A minimal input-output configuration for a priori identifiability of a compartmental model of leucine metabolism

To develop a model describing the structure and function of a metabolic system using data from an input-output experiment, it is useful to design a pilot tracer study first which contains a predicted maximal amount of information. Having postulated a physiologically reasonable model structure from the pilot data, two questions arise. First, are the model parameters a priori uniquely identifiable? That is, assuming an error-free model structure and data, can the parameters be uniquely identified from the information content of the pilot experiment? Second, if the model parameters are uniquely identifiable, is the pilot experiment a minimal one? That is, is the pilot experiment necessary and sufficient, in the sense of information content, among feasible experiments to guarantee a priori unique identifiability? The purpose of this paper is to determine a minimal input-output configuration for the a priori unique identifiability of a compartmental model describing the metabolism of leucine, an essential amino acid. The original pilot tracer experiment was a two-stage experiment consisting first of a two input-five output experiment followed by a single input-single output experiment. Here we show to guarantee a priori unique identifiability of the leucine model that the single input-single output experiment is not necessary, and that two of the outputs of the multi-input-multi-output experiment are not required.