Dynamics of target-mediated drug disposition

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.