# Chemical fate in vitro: A physiological biokinetic (PBK) model for cell-based assays

Daniela Brenner, Kévin Bernal, Eliska Sychrova, Jiří Kohoutek, Sophie Langouët, Cleo Tebby, Rémy Beaudouin, Rayane Boufalaas, Julien Dairou, Arnaud Tête, et al.

► To cite this version:

Daniela Brenner, Kévin Bernal, Eliska Sychrova, Jiří Kohoutek, Sophie Langouët, et al. Chemical fate in vitro: A physiological biokinetic (PBK) model for cell-based assays. ALTEX - Alternatives to Animal Experimentation, 2026, 10.14573/altex.2509261. hal-05456518

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Research Article

# Chemical Fate *In Vitro*: A Physiological Biokinetic (PBK) Model for Cell-Based Assays

Daniela Brenner¹, Kévin Bernal², Eliška Sychrová¹, Jiří Kohoutek¹, Sophie Langouet³, Cleo Tebby⁴, Remy Beaudouin⁴,⁵, Rayane Boufalaas⁴,⁶, Julien Dairou⁷, Arnaud Tête², Pavel Babica¹, Etienne B. Blanc², Iva Sovadinová¹ and Pierre-Andre Billat⁴

¹RECETOX, Faculty of Science, Masaryk University, Brno, Czech Republic; ²Université Paris Cité, INSERM, Health & Functional Exposomics - HealthFex, Paris, France; ³Université Rennes, INSERM, EHESP, Irset (Institut de recherche en santé, environnement et travail) - UMR_S 1085, Rennes, France; ⁴INERIS, Experimental toxicology and modeling unit (TEAM), Parc ALATA BP2, Verneuil en Halatte, France; ⁵UMR I 02 SEBIO, INERIS, Parc ALATA BP2, Verneuil en Halatte, France; ⁶University of Technology of Compiegne, CNRS, Biomechanics and Bioengineering, Centre of recherche Royallieu, CS 60319, Compiegne Cedex, France; ⁷Université Paris Cité, CNRS, Laboratoire de Chimie et de Biochimie Pharmacologiques et Toxicologiques, Paris, France

## Abstract

*In vitro* toxicology assays are widely used in the context of toxicology to study *in vivo* outcomes and to improve mechanistic understanding of toxic responses. For this purpose, a better characterization of actual exposure and the fate of chemicals within the cellular test system is required. The present study aimed to develop a novel model, INSIGHT (*In Silico* Guide for Harmonized *in vitro* Testing), that integrates physiological and physicochemical parameters to better describe chemical fate *in vitro* and to guide assay design. The newly developed model, integrating the dynamic features of the Virtual Cell Based Assay model with the partitioning framework of the Virtual *In Vitro* Distribution model, was calibrated using both a large literature dataset and original experimental data, comprising a total of 42 chemicals and 7 commonly used cell lines: HepaRG, HepG2, 3T3 Balb/c, PC12, MCF-7, RTgill-W1, and HEK293. These cell lines were selected for their diverse tissue and species origins, metabolic capacities, and potential for functional transport mechanisms, known to influence chemical kinetics. The INSIGHT model demonstrated flexibility and robustness across a range of cell lines when the parameters driving their metabolic activity or functional transport were informed. The present study underscores the pivotal function of logPow determination and the necessity for accurate calibration of partition coefficients, permeability, and metabolic processes to account for variability across cell lines and tested chemicals. This approach supports and facilitates enhanced experimental design and advancing quantitative *in vitro*-to-*in vivo* extrapolation (qIVIVE) in toxicology and strengthens next generation risk assessment (NGRA) workflows.

## Plain language summary

*In vitro* cell-based tests are increasingly being used as an alternative to traditional animal experiments for evaluating chemical safety. However, the actual exposure of cells to tested chemicals during these experiments is often uncertain and difficult to determine, which can limit the interpretation of results. In the present study, we introduce INSIGHT, a physiologically based model describing how chemicals are distributed, transported into cells, and metabolized over time in *in vitro* systems. By integrating physicochemical properties with the biological characteristics of different cell types, INSIGHT improves understanding of cellular exposure and supports better experimental design. The model was evaluated using data from multiple chemicals and commonly used cell lines, demonstrating consistent performance across diverse experimental conditions. INSIGHT contributes to new approach methodologies by improving the assessment of relevant exposure and supporting the replacement, reduction and refinement (3Rs) of animal testing in chemical safety assessments.

## 1 Introduction

*In vitro* systems are widely used in pharmacology and toxicology to explore the effects of chemicals under a controlled laboratory environment, while reducing the need for animal studies. As part of the New Approach methodologies (NAMs) and next generation risk assessment (NGRA) workflows, *in vitro* data can be integrated with *in silico* tools, to progressively establish themselves as credible alternatives to traditional animal studies, particularly for regulatory applications in chemical safety. Indeed, *in vitro* assays offer many advantages for toxicity testing, including the ability to perform tests in a cost-effective, rapid, and ethically compliant manner, as well as high-throughput testing (Murray et al., 2016). Beyond their use for screening toxicological events, these tests contribute to a better understanding of the mechanisms of action of chemicals, especially in humans

Received September 26, 2025; Accepted December 23, 2025; Epub January 8, 2026; © The Authors, 2026.

ALTEX 43(#), ###-###. doi:10.14573/altex.2509261

Correspondence: Pierre-Andre Billat, PhD
INERIS, Experimental toxicology and modeling unit (TEAM), Parc ALATA BP2, 5, rue Taffanel, 60550 Verneuil en Halatte, France
(Pierre-Andre.Billat@ineris.fr)

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OPEN
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(Chen et al., 2015; Wills, 2017). Human cell lines are available for all major organs, which further expands their applicability to diverse toxicological endpoints in these organs. Nevertheless, a challenge remains in extrapolating concentration-effect relationships observed in laboratory assays to the *in vivo* context, especially because traditional *in vitro* systems often fail in recapitulating the dynamics and physiological complexity of living organisms, thereby limiting their predictive capacity for risk assessment.

Physiologically based kinetic (PBK) models, are *in silico* models built on differential equations that describe the physiological processes of absorption, distribution, metabolism, and excretion (ADME) of chemicals in organisms. These models are essential for extrapolating *in vitro* concentration to *in vivo* exposure at the target organ level. Using free plasma concentrations is thus a practical and conservative default for quantitative *in vitro*-*in vivo* extrapolation (qIVIVE). However, when *in vitro* effects depend on intracellular processes or when tissue sequestration substantially alters local availability, predictions of tissue or intracellular concentrations become necessary. In such cases, the development of PBK and toxicodynamic models necessitates an accurate estimation of the actual exposure of cells to the chemical in the test systems (Bell et al., 2018). Indeed, In most NGRA applications, nominal concentrations are commonly used as dose surrogates, but considering actual free concentration at the target site may provide improved confidence in extrapolations of Nicol et al. (2024). This estimation should consider, among other factors, the freely available fraction, evaporation, and metabolism. Relying solely on nominal concentrations introduces a significant bias: the actual dose reaching cells is modulated by plastic sorption, volatilization, and degradation, resulting in systematic deviations from actual exposure (Gülden et al., 2001; Schreiber and Keating, 2011; Kramer et al., 2012; Groothuis et al., 2019). Despite this, intracellular concentrations are rarely measured, impeding the development of biokinetic models. However, there is a clear interest in gaining insight into the chemical fate within *in vitro* systems, in order to: i) Estimate the actual cell exposure to these compounds; ii) Contribute to the development of quantitative adverse outcome pathways; iii) Enable extrapolation of findings across diverse experimental exposure conditions; and iv) Facilitate relevant quantitative qIVIVE.

In this context, *in silico* modelling offers a complementary approach to address existing gaps and better characterize the fate of chemicals in the *in vitro* test systems. For this purpose, several models have been developed to date, including the Virtual Cell-Based Assay (VCBA) model from the Joint Research Center (Comenges et al., 2017), and the Virtual *In Vitro* Distribution (VIVD) model (Fisher et al., 2019). A detailed analysis of existing modelling approaches and their limitations is provided by Proença et al. (2021).

The VCBA model is a dynamic model (Worth et al., 2017; Paini et al., 2017a,b; Sala Benito et al., 2017; Graepel et al., 2017), predicting the intracellular concentrations responsible for cell perturbations at 37°C. The VCBA consists of four parts: a fate and transport model, a cell partitioning model, a cell growth and division model, and a toxicity model (Proença et al., 2019). The present study will thus focus on the fate and transport component of the VCBA model.

The VIVD model, in contrast, is a steady-state cell partitioning model that accounts for differential ionization of chemicals in both the culture medium and cells, incorporates ion permeability across cell membranes, and considers the effect of membrane potential (Fisher et al., 2019). It also accounts for the effect of temperature variations on logPow and volatilization values, as well as lipid and protein binding in the culture medium, binding to cell culture plastic, air partitioning, and cell lipid binding. Therefore, this model would be a good proxy for estimating partition coefficients of chemicals in an *in vitro* assay.

However, both models exhibit inherent shortcomings. The VCBA model addresses the issue of cytotoxicity assays but does not explicitly model biokinetics *per se*, and, its partitioning model does not distinguish between charged and neutral species regarding their cellular uptake. In contrast, the VIVD model assumes that the equilibrium between the external medium and intracellular compartments occurs instantaneously, which oversimplifies dynamic processes.

Plastic binding is another critical factor: chemicals can adsorb to plastic polymers of culture plates (mainly polystyrene), reducing the actual exposure of cells to the chemical of interest, and thus inflating the apparent safe concentration deduced from the assay (Gülden et al., 2001). Both the VIVD and the VCBA models integrate the QSAR model developed by Kramer et al. (2010) that predicts the binding of chemicals to the polystyrene of culture plates which represents the most common material used. This binding model was validated using seven polycyclic aromatic hydrocarbons as test compounds. A more recent study by Fischer et al. (2018) proposed an updated model for 14 neutral chemicals, which accounts for their diffusion into the polystyrene plastic walls of the cell culture plates.

Accordingly, the primary objective of the present study was to develop a novel biokinetic model, so-called INSIGHT (*In Silico* Guide for Harmonized *in vitro* Testing), that combines the dynamic features of the VCBA model with the partitioning framework of the VIVD model, and updated plate binding predictions by incorporating recently data (Fischer et al., 2018). The model was subsequently calibrated, and its predictive performance evaluated.

For a robust evaluation of the predictive performance of the model, an extensive literature search was performed to identify available cellular kinetics data. The literature review led to the selection of seven widely used cell lines that were incorporated into the model: HepaRG, HepG2, 3T3 Balb/c, PC12, MCF-7, RTgill-W1, and HEK293. These cell lines were selected because they originate from different tissues and thus have distinct biochemical compositions and features, such as metabolism and functional transport. These characteristics are a prerequisite for the parameterization of both VIVD and VCBA models and, therefore, of the present model. Indeed, variations in these parameters will result in changes to the partition coefficient (mainly based on the lipophilicity of the chemical and the lipid content of the specific cell line). Furthermore, while the VCBA model operates under the assumption of passive diffusion, incorporating the use of cells with active transport will assist in determining the impact of the net active transport (defined as the difference between active uptake, if any, and active efflux). For this purpose, several model structures were evaluated, including configuration that either integrate or exclude active transport across all or specific cell lines, with the aim of keeping the model as generic as possible.

For model development, a calibration and validation datasets combined original experimental data on bisphenols A (BPA), F (BPF), and S (BPS), using either HepG2 or HepaRG cell lines (BPA only) and literature data. The selection of these bisphenols reflects a strategic balance between regulatory relevance (BPA) and increasing use of BPF and BPS as BPA substitutes. BPA is a data-rich compound with well characterized *in vitro* kinetics, making it an appropriate benchmark for comparing
INSIGHT predictions across cell models. BPF and BPS, although less extensively studied, share structural similarity with BPA, overlapping receptor interactions and comparable endocrine disruptor potency (Rochester and Bolden, 2015). These bisphenols are also central to the objectives of the European H2020 OBERON project (Audouze et al., 2020), which requires a mechanistic understanding of their *in vitro* biokinetics to help interpret consortium-wide toxicodynamic findings. This dataset is a valuable test case for refining *in vitro* biokinetic modeling and integrating complementary *in silico* approaches, thereby enhancing qIVIVE and qAOP applications and supporting regulatory decision-making in chemical safety assessment.

INSIGHT was parameterized using chemical physicochemical properties, cell physiological characteristics, and the exposure conditions. Global sensitivity analyses identified the most influential parameters informing the calibration strategy. Bayesian inference was used to calibrate medium-cell exchange processes and adjust systematic bias in partition coefficients using a dedicated calibration dataset. Finally, the model performance was evaluated against an external validation dataset containing medium and intracellular concentrations. INSIGHT integrates, for the first time, the passive partitioning framework of VIVD with the dynamic medium-cell exchange mechanics of VCBA into a single biokinetic model. It additionally embeds a plastic-binding submodel and calibrated uptake/efflux processes informed by literature and new experimental data. As a result, INSIGHT provides an expanded and more mechanistic characterization of *in vitro* kinetics, complementing and building upon previous modeling approaches.

# 2 Materials and methods

## 2.1 Literature review

### 2.1.1 Selected cell types

The selection of cell lines was based on three key factors: their extensive use in toxicology or biokinetics modeling, the specific organ system under investigation, and their distinctive characteristics, particularly regarding chemical metabolic intensity and functional transport. The three most frequently used cell lines to date, based on the number of tested compounds, as determined by the ChEMBL database, are HepG2 (human hepatoblastoma cells), HEK293 (human embryonic kidney), and HEK293T (human embryonic kidney cells stably expressing the SV40 T-antigen) (Gaulton et al., 2017). Representative cell lines used for acute toxicity testing encompassed human liver (HepaRG, HepG2), mouse fibroblasts (3T3 Balb/c), human lung epithelial (A549), adrenal gland as a neuronal proxy (PC12), human embryonic kidneys (HEK293T, HEK293H), human intestinal epithelium (Caco-2) and other commonly used cell lines, including rainbow trout gill cells (RT-gill W1) and human breast cells (MCF-7). The characteristics of the cells were obtained or estimated from literature and are presented in Table S1¹.

### 2.1.2 Literature review and data handling

An extensive literature search (ELS) was conducted to identify experimental studies providing intracellular concentration data for chemicals in HepaRG, HepG2, 3T3 Balb/c, A549, PC12, HEK293T, HEK293H, Caco-2, MCF-7, and RTgill-W1. A search of the PubMed® and ISI Web of Knowledge™ databases was conducted over the period spanning 1 January 1990 to 1 January 2024. The following search request was used in the “All fields” query box: “((HepaRG) OR (HepG2) OR (Balb) OR (3T3) OR (A549) OR (PC12) OR (MCF) OR (RTgill) OR (HEK) OR (Caco) OR (HT296) OR (IVIVE)) AND ((intracellular) OR (cell)) AND ((concentration) OR (kinetics)) AND ((medium) OR (nominal) OR (unbound) OR (bound) OR (free)) NOT (nanoparticles)”.

A total of 10,042 records were retrieved from PubMed® and 15,332 results from the ISI Web of Knowledge™ databases. After merging the datasets, 4,653 duplicates were identified and removed using the library manager (EndNote™ X7.8).

An initial screening phase of the selected references was then performed using ASReview Lab 1.4, an open-source machine learning software (van de Schoot et al., 2021). The software was used in Oracle Mode (data review with interactive artificial intelligence), after providing a priori knowledge with at least 10 relevant and 10 irrelevant random records (abstracts). The Naive Bayes classifier was employed, with the query strategy set to maximum likelihood, and the balance strategy configured as dynamic resampling (double sampling). The review was stopped after the identification of 50 consecutive irrelevant abstracts.

A total of 76 unique references were selected based on their abstract. The papers were selected if i) at least one concentration was measured in cells, and ii) the cell viability was above 80% to reduce toxicity effects on cell kinetics. The content and references of each paper were also checked to ensure that no data article was omitted.

Finally, 12 unique references showed original intracellular concentrations of 42 chemicals (Tab. S2¹) (Stadnicka-Michalak et al., 2014; Dimitrijevic et al., 2022; Zhang et al., 2015; Pomponio et al., 2015; Wei et al., 2010; Mühlebach et al., 2006; Broeders et al., 2013, 2015; Bellwon et al., 2015; Truisi et al., 2015; Zhang et al., 2020; Kramer et al., 2012).

Only seven cell lines: 3T3 Balb/c, HEK293, HepaRG, HepG2, MCF-7, PC12, and RT-gill W1 had intracellular concentration data across multiple conditions to support model calibration and evaluation (Section 2.1.2). Caco-2 and A549 were retained in the manuscript because they are relevant for future extensions of the model particularly those for which permeability datasets are available.

To harmonize the datasets, all concentrations were converted to nmol·µL⁻<fnref n="1" /> (mmol·L⁻<fnref n="1" />) using the physiological parameters described in Table S1¹ where applicable. The resulting values are summarized in Table S3¹. For example, when chemical amounts were reported as mass per cell fraction, the values were normalized by dividing by the number of cells at the sampling timepoint (using both seeding density and the included cell growth model) and the average volume of a single cell. The literature data were then split into a calibration dataset and a validation dataset. When additional measurements were found

<footnote n="1">¹ doi:10.14573/altex.2509261s1</footnote>
for chemicals already included in the calibration dataset but generated under different experimental conditions (e.g., distinct cell models, concentration ranges), these data were reassigned to the validation dataset. This ensured that validation and calibration dataset remained independent while maintaining a comparable chemical space. The resulting validation dataset spans a broad physicochemical range and includes multiple chemical classes, including neutral hydrophobic compounds (hexachlorobenzene), weak acids (BPA), cationic amphiphilic pharmaceuticals (chlorpromazine), and polycyclic aromatic hydrocarbons (phenanthrene). This diversity enables evaluation of model performance across different lipophilicity, ionization states, and molecular structures, using data independent from calibration. The calibration dataset consisted of 219 intracellular concentrations and 42 molecules, while the validation dataset included 42 quantifiable intracellular concentrations and 7 molecules (Tab. S3¹), spanning a molecular weight range of 113–1203 g·mol⁻¹ and a logPow range of −3.9 to 9.97. In addition, experimental data generated in the present study with HepG2 cells were assigned to the calibration dataset, while those generated with HepaRG cells were allocated to the validation dataset.

The specific chemical parameters for the retained chemicals were identified in chemical data banks. The physical parameters (molecular weight, pKa, logPow, Henry's constant, molar volume) were obtained from ChemsPIDer or PubChem, while the biological parameters (unbound fraction, blood-to-plasma partitioning ratio) were obtained from the High Throughput ToxicoKinetics ("HTTK") database (Wetmore et al., 2015). The stability in water and air was determined using EPI's fugacity model implemented in EPI Suite V4.11. These parameters are presented in supplementary file 1¹.

## 2.2 Experimental original kinetic data

### 2.2.1 Cell culture

The HepG2 cell line (human hepatoblastoma carcinoma cell line, ATCC® HB-8065TM, CVCL 0027) was sourced from LGC Standards in Łomianki, Poland. The cell line was maintained as described in Grosso et al. (2025). Briefly, cell cultivations and experimental treatments were done in a 2D monolayer in low glucose (1 g/L) Minimum Essential Medium (MEM) containing phenol red (Gibco Cat. No. 61100, Thermo Fisher, Waltham, MA), supplemented with 1 % (v/v) MEM Non-Essential Amino Acids (Gibco Cat. No. 11140, Thermo Fisher), 1 mM sodium pyruvate (Thermo Fisher), sodium bicarbonate (1.5 g/L, Sigma-Aldrich, Prague, Czech Republic), and 10 % of fetal bovine serum (FBS, Cat No. 1001/500, Biosera, Nuaillé, France).

Human HepaRG hepatocellular carcinoma cells (CVCL 9720) were obtained from Dr. Philippe Gripon and cultured in William's E medium supplemented with 50 µM hydrocortisone hemisuccinate, 5 µg/mL insulin, 11 mM glucose, 2 mM glutamine, 50 UI/mL penicillin-50 µg/µL streptomycin, and 10% FBS (Corning). The cells were differentiated for 15 days by adding 1.7% DMSO (dimethylsulfoxide) to the proliferation medium, as previously described (Aninat et al., 2006).

The cells were incubated at 37°C in a humidified atmosphere of 5% CO₂.

### 2.2.2 Exposure of cells to chemicals

The HepG2 cells exposure set-up followed the study by Grosso et al. (2025). The cells between passages 15–30 were seeded at 14,000 cells/well (100 µL cell suspension/well) in black 96-well microplates with transparent bottoms (Cat. No. 655090, Greiner Bio-One, Kremsmunster, Austria), corresponding to a seeding density of 41,000 cells/cm². Bisphenols were purchased from Sigma-Aldrich (Prague, Czechia): Bisphenol A (BPA; Cat. No. 239658), Bisphenol S (BPS; Cat. No. 103039), Bisphenol F (BPF; Cat. No. B47006) and 1000× stock solutions were prepared in DMSO. After 24 h of cell growth, 100 µL of exposure solutions (500-fold diluted stocks in culture media) were added to each well, resulting in a final concentration of 1000-fold diluted compound stock solution and/or vehicle solvent (DMSO). The cells were exposed to BPA, BPF, and BPS at concentrations of 0.1, 1, 10, and 25 µM for 0, 24, and 48 h, with a vehicle control (0.1% DMSO) included. These concentrations were chosen based on findings in the study by Grosso et al. (2025) and were non-cytotoxic under this setup. The average cell density reached approximately 220,000 cells/cm² after 72 h of growth in these conditions, as reported by Grosso et al. (2025).

The exposure set-up for HepaRG followed the study by Bernal et al. (2024). Differentiated HepaRG cells were seeded at a density of 800,000 cells/well (1 mL of cell suspension per well) in 12-well plates (Falcon 353043), corresponding to a seeding density 209,000 cells/cm². BPA (Cat. No. 239658; Sigma-Aldrich, Saint-Quentin-Fallavier, France) was dissolved in DMSO to make 1000× stock solutions. Five days post-seeding, differentiated HepaRG cells were exposed by adding 1 mL of non-cytotoxic concentrations of BPA (final 10 and 25 µM) in medium with a final concentration of 1.7% DMSO. To ensure concurrent sample extraction at the end of the experiment, cells were subjected to inverse kinetics and treated for 1, 10, 20, 30 and 45 min and 1, 2, 4 and 24 h. Because preliminary experiments revealed a rapid decline in the concentration of the parent compound in the culture medium—dropping below the limit of detection within 1 to 4 h of incubation—subsequent experiments were repeated with a focus on shorter time intervals ranging from 1 min to 4 h.

### 2.2.3 Free concentration determination

The freely bioavailable concentrations of the selected bisphenols in the culture medium were determined using the Rapid Equilibrium Dialysis (RED) method. This technique enables the quantification of the fraction not bound to protein constituents in the medium (fu<sub>diluted</sub>). The procedure followed instructions for the RED kit (Thermo Scientific, Cat. Nos. 90006, 89809, 15036, 28372). A 200 µL medium sample (vehicle control – 0.1% DMSO, bisphenols at concentrations of 1, and 10 µM) was added to the sample chamber, while 400 µL of PBS (phosphate buffer, pH 7.2) was introduced into the buffer chamber. Following a 6-h equilibration period at 37°C, medium and buffer were collected, diluted, and mixed with an equal volume of buffer to the sample (and vice versa). Diluted samples of individual bisphenols at a corresponding concentration were pooled (50 µL from each sample). A 300 µL of ice-cold acetonitrile, including the internal standards (ISTD: BPA – Cat. No. CLM-4325-1.2, BPF – Cat. No. CLM-9866-1.2, BPS – Cat. No., CLM-9319-1.2, Cambridge Isotope Laboratories, Tewksbury, MA, USA; final concentration: 10 µg/L), was mixed with 150 µL of the pooled samples, vortexed for 1 min, sonicated for 15 min, and centrifuged (11,000 RPM; 4°C) for 10 min. The supernatant was transferred to methanol-prewashed minitubes. Subsequently, the
samples were dried using a vacuum DNA mini concentrator (Trigon-plus, Bratislava, Slovakia) at 45°C then dissolved in 80 µL of 50% methanol before measurement.

### 2.2.4 Extraction and analysis of medium and cell chemical concentrations

#### HepG2 experiments

The medium of HepG2 cell lines was sampled at 0, 24, and 48-h post-exposure. The media and procedural blanks (containing medium and chemicals without cells) were pooled from wells with the same bisphenol concentration. 150 µL of each pooled samples was mixed with 300 µL of acetonitrile containing ISTD and transferred to methanol-prewashed minitubes. Samples were vortexed for 1 min, sonicated for 15 min, and centrifuged (11,000 RPM; 4°C) for 10 min. A 383 µL supernatant was transferred to a new prewashed minitube, dried using a vacuum DNA mini concentrator (Trigon-plus) at 45 °C, and reconstituted in 80 µL of 50% methanol prior to measurement.

The cells were sampled at 0, 24, and 48-h post-exposure. The exposed cells were washed twice with ice-cold PBS (pH 7.2) and frozen in liquid nitrogen, then stored at -80°C until processing. 120 µL of ice-cold acetonitrile:water solution (2:1) containing ISTD was pipetted, and the plate was placed in a cooled sonication bath for 15 min. The plate was centrifuged (4000 × g, 4°C) for 10 min, and 80 µL of supernatant was transferred to methanol-prewashed minitubes. The samples were dried using a Savant SpeedVac (Trigon-plus) at 45°C and dissolved before measurement with 80 µL of 50% methanol.

The levels of BPA, BPF, and BPS were determined using liquid chromatography with tandem mass spectrometric detection (LC-MS/MS). The samples were analyzed using an Agilent 1200 series liquid chromatography (HPLC) system with a Waters Acquity BEH C-18 analytical column (100×2.1 mm, 1.7 µm) maintained at 30°C and equipped with an Acquity VanGuard C-18 pre-column. The mobile phases for the gradient separation of the analytes were a 0.1 mM water solution of ammonium fluoride (component A) and methanol with the addition of 0.1 mM ammonium fluoride (component B). The flow rate was 0.25 mL/min, and the injection volume was 5 µL. Analyte detection was performed using an Agilent 6495 tandem mass spectrometer operating in negative electrospray ionization mode at 400°C, with N₂ as the nebulizer gas and a capillary voltage of -4 kV. A ¹³C-labeled isotope dilution method was used for the quantification of the analytes. Quality control was ensured by participation in the HBM4EU quality assurance ICI-EQUAS programme (Esteban López et al., 2021) and the OSEQAS quality assessment scheme, organized by the Centre de Toxicologie du Québec (INSPQ), successfully completed since 2018. The limits of detection and quantification are 0.03/0.11, 0.06/0.21, and 0.04/0.13 µM for BPA, BPF, and BPS, respectively.

#### HepaRG experiments

Following exposure to BPA, 300 µL of the HepaRG medium from each condition's superior phase was collected in glass vials and stored at -20°C until processed with the extraction protocol. The protocol involved the addition of 600 µL of ice-cold acetonitrile containing 5 µM alpelisib (a fluorescent probe used as ISTD for liquid chromatography with fluorescence detection) to the exposure mediums. The solutions were then subjected to ultrasonication for a period of 15 min using an ultrasonic bath, followed by centrifugation at 11,000 RPM for 10 min at a temperature of 4°C. The resultant supernatants were subsequently transferred to a fresh tube and subjected to a process of drying using a SpeedVac system (ThermoFisher).

After the removal of the exposure medium, the cells were washed twice with ice-cold PBS. Then, 500 µL of an acetonitrile:water (2:1) solution containing 5 µM alpelisib. Following a 15-min incubation on ice, the cells were scraped, transferred into a new tube, and incubated for a further 15 min on ice. Thereafter, the solution was subjected to centrifugation at 11,000 RPM for 10 min at 4°C. The resultant supernatants were then transferred to a new tube and dried using a SpeedVac system.

Experiments were performed in three independent biological replicates. Once extracted, all samples were stored at 4°C until the completion of biological replicates. Finally, all residue samples were resuspended in 50 µL of an acetonitrile:water solution with 0.1% formic acid and sonicated in an ultrasonic bath before performing the LC-FLD analysis.

## 2.3 Cellular biokinetic model

### 2.3.1 Model structure

The biokinetic INSIGHT model is based on the VCBA and VIVD models developed by Comenges et al. (2017) and Fisher et al. (2019), respectively. It includes the six initial compartments of the previous VIVD model (i.e., lysosomes, mitochondria, a compartment lumping other organelles, medium, air, and plate). A microsomal compartment has been added due to its major involvement in chemical metabolism, especially in hepatocytes (Fig. 1). The overall compartmental architecture (plate, air, medium/water, and the target system represented as a set of internal compartments) is based on a previously published in vitro zebrafish eleutheroembryo model (Billat et al., 2023).

Sections 2.3.2 to 2.3.6 detail the modifications and adaptations implemented in the development of the revised/developed biokinetic model. These include refinements to the cell growth equation, modifications to the determination of partition coefficients, and revisions to dynamic aspects such as inter-compartmental exchanges and metabolic degradation processes.

### 2.3.2 Structural refinement and cell growth

#### Cell proliferation

The current version of the model assumes that cells will continue to grow until they cover the entire surface of the well, without overlapping cells, as follows:

$$ \frac{dN_{cell}}{dt} = R_{cell} \times N_{cell} \times (1 - \frac{N_{cell} \times S_{cell}}{S_{culture}}) \quad (1) $$
<figure><img src="image_3.png" /><figcaption>Fig. 1: Structure of the biokinetic model assuming that solely the free fraction can cross cell membranes, undergo vaporization, or bind to plate walls</figcaption></figure>

Where $N_{cell}$ is the number of cells at time t, $R_{cell}$ is the cell growth rate (h⁻¹), $S_{cell}$ is the surface area of a single cell (mm²), and $S_{culture}$ is the culture surface area (mm²) i.e. the surface available for cell growth. The possible cell multilayer formation was not investigated in this study.

### Surface coverage

Similarly, it is considered that the surface area of each cell in contact with the medium is equivalent to half a sphere per cell until the cells reach confluence. At this point, the surface area of the culture is defined as the maximal surface area for ex-changes.

$$ \frac{dS_{contact\ total}}{dt} = \frac{dN_{cell}}{dt} \times S_{contact} \times \left(1 - \frac{N_{cell} \times S_{cell}}{S_{culture}}\right) \quad (2) $$

Where $S_{contact}$ and $S_{contact\ total}$ are the cell and total cell surface area in contact with the medium (mm²).

### 2.3.3 Literature and QSAR-derived parameters

The partition coefficients of the chemical at steady-state are predicted as described in the VIVD model and the VCBA model, using a generic quantitative structure-activity relationship approach (Fisher et al., 2019; Comenges et al., 2017). The determination of the octanol-water partition coefficient at experimental temperature, the air-medium partition coefficient, the cellular and subcellular partition coefficients and the free chemical fractions, as described in the aforementioned publications, is recalled in Supplemental Information (Section S1.2¹). Plate polymer-medium and blood-to-plasma partition coefficients have undergone significant modification with respect to the original models and are detailed below.

#### Polymer/medium partition coefficients

A binding to the plate has been previously evidenced by Kramer et al. (2012) for polycyclic aromatic hydrocarbon compounds, where, a linear correlation between the octanol-water partition coefficient ($P_{ow}$) and the binding to the plate was demonstrated and used in both the VCBA and VIVD models.

Fischer et al. (2018) updated the previous equation using 14 neutral chemicals with physicochemical properties that cover a wide range of hydrophobicity and molecular weights in polystyrene plates:

$$ PC_{polymer:medium} = 1.04 \times (10^{0.56 \times \log P_{ow}T_{sys} - 0.05}) \quad (3) $$

Where $PC_{polymer:medium}$ is the polystyrene medium partition coefficient (L.L⁻¹, volume of polystyrene: volume of medium) and 1.04 is the density of polystyrene (kg.L⁻¹).

#### Blood-to-plasma partitioning

Biomembranes can contain neutral and charged acidic phospholipids. The acidic phospholipid association constant ($K_{aAP}$) describes the binding affinity of chemicals/compounds to acidic phospholipids and plays, therefore, a role in the modelling of the compound of interest with subcellular compartments. KaAP is mainly relevant for strong bases and ampholytes with a strong base. Therefore, for weak bases, acids and neutral compounds $K_{aAP}$ can be considered negligible. The blood-to-plasma partitioning ratio (BP) is employed in the VIVD model to estimate the $K_{aAP}$. Consequently, this parameter is indispensable for estimating the partition coefficient; however, there is a paucity of experimental data available. In the absence of data, a common approach is to use fixed ratios, specifically 0.55 for acidic compounds and 1 for neutral and basic compounds (Riley et al., 2005; Sohlenius-Sternbeck et al., 2010). Adachi et al. (2024) have recently proposed a QSAR model to approximate BP ratios as follows:

$$ BP = 0.45 \times \left( (0.617 \times \log\left(\frac{1-f_u}{f_u}\right) + 0.208) \times f_u - 1 \right) + 1 \quad (4) $$

With BP the blood-to-plasma ratio (unitless) and $f_u$ is the free fraction in plasma (unitless). This approach has been used in instances where data was not available.

### 2.3.4 Dynamic flows and intercompartmental exchanges

Partition coefficients are estimated at steady-state. However, in biological systems, the steady state is rarely reached. Therefore, dynamic flows were added to the model. The majority of these flows formulations were based on either QSARs or mechanistic models derived from the VCBA model (Comenges et al., 2017). Consequently, apart from the air flow presented in
supplementary file 1¹ which has not been modified from Comenges et al. (2017), the flows have been adapted to the proposed model structure.

### System exchanges (air and plate)

The concentration of chemical binding to the plate walls ($C_{polymer}$, nmol.mm⁻³) of the experimental device and the evaporation of the compound in the air ($C_{air}$, nmol.mm⁻³) were modeled with dynamic flows as described in Fischer et al. (2018) and Billat et al. (2023) assuming that only the free unionized fraction is able to reach these compartments:

$$ \frac{Q_{polymer}}{dt} = F_{polymer} \times \left( C_{water} \times f_{diluted} \times \frac{1}{1 + (1 - \sum Y_{medium})} - \frac{C_{polymer}}{PC_{polymer:medium}} \right) \quad (5) $$

$$ \frac{Q_{air}}{dt} = F_{air} \times S_{am} \times \left( C_{water} \times f_{diluted} \times \frac{1}{1 + (1 - \sum Y_{medium})} - \frac{C_{air}}{PC_{air:medium}} \right) - (Ke_{air} + Ke_{air:renewal}) \times Q_{air} \quad (6) $$

With $Q$ the quantity (nmol) fixed to the plate or in air, $F_{polymer}$ the exchange rate between water and the plate (µL.h⁻¹), $f_{diluted}$ the free fraction in the medium (unitless), $Y_{medium}$ the ionized fraction in the medium (unitless, estimated as described in supplementary file 1¹), $C_{water}$ the concentration in water (mM), $F_{air}$ the exchange rate between water and the air (mm.h⁻¹), $S_{am}$ the surface of air medium exchanges (mm²), $Ke_{air}$ is the abiotic degradation rate in headspace (h⁻¹) and $Ke_{air:renewal}$ is the loss of compound due to well-incubator exchanges (set to 1.73 h⁻¹ based on experimental O₂ gas exchange values (Allen et al., 2001)).

### Diffusion in polystyrene

Fischer et al. (2018) accurately described the sorption to the polystyrene wall of 14 chemicals with logPow ranging from 1.98 to 8.68 and molecular weight ranging from 178 to 396 g.mol⁻¹. They made the hypothesis that compounds equilibrate almost instantaneously with the most internal polystyrene layer and then enter the wall deeper with a time course. To spare the computing resources, the partial differential equation proposed by Fischer et al. (2018) was transformed into an ordinary differential equation by discretization of the plastic compartment. This step required the introduction of the polystyrene diffusion coefficient ($D_{PS}$), as described by the following equations:

$$ \frac{Q_{polymer_{layer_i}}}{dt} = F_{polymer:polymer} \times \left( C_{polymer_{layer_{i+1}}} - 2 C_{polymer_{layer_i}} + C_{polymer_{layer_{i-1}}} \right) \quad (7) $$

With

$$ F_{polymer:polymer} = D_{PS} \times S_{pm} \times \frac{PC_{polymer:polymer}}{\frac{thickness}{n_{layers}}} \quad (8) $$

Where $PC_{polymer:polymer} = 1 \cdot L \cdot L^{-1}$ by definition.

Where $D_{PS}$ is the diffusion coefficient in polystyrene mm².h⁻¹, $S_{pm}$ is the surface of exchanges between plate and medium (mm²), thickness is the thickness of the plate walls (mm), $n_{layers}$ is the number of polystyrene layers and $Q_{polymer_{layer_i}}$ is the amount of compound in the layer i (nmol). The number of layers has been set to 10 while increasing the number of layers would improve the accuracy of the plate chemical concentration but would require significantly more computing power.

### Medium/cell exchanges

In the VIVD model, the intracellular concentrations ($C_i$ in nmol.µL⁻¹ or mm⁻³) were assumed to be, at any time, proportional to the concentration in the medium ($C_{medium}$), suggesting an instantaneous equilibrium between the cells and the medium. To better describe the influx of the chemical in the cell, a flow from the medium to the cell was added to mimic the diffusion of the substance in the current biokinetic model:

$$ \frac{dQ_{others}}{dt} = F_{medium:cell} \times \left( C_{medium} \times f_{diluted} - \frac{C_{others} \times f_{u_{cell}}}{PC_{others:medium}} \right) - Ke \times C_{others} - \frac{dQ_{others:met}}{dt} \quad (9) $$

$$ \frac{dQ_i}{dt} = F_{medium:cell} \times ScV_i \times \left( C_{medium} \times f_{diluted} - \frac{C_i \times f_{u_{cell}}}{PC_{i:medium}} \right) - Ke \times C_i - \frac{dQ_{i:met}}{dt} \quad (10) $$

Where $Q_{others}$ quantity in the cell (including cytoplasm, cytoplasmic membrane, nucleus and excluding organelles of interest, nmol), $Q_i$ quantity in the organelles of interest (mitochondria, lysosomes and microsomes, nmol), $Ke$ the resulting net efflux rate (µL.h⁻¹), $ScV_i$ is the fraction (v/v) of the organelles i, considered as spheres, divided by the cell volume, $C_i$ is the concentration in the organelle i, $F_{medium:cell}$ is the permeability rate (µL.h⁻¹), $PC_{i:medium}$ are the partition coefficient between the compartment I and the medium, and $Q_{met}$ the metabolized amount when applicable (nmol). In the absence of data from the literature, the uptake flow has been initially estimated as in Comenges et al. (2017) using Caco-2 cells permeability data as follows:

$$ F_{medium:cell} = 10 \times 10^{1.1711 + 0.98 \frac{\text{Log}P_{\text{Pow}_{\text{Sys}}}}{0.0011 \text{MV}}} \times S_{\text{contact total}} \quad (11) $$

Where 10 is used to convert cm into mm, MV is the molar volume (cm³.mol⁻¹), $S_{contact total}$ the total surface area of cells in contact with the medium (as described in 0, mm²) and LogPow$_{Sys}$ the LogPow value at the experimental temperature (estimated as described in S.I. 1.2.1).

The molar volume replaced the initial molecular weight since it more accurately described the steric volume of the molecule (Edward, 1970).

### Medium mass balance

Finally, the variation of the parent compound amount (nmol) in the medium could be described as follows:
$$
\begin{equation}
\begin{aligned}
\frac{dQ_{\text{medium}}}{dt} = F_{\text{polymer}} &\times \left( \frac{C_{\text{polymer}}}{PC_{\text{polymer:medium}}} - C_{\text{water}} \times f u_{\text{diluted}} \times \frac{1}{1 + (1 - \sum Y_{\text{medium}})} \right) + \\
&F_{\text{air}} \times S_{\text{aw}} \times \left( \frac{C_{\text{air}}}{PC_{\text{air:medium}}} - C_{\text{water}} \times f u_{\text{diluted}} \times \frac{1}{1 + (1 - \sum Y_{\text{medium}})} \right) - \\
&\qquad \frac{dQ_{\text{others}}}{dt} - \\
&\qquad \sum \frac{dQ_i}{dt} - \\
&\qquad K e_{\text{medium}} \times Q_{\text{medium}}
\end{aligned}
\tag{12}
\end{equation}
$$

Where $Ke_{\text{medium}}$ is the abiotic degradation rate in medium (h⁻¹).

## 2.3.5 Metabolic processes

Few cellular models used in *in vitro* assays are metabolically competent (Qu et al., 2021). However, for these cell models, metabolism has been implemented in lysosomes, microsomes and other compartments (including the cytoplasm). Users should inform these metabolic values (using metabolic stability results for instance). The variation of metabolite amount in the cell compartment ($Q_{\text{met}}$, nmol) with time could be described either using linear metabolism as approximation in case of high clearance rates and low parent compound concentrations (13) or Michaelis–Menten kinetics which also considers a saturation of e.g. metabolizing enzymes (14) as respectively:

$$ \frac{dQ_{\text{met}}}{dt} = \frac{N_{\text{cell}}}{10^6} \times K_{\text{met}} \times (C_{\text{mic}} + C_{\text{lyso}} + C_{\text{others}}) \quad (13) $$

$$ \frac{dQ_{\text{met}}}{dt} = \frac{N_{\text{cell}}}{10^6} \times \left( \frac{C_{\text{mic}} \times V_{\text{max}}}{K_m + C_{\text{mic}}} + \frac{C_{\text{lyso}} \times V_{\text{max}}}{K_m + C_{\text{lyso}}} + \frac{C_{\text{IW}} \times V_{\text{max}}}{K_m + C_{\text{IW}}} + \frac{C_{\text{others}} \times V_{\text{max}}}{K_m + C_{\text{others}}} \right) \quad (14) $$

Where $C_{\text{mic}}$, $C_{\text{lyso}}$ and $C_{\text{others}}$ are the microsome, lysosome or other organelles concentrations of the parent compound (nmol.µL⁻¹ or mm⁻³), $K_{\text{met}}$ is the initial linear rate of apparent cellular metabolic clearance per 10⁶ cells (µL.h⁻¹. 10⁻⁶ cells), $V_{\text{max}}$ is the initial maximum rate of metabolism per 10⁶ cells (nmol.h⁻¹. 10⁻⁶ cells) and $K_M$ is the Michaelis-Menten constant (nmol.µL⁻¹) here considered to be identical for each compartment.

However, $K_{\text{met}}$ can be provided experimentally using observed clearance therefore including non-metabolizing organelles as well ($K_{\text{met,app}}$). Thus, a correction factor is required for this observed value as follows:

$$ K_{\text{met}} = K_{\text{met,app}} \times \frac{1}{\text{ScV}_{\text{mic}} + \text{ScV}_{\text{lyso}} + \text{ScV}_{\text{others}}} \quad (15) $$

Where $\text{ScV}$ are the ratio (volume/cell volume) of the microsomes (mic), lysosomes (lyso) and other compartments (others) in the cell (Table S1¹).

## 2.3.6 User defined parameters

This section lists the parameters requiring user input either measured experimentally or extracted from literature sources. These include the plate geometry, cell line–specific morphological parameters, experimental conditions (temperature, pH, serum fraction), chemical physicochemical properties (compound type, pKa, MW, MV, logPow, Henry’s constant), metabolic parameters, and abiotic degradation rates. An exhaustive list of the INSIGHT parameters can be found in Table S7¹.

These user-defined parameters are summarized in Table 1.

<table><caption>Tab. 1: Parameters used in the INSIGHT model</caption><thead><tr><th>Parameter name (unit, if any)</th><th>Code name</th><th>Note</th></tr></thead><tbody><tr><td colspan="3">Cell plate characteristics, sources: manufacturer specifications or user measurements</td></tr><tr><td>Culture area (mm²)</td><td>D_well</td><td rowspan="4">Plate type characteristics have been included in the model for 60cm² surface Petri dishes, 6, 12, 24, 48, 96, 384, and 1536 well plates</td></tr><tr><td>Top well diameter (mm)</td><td>D_top</td></tr><tr><td>Well depth (mm)</td><td>Depth</td></tr><tr><td>Plate wall thickness (mm)</td><td>Thick</td></tr><tr><td colspan="3">Cell line characteristics (see Section 2.1.1 and Table S1¹ for selected cell lines), sources: literature data or user measurements</td></tr><tr><td>Fraction of intracellular water (v/v)</td><td>ScV_2</td><td>Default: 0.82</td></tr><tr><td>Fraction of lipids (v/v)</td><td>ScV_lip</td><td>Default: 0.03</td></tr><tr><td>Fraction of proteins (v/v)</td><td>ScV_prot</td><td>Default: 0.15</td></tr><tr><td>Volume of a single cell (µL)</td><td>Vcell</td><td>Default: 2.71.10<sup>-6</sup></td></tr><tr><td>Radius of a single cell (mm)</td><td>Cellr</td><td>Default: 8.74.10<sup>-3</sup></td></tr><tr><td>Cell growing rate (h<sup>-1</sup>)</td><td>sc_cell</td><td></td></tr><tr><td colspan="3">Experimental conditions, sources: user specifications</td></tr><tr><td>Temperature (°C)</td><td>temp</td><td></td></tr><tr><td>Culture medium pH</td><td>pH_0</td><td>Default: 7.4</td></tr><tr><td>Fraction of serum in total media (v/v)</td><td>scV_10</td><td></td></tr><tr><td>FBS pH</td><td>pH_10</td><td>Default: 7.0</td></tr><tr><td colspan="3">Chemical-specific parameters, user specifications</td></tr><tr><td>Type of compound</td><td>cmp_type</td><td>neutral, monobase, dibase, monoacid, diacid, ampholyte</td></tr><tr><td>pKa1</td><td>pKa1</td><td>Not mandatory if neutral</td></tr><tr><td>pKa2</td><td>pKa2</td><td>Not mandatory if neutral, monobase, and monoacid</td></tr><tr><td>Molecular weight (g.mol<sup>-1</sup>)</td><td>MW</td><td></td></tr></tbody></table>
<table><caption>Tab. 2: Parameter values used in the sensitivity analysis</caption><tr><td>Molar volume (mL.mol<sup>-1</sup>)</td><td>MV</td><td></td></tr><tr><td>Decimal log of the octanol water partition coefficient at 25 Celsius degrees</td><td>log-Pow_Tref</td><td></td></tr><tr><td>Henry's law constant (Pa.m<sup>3</sup>.mol<sup>-1</sup>)</td><td>Henry</td><td></td></tr><tr><td>Flag for Michaelis-Menten vs linear metabolism (0 = linear, 1 = Michaelis-Menten)</td><td>Michaelis</td><td></td></tr><tr><td>Michaelis-Menten constant (nmol.µL<sup>-1</sup>)</td><td>Km</td><td>If Michaelis-Menten metabolism</td></tr><tr><td>Maximum rate of metabolism (nmol.h<sup>-1</sup>.10<sup>-6</sup> cells)</td><td>Vmax</td><td>If Michaelis-Menten metabolism</td></tr><tr><td>Linear rate of cellular metabolic clearance (µL.h<sup>-1</sup>.10<sup>-6</sup> cell)</td><td>K_m</td><td>If linear metabolism</td></tr><tr><td>Abiotic degradation in air (h<sup>-1</sup>)</td><td>Ke_air</td><td></td></tr><tr><td>Abiotic degradation in medium (h<sup>-1</sup>)</td><td>Ke_me-dium</td><td></td></tr></table>

For the Morris method, average values were calculated as the mean across all cell lines listed in Table S1¹, when applicable, with the parameter distribution fixed at 5%. For the Sobol' method, parameter distributions were defined based on the relative ranges reported in the literature dataset summarized in Table S2¹, when available.

<table><thead><tr><th>Parameters</th><th>Unit</th><th>Morris average value</th><th>Morris distribution</th><th>Sobol distribution</th><th>Code names</th></tr></thead><tbody><tr><td colspan="6"><strong>Assay characteristics</strong></td></tr><tr><td>Culture medium pH <sup>a</sup></td><td></td><td>7.4</td><td>Uniform ± 5%</td><td>Uniform ± 10%</td><td>pH_0</td></tr><tr><td>Fraction of serum in total media <sup>a</sup></td><td></td><td>0.05</td><td>Uniform ± 5%</td><td>Uniform ± 5%</td><td>scV_10</td></tr><tr><td>Temperature of the assay <sup>a</sup></td><td>°C</td><td>37</td><td>Uniform ± 5%</td><td>Uniform [20;37]</td><td>temp</td></tr><tr><td colspan="6"><strong>Cell characteristics</strong></td></tr><tr><td>Fraction (V/V) of cell water <sup>a</sup></td><td></td><td>0.81</td><td>Uniform ± 5%</td><td></td><td>scV_2</td></tr><tr><td>Fraction (V/V) of cell lipids <sup>a</sup></td><td></td><td>0.04</td><td>Uniform ± 5%</td><td></td><td>scV lip</td></tr><tr><td>Fraction (V/V) of cell proteins <sup>a</sup></td><td></td><td>0.15</td><td>Uniform ± 5%</td><td></td><td>scV_prot</td></tr><tr><td>Cell volume <sup>a</sup></td><td>µL</td><td>2.71.10<sup>-6</sup></td><td>Uniform ± 5%</td><td>Uniform [1.76.10<sup>-6</sup>;5.12.10<sup>-6</sup>]</td><td>Vcell</td></tr><tr><td>Cell radius <sup>a</sup></td><td>mm</td><td>8.74.10<sup>-3</sup></td><td>Uniform ± 5%</td><td>Uniform [6.5.10<sup>-3</sup>;1.5.10<sup>-2</sup>]</td><td>Cellr</td></tr><tr><td>Initial number of cells <sup>a</sup></td><td></td><td>4.00.10<sup>5</sup></td><td>Uniform ± 5%</td><td>Uniform ± 10%</td><td>Ncell</td></tr><tr><td colspan="6"><strong>Molecule characteristics</strong></td></tr><tr><td>pKa of the molecule <sup>a</sup></td><td></td><td>8</td><td>Uniform ± 5%</td><td>Uniform [-3.7;14]</td><td>pKa1</td></tr><tr><td>Molar volume <sup>a</sup></td><td>cm<sup>3</sup>.mol<sup>-1</sup></td><td>200</td><td>Uniform ± 5%</td><td></td><td>MV</td></tr><tr><td>LogPow at 25°C <sup>a</sup></td><td></td><td>2</td><td>Uniform ± 5%</td><td>Uniform [-3.9;9.97]</td><td>logPow_Tref</td></tr><tr><td>Henry constant at 25°C <sup>a</sup></td><td>Pa.m<sup>3</sup>.mol<sup>-1</sup></td><td>10<sup>-5</sup></td><td>Uniform ± 5%</td><td></td><td>Henry</td></tr><tr><td>Blood to plasma partitioning ratio <sup>a</sup></td><td></td><td>0.55</td><td>Uniform ± 5%</td><td></td><td>BP</td></tr><tr><td>Free fraction of the compound in plasma <sup>a</sup></td><td></td><td>0.1</td><td>Uniform ± 5%</td><td>Uniform [10<sup>-4</sup>;1]</td><td>fu</td></tr><tr><td>Free fraction of the compound in the medium <sup>b</sup></td><td></td><td>0.1</td><td>Uniform ± 5%</td><td>Uniform [10<sup>-4</sup>;1]</td><td>fu_diluted</td></tr><tr><td>Free fraction of the compound in the cell <sup>a, b</sup></td><td></td><td>0.1</td><td>Uniform ± 5%</td><td>Uniform [10<sup>-4</sup>;1]</td><td>fu_cell</td></tr><tr><td>Metabolic rate <sup>b</sup></td><td>nmol.h<sup>-1</sup>.10<sup>-6</sup> cells</td><td>0.2</td><td>Uniform ± 5%</td><td>Uniform [0.1;100]</td><td>K_m</td></tr><tr><td colspan="6"><strong>Partition coefficients</strong></td></tr><tr><td>Intracellular water/medium <sup>b</sup></td><td></td><td>50</td><td>Uniform ± 5%</td><td></td><td>P_iw_me-dium</td></tr><tr><td>Lysosome/ Intracellular water <sup>b</sup></td><td></td><td>50</td><td>Uniform ± 5%</td><td></td><td>P lyso_me-dium</td></tr><tr><td>Mitochondria/ Intracellular water <sup>b</sup></td><td></td><td>50</td><td>Uniform ± 5%</td><td></td><td>P mito_me-dium</td></tr><tr><td>Microsome/ Intracellular water <sup>b</sup></td><td></td><td>50</td><td>Uniform ± 5%</td><td></td><td>P mic_me-dium</td></tr><tr><td>Other compartments/ Intracellular water <sup>b</sup></td><td></td><td>50</td><td>Uniform ± 5%</td><td>Uniform ± 10%</td><td>P oth-ers_medium</td></tr><tr><td>Air/medium <sup>b</sup></td><td></td><td>0.01</td><td>Uniform ± 5%</td><td>Uniform ± 10%</td><td>P air_me-dium</td></tr><tr><td>Polymer/medium <sup>b</sup></td><td></td><td>0.01</td><td>Uniform ± 5%</td><td></td><td>P poly-mer_medium</td></tr><tr><td colspan="6"><strong>Exchange flows</strong></td></tr><tr><td>Medium to cell flow <sup>b</sup></td><td>µL.h<sup>-1</sup></td><td>10</td><td>Uniform ± 5%</td><td>Uniform [0.01;100]</td><td>F_cell</td></tr><tr><td>Elimination flow <sup>a,b</sup></td><td>µL.h<sup>-1</sup></td><td>0.01</td><td>Uniform ± 5%</td><td></td><td>Ke</td></tr></tbody></table>

<footnote>aused in the primary parameters analysis, bused in the secondary parameters analysis</footnote>
## 2.4 Model analysis

### 2.4.1 Sensitivity analysis

To identify the most influential parameters described in Section 2.3.6 on the cell and medium concentration, sensitivity analyses (SA) have been conducted in two steps, simulating a 96-well plate with a monoacid molecule in cells with average biochemical values (calculated as the mean across all cell lines listed in Table S1¹). The 6 most influential parameters were selected using a one-step-at-a-time (OAT) global SA using Morris method (Morris, 1991) at 3 different timepoints: 0.1, 1 and 12 hours. The sensitivity of the tested parameters has been estimated with uniform distributions ± 5% (Tab. 2). Then, retained parameters were evaluated using the variance-based Sobol' method (Saltelli et al., 2010; Sobol' et al., 2007) using the range of values observed in the literature search (Tab. S1 and S2¹).

Two different analyses were conducted, one for the exploration of the primary parameters *i.e.* parameters that are provided by the User, and one for the secondary parameters *i.e.* parameters that can be determined from the primary parameters.

### 2.4.2 Bayesian inference

Bayesian inference was used to calibrate the model of medium/plastic exchange. The concentration kinetics of 14 molecules in the medium and polystyrene, along with their partition coefficients retrieved from Fischer et al. (2018), were used to calibrate the individual D<sub>PS</sub> values and the population F<sub>polymer</sub> value using the proposed ordinary differential equations and Bayesian inference. For F<sub>polymer</sub>, neither experimental nor predicted values were available. Therefore, a uniform non informative prior distribution (10<sup>-3</sup> – 10<sup>3</sup> µL·h<sup>-1</sup>) was used to avoid impacting the posterior distribution. For D<sub>PS</sub>, a normal prior was centered on the value proposed by Fischer et al. (2018) with a wide variance to allow departure from this initial estimate (μ = 7.42·10<sup>-7</sup>, σ = 7.42·10<sup>-7</sup> mm<sup>2</sup>·h<sup>-1</sup>) truncated at [1.10<sup>-9</sup>–1.10<sup>-4</sup>]. Once convergence was reached (Gelman index < 1.1 (Gelman and Rubin, 1996)), the final 10,000 parameter vectors from each chain were retained to form the *a posteriori* distribution of parameter values, which were then used for subsequent simulations.

Bayesian inference was also used to fit the model parameter distributions of the medium/cell exchange flow to each observed concentration per chemical of the calibration data set using the prior distributions estimated by Comenges et al. (2017) using Caco-2 cell permeability data (Equation 11, Tab. 3).

The collected data from literature shows various kinetic profiles with a high variability, especially around the expected steady-state values¹. To avoid any systematic bias, the QSAR model for the intracellular/medium partition coefficient was corrected using an uncertainty factor on the cell:medium partition coefficient (ffpc). The ffpc was adjusted independently for each dataset at the cell line level and applied to account for systematic biases in model predictions (e.g., correction of QSAR prediction systematic bias and cell-type-specific biochemical composition).

Different model structures were tested and compared based on their performance (Akaike information criteria AIC and Bayesian information criteria BIC) and the fit to the observed data (Root Mean Squared Error – RMSE- and visual check) including or not, an elimination rate (Ke, µL·h<sup>-1</sup>) and, or ffpc calibrated for cell lines either globally (as a hyperparameter) or per cell type (using hierarchical Bayesian modeling per cell line).

<table><caption>**Tab. 3: Summary of prior and posterior distributions for the estimated parameters of the PBK model**
The distributions were obtained using a Bayesian calibration approach.</caption><thead><tr><th>Parameter</th><th>A priori distribution</th><th>Maximum posterior value (MPV)</th><th>Credibility interval 95%</th></tr></thead><tbody><tr><td>Flow F<sub>medium:cell</sub> (µL·h<sup>-1</sup>)</td><td>10 × 10<sup>Baseline + F<sub>logP</sub> × LogP<sub>owSys</sub> - F<sub>MV</sub> × MV</td><td></td><td></td></tr><tr><td>Baseline</td><td>Uniform [-5, 5]</td><td>-3.19</td><td>[-3.33;-2.82]</td></tr><tr><td>F<sub>logP</sub></td><td>Normal (0.98, 0.49)</td><td>0.45</td><td>[0.419;0.495]</td></tr><tr><td>F<sub>MV</sub></td><td>Normal (1.10<sup>-3</sup>, 5.5·10<sup>-4</sup>)</td><td>-0.00099</td><td>[-0.00123;-0.000578]</td></tr><tr><td>Correction for partition coefficient (ff<sub>pc</sub>)</td><td></td><td></td><td></td></tr><tr><td>HepaRG</td><td>LogNormal (1,2)</td><td>1.28</td><td>[0.608;4.76]</td></tr><tr><td>HepG2</td><td>LogNormal (1,2)</td><td>4.84</td><td>[2.39;13.1]</td></tr><tr><td>3T3 Balb/c</td><td>LogNormal (1,2)</td><td>1.15</td><td>[0.48;3.15]</td></tr><tr><td>PC-12</td><td>LogNormal (1,2)</td><td>0.424</td><td>[0.259;4.1]</td></tr><tr><td>MCF-7</td><td>LogNormal (1,2)</td><td>0.561</td><td>[0.237;3.93]</td></tr><tr><td>RTgill-W1</td><td>LogNormal (1,2)</td><td>10.0</td><td>[5.36;24.4]</td></tr><tr><td>HEK293T</td><td>LogNormal (1,2)</td><td>0.256</td><td>[0.145;0.705]</td></tr><tr><td>Net elimination rate (µL·h<sup>-1</sup>) (Ke)</td><td></td><td></td><td></td></tr><tr><td>HepaRG</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.658</td><td>[0.459;2.82]</td></tr><tr><td>HepG2</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.000976</td><td>[0.00149;0.00663]</td></tr><tr><td>3T3 Balb/c</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>8.57</td><td>[7.68;21.9]</td></tr><tr><td>PC-12</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.00480</td><td>[0.00136;0.0409]</td></tr><tr><td>MCF-7</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.651</td><td>[0.388;2.28]</td></tr><tr><td>RTgill-W1</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.148</td><td>[0.141;0.347]</td></tr><tr><td>HEK293T</td><td>Uniform [0, 1.10<sup>2</sup>]</td><td>0.0243</td><td>[0.00215;0.325]</td></tr><tr><td>Error σ</td><td>LogNormal (1.5, 1.5)</td><td>2.63</td><td>[2.58;2.95]</td></tr></tbody></table>
For the experimental data distribution, C<sub>cell</sub>(t) and C<sub>medium</sub>(t) were assumed to follow a lognormal distribution around the model predictions (taken as geometric mean). The error σ has been calibrated for the medium and the intracellular concentration, corresponding to analytical error and both inter-laboratory and inter-individual variability, and assumed to follow a lognormal distribution centered on 1.5 (i.e. 50% of error) and with a deviation of 150%. Three independent Monte-Carlo Markov chains of 50,000 iterations were run for each fit and different initial values have been randomly assigned to each chain. This number of iterations was selected because, in the present case, chains of 50,000 iterations consistently yielded stable posterior estimates and provided an acceptably low level of autocorrelations. Running multiple MCMC chains is a standard practice which enables assessment of convergence of the various chains by comparing between-chain and within-chain variability. The convergence of the chains was assumed when the Gelman and Rubin convergence criteria were lower than 1.1 (Gelman and Rubin, 1996). After convergence of the chains, the last 1000 parameter vectors of each chain were kept, forming the *a posteriori* distribution of parameter values used for subsequent simulations. The 95% credibility interval was constructed using the *a posteriori* quantiles (0.025 quantile and 0.975 quantile, respectively). Finally, the values of the estimated parameters for which the likelihood value is maximized were selected and referred to as the maximum posterior values (MPV).

### 2.4.3 Software

All the dynamic model simulations and MCMC calibrations were performed with GNU MCSIM version 6.1.0² (Bois, 2009) and R version 4.0.2. The complete model code is given in supplementary file 2³. An editable example input file<fnref n="4" /> and a detailed user guide<fnref n="5" /> are also supplied to facilitate reproducibility.

## 3 Results

### 3.1 In vitro kinetics

The free medium concentrations of BPA, BPF, and BPS were experimentally measured, using the RED (rapid equilibrium dialysis) device with culture medium for HepG2 cells spiked with 1 and 10 µM (in triplicate), to determine the free fraction of bisphenols and subsequently compared to model predictions (Tab. 4). The model displays a slight but consistent underprediction of the free fraction in the medium for the bisphenols.

No clear abiotic degradation could be evidenced since the recovery after 48 h exposure in the test systems without the cells was close to 100% (model predictions for the abiotic degradation of air and medium combined at 48 h were below 2% for BPA, 7% for BPF and 7% for BPS). Conversely, a significant variability in intracellular and medium concentrations of BPA, BPF and BPS was observed in assays containing HepG2 cells, with a downward trend in medium concentrations at 48h (Fig. 2).

A clear metabolic activity was evidenced in HepaRG cells, as indicated by the rapid disappearance of the parent BPA from the culture medium and the concomitant formation of a metabolite both intracellularly and extracellularly (Fig. 3). The parent compound exhibited a very short apparent half-life in the medium, suggesting rapid uptake and biotransformation: the estimated clearance was found to be 139 and 15.7 µL·h⁻¹·10⁻⁶ cell in the medium at 10 and 25 µM, respectively. Metabolite formation was tracked by semi-quantitative peak intensity measurements (expressed as arbitrary units, a.u.), confirming the presence of active phase II metabolism.

### 3.2 Exploration of dataset and model

Prior to model calibration, the dataset was explored to characterize the relationship between nominal exposure concentrations and intracellular concentrations. A simple log-log linear regression model was first fitted on the calibration dataset and subsequently evaluated on the validation dataset (Fig. 4). In a second step, to identify key determinants of intracellular concentrations, global SA were performed using a representative monoacid compound in a 96-well plate system seeded with cells of average physiology (Tab. 2). These analyses provided insights into the relative influence of model parameters on intracellular chemical disposition, supporting the subsequent calibration strategy.

<table><caption>**Tab. 4: Observed and predicted free fraction of bisphenols in HepG2 medium**

Results are expressed as average of three independent biological replicates ± standard deviation.</caption><thead><tr><th rowspan="2">Molecule</th><th colspan="2">Measured</th><th rowspan="2">Predicted</th></tr><tr><th>1µM</th><th>10µM</th></tr></thead><tbody><tr><td>BPA</td><td>0.431 ± 0.084</td><td>0.374 ± 0.124</td><td>0.345</td></tr><tr><td>BPF</td><td>0.431 ± 0.055</td><td>0.460 ± 0.087</td><td>0.310</td></tr><tr><td>BPS</td><td>0.551 ± 0.076</td><td>0.463 ± 0.076</td><td>0.387</td></tr></tbody></table>

<footnote n="2">² https://www.gnu.org/software/mcsim/</footnote>

<footnote n="3">³ doi:10.14573/altex.2509261s2</footnote>

<footnote n="4">⁴ doi:10.14573/altex.2509261s3</footnote>

<footnote n="5">⁵ doi:10.14573/altex.2509261s4</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 2: Fraction of the initial dose recovered in HepG2 cell systems at 24 and 48 h post-exposure**
Cells were exposed to four concentrations (0.1, 1, 10, and 25 µM) of bisphenol A (BPA), bisphenol F (BPF) or bisphenol S (BPS). Results are expressed as ± SD from three independent biological replicates per timepoint, tested concentration and molecule.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Fig. 3: Bisphenol A (solid line) concentration (mM) and metabolite intensity in arbitrary units (a.u., dotted line) in medium (upper graphs) and HepaRG cells (lower graphs) following exposure to 10 and 25 µM (green and red curves, respectively)**
The upper error bar is the standard deviation from three independent biological replicates (not displayed for metabolite since n = 1).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 4: Exploration of the dataset</figcaption></figure>

(A) Relationship between nominal medium concentration and observed intracellular concentrations (log-log regression). (B) Observed vs. predicted concentrations in the calibration dataset. (C) Observed vs. predicted concentrations in the validation dataset. The dotted intervals represent the 3-fold and 10-fold error intervals.

<figure><img src="image_7.png" /><figcaption>Fig. 5: Global sensitivity analysis of the primary parameters using Morris's method</figcaption></figure>

### 3.2.1 Exploration of the dataset

A correlation was observed between nominal medium concentration and measured intracellular concentrations ($R^2 = 0.611$, Root Mean Squared Logarithmic Error (RMSLE) = 0.334, Average Fold Error (AFE) = 25.8; Fig. 4A). The regression was described by the equation:

$$ \log_{10} C_{cell} = 0.641 \times \log_{10} C_{nominal} + 0.263 \quad (16) $$

This model allowed the prediction of intracellular concentrations in the calibration dataset (Fig. 4B) and in the validation dataset (Fig. 4C). However, systematic deviations from the identity line, together with the wide prediction intervals, confirmed that nominal concentrations are poor surrogates for actual intracellular exposure levels.

### 3.2.2 Primary parameters sensitivity analysis

For the primary parameters, the Morris's analysis indicates that the pH of the culture medium, the pKa of the monoacid (pKa1), the $LogP_{OWTref}$, and, in a lesser extent, the cells number (Ncell) and volume (Vcell), and the experimental temperature (temp) are the most influential parameters in the simulated conditions (Fig. 5).

The Sobol SA was conducted, using the six previously selected parameters and using their relative range of distribution reported in the literature dataset (Tab. 2). Regarding the medium concentration, the most influential parameters are the
Medium concentration

0.1 h

<figure><img src="image_8.png" /></figure>

1 h

<figure><img src="image_9.png" /></figure>

12 h

<figure><img src="image_10.png" /></figure>

Cell concentration

0.1 h

<figure><img src="image_11.png" /></figure>

1 h

<figure><img src="image_12.png" /></figure>

12 h

<figure><img src="image_13.png" /><figcaption>Fig. 6: Sobol's sensitivity analysis on the medium (up) and cell (down) concentrations predicted by the model at 0.1, 1 and 12 hours (left to right, respectively)</figcaption></figure>

The 6 most influential primary parameters are represented (sorted by the importance of the influence).

$LogP_{ow_{Tref}}$ and the pKa of the chemical up to 12 h of exposure (Fig. 6). The influence profiles of these two parameters on medium concentrations remain constant over time, however, the impact on intracellular concentrations exhibits a temporal evolution. In cells, the $LogP_{ow_{Tref}}$ of the compound consistently exerts the greatest influence predicted at all time points. Up to 1 h, the cell volume is the second most influential parameter. However, after 12 h, the influence profile shifts, with logPow then followed by pKa1, cell volume and medium pH. For intracellular concentrations, the first-order and total-order Sobol indices are nearly identical for all parameters, indicating that parameter interactions are negligible. In contrast, for medium concentrations, slightly higher total-order indices were observed for logPow and pKa. This reflects a limited indirect combined influence on compound depletion from the medium, as conditions favoring both hydrophobicity and neutral speciation were associated with increased and faster cellular uptake (through effects on partition coefficients and medium-to-cell fluxes, respectively).

### 3.2.3 Secondary parameters sensitivity analysis

For the secondary parameters of the model, i.e. parameters that could be estimated using primary parameters, the Morris analysis indicates that $fu\_diluted$ (free fraction in the medium) and $fu\_cell$, the flow of compound from the medium to the cell ($F\_cell$), the medium to other cell compartments, and medium to air partition coefficients ($PC\_others\_medium$ and $PC\_air\_medium$ respectively) and the metabolism constant rate ($K\_met$), are the most influential parameters in the simulated conditions (Fig. 7).

The Sobol's SA was performed using the six parameters that had been selected earlier along with their relative observed range distribution, retrieved from the literature dataset. In terms of medium concentration, the most influential parameters are the free fraction in the medium and the flow from the medium culture to the cell (Fig. 8). This is consistent with the hypothesis that only the free chemical is able to move from one compartment to another.

The influence profiles of the parameters on intracellular concentrations reveal a strong effect of the free fraction, the flow from the medium culture to the cell and the metabolism constant rate on intracellular concentrations, while others remain relatively low. The weight of the metabolism increases with time as the system approaches its steady state. For both intracellular and medium concentrations, first-order and total-order Sobol indices overlap for all parameters, suggesting that interaction effects are small relative to individual parameter contributions within the explored parameter ranges.
<figure><img src="image_14.png" /><figcaption>Fig. 8: Sensitivity analysis on the medium (up) and cell (down) concentrations predicted by the model at 0.1, 1, and 12 hours (left to right, respectively)</figcaption></figure>

The 6 most influential secondary parameters are represented (sorted by the importance of the influence).

### 3.3 Predicted concentrations in the calibration dataset

The proposed model structure was used to run simulations, and the predicted cell concentrations were compared with the observed concentrations. An overprediction of the model was identified by average fold error (AFE = 3.04), and the residue distribution was found to be high (RMSE = 16.5, RMSLE = 0.63) (Fig. 9).

Approximately 43% and 70% of the predictions fall outside the 10-fold and the 3-fold error ranges, respectively. Furthermore, the kinetic profiles do not align with the observations. The chemical permeability from the media to the cell, as determined in Comenges et al. (2017) seems to be overestimated, and the cells reached the steady state immediately, whereas
<caption>**Fig. 9: Evaluation of the model predictive capacities before calibration: observed vs. predicted internal concentrations (mM) for the molecules of the calibration dataset**</caption>

The horizontal error bar represents the upper margin of the 95% confidence interval. The dotted intervals represent the 3-fold and 10-fold error intervals. AFE: average fold error, RMSLE: root mean squared logarithmic error

<figure><img src="image_15.png" /><figcaption>**Fig. 10: In medium: observed versus predicted medium concentrations (mM) from the calibration dataset**</figcaption></figure>

The modeled medium concentrations were predicted based on maximum posterior values of parameters. The dotted intervals represent the 3-fold and 10-fold error intervals.

<figure><img src="image_16.png" /><figcaption>**Fig. 11: In cells: observed versus predicted intracellular concentrations (mM) from the calibration dataset**</figcaption></figure>

The horizontal error bars represent the 95% confidence interval. The modeled cell concentrations were predicted based on maximum posterior values of parameters. The dotted intervals represent the 3-fold and 10-fold error intervals.

<figure><img src="image_17.png" /></figure>
<figure><img src="image_18.png" /><figcaption>Fig. 12: Average fold error (AFE) of the calibrated predicted to observed intracellular concentrations per tested cell lines</figcaption></figure>

The violin plots show the distribution of AFE values for each cell type, with overlaid boxplots indicating the interquartile range and median. The black dots represent the geometric mean of AFE for each cell line. The red dashed line denotes an AFE of 1, representing perfect agreement between the predicted and observed concentrations. The plot is presented on a logarithmic scale to accommodate the wide range of AFE values.

<figure><img src="image_19.png" /><figcaption>Fig. 13: Observed versus predicted cell concentrations (mM) from the validation dataset</figcaption></figure>

The modeled cell concentrations were predicted based on maximum posterior values of parameters. The horizontal error bars represent the 95% confidence interval. The dotted intervals represent the 3-fold and 10-fold error intervals.

the observations suggest a much slower equilibration, thus requiring additional calibration. A more detailed analysis of the residuals, stratified by compound molecular weight, logPow, and cell type, is provided in S.I. (Section S2.3, Fig. S2¹), showing that the observed variability is more likely attributable to imprecision in the treatment of logPow and, consequently, in the QSAR-based parameterization, rather than to other compound-specific characteristics.

### 3.3.1 Bayesian calibration of medium/cell exchange flow

The maximum posterior values are given in Table 3. The convergence of chains has been successful for all calibrated parameters, with narrow posterior distributions.

The concentration profiles predicted in the medium are aligned with the observed data from the calibration dataset (Fig. 10), with the exception of experimental assays with cells expressing a high level of chemical metabolism (HepaRG exposed to amiodarone and chlorpromazine, as orange and green outliers in Fig. 10) and for pentachlorophenol (pink outliers).

For cell concentration predictions, 72% of the simulations are within a 3-fold error interval, and less than 3% of the simulations fall outside of the 10-fold error interval after the calibration process (Fig. 11 and the observed versus predicted concentrations per cell lines including model uncertainty are provided in Fig. S4-S10¹). The simulated individual cell kinetic profiles fits are presented in supplementary file 5⁶ (the blue lines represent the internal predicted concentrations at the joint a posteriori mode, the red dots are the observed concentrations).

A global overview of the kinetic profiles showed that the model simulations adequately reproduced the observed data. When assessed individually, several predicted TK profiles deviated from the corresponding observations. The calibration process yielded a high error estimate ($\sigma$ = 2.63), consistent with the variability observed in the experimental data.

The calibration decreases the observed bias between observations and predictions among the different cell lines which remain close to 1 (Fig. 12).

Using the *a posteriori* parameters on the validation data (18 experiments, 6 molecules, 5 different cell types), one prediction exceeded a 10-fold error, and 89% fell within a 3-fold error (Fig. 13), suggesting that the model is sufficiently robust to incorporate external data within the aforementioned constraints.

### 3.3.2 Impact of cell lines on the intracellular concentration of BPA

BPA kinetic profiles were compared in the 7 tested cell lines without considering metabolism (1µM BPA in 96-well plates, cells at confluency, Fig. 14). All the intracellular concentrations reached steady state or near steady state within 72 h, except for the cell lines with the lowest net efflux and especially the HepG2 cell line. In HepG2, intracellular concentrations

<footnote n="6">⁶ doi:10.14573/altex.2509261s5</footnote>
<figure><img src="image_20.png" /><figcaption>**Fig. 14: Simulated bisphenol A intracellular concentrations after exposure to 1µM in seven confluent cell lines without taking into account any chemical metabolism, linear scale (left) and semilogarithmic scale (right)**</figcaption></figure>

remained elevated, consistent with the highest measured cell-to-medium partition coefficient (Pcell:medium = 159) and the lowest net elimination rate among the tested lines. In contrast, other cell lines demonstrate an elimination rate that is at least 3-fold higher (with respect to PC12 and HEK cells, which almost reached the steady state at 72 h) (Tab. 3).

# 4 Discussion

The present study describes the development, calibration, and evaluation of INSIGHT, a mechanistic *in vitro* biokinetic model designed to meet two objectives: firstly, to improve our understanding of the fate of chemicals in an *in vitro* test system, and secondly, to provide a flexible and robust model to design *in vitro* assays. INSIGHT was developed to provide a model able to account for plastic binding, medium dynamics, and intracellular distribution while remaining generic enough to operate across various chemical classes and widely used cell lines. By combining physicochemical properties, cell physiological characteristics, and exposure conditions, INSIGHT was designed to capture the main processes influencing chemical fate *in vitro* without relying on compound-specific empirical adjustments. Compared with existing biokinetic models, it fills a conceptual gap between the dynamic, but uptake-simplified, VCBA and the equilibrium-based but more partition-focused VIVD model.

Indeed, the VIVD model is a theoretical model based on the assumptions set out by Armitage et al. (2014) incorporating a passive and immediate diffusion of compounds through the cell membranes (Fisher et al., 2019; Armitage et al., 2014). To the best of our knowledge, the VIVD model, as proposed by Fisher et al. (2019), has not yet been confronted with observed data. In this study, a diverse set of cell models was included to capture a range of biological characteristics: cell lines expressing transporters (HEK 293T, HepaRG and RTgill-W1 cell lines), those with varying metabolic capacities (HepG2 and HepaRG hepatic cell lines), and others that exhibiting minimal or no metabolic and transporter activity (Balb/c 3T3 and PC-12 cell lines) (Dimitrijevic et al., 2022; Ahlin et al., 2009; Kropf et al., 2020; Le Vee et al., 2013; Nauwelaerts et al., 2021). Therefore, a key limitation remains the incomplete characterization of lineage-specific physiology. Given the potential impact for such transporters and metabolic activity on permeability, it was essential to calibrate the partition coefficient for the different cell lines. For example, HepG2 and RTgill-W1 required large ffpc corrections, reflecting both differences in lipid/protein content and transporter expression.

Following the VIVD model structure, three distinct subcellular compartments were included (mitochondria, lysosomes and intracellular water) and an additional microsomal compartment was added to the model. However, few data regarding these compartments, their compositions (lipids, proteins) and their frequency per cell line is available or poorly described in the literature. Further dedicated studies using easily trackable compounds and/or, more sensitive analytical approaches, are required to better describe the entrance and distribution of chemicals into cells and improve the parameterization of these compartments.

Non-specific binding to the plastic was adapted from the publication of Fischer et al. (2018). The addition of this submodel better describes the fraction entering the plate polystyrene and the rate at which this occurs, which is dependent on the logPow. While Fischer et al. employed partial differential equations, MCSim, the software used for running the INSIGHT simulations in the present study, is only capable of solving ordinary differential equations. Accordingly, the plate has been divided into ten discrete compartments. The results obtained using the Fischer's method and the proposed method are equivalent. Moreover, Fischer et al. restricted the selection of compounds to those with a neutral molecular structure. Consequently, and on the assumption that only neutral molecules can bind to the polymer, only the molecular form of the compound was used to simulate the plate binding rate and partition coefficient as previously discussed (Seidensticker et al., 2018). Additionally, it was assumed that the proportion of plate bound ionized forms was negligible. However, it has not been possible to evaluate
this hypothesis, as no data accurately describes the behavior of ionized compounds in polystyrene. Additional updates to the partitioning model may also be required, as evidenced by the accurate prediction of hexachlorobenzene concentrations in the medium, and the poorest prediction accuracy for pentachlorophenol when comparing observed versus predicted medium concentrations, despite both compounds having similar log Pow values, with pentachlorophenol additionally exhibiting a low Henry's law constant. The dataset includes chemicals with properties beyond the submodel's validated range, extending validation would be informative but requires polymer-compound studies beyond the scope of the present study.

In the present work, it was not possible to evaluate chemical volatilization, as no data could be retrieved from the literature based on the specified research criteria. Furthermore, as the selected compounds are characterized by low to medium volatility (based on Henry's Law constants), it was assumed that the approach described in the VCBA model is appropriate (Comenges et al., 2017). Nevertheless, further research is required to gain insight into the loss of compound due to vaporization especially by exploring the chemical concentration in the headspace and gas exchange with the cell incubator (Tolosa et al., 2021).

The INSIGHT model includes apparent metabolism, which is easier to quantify than the actual clearance of each organelle. Previous studies have observed dynamic metabolism, likely attributable to increased cell numbers rather than metabolic induction (Pomponio et al., 2015; Truisi et al., 2015). Indeed, metabolic induction via target nuclear receptors (such as *AhR*, *CAR*, and *PXR*) is exponential and reaching a steady state can take several days or even weeks (Ibrahim et al., 2020; Ding et al., 2006; Donocoff et al., 2020; Tebbens et al., 2018), whereas the observed increase in metabolism is slow but consistent. The HepG2 cell line, despite its hepatic origin, exhibits impaired or no basal chemical metabolic activity from the current dataset. A comparative analysis of the mRNA profiles of the HepG2 and HepaRG cell lines has revealed significant discrepancies, with HepaRG exhibiting higher expression levels in metabolic and transport processes (Gerets et al., 2012). Classical pharmacokinetics emphasizes that only the unbound fraction (in plasma) is immediately available for diffusion and metabolism. Poulin et al. (2016) suggest that protein binding, such as to albumin, can enhance hepatocyte clearance. Similarly, intracellular binding proteins may facilitate the delivery of ligands to CYP enzymes, potentially lowering the apparent Km and promoting metabolism (Kandel and Lampe, 2014). Because protein-ligand interactions are reversible and assumed here to equilibrate instantaneously, both intracellular bound and free forms are considered metabolizable within metabolically competent compartments.

Exploration of the model using SA demonstrated and reinforced previous results reported in the case of the VCBA model, that the logPow of the chemical is of critical importance for its behavior within the test system (Proença et al., 2019). Accurately determining logPow is therefore essential, in order to make a more precise prediction of the chemical fate. Furthermore, the variability observed in this parameter when testing various QSAR models has been the subject of several critiques (Adachi et al., 2024). In the present model, the logPow influences cell concentration (including cell permeability and partition coefficients) as well as the plastic and protein binding.

The present work adopts a mechanistic, generalized calibration strategy rather than a per-compound approach, thereby balancing mechanistic fidelity with practical usability across diverse compounds and cellular systems. INSIGHT was developed using 42 different molecules and calibrated based on 7 different cell lines, rather than on a per-molecule basis. Indeed, if calibration on a per-molecule basis could significantly improve individual kinetic profiles, it would reduce the predictive ability of the model with respect to external datasets due to overfitting. Conversely, adopting a parsimonious calibration renders it more versatile for application in a broader range of scenarios. A minimal approach (i.e. a linear regression model between nominal and observed cell concentrations) provides an acceptable fit for the calibration dataset but fails to generalize to the validation dataset. Such regressions implicitly assume instantaneous equilibrium between medium and cells, which does not reflect steady state but rather an intermediate timepoint across simulations (resulting in a series of staircase-shaped points on the observed *versus* predicted graph, Fig. 4). These limitations show that a mechanistic calibration strategy, like the one used in INSIGHT, is required to better account for time-dependent processes and system-specific factors that influence both actual medium and intracellular concentrations. To assess whether the model performs differently across ionization classes, the RMSE were calculated separately for each chemical nature. RMSE values for medium concentrations displayed low variability across classes (0.0005–0.008), indicating that prediction accuracy is comparable for neutral, acidic, basic, ampholytic, and diacid compounds. In contrast, intracellular concentrations exhibited higher and more heterogeneous RMSE values (0.023–1.09). As illustrated in Fig. S12¹, no systematic bias was observed across chemical nature. However, the weighted residuals remained larger for neutral, monoacid, and monobasic compounds (Fig. S13¹), especially in the cells, suggesting that class-specific mechanisms such as partitioning, ion trapping, intracellular pH gradients, or transporter involvement may influence prediction accuracy. Future work should investigate whether integrating compound nature-specific uptake or efflux mechanisms can reduce the observed differences in intracellular accuracy.

The initial exchange flow was derived from the Caco-2 permeability QSAR model described by Comenges et al. (2012), but this parameterization resulted in overly rapid kinetics and required recalibration. According to this calculation method, logPow remained a central parameter facilitating uptake. However, our observations indicate a positive correlation between molar volume and absorption rate, consistent with the findings reported in studies on drug permeability (Mathia et al., 2002; Stigliani et al., 2016). The calibrated passive uptake flow was found to be comparable to the estimated flows previously reported in the literature for cyclosporine A (271 µL·h⁻¹ vs. 159 µL·h⁻¹, arbitrarily fixed values reported in Bellwon et al. (2015)). For ibuprofen: a passive uptake of 384 µL·h⁻¹ with a net efflux of 0.658 µL·h⁻¹ is estimated by the INSIGHT model vs a total uptake of 540 µL·h⁻¹ and efflux of 108 µL·h⁻¹ (arbitrarily fixed values reported in Truisi et al. (2015)). Chlorpromazine permeability tended to be overestimated (3.45 mm·h⁻¹ vs 0.486 mm·h⁻¹), as reported in Broeders et al. (2015). However, this predicted value is lower than the estimated uptake predicted by the VCBA model (35 mm·h⁻¹, (Worth et al., 2017)). Furthermore, the uptake of these three compounds, along with BPA, BPS and BPF, displayed non-linear kinetic profiles (less than dose-proportional increase in exposure), suggesting saturation in their uptake at higher concentrations. This phenomenon could explain the discrepancy between the predictions (assuming non-saturation) and the observed flows reported in the aforementioned publications. At this stage, saturation had not been incorporated into the calibration process for each compound. While
<figure><img src="image_21.png" /><figcaption>**Fig. 15: Impact of LogP<sub>owsys</sub> and net efflux rate (Ke, µL·h<sup>-1</sup>) variations on cell chemical concentration in a 96-well plate (nonvolatile compound, 1 µM, 200 cm<sup>3</sup>/mol)**</figcaption></figure>

saturation mechanisms can be readily integrated into the model, their implementation will require dedicated experimental studies to estimate half-saturation constants.

A net efflux parameter was incorporated to account for transporter-mediated export. It is defined as the difference between uptake and efflux and results in a unidirectional flow (from cell to medium). Due to the complexity and diversity of transporter expression and substrate specificity across cell types, a simplified approach was adopted in which the net efflux was estimated directly from intracellular concentrations over time, independently of physicochemical descriptors. Indeed, depending on their structures, ionic charge and lipophilicity, the transporters involved in the transport may differ when considering primary active transport (Giacomini et al., 2010) whereas for facilitated transport and notably vesicular transport (endo or exocytosis) all forms might be transported (Conner and Schmid, 2003; Shedden et al., 2003). The net efflux has been observed to be generally low but not negligible. For example, in the case of Balb/c 3T3 cell line, the net efflux was found to be 9.73 µL·h<sup>-1</sup>, while the uptake of a neutral chemical (MV = 350 cm<sup>3</sup>·mol<sup>-1</sup>) with a LogP<sub>owsys</sub> ranging from 1 to 5 in these cells was found to be between 52 and 3680 µL·h<sup>-1</sup>, respectively. Conversely, in the HEK293T cell line, the net efflux was markedly lower (24.3 nL·h<sup>-1</sup>), which is consistent with the low expression levels of major renal transporters in this cell line, as reported by Zhang et al. (2015). In the model, transport is divided into two parts: chemical passive uptake and net efflux. The model suggests that the passive uptake is mainly dependent on the LogPow value and governs the kinetic profile of the chemical. The net efflux (Ke) constant appears to significantly reduce the cell maximal concentration (C<sub>max</sub>) and the time to reach this maximal value (t<sub>max</sub>), as illustrated in Fig. 15. This observation underscores the interplay between passive and active mechanisms, which may complicate the interpretation of kinetic profile, as Ke could be, partially, confounded by passive uptake. The determination of this value could be enhanced by performing dedicated assays, such as permeability assays using combined apical to basal and basal to apical permeability assays or using selective transport inhibition assays (Blaser, 2007).

The ffpc correction factor was introduced to adjust systematic bias in partition coefficients across cell lines. Applying a single ffpc per cell line reduced the variability in predicted/observed ratios for substances tested in the same cell lines. For example, in HepG2 cells, the deviation between model predictions and observations decreased from a 6-fold to below 2-fold range once the ffpc was applied to all tested compounds. The ffpcs were found to require correction by a factor of 2.64 on average, ranging from 0.256 to 10.0 across all cell lines. However, the dataset is unbalanced with some cell lines represented by only one compound (e.g., PC-12 and MCF-7 with BDE-47). Therefore, the separation between a cell line effect and a chemical effect cannot be fully resolved, reflecting the limitations of two-way ANOVA under unbalanced conditions (Table S7'). Nonetheless, for cell lines represented by multiple compounds spanning diverse physicochemical space (HepaRG, HepG2, RTgill-W1, Balb/c 3T3), the ffpc calibration was robust. Cross-cell-line comparisons further supported this consistency: for example, INSIGHT reproduced the observed differences in BPA accumulation between HepG2 and HepaRG, in line with reported disparities in transporter expression (Gerets et al., 2012) (Fig. 14). Similarly, the observed chlorpromazine cell-to-medium partition coefficient in HepaRG cells was 870 ± 270 (Broeders et al., 2015), while the INSIGHT model predicts a cell-to-medium partition coefficient of 751. The correction factor for the partition coefficients varies among the selected cell lines, indicating that, in addition to the experimental error, either the VIVD model predictions within the current model could be enhanced and/or the actual cell line biochemical composition is not accurately described. In the context of qIVIVE, the cell line specific calibration achieved with ffpc provides a pragmatic solution to reduce inter assay bias while remaining comparable across chemicals tested in the same cellular background. Nevertheless, the use of empirical scaling factors has highlighted the necessity for enhanced methodologies in measuring cell composition and the functionality of active transporters. In the future, it is recommended to apply this approach to a wider range of compounds. Extending this calibration to a broader chemical domain will be essential to test the robustness of INSIGHT and to strengthen its integration into regulatory NAM frameworks such as qIVIVE (OECD, 2025).

The external validation dataset combined medium and intracellular measurements for six chemicals (BDE-47, BPA, chlorpromazine, cidofovir, hexachlorobenzene and phenanthrene) with various ionization states, lipophilicity, molecular structure and weight across multiple cellular systems, enabling an independent assessment of model performance. Even if the number of compounds is limited, their inclusion demonstrates that the calibrated model keeps its predictive capacity for combination of compounds and cell lines not used in calibration. BPA was evaluated in both Balb/c 3T3 fibroblasts and HepaRG cells,
providing an opportunity to examine cross-cell-line consistency. If the predicted Balb/c 3T3 fibroblast concentrations were in line with the observed data (12% deviation at max), the results of HepaRG cell line revealed a higher level of metabolic production than compared to the uptake of the compound. This may reflect ongoing enzymatic activity beyond experimental endpoint or the diffusion of intracellular enzymes into the medium.

These observations highlight the complexity of integrating experimental *in vitro* data with *in silico* biokinetic modeling. Integrated approaches have been demonstrated to have the capacity to address the issues inherent in such data. As a result, it facilitates enhanced data interpretation, raises new hypotheses and improves extrapolation of *in vitro* findings to real-world biological systems. The INSIGHT model enables users to quantify inter-experiment variability, guide assay design based on targeted intracellular concentrations, and support quantitative AOP development and qIVIVE workflows.

For practical application, a minimum of 14 parameters must be specified: 9 related to experimental conditions (e.g., dose, cell number) and 5 related to chemical properties (e.g., logPow, compound type). A user guide⁵ is provided to facilitate hands-on use and initiation of simulations. As with all PBK models, accurate parameterization is essential for achieving optimal predictive performance. Most chemical properties are available from public databases (e.g., PubChem, ChemSpider), while users can provide their own experimental conditions (Table S7¹). In contrast, data on cell line parameters remain limited, which restricts the number of cell lines that can be included in this study and the model.

The next challenges will aim to address several current limitations, with priority given to i) a better characterization of experimental cell lines, ii) an improved understanding of how compounds behave in test systems, iii) a deeper insight into intracellular trafficking, and iv) an elucidation of chemical interactions with lipid membranes and organelle content. Although new approach methodologies encourage more systematic use of *in vitro* assays, physiological and toxicological knowledge of these models remains in its early stages. Indeed, the behavior of the selected cells in this study was found to differ markedly. It is imperative to gain a deeper understanding of the inherent pros and cons inherent in each cell line and to establish a public database gathering this information. Given the considerable variation in intracellular concentration, which can differ by up to a 100-fold factor depending on the cell line, the toxicity determined with these approaches should be interpreted with caution. Further refinement and characterization of cell-specific parameters will be essential to expanding the utility of these models in toxicity assessment and their applicability in NGRA workflows.

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**Conflict of interest**

The authors declare that they have no conflict of interest to disclose.

**Data availability**

The datasets of the current research are available in the supplemental information.

**Acknowledgements**

This study was supported by the European Union's H2020 research and innovation program under grant agreements No. 825712 (OBERON) and No. 857560 (CETOCOEN Excellence) for performing experiments and for Kévin Bernal's PhD Fellowship. This publication reflects only the author's view, and the European Commission is not responsible for any use that may be made of the information it contains. The research was supported by the Czech Science Foundation Grant No. GA24-12116S. Authors thank the RECETOX Research Infrastructure (No. LM2023069) financed by the Czech Ministry of Education, Youth and Sports (DB, ES, JK, PB, IS), the Université Paris Cité (KB, JD, AT, EB) and the French National Institute of Health and Medical Research (Inserm) (KB, EB, SL), for supportive background.