Classical structural identifiability methodology applied to low-dimensional dynamic systems in receptor theory

Journal of Pharmacokinetics and Pharmacodynamics, vol. 51, pp. 39–63

Abstract

Mathematical modelling has become a key tool in pharmacological analysis, towards understanding dynamics of cell signalling and quantifying ligand-receptor interactions. Ordinary differential equation (ODE) models in receptor theory may be used to parameterise such interactions using timecourse data, but attention needs to be paid to the theoretical identifiability of the parameters of interest. Identifiability analysis is an often overlooked step in many bio-modelling works. In this paper we introduce structural identifiability analysis (SIA) to the field of receptor theory by applying three classical SIA methods (transfer function, Taylor Series and similarity transformation) to ligand-receptor binding models of biological importance (single ligand and Motulsky-Mahan competition binding at monomers, and a recently presented model of a single ligand binding at receptor dimers). New results are obtained which indicate the identifiable parameters for a single timecourse for Motulsky-Mahan binding and dimerised receptor binding. Importantly, we further consider combinations of experiments which may be performed to overcome issues of non-identifiability, to ensure the practical applicability of the work. The three SIA methods are demonstrated through a tutorial-style approach, using detailed calculations, which show the methods to be tractable for the low-dimensional ODE models.

Authors 3

1. Carla White corresponding

   Swansea University

   Affiliation as printed

   Swansea University, Swansea, UK

2. Vivi Rottschäfer corresponding Aachen

   Leiden University · University of Amsterdam

   Affiliation as printed

   Leiden University, Leiden, The Netherlands

   University of Amsterdam, Amsterdam, The Netherlands

3. Lloyd Bridge corresponding

   University of the West of England

   Affiliation as printed

   University of the West of England, Bristol, UK. lloyd.bridge@uwe.ac.uk

   University of the West of England, Bristol, UK