Beyond the Michaelis‐Menten: Accurate Prediction of In Vivo Hepatic Clearance for Drugs With Low KM

Back, Hyun-moon; Yun, Hwi-yeol; Kim, Sang Kyum; Kim, Jae Kyoung

doi:10.1111/cts.12804

Cited by 13 publications

(28 citation statements)

References 40 publications

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“…7) predicts that the metabolic rate also increases by

E_{ind}

‐fold. This prediction makes sense when the enzyme concentration after the induction is still much lower than

K_{m}

(i.e.,

E_{ind} E_{T} ≪ K_{m} false)

12,13,15 . However, when the enzyme concentration is not sufficiently low, such

E_{ind}

‐fold increase in the metabolic rate is certainly an overestimation.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, as

E_{ind}

becomes infinite, the MM model predicts an infinite‐fold change in the metabolic rate, which is unrealistic, but the new model predicts an

\frac{E_{T} + K_{m}}{E_{normalT}}

‐fold change (i.e., saturation). The new model can accurately capture the metabolic rate of a drug regardless of the ratio between

E_{T}

and

K_{m}

, unlike the MM model 12 . By using the new model, we derived a new equation for predicting AUCR, where

E_{ind}

is replaced by

E_{ind} \frac{E_{T} + K_{m}}{E_{ind} E_{T} + K_{m}}

in the FDA equation (Eq.…”

Section: Resultsmentioning

confidence: 99%

“…7) is accurate only when the enzyme concentration is small enough (i.e.,

E_{T} ≪ K_{m} + S \approx K_{m}

) 13–15 . To overcome such a limitation, an alternative model has been derived recently 12 using the total quasi‐steady‐state approximation 13 :

\frac{dP}{normald t} goodbreak= \frac{k_{cat} E_{T} S_{T}}{E_{T} + S_{T} + K_{m}} \approx \frac{k_{cat} E_{T} S_{T}}{E_{T} + K_{m}} goodbreak= {\overset{true~}{CL}}_{int} S_{T},

where

S_{T}

is the total substrate concentration regardless of its form and

{\overset{true~}{CL}}_{int} = \frac{k_{cat} E_{T}}{E_{T} + K_{m}}

is the modified intrinsic clearance. Note that the denominator of

{\overset{true~}{CL}}_{int}

contains

E_{T}

, unlike

normalC L_{int}

derived based on the MM model.…”

Section: Methodsmentioning

confidence: 99%

“…concentration after the induction is still much lower than K m (i.e., E ind E T ≪ K m ). 12,13,15 However, when the enzyme concentration is not sufficiently low, such E ind -fold increase in the metabolic rate is certainly an overestimation. For instance, when rifampicin increased CYP3A4 expression in primary human hepatocytes by ~20-fold, the metabolic clearances of midazolam and cyclosporine increased by only ~1.5-fold rather than ~20fold in humans administered with rifampicin.…”

Section: Articlementioning

confidence: 99%

“…Importantly, the FDA equation itself has limitations because it is based on the Michaelis-Menten (MM) model (see Supplementary Information for the details). 12,13 Specifically, the MM model is valid only when the MM constant (K m ) value of a substrate is sufficiently higher (~ 10-fold) than the concentration of the enzymes so that the enzyme-substrate complex concentration is negligible compared with the substrate concentration. [13][14][15] This condition does not hold for many drugs with low K m , and thus the MM model fails to accurately predict their in vivo clearances.…”

mentioning

confidence: 99%

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

Tran

Yun

et al. 2023

Clin Pharma and Therapeutics

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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).

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“…7) predicts that the metabolic rate also increases by

E_{ind}

‐fold. This prediction makes sense when the enzyme concentration after the induction is still much lower than

K_{m}

(i.e.,

E_{ind} E_{T} ≪ K_{m} false)

12,13,15 . However, when the enzyme concentration is not sufficiently low, such

E_{ind}

‐fold increase in the metabolic rate is certainly an overestimation.…”

Section: Resultsmentioning

confidence: 99%

“…In particular, as

E_{ind}

becomes infinite, the MM model predicts an infinite‐fold change in the metabolic rate, which is unrealistic, but the new model predicts an

\frac{E_{T} + K_{m}}{E_{normalT}}

‐fold change (i.e., saturation). The new model can accurately capture the metabolic rate of a drug regardless of the ratio between

E_{T}

and

K_{m}

, unlike the MM model 12 . By using the new model, we derived a new equation for predicting AUCR, where

E_{ind}

is replaced by

E_{ind} \frac{E_{T} + K_{m}}{E_{ind} E_{T} + K_{m}}

in the FDA equation (Eq.…”

Section: Resultsmentioning

confidence: 99%

“…7) is accurate only when the enzyme concentration is small enough (i.e.,

E_{T} ≪ K_{m} + S \approx K_{m}

) 13–15 . To overcome such a limitation, an alternative model has been derived recently 12 using the total quasi‐steady‐state approximation 13 :

\frac{dP}{normald t} goodbreak= \frac{k_{cat} E_{T} S_{T}}{E_{T} + S_{T} + K_{m}} \approx \frac{k_{cat} E_{T} S_{T}}{E_{T} + K_{m}} goodbreak= {\overset{true~}{CL}}_{int} S_{T},

where

S_{T}

is the total substrate concentration regardless of its form and

{\overset{true~}{CL}}_{int} = \frac{k_{cat} E_{T}}{E_{T} + K_{m}}

is the modified intrinsic clearance. Note that the denominator of

{\overset{true~}{CL}}_{int}

contains

E_{T}

, unlike

normalC L_{int}

derived based on the MM model.…”

Section: Methodsmentioning

confidence: 99%

Section: Articlementioning

confidence: 99%

mentioning

confidence: 99%

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

Tran

Yun

et al. 2023

Clin Pharma and Therapeutics

Self Cite

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Explicit Treatment of Non‐Michaelis‐Menten and Atypical Kinetics in Early Drug Discovery**

Srinivasan

2020

ChemMedChem

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Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more‐complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post‐translationally modified proteins), the initial axioms defined by Michaelis‐Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug‐discovery for such systems, to enable effective screening and characterisation of small‐molecule inhibitors with desirable physiological outcomes.

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The Michaelis–Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation

Eilertsen,

Schnell,

Walcher

2024

Bull Math Biol

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We demonstrate that the Michaelis–Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke’s comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation is $$s_0 \ll K$$ s 0 ≪ K , where $$K=k_2/k_1$$ K = k 2 / k 1 is the Van Slyke–Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.

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Beyond the Michaelis‐Menten: Accurate Prediction of In Vivo Hepatic Clearance for Drugs With Low K_M

Cited by 13 publications

References 40 publications

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

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

Explicit Treatment of Non‐Michaelis‐Menten and Atypical Kinetics in Early Drug Discovery**

The Michaelis–Menten Reaction at Low Substrate Concentrations: Pseudo-First-Order Kinetics and Conditions for Timescale Separation

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