Mathematical Models in the Description of Pregnane X Receptor (PXR)-Regulated Cytochrome P450 Enzyme Induction

The pregnane X receptor (PXR) is a drug/xenobiotic-activated transcription factor of crucial importance for major cytochrome P450 xenobiotic-metabolizing enzymes (CYP) expression and regulation in the liver and the intestine. One of the major target genes regulated by PXR is the cytochrome P450 enzyme (CYP3A4), which is the most important human drug-metabolizing enzyme. In addition, PXR is supposed to be involved both in basal and/or inducible expression of many other CYPs, such as CYP2B6, CYP2C8, 2C9 and 2C19, CYP3A5, CYP3A7, and CYP2A6. Interestingly, the dynamics of PXR-mediated target genes regulation has not been systematically studied and we have only a few mechanistic mathematical and biologically based models describing gene expression dynamics after PXR activation in cellular models. Furthermore, few indirect mathematical PKPD models for prediction of CYP3A metabolic activity in vivo have been built based on compartmental models with respect to drug–drug interactions or hormonal crosstalk. Importantly, several negative feedback loops have been described in PXR regulation. Although current mathematical models propose these adaptive mechanisms, a comprehensive mathematical model based on sufficient experimental data is still missing. In the current review, we summarize and compare these models and address some issues that should be considered for the improvement of PXR-mediated gene regulation modelling as well as for our better understanding of the quantitative and spatial dynamics of CYPs expression.