An asymptotic description of a basic FcRn-regulated clearance mechanism and its implications for PBPK modelling of large antibodies
Csaba Katai (1), Shepard J. Smithline (2), Jeroen Elassaiss-Schaap (1), Craig J. Thalhauser (2), Sieto Bosgra (3)
PD-value B.V. (1), Genmab US, Inc. (2), Genmab B.V. (3)
Introduction: Physiology-based pharmacokinetic (PBPK) models are being increasingly utilised in pharmacometrics to understand the whole-body disposition of various drugs. They are frequently employed to model large-antibody drugs, whose long half lives are usually attributed to Neonatal Fc Receptors (FcRn), which save antibodies from degradation in the endosomal space of endothelial cells. Mechanistic PBPK models incorporating FcRn salvage have been proposed and successfully implemented in the literature [1, 2]. However, due to the large size and complexity of these systems, a deeper understanding of the mechanism has remained elusive. To address this lack of understanding a simple PBPK model was studied by Patsatzis et al. (2022) [3]--although for an unusually high dose--through the lens of a computational singular perturbation analysis. In contrast, to understand the behaviour of the system at "lower" doses, which are more applicable in practice, an asymptotic analysis in the high FcRn-binding affinity limit was performed and the corresponding results were presented at PAGE2023. The present work, which has been submitted to the Journal of PKPD and is currently under peer review [4], builds on this previous work by appropriately analysing the solution structures of the basic FcRn system for all doses. The asymptotic techniques employed enjoy widespread use in fluid mechanics [5] and physics [6], but are being increasingly applied in the biomedical sciences as well--see for example the analysis of the classic target mediated drug disposition model by Peletier and Gabrielsson (2012) [7]. Hence, the exhibition of these techniques may benefit the wider pharmacometrics community.
Objectives:
- Obtain a deeper understanding of the problem through scaling relations, estimates, and reduced models valid over each characteristic time scale along with their appropriate "initial conditions".
- Shine light on the functional dependence of the model parameters on FcRn-mediated clearance and the AUC.
Methods: The equations governing the basic FcRn mechanism are first nondimensionalised, then the magnitudes of the emerging nondimensional groups are assessed based on physiological parameter values from the literature. The method of matched asymptotic expansions is employed to systematically deduce reduced models valid over each characteristic time scale.
Results: The analysis identifies three dosing regimes--low, intermediate and high doses--that correspond to the case for which FcRn is not saturated, for which it is "exactly" saturated, and for which it is "over" saturated, respectively. For low doses the antibody level in the endosomes remains low, whereas for high doses a non-negligible antibody level may build up there. It is shown that "excess" antibodies are eliminated at a rate much faster than that associated with the terminal phase.
If the clearance CL is defined through
Vp dCp/dt = - CL * Cp ,
with Vp and Cp being the plasma volume and concentration of antibodies in the plasma, respectively, then it is shown that the expression for clearance takes the form,
CL ~ s * Vp * Ve/(Vp + s * Ve) * kdeg/(kon * [FcRn]0) * (CLup/Ve + koff) * [FcRn]0 / ([FcRn]0 - Cp),
which is valid over the "longest" characteristic time scale. Here Ve is the volume of the endosomal space, the parameters kdeg, kon, koff, and CLup are the rate constants associated with endosomal degradation, antibody-FcRn association and dissociation, and pinocytosis, respectively, while [FcRn]0 is the initial FcRn concentration and s is the pinocytic uptake modulator, akin to Spino in [8]. Corresponding expressions for the AUC for all dose levels are also obtained. For typical doses used in practice an expression resembling the well-known pharmacometric relationship CL = Dose/AUC is derived, whereas for high doses the AUC is approximately dose-independent. The theoretical results on clearance are qualitatively supported using an in-house whole-body PBPK model, providing important implications for future PBPK modelling efforts.
Conclusions: The results show that such a systematic analysis provides an accurate and clear understanding of the basic FcRn mechanism for all doses. It also provides insight into some of the potential challenges of parameter identifiability in PBPK modelling.
References:
[1] D. G. Patsatzis, S. Wu, D. K. Shah, and D. A. Goussis. Algorithmic multiscale analysis for the FcRn mediated regulation of antibody PK in human. Sci. Rep., 12(1):1–21, 2022.
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[3] 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.
[4] C. B. Kátai, 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. (Accepted for publication) J. Pharmacokinet. Pharmacodyn., 2024.
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