On the coupling between a basic FcRn mechanism and target-mediated drug disposition of antibodies—an asymptotic analysis in the high binding affinity limit
Csaba Katai1
1PD-value B.V.
Introduction Antibody pharmacokinetics (PK) is typically governed by two key mechanisms: non-specific endosomal clearance modulated by neonatal Fc receptors (FcRn) and target-mediated drug disposition (TMDD). Usually the former is incorporated in a similar manner in many of the physiology-based pharmacokinetic (PBPK) models presented in the literature; see e.g. Willmann et al. (2003); Garg and Balthasar (2007); Shah and Betts (2012); Niederalt et al. (2018). On the other hand, TMDD is incorporated in PBPK models to address the effects of "high-affinity--low-capacity" binding sites on antibody PK and thereby account for target-mediated (specific) clearance. While the two mechanisms have been studied thoroughly and independently through minimal models, e.g. by Peletier and Gabrielsson (2012) and Kristiansen (2019), and by Katai et al. (2024), respectively, their coupling and interaction remains to be explored to that level of detail. The combination of the two mechanisms presents an opportunity to implement the classic TMDD compartmental setup in the FcRn framework and examine it on a consistent basis. The corresponding analysis may also aid in interpreting TMDD in a whole-body PBPK setting. One of the simplest combined models can be constructed by including target receptors in the plasma space of the basic FcRn model explored in Katai et al. (2024). An important aspect to consider is the magnitudes of the parameters involved. If there is a significant time scale gap between the two clearance processes, one or the other will dominate antibody clearance. Hence, the most relevant parameter regimes are likely those that result in both clearance mechanisms coming into play over the same time scale. Objectives - Develop a combined FcRn--TMDD model and examine its behaviour in various relevant parameter regimes. - Develop an asymptotic framework in the high binding affinity limit to describe the characteristic phases of the combined model. - Derive relevant pharmacometric expressions for the problems, and thereby obtain a deeper understanding of the dynamics governing an FcRn--TMDD system. Methods The equations governing the combined FcRn--TMDD model are first nondimensionalised, then the magnitudes of the emerging dimensionless groups are assessed based on their values reported in the literature. Relevant parameter regimes are identified for which both the non-specific and the specific clearances become important over the same time scale. The characteristic phases of the problems are analysed systematically using the method of matched asymptotic expansions. Results The analysis identifies two parameter regimes of interest. For the first, the baseline target receptor concentration is `low’, but it is combined with a `high’ drug-receptor complex elimination rate constant. In the second the settings are reversed: the baseline receptor concentration is instead `high’ and the corresponding elimination rate constant is `low’. In each case a characteristic phase emerges during which both the non-specific and the specific clearance contributions are on an equal footing. Analytic expressions are obtained, similar to that in Peletier and Gabrielsson (2012), that signify the end of such characteristic phases and that are good approximations of an inflection time point in the logarithmic free-drug concentration versus time curve. The drug concentration at this inflection point is shown to depend on dose, contrary to previous belief, and it is also shown to be the case for the classic TMDD system in Peletier and Gabrielsson (2012). Furthermore, it is shown that the free-drug concentration at this inflection point is approximately proportional to v(R0*KD*kout/kelim) when the time point of inflection is sufficiently large and where R0, KD, kout and kelim are the baseline receptor concentration, the usual binding equilibrium constant, the turnover rate constant and the rate constant associated with the drug-target complex elimination, respectively. Accurate approximations for the receptor occupancy are also derived. Conclusions The results show that the systematic analysis provides a clear understanding of the combined FcRn--TMDD mechanism for the two parameter regimes considered. It also provides some insight on when and under which circumstances one may identify the participating parameters.
A. Garg and J. P. Balthasar. Physiologically-based pharmacokinetic (PBPK) model to predict IgG tissue kinetics in wild-type and FcRn-knockout mice. J. Pharmacokinet. Pharmacodyn., 34:687–709, 2007. C. B. Ka´tai, S. J. Smithline, C. J. Thalhauser, S. Bosgra, and J. Elassaiss-Schaap. An asymptotic description of a basic FcRn-regulated clearance mechanism and its implications for PBPK modelling of large antibodies. J. Pharmacokinet. Pharmacodyn., pages 1–25, 2024. K. U. Kristiansen. Geometric singular perturbation analysis of a dynamical target mediated drug disposition model. J. Math. Biol., 79(1):187–222, 2019. C. Niederalt, L. Kuepfer, J. Solodenko, T. Eissing, H.-U. Siegmund, M. Block, S. Willmann, and J. Lippert. A generic whole body physiologically based pharmacokinetic model for therapeutic proteins in PK-Sim. J. Pharmacokinet. Pharmacodyn., 45:235–257, 2018. L. A. Peletier and J. Gabrielsson. Dynamics of target-mediated drug disposition: characteristic profiles and parameter identification. J. Pharmacokinet. Pharmacodyn., 39(5): 429–451, 2012. D. K. Shah and A. M. Betts. Towards a platform PBPK model to characterize the plasma and tissue disposition of monoclonal antibodies in preclinical species and human. J. Pharmacokinet. Pharmacodyn., 39(1):67–86, 2012. S. Willmann, J. Lippert, M. Sevestre, J. Solodenko, F. Fois, and W. Schmitt. PK-Sim®: a physiologically based pharmacokinetic ‘whole-body’model. Biosilico, 1(4):121–124, 2003.