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. 2017 Feb;44(1):17-26.
doi: 10.1007/s10928-016-9501-1. Epub 2017 Jan 10.

Target-mediated Drug Disposition With Drug-Drug Interaction, Part I: Single Drug Case in Alternative Formulations

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Free PMC article

Target-mediated Drug Disposition With Drug-Drug Interaction, Part I: Single Drug Case in Alternative Formulations

Gilbert Koch et al. J Pharmacokinet Pharmacodyn. .
Free PMC article

Abstract

Target-mediated drug disposition (TMDD) describes drug binding with high affinity to a target such as a receptor. In application TMDD models are often over-parameterized and quasi-equilibrium (QE) or quasi-steady state (QSS) approximations are essential to reduce the number of parameters. However, implementation of such approximations becomes difficult for TMDD models with drug-drug interaction (DDI) mechanisms. Hence, alternative but equivalent formulations are necessary for QE or QSS approximations. To introduce and develop such formulations, the single drug case is reanalyzed. This work opens the route for straightforward implementation of QE or QSS approximations of DDI TMDD models. The manuscript is the first part to introduce DDI TMDD models with QE or QSS approximations.

Keywords: Competitive; Drug–drug interaction; Target-mediated drug disposition; Uncompetitive.

Figures

Fig. 1
Fig. 1
Scheme of the necessary steps to construct a QE or QSS approximation of a TMDD system. The three systems in step 4 are equivalent
Fig. 2
Fig. 2
Schematic of the single TMDD model described by Eqs. (1–3)
Fig. 3
Fig. 3
Free concentration C(t) from the original TMDD model Eqs. (1–7) (dashed line) and the QE or QSS approximation Eqs. (46–50) (solid line) is shown. In panel a the QE and in panel b the QSS approximation without baseline for escalating doses (dose = 10, 100 and 1000) are presented. In panel c (QE) and in panel d (QSS) behavior for different baselines (C0 = 0.01, 0.1, 1 and 10) with a fixed dose (dose = 100) are visualized. In panels e (QE) and f (QSS) the effect for increasing kon = 2.5 and koff = 0.1 (by multiplying the factors 0.1, 1, 10 to both parameters with equal ratio KD for QE) for a fixed dose (dose = 100) and baseline (C0 = 1) are presented. In panel e (QE) the original system converges to the QE approximation and in panel f (QSS) the original systems and its QSS approximations converge for increasing kon and koff values
Fig. 4
Fig. 4
Free concentration versus time data (crosses) produced with the original model Eqs. (1–7) and fitted with the QE approximation Eqs. (46–50) (solid line)

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