Beyond the Michaelis-Menten: Accurate Prediction of Drug Interactions through Cytochrome P450 3A4 Induction

The US Food and Drug Administration (FDA) guidance has recommended several model-based predictions to determine potential drug-drug interactions (DDIs) mediated by cytochrome P450 (CYP) induction. In particular, the ratio of substrate area under the plasma concentration-time curve (AUCR) under and not under the effect of inducers is predicted by the Michaelis-Menten (MM) model, where the MM constant (Km$$ {K}_{\mathrm{m}} $$) of a drug is implicitly assumed to be sufficiently higher than the concentration of CYP enzymes that metabolize the drug (ET$$ {E}_{\mathrm{T}} $$) in both the liver and small intestine. Furthermore, the fraction absorbed from gut lumen (Fa$$ {F}_{\mathrm{a}} $$) is also assumed to be one because Fa$$ {F}_{\mathrm{a}} $$ is usually unknown. Here, we found that such assumptions lead to serious errors in predictions of AUCR. To resolve this, we propose a new framework to predict AUCR. Specifically, Fa$$ {F}_{\mathrm{a}} $$ was re-estimated from experimental permeability values rather than assuming it to be one. Importantly, we used the total quasi-steady-state approximation to derive a new equation, which is valid regardless of the relationship between Km$$ {K}_{\mathrm{m}} $$ and ET$$ {E}_{\mathrm{T}} $$, unlike the MM model. Thus, our framework becomes much more accurate than the original FDA equation, especially for drugs with high affinities, such as midazolam or strong inducers, such as rifampicin, so that the ratio between Km$$ {K}_{\mathrm{m}} $$ and ET$$ {E}_{\mathrm{T}} $$ becomes low (i.e., the MM model is invalid). Our work greatly improves the prediction of clinical DDIs, which is critical to preventing drug toxicity and failure.