Mathematical Institute, Leiden University, PB 9512, 2300 RA Leiden, The Netherlands.
Eur J Pharm Sci. 2009 Dec 8;38(5):445-64. doi: 10.1016/j.ejps.2009.09.007. Epub 2009 Sep 26.
We present a mathematical analysis of the basic model underlying target-mediated drug disposition (TMDD) in which a ligand is supplied through an initial bolus or through a constant rate infusion and forms a complex with a receptor (target), which is supplied and removed continuously. Ligand and complex may be eliminated according to first-order processes. We assume that the total receptor pool (free and bound) is constant in time and we give a geometrical description of the evolution of the concentrations of ligand, receptor and receptor-ligand complex which offers a transparent way to compare the full model with simpler models such as the quasi-steady-state (QSS) model, the quasi-equilibrium (QE) model and the empirical Michaelis-Menten (MM) model; we also give precise conditions on the parameters in the TMDD model for the validity of these reduced models. We relate characteristic properties of time courses to parameter regimes and, in particular, we identify and explain non-monotone dependence of the time-to-steady-state on the infusion rate. Finally, we discuss how the volume of the central compartment may be overestimated because of singular initial behaviour of the time course of the ligand concentration.
我们提出了一个数学分析，用于研究靶介导药物处置（TMDD）的基本模型，其中配体通过初始推注或恒速输注供应，并与受体（靶标）形成复合物，受体持续供应和去除。配体和复合物可根据一级过程消除。我们假设总受体池（游离和结合）在时间上是恒定的，并且给出了配体、受体和受体-配体复合物浓度的演化的几何描述，这为将完整模型与更简单的模型（如准稳态（QSS）模型、准平衡（QE）模型和经验米氏-门限（MM）模型）进行比较提供了一种透明的方法；我们还给出了 TMDD 模型中参数的精确条件，以验证这些简化模型的有效性。我们将时间过程的特征性质与参数范围联系起来，特别是，我们确定并解释了到达稳态时间对输注速率的非单调依赖性。最后，我们讨论了由于配体浓度时间过程的奇异初始行为，中央隔室的体积可能会被高估的问题。
