Dose Correction for the Michaelis-Menten Approximation of the Target – mediated Drug Disposition Model

Objectives: The target-mediated drug disposition (TMDD) pharmacokinetic (PK) model applies to drugs exhibiting a clearance mechanism due to binding to their targets followed by internalization and degradation [1]. The Michaelis-Menten (M-M) the TMDD PK model was derived based on the rapid binding or quasi steady-state assumptions that implied that the target and drug binding and dissociation were in equilibrium [2-3]. However, the initial dose for an IV bolus injection for the M-M model did not account for a fraction bound to the target. We postulated a correction to an initial condition that was consistent with the assumptions underlying the M-M approximation. Additionally, we determined conditions under which the correction of the initial dose affects the M-M model parameter identifiability and the parameter estimates.

Methods: We used the model algebraic equations for free drug concentration C to calculate the initial condition C(0) that is different from Dose/V used for an IV bolus injection. To demonstrate the influence of initial condition on the M-M approximation of TMDD model, M-M approximations with different initials were simulated and compared with the TMDD profile. Model parameter values were adopted from the PK/PD model of romiplostim, a TPO mimetic peptibody exhibiting TMDD pharmacokinetics [4]. We also performed a simulation exercise to check if the correction will impact the model performance and the bias of the M-M parameter estimates. The simulated data were refitted by both models. Parameter estimates were compared to ones used for simulations for assessment of bias and precision.

Results:  We determined that the difference between the injected dose and one that should be used for the initial condition is equal to the amount of drug bound to the target upon reaching the equilibrium. We also observed that the corrected initial condition made the internalization rate constant kint an identifiable parameter that was not for the original M-M model. All the parameters estimated from the original M-M model were substantially biased. On the other hand, the corrected M-M is able to accurately estimate these parameters except for equilibrium constant Km. The Akaike Information Criterion suggested better performance of the corrected M-M model compared with the original M-M model. We provided examples from the literature of the uncorrected M-M model applied to population PK analysis of therapeutic protein plasma concentrations in humans where the correction seemed to be necessary [5].

Conclusions: We postulated a correction to an initial condition for the M-M approximation of the TMDD PK model with an IV bolus input that was consistent with the assumptions underlying this approximation. We demonstrated that omission of this correction might lead to a bias in the parameter estimates. Further studies are necessary to determine the importance of this correction for the M-M model applications to analysis of TMDD driven PK data.

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[4] Wang Y-MC, Krzyzanski W, Doshi S, Xiao JJ, Perez-Ruixo JJ, Chow AT (2010) Pharmacodynamics-mediated drug disposition (PDMDD) and precursor lifespan model for single dose of romiplostim in healthy subjects. AAPS J 12:729-740.
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