz-Skretna, S. Kar, M. Piotrowska, J. Leszczynski, The kernel-weighted local 428 polynomial regression (KwLPR) approach: an efficient, novel tool for development of 429 QSAR/QSAAR toxicity extrapolation models, 13 (2021) 9. https://doi.org/10.1186/s13321430 021-00484-5. 431 [24] J.P.M. Andries, M. Goodarzi, Y.V. Heyden, Improvement of quantitative structure– 432 retention relationship models for chromatographic retention prediction of peptides applying 433 individual local partial least squares models, Talanta. 219 (2020) 121266. 434 https://doi.org/10.1016/j.talanta.2020.121266. 435 [25] K.L. Valkó, Lipophilicity and biomimetic properties measured by HPLC to support drug 436 discovery, J Pharmaceut Biomed. 130 (2016) 35–54. 437 https://doi.org/10.1016/j.jpba.2016.04.009. 438 [26] K. Valko, S. Nunhuck, C. Bevan, M.H. Abraham, D.P. Reynolds, Fast gradient HPLC 439 method to determine compounds binding to human serum albumin. Relationships with 440 octanol/water and immobilized artificial membrane lipophilicity., J Pharm Sci. 92 (2003) 441 2236–48. https://doi.org/10.1002/jps.10494. 442 [27] K. Valko, S. Rava, S. Bunally, S. Anderson, Revisiting the application of Immobilized 443 Artificial Membrane (IAM) chromatography to estimate in vivo distribution properties of 444 drug discovery compounds based on the model of marketed drugs., ADMET DMPK. 8 445 (2020) 78–97. https://doi.org/10.5599/admet.757. 446 [28] C. Stergiopoulos, F. Tsopelas, K. Valko, Prediction of hERG inhibition of drug 447 discovery compounds using biomimetic HPLC measurements., ADMET DMPK. 9 (2021) 448 191–207. https://doi.org/10.5599/admet.995. 449 [29] K.L. Valko, T. Zhang, Biomimetic properties and estimated in vivo distribution of 450 chloroquine and hydroxy-chloroquine enantiomers., ADMET DMPK. 9 (2021) 151–165. 451 https://doi.org/10.5599/admet.929. 452 [30] K. Ciura, S. Kovačević, M. Pastewska, H. Kapica, M. Kornela, W. Sawicki, Prediction of 453 the chromatographic hydrophobicity index with immobilized artificial membrane 454 chromatography using simple molecular descriptors and artificial neural networks, J 455 Chromatogr A. 1660 (2021) 462666. https://doi.org/10.1016/j.chroma.2021.462666. 456 [31] J. Fedorowicz, C.D. Cruz, M. Morawska, K. Ciura, S. Gilbert-Girard, L. Mazur, H. 457 Mäkkylä, P. Ilina, K. Savijoki, A. Fallarero, P. Tammela, J. Sączewski, Antibacterial and 458 antibiofilm activity of permanently ionized quaternary ammonium fluoroquinolones, Eur J 459 Med Chem. 254 (2023) 115373. https://doi.org/10.1016/j.ejmech.2023.115373. 460 [32] M. Pastewska, B. Żołnowska, S. Kovačević, H. Kapica, M. Gromelski, F. Stoliński, J. 461 Sławiński, W. Sawicki, K. Ciura, Modeling of Anticancer Sulfonamide Derivatives 462 Lipophilicity by Chemometric and Quantitative Structure-Retention Relationships 463 Approaches, Molecules. 27 (2022) 3965. https://doi.org/10.3390/molecules27133965. 464 [33] S. Ulenberg, K. Ciura, P. Georgiev, M. Pastewska, G. Ślifirski, M. Król, F. Herold, T. 465 Bączek, Use of biomimetic chromatography and in vitro assay to develop predictive GA466 MLR model for use in drug-property prediction among anti-depressant drug candidates, 467 Microchem J. 175 (2022) 107183. https://doi.org/10.1016/j.microc.2022.107183. 468 [34] K. Ciura, J. Fedorowicz, P. Žuvela, M. Lovrić, H. Kapica, P. Baranowski, W. Sawicki, 469 M.W. Wong, J. Sączewski, Affinity of Antifungal Isoxazolo[3,4-b]pyridine-3(1H)-Ones to 470 Phospholipids in Immobilized Artificial Membrane (IAM) Chromatography, Molecules. 25 471 (2020) 4835. https://doi.org/10.3390/molecules25204835. 472 [35] M. Pastewska, B. Bednarczyk-Cwynar, S. Kovačević, N. Buławska, S. Ulenberg, P. 473 Georgiev, H. Kapica, P. Kawczak, T. Bączek, W. Sawicki, K. Ciura, Multivariate assessment 474 of anticancer oleanane triterpenoids lipophilicity, J Chromatogr A. 1656 (2021) 462552. 475 https://doi.org/10.1016/j.chroma.2021.462552. 476 [36] K.L. Valko, S. Rava, S. Bunally, S. Anderson, Revisiting the application of Immobilized 477 Artificial Membrane (IAM) chromatography to estimate in vivo distribution properties of 478 drug discovery compounds based on the model of marketed drugs, ADMET DMPK. 0 (2020) 479 78–97. https://doi.org/10.5599/admet.757. 480 [37] M.D. Wilkinson, M. Dumontier, Ij.J. Aalbersberg, G. Appleton, M. Axton, A. Baak, N. 481 Blomberg, J.-W. Boiten, L.B. da S. Santos, P.E. Bourne, J. Bouwman, A.J. Brookes, T. Clark, 482 M. Crosas, I. Dillo, O. Dumon, S. Edmunds, C.T. Evelo, R. Finkers, A. Gonzalez-Beltran, 483 A.J.G. Gray, P. Groth, C. Goble, J.S. Grethe, J. Heringa, P.A.C. ’t Hoen, R. Hooft, T. Kuhn, 484 R. Kok, J. Kok, S.J. Lusher, M.E. Martone, A. Mons, A.L. Packer, B. Persson, P. Rocca485 Serra, M. Roos, R. van Schaik, S.-A. Sansone, E. Schultes, T. Sengstag, T. Slater, G. Strawn, 486 M.A. Swertz, M. Thompson, J. van der Lei, E. van Mulligen, J. Velterop, A. Waagmeester, P. 487 Wittenburg, K. Wolstencroft, J. Zhao, B. Mons, The FAIR Guiding Principles for scientific 488 data management and stewardship, 3 (2016) 160018. https://doi.org/10.1038/sdata.2016.18. 489 [38] P. Gramatica, N. Chirico, E. Papa, S. Cassani, S. Kovarich, QSARINS: A new software 490 for the development, analysis, and validation of QSAR MLR models, Journal of 491 Computational Chemistry. 34 (2013) 2121–2132. https://doi.org/10.1002/jcc.23361. 492 [39] Gajewicz, A., How to judge whether QSAR/read-across predictions can be trusted: a 493 novel approach for establishing a model’s applicability domain, Environ. Sci.: Nano. 5 (2018) 494 408–421. https://doi.org/10.1039/c7en00774d. 495 [40] H. Wickham, ggplot2, Elegant Graphics for Data Analysis, (2016) 109–145. 496 https://doi.org/10.1007/978-3-319-24277-4_6. 497 [41] K.L. Valko, S. Rava, S. Bunally, S. Anderson, Revisiting the application of Immobilized 498 Artificial Membrane (IAM) chromatography to estimate in vivo distribution properties of 499 drug discovery compounds based on the model of marketed drugs, Admet Dmpk. 0 (2020) 500 78–97. https://doi.org/10.5599/admet.757. 501 [42] A. Avdeef, K.J. Box, J.E.A. Comer, C. Hibbert, K.Y. Tam, pH-Metric logP 10. 502 Determination of Liposomal Membrane-Water Partition Coefficients of lonizable Drugs, 503 Pharm. Res. 15 (1998) 209–215. https://doi.org/10.1023/a:1011954332221. 504 [43] D. Vrakas, C. Giaginis, A. Tsantili-Kakoulidou, Electrostatic interactions and ionization 505 effect in immobilized artificial membrane retention: A comparative study with octanol–water 506 partitioning, Journal of Chromatography A. 1187 (2008) 67–78. 507 https://doi.org/10.1016/j.chroma.2008.01.079. 508 [44] G. Russo, L. Grumetto, R. Szucs, F. Barbato, F. Lynen, Screening therapeutics according 509 to their uptake across the blood-brain barrier: A high throughput method based on 510 immobilized artificial membrane liquid chromatography-diode-array-detection coupled to 511 electrospray-time-of-flight mass spectrometry, Eur. J. Pharm. Biopharm. 127 (2018) 72–84. 512 https://doi.org/10.1016/j.ejpb.2018.02.004. 513 [45] G. Russo, L. Grumetto, R. Szucs, F. Barbato, F. Lynen, Determination of in Vitro and in 514 Silico Indexes for the Modeling of Blood–Brain Barrier Partitioning of Drugs via Micellar 515 and Immobilized Artificial Membrane Liquid Chromatography, J. Med. Chem. 60 (2017) 516 3739–3754. https://doi.org/10.1021/acs.jmedchem.6b01811. 517 [46] T.E. Yen, S. Agatonovic-Kustrin, A.M. Evans, R.L. Nation, J. Ryand, Prediction of drug 518 absorption based on immobilized artificial membrane (IAM) chromatography separation and 519 calculated molecular descriptors, Journal of Pharmaceutical and Biomedical Analysis. 38 520 (2005) 472–478. https://doi.org/10.1016/j.jpba.2005.01.040. 521 [47] F. Hollósy, K. Valkó, A. Hersey, S. Nunhuck, G. Kéri, C. Bevan, Estimation of Volume 522 of Distribution in Humans from High Throughput HPLC-Based Measurements of Human 523 Serum Albumin Binding and Immobilized Artificial Membrane Partitioning, Journal of 524 Medicinal Chemistry. 49 (2006) 6958–6971. https://doi.org/10.1021/jm050957i. 525 [48] A. Nasal, M. Sznitowska, A. Buciński, R. Kaliszan, Hydrophobicity parameter from 526 high-performance liquid chromatography on an immobilized artificial membrane column and 527 its relationship to bioactivity, Journal of Chromatography A. 692 (1995) 83–89. 528 https://doi.org/10.1016/0021-9673(94)00689-7. 529 [49] A.W. Sobańska, E. Brzezińska, IAM Chromatographic Models of Skin Permeation, 530 Molecules. 27 (2022) 1893. https://doi.org/10.3390/molecules27061893. 531 [50] C. Stergiopoulos, F. Tsopelas, K. Valko, Prediction of hERG inhibition of drug 532 discovery compounds using biomimetic HPLC measurements, Admet Dmpk. 9 (2021) 191– 533 207. https://doi.org/10.5599/admet.995. 534 [51] M.A. Al-Haj, R. Kaliszan, A. Nasal, Test Analytes for Studies of the Molecular 535 Mechanism of Chromatographic Separations by Quantitative Structure−Retention 536 Relationships, Anal. Chem. 71 (1999) 2976–2985. https://doi.org/10.1021/ac9901586. 537 [52] B. Buszewski, P. Žuvela, G. Sagandykova, J. Walczak-Skierska, P. Pomastowski, J. 538 David, M.W. Wong, Mechanistic Chromatographic Column Characterization for the Analysis 539 of Flavonoids Using Quantitative Structure-Retention Relationships Based on Density 540 Functional Theory, Int. J. Mol. Sci. 21 (2020) 2053. https://doi.org/10.3390/ijms21062053. 541 542 543 544 545 546 547 548 549 550 Figures: 551 552 Figure 1. A) Distribution of chemical classes. C) Distribution of CHIIAM among chemical 553 classes 554 555 Figure 2. Results of exploratory analysis 556 557 Figure 3) Results of KwLPR regression; A) Observed CHIIAM vs. predicted by model; B) 558 RMSEP for tested groups of drug candidates; C) applicability domain defined using the 559 probability-oriented distance-based approach. 560 561 Tables: 562 Table 1. Summary of previously published QSRR models dedicated to IAM-HPLC. 563 564 Table 2. Compression of statical figures of obtained MLR and KwLPR models. 565 566 Table 1. Summary of previously published QSRR models dedicated to IAM-HPLC. Retention parameter, chromatographic condition, and type of analytes Descriptors chemometric tool number of analytes obtained statistical parameter ref. logkw IAM.PC.C10/C3; water-acetonitrile mobile phase; heterogeneous group of molecules LSER-Based Structural Descriptors of Abraham MLR 58 R = 0.988 [51] logkIAM IAM.PC.DD2 50 mM ammonium acetate (pH 7.0) - acetonitrile mobile phase; heterogeneous group of molecules LSER-Based Structural Descriptors of Abraham and net charge per molecule MLR 53 R2 = 0.958 [17] logkIAM IAM.PC.DD2 50 mM ammonium acetate (pH 7.0) - acetonitrile mobile phase; heterogeneous group of molecules ClogP, rotatory bond (RotB), rings, molecular weight (MW) and total surface area (TSA) PLS 55 Q2 = 0.902 RSMEP = 0.400 [18] logkIAM IAM.PC.DD2 50 mM ammonium acetate (pH 7.0) - acetonitrile mobile phase; heterogeneous group of molecules number of aromatic rings, mobility of  electrons, ClogP LLR 55 Q2 = 0.9305 RMSEP = 0.395 [19] logkw IAM.PC.DD2 10 mM ammonium acetate (pH 6.5) – methanol; ionic liquids logP and point charge MLR 8 R2 = 0,99 s = 0.09 [20] logkw IAM.PC.MG phosphate buffer (pH 7.0) - acetonitrile mobile phase; heterogeneous group of molecules milogP, Heavy Atoms, mean of calculated hydrophilic-lipophilic balance (HLBM), rotatory bond MLR 204 R2= 0.81 Q2 = 0.80 s = 0.438 [21] logkw IAM.PC.DD2 milogP, Volume Diameter, hydrophiliclipophilic balance corrected by polar surface area (HLBPSA), rotatory bond MLR 160 R2= 0.85 Q2 = 0.84 s = 0.459 [21] phosphate buffer (pH 7.0) - acetonitrile mobile phase; heterogeneous group of molecules logkIAM IAM.PC.DD2 0.1% trifluoroacetic acid (TFA) in water - acetonitrile mobile phases; flavonoids minimum O-H bond strength, global hardness (η), HOMO-LUMO energy gap, natural bond orbital (NBO) PLS 30 RMSE = 1.60 [52] CHIIAM IAM.PC.DD2 0.01 M Phosphate Buffer Saline (pH 7.4) positively charged fraction (F+), negatively charged fraction (F-), logDp.H 7.4, MLR 56 R = 0.938, S = 0.413 [43] CHIIAM IAM.PC.DD2 Morpholinepropanesulfonic acid (pH 7.4) positively charged fraction (F+), negatively charged fraction (F-), logDp.H 7.4, MLR 62 R=0.948, s = 0.505 [43] CHIIAM IAM.PC.DD2 phosphate buffer (pH 7.4) - acetonitrile mobile phase; oleanolic acid derivatives Dragon descriptors MLR 33 R2=0.947 Q2=0.906 RMSECV=2.236 RMSEP=2.171 [35] CHIIAM IAM.PC.DD2 50 mM ammonium acetate (pH 7.4) - acetonitrile mobile phase; arylpiperazines derivatives Dragon descriptors MLR 25 R2=0.968 Q2=0.942 RMSECV=0.042 RMSEP=0.058 [33] logKIAM IAM.PC.DD2 50 mM ammonium acetate (pH 7.4) - acetonitrile mobile phase; sulfonamides derivatives Dragon descriptors MLR 27 CCC = 0.884 RMSEP = 0.173 [32] CHIIAM IAM.PC.DD2 phosphate buffer (pH 7.4) - acetonitrile mobile phase; isoxazolone derivatives, Dragon descriptors PLS 26 Q2 = 0.933 RMSEP = 1.983 [34] CHIIAM IAM.PC.DD2 logDp.H 7.4, numbers of H-donors, polar surface area (PSA), molecular volume ANN 261 CCC = 0.822 RMSEP = 8.2 [30] 50 mM ammonium acetate (pH 7.4) - acetonitrile mobile phase; heterogeneous group of molecules MLR - multivariable linear regression, PLS - Partial least squares regression, LLR - local lazy regression, ANN - artificial neural network, s - standard error of estimates