On the structural identifiability of nonlinear models of ligand binding dynamics

Abstract

Quantification of drug-cell interactions and subsequent cellular responses by using experimental data together with mathematical models of assumed binding and signalling schematics is vital to many research programmes; data fitting provides estimates for important pharmacological parameters including kinetic parameters controlling drug affinity and efficacy. Ordinary differential equation (ODE) models are a key component of many receptor theory studies used for this purpose. In using ODE simulations to fit experimental data and estimate these parameters, the theory of the identifiability properties of the system is often overlooked. Indeed, structural identifiability analysis (SIA) is often overlooked in many fields of bio-modelling. Building on recent SIA for linear ligand binding models in receptor theory, we present a new analysis of identifiability properties of nonlinear receptor theory models. We include models of ligand depletion in binding assays and ligand-induced dimerisation (LID). The classical SIA approaches of Taylor Series and similarity transformation are applied, using detailed step-by-step calculations to illustrate the complexity of the implementations. New results are obtained which show that the nonlinear ligand-depletion counterpart models of non-identifiable linear ligand excess models are globally identifiable from a single timecourse. Also, the LID model is shown to be globally identifiable if an experimental aparatus-dependent parameter is obtained. The analysis highlights issues of tractability of the methods for similar and higher-dimensional nonlinear models in receptor theory.