Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis

Abstract

Receptor mediated endocytosis (RME) plays a major role in the disposition of therapeutic protein drugs in the body. It is suspected to be a major source of nonlinear pharmacokinetic behavior observed in clinical pharmacokinetic data. So far, mostly empirical or semi-mechanistic approaches have been used to represent RME. A thorough understanding of the impact of the properties of the drug and of the receptor system on the resulting nonlinear disposition is still missing, as is how to best represent RME in pharmacokinetic models. In this article, we present a detailed mechanistic model of RME that explicitly takes into account receptor binding and trafficking inside the cell and that is used to derive reduced models of RME which retain a mechanistic interpretation. We find that RME can be described by an extended Michaelis-Menten model that accounts for both the distribution and the elimination aspect of RME. If the amount of drug in the receptor system is negligible a standard Michaelis-Menten model is capable of describing the elimination by RME. Notably, a receptor system can efficiently eliminate drug from the extracellular space even if the total number of receptors is small. We find that drug elimination by RME can result in substantial nonlinear pharmacokinetics. The extent of nonlinearity is higher for drug/receptor systems with higher receptor availability at the membrane, or faster internalization and degradation of extracellular drug. Our approach is exemplified for the epidermal growth factor receptor system.

Fig. 1

Schematic representation of the detailed model of receptor mediated endocytosis. See text for description

Fig. 2

Models of receptor mediated endocytosis of different resolution: Detailed model (Model A), reduced model of saturable distribution into the receptor system with linear degradation (Model B), and reduced model of saturable degradation (Model C). See text for details

Fig. 3

Two two-compartment models with linear clearance from the central compartment and RME based on Model B (left) and Model C (right) in the peripheral compartment

Fig. 4

Concentration-time profile of the extracellular ligand concentration for the Model A (circles on blue solid line), Model B (squares on blue dashed line) and Model C (diamonds on red dashed line). Left: Parameter values used according to Table 2. Right: As in left figure, but decreasing k_degRL 10-fold

Fig. 5

Evolution of the ratio B_max/(K_M + C_ex) for the two scenarios shown in Fig. 4 left (solid line) and right (dashed line)

Fig. 6

Illustration of the dependence of RME on the rate of internalization using the detailed model of RME (Model A). Parameter values according to Table 2. Left: concentration-time profiles of the extracellular ligand EGF (L_ex) for three different internalization rate constants of the ligand–receptor complex: k_interRL (solid line), k_interRL/4 (dashed line), k_interRL/16 (dotted line). Right: same as before, but with decreased association and dissociation rate constants: k_on/100 and k_off/100, respectively. Note that K_D is identical in the left and right graphics

Fig. 7

Comparison of model predictions for zalutumumab (2F8) based on the Lammerts van Bueren et al. model (circles on solid line) and the herein proposed compartment models (20)–(23) (squares on solid line) and (24)-(25) (diamonds on dotted line). Left: parameterization as given in Table 3. Right: maximal receptor capacity B_max decreased to one 20th of the original capacity