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Roles of Fc Receptors in Disease and Therapy

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Front. Immunol. | doi: 10.3389/fimmu.2019.00674

Parameter identification for a model of neonatal Fc receptor-mediated recycling of endogenous immunoglobulin G in humans

 Felicity Kendrick1,  Neil D. Evans1, Oscar Berlanga2, Stephen J. Harding2 and  Michael J. Chappell1*
  • 1University of Warwick, United Kingdom
  • 2The Binding Site Ltd, United Kingdom

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 parameterised model of FcRn-mediated recycling of endogenous IgG to allow for predictive modelling, with the potential for optimising 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 radiolabelled 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, linearisation and reparameterisation -- can be used to ensure robust parameter identification.

Keywords: biological systems, Lumped-parameter systems, Immunoglobulin G, neonatal Fc receptor, parameter estimation, Structural identifiability analysis

Received: 10 Sep 2018; Accepted: 12 Mar 2019.

Edited by:

Latha P. Ganesan, Wexner Medical Center, The Ohio State University, United States

Reviewed by:

William C. Stewart, The Research Institute at Nationwide Children's Hospital, United States
Jayajit Das, The Ohio State University, United States  

Copyright: © 2019 Kendrick, Evans, Berlanga, Harding and Chappell. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Prof. Michael J. Chappell, University of Warwick, Coventry, United Kingdom,