The input-output relationship approach to structural identifiability analysis

Analysis of the identifiability of a given model system is an essential prerequisite to the determination of model parameters from physical data. However, the tools available for the analysis of non-linear systems can be limited both in applicability and by computational intractability for any but the simplest of models. The input-output relation of a model summarises the input-output structure of the whole system and as such provides the potential for an alternative approach to this analysis. In order for this approach to be valid it is necessary to determine whether the monomials of a differential polynomial are linearly independent. A simple test for this property is presented in this work. The derivation and analysis of this relation can be implemented symbolically within Maple either using the built-in Rosenfeld_Groebner algorithm or via the observability normal form, an alternative representation of the model derived from observability criteria. These techniques are applied to analyse models of two reaction schemes. Such systems form the building blocks of metabolic pathway models which are increasingly used in drug discovery and development.