On the coupling between a basic FcRn mechanism and target-mediated disposition of antibodies.

Understanding the pharmacokinetics of therapeutic antibodies often requires a detailed investigation of the mechanisms governing their distribution and clearance. Two of the most important mechanisms are the salvage and recycling of antibodies by the neonatal Fc receptor (FcRn), and target-mediated drug disposition (TMDD). While the two mechanisms have been analysed individually in detail, their combination and coupling is yet to be addressed. An important point of consideration is the characteristic time scales pertaining to the processes in each mechanism and how they can be related and thus integrated into a single framework. To this end a minimal 'physiology-based' pharmacokinetic model incorporating specific (TMDD) and non-specific (FcRn) antibody elimination is investigated in the high binding-affinity limit using the method of matched asymptotic expansions. The theory builds on previous asymptotic frameworks corresponding to each mechanism individually. The combined FcRn-TMDD model consists of a plasma space and an endosomal space, with target binding occurring in the former and antibody salvage in the latter. Two parameter regimes are studied in particular, that correspond to cases wherein both the specific and the non-specific clearance mechanisms provide comparable contributions to the total antibody clearance over the same time scale. The analysis offers insight into the processes dominating antibody pharmacokinetics during each characteristic phase of the problem. In addition to the accurate analytical description of the kinetics, relevant pharmacometric expressions are also derived, such as the approximate time and concentration when the target receptors are no longer 'fully' saturated, AUC and the terminal slope. The resulting insight on the dominant processes and model parameters in the specific characteristic phases may be utilised to guide parameter estimation in future modelling efforts. Additionally, the presented theory can be used to assess the validity of various quasi-equilibrium, quasi-steady and Michaelis-Menten type assumptions in each phase. In short, the presented theory can provide guidance for physiology-based pharmacokinetic as well as standard pharmacokinetic modelling efforts.