Parameter Identification for a Model of Neonatal Fc Receptor-Mediated Recycling of Endogenous Immunoglobulin G in Humans

Abstract

Salvage of endogenous immunoglobulin G (IgG) by the neonatal Fc receptor (FcRn) is implicated in many clinical areas, including therapeutic monoclonal antibody kinetics, patient monitoring in IgG multiple myeloma, and antibody-mediated transplant rejection. There is a clear clinical need for a fully parameterized model of FcRn-mediated recycling of endogenous IgG to allow for predictive modeling, with the potential for optimizing therapeutic regimens for better patient outcomes. In this paper we study a mechanism-based model incorporating nonlinear FcRn-IgG binding kinetics. The aim of this study is to determine whether parameter values can be estimated using the limited in vivo human data, available in the literature, from studies of the kinetics of radiolabeled IgG in humans. We derive mathematical descriptions of the experimental observations—timecourse data and fractional catabolic rate (FCR) data—based on the underlying physiological model. Structural identifiability analyses are performed to determine which, if any, of the parameters are unique with respect to the observations. Structurally identifiable parameters are then estimated from the data. It is found that parameter values estimated from timecourse data are not robust, suggesting that the model complexity is not supported by the available data. Based upon the structural identifiability analyses, a new expression for the FCR is derived. This expression is fitted to the FCR data to estimate unknown parameter values. Using these parameter estimates, the plasma IgG response is simulated under clinical conditions. Finally a suggestion is made for a reduced-order model based upon the newly derived expression for the FCR. The reduced-order model is used to predict the plasma IgG response, which is compared with the original four-compartment model, showing good agreement. This paper shows how techniques for compartmental model analysis—structural identifiability analysis, linearization, and reparameterization—can be used to ensure robust parameter identification.

Quantitative systems pharmacology modeling of macrophage‐targeted therapy combined with PD‐L1 inhibition in advanced NSCLC

“…Based on the initial estimates, including experimentally measured rates of FcRn‐mediated recycling (internalization, degradation, and recycling), 27 PK parameters were either fixed or further fitted to the mean ALX‐148 concentration and CD47 occupancy measured in the phase I clinical trial. 33 Seven parameters were fitted to PK data (population mean) on four dose levels simultaneously.…”

“…In addition, the population PK analyses of ALX‐148 showed that ALX‐148 exhibited nonlinear clearance and interacted with neonatal Fc receptors (FcRn) without triggering Fc‐gamma receptor (FcγR)‐mediated effector activity 25 . Therefore, target‐mediated drug disposition (TMDD) 26 via binding with CD47 on red blood cells (RBCs) in the central compartment, and neonatal Fc receptor‐mediated recycling 27 were incorporated into the PK module for ALX‐148. Equations 1–10 describe the dynamics of ALX‐148 (i.e., $$$ \left[\mathrm{aCD}47\right] $$$), CD47, and FcRn.…”

“…4 Figure 1c shows the best overall tumor size change in all virtual patients during anti-PD-L1 monotherapy and combination therapy with ALX-148. Overall, 163 patients showed improved tumor size reduction when ALX-148 k off,FcRn-aCD47 0.03 1/min Rate of dissociation between FcRn and ALX-148 (IgG1 Fc) (fixed) 45 k off,CD47-aCD47 1.1e-3 1/min Rate of dissociation between CD47 and ALX-148 (fitted) k on,FcRn-aCD47 3e-5 1/min/nM Rate of association between FcRn and ALX-148 (IgG1 Fc) (calculated by experimentally reported k off and affinity) 29,45 k on,CD47-aCD47 5.5e-4 1/min/nM Rate of association between CD47 and ALX-148 (calculated by the fitted k off and measured binding affinity) 25 (see Section 2) χ aCD47 100 Dimensionless Strength of cross-arm binding (fixed assuming a weak cross-arm binding) 28 V C 5 L Volume of the central compartment (fixed) 27 V P 60 L Volume of the peripheral compartment (fixed) 27 V T Varying mL Volume of the tumor compartment (varying over time) 15 V LN 1.4 mL Volume of lumped tumor-draining lymph node compartment (fixed) 27 V endo 340 mL Volume of endosomal compartment (fixed) 27 was combined with PD-L1 inhibition, 13 of which showed complete response. These patients had significantly higher levels of M1-type TAMs and M1/M2 ratio than others, which suggests this combination treatment is suitable for patients with high level of pro-inflammatory macrophages (Figure S3).…”

Modelling acute antibody-mediated rejection of human kidney transplants using ex-vivo warm machine perfusion

“…More enhanced induction and maintenance immunosuppression is also used and future protocols may utilise novel therapies such as Imlifidase 15 , 16 or neonatal FcR inhibition. 17 If desensitisation is successful and transplantation proceeds, recipients still may have an increased risk of severe post-operative AMR (which could be as early as within 14 days post transplantation), bleeding and mortality. 18 , 19 , 20 , 21 …”

Assessment of the parameter identifiability of population balance models for air jet mills

“…Being a data driven approach, the profile likelihood based method has the advantage of not imposing any restrictions on the algebraic form of the model (Raue et al, 2014). Due to this, the profile likelihood approach has been widely used in systems biology (Gross & Blüthgen, 2020;Lee et al;Coulibaly et al, 2019;Kendrick et al, 2019) wherein the large biological networks lead to complex mathematical models which cannot be assessed via analytical methods. Recently, this approach has seen use in studying identifiability of large scale or complex models for (bio)chemical processes like a lithium-ion battery (Zhou et al, 2020), and the fluidized bed agglomeration process (Golovin et al, 2018).…”