In Silico Comparison of Rifampicin and 25-desacetyl Rifampicin-Induced PXR-Mediated CYP450 Transcriptional Response in 3D Primary Human Hepatocytes

TL;DR

This study compares how two forms of rifampicin affect liver enzyme activity in human cells using mathematical models and gene analysis.

Contribution

The study introduces a novel in silico approach to compare PXR-mediated CYP450 transcriptional responses between rifampicin and its metabolite.

Findings

25-DRIF activates PXR at a rate 20 times lower than RIF.

CYP3A4 transcription rate constants were higher in 25-DRIF-treated cells compared to RIF-treated cells.

CYP2C9 transcription rate constants were similar in RIF- and 25-DRIF-treated cells.

Abstract

The pregnane X receptor (PXR) regulates the expression of cytochrome P450 (CYP) enzymes and plays a crucial role in the metabolism of various drugs. Rifampicin (RIF) is a PXR ligand that forms the primary metabolite, 25-desacetyl rifampicin (25-DRIF), which retains the antimicrobial activity of the original drug. In this study, we quantified PXR activation and its associated effects on CYP3A4, CYP2C9, and CYP2B6 enzymes in response to 25-DRIF treatment by combining mathematical modeling with long-term mRNA expression analysis of these enzymes in 3D primary human hepatocyte (3D PHH) spheroids. Our estimates suggest that 25-DRIF activates PXR at a rate 20 times lower than RIF. The PXR-dependent rate constant for CYP3A4 transcription was estimated to be higher in 3D PHHs treated with 25-DRIF than in those treated with RIF and also higher than that for CYP2B6 transcription in 3D PHHs treated with 25-DRIF. The rate constants driving PXR-dependent transcription of CYP2C9 were comparable in RIF- and 25-DRIF-treated 3D PHHs. These results demonstrate the ligand-specific nature of PXR activation and suggest that the transcription of PXR-controlled CYP enzymes is ligand- and CYP-specific in 3D PHHs. Finally, we showed that the half-maximal effective concentration (\documentclass[12pt]{minimal}
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\begin{document}$$\hbox {EC}_{50}$$\end{document}EC50) evaluated from our mathematical predictions was time-dependent, which was further validated by CYP3A4 gene reporter assays that measured RIF-induced PXR activity.

The online version contains supplementary material available at 10.1007/s11538-026-01619-1.

Figures

PXR- and CYP-specific parameters for RIF and 25-DRIF treatments of 3D PHHs. (A) The maximum PXR activation rate constants for RIF-treated (grey) and 25-DRIF-treated (black) 3D PHHs. (B) Fold transcription rate constants of CYP3A4 for RIF-treated (magenta) and 25-DRIF-treated (red) 3D PHHs. (C) Fold-transcription rate constants of CYP2B6 for RIF-treated (cyan) and 25-DRIF-treated (blue) 3D PHHs. The parameter posterior histograms for RIF-treated 3D PHHs were obtained from refitting Equations (6)–(10) from Lochman et al. ([2025](#CR22)) to the CYP mRNA expression data from 3D PHHs treated with 1

Full text

Introduction

The pregnane X receptor (PXR) is a ligand-regulated nuclear receptor that controls endogenous and exogenous metabolism in the liver (Blumberg et al. 1998; Kliewer et al. 1998; Lehmann et al. 1998; Wang et al. 2012). Activation of PXR leads to the transcriptional induction of several cytochrome P450 (CYP) enzymes, including CYP3A4, CYP2C9, and CYP2B6, which play a crucial role in metabolising a variety of xenobiotics (Goodwin et al. 1999, 2001; Maglich et al. 2002; Rae et al. 2001; Smutny et al. 2022; Tolson and Wang 2010). The antibiotic rifampicin (RIF) is a potent PXR agonist and is used as a reference compound to assess PXR activation in vitro (Lehmann et al. 1998; Maglich et al. 2002; Rae et al. 2001; Smutny et al. 2022; Kandel et al. 2016). In the liver, RIF is deacetylated by the enzyme arylacetamide deacetylase (AADAC) to form its primary metabolite, 25-desacetyl rifampicin (25-DRIF) (Kobayashi et al. 2012; Nakajima et al. 2011), which retains antimicrobiological activity (Verbeeck et al. 2019; Acocella 1978; Donald et al. 2011; Grégoire et al. 2016; Seng et al. 2015). Furthermore, it has been demonstrated that 25-DRIF activates PXR and induces the expression of CYP enzymes (Nakajima et al. 2011; Smutny et al. 2024), albeit at lower levels than RIF. These findings suggest that 25-DRIF contributes to RIF-induced changes in the expression of pharmacokinetics-related genes, particularly during long-term therapy, where repeated dosing may lead to metabolite accumulation (Aocoella et al. 1978). The metabolism of RIF to 25-DRIF was detected in in vitro models, including 2D primary human hepatocytes (PHHs), human liver slices, and microsomes, supporting its in vivo relevance (Smutny et al. 2024; Jamis-Dow et al. 1997). It is essential to quantify the impact of 25-DRIF on PXR-mediated CYP induction in order to evaluate the effects of RIF on drug interactions and metabolism.

Mathematical models have improved our understanding of PXR-mediated CYP mRNA induction in rat hepatocytes (Bailey et al. 2011; Li et al. 2012), in 2D PHHs (Luke et al. 2010; Yamashita et al. 2013), and in PHHs (spheroids) (Lochman et al. 2025), with a particular focus on describing PXR-controlled CYP induction mediated by RIF (Luke et al. 2010; Yamashita et al. 2013; Lochman et al. 2025) or other drugs, such as dexamethasone (Li et al. 2012) and pregnenalone-16 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} -carbonitrile (Bailey et al. 2011). However, quantitative mathematical modeling has not been used to investigate PXR-controlled CYP mRNA induction mediated by 25-DRIF. In this study, we evaluated 25-DRIF-induced PXR activation by integrating a mathematical model of PXR activation and PXR-mediated CYP mRNA induction with CYP mRNA expression data. The experimental data were obtained from the long-term treatment of phenotypically stable, physiologically relevant 3D PHHs with 25-DRIF, as previously published in Smutny et al. (2024).

We quantified the rate at which PXR is activated by 25-DRIF, and the rates at which PXR induces the transcription of CYP3A4, CYP2C9, and CYP2B6 in 3D PHHs, by fitting the mathematical model to the mRNA CYP expression data. Simulations showed that the rate at which 25-DRIF activates PXR is approximately 20 times lower than that of RIF. The PXR-dependent transcription rate constant for CYP3A4 was estimated to be higher in 3D PHHs treated with 25-DRIF than in those treated with RIF (Lochman et al. 2025). Additionally, we found that the PXR-dependent transcription rate constant of CYP3A4 was higher than that of CYP2B6 in 3D PHHs treated with 25-DRIF. However, the opposite was observed in 3D PHHs treated with RIF (Lochman et al. 2025). The rate constants driving PXR-dependent transcription of CYP2C9 were comparable in RIF- and 25-DRIF-treated 3D PHHs. Thus, our study supports a ligand-specific mode of PXR activation and suggests that the transcription rate of PXR-controlled CYPs is ligand- and CYP-specific in 3D PHHs.

Finally, our results from the mathematical analysis of CYP mRNA expression data in 3D PHHs revealed that the half-maximal effective concentration ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} ), defined here by the CYP3A4 mRNA expression fold change levels, was dependent on the time of exposure to RIF and 25-DRIF. More precisely, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} decreased over 12–72 h post-treatment, after which it increased. We validated the predicted decline in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} by performing CYP3A4 gene reporter assays that measured RIF-induced PXR activity.

Materials and Methods

Chemicals

Rifampicin was purchased from Merck, Darmstadt, Germany.

Primary Human Hepatocyte Spheroids

Cryopreserved human hepatocytes (PHHs) from three donors were purchased from BioIVT (Westbury, New York, USA). The characteristics of the donors were: donor 1: female, 27 years, African American; donor 2: female, 30 years, Hispanic; donor 3: female, 39 years, Caucasian. 3D PHHs were generated by spontaneous self-aggregation on ultra-low attachment 96-well plates (Corning, New York, USA) at a density of 1,500 cells per well. On day 8 after seeding, 3D PHHs were exposed to 25-DRIF (10 µM) for 12, 24, 48, 72, and 120 h. Total RNA was isolated from 30 spheroids. CYP3A4, CYP2B6, and CYP2C9 mRNA levels were assessed by qPCR and normalized to the TBP reference gene. Data are shown as a fold-change expression relative to the corresponding DMSO control at the same time point, which was set as 1. Further details can be found in Smutny et al. (2024). Here, the results for each 3D PHH donor are presented as individual changes in CYP3A4, CYP2C9, and CYP2B6 mRNA, rather than the means reported previously (Smutny et al. 2024).

Plasmids

The p3A4-luc reporter plasmid was used in our previous work (Smutny et al. 2024). It contains the basal promoter region (-361/+53) with the proximal PXR response element (ER6) and the distal xenobiotic responsive enhancer module XREM (-7835/-7208) of the CYP3A4 gene. The sequences were inserted into the pGL4.10 luciferase reporter vector (Promega, Madison, Wisconsin, USA). The expression plasmid for PXR (pSG5-hPXR) was characterized elsewhere (Smutny et al. 2024). The pRL-TK served as the control vector, constitutively expressing Renilla luciferase (Promega, Madison, Wisconsin, USA).

Gene Reporter Assays

The human liver cancer cell line HepG2 was obtained from the European Collection of Authenticated Cell Cultures (ECACC, UK). The HepG2 cells were seeded onto 48-well plates at a density of 110,000 cells per well and maintained at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {37}^\circ $$\end{document} C in a humidified incubator under 5 % \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {CO}_2$$\end{document} . The cells were grown in DMEM medium enriched with 10 % fetal bovine serum (FBS). 24 h post-seeding, the cells were transfected with p3A4-luc reporter plasmid (150 ng/well), pSG5-hPXR (100 ng/well), and pRL-TK plasmid (30 ng/well) employing Lipofectamine 3000 transfection reagent (Thermo Fisher Scientific, Waltham, Massachusetts, USA) following the manufacturer’s recommendations. The cells were then treated with rifampicin at concentrations of 0.1, 0.5, 1, 2.5, 5, 10, 20, and 30 µM or DMSO control in Opti-MEM medium supplemented with 5 % FBS. Conditioned medium was changed every day of the treatment period, ranging from 12 to 72 h (time points were 12, 24, 48, and 72 h). After treatment, the firefly and Renilla luciferase activities were detected in cell lysates using the Dual-Luciferase Reporter Assay System (Promega, Madison, Wisconsin, USA). Results are shown as the fold change in Renilla luciferase-normalized firefly luciferase activities to the corresponding DMSO control (set as 1). Three independent biological measurements were performed in technical triplicates.

Mathematical Model

We describe PXR activation by 25-DRIF and the subsequent induction of CYP3A4, CYP2C9, and CYP2B6 mRNA expression using a mathematical model that we developed in our previous work Lochman et al. (2025), where RIF was used as the PXR ligand. Briefly, 25-DRIF at the concentration \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\text {25-drif}$$\end{document} is assumed to be instantly transported into 3D PHHs and to activate free PXR, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(PXR_\text {tot} - [PXR])$$\end{document} , at the time-dependent rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr}(t)=k_\text {pxr,max}\,e^{-k_\text {r}\,t}$$\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} is the maximum PXR activation rate constant and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {r}$$\end{document} is the rate constant for the time-dependent decrease in PXR activation rate (Lochman et al. 2025). The parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} characterizes the affinity of 25-DRIF to PXR. We assume that the total concentration of PXR, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PXR_\text {tot}$$\end{document} , is fixed. We also assume that the total concentration of 25-DRIF, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\text {25-drif}$$\end{document} , in the culture medium remains constant over time, since the culture medium enriched with 25-DRIF was changed every two to three days. Activated PXR, [PXR], controls the transcription of the CYP genes at the rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp}}$$\end{document} and is degraded at the rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,deg}$$\end{document} . In the absence of 25-DRIF, CYP mRNA, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{mRNA}_\text {cyp}]$$\end{document} , is transcribed at the rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p_{{mRNA}_\text {cyp}}$$\end{document} . The CYP mRNA is degraded at the rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp,deg}}$$\end{document} . The mathematical model for the activation of PXR by 25-DRIF and the associated induction of CYP in 3D PHHs is as follows:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[PXR]}{dt}}&= k_\text {pxr}(t)\,(PXR_\text {tot} - [PXR])\,C_\text {25-drif} - k_\text {pxr,deg}\,[PXR], \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[{mRNA}_\text {cyp}]}{dt}}&= k_{{mRNA}_\text {cyp}}\,[PXR] + p_{{mRNA}_\text {cyp}} - k_{{mRNA}_\text {cyp,deg}} [{mRNA}_\text {cyp}]. \end{aligned}$$\end{document}

The initial conditions for Equations (1)–(2) are: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PXR(0)=0$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${mRNA}_\text {cyp}(0)=p_{{mRNA}_\text {cyp}}/k_{mRNA_\text {cyp,deg}}$$\end{document} .

We report the gene expression data as the relative change in mRNA expression level at the time point in the presence of 25-DRIF to the corresponding level at the same time point in the absence of 25-DRIF. In the absence of 25-DRIF, CYP mRNA levels are assumed to be at their basal steady state, that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${mRNA}^{*}_\text {cyp} = p_{{mRNA}_\text {cyp}}/k_{mRNA_\text {cyp,deg}}$$\end{document} . Dividing Equation (1) by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$PXR_\text {tot}$$\end{document} (i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[pxr]=[PXR]/{PXR}_\text {tot}$$\end{document} ) and Equation (2) by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${mRNA}_\text {cyp}^*$$\end{document} (i.e., \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[{mRNA}_\text {cyp}^\text {fold}] = [{mRNA}_\text {cyp}]/{mRNA}_\text {cyp}^*$$\end{document} ), we obtain

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[pxr]}{dt}}&= k_\text {pxr}(t)\,(1 - [pxr])\,C_\text {25-drif} - k_\text {pxr,deg}\,[pxr], \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[{mRNA}_\text {cyp}^\text {fold}]}{dt}}&= k_{{mRNA}_\text {cyp}^\text {fold}}\,[pxr] + k_{{mRNA}_\text {cyp,deg}}\left( 1 - [{mRNA}_\text {cyp}^\text {fold}]\right) , \end{aligned}$$\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp}^\text {fold}}=k_{{mRNA}_\text {cyp}}/{mRNA}_\text {cyp}^*$$\end{document} is the PXR-dependent fold transcription rate constant of the CYP gene. The initial conditions for Equations (3)–(4) are: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$pxr(0)=0$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${mRNA}_\text {cyp}^\text {fold}(0)=1$$\end{document} .

Recalling that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr}(t)=k_\text {pxr,max}\,e^{-k_\text {r}\,t}$$\end{document} , changes in the mRNA expression of CYP3A4, CYP2C9, and CYP2B6 are therefore described as

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[pxr]}{dt}}&= k_\text {pxr,max}\,e^{-k_\text {r}\,t}\,(1 - [pxr])\,C_\text {25-drif} - k_\text {pxr,deg}\,[pxr], \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[mRNA_\text {cyp3a4}^\text {fold}]}{dt}}&= k_{mRNA_\text {cyp3a4}^\text {fold}}\,[pxr] + k_{mRNA_\text {cyp3a4,deg}}\left( 1 - [mRNA_\text {cyp3a4}^\text {fold}]\right) , \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[mRNA_\text {cyp2c9}^\text {fold}]}{dt}}&= k_{mRNA_\text {cyp2c9}^\text {fold}}\,[pxr] + k_{mRNA_\text {cyp2c9,deg}}\left( 1 - [mRNA_\text {cyp2c9}^\text {fold}]\right) , \end{aligned}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \displaystyle {\frac{d[mRNA_\text {cyp2b6}^\text {fold}]}{dt}}&= k_{mRNA_\text {cyp2b6}^\text {fold}}\,[pxr] + k_{mRNA_\text {cyp2b6,deg}}\left( 1 - [mRNA_\text {cyp2b6}^\text {fold}]\right) . \end{aligned}$$\end{document}

Fig. 1CYP mRNA expression profiles in 3D PHHs. 3D PHHs were treated with 25-DRIF at 10 µM for an indicated time range (12–120 h). The expression levels of CYP3A4 (A), CYP2C9 (B), and CYP2B6 (C) mRNA were assessed by qPCR. The results are shown as fold change expression relative to the corresponding DMSO control at the same time point, which was set as 1. Data were previously published in Smutny et al. (2024)

Parameter Estimation

We fitted Equations (5)–(8) to CYP mRNA expression data (Figure 1) obtained from treatments of 3D PHHs with 25-DRIF at a concentration of 10 µM. The parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} were estimated or held fixed depending on the model configuration. Fitting was performed using |slicesample|, the Matlab implementation of the MCMC algorithm (The MathWorks Inc 2024). To assess the goodness of the proposed fit of Equations (5)–(8), we maximized the logarithm of the Gaussian likelihood function

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} -\frac{1}{2}\ln \mathcal {L}(\vec {p}), \end{aligned}$$\end{document}

where

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \begin{aligned} \ln \mathcal {L}(\vec {p}) = \sum _{i}\sum _{\text {cyp}}\sum _{k}\left[ \left( \frac{\text {data}_{i,\text {cyp}}(t_{k}) - \text {mRNA}^\text {fold}_{\text {cyp}}(t_{k},\vec {p})}{\sigma _{\text {cyp}}(t_{k})}\right) ^2 + 2\,\ln \left( \sqrt{2\pi }\sigma _{\text {cyp}}(t_{k})\right) \right] \end{aligned} \end{aligned}$$\end{document}

and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\vec {p}$$\end{document} is the parameter vector. In (10), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {data}_\text {i,cyp}(t_{k})$$\end{document} refers to the data point at the measured time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_k$$\end{document} for donor i, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i=\{\text {donor}~1,\,\text {donor}~2,\,\text {donor}~3\}$$\end{document} . The index ’cyp’ refers to CYP3A4, CYP2C9, and CYP2B6. The parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma _{\text {cyp}}(t_k)$$\end{document} denotes the standard deviation of all donor data at time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_k$$\end{document} for a given CYP. All parameter priors were assumed to be uniform.Fig. 2PXR activation by 25-DRIF and CYP mRNA expression. Graphical representation of Equations (5)–(8). Created with https://www.biorender.com/

CYP3A4 Gene Reporter Assay Concentration-Response Curve

The values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} were obtained by minimizing the weighted sum of squares between the predicted gene reporter activity levels expressed by the Hill function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y = Y_\text {min} + \frac{(Y_\text {max} - Y_\text {min})}{1 + 10^{N\left( \log \text {EC}_{50} - \log \text {C}_\text {rif}\right) }}$$\end{document} and the measured gene reporter activity levels using Matlab’s function |lsqnonlin|. Weights were defined as the inverse of the data variance at a concentration \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\text {rif}$$\end{document} . Fixed parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_\text {min} = 1$$\end{document} . Parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y_\text {max}$$\end{document} , N, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} were estimated. The concentrations of RIF, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\text {rif}$$\end{document} , for which fitting was performed, were 0.1, 0.5, 1, 2.5, 5, 10, 20, and 30 µM.

MC2 Predicted Concentration-Response Curve

The values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} for RIF and 25-DRIF were obtained by fitting the Hill function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$mRNA_\text {cyp3a4}^\text {fold} = mRNA_\text {cyp3a4,min}^\text {fold} + \frac{mRNA_\text {cyp3a4,max}^\text {fold} - mRNA_\text {cyp3a4,min}^\text {fold}}{1 + 10^{N\left( \log \text {EC}_{50} - \log \text {C}\right) }}$$\end{document} to the predicted CYP3A4 mRNA fold change levels using the Matlab’s function |lsqcurvefit|. Fixed parameters: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$mRNA_\text {cyp3a4,min} = 1$$\end{document} . Parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$mRNA_\text {cyp3a4,max}$$\end{document} , N, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} were estimated. The concentrations of RIF and 25-DRIF, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {C}$$\end{document} , ranged from 0.001 to 100 µM. The CYP3A4 mRNA fold change levels corresponding to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} were obtained using the Matlab’s function |csapi| for the cubic spline interpolation (The MathWorks Inc 2024).

Statistical Analysis

The Mann-Whitney U test was used to determine statistically significant differences between the estimated parameters using the |ranksum| function in Matlab, with the significance level set at p-value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$< 0.05$$\end{document} . The Bayesian Information Criterion (BIC) was used to select the most appropriate configuration of the gene expression model in terms of the number of estimated parameters. The model with the lowest BIC was considered the best.

Results

CYP mRNA Expression Data

We previously published data on changes in CYP mRNA expression induced by 25-DRIF in 3D PHHs in Smutny et al. (2024). Panels (A), (B), and (C) in Figure 1 display individual changes in CYP3A4, CYP2C9, and CYP2B6 mRNA, respectively, for each 3D PHH donor. In brief, 3D PHHs obtained from three donors were treated with 25-DRIF at a concentration of 10 µM for a period ranging from 12 to 120 hours. mRNA levels of CYP3A4, CYP2C9, and CYP2B6 were presented as fold change expression relative to the corresponding DMSO control at the same time point (set as 1). Treatment of 3D PHHs with 25-DRIF resulted in maximum increases in mRNA levels at 48 h, with mean fold changes of 2.6, 1.6, and 2 for CYP3A4, CYP2C9, and CYP2B6, respectively. Notably, peak CYP3A4 mRNA levels were higher than those for CYP2B6 in 3D PHHs treated with 25-DRIF (Figures 1A and C). In previously published studies (Smutny et al. 2022; Lochman et al. 2025), the opposite was observed in 3D PHHs treated with RIF where peak CYP3A4 mRNA levels were lower than those of CYP2B6. Following the peak, the long-term CYP mRNA expression decreased slightly, however, in contrast to previous observations in 3D PHHs treated with RIF (Lochman et al. 2025), CYP mRNA levels remained elevated at 120 h, with donor 3 exhibiting large variability (Figure 1).Table 1. Parameter estimates. Maximum likelihood estimate (best-fit) parameter values and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$95\%$$\end{document} credible intervals (CIs) obtained from fitting Equations (5)–(8) to the CYP mRNA expression data for model configurations MC1, MC2, and MC3Fixed parametersParameterDescriptionUnitsvalue95% CI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {r}$$\end{document} rate constant for decrease in PXR activation rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.049Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,deg}$$\end{document} activated PXR degradation rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.011Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4,deg}}$$\end{document} CYP3A4 mRNA degradation rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.044Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9,deg}}$$\end{document} CYP2C9 mRNA degradation rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.036Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6,deg}}$$\end{document} CYP2B6 mRNA degradation rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.034Fixed from Lochman et al. (2025)1. Estimated parameters for MC1ParameterDescriptionUnitsvalue95% CI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} maximum PXR activation rate constantµ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {M}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5.98\times 10^{-3}$$\end{document} [5.17, 6.92] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times 10^{-3}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} PXR-dependent CYP3A4 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.083Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} PXR-dependent CYP2C9 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.040Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} PXR-dependent CYP2B6 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.139Fixed from Lochman et al. (2025)2. Estimated parameters for MC2ParameterDescriptionUnitsvalue95% CI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} maximum PXR activation rate constantµ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {M}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.35\times 10^{-3}$$\end{document} [5.80, 9.05] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times 10^{-3}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} PXR-dependent CYP3A4 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.101[0.085, 0.121] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} PXR-dependent CYP2C9 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.040Fixed from Lochman et al. (2025) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} PXR-dependent CYP2B6 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.062[0.041, 0.086]3. Estimated parameters for MC3ParameterDescriptionUnitsvalue95% CI \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} maximum PXR activation rate constantµ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {M}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.46\times 10^{-3}$$\end{document} [0.183, 1.21] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times 10^{-3}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} PXR-dependent CYP3A4 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.342[0.401, 2.43] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} PXR-dependent CYP2C9 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.149[0.175, 1.10] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} PXR-dependent CYP2B6 mRNA fold transcription rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} 0.225[0.252, 1.70]

Mathematical Description of PXR Activation and CYP mRNA Expression

To quantify the influence of 25-DRIF on the mRNA expression of CYP3A4, CYP2C9, and CYP2B6, we collectively fitted the gene expression mathematical model (Equations (5)–(8)), graphically depicted in Figure 2, to the respective mRNA expression data (Figure 1) using Markov chain Monte Carlo (MCMC, see Materials and Methods for details). In our previous study (Lochman et al. 2025), we suggested that the PXR activation rate, defined as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr}(t)=k_\text {pxr,max}\,e^{-k_\text {r}\,t}$$\end{document} , was time-dependent and decreased over time. We considered the processes governed by the rate constant for decrease in PXR activation rate, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {r}$$\end{document} , and the rate constant for the degradation of activated PXR, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\text {pxr,deg}}$$\end{document} , to be inherent characteristics of PXR activation rather than of the ligand. Thus, we fixed these rate constants in Equations (5)–(8) to the corresponding best-fit values provided in Lochman et al. (2025) and reiterate them in Table 1. The degradation rate constants of CYP3A4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4,deg}}$$\end{document} , CYP2C9, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9,deg}}$$\end{document} , and CYP2B6 mRNA, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6,deg}}$$\end{document} , were estimated in Lochman et al. (2025) and we fixed their values to those provided in Lochman et al. (2025) (Table 1). We considered three approaches to fitting the CYP expression kinetic profiles.Fig. 3Fits of the gene expression model to the CYP mRNA expression data. Equations (5)–(8) were fitted simultaneously to mRNA expression data from 3D PHHs treated with 10 µM of 25-DRIF. (A1)–(A4) Fits for MC1, where only \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} was estimated and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} were fixed to the values in Table 1. (B1)–(B4) Fits for MC2, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} were estimated and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} was fixed to the value in Table 1. (C1)–(C4) Fits for MC3, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{mRNA_\text {cyp2b6}^\text {fold}}$$\end{document} were estimated. The black solid lines represent the model solution associated with the best-fit parameter values in Table 1. The grey filled areas around the best-fit lines indicate the model solutions associated with the MCMC-accepted parameter values. The data are presented as the mean ± standard deviation for three donors at each time point. The data values used to calculate the means and standard deviations are visualized in Figure 1

Fixed CYP Transcription Rate Constants (Model Configuration 1, MC1)

In MC1, we assumed that 25-DRIF affected only the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , but did not affect the transcription rate constants of CYPs. We adopted the PXR-dependent CYP mRNA fold transcription rate constants of each gene \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} from Lochman et al. (2025) (Table 1), where 3D PHHs were treated with RIF, and estimated only the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} . We note that the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} characterizes the affinity of 25-DRIF to PXR. The value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} was determined to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5.98\times 10^{-3}$$\end{document}  µ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {M}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} . Fits of Equations (5)–(8) are shown in Figure 3, panels A1–A4, and demonstrate that MC1 explained only the CYP2C9 mRNA expression profile (Figure 3, panel A3). Specifically, MC1 predicted notably lower levels of CYP3A4 mRNA fold expression and higher levels of CYP2B6 mRNA fold expression than the data indicated (Figure 3, panels A2 and A4, respectively). These results suggest that the PXR-dependent mRNA fold transcription rates of CYP2C9 induced by RIF and 25-DRIF may be comparable, whereas those of CYP3A4 and CYP2B6 may depend on whether RIF or 25-DRIF is used. The best-fit value and the 95% credible interval (CI) for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} for MC1 are given in Table 1.

Fixed CYP2C9 and Estimated CYP3A4 and CYP2B6 Transcription Rate Constants (Model Configuration 2, MC2)

Since fits from MC1 suggested that CYP2C9 mRNA expression data could be accurately fitted using the best-fit value of the PXR-dependent CYP2C9 mRNA fold transcription rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , from Lochman et al. (2025), where 3D PHHs were treated with RIF, we kept this parameter fixed and assumed that the fold transcription rate constants of CYP3A4 and CYP2B6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , respectively, together with the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , were ligand-specific and thus estimated. These fits are shown in Figure 3, panels B1–B4, and demonstrate a significant improvement in the fitting of Equations (5)–(8) to the CYP3A4 and CYP2B6 mRNA expression profiles. This model configuration MC2 performed better than the model configuration MC1, in which only \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} was estimated, as measured by the Bayesian Information Criterion (BIC, Figure S1 in Online Resource 1).Fig. 4PXR- and CYP-specific parameters for RIF and 25-DRIF treatments of 3D PHHs. (A) The maximum PXR activation rate constants for RIF-treated (grey) and 25-DRIF-treated (black) 3D PHHs. (B) Fold transcription rate constants of CYP3A4 for RIF-treated (magenta) and 25-DRIF-treated (red) 3D PHHs. (C) Fold-transcription rate constants of CYP2B6 for RIF-treated (cyan) and 25-DRIF-treated (blue) 3D PHHs. The parameter posterior histograms for RIF-treated 3D PHHs were obtained from refitting Equations (6)–(10) from Lochman et al. (2025) to the CYP mRNA expression data from 3D PHHs treated with 1 µM and 10 µM of RIF from Lochman et al. (2025). The parameter posterior histograms for the 25-DRIF-treated 3D PHHs were obtained by fitting the MC2 to the CYP mRNA expression data from the 3D PHHs treated with 10 µM of 25-DRIF. For MCMC estimation, five chains were run for 50,000 steps with a burn-in period of 25,000 steps, and the chains were thinned by accepting every 5th step

We estimated the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.35\times 10^{-3}$$\end{document}  µ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {M}^{-1}$$\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} , which was 20 times lower than that estimated for 3D PHHs treated with RIF (Lochman et al. 2025). The PXR-dependent CYP mRNA fold transcription rate constants differed between PXR-regulated CYP isoenzymes. The value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} was estimated to be 0.101  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} , which was 1.2 times higher than that estimated for 3D PHHs treated with RIF (Lochman et al. 2025). The value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} was estimated to be 0.062  \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {h}^{-1}$$\end{document} , which was 2.2 times lower than that estimated for 3D PHHs treated with RIF (Lochman et al. 2025). Interestingly, the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} was lower than that of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} in RIF-treated 3D PHHs. However, the value of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} was higher than that of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} in 3D PHHs treated with 25-DRIF. The differences in the estimated parameter values, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , in 3D PHHs treated with RIF and 25-DRIF were statistically significant (p-values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$< 10^{-5}$$\end{document} ). This was determined using a Mann-Whitney U-test in Matlab (details are in Materials and Methods). These differences are visualized as parameter posterior distributions associated with RIF and 25-DRIF treatments constructed from the MCMC-accepted parameter sets in Figure 4. The best-fit values and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$95\%$$\end{document} CIs for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} for MC2 are provided in Table 1.Fig. 5Comparison of the predicted levels of activated PXR and fold CYP mRNA expression in 3D PHHs treated with either RIF- or 25-DRIF. Solutions of the MC2 (Equations (5)–(8)) for 3D PHHs treated with 25-DRIF at a concentration of 10 µM (black) were generated using the best-fit parameter values in Table 1. Solutions of the Equations (5)–(8) for 3D PHHs treated with RIF at concentrations of 1 µM (blue) and 10 µM (red) were generated using the fixed parameter values in Table 1

Figure 5 shows a direct comparison of the effects of RIF and 25-DRIF on PXR activation and the induction of CYP3A4, CYP2C9, and CYP2B6 mRNA expression in 3D PHHs. The maximum PXR activation by 25-DRIF at a concentration of 10 µM was predicted to occur 37 h after treatment at the level of 58%, which was lower than the maximum PXR activation by RIF at a concentration of 1 µM 24 h after treatment at the level of 78% (Figure 5, panel A) (Lochman et al. 2025). Despite the low PXR activation by 25-DRIF, comparable levels of CYP3A4 and CYP2C9 mRNA expression were predicted to those induced by RIF at a concentration of 1 µM (Figure 5, panels B and C, respectively). However, significantly lower levels of CYP2B6 mRNA expression were predicted compared to those induced by RIF at a concentration of 1 µM (Figure 5, panel D).

Estimated CYP Transcription Rate Constants (Model Configuration 3, MC3)

In MC3, we assumed that the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , and the PXR-dependent CYP mRNA fold transcription rate constants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , were ligand-specific and thus estimated. The fits are depicted in Figure 3, panels C1–C4, and according to BIC (Figure S1 in Online Resource 1), MC3 did not perform better than MC2. The MCMC routine accepted extremely low values of the maximum PXR activation rate constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} (lower bound of the 95% CI was determined to be approximately 30 times lower than the lower bounds of the 95% CI for MC1 and MC2, Table 1) and increasingly high values of the PXR-dependent CYP3A4, CYP2C9, and CYP2B6 mRNA fold transcription rate constants, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , respectively. In contrast to MC1 (Figure S2 in Online Resource 1) and MC2 (Figure S3 in Online Resource 1), the MCMC chains for MC3 (Figure S4 in Online Resource 1) did not converge to stationary parameter distributions for any of the estimated parameters within \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {10}^5$$\end{document} steps. Additionally, such low values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} are unlikely to induce detectable changes in CYP mRNA expression; therefore, we consider MC3 to be inadequate with respect to the used dataset. The best-fit values and the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$95\%$$\end{document} CIs for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} for MC3 are in Table 1.

To elucidate why the MCMC chains did not converge to stationary posterior distributions of the estimated parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , we performed structural identifiability analysis on these estimated parameters (Appendix A). We showed that for any one CYP, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp}^\text {fold}}$$\end{document} were structurally identifiable, but not practically identifiable (Appendix B).

The Effects of Different 25-DRIF Concentrations on PXR Activation and CYP mRNA Expression

We used MC2 to predict PXR activation and changes in the CYP3A4, CYP2C9, and CYP2B6 mRNA expression levels in 3D PHHs following treatment with different concentrations of 25-DRIF (Figure S5 in Online Resource 1). The degree of PXR activation increased with increasing concentrations of 25-DRIF. More precisely, 20 µM of 25-DRIF was required to activate PXR by 78 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} , which was comparable to the degree of PXR activation that was predicted in 3D PHHs treated with 1 µM of RIF, as reported in Lochman et al. (2025). Nearly maximal PXR activation of 99 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} was predicted to be achieved with 200 µM of 25-DRIF, comparable to the degree of PXR activation achieved with 10 µM of RIF, as reported in Lochman et al. (2025).Fig. 6Time-dependent transactivation of CYP3A4 reporter plasmid by PXR in gene reporter assays. ** Experiments were performed in triplicates and data were displayed as the mean ± standard deviation of the fold change in Renilla luciferase-normalized firefly luciferase activities to DMSO control (set as 1). The black dashed line denotes the basal level of CYP3A4 gene reporter activity. The calculations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} are described in Materials and MethodsFig. 7Predicted RIF and 25-DRIF concentration-response curves evaluated from CYP3A4 mRNA in 3D PHHs.** At times 4, 8, 12, 16, 24, 48, 72, 96, and 120 h post-treatment, the concentrations of RIF and 25-DRIF were varied and the solutions of the Equation (6) were evaluated at the RIF- and 25-DRIF-associated best-fit parameters (Table 1). The blue solid line indicates the CYP3A4 mRNA fold change levels for the best-fit RIF-parameters at a given time, and the cyan solid line indicates the CYP3A4 mRNA fold change levels for the best-fit 25-DRIF-parameters at a given time. The shaded areas around the solid lines show the predicted CYP3A4 mRNA fold change levels for the MCMC-accepted parameter sets. The calculations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} are described in Materials and MethodsFig. 8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\textbf {Predicted time-dependent RIF and 25-DRIF EC}}_{50}$$\end{document} evaluated from CYP3A4 mRNA in 3D PHHs. The blue and cyan solid lines indicate RIF and 25-DRIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} , respectively, evaluated from the solutions of Equation (6) at the best-fit parameters in Table 1 for concentrations of RIF from 0.5 to 100 µM and of 25-DRIF from 5 to 100 µM. The shaded areas around the solid lines show the predicted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} for the MCMC-accepted parameter sets

Validation of RIF \documentclass[12pt]{minimal}

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			\begin{document}$$\hbox {EC}_{50}$$\end{document}EC50 Predicted from MC2 by Gene Reporter Assays

To validate RIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} predicted from MC2, we treated HepG2 cells transfected with a PXR expression plasmid and a CYP3A4 reporter vector with RIF at concentrations of 0.1, 0.5, 1, 2.5, 5, 10, 20, and 30 µM. We then quantified the transcriptional activity of PXR at times 12, 24, 48, and 72 h post-treatment. We determined \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} from the concentration-response curves (Figure 6). The gene reporter assays yielded \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} values that were qualitatively consistent with the predicted values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} from MC2 (Figure 7) and decreased over time (Figure 8). At 12 h, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} was determined to be 1.32 µM compared to 1.03 µM predicted from MC2. At 24 h, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} was determined to be 1.49 µM compared to 0.60 µM predicted from MC2. At 48 h, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} was determined to be 1.18 µM compared to 0.44 µM predicted from MC2. At 72 h, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} was determined to be 0.72 µM compared to 0.48 µM predicted from MC2.

Discussion

The pregnane X receptor (PXR) is an important transcription factor that regulates the metabolism of xenobiotics (Lehmann et al. 1998; Kliewer et al. 2002; Kliewer 2015; Ma et al. 2008). In the present study, we investigated the effects of 25-DRIF on PXR activation and the regulation of CYP3A4, CYP2C9, and CYP2B6 mRNA expression. This was achieved by combining a mechanistic mathematical model of PXR activation and PXR-induced CYP mRNA expression developed in Lochman et al. (2025) to CYP mRNA expression in 3D PHHs treated by 25-DRIF. Our results revealed significant variations in PXR activation and PXR-induced CYP mRNA expression in 3D PHHs treated by RIF and 25-DRIF. We demonstrated that the rate constant for PXR activation by 25-DRIF was approximately 20 times lower than the rate constant for RIF-induced PXR activation. The rate constant associated with the PXR-dependent CYP3A4 mRNA transcription was determined to be higher in 3D PHHs treated with 25-DRIF than with RIF. Furthermore, the rate constant associated with the PXR-dependent CYP3A4 mRNA transcription was determined to be higher than the rate constant associated with the PXR-dependent CYP2B6 mRNA transcription in 3D PHHs treated with 25-DRIF, whereas the opposite was observed in 3D PHHs treated with RIF (Lochman et al. 2025). The rate constant associated with the PXR-dependent CYP2C9 mRNA transcription was found to be comparable to that determined in 3D PHHs treated with RIF (Lochman et al. 2025).

We applied three different configurations of the mathematical model to describe the mRNA expression of CYP3A4, CYP2C9, and CYP2B6 in 3D PHHs treated with 25-DRIF. In MC1, we assumed that the PXR-dependent CYP mRNA fold transcription rate constants, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , were independent of the used ligand and thus fixed to the values obtained from 3D PHHs treated with RIF. This model was evaluated as the least descriptive of the data according to BIC (Figure S1 in Online Resource 1). In MC3, although the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , and the PXR-dependent CYP mRNA fold transcription rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp}^\text {fold}}$$\end{document} , were determined to be structurally identifiable from a single observed CYP mRNA fold expression profile, provided all other parameters were fixed, practical identifiability showed that none of the parameters were practically identifiable from the data. To reduce complexity of the model, we fixed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} .

Our analysis revealed that the model configuration MC2 was most consistent with the CYP mRNA expression profiles (Figure 3, panels B1–B4). In MC2, the PXR-dependent CYP2C9 mRNA fold transcription rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2c9}^\text {fold}}$$\end{document} , was fixed to the value estimated from RIF treatments of 3D PHHs (Lochman et al. 2025) and the maximum PXR activation, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , and PXR-dependent CYP3A4 and CYP2B6 mRNA fold transcription rate constants, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , respectively, were estimated. Interestingly, these results suggest that the control of CYP2C9 by PXR at the mRNA level may be independent of whether RIF or 25-DRIF is used, whereas the regulation of CYP3A4 and CYP2B6 by PXR may depend on a specific ligand.

Treatment of 3D PHHs with 10 µM 25-DRIF resulted in peak induction of CYP3A4, CYP2C9, and CYP2B6 mRNA levels at 48 h after treatment, after which they declined. However, the CYP mRNA levels remained elevated at 120 h in donor 3. The post-peak decline in CYP mRNA in 25-DRIF-treated 3D PHHs was possible because we assumed a time-dependent PXR activation in the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr}(t)=k_\text {pxr,max}\,e^{-k_\text {r}\,t}$$\end{document} , as introduced in Lochman et al. (2025). Such a decrease in PXR activation over time could stem from the depletion of transcription factors and cofactors (Pavek 2016). The differences in interactions between the 25-DRIF–PXR complex and co-regulators, especially in donor 3, compared to the RIF-PXR complex may have contributed to the prolonged expression of CYP mRNA. Ideally, the parameters governing the reduction in PXR activation by 25-DRIF, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {r}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,deg}$$\end{document} , would have been estimated directly from data obtained from 3D PHHs treated with 25-DRIF, rather than approximated using data from 3D PHHs treated with RIF. However, to ensure structural identifiability of the gene expression model, it would have been necessary to measure CYP mRNA fold expression levels under at least two distinct 25-DRIF treatment conditions in 3D PHHs, using at least two different concentrations, as indicated by the structural identifiability analysis presented in Appendix A. Nevertheless, structural identifiability does not guarantee practical identifiability (Raue et al. 2009; Wanika et al. 2024). Thus, our results suggest that the individual variability in PXR-mediated CYP regulation plays an important role in the experimental design and model parameterization.

For MC2, peak PXR activation by 10 µM 25-DRIF was achieved 37 hours post-treatment, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$58\%$$\end{document} of the total PXR being activated. By contrast, treatment with RIF at the same concentration was estimated to result in peak PXR activation at 5.8 hours post-treatment, at which point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$99\%$$\end{document} of the total PXR was activated (Lochman et al. 2025). This difference aligns with previous findings in Smutny et al. (2024) and in Nakajima et al. (2011), confirming that 25-DRIF is a significantly weaker PXR agonist than RIF.

Despite its weaker ability to activate PXR, 25-DRIF notably induces the mRNA expression of CYP3A4, CYP2C9, and CYP2B6. In 3D PHHs treated with 25-DRIF, CYP3A4 was transcribed at a faster rate than CYP2C9 and CYP2B6. In contrast, 3D PHHs treated with RIF exhibited a distinct transcriptional hierarchy, with CYP2B6 transcribed at a higher rate than CYP3A4 and CYP2C9 (Lochman et al. 2025). The reason why the PXR-dependent transcription rate of CYP3A4 mRNA is higher than that of CYP2B6 and CYP2C9 in 3D PHHs treated with 25-DRIF remains unclear. It should be investigated whether this can be attributed to the specific interaction of 25-DRIF-PXR with co-regulators that selectively enhance CYP3A4 transcription rather than CYP2B6 and CYP2C9 transcription.

The PXR-controlled regulation of CYP mRNA expression is affected by the rate of both PXR activation and mRNA transcription. Direct sensitivity analysis provided in Online Resource 1 revealed that the maximum PXR activation rate constant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , affected the solution of MC2 particularly within the first 24 h following 25-DRIF treatment of 3D PHHs (Figure S6 in Online Resource 1). However, changes in the PXR-dependent fold transcription rate constants of CYP3A4, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} , and CYP2B6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} , produced more significant alterations in predicted CYP mRNA levels than changes in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} , suggesting that variability in CYP mRNA levels may be attributed to variability in CYP-specific transcription rates rather than to variability in PXR activation. This conclusion is also supported by the results of the local sensitivity analysis (Online Resource 1). Varying the values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp3a4}^\text {fold}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{{mRNA}_\text {cyp2b6}^\text {fold}}$$\end{document} by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50 \% $$\end{document} from their best-fit values produced more significant alterations in the predicted CYP mRNA levels than varying \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_\text {pxr,max}$$\end{document} by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$50 \% $$\end{document} from its best-fit value (Figure S7 in Online Resource 1).

In gene reporter assays with CYP3A4 reporter plasmid and PXR expression plasmid, we observed that the potency of RIF to transactivate CYP3A4 reporter vector by PXR increases with time (Figure 6). Such a time-dependency could be explained by an increased availability of cofactors needed for transcriptional machinery at later times of the treatment. Alternatively, time-dependent changes in RIF transport into cells could also be a factor. Although not directly comparable due to the usage of different in vitro models (3D PHHs versus gene reporter assays), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} calculated from RIF treatments of 3D PHHs still supported a decreasing tendency of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} within 12–72 h period of treatment (Figures 7 and 8). Moreover, predictions from MC2 showed that at 24 h, 25-DRIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} was 21 times higher than RIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} . Previously, the gene reporter assays performed in Smutny et al. (2024) showed that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} at 24 h associated with 25-DRIF treatment was 59 times higher than that associated with RIF treatment (RIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} of 1.46 µM versus 25-DRIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} of 86.57 µM from the gene reported assay in Smutny et al. (2024)). Although theoretical results from the MC2 confirmed that RIF had significantly higher affinity to PXR than 25-DRIF (RIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} of 0.6 µM versus 25-DRIF \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} of 12.77 µM from MC2), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {EC}_{50}$$\end{document} varies depending on the used in vitro system.

The activation of PXR is a complex process that leads to different patterns of mRNA expression in its target genes depending on the ligand. The exact mechanisms underlying these differences are unclear. However, one possibility is that the ligand that activates PXR influences how the receptor interacts with co-regulatory proteins. PXR is known to recruit various co-regulators to facilitate transcription of target genes, which likely impacts overall transcriptional outcomes (Duintjer Tebbens et al. 2018; Hariparsad et al. 2009; Li and Chiang 2006; Pavek 2016; Rigalli et al. 2021). Future work should address these knowledge gaps.

Supplementary Information

Below is the link to the electronic supplementary material. Supplementary file 1 (pdf 2136 KB)Supplementary file 2 (xlsx 15 KB)