Beyond the Michaelis–Menten: Accurate Prediction of Drug Interactions Through Cytochrome P450 3A4 Induction

Abstract

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 (K m ) of a drug is implicitly assumed to be sufficiently higher than the concentration of CYP enzymes that metabolize the drug (E T ) in both the liver and small intestine. Furthermore, the fraction absorbed from gut lumen (F a ) is also assumed to be one because F 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, F 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 K m and E 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 K m and E 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.Cytochrome P450 (CYP) is the most important superfamily of enzymes, playing a crucial role in the metabolic clearance of an enormous number of compounds in humans. Approximately 70-80% of marketed drugs are metabolized by this superfamily of enzymes, especially CYP1A2, CYP2C, CYP2D6, and CYP3A4. 1 Such CYP enzymes can be induced by xenobiotic substances, including drugs, resulting in the increased metabolic activity of these enzymes. For instance, rifampicin, a prototype CYP3A4 enzyme inducer, enhances the metabolic process of midazolam, a probe substrate of CYP3A4, decreasing its plasma concentration and thus its therapeutic efficacy. 2 Therefore, the induction of CYP enzymes is one of the major reasons for clinical drug-drug interactions (DDIs).

The unreasonable effectiveness of the total quasi-steady state approximation, and its limitations

“…The validity of the tQSSA has been explored through heuristic approaches and numerical simulations. It appears that Vu et al [18] in their recent work do not explicitly address the necessity of small ε EV R for the validity of the tQSSA. They might be presuming A frequently reported advantage of the tQSSA is its purported accuracy at high enzyme concentration.…”

“…As evident from the analysis in [2], one can therefore argue that tQSSA is not universally valid, as claimed by some, but valid in the limiting case of low initial reduced substrate concentration. Note that this assumption on reduced substrate forms the foundation of Kim & Tyson [3] and Vu et al [7].…”

“…Consider the linearization of the governing equation for the Michaelis–Menten reaction mechanism (1) at the stationary point 0 Looking at this linearization is justified since Vu et al [7] are interested in small substrate concentrations only 2 . The eigenvalues of the matrix in (9) are with λ 1 of smaller absolute value.…”

Biomarkers Come of Age in Clinical Pharmacology

“…One final paper reminds us that in addition to refining and expanding the use of biomarkers for clinical DDIs, in vitro predictions also need to be continuously refined. In their paper entitled “Beyond the Michaelis–Menten: Accurate Prediction of Drug Interactions through Cytochrome P450 3A4 Induction,” Vu et al 12 . point out that the FDA has established guidelines for DDIs mediated by induction of cytochrome P450 enzymes (CYPs).…”

“…One final paper reminds us that in addition to refining and expanding the use of biomarkers for clinical DDIs, in vitro predictions also need to be continuously refined. In their paper entitled "Beyond the Michaelis-Menten: Accurate Prediction of Drug Interactions through Cytochrome P450 3A4 Induction, " Vu et al 12 point out that the FDA has established guidelines for DDIs mediated by induction of cytochrome P450 enzymes (CYPs). Challenging the assumptions of the FDA guidelines and refining equations, Vu et al provide new equations that more accurately predict the effects of CYP inducers especially for drugs that have high affinities for CYPs.…”